ChapteJl.. 8

PHASE DIAGRAMS OF SUPERCONDUCTING MATERIALS

R. Fltikiger

Kernforschungzentrum, Karlsruhe, Institut ftir Technische

Physik, 7500 Karlsruhe, Postfach 1640

Federal Republic of Germany

I. INTRODUCTION

It has become evident in the last years that the formation conditions of an intermetallic compound can have a strong influence on its supercon­ducting properties. The "intermetallic compounds" represent in principle all possible combinations between two or more metallic elements, but has in practice been extended to cases where one constituent is a nonmetal, i.e., B, C, N, S, etc. For several highTc materials, the maximum value of T c was found for atomic compositions corresponding to an extreme limit of the homogeneity range of the superconducting phase, stable at high temperatures only. At equilibrium, the formation temper­atures of the most interesting high T c superconducting phases are situated well above 1500oC; it is thus of fundamental interest to know accurately the high temperature relationships of this portion of the phase diagram. The precise knowledge of the formation conditions of a super­conducting phase is a necessary condition for the preparation of homo­geneous, well-characterized alloys suitable for low temperature measure­ments. The resulting consequence is that investigations up to 2000 0C and more must be carried out for a better phenomenological understanding of superconducting properties in the temperature range below 23 K. This statement is well accepted at present, but does not correspond to the way superconductors have been studied. A review of the published data shows that a large number of the investigations on superconducting materials have been made on insufficiently characterized samples, particularly before 1970. At that time the necessary dialogue between physicists and metallurgists was not well established. It is characteristic for the field of superconductivity that a large number of physicists performed precise and complex low temperature measurements, but very few metallurgists

511

S. Foner et al. (eds.), Superconductor Materials Science: Metallurgy, Fabrication, and Applications© Plenum Press, New York 1981

512 R. FLUKIGER

were disposed to study the high temperature relationships in superconduc­ting systems. In addition, many high temperature phase diagrams con­tained serious errors, which in certain cases were an obstacle to the understanding of the superconducting properties. In other cases, the high temperature relationships were correct, but the phase fields were given only approximatively and did not indicate if, for example, the stoichio­metric composition of the superconducting phase of interest was really included or not. This question is of primary importance for research in superconductivity, but may be of secondary interest for the metallurgist who established the phase diagram; there was thus a need for studying these regions of the phase diagram with particular care.

The present review article combines both the pOints of view of the physicist and of the metallurgist. From various remarks it will also follow that the research in the field of superconductivity also requires a good knowledge of crystallography and crystallochemistry. It will be shown how, under certain circumstances, the variation of Tc as a function of chemical composition for a given compound can be used as a supplemen­tary tool in determining composition with great accuracy. The conse­quent search for higher T c values in certain materials, i.e., Nb3Ge, Nb3Ga, Nb3AI and others has led to a new concept in determining high temperature phase diagrams. It is an unexpected result of the research in the superconductivity field that the search for higher Tc's contributed to the determination of phase diagrams above 20000C with an unpreced­ented precis ion.

Most of this paper is devoted to the study of bulk binary, pseudo­binary, or ternary superconductors at their equilibrium state. As will be shown in several cases, these data serve as standard values and are of great help in understanding the superconductiIig behavior in materials produced by non -equilibrium methods, i.e., splat -cooling, thin film preparation by either sputtering, co-evaporation, or CVD, and diffusion processes in multifilamentary composite wires. An example for the departure from thermal equilibrium is the retention of metastable compo­sition by a fast quenching rate. Another example is the introduction of impurities into a binary system transforming it in reality into a ternary or a multinary system. Finally, nonequilibrium can also be obtained by conSidering external pressures considerably above 1 bar, as they occur in multifilamentary composites. We will consider only such materials with grain sizes exceeding the coherence length, e.g., proximity effects will not be discussed in this paper.

II. EXPERIMENTAL DETERMINATION OF HIGH TEMPERATURE PHASE DIAGRAMS

Three factors define the phase field of an intermetallic phase:

(a) the type of formation of this phase (congruent from the melt or from the solid, peritectic, peritectoid, etc., and its eventual decomposition (eutectoid),

(b) the formation temperature and composition, and

PHASE DIAGRAMS 513

(c) the variation of the phase boundaries as a function of temperature (extreme solubility limits).

For the physicist interested in the superconducting properties of a com­pound, the most important point is the knowledge of the extreme composi­tions' which are often correlated to a maximum in Tc' For thermo­dynamical reasons, the homogeneity range of terminal solid solutions attains a maximum width at high temperature. This is also true for numerous intermetallic phases and means that the phase relationships at high temperature have to be accurately known in order to know precisely the extreme solubility limits. This accuracy is of particular importance for high T c compounds, where a variation of 1 at. % in composition may change T c by more than 2 K. In most cases the reason for often widely varying results from different investigations is the introduction of impur­ities in the system studied. These impurities may be contained by the starting materials, but they can als 0 be introduced during the high tem -perature analYSiS, either by contact with the crucible or by the surround­ing atmosphere. There are also other sources leading to errors, e.g., incorrect application of the phase rules, or observation of samples in a non -equilibrium state (thermal equilibrium not attained, the time of heat­treatment being too short). Another source of error is due to the incorrect determination of the effective compositions; this factor is of primary importance when studying complex regions of a phase diagram. The extreme sensitivity of the superconducting properties to changes in composition has led to severe requirements concerning the accuracy of high temperature phase diagram determinations. The key of successful high temperature work is to recognize that the results obtained using a given experimental device have to be treated with scepticism, unless their accuracy has been confirmed by other independent experiments under different conditions. When changing the experimental conditions one has to be careful to eliminate the causes which really influence the measured values.

In the following, the methods and devices used for the determina­tion of high temperature phase fields by the author and his co-workers at the University of Geneva are described. A multitude of other techniques exist, but they are complementary to those presented in this Section.

A. Sample Preparation

There are various methods for melting intermetallic compounds. The choice of the appropriate melting technique is dictated by the nature of the constituents.

1. Arc melting

The most universal melting device for intermetallic compounds is the arc furnace with non -cons uming electrode, where alloys can be melted with virtually no contamination. There are cases where arc melting is not adequate, i.e., for compounds with a too high thermal con­ductivity, as for C u, Ag, or C u bronzes. A feature of arc me lting is the high temperature gradient between the bottom of the sample, which is in

514 R. FLU KIGER

contact with the water-cooled crucible, and the top of the sample. In order to counterbalance this heat loss, the top of the sample has to be heated at temperatures which are considerably higher than the melting point or the liquidus temperature of the alloy. This is a major reason why arc melting is inconvenient in cases where one or more constituents have a high vapor pressure at the melting point of the formed alloy.

As a general rule, the arc current, generally between SO and 500 A, has to be regulated in order that no paint of the sample is heated above the boiling temperature of the most volatile element. As an example, Nb3Sn cannot be formed satisfactorily in an arc furnace since the melting point, 21300C, is too close to the boiling point of Sn, 21700C. Large melting losses and inhomogeneities are the consequence. Another example, the Chevrel phases: the vapor pressure of S, Se, Pb, Sn, •.••• at the melting pOint, > 16500C, is prohibitively high for arc melting. It should be recalled that the electric arc becomes unstable if the gas pressure exceeds 15 atmospheres of argon.

2. r.f. melting in water-cooled crucibles

The large temperature gradient encountered on arc melting is also present when r.f. melting in a water-cooled crucible. r.f. melting has two advantages over arc melting:

1. The power can be raised smoothly. The threshold current necessary for the formation of an electric arc causes a sudden heating of the samples, leading to the "explosion" of brittle A15 or Laves phases.

2. The working pressure can be varied from high vacuum to ;;: 100 atmospheres argon.

3. r .f. melting in graphite or ceramic crucibles

Nearly all alloys which cannot be melted by means of the two tech­niques mentioned above will be formed by r.f. melting in graphite or ceramic crucibles. NbJSn and Chevrel phases, for example, were successfully formed in the device shown in Fig. 1 under argon pressures up to 150 atmospheres [IJ. It consists of a cylindrical molybdenum box of 50 mm diameter and 1 mm wall thickness, in which up to 6 samples can be melted simultaneously. A Ta susceptor of 0.1 mm thickness is situated around the Mo cylinder. The temperature is measured at the center by a W - 3% Re vs W - 25% Re thermocouple. In order to mini -mize the gradient of temperature between the top and the bottom of the box, a number of reflectors are inserted. The crucible material is of particular importance and must be chosen carefully in order to prevent a reaction with the molten alloy. For Nb3Sn, Th02 was used. Al203 crucibles were convenient for most Chevrel compounds, M M06XS (X = S, Se). When M represents a rare earth, reaction with Al203 was. observed, and BN or Th02 has to be used. The r.f. melting in graphite crucibles is particularly useful in forming C u -rich compounds. As an example, the initial Cu - 20 wt.% Nb alloy for the preparation of insitu multifilamentary wires has been melted in a modified device with ---

PHASE DIAGRAMS 515

Fig. I r.f. melting device: I-upper radiation shield (molybdenum), 2 -low impedance r.f. coil, 3-tantalum support, 4-melting crucible, 5-sample, 6-thermocouple, 7-lower radiation shield (molybdenum), 8-susceptor, 9-molybdenum support.

Fig. 2 Levitation coil, combined with splat -cooling device • ~fter switching off the r.f. power, the melted sample falls through the levitation coil and is squeezed by electromagnetically driven Cu pistons (FHikiger et al. [6]).

516 R. FLUKIGER

graphite crucibles as proposed by Roberge et al. l2 J • 4 • Levitation melting

Levitation melting can be performed either in a conventional levitation coil (Fig. 2) or in a Cambridge crucible [49J (Fig. 3). The external pressure can be varied from high vacuum to '" 150 atmospheres of argon. Both techniques allow preparation of very homogeneous samples up to melting points of 30000C and more without any contamina­tion due to the crucible walls. Combined with the high argon pressure, it is perhaps the most convenient way to prepare small quantities « 50 g) of alloys with high melting points containing volatile constituents. A considerable advantage of melting in a levitation coil consists in the free choice of the cooling rate. It can be combined to a splat cooling device, as shown in Fig. 2, or with a system allowing the sample to cool at con­trolled cooling rates. Recently, Devantayetal. [3J have prepared a series of Nbl-{finR alloys by this method. In certain cases the levitation technique can De USed to study the influence of the crucible material on solidification or precipitation processes. This was done by Bevk, eta!. [4J and more recently by the author [5J, who compared the morphology of the Nb dendrites in a Cu -Nb in situ alloy as melted in a carbon crucible or crucible -free. A combination of levitation melting with thermal analysis called levitation thermal analysis (LTA [6, 7J will be presented in Section IIC2.

5. Other melting techniques

There are many other melting techniques designed for special cases, i.e., hot pressing up to 1 kbar in C crucibles and melting at ultra -high pressures up to 100 kbar pressure and 20000C in tungsten carbide multi­anvil devices [8]. Another special technique is the melting of alloys up to 20000C in an autoclave designed for argon pressures up to several thousand atmospheres of argon. Nearly all stable high temperature com­pounds (superconducting or not) can be formed by melting if the approp­riate melting technique is chosen.

B. Homogenization Heat Treatments

In the as -cast state, all alloys show a certain distribution of com­pOSitions which depends on the phase relationships around the solidus temperature. The goal of homogenization heat treatments is to reduce the width of this distribution as much as possible. There is no exact criterion for "fully homogenized" samples: the width of the distribution in compositions will always remain finite. Usually the homogenization conditions for a given alloy are chosen by comparison with similar systems. Experience shows that homogenization heat treatments should always be performed at temperatures as close as possible to the solidus, if necessary under high argon pressure. The annealing time should be very long, of the order of several days. The correct homogenization conditions are usually determined by the physical experiment performed on the alloy. After these remarks, it follows that the "homogenization" temperatures of 10000C reported in the literature for V 3Si and similar

PHASE DIAGRAMS

Fig. 4

Cambridge levitation crucible

o o o o ~~~

r.f .coils

Fig. 3 Cambridge levitation crucible.

Pyrometric observat ion

o 0 o 0 o 0 o 0 o 0

High temperature cell for homogenization heat treatments, "simultaneous stepwise heating" and for calibrations prior to the levitation thermal analysis (L T A): I-samples, 2 -molybdenum block, 3-thermocouple, 4,5-molybdenum radiation shields, 6-hole for pyrometric observation{6].

517

518 R. FLUKIGER

systems are definitively too low in order to produce the reduction of the width of the concentration distribution in the alloy.

An assembly used for homogenization heat treatments [6J is shown in Fig. 4. For these high temperature heat treatments, the temperature was measured with a thermocouple. The same device was also used for "simultaneous stepwise heating" analysis [6J (Section IID1), and for cali­brations prior to the levitation thermal analysis [6,7J described in Section IIC2.

The degree of homogenization is very difficult to define by metal­lurgical means: once an alloy has been found to be single -phased by X -ray and optical microscopy, the presence of a concentration gradient can be detected by scanning with the electron microprobe. However, if an alloy is superconducting, the low temperature specific heat is a far better way, which not only detects a concentration gradient, but also gives a picture of the concentration profile. At T c the width and the shape of the calorimetrically measured superconducting transition reflects the bulk state of the sample.

The effect of the homogenization heat treatment can be seen in the specific heat curves of M030s and Nb3Al (both crystallizing in the A15 type structure) and is shown in Figs. ;; and 6. Figure 5 shows the specific heat curves [8J of the same Mo30s sample after a I-hour heat treatment at 17700C and after 20 hours at 1800oC. The heat treatment at the higher temperature reduces the total width of the superconducting transition from 1.50 to 1.05 K, the value of T c (midpoint) being slightly increased from 11. 70 to 11.85 K. At the same time, the height of the specific heat jump is increased by 20%. This point is important: specific heat curves of inhomogeneous samples are always characterized by flat transitions at T c. An even stronger effect is observed in alloys of the Nb-Al system. Figure 6 shows two specific heat curves, the first one corresponding to a NbO ?SAIO 25 alloy 1effective composition Nb NbO 76AlO 2j,)' annealed 5· days at· 750°c without homogenization heat treatment C9 J, the second one corresponding to a NbO 76aAlO 231 alloy after a homogenization heat treatment of 48 hours at fss'O'OC Under an argon pressure of 4 atmospheres [1OJ. A comparison shows that the transition width is reduced from 1.5 K to 0.7 K by the homogenization heat treatment. At the same time, the height of the jump in specific heat at T c of the homogenized sample is doubled in spite of the higher T c value of the latter.

In alloys containing volatile constituents, a problem arises during homogenization heat treatments close to the solidus temperature: vapor­ization! The weight losses can be minimized by annealing under high argon pressure: for Nb3Al or Nb3Ga, 4 atmospheres are sufficient, while Nb3Sn, CuxMo6S8' CuxMo~e8' AgMo~8' ..•• require pressures up to 100 atmospheres. For PbMo~S' SnM06SS or R. E. Mo6SS several thousand atmospheres are necessary.

PHASE DIAGRAMS 519

Fig. 5

Fig. 6

20h.l1BOO°C

20

0

r-P '" "-E

;:: 10

23

0 100

T2(K2) 200 300

Different states of homogenization for M030s revealed by specific heat measurements at the superconducting transition [8].

80

CIT 70

[mJ ]60 K2at-g

50

40

30

20

10

200 600 800

Effect of the homogenization heat treatment on Nb3Al revealed by specific heat measurements. The alloy with the effective composition NbO 769AIO 231 has been homogenized 48 hours at 18500C; the alloy No"':' 76AI,....,24 (nominal composition NbO.75AIO 25) was heat-treated for only 5 days at 7500C and shows a wine transition (Fliikiger et al. [10].

520 R. FLUKIGER

C. Direct Observation Methods

The extreme concentrations in a phase field, often stable only at high temperatures, must be quenched at sufficiently high rates in order to be retained for a subsequent analysis. However, quenching experiments depend on the kinetics and thus give only an indirect image of the high tem­perature behavior. This image does not necessarily correspond to the real situation: it can even represent nonequilibrium. Thus quenching experiments alone cannot answer questions of the equilibrium phase limits at high temperatures. A way of accurately solving the problem is to combine the quenching experiments with direct high temperature observations. By direct observation methods we mean all techniques which are independent of kinetics, i.e., which reflect the equilibrium behavior at high temperatures.

1. Differential thermal analysis (DTA)

A commonly used method for the detection of phase transformations at high temperatures is DT A [11]. Phase transformations of the sample under investigation are indicated by a differential temperature signal due to latent heat at the transformation. A typical DT A apparatus is illus­trated schematically in Fig. 7. The apparatus generally consists of: (a) a furnace or heating device, (b) a sample holder, (c) a low-level de amplifier, (d) a differential temperature detector, (e) a furnace tempera­ture programmer, (f) a recorder, and (g) control equipment for maintain­ing a suitable atmosphere in the furnace and sample holder. There are many modifications of this basic apparatus, but all instruments measure the differential temperature of the sample as a function of temperature or time.

At the formation temperature of the most promiSing superconducting phases, i.e., in the range of 1500 ~ T ~ 2200oC, the contamination of the alloys by the crucible material or by impurities in the heating chamber becomes increaSingly important. Furthermore, the evaporation of the volatile constituents present in most compounds at these temperatures increases the fluctuations on the DT A base line, thus rendering the detection of thermal arrests more difficult. The analysis under these conditions presents another inconvenience, namely, the lifetime of the measuring cell may be shortened by the reactivity of the metal vapors either with the thermocouples or with the ceramics. It is thus not surprising that the high temperature phase fields of the majority of these systems are not well characterized.

A DTA apparatus working up to 22000C under an inert gas pressure of up to 10 atmospheres (required for the particular problem of phase diagrams of superconducting materials with volatile constituents) is not commercially available. Such a device was developed by the author [6] and will be discussed below. In principle, the best material for the heating resistance is tungsten: it has a low vapor pressure up to very high temperatures and permits work in a clean atmosphere. For the present device, W was excluded because it becomes brittle by recrystal­lization and reaction with small amounts of oxygen present in the furnace

PHASE DIAGRAMS

Temperature sensors

Atmosphere control

Microvolt amplifier

Furnace programmer

Recorder

Fig. 7 Schematic diagram of a DTA apparatus (Wendtlandt[ll]).

521

Fig. 8 DTA sample -holder, designed for temperatures up to 20000C . It is constructed entirely of BeO and molybdenum. The BeO crucibles (5 mm dia.) are directly supported by the W-3% Re vs W -25% Re thermocouple junctions (FHikiger et al. [6]).

522 R. FLUKIGER

atmosphere. Traces of oxygen are contained in the argon (99.995%), or arise from the water adsorbed at the surface of the ceramics or of the furnace walls. Carbon was found to be the heating resistance material having the longest lifetime under the required working conditions. In order to ascertain that the carbon impurities did not affect the phase relations of interest, the DTA results of all investigated systems were compared with those obtained using a carbon -free device. The cylindrical carbon resistance, supplied by Setaram (France) has a total length of 400 mm and an inner diameter of 34 mm. By applying a power of 8 kW, it develops a temperature of 24000C at the hot zone. The resistance has a complex shape, designed for a homogeneous tempera­ture zone of approximately 40 mm length at 22000C • The temperature gradient in this zone, parallel to the axis of the cylinder, is of the order of 0 .50C/cm.

In order to avoid the mechanical problems due to softening of the central 4 -hole BeQ tube at high temperatures, it was mounted hanging from the top of the furnace. The details of this holder are shown in Fig. 8. The materials used for its construction are BeQ and molybdenum, which form a cylindrical box of the approximate size of the homogeneous zone. The samples, contained by small BeQ crucibles, are located at the center of the box in a plane normal to the axis. The junction meas -uring the temperature was placed at. the center of this plane. The melting points of platinum (17720C) and rhodium (1966OC) were used as temperature standards. The size of these crucibles was kept as small as possible in order to minimize the temperature variation in the samples, which is estimated to be at less than 0.1 DC. The weight of the crucibles is comparable to that of the samples (0.2 - 0.25 g). The BeQ crucibles were supported by the thermocouple junctions and the samples separated from the latter by a thin BeQ wall of 0.4 mm thickness, thus providing a good thermal contact. The good contact between the thermocouple and the sample, combined with the very small temperature gradient across the sample, are decisive factors for the high sensitivity of the DTA signals up to 22000C . This is illustrated by Fig. 9, which shows a DTA run on the alloy NbO.74GaO.26. The observed thermal arrest corresponds to the liquidus temperature.

For a linear variation of the temperature, a proportional feedback temperature programmer was used. It was driven by a supplementary W -3% Re vs W -25%R~ thermocouple placed just below the sample -holder. The DTA signal was measured with a nanovoltmeter and registered with a multi -channel recorder. All parts of the sample -holder can be used for numerous runs, except the thermocouples, which had to be changed after 10 to 20 runs, depending on the substance under investigation and on their thickness (which, in our experiments, varied between 0.25 and 0.5 mm).

2 . Thermal analysis on levitating samples (L T A)

At first sight the possible influence of the crucible material on the DTA results seems to be easily avoidable by using different materials.

PHASE DIAGRAMS 523

Fig. 9

I I I I

1870 1900 1930 1960

increasing temp. rate: 9.6·C Imin.

I I I I

1960 1930 1900 1870

decreasing temp. rate :10.0·C/min.

High temperature DT A run of NbO 6GaO 24. The observed thermal arrest corresponds to the· liquiduS temperature, 19400C . Note the strong curvature of the base line on increasing temperature, which shows beginning evaporation. External argon pressure is 4 atmospheres (Fliikiger et al{6]).

2200

2100

180"'-_____________ --'

TIME

Fig. 10 Fusion of levitating Rh sample initially having a cubic shape. (1) A large jump in temperature is observed when fusion begins. (2) The same sample after the first melting, showing a considerably smaller jump than on the first run. The shape of the sample now approximates that of the levitating liquid. (3) Third run - the jump disappears; the shape of the sample is now the same as that of the levitating liquid (Jorda et ale [7]).

524 R. FLUKIGER

However, the number of commercially available ceramics which can be used at 18000C and more is small. In addition, the costs of DT A crucibles made from Th02 of Hf02, of the shape shown in Fig. 1, are prohibitively high. The generalized use of BN at T > 18000C is problem­atic because of the hygroscopic behavior of this material. In some cases, e.g., Nb3Ge, W crucibles were found to have virtually no influence on the solidus temperature. However, the reaction with the crucible material at high temperature varies from compound to compound and always must be checked. A technique which completely eliminates the problem of contamination by crucibles is the levitation thermal analysis (L TA) [6, 7J • LTA was performed on levitating samples weighing 1 -2 g, using a 30 kW rf generator at a frequency of 300 kHz and a water -cooled induction coil as shown in Fig. 2. The maximum temperature attained under these working conditions was 3000oC, limited by the generator power. As is usual in thermal analysis, the temperature of the sample is varied by a gradual change of the generator power at rates up to 500C/min, depending on the nature, the weight, and the shape of the sample.

The sample temperature was measured by a Leybold two-color pyrometer. The main problem arising in measuring temperatures by means of a pyrometer is the unknown behavior of the spectral emissivity of the materials studied at the wavelengths of the pyrometer (>'1 = 4500 A and >"2 = 6500 A) as a function of temperature. The observed alloys do not behave necessarily like "grey bodies", as required for an accurate temperature determination with a two-color pyrometer. In addition, the selective absorption of the optical components (glass window, crown glass prism and filter) must be included. Thus, a reliable determination of the temperature requires a careful calibration of the pyrometer. This calibration was carried out by comparing the temperature of a massive W sample as determined simultaneously by the pyrometer and a W - 3%Re/ W -25% Re thermocouple, in the device shown in Fig. 4. Tungsten was chosen because it behaves like a "grey body" [12J. As shown by Jorda et al. [7J, Nb-Ge also behaves like a "grey body": (r = (Al)/ (>"2) is constant and equal to (r = 1.070 for compositions between 5 and 27 at.% Ge and temperatures within the limits 1600 ~ T s; 20000C .

The determination of the melting temperature of Rh [7J by means of LT A is shown in Fig. 10. A plateau due to the latent heat appears with beginning fusion. The fusion process is characterized by a sudden change of the sample shape and position relative to the induction coil, its new shape being determined by the magnetic field gradient. The coupling between the melting sample in its new position and the levitation coil being now optimal, the temperature of the sample increases suddenly. In Fig. 10 it is seen how the jump in temperature for successive runs disappears, the shape of the solid sample approaches that of the liquified sample so that the equilibrium position in the coil no longer varies upon melting. The liquidus lines cannot be determined by this technique because the sample does not change its shape when crossing the liquidus. The high temperature part of the Nb-Ge phase diagram [6,7J, as deter­mined by LTA, is shown in Fig. 11 and demonstrates the possibilities of

PHASE DIAGRAMS

Tre)

"'" '100

....

....

Ofhennalan~on leYttating sample

I'!. W c.rUCIbIK} • leO cruclblls DTA eZr02cruclbln

525

Fig. 11 High temperature part of the Nb-Ge phase diagram obtained by thermal analysis on levitating samples (LTA), combined with DTA and "simultaneous stepwise heating". This figure also illustrates the effect of the crucible material on the s oUdus temperature (Jorda et al. [7]).

1.8

1.6

1.4

T (·e)

Fig. 12 High temperature resistivity measurement of arc -cast Vo .450s0 55. Initial state of the sample is B2 + A15. At '" 1000<>C, . tliere is a nonequilibrium transformation from the metastable A15 phase into the B2 phase (see phase diagram, Fig. 38). The change in slope at 15650C corresponds to the eutectic decomposition of the A15 phase (Susz et al. [13]).

526 R. FLUKIGER

this new high temperature analysis method. The accuracy at 20000C is estimated to -t lOOC.

3. Electrical resistivity at high temperatures

The detection of phase changes at high temperatures by means of electrical resistivity measurements can be considered a necessary complement to DTA and LTA. The use of electrical resistivity is restricted to solid state transformations. Although electrical resistivity measurements also detect first order phase transformations, their main advantage resides in detecting second order (for example, martensitic) and non -equilibrium phase transformations with more sensitivity than DT A. As non -equilibrium effects, we understand for example the transition from a metastable phase obtained by quenching into an equilib­rium phase as shown in Figs. 12, 13 and 14 for V-os [13J, V-Au [14J, Nb-Au [J5J, and Ta-Au [15,16J. Another example is the amorphous to crystalline transition. Where quantitative DTA measurements provide information about the latent heat, electrical resistivity measurements are a simple and powerful method in studying the kinetics of a phase trans­formation. In contrast to other analysis methods, the electrical resistivity can also be measured at a constant temperature. If this tem­perature just corresponds to a phase transition, the transformation as a function of time can be observed.

The alloy specimens used for the electrical resistivity measure­ments are small bars about 20 mm long and of square cross section (1 mm x 1 mm). They are usually cut by spark-erOSion and then polished on all faces. In all our measurements the four-point teclmique was used. The great problem of electrical resistivity measurements at high temperatures is that of the electrical contacts. If the sample crystallizes in a soft phase like bcc or hcp, good electrical contacts are obtained by four thin molybdenum spot-welded wires. For very brittle intermetallic alloys crystallizing in the phases A15, CIS, ••• , or for Chevrel compounds, thermal shock during spot-welding leads to the fracture of the sample, and special precautions have to be taken. First, the resistance to thermal shocks increases considerably if the alloys are fully homogenized by a prolonged heat treatment at high temperatures (Section IIB). Second, very thin (0, 01 mm diameter) Pd wires can be used instead of Mo; such wires have been spot-welded on fully homogen­ized NbJPt samples [15J. In some cases the operation is facilitated by first electroplating the contact zone with Ni before the spot-welding. Two other ways for obtaining electrical contacts have been used success­fully. The first one consists in immersing four thin W or W -Re wires in the melting alloy which is then cooled very slowly in order to minimize mechanical tensions. With this method, the ratio ,x.T)/P300 K is measured, and a calibration at room temperature must be pefformed in order to determine the absolute values P300 K' It has been used for the Ru -Sn system [17J and for C u2Mo~ 8 [1 J • A meas urement up to lOOOoC on the latter system is shown in Fig. 66. Another possibility to obtain electrical contacts for high temperature measurements was recently proposed by C. Susz [17J. The contacts are obtained by the pressure of

PHASE DIAGRAMS

1.1

1.01Ooolll::~--L---__ L--__ ---JL....J

a 500 1000 T (.C) 1500

Fig. 13 Variation of the resistivity ratio (i,.T)/po (300 K) of V 0 • 79AuO .21 as a function of temperature • TO and T 1 are the beginning and the end of the non -equilibrium transformation of A2 to A1S (FHikiger et ale [14]).

1.3

~ R. Nb.76A~24 1.2

1.1

1.00 500 1000 1500 2000

R 1.8 TqaoA L!20 ~

1~6

1.4

1.2

1.0 0 500 1000 1500 2000

r(OC)

527

Fig. 14 Variation of the resistivity ratio (i,.T)/po (300 K) of NbO 76AuO 24 and TaO 80Aua 20 as a function of the tempera­ture·. T and T1 are the temperatures at the beginning and the end of the nonequilibrium transformation of A1S to A2. The dotted lines represent the resistivity ratio of the meta­stable A2 phase (FHikiger [15]).

528 R. FLUKIGER

two pairs of sharp molybdenum knives against the sample. The whole assembly is held in place by individual weights on the voltage leads. The distance between the voltage lead knives is well known, so the absolute value of p(T) can be measured with precision.

The analysis of the data is not always simple, and requires some experience and the possibility of an independent check. Since pis different from phase to phase, the signal indicating a change from a phase to another may be very different. Often only a sudden change in the slope of P(T) indicates that a line in the phase diagram has been crossed. For example, the change in slope of the p(T) curve for VO.450s0.55 at 15700C in Fig. 12 corresponds to the eutectic decomposition of the .A15 phase at this temperature [13J. If the electrical resistivity is very different between two consecutive phases, the transition is characterized by a step in P(T). Several examples of such sudden changes of p(T) are now presented. The first one is shown in Fig. 12 and indicates the transition from the metastable A15 phase in Vo 450s0 55 [13J as obtained by quenching into the equilibrium bec + hcp mixture. The second one indicates the non -equilibrium transition A15 to bec in the three systems V-Au [14J (Fig. 13), Nb-Au [15J and Ta-Au [15,16J (Fig. 14). The transformation A15 to bcc in these three systems occurs at 600, 820, and 9800C, respectively, which reflects the congruent formation temper­atures of the A15 phase: 1295 [14J, 1560 [18J, and 16800C [16J, respectively. An interesting pOint in Figs. 13 and 14 is that the full reSistivity curve of the high temperature bcc phases can be drawn, the intermediate region being optained by interpolation. The third case of a sharp change in P(T) is observed for the congruent formation of the A15 phase from the solid bec solid solution. This case is shown for the three systems mentioned above (Figs. 13 and 14). In all three cases the resistivity of the A15 phase exceeds that of the high temperature bcc phase, by 5, 6, and 9%, respectively.

D. Indirect Observation Methods

1. Simultaneous stepwise heating

The horizontal lines in the phase diagram, such as eutectic, peri­tectic or peritectoid temperatures as determined by DTA (Section lICl) can be checked by using a very simple technique, "simultaneous step­wise heating", which is based on the fact that the number of liquid phases changes on crossing the eutectic or a portion of the peritectic line. This technique cpnsists of heating pieces of the same master sample at different temperatures above and below the desired eutectic or peritectic temperature. Mter cooling, they are analyzed visually or micro­scopically in order to decide whether the solidus had been reached during the high temperature exposure. The step between the annealing tempera­tures being of the order of SoC, the value of the eutectic or the peritectic temperature can be found with good precision and can be compared with that obtained by DT A •

When studying the phase diagrams of the binary systems Nb-Ge and

PHASE DIAGRAMS 529

Nb-Ga, we found in addition that this technique furnishes precise inform­ation on the extreme Ga or Ge solubility in the A1S phase if several samples of different but neighboring compositions are heated simultan­eously. It is thus possible to study simultaneously the influence of car­bon impurities on the eutectic or peritectic temperature and the extreme composition of a given phase. This combination renders the method quite powerful.

Figure 4 illustrates the high temperature cell which was used for the "simultaneous stepwise heating" experiments. The samples were contained in BeO crucibles located inside a double -walled molybdenum cylinder which, in turn, was placed in a tantalum susceptor. Because of the cylindrical symmetry, the difference in temperature between the samples is less than SoC at 18000C • As for DT A measurements, the temperature was measured with a W-3%Re vs W-2S%Re thermocouple, which was in good thermal contact with one of the BeO crucibles.

2. Splat cooling of liquid samples

In order to retain a high temperature phase or a composition of this phase which is stable at high temperatures only, very rapid quenching is necessary. The quenching rate is considered to be sufficient if it is higher than the rates of phase transformations or segregation occurring during the cooling process. However, analysis of a quenched sample alone cannot confirm with certainty whether the quenched sample reflects the equilibrium high temperature relationships. It may represent a non­equilibrium situation due to an insufficient cooling rate. The latter possibility must be considered, particularly if solid samples are quenched. Liquid samples of the same material can be quenched at much higher rates.

Splat cooling was first used by Duwez et al. [19J and has since been modified by many authors. We used a combination of magnetic levitation and two water-cooled Cu pistons (see Fig. 2). By suddenly switching off the rf power, the levitating, melting sample falls through the levitation coil and is squeezed by the polished front of the Cu pistons, which are accelerated against each other by two strong electromagnets. The magnets are activated by the rf power switch with an appropriate time delay which takes into account the fall time of the sample. The thick­ness of the splat-cooled sample varies between 50 and 100 1J.ffi, the initial quenching rate being estimated at '" 1060C per second.

3. Argon jet quenching on solid samples

A solid sample can be quenched by falling into a liquid metal (Ga or Ga -Sn) or an oil bath. However, this method has a disadvantage: as the hot sample enters the bath, the liquid in contact with its surface evapor­ates, forming an insulating layer which reduces the heat exchange and thus the cooling speed. We have used another rrethod, the argon jet quenching, which allows higher cooling rates to be reached, provided that the sample is small enough. On samples weighing 0.3 g, we have measured initial quenching rates of the order of 1040C per second, i.e., 100 times less than for the splat cooled samples.

530 R. FLOKIGER

Our argon jet apparatus (Fig. 15) was mounted in an rf furnace which has the advantage that the total mass of the heated assembly is small, which is a stringent condition for a rapid quench. The argon gas is introduced through a thin -walled tantalum tube into the high tempera­ture cell. This cell consists of a double -walled molybdenum cylinder made from rolled Mo sheets of 0.1 mm thickness. It is designed in such a manner that the top and the bottom of the cylinder can be blown away by the argon jet, leaving the thermocouple in place. The sample hangs on a tantalum wire fixed inside the tantalum tube and is located at the center of the cell, just above the thermocouple.

4. Superconducting "memory"

We will now consider the case where the boundaries of a super­conducting phase are strongly temperature dependent, the extreme solubility limit being attained at high temperature. This situation is illustrated in Fig. 16, where the minimum Pt content of the e' phase (of the hexagonal 0019 structure) in the system Mo-Pt (Fig. 35) is 32 at.%Pt at ISS00C [20]. It is obvious that the preparation of the Single -phased alloy MoO. 7oPtO. 30 requires high rate cooling techniques, i.e., argon jet quenching (> 1000C/sec). If the same quenching technique is applied to the same MOO.7oPtO 30 alloy, but at different temperatures well below ISS00C, the resulting s·ample will no longer be siilgle -phased. A certaiil amount of the neighboring phase (in this case the A15 phase MOO.SI5PtO ISS> will appear, depending on the quenchiilg temp~rature • At the same time, the effective composition of the e' phase will exhibit values well above 32 at.% Pt, for example, 37 at.% Pt at lOS50C.

The effective composition can be determined by x-ray diffraction (lattice parameters) or by electron microprobe (the result of a chemical analysis would be meaningless, due to the presence of a second phase). There is another way to determine the effective composition of the £' phase: once the correlation of T c vs Pt content is known, the latter can be deduced from a T c meas urement . This is an application of T c measurements as a supplementary analysis method. The correlation between the quenching temperature and Tc for the e' phase is also shown in Fig. 16. We have used this correlation for calibrating the tempera­ture of the argon jet quenching device (Fig. 15). The particular method of iiltroducing the high pressure argon jet through a tantalum tube causes an inhomogeneous temperature distribution around the sample. The temperature indicated by the thermocouple must be checked to assure that it is identical with the temperature of the sample. On a certain number of quenching runs, a small MoO. 6~to 31 alloy was attached to the test sample and was simultaneously argon jef quenched. The T c value of both the test sample and the Mo-Pt sample was measured simultaneously by induction methods. From the T c value of the MoO. 6o/'ta 31 alloy and using the correlation Tc vs T A in Fig. 16, the quencrllrig temperature could be posteriori determined to better than t 150C (superconducting "memory ") • Other examples of a strong variation of T c as a function of the quenching temperature will be presented later on hcp phases (Section VA), Nb-Ga (Section VIF 1) and Nb-Al (Section VIF3).

PHASE DIAGRAMS

Argon

o 5_~_""",,~ P---I 1 r-~-~-I

o o 0t...=::=::::l o

531

Fig. 15 Argon jet quenching device: l-r.f. coil, 2-sample hanging on a tantalum wire, 3-thermocouple, 4-tantalum tube, 5 -molybdenum lid is blown away by the argon jet, 6 -two -hole BeO tube for the thermocouple wires (Flfikigeretal[6], [26]).

8 Tc

7 rK)

6

1500

Fig. 16 Correlation between quenching temperature, TR' and Tc for MoO 70PtO 30' reflecting the temperature -dependent Mo -rich phase Iimit of the D019 phase (Flfikiger et al.[20], [38]).

532 R. FlOKIGER

III. DETERMINATION OF PHASE DIAGRAMS BELOW 300 K

The superconducting transition temperature can be determined either by induction methods or by measuring the resistivity of a sample by the four point method. For several purposes, particularly for bulk samples, the contactless inductive method is more convenient. It detects the change in permeability during the superconducting transition. Usually, Tc is defined as the temperature at which the change in perm­eability is one -half of the total change. As several measuring devices have been reported in the literature, the following discussion is limited to the practical problems related to the analysis of the measured T c values.

A. Factors Influencing the Superconducting Data

In general, the Tc value of a superconducting phase is influenced by its formation conditions, which determine both the effective composition and the degree of ordering. We first discuss effects which may cause apparent variations of T c on bulk samples having the same chemical com­position. The first effect is due to atomic ordering and has so far been observed on compounds of the A15 type structure. The second is a result of possible inhomogeneities in the sample. It is known as the shielding (or screening) effect and occurs independent of the crystal structure.

1. Ordering effects

The following description of long-range atomic ordering effects in A15 type compounds is limited to a few important features. These remarks are necessary to understand the complex cases where ordering and compositional effects are superimposed, e.g., Nb3Ga [21J or Nb3Al [1OJ, which will be described in Section VIF.

There are two methods inducing changes in the order parameter. The thermal method submits the alloys to heat treatments at different temperatures, followed by cooling at different rates. The irradiation method exposes the alloys to irradiation by high energy particles which are usually neutrons at energies higher than 1 MeV [22J or oxygen ions at energies of 25 MeV [23J. Particle irradiation produces a larger amount of atomic disorder (in addition to other effects) than the thermal method, causing spectacular changes of Tc [22, 23J. The discussion here will be limited to the case of thermally induced disorder.

The first accurate determination of the Bragg-Williams long-range order parameter, S [24J, on A15 type superconductors was performed by Van Reuth etal. [25J on V3Au. This work was motivated by the observed variation of Tc from < 0.012 to 3.2 K on the same sample after different heat treatments. Later experimental work by Van Reuth etal. [25J and Fllikiger etal. [14,26,27J has shown that A15 compounds exhibit in general a high degree of ordering. Fast quenching from high temperatures produces a small, but significant, reduction of the order parameter which is responsible for the observed variations in T c. The physical origin of the observed reduction in T c lies in the decrease of the electronic density of states as a consequence of atomic exchanges on the chain sites, as

PHASE DIAGRAMS 533

shown theoretically [30,31, 57J and experimentally [32, 33, 34J.

The degree of ordering in a compound of the A15 type structure with the composition Al-f!3f3 is described by the Bragg-Williams order param­eters Sa and Sb for the chain sites (6c) and the cubic sites (2a), respect­ively. At the stoichiometric composition f3 = 0.25, i.e., Sa = Sb = S . In some cases it is convenient to use the occupation factors ra and rb for the A atoms on the (6c) sites and for the B atoms on the (2c) sites, respectively. These quantities are connected by the relations

r a - f3 rb - (1 - f3) Sa = 1 - f3 and Sb = 1 - (1 - fJ) •

In samples with thermally induced disorder, it is assumed that the con­centration of vacancies and interstitials can be neglected and that only site exchanges take place at high temperature. By means of density measurements on a V;#ii single crystal, Guha etal. l28J determined that if lattice vacancies are present in V;#ii, their number would be smaller than 0.25%, the limit of accuracy. The same result has been obtained on homogenized V 3Si polycrystals [15J and on Nbo. 74IrO .26 single crystals [15J, grown by electron beam zone melting on an ultra -high­vacuum furnace. Even after argon jet quenching of the NbO 7~IrO .26 crystal from 19000C, the density was found to be unchanged 'wlthin the limits of accuracy [15J.

The dependence of T c as a function of the thermal treatment can conveniently be studied in V 3Ga [21 J (Fig. 17), where the stoichiometric composition is stable at all temperatures [27,2 9J • In Fig. 17, an arc­cast V 3Ga sample (T c = 13.9 K) is successively treated at increasing temperatures up to l:l950C, the solid congruent formation temperature of the A15 phase. Curve Ia represents the irreversible transition from the quenched-in order parameter to the equilibrium order parameter at T = 700OC. Curves IIa and IIb are reversible and reflect the variation of the equilibrium order parameter between 7000C and 12950C • Curve IIa was obtained on argon jet cooled samples, whereas IIb was measured on samples cooled by radiation quenching. The difference between the curves IIa and lIb shows that the degree of ordering increases during the cooling process: high quenching rates are necessary in order to avoid reordering. It follows that the degree of ordering of V 3Ga (and other A15 compounds) is not sufficiently characterized by the quenching temper­ature only: the quenching rate is also needed. Below 7000 C, ordering effects are slow and the cooling rate is no longer important, so that the curves IIa and lIb in Fig. 17 join (curve Ib). The highest value of T c' 15.9 K, known so far was obtained after 7 weeks annealing at 5600C (FlUkiger etal. l21J). The system V3Ga can be considered as a model system for studying ordering effects on Tc ' because compositional effects are absent. For high Tc compounds like Nb3Ga [21J and NbJAI [10J, both ordering and compositional effects are present simultaneously. It will be shown in Sections VIE 3 and VIF4 how the separation of both effects can be used to obtain maximum values of T c for both compounds •

534 R. FLUKIGER

sao 1000 T I'C) TF

Fig. 17 The variation of T c as a function of the heat treatment for the A15 type compound V 3Ga. This reflects the variation of the atomic order parameter with temperature. The minimum temperature at which ordering effects can be detected by variations of Tc is 5600C (Fliikiger et al. [21], [27]).

10

8

• [ M0.81 Pt I9 I 170 h. 1600'C)

, [Mo80Pt,20 I 13h, ISOO'C )

. [Mo.7S Pt,2S I 110 h 18S0'C)

OL---~2~0 --~'O~--~ro----~80~

T('K']

Fig. 18 Specific heat meas urement on a M~. 75PtO.2 5 sample after heat-treatment of 10 hours at 1850UC reveaTs superconducting transitions at 1.9 K (A2 phase) and at 6.5 K (DOI 9 phase). Micrograph at right shows two phasesw The A2 phase (dark) is surrounded by the 0019 phase, which produces shielding effects (Fliikiger et al. [20], [44]).

PHASE DIAGRAMS 535

2. Shielding effects

Shielding effects often cause erroneous meas ureme nts of T c • They are a consequence of the field expulsion at the surface by the supercon­ductor (Meissner effect) • Shielding effects are connected to inhomogen­eities in the sample. There are several configurations leading to shield­ing effects:

(a) an additional phase is formed at the surface of V -based com -pounds due to contamination during the heat treatment in quartz tubes (reduction of Si in Si02);

(b) one of the components of the alloy evaporates during the heat treatment, creating a layer at the surface of the same phase, but with different composition;

(c) the layer formed in (b) is of another phase type;

(d) the microstructure of the sample shows that the phase of interest is enclosed in a matrix of another phase with a higher Tc;

(e) in single -phased, but non -homogenized alloys, there is a distribution of microscopic islands of the same phase, but at different composition from the average.

For all configurations the apparent value of T c is higher than the value corresponding to the bulk of the sample. A layer thickness of the order of 1 J.I1Il is sufficient for a total screening of the lower superconducting transitions. After grinding, the shielding effects are thus eliminated for the cases (a), (b), and (c), but they persist for the cases (d) and (e).

Examples for the cases (a), (b), (c):

(a) V3X alloys are known to form a very thin layer of Va5i (or V 3(Si I-xXx) at the surface as a consequence of the reduction of Si02 during heat treatments in quartz tubes at T > 900<>C This effect is best illustrated by V 3As alloys where annealing in quartz tubes at 9000C yielded an apparent T c value close to 17 K; the correct value (after grinding) was Tc = 0.3 K [35J. This effect is probably responsible for the high reported value Tc = 16.5 K [36J for V3Ga, which could never again be reproduced, even after systematic efforts [15, 27J •

(b) This case is represented by the system M03(Os l-xFex)' studied by Bongi et ale [37J. After a homogenization heat treatment at 1800OC-under high vacuum, the inductively measured Tc was 12 K, the same as in pure M030s [38J, but dropped to values below 4.2 K after grinding. The effect was caused by Fe loss at the surface during the heat treatment.

(c) Nb3Ir (T c = 1.7 K) [39J exhibits T c values close to 9 K after annealing in quartz tubes at 10000C (Koch etal. [40J showed that this effect is due to an oxygen -stabilized phase formed at the surface).

536 R. FLUKIGER

The cases (d) and (e) are more difficult to avoid. In principle a low temperature specific heat measurement is required in order to deter­mine the T c to the appropriate phase (Section lIIB).

A simple way to reveal unambiguously the lower superconducting transitions is to crush the samples down to particles with sizes of the order of the grain size (20 to 40 1JITl). The best way is to measure the specific heat at low temperatures.

B. Low Temperature Specific Heat

Measurement of the low temperature specific heat provides the following information:

(a) the electronic density of states at the Fermi level; (b) the width of the energy gap; (c) the phonon spectrum at long wavelengths; (d) the superconducting transition of the bulk sample and

its concentration profile; (e) the transformation temperature and the heat of transformation.

The attention of the solid state physicist is often directed toward the first three properties because they are basic quantities for current supercon­ductivity theories. Points (d) and (e) give important information about the metallurgical state of the alloy. Point (d) has been discussed in Section lIB, where the correlation between the shape of the calorimetric­ally measured superconducting transition and the homogeneity of the sample has been emphasized. Point (e) is inaccessible to most calor­imeters, which are usually designed for the temperature range T ~ 40 K.

Specific heat meas urements in the temperature range 40 ~ T ~ 300 K are the most powerful means for the determination of low tempera­ture phase relationships. Detailed descriptions of low temperature specific heat devices can be found in the literature. All measurements discussed here have been performed on an improved version of the apparatus described by Spitzli [41J. It was later modified in order to detect phase transformations up to 300 K [42 J on 5 g samples. Improved methods of measurement, in particular the relaxation method [43J have recently been developed for measurements on samples of several mg. It is thus possible to measure very small quantities of material produced by non -equilibrium techniques, i.e., sputtering, CVD, PVD, or splat­cooling.

1. Calorimetric detection of shielding effects

An example for the shielding effect (d) for the alloy MoO. 75PtO 25 [20,44J is shown in Fig. 18b. The bec phase (dark) is surrounded oy the hexagonal DOl? phase (clear) with Tc = 6.5 K, reSUlting from a rapid quench from 1850 C (Fig. 16). The specific heat measurement (Fig. 18a) shows that both phases, D019 and bec, are superconducting. The lower T c value for the bcc phase (T c = 1.9) could not be revealed by grinding or by by powdering. The size of the crystallites was too small « 5 1JITl). Here, the specific heat is the only method capable of detecting

PHASE DIAGRAMS 537

the lower superconducting transition.

A case similar to Mo-Pt is encountered in another Mo-based system, Mo-Ge [26]. The two concurrent phases here are the bcc phase (Tc = 2.2 K) and the A15 phase (Tc = 1.6 K). In an insufficiently homogenized alloy, MOO.762GeO.238' 2 hours at 1400<>C (Fig. 19), the lower transition is masked by that of the bec phase, but appears on the specific heat measurement. The very broad transition of the bcc phase indicates distribution of concentration in the phase and is typical for segregational effects. The system Mo-Ge is one of the very few systems where the bec solid solution has a higher Tc than the neighboring A15 phase.

The most important type of shielding effects for our considerations is case (e) in lIIA2 above. It is usually encountered in nonstoichiometric "typical" A15 compounds, where Tc max occurs at the stoichiometric composition, but is also known to occur in other crystal structures. The reason is a distribution of compositions within the sample, centered at the nominal composition, but extending up to stoichiometry. In order to suppress shielding in these alloys, prolonged heat treatments close to the solidus temperature are necessary. This difficulty in removing micro­scopic, stoichiometric portions in the sample may be explained by a minimum of the free enthalpy for this composition, rendering it partic­ularly stable relative to the other compositions and thus difficult to eliminate.

The effects of homogenization on a Nb-AI alloy were discussed in Section lIB. Figure 6 illustrates the difference between a calorimetric and an inductive measurement of Tc on the alloy Nb,....3AI without homo­genization after 5 days at 7500C. The inductive measurement is quite sharp, but the specific heat jump reveals a transition width of more than 1. 5 K. Another example is represented in Fig. 20 where the calori­metric and the inductive measurements of Tc of the arc cast alloy Nb#t are drawn. The specific heat curve for the as -cast state shows a broad transition from 7 to 8.5 K. However, the inductive measurement on the same bulk sample shows an apparently narrow transition at 8.5 K. The inductive measurement on the same sample in the powdered state, shown in the same figure, reveals the presence of a composition distribution and confirms the specific heat measurement. The analysis of this result is delicate, due to the particular variation of T c in Nb #t as a function of the Pt content (Fig. 42). Indeed the phase field of the NbJPt phase as determined by Waterstrat etal. [45J extends from 19 to 28 at.% Pt, but Tc shows a maximum at 25 at-:96Pt and decreases at both sides. From Fig. 20 it can be concluded that our arc cast sample (having an average composition of 25 at.%Pt) consists of a "single -phased" distribution of compositions in the range,.... 23 ~ {3 ~ ,....27 at.%Pt.

These remarks were necessary to understand why a specific heat measurement on the same Nb3Pt sample annealed for five days at 9000C reveals two superconducting transitions (Fig. 20). This effect is based on the asymmetrical behavior of Tc as a function of the Pt content (Fig. 42). After the ordering heat treatment at 9000C (Nb3Pt requires

538

\ /A2 , ,

3 ~A15 G :l~~~ ____ ~ __ ~~--~----·--1<: 2 150 .;l

Cl

iii ---, 100 E l-

t:; 1

50

2

,/ 4 6 8 10

M~62G~238 2h/1400° C

12 14 2 . .7 16 T (0,,)

R. FLUKIGER

Fig. 19 Calorimetric detection of shielding effects on MoO. 762GeO.238 after 2 hours at 1400oC. The specific heat measurement shows transitions at Tc ~ 1,6 K for the A15 phase and a broad transition with an onset at 2.2 K for the A2 phase. The inductive measurement (lower curve) shows only the 2.2 K transition (FItlkiger [26]).

Fig. 20

35

N", 30 ., CI

! 25 .!!

1.20 ... U 15

10

Specific heat measurement on non -homogenized NbO. 7SPtO 25 after different ordering heat-treatments at 900OC. TIle • specific heat reveals a large concentration gradient in the sample, but the inductive Tc measurements on the bulk samples (insert) show .an apparently sharp transition [41].

PHASE DIAGRAMS 539

higher ordering temperatures than other A15 compounds [26J), the portions of the sample with compositions < 25 at.%Pt exhibit Tc values up to 10.7 K, in contrast to the portions with> 25 at.%Pt, where the enhance­ment of T c is less important.

The above discussion shows that the inductively measured T c value of nonstoiChiometric A15 compounds tends to be too high as a consequence of shielding effects. This leads to erroneous correlations Tc vs compo­sition, showing an apparent "saturation" at compositions close to stoichio­metry. As will be shown in Sections V and VI, the correlation of T c vs composition for the great majority of A15 type compounds is nearly linear, but there are exceptions such as NbJAI [IOJ (Section VIF3).

2. Shielding in multifilamentary Cu -Nb3Sn wires

There is only one specific heat measurement on multifilamentary superconducting Cu-NbsSn wires [46J, but it is possible to draw some conclusions about possible shielding effects. The pre -stress effect of the Cu bronze matrix on the Nb~n filaments of!!O 1 to 5 ,.un reduces the Tc value of bulk NbsSn (Tc = 18'K) to values lying between 16 and 17 K, as measured inductively [47J. Inhomogeneities in the field of the external stresses certainly lead to a broadening of the superconducting transition. The question arises if shielding effects are also present in those sample wires. The only available specific heat measurement on a Cu -Nb3Sn wire by Gegel eta!. [46J, shown in Fig. 21, indicates a wide transition between 14.5 and-17 K. Ziegler eta!. [47J measured inductively the effect of the pre -stress on Tc by etching away the bronze matrix. In both cases relatively sharp transition curves were observed with T c values lying above 16 K. The broadening of the calorimetric transition is thus caused by the superposition of two effects, the inhomogeneity in both stress and composition. The occurrence of wire portions with Tc values as low as 14.5 K [46J as measured by calorimetric methods seems to indicate that shielding effects are also present in Cu -Nb3Sn multifila­mentary wires. This means that in spite of the very short diffusion paths (below 1 JJffi), a concentration gradient is built up in the Nb3Sn filaments.

3. Calorimetric observation of low temperature phase transitions

The small energies involved in phase transformations of inter­metallic compounds at temperatures below 300 K do not favor important rearrangements of atoms by site exchange or diffusion. In the great majority of cases these transitions are diffusionless; the major change is a change in symmetry. The term "martensitic transformation" for low temperature transformations is current, but should not be used before one knows the transformation mechanism for each individual case. Specific heat measurements are very sensitive to transformations at temperatures below 30D K; they indicate the transformation tempera­ture' the heat of transformation, and give qualitative information on whether the transition corresponds to a horizontal or to an oblique line in the equilibrium phase diagram.

540 R. FLOKIGER

Chevrel phases. Agood example showing the use of specific heat in establishing low temperature phase relationships is the rhombohedral compound CuxMo6)S studied by FHikiger etal. [4S, 49J. In Figs. 22 and 23, specific heat curves for compounds with different Cu content are shown. The structural transformations show up as large peaks, the tops of which coincide with the discontinuity in the slope of the resistivity (Fig. 22). The low temperature phase diagram shown in Fig. 24 for l.5 ~x ~3.5 has been established [4SJ on the basis of these measurements, in combination with additional resistivity and x -ray diffraction data. At x = 1. S in Fig. 22 there is a single peak corresponding to the congruent formation of triclinic [50JCul.SMo6)s from the high temperature rhombohedral phase (Chevrel phase). A small bump in the specific heat of the x = 2.0 compo­sition at lS7 K indicates that below this temperature the alloy sits in a two-phase field, i.e., CUl.SMo6'S + CU3 .2M06SS. On heating the x = 2.7 alloy from the lowest temperatures, where the phase ratio according to Fig. 24 is 1/3 (Cul.SM06Ss) + 2/3 (Cu3.2M06SS), the first peak occurs at the peritectoid, lS7 K. At this point the x = 3.2 phase transforms into the high -temperature Chevrel phase, RH, and the heat of transformation amounts to approximately 2/3 of that observed in CU3 .2Mo6'S. Between lS7 and 230 K, the x = 1.S phase gradually trans­forms into the phase RH, following the CUl.SMo6SS + RH/RH phase boundary. The associated specific heat of transformation drops to zero when this process is over (near 230 K). The very broad peak in specific heat at ,..".230 K thus indicates that an oblique line in the equilib­rium phase diagram is crossed.

Both phases, CU1.sMo6Ss and CU3.2Mo6)s are superconducting, and the jump of the specific heat at T c in Fig. 23 permits determination of the limits of these phases by applying the "lever law" . Inductive meas ure -ments of T c on powdered samples confirm the phase limits obtained by specific heat. It should be noted that at the time this phase diagram was established [42,4SJ, the low temperature structure of CUl.SM06'S was not known. The determination of this phase was undertaken once the above­mentioned methods had established the low temperature phase field: 1. 75 ~ x ~ 1.S5. In Section VII the complete phase field of CuxMo6Ss will be discussed.

Laves phases. Another example of a low temperature phase trans­formation detected by specific heat measurements is illustrated in Fig. 25 (Hafstr!)m etal. [51J). Very sharp peaks occur at 115 K for the com­pound V2Hfand its variation with Ta additions.

Other phase!>. Several crystal structures with values of T c above 10 K are known to exhibit low temperature phase transformations. The cubic-to-tetragonal phase transformation for V3Si [52J and Nb3Sn [53J is well known (Section VI). A phase transformation also occurs in NbTi. It is tempting to correlate the presence of structural instabilities with the high T c values or high electronic dens ity of states, but the exceptions are too important to be neglected. For example, V 3Ga has the highest known electronic density of states for a superconductor, but does not transform ; earlier indications of a transformation [54 J have not been

PHASE DIAGRAMS

en ":.;:

? I-

0'

0.6

0.5

OJ.

03

10 12 14 16 18 20 22 24 T(K)

541

Fig. 21 Specific heat data of a partially reacted Cu -Nb3Sn composite wire. The Nb3Sn phase undergoes a broad transition at tem­peratures between 14 and 17.5 K (after Gegel et al. [46J).

4o. nr---,----,----,-,--",

30

i" '" ~ 20.

.2 u

.' 3.2

100 150.

" " .'

200 250. 300

T[KI

UE" .., 10. c: ~

0.90-

0..8

Fig. 22 Low temperature specific heat and electrical resistivity data for CuxMo()SS with x = 1.S, 2.0, 2.7 and 3.2. The lower transition temperature at IS7 K for the composition x = 2 can be detected only by specific heat measurements [42].

542 R. FLUKIGER

300 r---r"-r----r"-,...,

200

100

10

~ 5

15 2.5 35

Fig. 24 Portion of the low temperature phase diagram ofCllxMo6S8' This diagram serves as a basis for understanding the specific heat data in Figs. 22 and 23 [42 J .

. '}"/ ~ r"~24~--r-----r-~-1

20

5

o 5

TIKI 10

j ~

50% ! " ~

15

Fig. 23 Specific heat curves for CU2.4Mo&58 and CU2.7Mo6S8 show two superconducting transitions, confirming inductive measure­ments of Tc on powdered samples (Fliikiger et al. [42 J) .

PHASE DIAGRAMS

en I • w, "'o.n Too . .,

.", ... 0. .. , .... , o N : :: ::: :~': ~30 ..... -, E I-

'-'20

543

Fig. 25 Specific heat curves in the vicinity of the lattice transformation temperature, T L' V2Hf1-xTa...x which crystallizes in the Laves phase (after HafStrBm et~. [::>1J).

1

O~--~--~----~--~--~----L---~

a 100 200 300 T( OK)

Fig. 26 Low temperature electrical resistivity of CU2Mo~e8 shows a lattice transformation at 162 K [153].

544 R. FLOKIGER

confirmed. Furthermore, it was found that the value of Tc is not seriously affected by the transformation into a tetragonal phase for V3Si [55J or for Nb;j)n [56J; ATc = Tc (cub) - Tc (tetr) does not exceed a few tenths of a degree.

C. Electrical Resistivity Below 300 K

Application of electrical resistivity measurements for determination of low temperature phase transitions is illustrated in Fig. 22 for CuxMo()SS. In this case the phase transformations are characterized by changes in the slope of p(I'). In CuxMo()SeS' the transformation is indicated by a sharp drop of p(I') (Fig. 26). The main advantage of electrical resistivity measurements over specific heat measurements is the possibility of cycling the temperature about the transformation tem­perature, either point-by-point or continuously. Occurrence of hysteresis permits determination of a first order transformation. CuxMo~S and CuxMo()SeS exhibit hysteresis of 1 and 3 K respectively (i.e. they have first order transformations). Another example of hysteresis of p(T) at the phase transition is shown in Fig. 27 for the Laves compound ZrV2, as determined by Levinson [57J. The hysteresis here is about 10 K.

IV. CRITERIA FOR PHASE STABILITY AND SUPERCONDUCTIVITY

A. The Brewer Plots

Hume -Rothery first remarked that intermetallic phases of elements with high valency tend to occur at definite valence electron -to-atom ratios, e/a. Such "electron compounds" are mostly encountered in elementary structures, i.e., bec, fcc or hcp structures. There is a close connection between these characteristic e/a ratios and the electronic density of state curve N(E) for the crystal structure concerned. A general crystallo­chemical concept for intermetallic phases has not been established. The theory of structural stability should include the band energies and also geometrical and electrochemical factors. A rough indication of the stability of an intermetallic phase can be obtained by considering the sequence of the phases in a multicomponent Brewer plot [5SJ. These plots can be established for an element, for example V, and a sequence of neighboring 3d, 4d, or 5d elements with increaSing atomic numbers, for example Re, Os, Ir, Pt, Au (Fig. 29a). These plots give a simplified view, since only the extreme solubility limits of the corresponding binary phase diagrams, V-Re, V-Os, V-Ir, •.• are considered. They corres­pond to a projection of the binary phase diagram on the abscissa; the tem­perature dependence of the phase limits is neglected. Though oversimpli­fied' the Brewer plots are a convenient representation of a multicomponent system in two dimensions.

A series of Brewer plots for intermetallic compounds containing only transition metals are shown in Figs. 29a, b, and c and in Figs. 30a and b. The extreme solubility limits given in these plots have been taken from the reported data of Hansen [59J, Elliott [60J, Shunk [61J, Moffatt [62J, and

PHASE DIAGRAMS

1.05

o 1.00 8 a: " 0.95

E a: 0.90

_.- Single crystal

---- Polycrystal - Inclusion filled polycrystal

0.8~~0--:7~:L:--L-.---L---L...--13LO~140

Fig. 27 Low temperature electrical resistivity of ZrV2 shows a marked hysteresis at the transformation temperature (after Levinson et al. [57J).

L T"j lobs [~ISJ

10 15 20 30 35 La 45 50

1000 s' 21i Ii)

'"

.~ '"

r ~ 30'

20i '02 '" 110

2~2 3~ lobs

[~J 10 15 20 2S 30 35 La 45 50

2-& [oJ

Fig. 2S. Powder x-ray diffraction data for CUj SMo6SS at 5 K (top) and 293 K (bottom) (Baillif et aI. [50J):

545

546 R. FLOKIGER

ela 6.0 6,5 7,0 8,0 !lO I

, Au , ,

PI

V (a)

A2

o 10 20 30 40 90 100

f/a 6,0 6,5 7,0 8,0 9,0

Nb

(b)

o

To (e)

o 10 20 30 40 50 60 70 80 90

ot.%

Fig. 29 Brewer plots: (a) V-(Re,Os,Ir,Pt,Au); (b) Nb-(Re,Os,Ir,Pt,Au); (c) Ta-(Re,Os,Ir,Pt,Au). (after Ref. 26)

PHASE DIAGRAMS 547

Waterstrat [45, 78J. Data for V-Au [14J, Ta-Au [17J, Nb-Au [15, 18J, Mo-Pt [20J, V-Os [13J are more recent. As shown in Figs. 29 and 30, the multiphase diagram (y, Nb, Ta, Cr, Mo, •.. ) - W, Re, Os, Ir, Pt,Au) is described the following sequence of crystal structures:

A2 I A15 I (] A12 A3 I Al I I I I I I I I I I I I I

B2 A13, ••• LlO, L12, ••• BI9,DOI9, •.•

One or more of these crystal structures may be absent from this scheme, but the sequence is generally followed. Our discussion is limited to the elements X = 5d. In general, the combinations with X = 3d and 4d show the same behavior. In all these plots the curves with constant e/a have been added as a guide for the reader. The influence of the increasing number of electrons on the phase relationships can be immediately seen from Figs. 29 and 30. The phases in the line A2 to Al above are easily identified as "electron compounds". With very few exceptions, the limits of these phases are located very close to constant values of e/a.

1. Does Au behave like a transition element?

The plots in Fig. 29 show unambiguously that there is a real change in behavior in going from Pt to Au. In particular the homogeneity ranges of the Al and A2 terminal solutions show a considerable broadening, as do V-Au [14J, Nb-Au [15, 18J, and Ta -Au [17J. In all three cases, the A15 phase is formed congruently from the A2 phase in a way similar to V -Ga [27, 29J • This suggests that Au (with a filled d -shell and a 6s -electron) behaves like a non -transition metal. This observation is confirmed in Sections V and VI, where the superconducting properties of intermetallic phases containing Au are discussed. Here we discuss the multicomponent system excluding Au.

2. The relative stability of intermetallic phases

The study of the stability of one intermetallic phase involves the stability of its neighboring phase based on free energy considerations. Figures 29 and 30 show the concurrence between adjacent phases; the width of one phase increases at the expense of the neighboring phase. This is clearly seen for the three phases A2, A15, and (] in Fig. 29. In V-based compounds, the A15 phase is dominant and replaces the a phase. In Nb-based compounds, both the A15 and a phases are stable. The width of the one is a maximum when that of the other is a minimum. Finally in the Ta -based systems the a phase is dominant and excludes the A15 phase, except in the case of Ta -Pt and Ta -Au, where the latter is highly non -stoichiometric with 14 and 18 at.%, of Pt and Au, respectively [15, 17J. In one system, Nb-Os [45J, both the A15 and the a phases are stable at the same composition. This is possible because the phase limits vary as a function of temperature [45J. The largest homogeneity range of the A2 phase corresponds to the narrowest one of the A15 phase, except for Au-

548 R. FLUKIGER

based compounds, where the latter is "covered" by a wide A2 phase and is fonned by a solid state reaction [14, IS, 17, 18J (Figs. 38 and 42).

3. The A15 phase

Going from the V-based to the Ta-based A15 compounds (Fig. 29), there is a transition from an electron compound to a compound with fixed composition. In the V-X(5d) systems, the X-rich limit coincides remark­ably well with the curve at e/a = 6.5, whereas in the Nb-X(5d) systems it is pushed towards e/a values lower than 6. This tendency is accentuated for Ta -Pt (e /a = 5.7) and can be understood by means of geometrical arguments. The lattice parameters for Nho. 72IrO .28 and NbO• 700s0. 30 are the smallest measured for Nb-based A15 compounds: a = S.118 A [26J. Assuming a phase limit at 6.5 electrons per atom, the lattice parameter for the hypothetical compound "Nho 500s0 50" would be below a = 5.0 AI This value would be even lower thin the eXtrapolated value for the hypothetical, metastable Nb3Si (Fig. 64). Thus, the phase fields of the Nb-based A15 compounds Nb-Os and Nb-Ir seem to be influenced by a strong repulsion between the Nb atoms on the chains. This could also be the case for the Ta-based A15 compounds, where the repulsion seems to be even stronger. The repulsion argument is supported by the fact that the chain atoms in the A15 type structure are under compression relative to their elementary state; . the Nb -Nb distance in Nbo 700s0. 30 is 2 .5S9 A, which is 10% smaller than in bec Nb (2.85a' 1).

Figures 30a and 30b show the Brewer plots for Cr-(W, Re,Os, Ir, Pt) and for Mo -(W , Re, Os , Ir, Pt), respectively. Au is not included because it is insoluble in Mo (and W) and shows a very limited solubility in Cr. The AlS phase Mo-Re has been extrapolated [38J. The phase sequence is the same as in Fig. 29, but the hexagonal A3 phase now has a very large homogeneity range, thus reducing the total number of phases for each individual phase diagram. The A15 structure of Cr and Mo based compounds shows a behavior similar to that of V and Nb; Cr3X compounds have a larger homogeneity range than M03X compounds. Again, the AlS phase and the C1 phase are in concurrence. The C1 phase finally dominates in the W -X systems and, in equilibrium, it excludes the forma­tion of the A15 phase. (In the W -Re system, the AlSphase was formed by sputtering [68J, which is a non -equilibrium method.) It is interesting to follow the X-rich limit of the A15 phase in Mo-X compounds for Mo-Pt and Mo-Ir. The limit is at e/a = 6.75, but shows a deviation for MOaOs (e/a = 6.5). For ternary compounds without Os (e.g., Mo-Pt-Re [63J and Mo-Ir-Re [63J), the limit is again at e/a ~ 6.75 (see the dotted line in Fig. 30b). As for Nb-X, it is tempting to use a geometrical argument. Indeed, M030s has the smallest lattice parameter of the series Re, Os, Ir, Pt (a = 4.969 A), reflecting the smaller atomic radius of Os. All points on the dotted line in Fig. 30b have lattice parameters between 4.972 and 4.980 1 [63]. The Brewer plots were developed to represent multiphase systems where both constituents are transition metals with high valency. If one of the constituents is a nontransition element, i.e., Au, AI, Ga, Sn, ••. , the same representation as in Fig. 29 or Fig. 30 can be used, but it then has a different meaning. The compounds are no

PHASE DIAGRAMS

e/a 6,5 7. 0 7. 5 8,0

Cr

o 10 20 30

e/a 6.5 7.0 7.5

Mo

A2

0 10 20 30

40

['0

50 at.%

8,0

50 at.%

549

8,5 9,0

( a)

60 70 80

8,5 9,0

Os (b)

Re _x

_A15

60 70 80 90 100W

Fig. 30 Brewer plots: (a) Cr -(W, Re, Os, Ir, Pt); (b) Mo -(W, Re, Os, Ir, Pt) • The dotted line represents the phase limits for the Mo-Ir-Re and Mo -Pt -Re [38 ] (after Ref. 26).

550 R. FLOKIGER

more "electron compounds"; the phases have the tendency to form at fixed compositions. This is illustrated in Fig. 31, which shows the systems Nb-(AI,Sn,Sb) and Nb-(Ga, Ge, Sb). It is obvious that e/a values in such diagrams do not have anything to do with the variation of phase limits •

The plots in Figs. 29, 30 and 31 rapidly show the phase relation­ships in a whole family of compounds, but also allow prediction of possible metastable compounds at the end of a series. Two examples, the meta­stable "M050Re 50 " , as mentioned above [63,64, 66J and Va 29ReO 'Z1 [67J (the recently discovered A15 compound with Tc = 9.3 K) illustrate· the possibilities of such diagrams. As an example, Cr",50Re",50 could be another new A15 compound.

B. Criteria for Superconductivity

One driving force in superconductivity is the search for higher values of Tc ' Hc2' and lc. To date the superconducting properties of intermetallic compounds have been discussed in several thousand publications, but it is still not possible to predict T c of an unknown compound, even approximatively. The complex behavior of the super­conducting properties reflects the behavior of the electronic structure which in most cases is insufficiently known. It appears that anomalies in the phonon spectrum, which also influence Tc ' may be generated by the electronic structure. This illustrates the formidable difficulties for a general description of these phenomena. The difficulties in predicting new high Tc materials are very similar to those arising on the search of a new intermetallic phase. The main link between both problems is the electronic density of states at the Fermi level. A substantial difference in the treatment of both problems arises from the fact that for super­conductivity the value N(E) at low temperature is the determinant, whereas phase stability is governed by N(E) at very high temperatures. It is thus not surprising that the only criterion for superconductivity known so far, the Matthias rule [69J, is a qualitative one. It relates the probability for a specific compound being superconducting to certain numbers of valence electrons per atom in the lattice. The number of valence electrons is normally taken directly from the periodic table. This simple rule holds for most binary and pseudobinary compounds, as illustrated in Fig. 32 for compounds belonging to different crystallo­graphic structures. Heiniger [70J has shown that the variation of the electronic specific heat, ')I, is very similar to that of e/a (Fig. 33). From Figs. 32 and 33, it follows that the maxima of T c and ')I are observed at e/a values ranging from 4.5 to 4.75 and from 6.4 to 6.7. These values vary somewhat with the crystal structure, but it is still remarkable that this variation only occurs in narrow limits. For ternary compounds, e.g., Chevrel phases, the Matthias rule in its simple form is no longer valid. Recently, Yvon [71J introduced a modified valence electron concentration (VEC) and obtained the plot shown in Fig. 34 for ternary sulfides. Other criteria for the occurrence of super­conductivity have also been proposed, involving the atomic volume or

PHASE DIAGRAMS

Nb Sn

AI 4.75 4.5 4 3.5

0 20 40 ot.%

60 80 100Sb

Nb Ge

113

% 475 4.5 4 Go

3.5

Fig. 31 Brewer plots for Nb-(Al,Sn,Sb) and Nb-(Ga,Ge,Sb). In contrast to Figs. 29 and 30, the phases now occur at fixed compositions. The values of e/a are not relevant.

551

552 R. FLU KIGER

25 A15 Tc(K)

20

4 5 6 7 8

% Fig. 32 Maximum Tc values as a function of e/a for different crystallo­

graphic structures. For most structures, the highest T c values are situated around e/a = 4.5 - 4.75 and e/a == 6.5 -6.7. Only the ternary Chevrel phases (RH) show a different behavior (see Fig. 34).

3 4 5 6 7 8 electrons /otom

~, / \

/ I /\ !

/ \ I / \

/ ill / \\ . .~

\ \ \ \

~

9 10 II

Fig. 33 Comparison of the specific heat coefficient yvs the number of valence electrons per atom in 3d-, 4d- and 5d- alloys. (After Heiniger [70J.)

Fig

. 34

15

10

TCO

() 5

I M xM0

6\J

Mo,

5 11

... ••

• .

. . ·_

--s..

-

.. " .'"

.. " . . -.. .. .

• •

:-. M

oZ,,-

.. S.,

CO·t

tTlt

Clu

ster

-VEC

(ele

ctro

ns I

clus

ter

atom

)

Clu

ster

-V

Ee

(va

lenc

e el

ectr

on

co

nce

ntr

atio

n)

for

MxM

o6S

s co

m­

poun

ds (

afte

r Y

von

[71

J) .

Fig

. 35

T

(oC

)

25

00

20

00

1-

//

<

Tc

\ \ \ \ \ 1

50

01

-\

T

(OK)

\ \

7.0

e/o

Th

e v

aria

tio

n o

f T

c w

ith

e/a

fo

r se

ver

al

hexa

gona

l M

o-X

co

mp

ou

nd

s.

Th

e ar

row

s de

note

the

hig

hes

t va

lue

of T

c in

a g

iven

sy

stem

, co

rres

po

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ing

to

th

e ex

trem

e so

lub

ilit

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imit

of

the

hexa

gona

l p

has

e at

high

tem

pera

ture

. T

his

fol

low

s fr

om

th

e u

pp

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iag

ram

(af

ter

Ref

. 6)

.

-g

:::c ~

C/l m

o ~

G)

:lJ

~ :s: C

/l (.II

(.

II

Co)

554 R. FLUKIGER

even the atomic masses, or other quantities. However, none of these criteria predicts new superconductors, or adds very much to the present understanding of superconductivity.

V. PHASE FIELDS AND SUPERCONDUCTIVITY IN BINARY "ELECTRON COMPOUNDS"

The present section describes the properties of "electron compounds", defined in Section IlIA, beginning with the hcp (A3) structure and the bec (A2) structure. This will serve as an introduction for the discussion of "atypical" A15 type compounds, consisting of transition metals only. The reported phase fields have been carefully selected from the literature [45,59,60,61, 62J. A certain number were determined in our laboratory, using the methods described in Sections II and III. In some cases slight modifications to existing phase diagrams have been made, based on results of detailed studies of particularly interesting regions of these phase fields by the author [15J .

A. The hcp Structure (A3 type)

It can be seen from Fig. 35 that the Mo-rich side of Mo-based A3 phases occurs between the limits 6. 9 ~ e/a :l!: 7.3. All these phase fields are very broad and show a strong variation of the Mo-rich limit as a function of temperature [6J. The temperature of minimum Mo content decreases with the melting temperature of the second element. As shown in the lower part of Fig. 35, T c increases with lower Mo content [6J, reaches values close to 10 K for Mo-Re and Mo-Ru (and even 15 K for Mo-Tc [72J). Although there is much less data available for the iso­electronic Cr-X and W-X compounds, a very similar variation of Tc as a function of the phase limits is observed. The superconducting "memory" effect discussed in Section IID4 was observed on each one of these systems.

B • The A2 C omp ounds

Terminal bec solid solutions between Mo and several 4d and 5d elements show very similar characteristics to the hcp solid solutions. Broad phase fields and a strong variation of the low Mo limit (situated between 6.2 and 6.5 electrons per atom) are observed. As shown in Fig. 36, the Tc values increase with e/a and reach maximum values of 14 K for Mo-Re [20.73J and Mo-Tc [72J. However, the increase of Tc occurs at different rates for each system; it is maximum for Re and T c' smaller for Os, Ir, and nearly zero for Pt. Earlier, Matthias [74J suggested that superconductivity and microhardness of a phase could be correlated. If there is such a correlation, it is certainly of a complex type, because for each compound in Fig. 36 an increase in T c with higher e/a is correlated with an increased microhardness. On the other hand, the system with the smallest T values, Mo-Pt, exhibits the highest microhardness. In general, ;Xo-X bec solid solutions exhibit an increase of Tc if X is at the right of Mo in the periodic system (see also Mo-Ge in Fig. 19). If X has less than 6 valence electrons, a decrease in T c is observed. V, Ta and Nb based solid solutions show a variation opposite

PHASE DIAGRAMS

900 Hy

Ik~

700

500

6.1 6.2 6.3

555

10

Os

Ir

Pt

0 6.4 ~

Fig. 36 Superconductivity and microhardness in bcc solid solutions of Mo-Re, Mo-Os, Mo-lr and Mo-Pt (after Ref. 20).

10

5

Ta-Pt O~------~ ______ -L ______ ~ ______ ~ ____ ~

o 5 10 15 20 ot.%

Fig. 37 Variation of Tc as a function of composition for bec Nb-rich solid solutions (after Ref. 26).

556 R. FLUKIGER

to Cr, Mo and W based solid solutions. As will be seen later, the antagonism between both groups of elements, due to the difference of 1 valence electron, occurs for the metallurgical as well as for the super­conducting properties. For Nb-X bec solid solutions, a maximum of Tc occurs at e/a < 5 for X = Ti, Zr. No case is known where T c of the bec solid solution is higher than that of Nb (e/a = 5) if X is an element at the right of Nb in the periodic table. Charge transfer effects can be advanced to explain this shift in e/a. The variation of Tc as a function of composition is shown in Fig. 37 for the A2 systems V-Au [26J, Nb-Pt [26J, Nb-Au [26, 75J, Ta -Pt [26J, Ta -Au [17, 26J and Nb-Sn [76J. The case of the A2 solid solutions with Au in Fig. 37 is particularly interesting. Assuming 11 valence electrons for Au, the value e/a for the bcc alloy Nbo.7sAuo 25 would be 6.5, whereas this alloy exhibits a minimum in Tc of 1.2 K [7~J. Based on remarks in Section IVA, this is one more argument in favor of aSSigning 1 valence electron for Au.

C. "Atypical" A15 Compounds

The overwhelming majority of investigations on A15 type compounds have been performed on the high Tc materials, i.e., Nb3Ge, Nb3Al, Nb~n, V 3Ga, V ~i, •..• Low T c materials of the same structure have received much less attention. However, there is much to be learned from a detailed study of their superconducting and metallurgical properties. The question why the T c values are low is complementary to the question why the Tc values of the former are high. We will start our analysis of A15 type materials with the Brewer plots represented in Figs. 29 and 30. From these plots it can be seen that a considerable part of A15 compounds, i.e., Vo 290s0 71' Vo 500s0 50' .•• are "electron compounds". This class of compounds is also calted "atypical" A15 compounds, in contrast to V~i, Nb;3Sn, •.• which exhibit the "typical", extraordinary supercon­ducting properties of A15 superconductors, generally attributed to a singularity in the electron density of states. There is a continuous transition between "atypical" and "typical" A15 type compounds. The best illustration for this transition is given by the series V -(Re, Os , Ir, Pt, Au). We will first discuss this series in detail. The conclusions will then be generalized to other "atypical" A15 type systems.

1. The V -(Re, Os , Ir, Pt, Au) system

It follows from Fig. 29a that the A15 compounds VO.21ReO.79 [67J and VO.500s0.50 [13J have phase fields far away from stOichiometry, whereas the A15 phase is stable for V-Ir [77J and V-Pt [45, 78J. The low V limit of the A15 phase in all these systems occurs always at e/a = 6.5. There is a change in behavior in going from V3Pt to V"",3Au; the pseudo­binary V,.., 3(Pt1-xAuX> [26J shows a deviation from stoichiometry. However , V,.., 3Au is not stoichiometric at all, its highest stable composi­tion being VO. 76Auo .24 [14J.

The change in behavior going from Re to Au is illustrated in Fig. 38, which shows the phase fields of these systems and the corres­ponding variation of Tc as a function of composition. The A15 phase

Fig

. 38

IV-I

rl

I V-p

t I

IV-A

u I

" 1600

·C

-qu

ench

ed

7d/1

300·

C

5

! 1650

"(;

-wan

ei'

0'

It,'

I ..

....

-I

-,

r=

! ...

60

ro

60

00

W

W

ro

m

~%~

.%~

al.%

lr

at%

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at.

%A

u

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ph

ase

fiel

ds

in t

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syst

em

s V

-Re,

V

-Os

[13J

, V

-Ir

[77J

. V

-Pt

[78J

. an

d V

-Au

[14

J.

Th

e v

ari

ati

on

of

Tc i

n t

his

ph

ase

is r

ep

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nte

d in

th

e lo

wer

part

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the

fig

ure

(G

iorg

i eta

l. [

67J,

Su

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tal

[13J

, G

iess

en

eta

l [7

7J.

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F

IUk

iger

eta

l. [

UJ.

"tI

::I: t'i; m

!2 e; :ll ~ en

01

~

558 R. FLOKIGER

field in V -Re is indicated by a dotted line, because no precise high tem -perature data are available. The compound VO.29ReO.71 decomposes eutectoidically at 1600<>C [67J, like VO. 50°80.50 which shows the same type of decomposition at 1570<>C [13J. The formation of Vo .29ReO 71 is uncertain, but the insertion of the A15 phase in the existing V-Re phase diagram [59J is best accomplished by assuming a peritectoid formation, again like V.o 5Q.0sQ 50 [13J (Fig. 38). The recently discovered A15 phase in V-Re Lo7J is an example of how phases decomposing eutectoidic­ally at high temperatures can be missed if the appropriate direct high temperature analysis methods are not used. Figure 38 shows that V3Ir forms congruently from the melt and V 3Pt forms peritectically. Both systems are characterized by very large A15 phase fields. Finally, V", aAu forms congruently from the bcc solid solution [14J. The stoichio­metric composition is not stable, the phase field ranging from 19 to 24 at.%Au. The difference between V",3Au and V-(Re,Os,Ir,Pt) consists in the variation of the Au -rich limit as a function of temperature. The compos ition closest to stOichiometry is reached at high temperature (24 at.%Au at 1244<>C [14J), which is characteristic of "typical" A15 com­pounds such as Nb",3Ge, Nb3Ga, Nb3Al.

The variation of T c in the system V -(Re, Os, Ir, Pt, Au) als 0 illus -trates the transition between "atypical" and "typical" A15 systems (Fig. 38) . In V -Os and V -Ir the variation in T c is mainly guided by the change in e/a; Tc max occurs at the phase limit, e/a = 6.5. This is no longer the case for VaPt, where the maximum of T coccurs at stoichiometry. In V",3Au, Tcmax =:::3 K occurs at 24 at.%Au. As shown in Ref. 14, an extrapolation to 25 at.%Au combined to enhanced atomic ordering yields T c ,... 5 K. A complete picture of the variation of T c from V -Os to V-Pt is given in Fig. 39, along with the pseudobinary systems V-os -Ir, V -Ir -Pt. There is an almost linear variation of T c for the "atypical" region of V-(Os -Ir-Pt), with the maximum of Tc at e/a = 6.5 A singular peak for T c is encountered for V 3Pt at the stoichiometric composition. The system V-(Pt,Au) is more complex and will be discussed in Section VIB.

2. The electronic structure of electron compounds: the two-band model

The continuous change of the metallurgical and superconducting properties in the system V-(Re,Os,Ir,Pt,Au) illustrates the interconnect­ion of both with the electronic density of states, N(E). For these systems, two energy bands are expected to interact at the Fermi level. These arise from the V 3d -electrons at the (6c) chain sites and the 5d -electrons of (Re, Os, Ir, Pt, Au) at the (2a) cubic sites. For non­stoichiometric systems, i.e., VO.21ReO.79 or VO.500s0.50' there is an appreciable amount of Re or Os at the cham sites which leads to an additional 5d -electron contribution.

An attempt to determine experimentally the band structure of the series V-(Os,Ir,Pt,Au) has been undertaken by Kurmaev and co-workers by means of soft x-ray [79, 80J and photoemission [81] spectroscopy.

PHASE DIAGRAMS

6.0 e/a \ ~" 20 \ ~ .

\ <;> .... \ 0\0

;-(,,30 4)

6.0 e/a 4) • Re . _._._._._.--.-._._.-._.-._._ .

•

•

Fig. 39 Superconductivity and A15 phase field in V -(Os, Ir, Pt) (Flilkiger, Ref. 26).

Fig. 40 Band structure in several V -based A15 compounds as deter­mined by soft x-ray emission [79, 80J and photoemission spectroscopy (Kurmaev etal. Refs. 79, 80, 81).

559

560 R. FLUKIGER

Like other investigators [9SJ, these authors [79 -81J failed to detect the expected fine structure of the density of states at the Fermi level. The energy resolution of these techniques is about an order of O.S eV compared with 0 .OS eV for the calculated bandwidth. Nevertheless, the gross features of the different d -bands can be observed and are shown in Fig. 40 01-Rh, V -Pd and V -Ni are also included) • The data show a strong hybridization of the V 3d -band and the Os Sd -band at the Fermi level. Going from Os to Au, the 3d -band and the Sd -band are success -ively decoupled. Based on these observations, a qualitative two-band model was established L26J (Fig. 41) which can be described as follows. At the Fermi level the electronic density of states of V"" 3Au is essentially due to the V 3d -electrons. The gradual approach of the Au 5d -band to the V 3d -band going from Pt to Os leads to an increasing influence of the Sd-electrons at the Fermi level. For VO.SOOsO.SO' where the position of both bands coincides, the contribution of the Os So -electrons on the electronic density of states becomes dominant, because the Os Sd­electrons arise from the (2a) cubic sites (occupied by Os atoms only) as well as from the (6c) chain sites (occupied to 33% by Os atoms). Although no meas urements of the V -Re system are available, an enhanced contri­bution of the Re Sd-electrons to N(EF) is expected, since S4% of the chain sites are now occupied by Re atoms. It can thus be concluded that the superconducting properties of "atypical" AlS compounds are similar to those of electron compounds crystallizing in other crystallographic structures, i.e., hcp, bec, ..••

It is now clear why the simple ratio e/a is not sufficient for a full description of T c' It is essential to know the contributions of all electrons at the Fermi level. This is demonstrated for the e/a == 6.S limit at the AlS phase in the system V -(Re, Os, Ir, Pt), where the maximum T c values are 9.3, S .4, 3.7, and < 0.1 K, respectively. The corres -ponding values of the electroni£ specific heats, y, are 4.3 [67J, 4.76 [41J, 4.34 [41J, and S.lS [41JmJ/K 'g-at, respectively. The shift of the AlS phase fields in the system V -(Re, Os, Ir, Pt, Au) thus seems to be correlated to a varying degree of band hybridization at the Fermi level. However, it should be added that one has to be careful to consider temperature dependence of N(E) when comparing superconducting (low temperature) with metallurgical (high temperature) properties. We will take the V -(Re, Os, Ir, Pt, Au) system as a model to explain the properties of other "atypical" AlS type systems.

3. The Nb-(Os,Ir,Pt,Au) system

The metallurgical and superconducting properties of the Nb-(Os, Ir, Pt, Au) series are represented in Fig. 42. The upper part of this figure showstheAlSphasefields of Nb-Os [26,4SJ, Nb-Ir l26,82J, Nb-Pt[4SJ, and Nb-Au [IS, 18J. As in V-X, these successive phases form peritect­oidically, congruently from the melt, peritectically and congruently from the bcc phase, respectively. In spite of the similarities between Fig. 38 and Fig. 42, there is a major difference - the Nb-based systems do not show the pronounced deviation from stoichiometry encountered for the V-X series. As mentioned earlier, this difference of behavior is

PHASE DIAGRAMS 561

Fig. 41

Fig. 42

V-Au

V-Pt

V-Ir

V-Os ---=:.--++:-.-:.....:~- E

Successive hybridization of the V3d and XSd bands going from X = Au to X = Os (two-band mode) (FlUkiger, Ref. 26).

I Nb-Osl I Nb-Ir I 10d/900'C

t 11 ~I

~=02S ~=02S t~2S I

I I I

I I I -quenched

"-10 20 ]0 40 20 30 40 20 30 LO 20 30 LO

ot%Os at.%Ir ot%pt ot%Au

A1S phase fields and superconductivity in the systems Cr-Os [26,4SJ, Nb-Ir [26,82J, Nb-Pt [8SJ, and Nb-Au (Waterstrat etal. [4SJ, Giessen ~al [82J, Rl:Sschel etal. U8J, FlUkiger 126, 63J).

562 R. FLUKIGER

attributed to geometrical reasons. The behavior of Tc as a function of composition is also similar for V3X and Nb3X. In Nb3Au [98J, Tc max occurs at the highest Au content (23.6 at.%Au [lSJ; in Nb;3Pt, Tc decreases on both sides of the stoichiometric composition [83J; and in Nb3Ir, Tc increases linearly with the Ir content, with a maximum of 3.3 K at 28 at.%Ir, where e/a = 6.S [26J. The variation of Tc in Nb30s [26J is opposite to that encountered in VO.SOOsO.SO' but this difference is explained by the very different e/a values of both compounds. In both cases, Tc extrapolates to zero at e/a ~ 6.0.

The separation of the energy sub-bands in Nb3X and V 3X compounds was determined by Kurmaev etal. [81J by means of x-ray photoemission spectroscopy. Their data (Tabfe I) show that this separation is approxi­matively the same for Nb3X and V 3X compounds where X = Au, Pt, Ir. A significant difference is only observed for X = Os, where E 3d - E Sd = loS eV, compared with E4d - ESd = 2.2 eV. The sub-bands are thus considerably closer in the case of the highly non -stoichiometric VO.SOOsO.SO' suggesting an enhanced contribution of the Os Sd-electrons to the electronic density of states at the Fermi level with respect to Nb30s.

4. The Cr-(Os,Re,Pt) system

The AlS phase fields for Cr-Os [26,87J, Cr-Ir [IS, 4SJ and Cr-Pt [4SJ are shown in Fig. 43, together with the corresponding variation of Teas a function of composition. For Cr-Os [26J and Cr-Ir [26, 88J, the maximum of Tc occurs at e/a = 6.S, whereas Cr-Pt is not superconducting down to 0.012 K [88J. The AlS phase limits of these three systems follow the e/a = 6.Sline. This also holds for the Cr-based compound with the 4d element Ru, where the highest Ru content is 29 at.%Ru [88J. It would be interesting to see if AlS phases are stable or can be stabilized in the systems Cr-Re or Cr-Tc, situated at the end of the series in Fig. 30a. In analogy to the Mo-X systems (Section VCS), both would be expected at the equi -atomic compOSition, with T c values > S K based on the maximum Tc values of 4.7 K [26Jfor CrO.720s0.28 and 3.43 K [88J for CrO. 72RuO .28. S. The Mo-(Re, Os, Ir,Pt) system

The AlS type structure is not included in the Mo-Re equilibrium phase diagram established by Knapton etal. [84J. By means of the sputtering teclmique, Gavaler etal. [66} synthetized the metastable compound Mo""SORe ....... SO. This is comparable to the compound MOO.SOTcO.SO L72J, which is superconducting at IS K. The best way to study the properties of the equilibrium AlS phas~ in Mo-Re is to extrapolate its properties starting from the ternary Mo-Re -Pt [26,38, 64J system, which has the unusual AlS phase field shown in Fig. 44 deter­mined by FlUkiger etal. [38J. The variation of Tc in this system (Fig. 44) increases linearly from 4.6 K for MOO.81sPtO.18S to 12 K for MOO.S~.01sReo.42S. The AlS phase in the Mo-Re system is thus at the verge of stability since it can be stabilized with 1.S at.% of Pt. By extrapolation, the composition of the binary AlS phase is MoO .SOReO. SO,

PHASE DIAGRAMS 563

with a T c value close to 14 K. The variation of T in Fig. 43 is "atypical", Le., the maximum occurs ate/a~6.5, but the stoichio­metric composition with 75% Mo is not observed. This is also the case for the system Mo-Ir-Re in Fig. 43. The A15 phase fields for the systems "Mo-Re" (by extrapolation from the ternary Mo-Pt-Re) [38], Mo-Os [85J, Mo-Ir [15,86J, and Mo-Pt [20,26] are shown in Fig. 45. M030s has a narrow phase field concentrated around the stoichiometric composition (Tc = 12.7 K [38J). The A15 phase in the Mo-Ir system ranges from 22 to 24 at.%Ir [38] and Tc is maximum at 22 at.% Ir (Tc = 8.45 K [38]). The pseudobinary Mo-Pt -Re phase diagram (Fig .43) shows that at the Re side the limit of the A15 phase field approaches 6.5 electrons per atom. The phase limits for Mo-Pt-Re and Mo-Ir-Re differ from the phase limit encountered with Os. These limits are marked by a dotted line in Fig. 30b. In Section IVA, the deviation of the Mo30s phase limit from e/a = 6.75 was tentatively explained by a geometrical argument. A point in favor of this argument is furnished by the work of Johnston etal. [89J who studied the pseudobinaries M03(Os l-xRu) and M03(Irl ~xRuX> and found that the A 15 phase is stable in both cases up to x = 0.8 • Their extrapolated parameters for metastable "Mo3Ru" are T c ~ 11 K and a ~ 4.95 - 4.96 A. The situation is similar to that for Cr -X compounds, where CrO. nRuO.28 has a smaller lattice parameter than Cro. nOsO.28, a = 4.677 [26] and a = 4.682 [26J, respectively. This lattice parameter for "Mo3Ru", which is even smaller than that of M030s, could explain why M03Ru is not stable, at least at the stoichiometric composition.

6. The Ti -system

The A15 phase fields Ti -Ir [90J, Ti -Pt [91J, and Ti -Au [92] are shown in Fig. 46, together with the corresponding variation of Tc of Junod etal. [93J. Ti3Ir forms by a peritectic reaction, whereas Ti3Pt and Ti3Au form congruently. The diagram of Ti3Hg is not known; this compound is normal down to 0.2 K [93,94 J . For the compound Ti3Ir, T c increases from 4.0 to 5.1 for compositions from 25 to 27 at.%Ir. The Pseudobinary system Ti3Irl-xPtx shows a maximum Tc at 5.4 K for x = 0.2 [93J. The system Ti -(Ir, Pt, Au, Hg) occurs at unusual e/a values with respect to Cr, Mo, Nb or V based systems. A comparison between the T c and y values of all these systems is given in Figs. 60 and 61.

7. Characterization of "atypical" A15 compounds

There are few Ta3X and Zr3X compounds and they have not been discussed in this section. The choice of the X atoms was restricted to the 5d elements Re, Os, Ir and Pt. The compounds containing 3d and 4d X atoms were not included in the discussion because of their small number and because of their similarity to the corresponding systems with 5d X atoms. As an example, V3Ir and V3Rh have the same type of form­ation (congruent), have the same width of the A15 phase field (14 at.%) and the same variation for Tc (a linear increase with T c max at e/a = 6.5).

In Cr and Mo based compounds the 4d elements Tc and Ru furnish additional information about the behavior of these compounds at the end of series; the A15 phase "MoO. 50ReO. 50" is unstable at equilibrium.

564

i-I I

(3 = 025

(3 =Q25 I normal

>0012K

0 0 10 2030 0 10 20 30 0 10 20 30 40 at.%

R. FLUKIGER

Fig. 43 A15 phase fields and superconductivity in Cr-Os, Cr-Ir and Cr -Pt (R~f5. 38, 45, 87).

110

ttotherma' sechon a' .Oc

15 r-.----.----.-------,,-----, Tc

('KJ

80 70

Mo-Pt-Ra

60 50 40 al-I.Mo

Fig.44 The A15 phase field at 16000C in Mo-Pt-Re. Variation of Tc as a function of the Mo content in the pseudobinaries Mo-Pt-Re and Mo-Ir-Re. The curvature is due to the fact that the Ir/Re and the Pt/Re ratios are not constant. An extrapolation to at.% Mo would give a Tc between 14 and 15 K (after Ref. 38).

PHASE DIAGRAMS

3000 I Mo-Rel CoO

A2 2000

1000

10 l(K)

•

meta stable

•

..

I Mo-Pt I

quenched from 1600·C

I •

o~~wom~~om~~om~~~ at%

565

Fig. 45 A15 phase fields and superconductivity in Mo-Re, Mo-Os, Mo-Ir and Mo-Pt. The metastable A15 phase in the Mo-Re system has been tentatively drawn by extrapolation

Fig. 46

(Refs. 20, 66, 84, 85, 86).

2000 / ~I

TIDe) t.I!:!!:J I I

1000 5

TclK)

00

I I

( (l = 0.25

25 at.%Ir

"

p=0.,25 i

! 0 25

at.% Pt

p=or i

0 25 50 at.% Au

A~5 phase fields and superconductivity in Ti -Ir, Ti -Pt and Tl-.A:u (Refs. 90, 91, 92).

S66 R. FLUKIGER

Illustration of the behavior of "atypical" AlS compounds (electron compounds) is given by Figs. 60 and 61. These show the variation of T c and 'Yas a function of the number of valence electrons of the element X for the systems Ti -X, Cr-X, Mo-X, V-X and Nb-X. These figures show clearly the shift of the minimum for the different series of compounds • The minimum of 'Y is believed to be the point where the energy separation of the d sub-band is smallest. The "atypical" compounds can be described by a rigid band model. This is also concluded from the fact that Tc for the pseudobinaries Nb3Ir-V3Ir or M03Ir-NbaIr or Nb30s -VOs is linear [26J, in sharp contrast to the behavior encountered for "typical" AlS type compounds, i.e., Nb~ 3Au -V ~ 3Au [26, 70J •

VI. PHASE FIELDS AND SUPERCONDUCTIVITY IN BINARY AND PSEUDOBINARY ''TYPICAL'' AlS COMPOUNDS

A. The V,... 3Au and Nb,... 3Au systems

As shown in Section VC2, the dominant contribution to the electronic density of states at the Fermi level of "atypical" AlS compounds is due to the relatively broad X Sd (or X 4d) sub-bands. A particularity of this class of compounds is that an increase in the atomic number of the X element reduces the degree of hybridization between the X Sd (or X 4d) and either the V 3d sub-band or the Nb 4d sub-band. The energy separ­ation between the two sub-bands is maximum for X = Au [79, 81J • The electronic density of states is then due to the V 3d sub-band or the Nb 4d sub-band. In spite of the 6s electron of Au, this element is in general considered as a transition element with 11 valence electrons when included in the AlS structure. This choice is only justified by the fact that the e/a value for VaAu or NbaAu is now 6.S instead of 4.0. Because both compounds, V 3Au as well as Nb3Au, exhibit the maximum of 'Y with respect to the series V -(Re, Os, Ir, Pt, Au) and Nb -(Os, Ir, Pt, Au), it was thought that the value e/a = 6.S would be more reasonable than 4.0. However, from the electronic band structure (Fig. 41), it follows that Au in AlS structures behaves like a nontransition metal with 1 valence electron, because the Sd electrons do not contribute much to the electronic density of states. There are several additional reasons for considering VaAu and Nb3Au as "atypical". Reasons for considering Au as a non­transition metal in the AlS type compounds V 3Au and NbaAu are:

(a) The formation of both compounds VaAu [14Jand Nb3Au [18J, as well as of Ta3Au [17J is congruent from the bcc solid solution, like the "typical" comp ounds V 3Ga [27, 29J and V 3(Gal-xAlx) [96J.

(b) Both phase fields of V 3Au and Nb3Au show the character­istics of "typical" AlS type compounds like Nb3Ge, Nb3Ga, Nb3Al, etc. The Au -rich phase limit varies as a function of temperature [14, ISJ and the highest Au content is reached at high temperature, 24 at.%Au for V3Au [14Jand 23.S at.%Au for NbaAu [ISJ. The stoichiometric composition does not occur in the equilibrium phase fields of these systems .

PHASE DIAGRAMS

(c) The extrapolated values of'Y for stoichiometric V3Au and Nb3Au are comparable to those measured for the corres­ponding V and Nb based "typical" A15 compounds (Fig. 61).

(d) The magnetic susceptibility [97, 98J, X(T), of V.3Au varies strongly with temperature, similar to V 3Ga [99 J or V 3S i [99J (Fig. 47). This means that the Fermi ene rgy is situated on a region where the N(E) curve changes very rapidly. This observation was originally the basis of the "linear chain model" of Labbe -Friedel-Weger [lOOJ used to describe the "typical" A15 compounds (V3Ga or V3Si). Nb,YC compounds exhibit a smaller variation of X with temperature than V 3X compounds. Nevertheless, the variation X(T) for Nb3Au is comparable to that of Nb3Sn.

(e) The critical magnetic field, Hc2(0), for Nbo. 764AuO .23.6 [101] is 240 kG, and 300 kG for Nbo.75Auo.17SPto 75 L101J comparable to the "typical" compounds Nb3AI L102], Nb"",3Ga [103Jand Nb3Sn (cubic) [104J (Fig. 62). Nb3Pt, with a similar T c value to Nb"", 3Au exhibits only 158 kG [101, 105J. A comparison of Hc2(0) for VsAu with the values for V 3Ga [101J and V 3Si [106J can be made if its low T c value (2.9 K) is taken into account. As for Nb3Au, the value of Hc2(0) for V 3Au, 56 kG [26J is nearly twice the value for V 3Pt, 30 kG [101J. Thus it follows that Au

567

behaves rather like a non -transition metal in A15 compounds.

B. The Systems V3B (B = Ga, Si, Ge, "AI", and Sn)

The A15 phase fields of these systems, together with the known variation of Tc as a function of temperature were shown in Fig. 48.

1. V3Ga

V 3Ga forms by a congruent reaction from the bcc solid solution [27,29J and its phase fields are stable from 20 to 32 at.% Ga. The Tc value shows a marked maximum at stOichiometry, and decreases almost linearly on both sides. Such behavior has so far been encountered only in two other A15 compounds, V 3Pt and Nb3Pt. The variation of T c has has been measured .Qy both inductive and calorimetric methods [112J. The rounded behavior of T c around stoichiometry reported in the litera­ture [29J seems to be caused by shielding effects.

2. V 3Si and the martensitic transformation

The formation of V 3Si is controversial; a peritectic [108, 109J as well as a congruent [110J type of formation have been reported. There is a strong argument in favor of a congruent formation (Fig. 48). Large single crystals of V sSi at different compositions can be formed quite easily by zone melting [111J. The variation of T c as a function of the Si content in the range 19 ~ f3 ~ 25 at.%Si is almost linear, as determined by both inductive and calorimetric methods [112J. At stoichiometry, Tc decreases by 0.2 K, due to a phase transformation at 21 K. A review

450

r'.

400

~

, '\

'\

0

} ~O~ v~

l '0

~

X<f.

300

250

o 10

0 T

(K)

200

300

Fig

. 47

M

agn

etic

su

scep

tib

ilit

y o

f V

3Ga

[99

],

V3A

u l5

7],

an

d V

3Pt

L97

] as

a f

unct

ion

of t

em

pera

ture

.

2000

T("C

)

1500

II i\J

i ~ I I

Ail 10

00 ~t

~~~/ll

5L

•

o 50

o

t.%

AI

ot.

%G

o

ot.%

Si

ot.%

Ge

ot.

%S

n

Fig

. 48

A

15 p

has

e fi

eld

s an

d s

up

erco

nd

uct

ivit

y i

n

V-G

a, V

-Si,

V

-Ge,

an

d V

-AI

(Ref

s. 2

7,

29

, 10

8,

109,

11

0,

113,

1

21

).

1.11 ~ ::c

"T1 r C'

7\

Gl

m

::c

PHASE DIAGRAMS 569

of the multitude of theoretical and experimental work dealing with the problem of this transformation (generally called martensitic, of the Jahn­Teller type) will not be attempted. Why this transformation occurs only in V.JSi and Nb.JSn is unknown. At the present state of knowledge the following necessary criteria for the occurrence of the martensitic transi­tion in AlS compounds are:

1. Sufficiently high electronic density of states; 2. Stoichiometry; 3. Perfect atomic order.

The fulfillment of only two criteria is apparently not sufficient, as demon­strated for V3Ga. This compound has the highest I' value of any super­conductor (I' = 24 mJ/K2 • g-at [33]), and can be formed at stoichiometry, but does not transform. Its degree of atomic order is very high, but distinctly different from perfect order (Sa = 0.98 [27]).

3. V3Ge

As shown in Fig. 48, the phase V,3Ge forms congruently from the melt, as determined by Savitskii etal. L1l3]. This is indirectly confirmed by the fact that it is possible to form V 3Ge single crystals by zone melting. The homogeneity range of V 3Ge at equilibrium is very narrow. It is centered at 23. S to. S at. % Ge, as determined by optical microscopy and microprobe analysis [IS]. This confirms earlier results of MUller [116], who also found that alloys with the nominal composition Vo 7SGeO 25 contained a second phase, VSGe3' The shift of the Ge-rich liniit towarcls higher Ge content at high temperatures reported in Ref. 113 could not be confirmed, either by argon jet quenching or by splat cooling [IS] • Although the stoichiometric compos ition is not stable in the V 3Ge equilibrium phase field, it can be approached by forming the pseudobinary systems V3(Gel-xGax) [26,114] andV3(Gel-xAlx) [26, l1S,116]. The corresponding variation of Tc is shown in Fig. 49. By substituting Ge by Al or Ga, the Tc value of V3Ge (Tc = 6.2 K) increases at two distinctly different increasing rates. the higher initial rate reflects the shift of the low V limit of the pseudobinary AlS phase towards stoichiometry. The lower rate indicates that for x :<: 0.2 the stoichiometric composition is contained in the pseudobinary phase field. The AlS phase is stable up to x = 1 for Ga, whereas x == 0.4 is the Al solubility limit. The behavior of T c in pseudobinary AlS compounds will be discussed in Section VIC. For V3Ge, the extrapolated Tc value for stoichiometric V3Ge would be about 10 K (Fig. 49). This value [26] was later confirmed by Somekh etal. [118], who found 11 K for s-futtered V 3Ge. By comparing this valueto that corresponding to 23.S _ O.S at.%Ge (6.2 K), it follows that a change in composition of 1 at.%Ge corresponds to a change in Tc of "" 2.S K. This rate is considerably higher than"" 1.7 K/at.% observed in V3Ga or V 3Si (Fig. 48).

4. "V 3AI"

The AlS phase V 3AI is not stable at equilibrium. From the work of MUller [116], who studIed the system V-Ga-Al (Fig. SO), the formation

570

Fig. 49

R. FLOKIGER

Te (OK)

18 V3Si

16

14

12

V3Ge

8

V-Ge

0 0.5 -x

Variation of T c in the pseudobinaries V 3 (Ga l-xGex) and V 3 (Ge l-xAlx). A value T c R:$ 10 K is extrapolated for stoichiometric V3Ge (Fltlkiger, Refs. 26, 35; Kodess et al. Ref. 114).

PHASE DIAGRAMS

Te (OK)

18

12

8

2 V3Sb V3As "'--___ --' ____ -L

o 0.5 -x

Fig. 50 Variation of Tc in the pseudobinaries V ....... a(Br-xAlx} with B=Ga, Ge, Sb, As and Sn. The system V3Sil_xAlx has

571

been omitted because the Al5 phase field deviates from stoichiometry. The off-stoichiometry system Va. so (Snl_xAIX> can be used to extrapolate the Tc of Va. soAlo.20 to T c ~ S K (after Ref. 26).

572 R. FLUKIGER

temperature of V 3AI would be of the order of 600 -700oC • This appears to be just below the temperature where the diffusion is high enough to permit the formation of an A15 compound. The lowest known formation temperature for this structure is 9000C for V3Ni [119J. The V 3AI phase is probably on the verge of stability, at least for nonstoichiometric com­positions, since it can be easily formed by non -equilibrium methods and can be approached to a certain extent by substitution.

High values of T c (14 K) were reported by Somekh et al. [118J for V 3AI obtained by high -rate sputtering. The question arises whether this value corresponds to the stoichiometric composition. A qualitative answer can be obtained by substituting Al for the B element in stable V3B compounds, where B = Ge, Ga, As, Sb, Sn, Si, •.•• The variation of Tc for these pseudobinaries, taken from Refs. 26, 35, 114, 115, and 116, is shown in Fig. 50. Data are also included for nonstoichiometric VO.78 (Si1-xAI;J0 22 [26J, VQ..765(Ga1-xAlx.>0 235 [26J, and Vo .80 (Sn1-xA1X>0' 20 [26,117 J. This perm1ts'extrapolation of Tc for stoichiometric v3Ar rrc ~ 17 t 1 K), for 19 at.%AI (Tc ~ 7 -t 1 K), and for 22 at.%AI (Tc ~ 12 K). These hypothetical values are given in Fig. 48. In addition to T c' the lattice parameter and 'Y for V 3AI can be obtained by extrapolation. This extrapolation was carried out based on a series of specific heat measurements [26, 120J (Fig. 51) and give 'Y""'1O mJ/KZ • g-at and ,.... 17 mJ/K2 • g-at at ,.... 19 and at ,.... 23 at.%Al, respectively. At stoichiometry, 'Y ,.... 20 mJ/K2 • g-at would occur, which is of the same magnitude as for V 3Ga •

5. V#n

According to Marchukova et ale [121 J, V 3Sn forms peritectically. Its .fhase field is very narrow and concentrated at the composition 19 _ 1 at.%Sn. Our own results [26, 117J c.onfirm the off-stoichio­metric position of this A15 phase. For this compound Tc = 3.8 K; higher values [127J could not be confirmed, even after splat cooling or argon jet quenching [15J.

C. V Based Pseudobinary Compounds

In Section VIB, we extrapolated the superconducting properties of stoichiometric V 3Ge and V 3AI, assuming that a gradual substitution of the B element by an element B' in the formula A3(B1-:xB'x) causes a linear variation as well in Tc as in 'Y. This assumption seems to be justified for all known V -based pseudobinaries for the stoichiometric composition in the A15 phase field. Recent results on Nb3AI [1OJ, Nb3Ga [21J, and possibly Nb3Au (Fig. 42) show that this rule cannot be applied for all A15 type systems (Section VIE).

1. V 3(Au1-:xl't~

The A15 phase in the pseudobinary system V 3(Au1_Yt ) [26,107J (Fig. 52) is characterized by a deviation from stoichiometryXfor x ~ 0.2 • The variation of Tc for two series of alloys, Vo 75 (Au 1-xPtx)0 25 (nominal composition) and Vo 77 (Au1-xPtx)0 23'lS shown on the same figure. For the series with 17 at. % V (always contained in the A15 phase

25

't

mj,

010

latg

KjL

Si.2

5 ~G

.9 __

__

__

__

~-=-..:

-.::-~

'/.,77

A~2

3 sG

a.23

5 _

--/

15 1

-A

ISi

_--

--///

~-----

AIG

e //'

..J

Al

S!22

/

----

-,'!

;SO

-2

0 10

IG

e A

ISn ~".::._---

. -,

Sn --:'~As

5 1-·20~b

...

As Sb o

0.5

_xl

Fig

. 51

V

aria

tio

n o

f sp

ecif

ic h

eat

coef

fici

ent,

'Y

, in

th

e p

seu

do

bin

arie

s.

V""

'3(B

1_ x

Al x

) w

ith

B =

Si,

Ga,

G

e, S

n, A

s,

Sb.

U

sing

th

e 'Y

val

ues

fo

r

VO

. 76

5Ga o

. 235

[9]

and

VO

. 78S

i O. 2

2 [9~, a

n

app

rox

imat

e v

alu

e of

'Y ~ (

16

+2

)mJ/

K

g-a

t ca

n b

e ex

trap

ola

ted

fo

r "V

"", 7

7Al..

,23

" (F

ltlk

iger

et

al.

, R

efs.

26

, 12

0).

...... ~ ......

'IT

1.00

K

2.00

K

v

30Y

,

v v

' I

30

I

21 9

:0

0

Tc(K

) : 11

V 77

(Au

xP

t 1- x

)

O~ I I,

I :

4!Y

77P

t d

0.5

x V 7

78u 2

3

0'

, V 3

Pt

0.5

x "V

3A

u"

Fig

. 52

A

15 p

has

e fi

eld

and

var

iati

on

of

Tc

for

the

pse

ud

ob

inar

y s

yst

em

V3(

Au1

-xP

tx)

[26

,10

7].

-c

:c » (J

) m

o » C

) :0

» s:

(J)

01

;j

574 R. FLUKIGER

field), T c remains practically constant at 2 K. The superconducting properties between the binaries VO. 77Pto.....2 3 and Vo 77AuO 2 ~ thus can be interpolated linearly. The variation of Tc m the series with 75% V is more complex. T c first decreases linearly from VaPt to x = 0.2, which is the A15 phase boundary (Fig. 52), then undergoes a broad minimum, corresponding to the curved shape of the low V limit of the A15 phase field.

2. VO.75(Gal-~ix)

The pseudobinary A15 phase field in this system [35J, together with the variation of T c for a series of alloys with nominal composition VO.75(Gal-x~)iX>0.25 are shown in Fig. 53. This system is characterized by a solubility gap and decomposes in two distinctly different A15 phases, {31 and {3z (Fig. 53). It is remarkable that the Ga -rich {31 phase shows a deviation from stOichiometry with the addition of Ga. The variation of T c in V 3(Gal-xSiX> has been investigated by several authors [123, 124J, who found a broad minimum at B K. Figure 53 shows that this minimum of T c corresponds to the T~ for VO.BO(GaO. 70Sio.30)0.20 in the three-phase field 0'+ {31 + {3z [35J. It is obvious that a linear interpolation of Tc between the values of the binaries V 3Ga and V 3Si can only be made for the compositions x ~ O.OB. In this narrow range, the substitution of Ga by Si causes a slight increase [15J in Tc (Fig. 53).

D. Nb3B (B = Ge, Ga, AI, Sn, and Sb)

The A15 compounds Nb3Ge, Nb3Ga, and Nb;t.l exhibit the highest values ofTc known: 23 K [125, 126,127J, 20.7 K L:ll,12BJ, and 19.1 K [1OJ, respectively. The interest in the A15 phase fields of these three systems has been considerable. The key question is whether the stoichio­metric composition is stable or not at equilibrium. The experimental determination of these phase diagrams was particularly difficult, because of the formation temperatures of the A15 phase above IB50 0C (Fig. 54). The A15 phase field in these three systems has common features, which can be characterized as follows:

1. Peritectic formation; 2. Neighboring phases: bec and tetragonal; 3. Low Nb phase limit which is strongly temperature dependent; 4. Stoichiometric oomposition stable only at high temperature

if at all, at the temperature of the next lower peritectic or eutectic line.

Another type of A15 phase field is observed in Nb-Sn and Nb-Sb, as shown in Fig. 57. Both systems form peritectically, but the boundary AI5/AI5+L reaches unusually low temperatures, 1050 and 1140oC, respectively. The highest solubility of Sn and Sb, respectively, occurs at these temperatures.

1. Nb-Ge

The most striking feature of the Nb Ge phase field, recently determined by Jorda etal. [129J, is that tfte stoichiometric composition is not included at equilibrium. The maximum solubility of Ge is 23 at.%.

PHASE DIAGRAMS

v

V-Go-Si

1000·C

10 ~o ~

0\0

0-IJ).

e;-. 85 .. .. 15

IJ).

\ 70~~ __ ~ ____ ~ ______ ~ ____ ~ ____ ~~~~30

6 4

2

25 20 15 10 5

Ot.% Go

Vf30 2.5 5 7.5 10 12.5 15 17.5 20 22.5 V:3Si ot.% Si

575

A15 phase field for V3(Gal-xSj,X>' showing the existence of a miscibility gap. This phase field allows one to lll1derstand the variation of T c in this system (lowest figure) (after Ref. 35).

576

1500

1000

25 25

15 ~02S 10

5

R. FLUKIGER

I Nb-Ge I

20 2f ,'i

, i , !

I , , !

,( j ,

I I

/ ~ ';'0.25 I

I I

I I

I I

I I

I ,I

I I

r

o~~----~----~--~----~--~----~----~~ 20 25 20 25 20 25

ot.% Go ot.% AI ot.% Ge

Fig. 54 A15 phase fields and superconductivity in Nb-Al, Nb-Ga and Nb-Ge. Note the "saturation" of Tc , very marked for NbJAl [10J. but less pronounced than in Nb3Ga (after references 10, 21, 129, 133, 134).

PHASE DIAGRAMS 577

2C

15

10

!Ordering! SegregatIon

Non- : ieqJilibrrumi Equilibrium

500 1000 1500

mo'c (Eutectic temperature)

Fig. 55 The variation of T c for an alloy of the total composition NbO l4GaO 26 as a function of the annealing temperature. Part" represents the region where only long -range order effects take place, while part II reflects the curved shape of the Ga -rich A15 phase boundary (see Fig. 54). To and T s represent the minimum ordering and segregation temperature (Fllikiger etal., Ref. 21).

Fig. 56

at.% Al 22 23 24 25 21

20,---,--------,---,--,-,-,

T~ I

Nb75 AI 25

15

11 L-10-'--0-0 -'--~---'--'--'-::15'::-:00:-'-------'-------'-----'---'2:-:"0-::-:'00

TAI'C]

T as a function of the quenching temperature for a sample wfth total composition NbO• 75AIO 25. This curve is reversible and corresponds to part II in Fig. 55. It reflects the curved shape of the AI-rich A15 phase boundary (Fllikiger et al., Ref. 10).

578 R. FLUKIGER

At 10000C the homogeneity range of the A15 phase is very narrow and is centered at 18 at.%Ge with a total width of 1 at.% [129,130, 131J. There is a difference between the kinetics of segregation in Nb3Ge and that of Nb3Ga or Nb3AI. It is particularly difficult to retain compositions above 19 at.%Ge, even by using very fast quenching rates. The highest Tc onset value, 17 K, was obtained by splat -cooling an alloy having the nominal composition of 23 at.% [129, 132J. Thus, the variation of Tc as a function of the Ge content cannot be determined as accurately as for Nb3Ga (Section VIDa.) or Nb3AI (Section VI). Only the T c values for 17.5 at.%Ge (4.2 K), for 18.5 at.%Ge (6.0 K), for ",23 at.%Ge ('" 17 K), and for ...... 25 at.%Ge (,....23 K) can be given. These values are given in Fig. 54 and suggest a nearly linear variation of T c as a function of the Ge content. However, there is no proof that stoichiometry has been attained for Nb3Ge.

2. Nb-Ga

The A15 phase field determined by Jorda etal [133J, together with the variation of T c as a function of the Ga content is represented in Fig. 54. The maximum value of T c' 20.7 K [21, 128 J can be obtained by com­bined heat treatments which improve both stoichiometry and atomic ordering. The sequence of heat treatments leading from an arc cast NbO. 74GaO .26 alloy with an initial Tc value of 14 K to a final value of 20.7 K is indicated in Fig. 55. This figure allows the effects of compo­sition and atomic ordering on Tc to be separated. Once the stoichio­metric composition has been reached by argon jet quenching from 17400C, a further increase of Tc from 18 K to 20.7 K can be obtained after prolonged heat treatments at 6500C.

3. Nb-AI

The most recent Nb-AI phase diagram was determined by Jorda etal. [134J and confirms the peritectic formation of the A15 phase originally reported by Lundin etal. [135J. As shown in Fig. 56, the AI-rich limit of the Nb3AI phase is strongly temperature dependent, as for Nb3Ge and Nb3Ga. The stoichiometric composition is metastable. Recently, stoichiometric Nb3Al. with a lattice parameter a = 5.180 A was prepared by argon jet quenching [1O,134J from 19400C (the second peri­tectic line in the Nb-AI phase diagram [134J).

Variation of Tc vs the Al content. MUller [130J found that the value 01 Tc as a function of the Al content shows a slower increase for compositions close to stoichiometry. This "saturation" of Tc in Nb3AI (Fig. 54) was recently confirmed by FWkiger etal. [1OJ, who performed a series of experiments including specific heatmeasurements. These data unambiguously show that the saturation is a real effect and is not due to shielding effects (Section IIIA2). The "saturation" is also shown by the variation of T c of NbO. 75AIO 20 (nominal composition) as a function of the quenching temperature. ThiS reflects the temperature dependent shape of the AI-rich phase limit (Fig. 56). This curve is reversible, which is additional proof for the absence of shielding effects. At the top of Fig. 55 the effective compositions of the A15 phase are shown. This

PHASE DIAGRAMS 579

reflects a slower increase of T c for compositions close to stoichiometry. The maximum T c value for stoichiometric Nb3AI after 7 weeks at 6500C is 19.1 K [1OJ, only 0.3 K higher than the value Tc = 18.8 K [136J for 24 at.% AI. This "saturation" of Tc is unusual for A15 type compounds, for which Tc varies almost linearly with composition. Nb3Ga is another compound where a curved Tc vs composition relationship was measured [21J (Fig. 54). The reasons for this behavior are still unclear. Peculiarities in the shape of the electronic density of states curve at the vicinity of the Fermi energy could be advanced. In our recent work [1OJ. we have shown that the order parameter of Nb3AI is quite high, Sa = 0.97 to .Ol. The saturation of T c thus can not be explained by assuming a decrease of the order parameter alone for compositions close to stOichiometry •

4. Nb3Sn

The A15 phase field in Fig. 57 is taken from the phase diagram of Charlesworth etal. [137J. The variation of Tc as a function of the Sn content has been recently studied by Devantay etal. [3J on a series of Nb-Sn alloys melted in a Cambridge levitation crucible [49J (Fig. 3) and subsequently annealed at 1800oC. Melting as well as annealing were performed under high argon pressures (> 50 atmospheres). This study shows a linear variation of T c with the Sn content. as shown in Fig. 57. The stoichiometric composition Nb3Sn is stable up to '" 1600oC. At 43 K a phase transformation of the first order [138J occurs, which does not have a serious influence on the value of Tc ' as recently shown by Junod etal. [56J. The high temperature (cubic) and low temperature (tetragonal) modifications exhibit Tc values close to 18 K.

5. NbJSb

The formation of the Nb3Sb phase [139J is shown in Fig. 57. but the homogeneity range is not known with precision. In particular, it is not known if the stoichiometric composition is in the equilibrium phase field. It follows from the work of Junod etal. [140J that the stoichiometric com­position in Nb3Sb would correspond to a minimum of T c; the maximum value (T c = 2 K) is observed for'" 17 at. % Sb.

E. Nb-Based Pseudobinary Compounds

Like that of B-vased alloys (Section VIC), the behavior of Tc in a pseudobinary system Nb3(B1-xB~) with respect to the T values of the binaries Nb3B and Nb3B' is governed by the particular ~pe of the A15 phase field. Considerable increases in Tc have been reported for the systems Nb3(Au1-xPtx) [63J and Nb3 (Al1 -xGex) [76J.

1. Nb3(Aul-xl'~)

From the A15 phase field of this system (Fig. 58), it follows that the stoichiometric composition is stable across the major part of the A15 phase field (x ~ 0.35) [26, 107J. The stabilization of this composition at the Au-rich side leads to a sharp rise from Tc = 11 K for the binary NbO.764AuO.236 to Tc = 13 K for NbO.75AuO.175Pto.075 [26, 107J. As

Fig

. 57

25

oo

rr--

.--.

"ro

--.-

-..-

"

T(O

C)

1000

15

Tc(K

) 10 5

...... ,

I Nb-Snl~\' I N

b-S

bl

" \

'" "

\"

A15

19V

-125

.5

)025

\ "

\ "

\ "

\ , , / (I

/

j/I

IYJ

I/~

/ A

15

t:12

5 I

Vt

VI

I vi

I

r , . \.

01

10

2'0 '

30

' 1'0

2

0' 3

'0 I

at.

% S

n o

t.%

Sb

A15

ph

ase

fiel

ds

and

su

per

con

du

ctiv

ity

in

th

e sy

stem

s N

b-S

n [

137J

an

d N

b-S

b L

139J

.

Nb

10 ,

( )."

Q. ....

11.4

o 0.;>

" .~

n .. -

1i.6

1i

.6

\30

30

I

\I

V

, I I I ! y-

y':

Nb7

5,A

u1_x

Ptxl

.25

, Te

13

~ 0

o;

;;:,.-

------

-----:

r

'OK

112

11

10 I

I

Nb

3Pt

x~

Nb 3

Au

Fig

. 58

A

15

ph

ase

fiel

d a

nd

var

iati

on

of

Tc

in t

he

pse

ud

ob

inar

y s

yst

em N

b3 (

Au

1-xP

tX>

(aft

er R

efs.

26

, 63

, 10

7).

til

co

o :IJ

"T1 r c'

7\ G5

m

:IJ

PHASE DIAGRAMS 581

shown in Fig. 58, the variation of Tc in the pseudobinary Nb3(Aul_ytx) yields a Tc value between 13 and 14 K for stoichiometric Nb3Au Ll41J.

2. Nb3(Al1 -xBx) (B = Ge, Si, Ga, Be, B, As, ••• )

For the compound Nb3AI, substitution of Al by other elements like Ge, Si, Ga, Be, B, As, Sb, ••• , always leads to an increase in Tc- The most known ternary addition is Ge [76J. The highest reported T value for the allo~ NbO. 75AlD .20GeO .05 is close to 21 K, but Be and B a~e al,so known to ra1se Tc of Nb3AI above 20 K [142 J • In two cases (Ge and S1) it has been shown by MUller [130, 143J that the increase of Tc is at least partly due to the approach to stoichiometry. However, the recent results on NbJAI (19.1 K for stoichiometric Nb3Al [1OJ) show that this argument alone is not sufficient to explain an increase up to 21 K by the addition of 5 at.%Ge. Very probably the "saturation" effect on Tc is less pronounced for Nb3(All-xBx) pseudobinaries than for the binary Nb3Al system. This hypothesis (to be proved) could explain why such a large number of substituting elements increase T c of Nb3Al.

F. Mo -Based Binaries and Ternaries

1. M03Ge and MOJSi

Although these compounds have a low Tc value, they are still "typical" A15 type compounds in our classification. The A15 phase fields of both systems are shown in Fig. 59, together with the corresponding variation of T c . In both cases T c is minimum for the stoichiometric composition [38J and increases slightly up to 23 at.% of Si and Ge, respectively. This behavior is similar to that observed in Nb3Sb, but is the inverse to that observed in Nb and V based "typical" A15 com­pounds with high T c values. This suggests that probably for Nb3Sb, M03Ge and M03Si, the Fermi energy is close to a valley of the density of states curve.

2. M03(Ge l-xSix)

Interesting behavior is observed for the pseudobinary M03(Ge l_-xSix), which shows a deviation from stoichiometry [38J. The value of Tc lor the alloy MoO 76SiO 12GeO 12 is 1.71 K, which is higher than that of M03Ge and Mo3Si, f .43 and 1.24 K, respectively ~6, 38J.

G. General Correlations for A15 Compounds

In order to represent the following correlations for A15 type com­pounds of the formula A,qB (more general: A 1-J3B)' Tc and 'Y have been plotted as a function of the atomic number of tHe B element. Each curve represents the data for the same A element. This representation is more transparent than an e/a representation. It allows one to follow the influence of the B elements directly. For "atypical" A15 compounds, the effects of the decoupling of the two d -bands when going from Re to higher atomic numbers can be seen. For "typical" A15 compounds, there is some evidence that p-electrons will contribute to the electronic density of states at the Fermi level, and the situation is expected to be more complex.

2500

T("

c)

" , \ 20

001-

\ \ I I I

1000

1-/

A15

n II

A15

I

'CI~[

'I

'{ (.I

=o.k

s fl

=o.is

00

10

25·

at.

% G

e ot

.%S

i

Ref

. 59

A

15 p

has

e fi

eld

s an

d s

uper

cond

ucti

vity

in

th

e sy

stem

s M

o -G

e an

d M

o -8

i (R

efs.

38,

60.

61

).

25~

oN

b

DV

.Cr

20

, •

Mo

Tc(

Kl

6 T

i ,

Zr

5 r'

Sb

VIIB

Fig

. 60

T

he

sup

erco

nd

uct

ing

tra

nsi

tio

n t

emp

er­

atu

re,

Tc.

fo

r d

iffe

ren

t se

ries

of A

15

com

poun

ds h

avin

g th

e fo

rmu

la A

1-f3

Xf3

as

a f

unct

ion

of t

he a

tom

ic n

um

ber

of

the

X a

tom

. T

he

exp

ecte

d T

c v

alu

es f

or

Nb"

, sA

-u a

nd

V""

JAu

wou

ld 1

00 h

igh

er if

sto

ich

oim

etry

co

uld

be

rea

ched

.

til

go

..., ?J " r- C' " Gl m

::0

PHASE DIAGRAMS 583

1. The superconducting transition temperature

The Tc values for different series of A15 type compounds have been plotted in Fig. 60. For V 3Au and Nb3Au, the extrapolated T c values, T c > 5 and > 13 K, respectively, have been used. This representation reflects that Au behaves like a nontransition metal, as shown in Section VIA. The maximum of Tc for "typical" V and Nb based compounds falls close to the minimum of Tc for the Mo-X and Ti -x series. For "typical" A15 compounds, Tcmax seems to coincide for all represented A15 series. This representation suggests that high Tc would be expected in the unstable V 3 (lIB) and Nb3(IIB) compounds •

2 • Electronic specific heat

Figure 61 shows the striking difference between the 'Y values of V­based and thos of Nb-based compounds. Again, the 'Y values for stoichio­metric, ordered Nb3Au and V 3Au should be higher than the measured values. This is indicated by arrows. The 'Y values for V 3Au and Nb3Au compounds are comparable to those of other "typical" compounds • Figure 61 shows that the variation of 'Y in Nb and V based compounds is opposite to that of Cr, Mo and Ti compounds. It is remarkable that there is no series where the position of Tcmax coincides with that of 'Ym~x. The shift is particularly evident for the Cr and Mo based "atypical compounds •

From Fig. 61 it is seen that V 3Ga, the A15 compound with the highest density of states, is stable. This indicates that the stability of a compound is not directly correlated to its electronic density of states at low temperatures. Other examples are V 3Si and Nb~n, which exhibit structural instabilities at low temperatures. At their formation tem­perature, these compounds have the highest stability index (as defined by Raynor [144J) of all known V and Nb based compounds •

3. Type of formation of A15 compounds

There are no general rules allowing a direct comparison between low temperature and high temperature properties. Each case has to be considered separately. Nevertheless, it is interesting to examine the type of formation of the different A15 compounds and to look for general rules. The known data are collected in Fig. 63 for three regions of interest. Figure 63 shows that the type of formation is determined by the B element.

Region A. All compounds in this region form pe rite ctoidally • They all contain the 5d elements Os and Re, but also the 4d elements Tc, Ru, Rh and Pd, and the 3d elements Co and Ni. This is just the region of the "atypical" A15 compounds with severe band overlapping (Section VC7). Because the electronic density of states of these compounds are low (Fig. 61), and the variation of X(T) is small [97J, it is tempting to assume that the band configurations are similar at the formation temper­ature of these A15 compounds. The existence of a correlation between overlapping d -bands and peritectoidal formation of the A15 phase is supported by the study of the region A in Fig. 63 marked by the dashed lines.

25.

o N

b o

V

, •

Cr

I I

• M

o I I

201-

• Ti

I I I I I I I

15L

I

2'

NO

:.::

.....

. ]'

10

)0

,

\"

H ~

~-~~e

-'-

-G

o .5

,

',-------~

01' Re

05

Ir

P

t A

u H

g AI

. S

i

IVIlB

Go

Ge

As

Sb VA

Fig

. 61

T

he

elec

tro

nic

sp

ecif

ic h

eat

coef

fici

ent,

')I

, F

ig.

62

for

dif

fere

nt

seri

es

of A

15 c

ompO

lmds

hav

-in

g th

e fo

rmu

la .A

1-{3

X B

as

a fu

ncti

on o

f th

e at

om

ic n

um

ber

of

tHe

X a

tom

. T

he '

)I v

alu

es

for

sto

ich

iom

etri

c V

3Au

and

Nb3

Au

are

ex

pec

ted

to

be

hig

her

. T

he

')I v

alu

es o

f N

b-G

a, N

b-G

e an

d N

b-A

I ha

ve b

een

dete

r-m

ined

on

allo

ys

show

ing

a la

rge

dis

trib

uti

on

o

f co

mp

osi

tio

ns

and

are

ex

pec

ted

to b

e h

igh

er f

or

hom

ogen

eous

sto

ich

iom

etri

c co

mp

ou

nd

s.

Not

e th

e d

iffe

ren

ce b

etw

een

cub

ic (

c) a

nd

tet

rag

on

al (

t) N

b 3S

n [5

6J.

400

Hc2

(kG

l

300

200

oNb

oV

.Mo

I

" I

/ '

/ b /"~AI-

&

I AI

G

e

Au-

Pt i,

G

o ,

0

! S

nCU

b.

bA~,

//.G

a~ ~ntetr.

/ 0

Si

" G

e

A

,/ I

As-A

I

/ bA

u r

J!'P

t 01~1~~L-~~~~~~~

Re

05

Ir

PI

Au

Hg

AI

Si

Go

Ge Sn

Th

e u

pp

er c

riti

cal

fiel

d,

Hc2

(O),

fo

r d

if­

fere

nt

seri

es

of

Al5

-ty

pe

com

poun

ds h

av­

the

form

ula

A3X

as

a fu

ncti

on o

f th

e at

om

ic n

um

ber

of

the

X a

tom

. T

he

Hc2

(O)

val

ues

fo

r st

oic

hio

met

ric

V.3

Au,

N

bS

Au

an

d

Nhs

Al

are

ex

pec

ted

to

be

hig

her

. N

ote

the

dif

fere

nce

in

Hc2

(O)

betw

een.

cub

ic a

nd

an

d t

etra

go

nal

Nb

3Sn

[10

4 J

.

U'I ~

::0

"T1 r c'

A C5

m

::0

PHASE DIAGRAMS

Co Ni Te Au Rh Pd AI Si Re as Ir Pt Au Hg Go Ge As

Sn Sb

VItB I VIII JIB jue ]IlIAjIVA I VA

585

Fig. 63 The type of formation of the A15 phase for different series of compounds. Po: peritectoid, P: peritectic, Cs : congruent from the solid, CL: congruent from the melt, S: syntectic. The symbols in parenthesis need further confirmation. Three regions A, Band C can be clearly distinguished, showing that the minoritary X atom rather than the A atom determines the type of formation of the A15 phase. (A): X = transition metal, d band overlapping, (B): X = Au, Ga (if A = V), Si, (C): X = nontransition metal.

5.300r----r--,------,--.-----,---,----, a(AI

5200

5.150

Nb-Sn

~Nb-AU

~Nb-AI Nb,B (bUlklimifl __ ":_~~_ Nb-Go

~~Nb-G Nb-Pt Nb,B (metastable limitl_._._._. __ ."'" ""

Nb,T (bulk limitl- - - - -Nb'Si- -'... -;:- -.: '-- - - Nb-

5100L-_--'-__ ...L.-_----' __ --'-_' "-' .....1-__ Nb.L.-I '---:l

o 10 15 20 25 30 (.3 [at%X (X;B,TI]

Fig. 64 Lattice parameter of Nbl_~Xf3 compounds as a function of the X content. For X = B (nontransition element), the extrapola­tion to f3 = 0 meets the value ao = 5.246 A recently reported for ''Nb3Nb''. For X = T (transition element), a extrapolates to values a < ao• This representation illustrates the stronger repulsion between Nb atoms in the case of localized d electrons. The lattice pa.;rameter of "Nb3Si" is extrapolated to values around a = 5.09 A.

586 Ro FLUKIGER

In this region the peritectoidal formation of the A15 phase is only observed for compounds containing the 3d elements Co, Ni and the 4d elements Rh and Pd 0 The is oelectronic systems containing Ir and Pt form congruently or peritectoidally 0 This corresponds to the observation made in Figs 0 40 and 41 for V3S compounds 0 The V 3d subo-band and the (Ir,Pt) 5d sub-band show the most pronounced energy separation. A similar observation has been reported for Ti -x compounds [145J. A supplementary argument for a correlation between overlapping d-bands and peritectoidal formation of the A15 phase arises from the fact that this type of formation usually represents a concurrence between the A15 phase and the neighboring CT phase. With two exceptions (one is Nb2AI), peri­tectoidal formation occurs exclusively in compounds containing transition elements only, where d -band overlapping is expected.

Region B. There is an extended region where the A15 phase forma­tion is congruent, either from the liquid (Cd or from the solid (Cs )' The main differences between V and Nb-based A15 compounds are encountered in this region. V3Ga, "V3AI", V3Si and V"'3Ge form congruently, but the corresponding compounds Nb3Ga, Nb3AI, and Nb", 3Ge form peritect­oidally. Nb3AI is a particular case, since the extreme solubility limit of the bcc phase and the formation composition of the A15 phase differ by only 0.5 at. % AI. This type of peritectic formation is very close to a congruent formation from the solid bcc phase.

4. Variation of the lattice parameter in Nb-based A15 type compounds

Recently, Stewart etal. [146J were able to synthesize an A15 phase of the overall composition Nbo. 9SGeO .02 frq,m which they extrapolated the lattice parameter for "Nb3Nb" to a = 5.246 A . The question arises whether the extrapolation of the lattice parameter of different A15 com -pounds to f3 = 0 meets this value. In Fig. 64 we show the lattice parameters for different Nb-X compounds. It is clear that if X is a non­transition element like Sn, Ga, Ge, AI, the extrapolated lattice parameter is equal to that for Nb3Nb. This is no longer the case if X is a transition element, like Os or Ir, where the extrapolation to f3 = 0 yields lower values, indicating a contraction. Nb-Pt is a particular case; the slope in Fig. 64 is different for f3 < 0.25 and f3 > 0.25 as shown by Moehlecke etal. [83J.

Figure 64 shows an interesting difference between the compounds Nb3B (B = nontransition element) and Nb3T (T = transition element) • The smallest l~ttice parameter measured so far for bulk Nb3B compounds is a = 5.150 A. This value was observed for Nb-Ge [14SJ and Nb-Si [147J alloys (both obtained by splat cooling) and is denoted as "bulk limit" in Fig. 64. Smaller lattice parameters for Nb3B compounds have only been observed on alloys prepared by nonequilibrium methods, i.e., sputtering, co-evaporation or CVD. From the available data, the smallest value observed in Nb-Si is a = 5.123 A [160J (the Nb3B metastable limit in Fig. 64). It is remarkable that considerably smallEl,r lattice parameters can be reached q,n bulk Nb3T compounds: a = 5.140 A fq,r Nbo.nPtO.29 [S3J, a = 5.11S AforNho.32IrO.2SI26J, and a = 5.117 A for

PHASE DIAGRAMS 587

NbO . 700s0 .30 [26 J • The latter is the smallest known lattice parameter for a bulk Nb3X compound observed so far and is denoted as "Nb3T bulk limit" in Fig. 64. This difference between the lattice parameters of Nb3B and Nb3T compounds suggests a different bonding between Nb and either a nontransition or a transition element. The repulsion between Nb atoms on the chains decreases with enhanced hybridization of the d bands.

From Fig. 64 it is possible to extrapolate the lattice uarameter for the metastable compound Nb3Si. With the value a = S .lS0 A for IS. S at. % Si found by': Waterstrat etal. Cl47J, a lattice parameter slightly above a = S .100 A is found. Another set of lattice parameters for Nb -Si (obtained by co-evaporation by Feldman etal. [149J) yields an even lower value of a = S .09 A. This illustrates that the difficulties in obtaining stoichiometric Nb3Si are due to the relative sizes of Nb and Si atoms. This instability of Nb3Si has been repeatedly correlated to its supercon­ducting properties, and very high values of Tc have been predicted for this compound. However, the T c value for Nbo. slzSio .1SS is S K [147J. Assuming a similar variation of T c as a function of the Si content as in Nb-Ge, the expected Tc value for "Nb3Si" is not expected to be signifi­cantly above that of Nb3Ge. In analogy to Nb-X, the variation of the lattice parameter of the AlS phase with the composition for V-X, Mo-X, Cr-X, and Ti-X compounds has been plotted in Fig. 6S. For V-X, where most data are available, the tendency is the same as for Nb-X. The lattice parameters of the systems containing nont~ansition elements, V -Si, V -Au and V -Ga (iJ 1!0 O. Z S) extrapolate to a = 4. SO A for "V 3 V", while V -Ir and V-Os yield lower values. Less data are known for Ti -x compounds, but a strong contraction of Ti -Ir and Ti -Pt with respect to Ti -Sb is observed.

The situation is reversed for Cr-X and Mo-X. The system Cr-Si extrapolates to a = 4.60 A, the measured value for "Cr3Cr" as obtained by sputtering Cl12J, while Cr-Ir and Cr-Os yield higher values (showing an expansion). The same situation is encountered for Mo-X compounds, where the values for Mo-Ir lead to higher extrapolated lattice constants than the systems Mo-Si and Mo-Ge. It follows from Fig. 6S that the systems Nb-T, V-T and Ti -T show a contraction (-), while the systems Cr-T and Mo-T show an expansion (+). This behavior reflects the variation of the atomic volume for different systems containing transition metals only. The atomic volume of the AlS phase of Cr-T and of Mo-T alloys (Fig. 66) shows an expansion with respect to a linear variation between Mo and the metals Os, Ir and Pt. The inverse behavior is observed for the systems Nb-T, V-T and Ti -T, where a contraction of the atomic volume with respect to the linear variation is observed.

VII. PHASE FIELDS AND SUPERCONDUCTIVITY IN RHOMBOHEDRAL Mo CHALCOGENIDES (CHEVREL PHASES)

A considerable number of investigations on rhombohedral terna_ry molybdenum chalcogendies of the formula MxM06XS' space group R 3, have been published since the discovery of these compounds USO, lSI]. In this formula, M represents a large number of elements (pb, Sn, Cu,

588

~ "--Ti-Sb 5200

alA)

5.100

-----=--~ "'-0....0-0 Ti-Pt(-) 5.000 "M0:3Mo"(extr.l a...... Ti-IrH

~Ooo Mo-Ir(+l

- ~ Oaoo Mo-Ge

4.900 Oa" Mo-Si

~-AU

~ ~V-Ga V-OsH 4.800 . Q ...,---

'V3V" (extr. -- V-Ir(-)

4.700

-----~V-Si

Cr-Irtl,...e.,.oo-­~ Cr-Os(+)

4.600 "Cr. Cr"(measured)

""""-a...c.Cr- Si

o 10 20 30 (3 [at.% X (X=B,Tl]

40 50

R. FLUKIGER

Fig. 65 Lattice parameter of A15 type Ti1_fjXfj' M01_fjXfj' V I-fjXfj and Crl-fjXfj compounds.

A2

15.5~-~

~ V/atomr~~

(A3) 15

.0

14.5

14.0

Pt

1 r

Os

Mo

10

20

30

40

50

60

70

80

90

10

0 "10

at

Os,

1r,P

t

Fig

. 66

A

tom

ic v

olum

e fo

r d

iffe

ren

t in

term

etal

lic

ph

ases

in

the

syst

ems

Mo

-T (

T =

as,

Ir,

Pt)

. F

or

the

A2,

A

15 a

nd

C1

ph

ases

, a

po

siti

ve

devi

atio

n w

ith

res

pec

t to

a l

inea

r v

aria

tio

n

betw

een

Mo

and

T

is o

bse

rved

(Fli

ikig

er e

t al.

Ref

. 2

0).

"C

:J: ~

m

C » G)

::D » s: en

til ~

590 R. FLUKIGER

Ag, Zn, R.E., ••• ), x is the content of the M element, and X represents S, Se, Te, or combinations of these elements with I and Br U52J. There are binary Chevrel phases, such as Mo()SeS or M06TeS, but the most interesting physical properties occur for the corresponding ternary sulfides, the binary "M06SS" being metastable. Very few studies have been undertaken in order to understand the metallurgY of these compounds; most physical properties have reertmeasutedon alloys produced by sintering.

Special high pressure furnaces are needed for melting Chevrel compounds without excessive losses (Fig. 1). A number of large single crystals have been grown by aPRlying the Bridgman -Stockbarger technique with fixed crucible and furnace Ii, 153J. In this section we will briefly examine the phase diagram work known for Chevrel compounds, and discuss the variation of T c for these phase diagrams. The crystallo­chemistry of these phases is discussed by Chevrel (Chapter 10) . The occurrence of low temperature phases is characteristic for sulfide and selenide systems. It is thus not surprising that a great number of Chevrel phases how low temperature phase transformations; the most complex case shows four low temperature modifications. This system was studied with particular attentionhy the author and cO"workers and is a prototype for the application of the phase rules to phase diagrams below room temperature.

A. Binary Mo-S System

The phase diagram of the binary Mo-S system is shown in Fig. 67 and was established on the basis of the high temperature data of Moh U 54 J and our res ults . All solidus temperatures are approximate. The main features of this diagram are: (a) no solubility of S in Mo; (b) two eutectics between the phase M02S3 and Mo; (c) the Chevrel phase "M06SS" is not stable in the binary Mo-S system at equilibrium; (d) the M02S3 phase shows a low temperature phase transformation at 195 K U55J; and (e) the phases M02S3 and MoS2 exhibit very high melting points, 1950 and 23750C, respectively. In ternary systems the M02S3 phase is extremely stable. The problem of preparing single -phased samples of the Chevrel phase is to avoid the M02S3 phase. There have been several attempts to form metastable binary compound M06SS' The most successful one, the "leaching technique", was first used by Chevrel eta!. U56J. It consists in preparing Ni2Mo()SS or CU2Mo~S' followed by etching in HCl. The resulting compound, "M06SS'" is superconduct­ing at 1. S K regardless of whether the starting material was Cu or Ni based. It was recently shown by FlUkiger etal. [48J that the density of "M06SS" is approximately 2% lower than expected from a linear extrapo­lation of the density values in CllxM06SS' Since chemical analysis and neutron activation experiments revealed less than 0.1 wt. % Cu, Ni or Cl, stabilization of "Mo()SS" by impurities is excluded. It is thus thought that the bonding in "M06SS" and M06SS may be different, leading to an instability of the former.

2500

TID

e)

2000

1500

1000

, , \ I M

o-S

I \ \ \ \ \ \

,,,,"

,

\,.

... 19

50

"

,6\0

-23

75

"" ..

, , , I I/'

'MoS

:1 \

'.'8

50

\ \

I \

I ,I

"~t '''t

j M

o 10

20

30

40

50

60

70

at

.% 5

Fig

. 67

T

he

Mo-

S p

has

e d

iag

ram

(R

efs.

154

, 15

5,

15

).

5 10

at.%

C

u

15

20

25

It]

..--,

/ ...

--;:

:;..

. CU

xM0 6

Ssi

" /

, .... ,

T

~

-175

0 I

.15

00

' ,'"

1500

-~

\

RH

1000

rK]

1

\ \

T l'

: 2 n

on

-!

30

0

eq

Ul-

_i_

eq

Ullib

nu

m

Iibflu

m

L

2°l

II """

-?

100

?

0'

II!

,I

I

x

RH RH

+

lie

u)

4

Fig

. 68

T

he CuxMo~8 p

has

e d

iag

ram

in

th

e ra

ng

e 10

~ T

~ 2

000

K.

Th

e li

mit

s of

th

e rh

om

bo

­h

edra

l p

has

e are

str

on

gly

tem

per

atu

re

dep

end

ent.

T

he

com

po

siti

on

s 1

.2 ~ x

~ 1

. 8

are

met

asta

ble

an

d c

an o

nly

be

reta

ined

by

qu

ench

ing

. A

t 60

K t

hes

e m

etas

tab

le c

om

­p

osi

tio

ns

un

der

go

a p

has

e tr

ansf

orm

atio

n

into

a n

ew p

has

e (F

lUki

ger

eta

l.,

Ref

. 4

8).

" ::c ~

m

o ~ :0

:t> ~

C/)

u. ~

592 R. FLUKIGER

B. CuxMo6S8 System

The only rhombohedral phase for which the phase diagram has been extensively studied is CuxMo6S8 [42,48, 157J. A portion of the low tem­perature part of this system was shown in Fig. 25. The whole phase diagram from 11 to 2000 K was established by Fllikiger etal. [48J and is shown in Fig. 68. The rhombohedral phase forms congruently at 1750 ~ 300C at a composition close to x = 2 (12 at. % Cu). The phase limits are strongly temperature dependent; at lS000C the phase is stable within the range 1.2 lIi: x ~ 3 (7.9 s: x s: 17 at.% Cu), whereas at 8500C the limits are shifted to 1.8 ~ x ~ 4 (11 s x s;; 22 at.% Cu). At the low Cu side there is a three -phase region RH + M02S3 + Mo, whereas at the copper­rich side the rhombohedral phase is in equilibrium with Cu. These phase limits were found by analyzing the variation of the lattice parameters after argon jet quenching from different temperatures using Fig. 69 as the standard.

The composition CU1.2M06S8 can be obtained only by quenching, this composition being metastabIe at room temperature. It is remarkable that at 60 K this metastable composition undergoes a transformation into a new low temperature phase. The system CuxM06S8 shows an extra­ordinarily complex behavior: below 300 K the rhombohedral phase decomposes into 4 different modifications. The low temperature relation­ships for x ~ 1. 8 (equilibrium part in Fig. 68) can be drawn following the phase rules and first order phase transformations [42, 48J . The region x :s: 1.8 is metastable and is called the nonequilibrium region in Fig. 68. The superconducting properties of the four low-temperature modifications are T c = 5.6 K for x = 1. 2, T c = 11 K for x = 1. 8, T c = 6.4 for x = 3.2, while the phase at x =4, the untransformed rhombohedral phase, is nonsuperconducting down to 0.8 K.

The phase at x = 1.8 is triclinic [50J; the value Tc = 11 K is the highest value found so far for a triclinic phase. Moh [154J reported earlier an eutectoidal decomposition of the CuxMo~8 phase at 594 K. H.owever, DTA and resistivity measurements (Fig. 70) on a CU1.8M06S8 smgle crystal from 1.2 to 1300 K [48J do not show any evidence for such a decomposition; the rhombohedral CuxMo6S8 phase is stable up to the melting temperature. The ternary Cu -Mo-S phase diagram at lS000C and 7000C from our data [15, 42, 48 J is shown in Fig. 71. F or better clarity the width of the two-phase regions Mo + M02S3, M02S3 + MoS2' Cu + Mo, .•. has been drawn larger than in reality. The homogeneity range of the CllxMo6'8 phase extends from x = 1.2 to x = 4, corresponding to a range of 14'-at. % Cu. An investigation on a series of single crystals [48J has shown that the ratio Mo:S is 6:8 over the whole homo­geneity range.

C. PbxMo6S8 _y System

In contrast to Cu M06S&, the system PbxMo6S8 _y does not exhibit a low-temperature transformatIOn. However, the volafility of Pb renders the preparation of single -phased samples very difficult. As a conse-

PHASE DIAGRAMS

0 5 10 15 at.%Cu 20

10.90 • .Chevrel 9.90 \ o this work

\ 10.80

9.S0 \ unstable stable e [A] \--

a [AJ \ \

9.70 \ \ \ 10.60

9.60 \ \ \ 10.50 \

9.50 \ .\( I

I cu x M06Ss i 10.40

9.40 1'". I

I I 10.30

9.30 I I

I I

I 9 2rA'-

I

0 -. -x

Fig. 69 Variation of lattice parameters c and a of the rhombohedral phase CuxMoGi8 with the Cu content, x (FlUkiger etal., Ref. 48).

1.5 E g ..s 01

1.0

0.5

500 1000 TIKI

Fig. 70 The electrical resistivity of CU1.8Mo6S8 in the temperature range 1.0 ~ T :s; 1350 K (FlUkiger etal., Ref. 48).

593

594

Cu Cu-Mo-S 800°C

CU-Mo-S 1500°C

R. FLUKIGER

Fig. 71 The ternary phase diagram Cu-Mo-S at sao and 1500oC, showing the shift of the CuxMo()SS phase limits with temperature. For better clarity, the two-phase regions have been drawn wider than in reality.

PHASE DIAGRAMS 595

quence, the precise shape of the phase field is still not clear. On the basis of a study on sintered samples, Hauck U58J established the rhom­bohedral phase field of the system Pb-Mo-S at 1l000C. He found a variation in both the Pb and the S content and proposed the formula PbxM06S8-y' withO.85l!Ox ~ 1,05andO.6 ~y ~ 1.2, which does not include the stoichiometric composition PbM06S8, thus suggesting S defects. However, density measurements on single crystals [IJ yielded the compo­sition PbM06 2S8' while an X-ray refinement on the same crystals by Yvon [71 J yielded the composition PbM06S8' Both observations practic­ally exclude the presence of S vacancies; the phase field indicated by Hauck should thus be extended up to the stoichiometric composition. The simultaneous variation of x and y has a strong effect on Tc; variations between 5 and 15 K have been observed on this compound. In Fig. 72, the variation of T c for PbxM06S8 -y. as a function of the rhombohedral angle O! has been plotted. Metallograpruc analysis and crystal growth experi­ments on PhxM06S8 _y suggest a peritectic formation of the rhombohedral phase [IJ. The pentectic temperature is situated between 15300C and 16000C U58J.

D. M06-Se8, CuxM06Se8, PbxM06Se8 The formation of the rhombohedral phase in Mo selenides is less

complex than for the analogous case of the sulfides. For Mo-Se as in Cu -Mo-Se and Pb-Mo-Se, the rhombohedral phase is stable and forms congruently uJ. The formation temperatures have so far not been deter­mined precisely, but are between 1550 and 16500C. In all three cases, large single crystals can be prepared easily with the Bridgman technique uJ. The superconducting transition temperatures of selenides are inferior to those observed on sulfides, with the exception of the R.E. M06S8 compounds, where they are higher (Fig. 73).

E. General Correlations for Rhombohedral Compounds

There is much less data on rhombohedral compounds than on A15 phases. No phase diagrams (exception: Cu~M06S8) or XPS measurements are available. Nevertheless, it is interestmg to represent the known data in an analogous way to that for A15 compounds. Figure 73 shows the variation of T c as a function of the atomic number of the M element in MXM06Xg, where X = Sand Se. There are essentially three stability regions for the rhombohedral phase for both Sand Se based compounds. The first region, (A), includes the alkalines, earth alkalines, rare earths and actinides. The second region, (B), contains transition elements with nearly filled electron shells (noble metals are excluded) and elements of the IB and lIB groups of the periodic system. The third region, (C), is essentially limited to M = Pb, Sn, Al and In. The highest transition temperatures in region A are reached by the R.E. M06X8 compounds, the values of selenides being systematically higher than those of sulfides U59J. The situation is reversed in both regions Band C where sulfides exhibit higher values of T c than selenides. PbM06SS and SnMo~S show the highest Tc values, close to 15 K. In spite of the lack

596

15 -

n

12

11

10

9

89.1 892

II , , '~ ,e c. 'l. e Oe " o ,

893 89.4 89.S

R. FLOKIGER

,

Fig. 72 Correlation between T c and the rhombohedral angle for different PbMo6SS samples (squares), Ref. 159, and for different PbxMo6SS-y samples (circles), Ref. ISS.

La

10 Rare f' Earths: iYb

I H.-Rare I La Earths

o

o MxMo6SeS o MxMo6 SS

Cr Mn Fe Co o 0 0 ~

Pd

C\ Pb 0./oSn

PPb Sn

I I I ,

Fig. 73 Superconducting transition temperature, T c ' for rhombohedral sulfides and selenides MxMo6XS (X = S,Se) as a function of the atomic number of the M atom. Superconductivity occurs in three regions: A (earth alkalines, rare earths); B (Cu, Ag) and C (Sn, Pb). The type of formation of the rhombohedral phase is indicated below.

PHASE DIAGRAMS 597

of high temperature data on Chevrel phases, the type of formation can be estimated as follows. It is well known that phases with a congruent formation from the melt have a higher ability to form single crystals. Rhombohedral compounds such as M06SS' CuxMo~eS' SnM06Se8' PbMo4)eg, AgM06Ses, can be easily ootained as single crystafs of 0.5 to 1 cm3'volume U5,42J, using the Bridgman technique described in Ref. 1. In the case of CuxMoe;Ss it was proved by direct observation methods that the formation of the rhombohedral phase is really congruent. There are good reasons to assume a congruent formation for the other compounds which easily form single crystals. As mentioned above, PbMoe;SS U, 15,42] is an example for the peritectic type of formation. Based on microscopic observations on melted samples US], a peritectic formation can be assumed for SnM06Ss, R.E. M06SS' AgM06SS' ..• (in some cases peritectic and peritectoid formations cannot be distinguished). The type of formation of the rhombohedral phase is tentatively added in Fig. 73; c stands for congruent and p for peritectic. It is seen that in Region A, the peritectic formation is favored for both sulfides and selenides. In Region B, congruent formation is observed - again in both cases for sulfides and selenides. The main difference is observed in region C, where the sulfides form peritectically, in contrast to the selenides which form congruently. The Goldschmidt radii for various MxM06SS and MxM06SeS compounds are shown in Figs. 74 and 75 respectively.

F. Comparison with the A15 Compounds

The correlation in Fig. 73 is not as well established as for the A15 compounds, but several conclusions are nevertheless possible. The type of formation (congruent or peritectic) is determined by the M element. This is analogous to the case of A15 type compoundsA3X, where the minoritary X atom has a dominant effect on the phase formation. For both phase types, regularities in the type of phase formation are encoun­tered for increases of the group number of the M or the X element, respectively. The width of the rhombohedral phase is different for the regions A, Band C. In region A (R.E., actinides), the rhombohedral phase field must be very narrow since no variation of T c as a function of composition has been reported so far. The widest homogeneity ranges occur in region B, where they reach up to 14 at. % in the case of CuxM06SS' It was mentioned in Section VIlC that the homogeneity range in PbxM06SS-v is appreciable, with important variations ofTc as a function of temperature (Fig. 72).

ACKNOWLEDGMENTS

The experimental part of this work represents continuous efforts for more than ten years, mostly accomplished at the University of Geneva. It was completed at the Francis Bitter National Magnet Laboratory and at the Kernforschungszentrum in Karlsruhe. The author wishes to thank all

86

0

V (;.

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85

0

84

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G

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Go

ldsc

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idt

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ius

ot

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m

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Fig

. 74

C

ell

vo

lum

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f th

e rh

om

bo

hed

ral

ph

ase

Fig

. 75

M

xMo6

S 8

as

a fu

ncti

on o

f th

e G

old

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PHASE DIAGRAMS 599

those who contributed actively to develop some of the techniques described in this work and to apply them successfully on an appreciable number of systems. This is particularly the case for Drs. C. Susz, J. L. Jorda, J. L. Staudenmann, P. Sp itzU , A. Junod, Mrs. H. Devantay, R. Baillif, A. Paoli, A. Naula and F. Liniger. It is a pleas ure to thank Prof. J. Muller and Dr. S. Foner for their constant interest and support when the author was working in their laboratories, as well as Prof. C). Fischer, K. Yvon and F. Heiniger for many fruitful discussions.

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PHASE DIAGRAMS 601

46.

47. 48.

49. 50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60'.

61.

62.

63.

64. 65. 66.

67.

68. 69. 70. 71.

72. 73. 74. 75.

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603

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604 R. FLOKIGER

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