phase equilibria in prototype nb-pd-hf-al alloyssrg.northwestern.edu/publications...

Phase Equilibria in Prototype Nb-Pd-Hf-Al Alloys

A MISRA R BISHOP G GHOSH GB OLSON

The phase equilibria in two prototype alloys with nominal compositions 60Nb-20Pd-10Hf-10Al and40Nb-30Pd-15Hf-15Al (in at pct) are investigated using scanning electron microscopy and X-ray dif-fraction The alloys were heat treated at 1200 degC and 1500 degC for 200 hours each The phase analy-sis revealed that the alloys were for the most part in the three-phase equilibrium between (Nb)Pd2HfAl and Pd3Hf The compositions of these three phases along with other observed phases suchas PdAl and (a-Hf) provide important data for establishing the Nb-Pd-Hf-Al quaternary phase dia-gram A preliminary Nb-Pd-Hf-Al phase diagram with pertinent tie-tetrahedra was constructed basedon the available composition data The lattice parameters of (Nb) Pd2HfAl Pd3Hf and the coeffi-cient of thermal expansion of Pd2HfAl were measured and models were developed to predict thecomposition dependence of the mean atomic volumeslattice parameters of (Nb) and Pd2HfAl andthe temperature dependence of the lattice parameter of the (Nb) phase The validity of the modelswas confirmed by good agreement between predicted and experimental values

I INTRODUCTION

THE operating temperature currently limits the efficiencyof turbine engines prompting a great deal of research in aneffort to design new high-temperature alloys Nickel-basedsuperalloys are nearing their operating limit as they approachtheir melting point thus triggering the need for new alloysthat can operate at around 1300 degC Ideally such an alloyshould have a substantially higher melting point (or low hom-ologous temperature (05Tm) at 1300 degC) and at the oper-ating temperature it should have high creep strength and highoxidation resistance For oxidation resistance the materialshould be capable of passive oxidation making it capable offorming a protective oxide scale The refractory metal nio-bium has a melting temperature of 2467 degC and also has alow density thus making it an attractive candidate for replace-ment of nickel[1] However Nb has poor oxidation resistance[2]

and only moderate strength at high temperatures[3]

A systems-based approach[4] is underway to develop a newniobium-based alloy for usable performance at 1300 degC orabove The principles of strengthening in classical gg9 Ni-based superalloys[5] is extended to design a Nb-based super-alloy strengthened by an ordered bcc aluminide phase In bccalloys such strengthening can be achieved by precipitatingeither B2 or L21 (Heusler) phase[67] The ordered intermetallicneeds to have high thermodynamic stability to promotemicrostructural stability at high temperatures Furthermoreto maintain coherency over a long period of time and to obtaina uniform distribution of the precipitates the lattice mismatchshould be very small (preferably 01 pct)

Quantum mechanical total energy calculation has beencarried out using the full potentialndashlinear muffinndashtin orbital(FLMTO) method to obtain the heat of formation of severalHeusler compounds at 0 K (with the pure elements as the

reference state) and their lattice constants[8] These are listedin Table I Based on these calculations it is seen that theNi-based intermetallic with the lowest lattice mismatch withbcc Nb and highest stability is Ni2HfAl In order to decreasethe lattice mismatch even more the Ni was replaced withPd which has the same electronic structure but a largeratomic radius Quantum mechanical calculations of Pd2HfAlhave been performed[9] using the Full Potential LinearizedAugmented Plane Wave (FLAPW) method[10] The calcu-lations show a decreased lattice mismatch and a reasonablyhigh thermodynamic stability The cohesive properties ofPd2HfAl are also listed in Table I

To assist the modeling of phase stability of relevant multi-component Nb-based alloys the phase equilibria in twoprototype Nb-Pd-Hf-Al alloys are investigated The equi-librium microstructure of these alloys established at 1200 degCand 1500 degC are characterized by measuring the composi-tions of the phases and their lattice parameters Models aredeveloped to predict the atomic volumeslattice parameters ofthe niobium solid solution and the Heusler phase The modelpredictions are then tested against the experimental data

II EXPERIMENTAL PROCEDURE

Two prototype alloys (numbered 995 and 996) weredirectionally solidified at the GE Corporate Research andDevelopment Center (Schenectady NY) The alloys were pre-pared to have the nominal compositions (in at pct) of 60Nb-20Pd-10Hf-10Al (alloy 995) and 40Nb-30Pd-15Hf-15Al (alloy996) The compositions of the alloys were based on a con-ceptual design with the goal of obtaining a two-phasemicrostructure containing (Nb) and Pd2HfAl at 1300 degC Theinitial composition designs used the heat of formation dataobtained from first principles calculations[14] coupled with theThermo Tech (Surrey Technology Park Surrey UK) ther-modynamic database[15] The starting materials were pureelements of at least 9995 pct purity These were weighed tothe desired amounts on a Mettler (Columbus OH) H80 scalewith four decimal place accuracy with a total mass of about50 g The melting chamber was evacuated to 133 3 1022 Paand then backfilled 3 times with high-purity argon The charge

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A SEPTEMBER 2003mdash1771

A MISRA Graduate Student G GHOSH Research Assistant Profes-sor and GB OLSON Wilson-Cook Chaired Professor in EngineeringDesign are with the Department of Materials Science and EngineeringNorthwestern University Evanston IL 60208-3108 Contact e-mailg_ghoshnorthwesternedu R BISHOP Consultant is with McKinseyamp Company Chicago IL 60603

Manuscript submitted August 16 2002

was then melted by cold crucible induction levitation melt-ing[16] A Nb seed crystal attached to a water-cooled pullingrod was then lowered into the melt However despite a vari-ety of withdrawal rates and rotation speeds only 5 g of aHf-Alndashrich crystal was pulled from the first alloy (995) andno crystal could be pulled from the second alloy (996) As aresult the alloys created in this manner were not directionallysolidified but only cold crucible induction melted The com-positions turned out to be unintentionally nonuniform but thisallowed us to survey a wider range of phase relations aswill be discussed further in Section IIIndashA

Samples were cut from the ingots and were then heattreated at 1200 degC and 1500 degC for 200 hours each Sam-ples for the 1200 degC heat treatment were vacuum encapsu-lated in a quartz tube with tantalum foil to getter residualoxygen The 1500 degC heat treatment was performed at theUniversity of Wisconsin at Madison in a high-purity argonatmosphere furnace

For equilibrium to be attained the heat treatment periodshould be sufficiently long to enable the elements involvedto diffuse over lengthscales comparable to the microstruc-tural features The tracer diffusivities (D) of Al and Nb inbcc Nb are known[17] but those of Pd and Hf in bcc Nb arenot known As an approximation we treat the tracer diffu-sivities of Pd and Hf in bcc Nb to be the same as Ni andZr in bcc Nb respectively which have been reported in theliterature[17] Resulting estimates of the tracer diffusion dis-tances of each of these elements in bcc Nb at1200 degC and at 1500 degC in 200 hours are listed in Table II

Most of the features that are observed in the microstruc-tures (Section IIIndashA) are of the order of 1 to 40 mm Basedon the estimated distances in Table II we conclude that the1500 degC samples are very likely at equilibrium and the1200 degC samples should be reasonably near equilibrium

A 10-g button of Pd2HfAl was made by arc melting inan inert argon atmosphere to determine its lattice parameterand the coefficient of thermal expansion The startingmaterials used were the same as those used for making theprototype alloys A computer-controlled MMC metallurgical

(lto

Dt)

1772mdashVOLUME 34A SEPTEMBER 2003 METALLURGICAL AND MATERIALS TRANSACTIONS A

Table I Calculated Cohesive Properties for Selected Heusler Phases[89]

a (Calc) nm a (Expt) nm Lattice Mismatch 2DE (Formation)Compound (at 0 K) (at 298 K) (with respect to pure Nb at 298 K) (kJmol)

Ni2TiAl 0587 05872[11] 05865[12] 111 pct 8271Ni2VAl 0578 0633[12] 124 pct 6236Ni2ZrAl 0610 06123[1112] 759 pct 8035Ni2NbAl 0600 05974[1112] 911 pct 6683Ni2HfAl 0610 06081[1112] 759 pct 9151Ni2TaAl 0595 05949[11] 986 pct 7589Pd2HfAl 0634 06367[13] 396 pct 7769

Table II Tracer Diffusion Distances of Elementsin bcc Nb Matrix

Diffusion Distance Diffusion distanceat 1200 degC at 1500 degC

Element in 200 h (mm) in 200 h (mm)

Nb 05 80Pd 278 2848Hf 20 253Al 43 831

dilatometer was used to determine the coefficient of thermalexpansion of Pd2HfAl

A Hitachi 4500 scanning electron microscope (SEM) havinga cold field emission gun was used for microstructural char-acterization Standards-based composition analysis was carriedout on a Hitachi (Hitachi Ltd Tokyo Japan) 3500 SEMhaving a tungsten filament and fitted with a PGT (PrincetonGamma-Tech Inc Princeton NJ) energy-dispersive spec-trometer and PGT-IMIX (Integrated Microanalyzer for Imag-ing and X-ray) software and ZAF (Z 5 Atomic numberA 5 Absorption F 5 Fluorescence) parameter database A20 kV accelerating voltage was used for both imaging andenergy-dispersive X-ray analysis NIH Image software[18] wasused to measure the area fraction of the different phases fromthe representative micrographs X-Ray diffraction was per-formed on a Scintag (Scintag Inc Cupertino CA) XDS 2000diffractometer with a Cu Ka source The diffraction patternswere then analyzed using MacDiff[19] software to preciselydetermine the peak positions assuming split pseudo-voigtshape of the peaks Lattice parameter values were obtainedfrom the peak positions and in the case of (Nb) and Pd2HfAlthese were plotted against the NelsonndashRiley function[20] inorder to obtain precise lattice parameter values In the caseof the hexagonal Pd3Hf phase Cohenrsquos method[20] was usedto obtain the lattice parameters

III RESULTS

A Microstructure and Phase Analysis

Alloy 995 showed the presence of three phases after1200 degC and 1500 degC heat treatments The phases are identifiedas (Nb) Pd3Hf and Pd2HfAl Representative micrographs areshown in Figures 1(a) and (b) The measured compositionsof the phases and lattice parameters are summarized in TableIII As seen in the micrographs (Nb) has a dendritic shapeimplying that it has solidified first Pd2HfAl is the interden-dritic phase in Figures 1(a) and (b) Pd3Hf almost alwaysappears at the interface between (Nb) and Pd2HfAl suggest-ing that it is a product of solid-state reaction between (Nb)and Pd2HfAl at 1200 degC and 1500 degC However some iso-lated particles of Pd3Hf can also be seen in the micrographs

Alloy 996 heat treated at 1200 degC showed consider-able compositional inhomogeneity As mentioned in SectionII this inhomogeneity was not intentional but was a result ofmacrosegregation occurring during solidification of the sampleafter cold crucible induction melting The nonuniform samplenonetheless yields important data as it gives information aboutthe tie-triangles of different equilibria in the Nb-Pd-Hf-Al quar-ternary phase diagram Three 3-phase and one 2-phase region


Table III Measured Composition of the Phases (in Atomic Percent) and Their Lattice Parameters in Alloy 995

HeatTreatment Phases Nb Pd Hf Al Lattice Parameter (nm)

1200 degC (Nb) 885 6 12 79 6 08 12 6 04 24 6 03 a 5 032912 6 000022200 h Pd2HfAl 02 6 02 572 6 05 192 6 06 234 6 05 a 5 063159 6 000005

Pd3Hf 04 6 05 735 6 13 246 6 11 14 6 03 a 5 056178 6 000030c 5 092019 6 000030


Pd3Hf 06 6 03 754 6 03 236 6 02 04 6 04 a 5 055653 6 000030c 5 091988 6 000030

(a)

(b)

Fig 1mdashMicrostructure of alloy 995 showing the presence of three phases(a) heat treated at 1200 degC and (b) heat treated at 1500 degC

were observed in the sample These are (Nb) 1 (a-Hf) 1 PdAl(region 1) (Nb) 1 Pd2HfAl (region 2) (Nb) 1 PdAl 1 Pd3Hf(region 3) and (Nb) 1 Pd2HfAl 1 Pd3Hf (region 4) Howeverthe three-phase region of (Nb) PdAl and (a-Hf) extendedover the major part of the sample and the other regions wereobserved near the edge of the sample Representative micro-graphs are shown in Figures 2(a) through (d)

Alloy 996 heat treated at 1500 degC showed the presence ofthree phases (Nb) Pd2HfAl and a trace amount of Pd3HfHowever Pd3Hf phase in alloy 996 heat treated at 1500 degCwas fine and thus it was not possible to perform defini-tive composition analysis on it in the SEM Representativemicrographs are shown in Figures 3(a) and (b) As can beseen from Figure 3(b) the Pd3Hf phase appears mainly atthe interface between (Nb) and Pd2HfAl The compositionsof the phases present in alloy 996 along with the latticeparameters for (Nb) and Pd2HfAl in the alloy heat treatedat 1500 degC are summarized in Table IV

The Pd2HfAl alloy was confirmed to be single-phaseHeusler by both SEM analysis and X-ray diffraction Thecomposition of the phase along with the lattice parameteris summarized in Table V

As a result of the Hf-Alndashrich crystal being pulled out fromalloy 995 during processing its actual composition wasdifferent from the nominal composition From SEM obser-vations it was seen that there was a difference between therelative fractions of the phases at the center region of thesample (where all composition analysis had been carriedout) and at the edge of the sample in alloy 995 at both heattreatments Alloy 996 was obviously inhomogenous asevident from the presence of four different regions ofequilibrium in the sample heat treated at 1200 degC Due tothe preceding considerations a re-evaluation of the overallcompositions of the alloys in the regions of interest wascarried out At least five different low-magnification micro-graphs from each region were analyzed and the area frac-tion of each phase was measured from the micrographs Itwas assumed that the apparent area fraction in two-dimensions corresponds to the volume phase fraction inthree-dimensions After rejection of outliers the values wereaveraged to obtain the phase fraction at each region Themeasured phase fractions are listed in Table VI

Based on the phase fractions and the composition of eachphase the actual overall compositions of the alloys at theregions of interest were calculated The calculated overallcompositions are listed in Table VII The listed error barsrelated to the uncertainty in the measured compositions(Tables III and IV) and the uncertainty in the measured phasefractions (Table VI) were calculated using a standardmathematical procedure

B A Tentative Phase Diagram for the Nb-Pd-Hf-Al System

Based on the composition analysis Nb-Pd-Hf-Al phasetetrahedra were constructed to represent the equilibriumbetween the observed phases in the four-component system


Fig 3mdashMicrostructure of alloy 996 heat treated at 1500 degC (a) at lower magnification showing (Nb) and Pd2HfAl and (b) at higher magnification showingvery fine Pd3Hf phase mostly along (Nb)Pd2HfAl interface

Fig 2mdashMicrostructure of alloy 996 heat treated at 1200 degC (a) region 1 (b) region 2 (c) region 3 and (d) region 4

Figure 4 shows the various three-phase equilibria presentin our alloys heat treated at 1200 degC We can then proceedto represent an isothermal section of the Nb-Pd-Hf-Alphase diagram at 1200 degC by projecting the compo-sitions of the Pd2HfAl phases the Pd3Hf phases the PdAlphases and the a-Hf phases in equilibrium with bcc Nbon to the Pd-Hf-Al basal plane This is shown in Figure 5The phase boundaries represent our best estimate basedon available composition data The solid circles corres-pond to the projected data points and the open circlesrepresent the reported solubility limits of the binary

system[212223] The Pd2HfAl data point ldquoArdquo denoted bya solid square is based on ongoing research that will bepublished as part of a future publication[24] The figuresin parentheses indicate the actual Nb content of the phasesThe experimental tie-lines are represented by the dashedlines As seen in Figure 5 the Pd2HfAl phase tends to bePd-rich

Figure 5 shows two three-phase regions projected onthe Pd-Hf-Al plane The Nb solid solutions in equilibriumwith those three-phase regions then define unique tie-tetrahedra in the Nb-Pd-Hf-Al system This is represented


Table IV Measured Composition of the Phases (in Atomic Percent) and Their Lattice Parameters in Alloy 996


1200 degC Region 1200 h (Nb) 907 6 18 39 6 08 22 6 11 32 6 13 mdash

PdAl 04 6 05 525 6 04 05 6 02 466 6 05 mdash(a-Hf) 05 6 09 06 6 06 907 6 08 82 6 06 mdashRegion 2(Nb) 905 6 09 39 6 04 20 6 07 36 6 04 mdashPd2HfAl 03 6 02 541 6 20 207 6 12 249 6 12 mdashRegion 3(Nb) 900 6 13 69 6 09 10 6 02 21 6 05 mdashPdAl 02 6 01 551 6 04 66 6 09 381 6 11 mdashPd3Hf 03 6 03 729 6 07 232 6 03 36 6 05 mdashRegion 4(Nb) 922 6 09 47 6 08 12 6 03 19 6 05 mdashPd2HfAl 05 6 04 563 6 06 160 6 05 272 6 04 mdashPd3Hf 03 6 03 732 6 05 231 6 04 34 6 06 mdash

1500 degC (Nb) 896 6 08 39 6 04 21 6 02 44 6 04 a 5 032962 6 000005Pd2HfAl 02 6 02 516 6 05 229 6 03 253 6 05 a 5 063759 6 000002

200 h Pd3Hf mdash mdash mdash mdash mdash

Table V Measured Composition of Pd2HfAl (in Atomic Percent) and Its Lattice Parameter in Pd2HfAl Alloy

Heat LatticeTreatment Phases Nb Pd Hf Al Parameter (nm)

As cast Pd2HfAl 00 496 6 04 253 6 03 251 6 04 a 5 063680

Table VI Phase Fractions of Individual Phases

Alloy Region (Nb) Pd2HfAl PdAl Pd3Hf (a-Hf)

995 at 1200 degC central 0508 6 0013 0423 6 0007 mdash 0069 6 0010 mdash995 at 1500 degC central 0515 6 0026 0409 6 0029 mdash 0076 6 0011 mdash996 at 1200 degC region 1 0833 6 0027 mdash 0064 6 0025 mdash 0103 6 0006996 at 1200 degC region 2 0474 6 0031 0526 6 0031 mdash mdash mdash996 at 1200 degC region 3 0063 6 0025 mdash 0345 6 0017 0592 6 0008 mdash996 at 1200 degC region 4 0410 6 0105 0365 6 0085 mdash 0225 6 0043 mdash996 at 1500 degC central 0863 6 0016 0137 6 0016 mdash mdash mdash

Table VII Actual Overall Compositions of Alloy Samples

Alloy Region Nb (At Pct) Pd (At Pct) Hf (At Pct) Al (At Pct)

995 at 1200 degC central 451 6 19 333 6 19 104 6 09 112 6 06995 at 1500 degC central 462 6 31 330 6 32 104 6 13 104 6 12996 at 1200 degC region 1 756 6 41 67 6 22 112 6 16 65 6 25996 at 1200 degC region 2 430 6 34 303 6 31 119 6 16 148 6 17996 at 1200 degC region 3 60 6 26 625 6 23 161 6 08 154 6 15996 at 1200 degC region 4 380 6 103 390 6 91 115 6 29 115 6 32996 at 1500 degC central 773 6 22 104 6 13 50 6 06 73 6 09

in Figure 6 As a preliminary estimate the compositionof (Nb) in the equilibrium tie-tetrahedron (Nb)-Pd2HfAl-Pd3Hf-PdAl is taken as the same as that of (Nb) in equi-librium with Pd2HfAl and Pd3Hf in region 4 of alloy 996heat treated at 1200 degC (Table IV) The composition of(Nb) in the equilibrium tie-tetrahedron (Nb)-Pd2HfAl-PdAl-(a-Hf) is taken as the same as that of (Nb) in equilibriumwith PdAl and (a-Hf) in region 1 of alloy 996 heat treatedat 1200 degC (Table IV) Any alloy composition within thetie-tetrahedra will result in a four-phase equilibrium withthe composition of the phases being given by the cornersof the tie-tetrahedra The separation of the two tie-tetra-hedra bases in Figure 6 defines the width of the three-phase fields between them These three-phase fields inturn define the limits of the desired (Nb)-Pd2HfAl two-phase field for dispersion-strengthened alloys

C Mean Atomic Volume and Lattice Parameterof Nb-Based Solid Solution and Pd2HfAl

To design alloys with controlled misfit between the matrixand the strengthening phase models are needed to accuratelypredict the mean atomic volumeslattice parameters of bothphases as a function of composition and temperature Basedon existing literature data simple analytical functions werederived to express the temperature and compositiondependence of the mean atomic volumelattice parameter ofthe Nb solid solution and the composition dependence ofthe lattice parameter of Pd2HfAl The coefficient of thermalexpansion (CTE) of Pd2HfAl was measured by dilatometry

1 Composition dependence of the mean atomic volumeof bcc Nb-based solid solutionIn the spirit of CALPHAD (Calculation of Phase Dia-

grams) formalism we present a model to predict the meanatomic volume of bcc Nb with dissolved amounts of Pd Hfand Al In this approach the composition dependence of themean atomic volume (or lattice parameter) is expressed usinga RedlichndashKister polynomial[25] which is also used to expressthe composition dependence of excess Gibbs energy Thenone advantage is that the effect of misfit strain on phaseequilibria can be readily calculated

The mean atomic volume (Va) represents half of the vol-ume of the bcc unit cell as there are two atoms per bccunit cell The ambient atomic volume of bcc Nb has beenreported by King[26] to be 1798 3 1023 nm3 Literature datareporting the variation of room-temperature lattice param-eter of bcc Nb with dissolved amounts of Al[272829]

Hf[30313233] and Pd[3435] was collected and the data pointswere converted to mean atomic volumes

The lattice parameters at 0 K of bcc Al (metastable) bccHf bcc Nb and bcc Pd (metastable) and bcc-based orderedcompounds (B2 and B32 structure with AB stoichiometryand DO3 structure with A3B and AB3 stoichiometry) in theNb-Pd and Nb-Al systems were calculated36 using first-principles techniques using the Vienna AbInitio SimulationPackage (VASP) package[37] These values were convertedto room-temperature (298 K) values by multiplying each valuewith a correction factor of 100237 The correction factor


Fig 6mdashTie-tetrahedra in the Nb-Pd-Hf-Al quarternary system at 1200 degCFig 4mdashExperimental tie-triangles in alloys 995 and 996 at 1200 degC

Fig 5mdashProjection of Nb-Pd-Hf-Al tie-tetrahedra bases on Pd-Hf-Al plane(1200 degC)


was calculated by taking the ratio of the ambient lattice para-meter of bcc Nb as reported by King[38] over the latticeparameter of bcc Nb at 0 K obtained from first-principlescalculations[36] Before the application of the temperature cor-rection an initial correction had to be applied to the first-principles calculations of the lattice parameter of bcc Pdand the bcc-based ordered compounds involving Pd First-principles calculations carried out for fcc Pd at 0 K[36] hadresulted in a lattice parameter of 039605 nm which waslarger than the value of 038783 nm reported by King andManchester at 25 K[39] (However recent FLAPW calcula-tions carried out for fcc Pd have been found to give betterresults[9]) This implied that a correction factor of 09792needed to be multiplied with the first-principles value for fccPd in order to obtain the value reported in literature It was

Fig 7mdashVariation of mean atomic volume (a) of Al-Nb bcc alloys at 298 K showing strong negative deviation from ideal behavior (b) of Hf-Nb bccalloys at 298 K showing a weak negative deviation from ideal behavior and (c) of Nb-Pd bcc alloys at 298 K showing a moderate negative deviationfrom ideal behavior

(a) (b)

assumed that the same correction would apply to the first-principles calculations for bcc-based Pd systems and thiscorrection was applied to bcc Pd and the bcc-based orderedcompounds by taking into account the mole fraction of Pdin those compounds Combining the available experimentallattice parameter data for bcc solid solution and the latticeparameters of the bcc-based ordered intermetallics obtainedby first-principle calculations the compositional dependenceof the ambient mean atomic volume of bcc Nb-Al Nb-Hfand Nb-Pd binary solid solutions was expressed asRedlichndashKister polynomials Even though ordering of a solidsolution at the same composition usually results in a slightdecrease (05 pct) in lattice parameter (or mean atomic vol-ume) the underlying approximation helps us in expressingcomposition dependence in the entire composition range

(c)

The composition dependence of the mean atomic volumeof bcc Nb-Al Nb-Hf and Nb-Pd binary solid solutions isshown in Figures 7(a) through (c) respectively The fol-lowing equations represent the compositional variation ofthe ambient mean atomic volumes of bcc Nb-Al Nb-Hf andNb-Pd binary solid solutions

[1]

[2]

[3]

where Xi represents the mole fraction of the correspondingspecies (i 5 Nb Al Hf or Pd)

As can be seen from Eqs [1] through [3] the ambientatomic volumes of bcc Al Hf and Pd are 17169 3 1023

nm3 21815 3 1023 nm3 and 14815 3 1023 nm3 respect-ively In Eqs [1] through [3] the coefficients multiplied byXiXj were obtained by least-square fits The error associatedwith each coefficient related to the scatter in the data isshown in Table VIII

The linear behavior of the mean atomic volumes for thebcc Nb-Al Nb-Hf and Nb-Pd solid solutions are representedby dashed lines in Figs 7(a) through (c) respectively As canbe seen from Figure 7(a) there is considerable deviation fromlinearity for the mean atomic volume of the bcc Nb-Al solidsolution and hence it is necessary to introduce higher-orderterms to account for the nonlinear behavior The mean atomicvolume of the bcc Nb-Pd solid solution also shows a negativedeviation from linearity(Figure 7(c)) The variation of themean atomic volume of the bcc Nb-Hf solid solution showsonly a slight negative deviation from linearity (Figure 7(b))However as can be seen from Table VIII the absolute valueof the higher-order coefficient in Eq [2] is much larger thanthe error associated with the experimental scatter

Based on the least-square fitting parameters and assumingsuperposition of Nb-X binary systems the followingRedlichndashKisterndashMuggianu polynomial[40] is proposed todescribe the ambient mean atomic volume of bcc Nb-Al-Hf-Pd solid solution

209695XNbXPd

VNb2Pda 3 103 nm3 5 17980XNb114815XPd

203573XHfXNb

VNb2Hfa 3 103 nm3 5 21815XHf 1 17980XNb

1 XAlXNbg228267226218(XAl2XNb)

h

VNb2Ala 3 103 nm3 5 17169XAl 1 17980XNb

[4]

The lattice parameter can be obtained from the mean atomicvolume by the relation

[5]

The lattice parameters for the Nb solid solutions in alloys995 and 996 were calculated by using Eqs [4] and [5] Theerror bars for the predicted lattice parameters related to theuncertainty of the measured compositions (Tables III andIV) were calculated using a standard mathematicalprocedure The measured lattice parameters and the predictedvalues (using Eqs [4] and [5]) for the Nb solid solutions(compositions listed in Tables III and IV) are compared inTable IX Alloy 996 heat treated at 1200 degC was not usedfor the lattice parameter measurements because of the super-position of several peaks resulting from the different phasespresent in the sample As seen in Table IX the agreementis within 04 pct

2 Composition dependence of lattice parameterof Pd2HfAlIn the following a model is presented to predict the com-

position dependence of the lattice parameter of Pd2HfAlOur approach is to express the lattice parameter of theHeusler phase (L21) in terms of the site occupancy and theatomic volume of constituent species Two importantassumptions are made (1) the atomic volume of a speciesis independent of the site it occupies and (2) only antisiteatoms are considered as constitutional defects in Pd2HfAlie no vacancy is present Then the volume of the unit cellis the weighted sum of volume of the species There arethree distinct crystallographic sites in a Heusler phase A2BCwhere eight A atoms occupy site I four B atoms occupysite II and four C atoms occupy site III In a multicompon-ent system these sites may be occupied by one or moreatomic species Knowing the site occupancy of the atomicspecies j (yj) either from experiment or from thermodynamicprediction the lattice parameter may be expressed as

[6]

with

where Vj is the atomic volume of species j and n is the totalnumber of each species

At first the atomic volumes of Pd Hf and Al in Pd2HfAlwill be determined For a stoichiometric composition when

a yIj 5 a yII

j 5 a yIIIj 5 1

1 4 an

j21yII

j VL21j 1 4 a

n

j21

IIIj V L21

j a3 5 8 an

j5 1yI

jVL21j

a (nm) 5o3

2Va

203573XHfXNb209695XNb XPd


h 1 17980XNb 1 14815XPd

Va 3 103 nm3 5 17169XAl 1 21815XHf


Table VIII Error Associated with Higher-OrderCoefficients in Eqs [1] through [3]

Equation Higher-Order Term Coefficient Error

1 XAlXNb 28267 007441 XAlXNb(XAl 2 XNb) 26218 013122 XHfXNb 03573 017643 XNbXPd 09695 00940

Table IX A Comparison of the Calculated and Experimental Lattice Parameter Results for Bcc Phase in Nb-Pd-Hf-Al Samples

Alloy and Heat Treatment a (nm) Measured a (nm) Eqs [4 and 5] Difference

Alloy 995 at 1200 degC 032912 6 000022 032817 6 000013 029 pctAlloy 995 at 1500 degC 032944 6 000006 032826 6 000009 036 pctAlloy 996 at 1500 degC 032962 6 000005 032921 6 000009 012 pct

xPd 5 050 xHf 5 025 xA 5 025 and xNb 5 0 Eq [6]reduces to

[7]

where ao is the lattice parameter of stoichiometric Pd2HfAlTo express the lattice parameter variation of Pd2HfAl with

varying composition we follow a method similar to thatdeveloped by Kitabjian and Nix[41] for the B2 phase andJung et al[42] for the Heusler phase In the Pd-rich side ofPd2HfAl the volume (V) of a unit cell can be expressed as

[8]

where is the number of antisite defects and

[9]

Also the atomic fractions of Pd and Hf in Pd2HfAl can beexpressed as

[10a]

[10b]

Differentiating Eq [8] with respect to and using Eq [9]we obtain

[11]

Differentiating Eqs [10a] and [10b] we obtain

[12a]

[12b]

Combining Eqs [11] and [12] we obtain

[13a]

or

[13b]

So we have two equations (Eqs [7] and [13b]) for theatomic volumes and three unknowns (VPd VHf VAl) Alsothere is no reported lattice parameter data of Pd2HfAl as a

2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl

and dnIIPd 5 2100dxHf

dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf

a30 5 8VPd 1 4VHf 1 4V Al

function of composition and thus further approximationsare needed As a first approximation the atomic volumesof Hf and Al in Pd2HfAl are assumed to be the same as inthe B2 compounds PdHf and PdAl respectively Theatomic volume of Pd in Pd2HfAl is assumed to be themean of the atomic volumes of Pd in B2 PdHf and B2PdAl This assumption has some physical basis becausein L21 Pd2HfAl both the Hf atoms and the Al atoms havePd atoms as their nearest neighbors So the atomicvolumes of Hf and Al in Pd2HfAl are most likely to beinfluenced by the interaction of those atoms with Pd atomsThe Pd atoms however have 4 Hf atoms and 4 Al atomsas their nearest neighbors So the atomic volume of Pdin Pd2HfAl is going to be equally influenced by Pd-Hfand Pd-Al interactions The problem now reduces tofinding the atomic volumes of the constituent species inB2 PdAl and B2 PdHf

Literature data of lattice parameter variation of B2 PdAlwith composition[4344] was analyzed and least-square linearfits to the data were carried out on the Al-rich side andthe Pd-rich side of stoichiometry The nature of the var-iation suggests the following defect chemistry (1) on thePd-rich side the Pd atoms substitute Al atoms on the Alsublattice and (2) on the Al-rich side vacancies resideon the Pd sublattice[43] Thus on the Pd-rich side onlythe atomic volumes of Pd and Al are involved and theatomic volume of the vacancies need not be consideredSo by considering the Pd-rich side one can minimize thenumber of unknown variables By using the experimentallattice parameter data of B2 PdAl the atomic volumesof Pd and Al in B2 PdAl were obtained using a methoddeveloped by Kitabjian and Nix[41] The followingequations used were

[14]

[15]

The slope of the a vs XPd plot on the Pd-rich side was obtained as 258 3 10204 nm per mole fraction Pd and thelattice parameter of stoichiometric PdAl (ao) was taken tobe 030532 nm Then we obtained and

Although the formation of PdHf has been established its

structure has not been determined Based on related systemsit is likely that PdHf has the CsCl structure at higher tem-perature[21] In the absence of any experimental data for B2PdHf we have used an alternative approach to estimate theatomic volumes of Pd and Hf in hypothetical B2 PdHf Ghoshand Asta[36] have calculated the lattice parameters of bcc-type ordered compounds at 0 K in the Pd-Hf system Thelattice parameter of B2 PdHf was calculated36 to be 033149nm at 0 K By applying the correction for Pd and thecorrection for temperature as described in Section IIIndashCndash1the lattice parameter of B2 PdHf was obtained to be 032883nm at 298 K Assuming that there are no vacancies presentin the system and complete substitution takes place on eitherside of stoichiometry the variation of the lattice parameterof ordered PdHf will be essentially a straight line We appro-ximate the slope of that line to be equal to the slope of a

VPdAlAl 5 0014272 nm3

0014191 nm3VPdAlPd 5

b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c


straight line joining the lattice parameters of bcc Pd and bccHf With the preceding approximation the slope of the curve

was obtained to be 426 3 10202 nm per mole fraction Hf Using the preceding values and Kitabjianrsquosmethod[41] the atomic volumes of Pd and Hf in B2PdHf were estimated to be and

Literature data suggest that in B2 transition metal alu-

minides there is a large reduction in the atomic volume ofAl but only a small reduction in the atomic volume of thetransition metals[41] Based on this trend and also noting thatthe amount of Nb in Pd2HfAl in our samples is small wetake the atomic volume of Nb in Pd2HfAl to be the sameas the atomic volume of pure Nb

Taking VPd 5 0014257 nm3 VHf 5 0021233 nm3 andVAl 5 0014272 nm3 and by using Eq [6] the lattice para-meters for the observed Pd2HfAl compositions (listed inTables III IV and V) were calculated However it isfound that our model consistently underestimates the latticeparameter compared to the measured values This impliesthat there is a systematic error in the model parametersThus further refinement of the model is necessary

Due to the lack of reported lattice parameter data of Pd2HfAlas a function of composition we make use of the measuredlattice parameter data of Pd-rich Pd2HfAl phase (compositionslisted in Tables III and IV) and also the lattice parameter ofstoichiometric Pd2HfAl[13] to further refine the model para-meters In order to reduce the number of unknown variablesthe Nb contribution to the Pd2HfAl lattice parameters wasignored It is important to note that the compositions of theobserved Pd2HfAl phases correspond to approximately con-stant Al and differ mainly in Hf and Pd contents Thus weassume that the observed variation in the lattice parameter ismainly due to the variation of Pd and Hf In order to furtherreduce the number of unknown variables the atomic volumeof Al in Pd2HfAl was taken to be the same as the atomic

VPdHfHf 5 0021233 nm3

VPdHfPd 5 0014323 nm3

eda

dXHf

fvolume of Al in PdAl Thus we have two unknowns (VPdand VHf) and two equations (Eqs [7] and [13b]) The slopes

and in Eq [13b] can be evaluated by plotting theobserved Pd2HfAl lattice parameters as a function of Pdcomposition and as a function of Hf composition respectivelyBy using this method the slopes are obtained to be 200599 nm per mole fraction Pd and 00777 nm permole fraction Hf Equations [7] and [13b] are then solved forVPd and VHf by using the preceding values and by takingao 5 06367 nm Then we obtain VPd 5 0014737 nm3 andVHf 5 0020780 nm3

As previously done we take the atomic volume of Nb inPd2HfAl to be the same as the atomic volume of pure Nb

The atomic volumes of the different components used inthis model and their atomic volumes in their pure state aresummarized in Table X

The lattice parameter of different compositions of theHeusler phase (compositions listed in Tables III IV and V)was then calculated by using the preceding atomic volumesand by using the site occupancy relations The error bars forthe predicted lattice parameters related to the uncertaintyof the measured compositions were obtained using a stan-dard mathematical procedure The measured lattice par-ameters and the predicted lattice parameters of the Heuslerphase present in the different samples are summarized inTable XI

3 Temperature Dependence of lattice parameterof bcc NbSeveral authors have reported the room-temperature lattice

parameter of bcc Nb[384546] as well as the temperature depend-ence[34364547 ndash49] The ambient lattice parameter (033007 nm)as reported by King[38] is more consistent with the high-temperature and low-temperature lattice parameter values asopposed to the value reported by Roberge[45] (033063 nm)Overall the low-temperature lattice parameter values reported

dadxHf

5

dadxPd 5

dadxHf

dadxPd


Table X A Comparison of the Atomic Volumes of Constituents in Pd2HfAl in Metastable Bcc State and in the StableStandard State

Atomic Volume Atomic Volume in Atomic Volume in Standardin Pd2HfAl (nm3) Bcc form36 (nm3) Element Reference[25] (nm3)

Element at 298 K at 298 K at 298 K

Pd 0014737 0014815 0014717 (fcc)Hf 0020780 0021815 0022321 (hcp)Al 0014272 0017169 0016603 (fcc)Nb 0017980 0017980 0017980 (bcc)

Table XI A Comparison of the Calculated and Experimental Lattice Parameters for Pd2HfAl

Alloy and Pd2HfAl Composition (At Pct) DifferenceHeat Treatment Nb Pd Hf Al a (nm) Measured a (nm) Eq [6] Pct

Pd2HfAl alloy 00 6 00 496 6 04 253 6 03 251 6 04 063680 063693 6 00002 2002Alloy 995

at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039

by Roberge[45] are not consistent with other literature data andwere not used for the analysis Taking the room-temperaturevalue of the Nb lattice parameter to be 033007 nm a least-square fit to the literature data yields the following relation

[16]

Figure 8 shows the variation of the lattice parameter ofNb with temperature The temperature dependence of theNb-based solid solution in our system is approximated to bethe same as that of pure Nb

4 Temperature dependence of lattice parameterof Pd2HfAlX-ray diffraction analysis on the Pd2HfAl sample revealed

the existence of only Heusler phase The measured latticeparameter has been reported in Table V Dilatometry testswere carried out on the Pd2HfAl sample to determine theCTE The CTE as measured is 863 3 1026K for Pd2HfAlThus the variation of the lattice parameter of stoichiometricPd2HfAl with temperature can be expressed as

[17]

D Lattice Misfit at 1300 degC

To determine the unconstrained lattice misfit at an oper-ating temperature of 1300 degC we use the relation

[18]

We use Eqs [16] and [17] to calculate the lattice parametersof (Nb) and the Heusler phase at 1300 degC The compositionsof the Nb solid solution and the Heusler phase are taken tobe the same as that in alloy 996 heat treated at 1500 degC (TableIV) The lattice parameters of the Nb solid solution and theHeusler phase and the corresponding misfits at room temper-ature and 1300 degC are shown in Table XII

misfit (pct) 5b2aNb2aPd2HfAl

2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026

Thus the lattice misfit between (Nb) and Pd2HfAl is appro-ximately the same at the operating temperature as it is at theroom temperature This implies that the only way to reducethe lattice misfit is by the addition of alloying elements suchthat the lattice parameter of (Nb) is decreased while that ofthe Heusler phase is increased This also requires knowledgeof the partitioning behavior of various elements in these twophases as a function of temperature and composition

IV CONCLUSIONS

Based on our microstructural characterization and latticeparameter analysis the following conclusions are drawn

1 Alloys 995 and 996 were for the most part in the three-phase equilibrium between (Nb) Pd3Hf and Pd2HfAlThree-phase equilibrium was also observed between (Nb)PdAl and (a-Hf) and (Nb) Pd3Hf and PdAl

2 Two tie-tetrahedra were identified in the Nb-Pd-Hf-Alquarternary system at 1200 degC defining limits of thedesired (Nb)-Pd2HfAl two-phase field

3 A model is developed and tested to predict the compos-ition dependence of the mean atomic volume and hencethe lattice parameter of Nb solid solution with dissolvedamounts of Pd Hf and Al

4 A model is developed and tested to predict the compos-ition dependence of the lattice parameter of Pd2HfAlThis model is based on the site occupancy and atomicvolume of constituent species

5 A model based on least-square fit to literature data wasdeveloped to predict the temperature dependence of thelattice parameter of the bcc Nb solid solution

6 The CTE of Pd2HfAl was measured by dilatometry testsThe CTE of Pd2HfAl suggests that its CTE is almost thesame as that of Nb at higher temperatures and as a resultthe lattice misfit will remain independent of temperature

ACKNOWLEDGMENTS

This work was financially supported by the AFOSR-MEANS Program (F49620-01-1-0529) and Reference MetalsCompany Inc We also thank Professor John PerepezkoUniversity of Wisconsin Madison for help in heat treatingthe alloys at 1500 degC

REFERENCES1 EA Brandes and GB Brook Smithells Metals Reference Book 7th

ed Butterworth-Heinemann Jordan Hill Oxford UK 1992 p 22 C Bouillet D Ciosmak M Lallemant C Laruelle and JJ Heizmann

Solid State Ionics 1997 vol 101 pp 819-243 MJ Davidson M Biberger and AK Mukherjee Scripta Metall

Mater 1992 vol 27 pp 1829-344 GB Olson Science 1997 vol 277 pp 1237-42


Table XII Calculated Lattice Misfits between (Nb) andPd2HfAl (Listed in Table IV) at 25 degC and 1300 degC

Lattice Parameter Lattice Parameter MisfitT (degC) of (Nb) (nm) of Pd2HfAl (nm) (Pct)

25 032962 063759 3281300 033331 064461 330

Fig 8mdashVariation of lattice parameter of bcc Nb with temperature

5 E Nembach and G Neite Progr Mater Sci 1985 vol 29 pp 177-3196 Y Koizumi Y Ro S Nakazawa and H Harada Mater Sci Eng

AmdashStruct 1997 vol 223 pp 36-417 K Oh-ishi Z Horita and M Nemoto Mater Sci Eng AmdashStruct

1997 vol 240 pp 472-788 W Lin and AJ Freeman Phys Rev B 1992 vol 45 pp 61-689 AJ Freeman and M Kim Northwestern University Evanston IL

unpublished research 200210 E Wimmer H Krakauer M Weinert and AJ Freeman Phys Rev

B 1981 vol 24 pp 864-7511 JH Westbrook Intermetallic Compounds John-Wiley amp Sons New

York NY 1967 p 17412 P Villars and LD Calvert Pearsonrsquos Handbook of Crystallographic

Data for Intermetallic Phases ASM INTERNATIONAL MaterialsPark OH 1991 vol 1 pp 877-968

13 R Marazza G Rambaldi and R Ferro Atti Della AccademiaNazioonale Dei Lincie Classe Di Scienze Fiiche Matematiche E Naturali Rendiconti 1973 vol 55 pp 518-21

14 AJ Freeman and SJ Youn Northwestern University Evanston ILunpublished research 1998

15 N Saunders Niobium Database Thermotech Ltd Surrey UK 199816 A Gagnoud J Etay and M Garnier Trans Iron Steel Inst Jpn

1988 vol 28 pp 36-4017 EA Brandes and GB Brook Smithells Metals Reference Book

7th ed Butterworth-Heinemann Jordan Hill Oxford UK 1992pp 9-23

18 httprsbinfonihgovnih-image19 httpservermacgeologieuni-frankfurtdeMacDiffhtml20 BD Cullity Elements of X-Ray Diffraction 2nd ed Addison-

Wesley Pub Co Reading MA 1978 pp 350-6721 SN Tripathi and SR Bharadwaj J Phase Equilibrium 1995 vol 16

pp 527-3122 JL Murray AJ McAlister and DJ Kahan Binary Alloy Phase Dia-

grams 2nd ed ASM INTERNATIONAL Materials Park OH 1990vol 1 pp 156-57

23 AJ McAlister Binary Alloy Phase Diagrams 2nd ed ASMINTERNATIONAL Materials Park OH 1990 vol 1 pp 189-92

24 A Misra G Ghosh and GB Olson J Phase Equilibria 2003in press

25 O Redlich and A Kister Ind Eng Chem 1948 vol 40 pp 345-4826 HW King Bull Alloy Phase Diagrams 1982 vol 2 p 528

27 H Hosoda T Tabaru S Semboshi and S Hanada J Alloys Com-pounds 1998 vol 281 pp 268-74

28 JL Jorda R Flukiger and J Muller J Less-Common Met 1980vol 75 pp 227-39

29 VN Svechnikov BM Pan and BI Latiesheva Metallofizika 1968vol 2 pp 54-61

30 P Duwez J Appl Phys 1951 vol 22 pp 1174-7531 A Taylor and J Doyle J Less-Common Met 1964 vol 7 pp 37-5332 RW Carpenter CT Liu and PG Mardon Metall Trans 1971

vol 2 pp 125-3133 WA Jackson AJ Perkins and RF Hehemann Metall Trans 1970

vol 1 pp 2014-1634 CE Krill III J Li CM Garland C Ettl K Samwer WB Yelon

and WL Johnson J Mater Res 1995 vol 10 pp 280-9135 BC Giessen NJ Grant DP Parker RC Manuszewski and

RM Waterstrat Metall Trans A 1980 vol 11A pp 709-1536 G Ghosh and M Asta Northwestern University Evanston IL unpub-

lished research 200337 G Kresse and J Furthmuumller Phys Rev B 1996 vol 54 pp 11169-1118638 HW King Bull Alloy Phase Diagrams 1981 vol 2 pp 401-0239 HW King and FD Manchester J Phys F Met Phy 1978 vol 8

pp 15-2640 YM Muggianu M Gambino and JP Bros J Chim Phys 1975

vol 72 pp 83-8841 PH Kitabjian and WD Nix Acta Metall 1998 vol 46 pp 701-1042 J Jung G Ghosh D Ishiem and GB Olson Metall Mater Trans

A 2003 vol 34A pp 1221-3543 M Ettenberg KL Komarek and E Miller Metall Trans 1971

vol 2 pp 1173-8144 LA Panteleimov DN Gubieva NR Serebryanaya VV Zubenko

BA Pozharskii and ZM Zhikhareva Vestnik Moskovskogo Univer-siteta Khimiya Moscow Russia 1972 vol 27 pp 70-74

45 R Roberge J Less-Common Met 1975 vol 40 pp 161-6446 GB Grad and JJ Pieres Armando Fernandez Guillermet GJ Cuello

RE Mayer and JR Granada Z Metallkd 1995 vol 89 pp 395-40047 BM Vasyutinskiy GN Kartmasov YM Smirnov and VA Finkel

Phys Met Metallogr 1966 vol 21 pp 134-3548 A Pialoux ML Joyeux and G Cizeron J Less-Common Met 1982

vol 87 pp 1-1949 JW Edwards R Speiser and HL Johnston J Appl Phys 1951

vol 22 pp 424-28


was then melted by cold crucible induction levitation melt-ing[16] A Nb seed crystal attached to a water-cooled pullingrod was then lowered into the melt However despite a vari-ety of withdrawal rates and rotation speeds only 5 g of aHf-Alndashrich crystal was pulled from the first alloy (995) andno crystal could be pulled from the second alloy (996) As aresult the alloys created in this manner were not directionallysolidified but only cold crucible induction melted The com-positions turned out to be unintentionally nonuniform but thisallowed us to survey a wider range of phase relations aswill be discussed further in Section IIIndashA

Samples were cut from the ingots and were then heattreated at 1200 degC and 1500 degC for 200 hours each Sam-ples for the 1200 degC heat treatment were vacuum encapsu-lated in a quartz tube with tantalum foil to getter residualoxygen The 1500 degC heat treatment was performed at theUniversity of Wisconsin at Madison in a high-purity argonatmosphere furnace

For equilibrium to be attained the heat treatment periodshould be sufficiently long to enable the elements involvedto diffuse over lengthscales comparable to the microstruc-tural features The tracer diffusivities (D) of Al and Nb inbcc Nb are known[17] but those of Pd and Hf in bcc Nb arenot known As an approximation we treat the tracer diffu-sivities of Pd and Hf in bcc Nb to be the same as Ni andZr in bcc Nb respectively which have been reported in theliterature[17] Resulting estimates of the tracer diffusion dis-tances of each of these elements in bcc Nb at1200 degC and at 1500 degC in 200 hours are listed in Table II

Most of the features that are observed in the microstruc-tures (Section IIIndashA) are of the order of 1 to 40 mm Basedon the estimated distances in Table II we conclude that the1500 degC samples are very likely at equilibrium and the1200 degC samples should be reasonably near equilibrium

A 10-g button of Pd2HfAl was made by arc melting inan inert argon atmosphere to determine its lattice parameterand the coefficient of thermal expansion The startingmaterials used were the same as those used for making theprototype alloys A computer-controlled MMC metallurgical

(lto

Dt)


Table I Calculated Cohesive Properties for Selected Heusler Phases[89]

a (Calc) nm a (Expt) nm Lattice Mismatch 2DE (Formation)Compound (at 0 K) (at 298 K) (with respect to pure Nb at 298 K) (kJmol)

Ni2TiAl 0587 05872[11] 05865[12] 111 pct 8271Ni2VAl 0578 0633[12] 124 pct 6236Ni2ZrAl 0610 06123[1112] 759 pct 8035Ni2NbAl 0600 05974[1112] 911 pct 6683Ni2HfAl 0610 06081[1112] 759 pct 9151Ni2TaAl 0595 05949[11] 986 pct 7589Pd2HfAl 0634 06367[13] 396 pct 7769

Table II Tracer Diffusion Distances of Elementsin bcc Nb Matrix

Diffusion Distance Diffusion distanceat 1200 degC at 1500 degC

Element in 200 h (mm) in 200 h (mm)

Nb 05 80Pd 278 2848Hf 20 253Al 43 831

dilatometer was used to determine the coefficient of thermalexpansion of Pd2HfAl

A Hitachi 4500 scanning electron microscope (SEM) havinga cold field emission gun was used for microstructural char-acterization Standards-based composition analysis was carriedout on a Hitachi (Hitachi Ltd Tokyo Japan) 3500 SEMhaving a tungsten filament and fitted with a PGT (PrincetonGamma-Tech Inc Princeton NJ) energy-dispersive spec-trometer and PGT-IMIX (Integrated Microanalyzer for Imag-ing and X-ray) software and ZAF (Z 5 Atomic numberA 5 Absorption F 5 Fluorescence) parameter database A20 kV accelerating voltage was used for both imaging andenergy-dispersive X-ray analysis NIH Image software[18] wasused to measure the area fraction of the different phases fromthe representative micrographs X-Ray diffraction was per-formed on a Scintag (Scintag Inc Cupertino CA) XDS 2000diffractometer with a Cu Ka source The diffraction patternswere then analyzed using MacDiff[19] software to preciselydetermine the peak positions assuming split pseudo-voigtshape of the peaks Lattice parameter values were obtainedfrom the peak positions and in the case of (Nb) and Pd2HfAlthese were plotted against the NelsonndashRiley function[20] inorder to obtain precise lattice parameter values In the caseof the hexagonal Pd3Hf phase Cohenrsquos method[20] was usedto obtain the lattice parameters

III RESULTS

A Microstructure and Phase Analysis

Alloy 995 showed the presence of three phases after1200 degC and 1500 degC heat treatments The phases are identifiedas (Nb) Pd3Hf and Pd2HfAl Representative micrographs areshown in Figures 1(a) and (b) The measured compositionsof the phases and lattice parameters are summarized in TableIII As seen in the micrographs (Nb) has a dendritic shapeimplying that it has solidified first Pd2HfAl is the interden-dritic phase in Figures 1(a) and (b) Pd3Hf almost alwaysappears at the interface between (Nb) and Pd2HfAl suggest-ing that it is a product of solid-state reaction between (Nb)and Pd2HfAl at 1200 degC and 1500 degC However some iso-lated particles of Pd3Hf can also be seen in the micrographs

Alloy 996 heat treated at 1200 degC showed consider-able compositional inhomogeneity As mentioned in SectionII this inhomogeneity was not intentional but was a result ofmacrosegregation occurring during solidification of the sampleafter cold crucible induction melting The nonuniform samplenonetheless yields important data as it gives information aboutthe tie-triangles of different equilibria in the Nb-Pd-Hf-Al quar-ternary phase diagram Three 3-phase and one 2-phase region





Pd3Hf 04 6 05 735 6 13 246 6 11 14 6 03 a 5 056178 6 000030c 5 092019 6 000030


Pd3Hf 06 6 03 754 6 03 236 6 02 04 6 04 a 5 055653 6 000030c 5 091988 6 000030

(a)

(b)




















1500 degC (Nb) 896 6 08 39 6 04 21 6 02 44 6 04 a 5 032962 6 000005Pd2HfAl 02 6 02 516 6 05 229 6 03 253 6 05 a 5 063759 6 000002




As cast Pd2HfAl 00 496 6 04 253 6 03 251 6 04 a 5 063680





















(a) (b)


(c)


[1]

[2]

[3]






209695XNbXPd

VNb2Pda 3 103 nm3 5 17980XNb114815XPd

203573XHfXNb

VNb2Hfa 3 103 nm3 5 21815XHf 1 17980XNb


h

VNb2Ala 3 103 nm3 5 17169XAl 1 17980XNb

[4]


[5]




[6]

with



a yIj 5 a yII

j 5 a yIIIj 5 1

1 4 an

j21yII

j VL21j 1 4 a

n

j21

IIIj V L21

j a3 5 8 an

j5 1yI

jVL21j

a (nm) 5o3

2Va



h 1 17980XNb 1 14815XPd

Va 3 103 nm3 5 17169XAl 1 21815XHf









[7]



[8]


[9]


[10a]

[10b]


[11]


[12a]

[12b]


[13a]

or

[13b]


2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl


dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf




[14]

[15]






b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28






Pd3Hf 04 6 05 735 6 13 246 6 11 14 6 03 a 5 056178 6 000030c 5 092019 6 000030


Pd3Hf 06 6 03 754 6 03 236 6 02 04 6 04 a 5 055653 6 000030c 5 091988 6 000030

(a)

(b)




















1500 degC (Nb) 896 6 08 39 6 04 21 6 02 44 6 04 a 5 032962 6 000005Pd2HfAl 02 6 02 516 6 05 229 6 03 253 6 05 a 5 063759 6 000002




As cast Pd2HfAl 00 496 6 04 253 6 03 251 6 04 a 5 063680





















(a) (b)


(c)


[1]

[2]

[3]






209695XNbXPd

VNb2Pda 3 103 nm3 5 17980XNb114815XPd

203573XHfXNb

VNb2Hfa 3 103 nm3 5 21815XHf 1 17980XNb


h

VNb2Ala 3 103 nm3 5 17169XAl 1 17980XNb

[4]


[5]




[6]

with



a yIj 5 a yII

j 5 a yIIIj 5 1

1 4 an

j21yII

j VL21j 1 4 a

n

j21

IIIj V L21

j a3 5 8 an

j5 1yI

jVL21j

a (nm) 5o3

2Va



h 1 17980XNb 1 14815XPd

Va 3 103 nm3 5 17169XAl 1 21815XHf









[7]



[8]


[9]


[10a]

[10b]


[11]


[12a]

[12b]


[13a]

or

[13b]


2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl


dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf




[14]

[15]






b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28













1500 degC (Nb) 896 6 08 39 6 04 21 6 02 44 6 04 a 5 032962 6 000005Pd2HfAl 02 6 02 516 6 05 229 6 03 253 6 05 a 5 063759 6 000002




As cast Pd2HfAl 00 496 6 04 253 6 03 251 6 04 a 5 063680





















(a) (b)


(c)


[1]

[2]

[3]






209695XNbXPd

VNb2Pda 3 103 nm3 5 17980XNb114815XPd

203573XHfXNb

VNb2Hfa 3 103 nm3 5 21815XHf 1 17980XNb


h

VNb2Ala 3 103 nm3 5 17169XAl 1 17980XNb

[4]


[5]




[6]

with



a yIj 5 a yII

j 5 a yIIIj 5 1

1 4 an

j21yII

j VL21j 1 4 a

n

j21

IIIj V L21

j a3 5 8 an

j5 1yI

jVL21j

a (nm) 5o3

2Va



h 1 17980XNb 1 14815XPd

Va 3 103 nm3 5 17169XAl 1 21815XHf









[7]



[8]


[9]


[10a]

[10b]


[11]


[12a]

[12b]


[13a]

or

[13b]


2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl


dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf




[14]

[15]






b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28
















(a) (b)


(c)


[1]

[2]

[3]






209695XNbXPd

VNb2Pda 3 103 nm3 5 17980XNb114815XPd

203573XHfXNb

VNb2Hfa 3 103 nm3 5 21815XHf 1 17980XNb


h

VNb2Ala 3 103 nm3 5 17169XAl 1 17980XNb

[4]


[5]




[6]

with



a yIj 5 a yII

j 5 a yIIIj 5 1

1 4 an

j21yII

j VL21j 1 4 a

n

j21

IIIj V L21

j a3 5 8 an

j5 1yI

jVL21j

a (nm) 5o3

2Va



h 1 17980XNb 1 14815XPd

Va 3 103 nm3 5 17169XAl 1 21815XHf









[7]



[8]


[9]


[10a]

[10b]


[11]


[12a]

[12b]


[13a]

or

[13b]


2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl


dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf




[14]

[15]






b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28



[1]

[2]

[3]






209695XNbXPd

VNb2Pda 3 103 nm3 5 17980XNb114815XPd

203573XHfXNb

VNb2Hfa 3 103 nm3 5 21815XHf 1 17980XNb


h

VNb2Ala 3 103 nm3 5 17169XAl 1 17980XNb

[4]


[5]




[6]

with



a yIj 5 a yII

j 5 a yIIIj 5 1

1 4 an

j21yII

j VL21j 1 4 a

n

j21

IIIj V L21

j a3 5 8 an

j5 1yI

jVL21j

a (nm) 5o3

2Va



h 1 17980XNb 1 14815XPd

Va 3 103 nm3 5 17169XAl 1 21815XHf









[7]



[8]


[9]


[10a]

[10b]


[11]


[12a]

[12b]


[13a]

or

[13b]


2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl


dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf




[14]

[15]






b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28



[7]



[8]


[9]


[10a]

[10b]


[11]


[12a]

[12b]


[13a]

or

[13b]


2b

1 1dxHf

da3

da

dxPd

cVAl

3a2

o

16b da

dxPd

c 5 VPd 1

bdxHf

da3

da

dxPd

cV Hf

3a2o

16

b da

dxPd

c5 VPd 1

bdxHf

dxPd

cVHf 2 (1 1

dxHf

dxPd)VAl


dnPd 5 100dxPd

2 425

b

1 2 dnII

Pd

dnPd

cVAl lt 3a2

oda

dnPd

3a2 da

dnPd

58

50VPd 2

425

dnPdII

dnPd

VHf

nPd

and xHf 5(25 2 nII

Pd )

1005

14

2 nII

Pd

100

xPd 5(50 1 n

Pd)

1005

12

1n

Pd

100

nPd 5 nII

Pd 1 nIIIPd

nPd

14

25 (25 2 nIII

Pd )V Al 5 a3

V 5850

(50 1 nPd )VPd 1

425

(25 2 nIIPd )V Hf




[14]

[15]






b dadXPd

c

VPdAlAl 5

a3o

22

3a2o

4b da

dXPd

c

VPdAlPd 5

a3o

21

3a2o

4b da

dXPd

c










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28










eda

dXHf








dadxHf

5

dadxPd 5

dadxHf

dadxPd









at 1200 degC 02 6 02 572 6 05 192 6 06 234 6 05 063159 6 000005 063226 6 00005 2011Alloy 995

at 1500 degC 06 6 04 571 6 06 196 6 08 227 6 05 063331 6 000001 063280 6 00007 008Alloy 996

at 1500 degC 02 6 02 516 6 05 229 6 03 253 6 05 063759 6 000002 063507 6 00008 039


[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28



[16]




[17]



[18]



2aNb

c3 100

aPd2HfAl(nm) 5 06367g1 1 863 3 1026(T2298)

h

(T2298) 1 39363 3 10210(T2298)2 haNb(nm) 5 033007

g1 1 82987 3 1026


IV CONCLUSIONS








ACKNOWLEDGMENTS









25 032962 063759 3281300 033331 064461 330







































vol 22 pp 424-28







































vol 22 pp 424-28


phase equilibria in prototype nb-pd-hf-al alloyssrg.northwestern.edu/publications...

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