Physica B 413 (2013) 64–68

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Physica B

0921-45

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Structural stability of URh3 at high pressure

B. Shukla a,n, V. Kathirvel c, N.V. Chandra Shekar a, S. Chandra b, P.Ch. Sahu a

a Condensed Matter Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, Indiab Materials Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, Indiac Department of Physics and Nanotechnology, SRM University, Kattankulathur 603203, Tamil Nadu, India

a r t i c l e i n f o

Article history:

Received 18 October 2012

Received in revised form

31 December 2012

Accepted 2 January 2013Available online 9 January 2013

Keywords:

Actinide intermetallics

High-pressure

X-ray diffraction

Structural stability

Equation of state

Band structure calculations

26/$ - see front matter & 2013 Elsevier B.V. A

x.doi.org/10.1016/j.physb.2013.01.001

esponding author. Tel.: þ91 7200384234.

ail addresses: physics1234@gmail.com, bshuk

a b s t r a c t

URh3 stabilizes in the cubic AuCu3 type structure at normal temperature and pressure. High-pressure

angle-dispersive X-ray diffraction experiments were performed on URh3 up to 25 GPa using a diamond-

anvil cell. URh3 remains in its cubic AuCu3 type structure up to the maximum pressure studied. The

Birch–Murnaghan equation of state fit to the P–V data yields the bulk modulus to be 133 GPa. The

Villars structural stability map gives a clue of a possible high pressure phase transition to a Ni3Sn type

structure. The electronic structure calculations were carried out for both the ambient AuCu3 type cubic

phase and the expected Ni3Sn type hexagonal high pressure phase. However, the total energy curves of

these two structures do not intersect even at pressure as high as 360 GPa, removing the possibility of

transition to Ni3Sn type structure.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Study of uranium intermetallics is very interesting for basicsciences as well as relevant for nuclear energy [1]. In a recentreport, the phase transition behavior of uranium intermetallicshas been reviewed [2]. Among various uranium intermetalliccompounds (U-IMCs), UX (where X belongs to p or d block metal)mostly show phase transition from B1 to B2 type structure underpressure [3]. The UX2 compounds stabilize either in the MgCu2

type cubic or AlB2 type hexagonal structure and show interestingstructural transitions under pressure [4,5]. The UX3 compoundson the other hand stabilize in AuCu3 type cubic structure andshowed high structural stability under pressure [6,7]. Earlier, highpressure structural studies on UGa3 up to 30 GPa show that theambient phase (AuCu3 cubic type structure) remains stable [8].Moreover, the electronic structure calculations on UGa3 as afunction of reduced volume show very little change in Densityof States (DOS) at the Fermi level EF, supporting the structuralstability of this compound under pressure.

URh3 stabilizes in the cubic AuCu3 type structure at ambientconditions. Although, the U–U distance is much larger than theHill limit (�3.5 A), the 5f states in the URh3 system exhibititinerant nature due to strong hybridization between the U-fand Rh-d electron orbitals [9–11]. Transport, mechanical and

ll rights reserved.

la@igcar.gov.in (B. Shukla).

thermal properties of URh3 compound are well studied [12–15].Several computational studies have been carried out investigatingthe electronic structure of URh3 [16–22]. Recently, Petit et al. [23]have done electronic structure calculations on URh3, UPt3, UPd3

and UAu3 compounds using the self-interaction corrected local-spin-density approximation. In general, these experiments andcomputations help understand the stability of the structure andthe change in hybridizations under compression and across thephase transition. In URh3, the DOS shows that the EF is situatedbelow the f peak, and intersects a strongly hybridized f–d band.Although there are several reports on the electronic structure ofURh3 for ambient conditions, no such reports exist at highpressure conditions.

In order to understand the structural stability and bondingnature of f-electrons on UX3 type systems, Kathirvel et al. [24]carried out the electronic structure calculations on URh3 up to40 GPa [24]. In this case the self-interaction correction was notused since the interest was in the compression and structuralstability rather than magnetism. Their calculations show that theposition of the Fermi level EF lies on a small peak in the DOS curveand it remains pinned at the same position even at 40 GPa. Thecharge density plots indicate increase in metallic character underpressure. The small changes of the DOS at EF support thestructural stability of the URh3 at least up to 40 GPa [24]. Inorder to look for possible high pressure phases, they have madeuse of an empirical method of using 2-D structural stability mapsfor AB3 type (where A belongs to lanthanide or actinide metalsand B belongs to p or d block metal) compounds [25,26].

B. Shukla et al. / Physica B 413 (2013) 64–68 65

The stability maps are used to explore the occurrence ofdifferent domains of structure as a function of parameters likeaverage valence electron (VE), average electronegativity (DX) andaverage Zunger-pseudo-potential radii (DR) [26]. These mapscorrelate the crystal structure and the electronic configurationof the constituents of several thousands of known compounds.However, construction of such stability maps for the high pres-sure phases has not been explored yet, because of inadequacy ofhigh pressure structural data. In general, one can expect theincrease in VE and decrease in DR with pressure and this isconsistent with the predicted increase in the metallic character ofUX3 compounds [24]. Moreover, the electronegativity values ofmetals are expected to increase monotonously with pressure [27].With this information, one can determine candidate high pressurephase (structure). Recently, we have validated the 2-D structuralstability maps for f-electron based AB2 type compounds forseveral high pressure phases obtained from the experimentalresults [25].

For URh3, the calculated DX, DR, and VE values are �0.232, 1.2(a.u) and 7.5 respectively. In 2-D stability maps (AB3 typecompounds), the important observation is that the domainbelonging to Ni3Sn type structure overlaps with that of thedomain with AuCu3 type structure (where the URh3 system islocated). The range of values of the three parameters for theAuCu3 type and Ni3Sn type structure is listed in Table 1. Theoverlap indicates that URh3 may transform to the Ni3Sn typestructure at very high pressures due to the changes in its DX, DR

and VE.In this paper, we report the results of the HPXRD studies on

URh3 up to 25 GPa and also electronic structure and the totalenergy of the URh3 compound in AuCu3 and Ni3Sn type structureas a function of reduced volume to compare their structuralstability and understand the bonding nature of the f electronstates.

2. Experimental and calculation details

2.1. Sample preparation

URh3 was prepared by using a standard arc melting technique.Stoichiometric quantities of U (99.98%) and Rh (99.999%) weremelted in He atmosphere and the melted ingot was flipped 2–3times to obtain a homogenous compound. The ingots were thenvacuum sealed in Ar atmosphere in silica tube and annealed forabout 4 weeks at temperature of 1100 K. In order to remove anyoxide layer, the annealed ingots were etched in 1:1 mixture ofnitric and sulfuric acid for about 2 min. The annealed sample waspowdered and XRD pattern showed single phase compound withcubic structure [28].

2.2. High pressure X-ray diffraction

In-situ high pressure X-ray diffraction experiment (HPXRD)was carried out using a Mao–Bell type diamond anvil cell (DAC) inthe angle dispersive mode. The sample in the powder form wasloaded into a 200 mm diameter hole drilled in pre-indentedstainless steel (SS) gasket along with the pressure calibrant

Table 1

Ranges of values of VE, DR, DX of AuCu3 (cubic) and Ni3Sn (hexagonal) type structures

Structure type Average valence electron (VE) Avera

AuCu3 (cubic) (where URh3 is located) (7.25–7.75) (0–1.

Ni3Sn (hexagonal) Z9.75 (þ1.0

material. An internal X-ray collimator of size 100 mm was usedto avoid SS gasket peak. For pressure calibration the material ischosen in such a way that its diffraction lines of the calibrant donot overlap with that of the sample. In this experiment, equationof state (EOS) of platinum was used for pressure calibration. Pt,having higher bulk modulus than URh3, does not see the pressureeasily and its (1 1 1) peak shifts slower with pressure than thesample peak thereby preventing overlap of Pt and URh3. Amixture of methanol, ethanol and water (MEW) in the volumeratio 16:3:1 was used as the pressure transmitting medium. Thepressure medium MEW freezes at about 14 GPa. However, the X-ray diffraction patterns do not show any discernable change inthe pressure range. The collection time for each spectrum was 2 h.

The incident Mo X-ray beam obtained from a RigakuULTRAX18 (18 kW) rotating anode X-ray generator was mono-chromatised with a graphite monochromator which gives Mo Ka1

radiation with wavelength 0.7107 A. An image plate basedmardtb345 diffractometer was used to carry out the HPXRDexperiments. The overall resolution of the diffractometer systemis dd/d�0.001. The sample to detector distance was calibratedusing LaB6 as standard.

2.3. Calculations

The electronic structure calculations of URh3 were carried outusing WIEN2k code [29] implemented with Full Potential–LinearAugmented Plane Wave (FP–LAPW) method. The exchange-correlation interaction was treated within GGA approximationof Perdew et al. [30]. Previous work suggests that the FP–LAPWmethodology provides more reliable insights into the electronicstructure of these compounds, as compared to Tight-Bindingbased approaches [31].

Fig. 1a and b shows the structures of URh3 in AuCu3 and Ni3Sntype structures. In order to find out the equilibrium volume forURh3 system in Ni3Sn type structure (hexagonal structure),approximate volume was calculated from the equilibrium volumeof AuCu3 type structure. Hereafter, the cubic AuCu3 (SG Pm-3m)and Ni3Sn (SG P63/mmc) type structures will be mentioned as Cand H type structures respectively. Standard crystallographic dataand atomic positions are available for C type structure. C typestructure has only one formula unit per unit cell (i.e. 4 atoms perunit cell). But, the H type structure has two formula units per unitcell (i.e. 8 atoms per unit cell). Hence, the unit cell volume of theH type structure is two times that of the C type structure. Thefollowing procedure was adopted to estimate the approximatelattice parameters and cell volume for H type structure.

Equilibrium unit cell volume of the C type structure [24] is64.843 A3.

Unit cell volume of the H type structure (VH)¼2* equilibriumvolume of the C type structure:

VH ¼ 2n64:843¼ 129:687 A3; a¼ 5:714 A;

c¼ 4:587 A; c=a ratio¼ 0:802

Further, these approximated lattice parameters were fed intothe WIEN2K code to optimize the lattice parameters. The calcula-tion was performed in two steps. The first step was to optimize a

and c values by varying volume and keeping the c/a ratio asconstant. The lattice parameters a and c were derived from the

from the 2-D stability maps.

ge Zunger pseudo-potential radii DR (a.u) Average electronegativity DX

25) [(�0.5)–(�0.1)]

)–(�0.9) (�0.2)–(þ0.15)

Fig. 1. Structure of URh3: (a) AuCu3 type cubic structure and b) Ni3Sn type hexagonal structure.

Fig. 2. Powder X-ray diffraction pattern of URh3 up to 25 GPa.

B. Shukla et al. / Physica B 413 (2013) 64–6866

volume which corresponded to minimum total energy. Theselattice parameters were fed as input into the second step tooptimize c/a ratio. Here, the volume was kept constant and c/aratio was changed. Different c/a ratios are obtained for a constantvolume or energy. In order to find out the c/a ratio which wascloser to constant energy, percentage of deviation of c/a ratio wascalculated. This deviation was included in constant c/a ratio (c/aratio was used in step one) and the corrected c/a ratio wasobtained. The lattice parameters a and c were calculated fromthe corrected c/a ratio. In the above optimization procedure theinternal degrees of freedom were included and symmetry con-straints were applied.

Again, these a and c values were fed into the steps 1 and 2 andrepeated several times until the optimization reached up to thevery low percentage of c/a ratio deviation value (i.e., o0.1%;lower percentage of c/a ratio deviation value indicates theoptimized c/a ratio value).

In order to optimize the volume and c/a ratio, around 20calculations were carried out following the procedure mentionedabove keeping the percentage of c/a ratio deviation value to �0.11%.The optimized lattice parameters are a¼5.6806 A and c¼4.6791 A;c/a¼0.8237. The initial positions of rhodium atoms in the URh3

(H type structure) are Rh1(0.833,0.666,0.25); Rh2(0.167,0.333,0.75);Rh3(0.167,0.833,0.75); Rh4(0.833,0.167,0.25); Rh5(0.666.0.833.0.75);and Rh6(0.334,0.167,0.25). The URh3 compound in H type structurehas free internal structure parameters for rhodium atom and it wasoptimized using the calculated forces on nuclei. Here, the 2 uraniumatoms occupy the positions (0.333,0.667,0.250) and (0.667,0.333,0.750). The optimized internal positions of rhodium are Rh1(0.834,0.669,0.25); Rh2(0.165,0.33,0.75); Rh3(0.165,0.834,0.75); Rh4(0.834,0.165,0.25); Rh5(0.669,0.834,0.75); and Rh6(0.33,0.165,0.25).

Fig. 3. Variation in inter-planar spacing with pressure.

3. Results and discussions

3.1. HPXRD results

Fig. 2 shows the angle-dispersive X-ray diffraction pattern ofURh3 by using area sensitive detector at various selected pres-sures. The 2y value in the X-ray diffraction pattern was limited toabout 5–281 because of mechanical restriction of the exit slit inthe diamond-anvil cell. The intensities of the Bragg peaksdecrease with pressure. It is evident from X-ray diffractionpatterns that there is no change in the structure up to 25 GPa.The lattice parameters the sample at different pressures werecalculated by using AIDS83 program. The variation of interplanarspacing with pressure is given in Fig. 3. It is clear from the plotthat all the ‘d’ spacings decrease with increasing pressure in thesame fashion. The P–V data was fitted to Birch–Murnaghanequation of state as well as Vinet equation of state as shown inFig. 4 [32–34]. The bulk moduli values obtained by fitting theseEOS to the P–V data are shown in Table 2. As expected, the

Murnaghan EOS gives slightly higher Bo value compared to theother EOSs.

The universal equation (Vinet) in another form is given as [35]

lnH�PX2

3 1�Xð Þ¼ lnBþ

3

2B0�1� �

1�Xð Þ

where

X ¼v

vo

� �1=3

Fig. 4. Birch–Murnagahan equation fit for the experimental data.

Table 2Comparison of bulk modulus obtained using different EOSs.

Equation of state B0 (GPa) B00

Birch–Murnaghan 133.0711.17 5.2571.56

Vinet 133.0711.26 5.2571.55

Fig. 5. Comparison of different samples for universal equation of fit. P–V data for

samples UGa3, UAl3 and ThAl2 are adapted from Refs. [8,36,37].

Fig. 6. Total energy curve for both the cubic AuCu3 and hexagonal Ni3Sn type

structures up to 360 GPa.

Fig. 7. Total DOS of AuCu3 type structure at ambient pressure.

B. Shukla et al. / Physica B 413 (2013) 64–68 67

and it reveals that ln H must be linear with 1�X with pressureunless there is any kind of transformation. Therefore, it can be asuitable method to view any electronic transition or smallstructural changes in volume for the sample under study. Tocheck the validity of above equation at ambient temperature weselected P–V data for a few samples such as URh3, UGa3, UAl3 andThAl2 [8,36,37]. Using the P–V data for these samples, theuniversal curve is plotted in Fig. 5 andthe expected linearity forURh3, UGa3 and UAl2, is found as they do not undergo anyelectronic or structural transformation up to the pressure studied.However, ThAl2, which shows electronic transition at around5 GPa, deviates from the linearity in the above plot, clearlyindicating a transformation.

3.2. Electronic structure and total energy calculation

The total energy curves for the two structures are obtained byusing the optimized lattice parameters. At ambient pressure, thetotal energy difference between the AuCu3 (cubic) and Ni3Sn

(hexagonal) type structure is 0.0163 Ry/cell. This shows that totalenergy of Ni3Sn (hexagonal) type structure is very close to that ofthe AuCu3 (cubic) type structure. Fig. 6 displays the total energycurves of both the cubic AuCu3 and hexagonal Ni3Sn typestructures of URh3. This figure illustrates that there is no possi-bility of phase transition, as the two curves do not intersect andboth the curves exhibit similar kind of behavior. However, thetwo curves come closer to each other at lower values of V/V0 (orhigher pressure). In order to see the possibility of intersection ofthe two curves at higher pressures, we extended the calculationsup to 0.65 V/V0 (360 GPa), but there was no intersection. Theextrapolated curves from 360 GPa to 900 GPa also did notintersect.

Figs. 7 and 8 display the total DOS of URh3 at ambientconditions in AuCu3 and Ni3Sn type structures respectively. InFig. 7, the EF lies very close to a maximum in the DOS curve andthe sharp narrow peak due to the U-f band is located above theFermi level at around 0.2–1.5 eV. The tail of the f-band extendstoward lower energy below the Fermi level, indicating theitinerant nature f-electrons in URh3 in AuCu3 type structure.Fig. 7 shows that the Rh-d band states mostly dominated atlower energy region. Fig. 8 for Ni3Sn type structure exhibits asimilar kind of behavior as far as the itinerancy of the f-electronsis concerned. Above EF, there is a sharp narrow peak due to theU-f band and the tail of the f-band extends below EF which showsthe strong hybridization of U-f band with Rh-d band states.

Fig. 8. Total DOS of Ni3Sn type structure at ambient pressure.

B. Shukla et al. / Physica B 413 (2013) 64–6868

However, the position of the Fermi level in the DOS curve isslightly different. Total DOS around the EF of Ni3Sn type structurelooks different from the total DOS of AuCu3 type structure.

4. Conclusion

URh3 stabilizes in cubic AuCu3 type structure. HPXRD studiesup to 25 GPa do not show any phase transition. Moreover,electronic structure calculations up to 300 GPa do not showexpected phase transition to the Ni3Sn structure.

Acknowledgment

The authors thank members of High Pressure Physics Sectionfor help in various stages of the experiment. They also thank ShriM.P. Janawadkar, Dr. C.S. Sundar and Shri S.C. Chetal for theirencouragement and support.

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