anomalous elastic behavior in hcp- and sm-type dysprosium

Published: September 09, 2011

r 2011 American Chemical Society 2090 dx.doi.org/10.1021/jp205156v | J. Phys. Chem. C 2012, 116, 2090–2096

ARTICLE

pubs.acs.org/JPCC

Anomalous Elastic Behavior in hcp- and Sm-Type DysprosiumOliver Tschauner,*,† Ognjen Grubor-Urosevic,† Przemyslaw Dera,‡ and Sean R. Mulcahy§,^

†High Pressure Science and Engineering Center, Department of Physics, University of Nevada, Las Vegas, Las Vegas, Nevada 89154-4002, United States‡Center of Advanced Radiation Sources, Argonne National Laboratory, University of Chicago, Argonne, Illinois 60439, United States§Department of Geoscience, University of Nevada, Las Vegas, Las Vegas, Nevada 89154-4002, United States^Department of Geoscience, University of California Berkeley, Berkeley, CA, United States

I. INTRODUCTION

The principal features of the phase diagram of lanthanides wereworked out many years ago.1�4 The sequence of structuresoccurring with increasing compression of a lanthanide metal isalso found at ambient conditions as a sequence of structuresoccurring along with decreasing atomic number. Thus, at a givenpressure, the lanthanide contraction induces stabilization of struc-tures that occur for lighter lanthanides at lower (or hypotheticallynegative) pressure; the phases found in light lanthanides atambient pressure occur in heavier lanthanides at elevated pressurewith transformation pressure increasing with atomic number.

Duthie and Pettifor,5 Johansson and Rosengren,2 and subse-quently Skriver6 successfully explained these systematics as resultof partial occupancy of 5d-like bands hybridized with the valence6s-like bands. This regular sequence of lanthanide phase trans-formations suffers some exceptions4 because of magnetism (Eu,Yb) and contributions from f electrons to the valence state (Ce).The gradual change in chemical potential with pressure accountsfor many of the interesting properties of lanthanides. In parti-cular, it is worthwhile examining the detailed response of elasticproperties to the changes in electronic density of state at Fermilevel and to eventual topological changes of the Fermi surface.

Here, we revisit the transition from the hcp- to Sm-typestructure in one of the heavier lanthanides: dysprosium. Earliercompression studies on Dy mostly focused on the high-pressurephases,7,8 and the compression behavior of the hcp- and the Sm-type phases is presently constrained only by a few data points.Weshow the occurrence of elastic anomalies in both phases in theabsence of observable structural changes. In hcp-type dyspro-sium, these elastic anomalies are accompanied by sharp changesin the pressure derivative of the c/a ratio.

II. EXPERIMENTAL SECTION

Dy specimens of 10�150 μm edge length and hexagonal�prismatic or rhombohedral crystal habit were selected from ali-quots of Dy metal crystallized in tantalum crucibles. The samplematerial was analyzed with a Jeol JXA-8900 Superprobe electronprobemicroanalyzer (EPMA) using 20 keV accelerating voltage and10nAbeamcurrent and found to have a purity of >97%(Dy99.73%,Ce 0.08%, Nd 0.06%, Eu 0.06%, Sc 0.02%, all other impurities<0.01%). Individual crystal specimens were examined by wideoscillation diffraction records using a MAR345 detector at X-raydiffraction station B2; CHESS and the GSE-ADA 1.1 software,for extraction of angular coordinates.11 We found that of severaldozens apparent single crystals, all were composed of multiplesubindividua slightly titled relative to each other (Figure 1).

In a first step of data evaluation, we attempted to index allreflections of all crystallites as belonging to the hcp phase. Wealso attempted indexing without extinctions and allowing forreplication of the cell dimensions in both the a + b and cdirections. In other words, we examined if the observed addi-tional reflections were the result of stacking faults. However, allsuch fits suffered from marked angular mismatch and suggestedlarge density reductions of the hcp cell. Both observations indi-cate that a subset of reflections belongs to a different phase. Unex-pectedly, we found that all examined crystals were intergrowths

Special Issue: Chemistry and Materials Science at High PressuresSymposium

Received: June 1, 2011Revised: August 12, 2011

ABSTRACT: The compression behavior of elemental dysprosium in the hcp- andthe Sm-type phases has been examined under hydrostatic pressure. Sm-type Dy hasbeen found about 1% denser than the hcp phase. This increase in density is due toc-axis contraction in Sm-type Dy, whereas the a-axis even expands compared with thehcp-phase. Both the hcp- and the Sm-type phases show an inversion in the pressurederivative of the c/a ratio. For hcp-Dy this inversion is very sharp withminimal c/a at2.5 GPa. At the same pressure, the compression behavior of hcp-Dy changesabruptly from dominantly c-axis compression to almost isotropic compression withslightly softer S11. The bulk modulus increases at this point by a factor of∼2. Bothhcp- and Sm-type Dy exhibit a crossover from highly anisotropic compressionmostly along the c-axis to almost isotropic compression. We discuss these anomalieswith respect to a possible Lifshitz transition and structural soft modes.

2091 dx.doi.org/10.1021/jp205156v |J. Phys. Chem. C 2012, 116, 2090–2096

The Journal of Physical Chemistry C ARTICLE

of domains of hcp- and Sm-type dysprosium. Recovery of theSm-type phase from high pressure has been reported for heavylanthanides including Dy.9,10 However, it seems surprising thatthe high-pressure phase already occurs in the starting material.On the other hand, intergrowth of dhcp- and fcc-type La arecommonly observed in lanthanum samples synthesized at ambientconditions, although the transformation between dhcp- and fcc-La occurs at 2.6 GPa.12

The density difference between hcp- and Sm-type phases oflanthanides is smaller than that between dhcp- and fcc-La. Wechoose two multidomain crystals of minimal internal strain with20 � 20 μm edge length and 10 μm thickness and loaded onespecimen in a 4:1 methanol�ethanol mixture; the other one, inneon in diamond cells with wide-angle slotted backing plates of15�� 40�X-ray aperture. Neonwas loaded into the diamond cellwith a high-pressure gas loading device at GSECARS, APS, ANL.No reaction of sample and pressure media was observed overseveral days and after recovery. Diffraction experiments werecarried out in ω-step scan mode with 1� step width and atdifferent fixed χ-angle settings at B2, CHESS using a MAR 345image plate detector. A primary beam of 25.514 keV energy wascollimated to 150 μm diameter. All experiments were conductedat 300 K. Because of plastic deformation of the gasket after eachincrease in the load, the diffraction experiments were started notbefore 1/2 h after each increase, and the pressure was monitoredbefore and after data accumulation. Pressure was determinedspectroscopically with the ruby fluorescence method.13

The fact that all samples were composed of several intergrowncrystal subindividua of two phases in combination with thelimited aperture of the diamond anvil cell made it difficult todetermine the orientation of each subindividuum. Therefore, werefined cell shapes of the coexisting hcp- and Sm-type Dy usingthe d-spacings of the observed reflections of both phases usingUnitcell.14 We observed in total between 20 and 30 reflections,disregarding side peaks at equal Bragg angle, such as those shownin Figure 1a. These sets of reflections yielded between 6 and 8symmetry-merged reflections for the hcp- and 8�10 mergedreflections for the Sm-type phase. Wherever we had at least 8merged reflections, we refined cells both with symmetry con-straints and in triclinic metric to assess the internal strain in thesamples. We evaluated the dimensions of all coexisting crystal-lites wherever the number of reflections was sufficient and foundthat variations on cell parameters were always within twice theuncertainties of the cell refinements.

Table 1 lists the merged sets of reflections for Sm- and hcp-type Dy at 5.89 GPa plus observed and calculated d-spacings asan example. The indexing of three crystallites of the Sm-typephase (Table 1) agrees within margins significantly smaller thanthe pressure-induced changes in cell parameters between pres-sure points (Table 2). In addition, the symmetry-unconstrainedindexing agrees similarly well with the hexagonal indexing. Bothobservations indicate that internal strain in the Dy multidomaincrystal and its evolution with increasing compression is smallerthan the pressure-induced changes in cell parameters.

A marked deviation between the angles in the triclinic indexingfrom hexagonal values indicates large strain in the whole sampleand signals anomalous softening, since the sample is embedded in

Figure 1. Left side: Reflection -44-1 of hcp-Dy. One distinguishes twopeaks at equal 2ϑ that have slightly different angular χ (and, not visible,ω) coordinates, indicating that they belong to two crystal domains ofsimilar orientation. Right side: Reflections 202 and 119 of Sm-type Dy.As in the case of hcp-typeDy, there are two ormore domains. The visiblemosaicity indicates that the crystallites are slightly strained.

Table 1. List of Calculated and Observed d-Spacings (Å) forthe Symmetry-Merged Set of Reflections of Sm-Type andhcp-Dy at 5.89 GPaa

(a) Sm-Type Phase

Xtal I Hexagonal Indexing Triclinic Indexing

h k l

d

(obs)

d

(calcd)

res

(d)

d

(obs)

d

(calcd)

res

(d)

1 1 9 1.515 74 1.517 4 �0.001 67 1.515 74 1.515 74 0

1 0 16 1.450 19 1.457 33 �0.007 14 1.450 19 1.450 47 �0.000 28

0 0 9 2.911 1 2.944 51 �0.033 4 2.911 1 2.948 95 �0.037 84

0 3 9 0.966 08 0.965 72 0.000 35 0.966 08 0.966 08 0

0 0 15 1.777 81 1.766 7 0.011 1 1.777 81 1.769 37 0.008 44

2 0 5 1.471 1.472 99 �0.001 99 1.471 1.470 3 0.000 71

0 2 19 1.034 21 1.031 79 0.002 42 1.034 21 1.034 21 0

2 0 2 1.523 45 1.523 23 0.000 21 1.523 45 1.523 23 0.000 21

b) Sm-Type Phase Xtal II Hexagonal Indexingh k l d (obs) d (calcd) res (d)

0 2 4 1.497 1 1.495 0 0.002 0

1 1 15 1.253 6 1.252 2 0.001 4

0 0 21 1.267 0 1.264 2 0.002 8

0 2 10 1.333 4 1.328 5 0.004 8

1 2 11 1.043 2 1.045 5 �0.002 2

1 0 13 1.686 6 1.700 2 �0.013 6

0 2 19 1.034 21 1.031 79 0.002 42

2 0 2 1.523 45 1.523 23 0.000 21

b) hcp-Type Phaseh k l d (obs) d (calc) res (d)

0 2 0 1.521 7 1.520 53 0.001 17

2 1 3 0.966 08 0.971 87 �0.005 79

2 0 1 1.471 55 1.464 8 0.006 74

1 0 3 1.566 04 1.561 83 0.004 2

0 1 3 1.565 86 1.561 83 0.004 03

2 0 1 1.467 1.464 8 0.002 2aThere were a total of 8 reflections for the hcp- and 18 reflections for theSm-type phase. (a) The Sm-type cell was refined both with and withoutsymmetry constraint. The latter refinement gave a cell 3.541(14) �3.528 (14)� 26.546(33) Å3 with α = 89.22(21)�, β = 91.15(25)�, andγ = 119.75(40)�. The deviations from the hexagonal metric indicatelattice strain. (b) The hcp-type cell was refined with symmetry con-straints only. Indexing of a second crystallite of Sm-type Dy at 5.89 GPa.The refined cell parameters are a = 3.544(1) Å and c = 26.544(14) Å.A third crystal has dimensions a = 3.543(1) Å and c = 26.549(14) Å.



a hydrostatic medium and internal stresses within the sample areexpected to be rather low. Moreover, a significant discrepancybetween symmetry-constrained and unconstrained indexing in-dicates that cell shapes and volumina from the symmetry-con-strained cell refinement may not be reliable in the absence of fullythree-dimensional reciprocal space data. We found such a stronganisotropic deformation in Sm-type Dy at 2.73 GPa. The numberof reflections for hcp-Dy was in most cases too low to allow for atriclinic indexing. Above 6 GPa, we observed that the total numberof observed reflections from the hcp phase decreased, and evensymmetry-constrained indexing gave high residuals. For thisreason, we discarded the cell refinements for hcp-Dy above 6GPa. The refined cell parameters for Dy in the hcp- and the Sm-type structures as a function of pressure are listed in Table 2.

III. DISCUSSION

Figure 2 shows the volume of hcp- and Sm-type Dy as afunction of pressure at 300 K. The volume of the Sm-type phasehas been divided by a factor of 5 for better comparison. We notethat the measured volume of Sm-type Dy at 2.73 GPa and thevolume of hcp-Dy above 6 GPa have been omitted here and inany further discussion for the reasons given in the Experimentalsection. Figure 2a shows clearly a small but distinct densitydifference between Sm- and hcp-type Dy. The Sm-type phase is∼1% denser than the hcp-phase throughout the examinedpressure range. This compares well with reports on the densitydifference between hcp- and Sm-type phases of Tb and Gd of 1.0and 1.3%, respectively.10 Above 2�3 GPa, the compressibility ofhcp-Dy appears noticeably reduced compared with the 0�2 GPa

regime. This effect is more pronounced in the axial compres-sion behavior (Figure 3, lower panel): The a-axis compression of

Table 2. Cell Parameters and Volumina of Dy as a Functionof Pressurea

(a) pressure (GPa) a (Å) c (Å) V (Å3)

0 3.603(2) 5.582(2) 62.755(10)

0.41 3.598(1) 5.575(3) 62.50(5)

0.78 3.590(3) 5.553(4) 61.94(10)

2.29 3.557(1) 5.487(2) 60.11(4)

2.73 3.556(4) 5.48(3) 59.96(7)

3.70 3.541(2) 5.473(3) 59.30(10)

4.67 3.529(2) 5.467(4) 58.96(8)

5.89 3.511(1) 5.461(4) 58.30(8)

(b) pressure (GPa) a (Å) c (Å) V (Å3)

0 3.623(2) 27.567(55) 313.39(42)

0.41 3.612(1) 27.357(11) 309.16(22)

0.78 3.600(4) 27.212(15) 305.42(70)

2.29 3.582(1) 26.916(12) 299.08(31)

2.73 3.555(7) 26.771(11) 293.01(22)

3.70 3.558(1) 26.754(9) 293.41(22)

4.67 3.555(1) 26.637(12) 291.53(14)

5.89 3.541(1) 26.500(12) 287.80(18)

6.85 3.518(3) 26.459(14) 283.59(29)

9.07 3.482(2) 26.355(5) 276.73(37)aThe data points at 0.78 and 3.70 GPa were collected on a samplecompressed in a neon pressure medium. All other data are from anexperiment with a methanol�ethanol medium. (a) Cell parameters andvolumes of hcp-type dysprosium as function of pressure. Uncertaintiesin brackets. (b) Cell parameters and volumes of Sm-type dysprosium asfunction of pressure. Uncertainties in brackets.

Figure 2. Unit cell volume of Dy (Å3) as function of pressure (GPa).],hcp-Dy; 9, Sm-type Dy (labeled as hR9). Sm-type Dy is always denserthan hcp-type Dy by ∼1%. Around 2 GPa, the pressure dependence ofbulk compressibility of hcp-Dy decreases.

Figure 3. Evolution of cell axis length with pressure.], hcp-Dy;9, Sm-type Dy (labeled as hR9). Units are Å. Upper panel, c-axis; lower panel,a-axis. The c-axis is significantly softer than the a-axis for both phases atlow pressure. In hcp-Dy, the c-axis exhibits a noticeable change incompressibility around 2.5 GPa. In Sm-type Dy, the c-axis becomesgradually less compressible.



hcp- and Sm-type Dy changes almost linearly with pressure. Thea-axis of Sm-type Dy is larger throughout the examined pressurerange. Thus, the higher density of the Sm-type phase is solely theresult of c-axis contraction relative to the hcp-type phase. Around3�4 GPa, the a-axis of Sm-type Dy exhibits a small decrease incompression. Above 4 GPa, axial compression is linear, with aslope smaller than between 0 and 2 GPa.

The c-axis compression in both hcp- and Sm-type Dy is muchdifferent (Figure 3, upper panel): c-axis compression exhibits asignificantly stronger pressure dependence than the a-axis com-pression; in particular, within the first two GPa's. Moreover, inhcp-Dy, there is a sharp transition from this soft compressionregime to much stiffer behavior above 2.5 GPa. In contrast, Sm-type Dy c-axis compression decreases rather gradually. Wefurther illustrate this unexpected highly anisotropic compressionbehavior in hcp-type Dy by examining incremental axial com-pressibilities as function of pressure. The experimentally mea-sured axial elastic strain, εii, under hydrostatic conditions relatesto the axial compressibility, Sii, as εii =�P(Sii) where P = σijδij isthe hydrostatic pressure, and σij, the stress. The axial compres-sibilities relate to the longitudinal elastic compliances in thehexagonal system as S11 = S22 = (s1111 + s1122 + s1133) and

S33 = (2s1133 + s3333).15We assumeHooke’s law to be valid within

each experimental pressure increment, ΔP, and calculate axialcompressibilities Sii = �εii/P ∼ Δai/ai 0.1/ΔP (i = 1, 2, 3 anda1 = a2 = a, and a3 = c). We note that the conditions of Hooke’slawmay not be exactly fulfilled in pressure increments that encom-pass marked changes in the elastic properties. However, thecalculated Sii serve primarily to illustrate the pressure-inducedchanges in elastic behavior of Dy.

Figure 4, upper panel, shows the S33 axial compressibity ofhcp- and Sm-type Dy (diamonds and solid squares, respectively).We note that the pressure points plotted in Figure 4 are themiddle pressures of each pressure increment for which thecompressibility was determined. Thus, they are intermittent tothe pressures given in Table 1 and Figure 2. Further, the pressurepoints for axial compressibilities of the two phases differ slightlyabove 2 GPa because the 2.73 GPa data point for the Sm-typephase has been discarded (see the Experimental Section). S33decreases by a factor of 3�10 within 2�3GPa for both phases. Inhcp-Dy, there is a sharp transition from a regime of largecompressibility with strong pressure dependence to a regime oflow compressibility with insignificant pressure dependence. Thistransition occurs between 2.5 and 3 GPa.

Figure 4. (a) Axial compressibilities S11 and S33 as a function of pressure. Upper panel, S33; lower panel, S11. ], hcp-Dy; 9, Sm-type Dy (labeled ashR9). The figure illustrates that S33 in both materials changes dramatically with pressure, but S11 remains almost pressure-invariant. In hcp-Dy, thecompression behavior changes abruptly at 2.5 to 3 GPa from dominantly c-axis compression to almost isotropic compression with slightly softer S11. InSm-type Dy, S33 becomes gradually stiffer with increasing pressure, suggesting an elastic anomaly at ambient pressure or under slight torsion. (b) Bulkmodulus of hcp- and Sm-type Dy as a function of pressure (upper and lower panel, respectively). The bulk modulus of hcp-type Dy increases between 2and 3 GPa by about a factor of 2, disregarding a potential singularity at 2.5 GPa.



S33 of the Sm-type phase exhibits a more gradual change fromhigh to low values. In contrast to the unusual compression behaviorof Dy along the c-axis, S11 does not exhibit any anomalous featuresfor either phase. The scatter of S11 in the hcp phase is too large toobserve subtle changes. In Sm-type Dy, S11 exhibits a gentle localminimum between 1 and 4 GPa that reflects the intermediate lowa-axis compression already seen in Figure 3, upper panel.

The bulk modulus of hcp-type Dy (Figure 5 upper panel)increases between 2 and 3 GPa by about a factor of 2: Below 2GPa, it is 25 ( 7 GPa; above 3 GPa, it is 55 ( 7 GPa both onaverage. This sudden increase is obviously related to the changein c-axis compression at 2.5 GPa. Right at 2.5 GPa, there may be asingularly high B as result of an unusually low correspondingvalue of S11. However, the uncertainty for both S11 and B at thispressure is quite large, and therefore, we do not discuss here thepossibility of such a singularity any further.

In Sm-type Dy, the bulk modulus is initially very low andincreases between 1 and 2 GPa to a rather constant value of42( 8GPa from 2 to 9 GPa. The substantial softening of B towardambient pressure is obviously due to the softening of S33 (Figure 4).

Figure 6 shows the c/a ratio of hcp- and Sm-type Dy. The axialratio of Sm-typeDy ismarkedly lower than the ratio of hcp-typeDy.The lower c/a of Sm-type Dy is the result of the c-axis contractionalong with a-axis expansion upon transition from hcp-type Dy(Figure 3). We recall that the geometric c/a ratio of an hcp-latticebuilt from hard spheres is ∼√

8/3�1.633. Lanthanides in the hcpstructure exhibit generally much lower c/a ratios. This fact has beenexplained by Zheng-Johansson et al.,16 who showed that anom-alously small c/a ratios in hcp structures reflect anisotropic filling ofthe d-like bands hybridized with the s-like valence band.

Dutrie and Pettifor5 and Skriver6 successfully explained thestructural transitions of the lanthanides by different degrees ofoccupancy of the 5d bands. Sm-type phases of lanthanides exhibitd-band occupancy of 1.75�1.85 electronic charge equivalents,6

and the hcp phases are stable with occupancies below 1.75.6 Thetransition from the hcp- to the Sm-type phase in Dy thereforecorresponds to an increase in the occupancy of d-like bands nearthe Fermi level beyond 1.75 electrons by enhanced hybridization

with s-like bands. Calculations of the electronic band structure inheavy lanthanides17,18 indicate that the density of s- and d-likebands near the Fermi level is high in the a�b plane in the hcp-type phase but rise far above and below the Fermi level along thedirections from the Brillouin zone points R and Q toward A.17,18

This picture is confirmed by measurements of the valence bandstructure and Fermi surface of Tb by ARPES19 showing theFermi surface basically as ring-enclosed by a hexagon withcommon axes along Δ. Hence, the increase in the electrondensity near the Fermi level upon compression of hcp- andSm-type Dy occurs mostly in the a�b plane, and consequently,the screening of the Coulomb repulsion is reduced in the a�bplane. In other words, the electron density distribution of the Dyatoms extends upon compression to farther away from the nucleiin the a�b plane, but it remains close to the nuclei along thec-axis. This is equivalent to a deformation of metal radii toellipsoids with long axes in the a�b plane in a quasiclassicalmodel (which had been proposed earlier as an explanation ofphase transformation in lanthanides and actinides20).

In sum, the low axial compressibility, S11, can tentatively beexplained by a gradually reduced Coulomb screening in the a�bplane upon compression. The soft S33 in both phases is com-pensatory. The c-axis contraction and the expansion of the a-axis

Figure 5. Axial ratio, c/a, of hcp- and Sm-type Dy as a function ofpressure.], hcp-Dy;9: Sm-type Dy (labeled as hR9). For both phases,the pressure-evolution of c/a changes sign. In hcp-Dy, the inversion isvery sharp at 2.5 GPa. This is also the pressure of the change in the c-axisand bulk compression and may mark an isostructural electronictransition.

Figure 6. Unit cell volume of Dy (Å3) as function of pressure (GPa).9,present study; hashed ], data from references.7,8,30 The data by Bridg-man30 match our compression data of hcp-Dy very well, but other dataare closer to our compression data of the Sm-type phase. These data7,8

may be affected by strain. It is also possible that some of these resultssuffer from misindexing reflections from the Sm-type phase as hcp andvice versa if oriented intergrowth of both phases passed unnoticed.



upon transition to the Sm-type phase have the same origin, whichthen also accounts for the reduction in the c/a ratio comparedwith the hcp-type phase.

An unexpected feature in the pressure evolution of the c/aratio for both phases of Dy is the inversion of the pressure-derivative at 2.5 GPa for hcp- and at 6 GPa for Sm-type Dy. Theinversion is quite sharp (within 1 GPa) for hcp-type Dy, and itmatches the pressure of abrupt change in c-axis compressibility,S33 (Figure 4, upper panel). This suggests that both phenomenaare related. An inversion of the pressure derivative of the c/a ratiowith accompanying elastic anomalies has been reported for α-Co.21 It has been shown that this phenomenon is related to anantiferro- to paramagnetic transition in α-Co.21 However, therehas been no indication that Dy in the hcp- or Sm-type phase ismagnetically ordered between 1 and 10 GPa at 300 K.22,23

Marked changes in the compression behavior of solids maynot be uncommon over extended pressure ranges. However, thevery strong change in c-axis compressibility in hcp-Dy occurswithin a very narrow pressure range rather than as a continuousevolution throughout the examined pressure range. Nonetheless,this abrupt change in compression behavior does not correspondto an observable structural change in hcp-Dy. The term “abrupt”refers to the fact that this change occurs within a 1 GPa interval,whereas commonly pressure-induced changes in compressionbehavior (for instance, from competing repulsive forces alongdifferent bond vectors) occur over pressure intervals on the orderof the bulk modulus.

Above, we have argued that the inversion of the pressurederivative of c/a is related to the pressure-induced hybridizationof s- and d-like bands at Fermi level. However, it needs to bediscussed why this change occurs as a sharp transition in hcp-typeDy. Further, it remains to be seen why the anisotropic compres-sion of hcp-Dy does not simply continue until all hcp-Dy istransformed to the Sm-type phase. It is also unclear why thechange in the pressure evolution of the axial compressibilitiesoccurs in a sharp, transition-like, rather than continuous, fashion.Elastic anomalies without apparent structural change can indicateLifshitz transitions.24,25 Such “topological” transitions have beenreported for Cd and Zn26,27 and have been proposed for Os,28 allelemental metals assuming the hcp-structure.

Tension experiments on hcp-type Tb indicated an elasticanomaly, which has been interpreted as due to a Lifshitztransition.29 The Fermi surface of Dy is not known; however,its symmetry is expected to be equal to that of the Fermi surfaceof isotypic Tb.19 In hcp-Dy, the anomalous abrupt change incompression behavior at 2.5 GPa affects S and S33, but not S11.However, the Fermi-surface does not intersect kz (001). Conse-quently, the s3333 compliance cannot be affected by any topolo-gical change of the Fermi surface. However, S33 also includes thes1133 compliance, which is correlated to the longitudinal acousticphonon branch intersecting the Brillouin zone boundary at L andH (which are symmetry equivalent in the hexagonal system). TheFermi surface intersects any ray between Γ and L or H, and atopological change can therefore affect a phonon branch runningtoward L and H. The known strong correlation between the c/aaxial ratio and changes in the electronic structure of lanthanidesin general and the observation of a sharp inversion of c/a at2.5 GPa in hcp-type Dy together support the suggestion of anabrupt change in electronic structure at 2.5 GPa.

One can also argue that the c-axis compression of hcp-typeDy above 2.5 GPa is normal, but the significant softeningtoward ambient pressure indicates a softmode process. However,

the hcp-phase is the thermodynamic phase of Dy at ambientconditions.

In the case of Sm-type Dy, such an argument can be made. Apossible critical anomaly at ambient pressure and temperature orunder torsion matches conditions where the Sm-type phase is notstable. Other than in the case of hcp-type Dy, the crossover fromhigh to low axial compression along the c-axis is not abrupt butgradual. Therefore, a soft mode process in metastable Sm-type Dyat ambient pressure is conceivable. We also note that the sig-nificant softening of S33 toward ambient pressure is correlatedwitha strong softening of the bulk modulus (Figure 4b), suggesting anelastic instability at ambient pressure or under tension.

It is useful to compare the present data on the compression ofDy in a hydrostatic medium with earlier results. In all earlierstudies, either solid7 or no pressure transmitting medium8 wasemployed. Thus, in comparison with the present work, thesestudies allow us to examine the response of Dy to largeranisotropic stresses (nonhydrostatic conditions).

Figure 6 shows a comparison of the pressure�volume relationof Dy as reported in the earlier studies (diamonds) and from thepresent study (solid squares). We note that the two data points byBridgman30 match our results for the compression of hcp-Dy verywell, whereas results from two other studies7,8 are a closermatch toour volume data for Sm-type Dy. This suggests that some of theprevious experiments suffer from misindexing Sm-type reflectionsas hcp or that pressure gradients in experiments without mediumsignificantly affect the apparent volume compression.

We note that the present data, although collected on a samplecompressed by a hydrostatic medium, may not represent fullyhydrostatic conditions because the examined specimens wereintergrowth of hcp- and Sm-type Dy crystals. These intergrowthswere highly oriented, but differences in the elastic response to theapplied hydrostatic pressure induce small anisotropic stressesbetween these crystallites. We found strain-induced differencesbetween cell parameters of coexisting crystallites to be markedlysmaller than the observed pressure-induced changes, but we notethat even small anisotropic stress fields can trigger structural andelectronic transitions.

IV. CONCLUSIONS

The present study examines the compression behavior ofdysprosium in the hcp- and the Sm-type phases. We find a smallbut distinct density difference between the hcp- and Sm-typephases of ∼1%. This difference results from a marked contrac-tion of the c-axis of the Sm-type phase compared with the hcp-type phase. This contraction alongwith an expansion of the a-axisresults in a much smaller c/a axial ratio of the Sm-type phase.These effects as well as the comparatively stiff a- and soft c-axiscompressions are tentatively explained by the known changes inthe s�d band hybridization at the Fermi level in compressedlanthanides. These changes result in an increase in electrondensity near th eFermi level upon compression, mostly in thea�b plane, and consequently, the screening of the Coulombrepulsion is reduced in the a�b plane. For both hcp- and Sm-typeDy, the pressure derivative of the axial ratio c/a changes sign. Inthe case of hcp-Dy, this inversion is very sharp with minimal c/aat 2.5 GPa. At the same pressure, the compression behavior ofhcp-Dy changes abruptly from dominantly c-axis compression toalmost isotropic compression with slightly softer S11. The bulkmodulus increases at this transition by a factor of ∼2. Thischange in elastic properties is not accompanied by an observable



structural transition. We examined the transition-like elasticanomaly in hcp-type Dy at 2.5 GPa with respect to a possibleLifshiz transition and note that a potential topological changemay occur along the ray between Γ and L.

Sm-type Dy exhibits significant softening of S33 towardambient pressure. Other than in the case of hcp-Dy, the crossoverfrom very soft to stiff axial compression along the c-axis is gradual.In addition, Sm-type Dy exhibits substantial softening of the bulkmodulus below 1 GPa. Both the axial and the bulk elasticsoftening suggest proximity of an elastic instability in metastableSm-type Dy at ambient conditions.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

’ACKNOWLEDGMENT

We gratefully acknowledge comments by an anonymousreviewer and discussions with the late M. F. Nicol and with D.Schiferl as well as technical support and provision of beamtime atstation B2, CHESS, by Z. Wang and P. Sorensen. This projectwas supported by the NNSA Cooperative Agreement DE-FC52-06NA27684 and NSF-MRI Award DMR-0521179. CHESS issupported by the NSF & NIH/NIGMS via NSF award DMR-0225180.We acknowledge S. Tkachev,GSECARS, andCOMPRESfor the use of the gas loading system at GSECARS (Sector 13),APS, ANL. GSECARS is supported by the NSF and DOE viaAwards EAR-0622171 andDE-FG02-94ER14466. COMPRES issupported by the NSF Cooperative Agreement EAR 10-43050.

’REFERENCES

(1) Jayaraman, A.; Sherwood, R. C. Phys. Rev. 1964, 134, A691.(2) Johansson, B.; Rosengren, A. Phys. Rev. B 1975, 11, 2836.(3) PLEASE PROVIDE CITATION INFORMATION.(4) Benedict, U.; Grosshans, W. A.; Holzapfel, W. B. Physica B&C

1986, 144, 14.(5) Duthie, J. C.; Pettifor, D. G. Phys. Rev. Lett. 1977, 38, 564.(6) Skriver, H. L. Phys. Rev. B 1985, 31, 1909.(7) Grosshans, W. A.; Holzapfel, W. B. Phys. Rev. B 1992, 45, 5171.(8) Patterson, R.; Saw, C. K.; Akella, J. J. Appl. Phys. 2004, 95, 5443.(9) Tonkov, E. Y.; Aptekar’, I. L.; Degtyareva, V. F.; Krasavin, Yu.I.

Dokl. Akad. Nauk. SSSR 1976, 230, 85.(10) Stephens, D. R.; Johnson, Q. J. Less-CommonMet. 1969, 17, 243.(11) Dera, P. GSE, a shell data analysis program for monochromatic

powder diffraction with area detector; GeoSoilEnviro Consortium forAdvanced Radiation Sources: Chicago, IL, 2008.(12) Grosshans, W. A.; Holzapfel, W. B. Phys. Rev. B 1992, 45, 5171.(13) Dewaele, A.; Loubeyre, P.; Mezouar, M. Phys. Rev. B 2004,

70, 094112.(14) Holland, T. J. B.; Redfern, S. A. T.Mineral. Mag. 1997, 61, 65.(15) Hauss€uhl, S. Physical Properties of Crystals; Wiley: Weinheim,

2007; p 215.(16) Zheng-Johansson, J. X.; Eriksson, O.; Johansson, B. Phys. Rev. B

1999, 59, 6131.(17) Keeton, S. C.; Loucks, T. L. Phys. Rev. 1968, 168, 672.(18) Ahuja, R.; Auluck, S.; Johansson, B.; Brooks,M. S. S. Phys. Rev. B

1994, 50, 5147.(19) D€obrich, K. M.; Bihlmayer, G.; Starke, K.; Prieto, J. E.;

Rossnagel, K.; Koh, H.; Rotenberg, E.; Bluegel, S.; Kaind, G. Phys.Rev. B 2007, 76, 035123.(20) Dmitriev, V. P.; Kuznetsov, A. Y.; Machon, D.; Weber, H. P.;

Toledano, P. Europhys. Lett. 2003, 61, 783.

(21) Antonangeli, D.; Benedetti, L. R.; Farber, D. L.; Steinle-Neumann,G.; Auzende, A. L.; Badro, J.; Hanfland, M.; Krisch, M. Appl. Phys. Lett.2008, 92, 111911.

(22) Jackson, D. D.; Malba, V.; Weir, S. T.; Baker, P. A.; Vohra, Y. K.Phys. Rev. B 2005, 71, 184416.

(23) Iwamoto, T.; Mito, M.; Hidaka, M.; Kawae, T.; Takeda, K.Physica B 329, 667.

(24) Lifshitz, I. M. Sov. Phys. JETP 11 1960, 1130.(25) Varlamow, A. A.; Egorov, V. S.; Pantsulaya, A. V. Adv. Phys.

1989, 38, 469.(26) Bud’ko, S. L.; Voronovskii, A. N.; Gapotchenko, A. G.; Itskevich,

E. S. Sov. Phys. JETP 59 1984, 454.(27) Morgan, J. G.; von Dreele, R. B.; Wochner, P.; Shapiro, S. M.

Phys. Rev. B 1996, 54, 812.(28) Ocelli, F; Farber, D. L.; Badro, J.; Aracne, C. M.; Teter, D. M.;

Hanfland, M.; Canny, B.; Couzinet, B Phys. Rev. Lett. 2004, 93, 095502.(29) Andrianov, A.Vl.; Savel’eva, O. A. Phys. Rev. B 2003, 67, 012495.(30) Bridgman, P. W. Proc. Am. Acad. Arts Sci. 1954, 83, 1.

anomalous elastic behavior in hcp- and sm-type dysprosium

Documents