Research Article Theoretical Investigations of Structural ...to be crystallizing in three other...

Research ArticleTheoretical Investigations of Structural Phase Transitionsand Magnetic Electronic and Thermal Properties of DyNiUnder High Pressures and Temperatures

Pooja Rana and U P Verma

School of Studies in Physics Jiwaji University Gwalior 474 011 India

Correspondence should be addressed to Pooja Rana poojafizixyahoocom

Received 9 September 2013 Accepted 17 December 2013 Published 4 February 2014

Academic Editors H-D Yang and A D Zaikin

Copyright copy 2014 P Rana and U P Verma This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Present work is influenced by the requirement of investigation of rare earth intermetallics due to the nonavailability of theoreticaldetails and least information from experimental results An attempt has been made to analyse the structural electronic magneticand thermal properties of DyNi using full potential linear augmented plane wavemethod based on density functional theory DyNidiffers from other members of lanthanides nickelates as in ground state it crystallizes in FeB phase rather than orthorhombic CrBstructureThe equilibrium lattice constant bulkmodulus and pressure derivative of bulkmodulus are presented in four polymorphs(FeB CrB CsCl and NaCl) of DyNi At equilibrium the cell volume of DyNi for FeB structure has been calculated as 109816 Bohr3which is comparable well with the experimental value 107475 Bohr3 The electronic band structure has been presented for FeBphase The results for thermal properties namely thermal expansion coefficient Gruneisen parameter specific heat and Debyetemperature at higher pressure and temperatures have been reported The magnetic moments at equilibrium lattice constants havealso been tabulated as the rare earth ions associated with large magnetic moments increase their utility in industrial field for thefabrication of electronic devices due to their magnetocaloric effect used in magnetic refrigeration

1 Introduction

Because of the technological importance the rare earthcompounds have attracted interest of the experimental aswell as the theoretical scientists during past decade Therare earth elements on combining with transition metalsshow peculiar characteristics like good oxidation resistanceand excellent strength [1] Due to large magnetic momentsand magnetocaloric effect (MCE) they also have applicationsin the fabrication of permanent magnets magnetostrictivedevices magnetooptical recorders [2] and magnetic refrig-eration [3ndash10] These are also taken as first choice forthe purpose of hydrogen storage materials [11] Among alltransition metals nickel is one of the promising materialsin its pure form and also in alloy form doped with othermaterialsThe structural parameters of someGadoliniumandDysprosium intermetallics and their related compounds havebeen reported by Baenziger andMoriarty Jr [12] A sample of

polycrystalline DyNi was prepared by Tripathy et al [13] andits magnetocaloric effects have been studied on varying tem-perature scale by using powder X-ray diffractogram Laterthe magnetic properties of lanthanides-nickel intermetalliccompounds and their relative hydrides have been studied byYaropolov et al [3 4]

Thus it is clear from the above paragraph that someattention has been paid on the studies of magnetic propertiesof rare earth nickel compounds and its hydrides whereastill so far no attention has been paid on the properties likeelectronic mechanical thermal and so forth Realising theneed of theoretical exploration of rare earth compounds wefocus our attention around rare earth nickelates (RNi) toexplain them on the basis of earlier mentioned properties byusing first principles approach

DyNi compound has attracted much attention becauseof their magnetic and extraordinary magneto-elastic andmagnetocaloric properties and its uses in the fabrication of

Hindawi Publishing CorporationISRN Condensed Matter PhysicsVolume 2014 Article ID 763401 7 pageshttpdxdoiorg1011552014763401

2 ISRN Condensed Matter Physics

Figure 1 Cell structure of DyNi in FeB phase

materials in magnetic refrigerators [14ndash16] Moreover thiscompound is also having peculiarities of the interaction withhydrogen and ability to absorb up to 3 atomsformula units(fu)

The goal of present communication is to report lackingbulk properties of DyNi using first principles study namelymagnetic electronic and structural properties The struc-tural studies of DyNi has been reported in FeB CrB CsCl andNaCl structures The effects of high pressure and high tem-perature on the electronic magnetic and thermal propertiesof the compound have also been reported Methodology ofthe study results and discussions and conclusions are givenin subsequent sections

2 Computational Methodology

In ground state DyNi crystallizes in orthorhombic structureof FeB with space group (62-Pnma) [6] The primitive cellstructure of DyNi in FeB phase is shown in Figure 1 Thestructure contains two pairs of Fe as well as Ni atoms

The DyNi has been investigated using full potentiallinear augmented plane wave (FP-LAPW)method within theframe work of density functional theory (DFT) [17 18] asimplemented in code Wien2k [19] The generalized gradientapproximation (GGA) for the exchange-correlation interac-tion given by Perdew Burke and Ernzerhof (PBE) [20] hasbeen used In thismethod the basis set inside eachmuffin-tinsphere is split into two parts core subset and valence subsetThe states under core region are treated as being sphericallysymmetric of the potential and are assumed to have a spher-ically symmetric charge density confined inside the muffin-tin spheres The valence part is treated within a potentialwhich is expanded into spherical harmonics up to 119897 = 4 Thevalence wave functions inside the spheres are expanded upto 119897max = 8 The energy convergence criterion of electronicself-consistency is chosen as 10minus4 Ry whereas charge conver-gence as 10minus3 eminus At ambient conditions DyNi crystallizes inorthorhombic FeB structure having space group 62-Pnma[21] The primitive cell structure of DyNi in FeB phase isshown in Figure 1 From the inspection of Figure 1 it indicatesthat the structure contains two pairs of Fe as well as Niatoms Each Dy atom is shared by four tetrahedral where Dyatoms are placed at the corners sharing by the corners and

Table 1 Lattice coordinates (119909 119910 119911) in FeB CrB CsCl and NaClphases of DyNi

Atoms Lattice coordinates119909 119910 119911

FeB phaseDy 0179 0250 0132Ni 0035 0250 0609

CrB phaseDy 0000 0146 0250Ni 0000 0440 0250

CsClNaCl phasesDy 0000 0000 0000Ni 0500 0500 0500

edges with other tetrahedral The calculations are made torelax the lattice coordinates for the atoms Dy and Ni in all thefour structures Atomic positions in four different structuresare given in Table 1 The energy that separates the valencestates from core states has been taken asminus60 RyThe 119896-pointswithin first Brillouin zone of the reciprocal space have beenchosen to be 2500 for DyNi in FeB structure

The electronic structure has also been computed usingPBE-GGA Since knowledge about thermodynamical prop-erties in the fabrication of modern devices is essentialtherefore the effects of temperature and pressure have alsobeen studied related to DyNi based on quasiharmonic Debyemodel as implemented in Gibbs Program [22]

Further rare earth intermetallics were generally foundto be crystallizing in three other crystal structures namelyCsCl NaCl and CrB Hence analysis of the stability of DyNiin these three phases has also been reported The 119896-pointswithin first Brillouin zone of the reciprocal space have beenchosen as 1331 1331 and 1000 respectively for CrB CsCl andNaCl phases

3 Results and Discussions

31 Structural Properties The total energy has been calcu-lated corresponding to different cell volumes of FeB CrBCsCl and NaCl phases of DyNi and fitted to the Murnaghanequation of state [15] During simulations it has been noticedthat the total energy and volume of the unit cell of FeB phaseare two times as compared to those of CrB phase while theyare four times of the total energy and volume of the unit cellof CsCl and NaCl phases The cause behind this is that theunit cell of FeB phase is made up of 4 primitive cells whileCrB phase contains 2 and CsCl and NaCl phases containsingle primitive cell In order to normalise the energy aswell as the volume of all four phases supercells have beengenerated for CrB phase and CsCl and NaCl phase of size of2times1times1 and 2times2times1 respectivelyThe results of the supercellcalculations are two and four times to their respective unitcells The four optimized plots are depicted in Figure 2 It isevident from this plot that ground state phase of DyNi is FeBstructure and its curve for CrB phase is found to be very closeto ground state The CsCl and NaCl optimization curve lies

ISRN Condensed Matter Physics 3

650 850 1050 1250 1450

DyNi

FeBCrB

CsClNaCl

850 900 950 1000

Volume (Bohr3)

Volume (Bohr3)

Ener

gy +

109

513

(Ry) En

ergy

+ 1

0951

3 (R

y)

minus029

minus039

minus049

minus059

minus069

minus079

minus089

minus099

minus078

minus083

minus088

minus093

PT1 = 1839GPa

PT2 = 1407GPa

Figure 2 Plots of total energies as function of cell volumes in FeBCrB CsCl and NaCl phases of DyNi

above ground state curveThe equilibriumvolume inCrB andNaCl structure are more than the ground state equilibriumvolume while it is less in the case of CsCl phase Looking intoplots phase transitions are noticeable from FeB to CsCl andCrB to CsCl phase Details about the transition pressures aregiven under section phase transition The equilibrium latticeconstants and bulk modulus and its pressure derivativesobtained after fit are listed in Table 2 along with earlierreported experimental results [6]

In our present study the values of lattice parameters forFeB structure have been computed as 119886 = 13435Bohr 119887 =7959Bohr and 119888 = 1027Bohr which is quite agreeablewith the experimental lattice constants 119886 = 1327Bohr 119887 =789Bohr 119888 = 1028Bohr For CrB structure 119886 = 7085Bohr119887 = 19424Bohr and 119888 = 7859Bohr for CsCl structure 119886 =6366Bohr and for NaCl structure 119886 = 10409Bohr In thesestructures of DyNi experimental results are not available

311 Phase Transitions The aim of studying DyNi in fourstructures is to look for possible structural phase transfor-mations from one phase to another Figure 2 reveals the factthat optimization curves in FeB and CrB phase are veryclose to each other near equilibrium With the increase inpressure near 57GPa both the curves overlap each other Theoptimization curve in CsCl phase crosses to the optimizationcurves in FeB and CrB phases The ground state FeB phasetransforms to CsCl phase at pressure 119875

1198791= 1839GPa

while CrB phase shows structural phase transitions at 1198751198792=

1407GPa The NaCl phase shows separate optimizationcurve that is there is no interconnection between NaCl andother phases

32 Electronic Properties The self-consistent electronic bandstructures in spin-up and spin-down channels of DyNi forFeB phase are presented in Figure 3 In both the channelsDyNi shows metallic nature In order to explicate band

structures total and partial densities of states (DOS) for Dyand Ni atoms are shown in Figure 4 Total DOS of DyNiand atoms Dy and Ni are drawn in Figure 4(a) In both thespins total DOS of DyNi is less than four times the sum ofatomic total DOS because of the reason that FeB structure ofDyNi contains 4Dy and 4Ni atomsThis difference shows thepresence of some itinerant electrons which are free to moveanywhere within the compound

In the partial DOS of atomDymajor contribution inDOSis from 119891-states In spin-up channel peaks are concentratedin the range minus20 to minus40 eV (below Fermi level) while inspin-down channel 119891-states overlap Fermi level completelyfrom minus05 to 14 eV Negligible contribution of other electronstates namely 119904-states 119901-states and 119889-states is seen in boththe channels In case of Ni atoms it can be noticed that DOSplots for spin up and spin down channels are nearly the samefor all the electrons and major contribution is from 119889-statesbetween minus30 eV and Fermi energy level

33 Thermal Properties Lattice dynamics is an importantaspect to study properties of materials It concerns the vibra-tions of the atoms about theirmean positionThese vibrationsare entirely responsible for thermal properties namely heatcapacity thermal expansion entropy and so forth Thermalproperties of DyNi have been quite useful from differentaspects of magneto-caloric effect As the temperature andpressure of the material vary it affects the density of thematerial which indicates the thermal expansioncontractionwithin the material leading to important and interestingresults Obtained thermodynamical results are listed inTable 3 To compute reported properties temperature rangehas been varied from 0 to 1000K and pressure was takenbetween 0 and 20GPa Various parameters like thermalexpansion coefficient (120572) Gruneisen parameter (120574) debyetemperature (120579

119863) and specific heat (119862

119875and 119862V) as a function

of pressurestemperatures have been presented in Figure 5Their analysis is presented in the following sections

331 Thermal Expansion Coefficient Effect of temperatureon thermal expansion coefficient (120572) has been analysed andshown in Figure 5(a) at hydrostatic pressure 119875 = 0 8 and16GPa Figure 5(a) shows that thermal expansion increaseswith the increase in temperature up to 100K after that itattains saturation At this particular temperature expansioncoefficient decreases with the increase in pressure

332 Gruneisen Parameter Gruneisen Parameter (120574) is thenext parameter of solids related with the effect in latticevibrations and gives details about vibrational anharmonicityThe variation of 120574 with respect to pressure has been depictedin Figure 5(b) for three different temperature (119879 = 0K500K and 1000K) The behaviour of this parameter is that itdecreases with increase in pressure at constant temperaturewhile at constant pressure it increases as the temperatureincreases

333 Specific Heat and Debye Temperature The amount ofenergy given to lattice vibrations in the crystalline solids is


Table 2 Optimized results for equilibrium lattice constants ldquo119886rdquo (Bohr) 119886119888 ratio unit cell volumes 1198810(Bohr3) and bulk modulus 119861

0(GPa)

and its first order pressure derivative

Structure Results Lattice constants119886119888 ratio 119881

01198610

1198611015840

0119886 119887 119888

FeB Present work 1344 796 1027 131 109816 7205 463Expt [6] 1327 789 1028 129 107475

CrB Present work 709 1942 786 090 108155lowast 7161 418CsCl Present work 637 mdash 103196lowast 7433 468NaCl Present work 1041 mdash 112780lowast 6692 465

Transition pressure 119875119879(GPa)

1198751198791

(FeB rarr CsCl) Present work 1839GPa Expt mdash1198751198792

(CrB rarr CsCl) Present work 1407GPa Expt mdashlowast1198810 corresponds to supercell volume

6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(a)

6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(b)

Figure 3 Band Structures of DyNi in FeB phase at ambient pressure and temperature (a) spin up channel and (b) spin down channel

Table 3 Calculated results for thermodynamical properties in FeBstructure of DyNi

Properties 119875 = 0GPa119879 = 0K

119875 = 0GPa119879 = 300K

Thermal expansioncoefficient 120572 (105K) 0 143

Specific heat atconstant volume 119862V(Jmol K)

0 4932

Specific heat atconstant pressure 119862

119901

(Jmol K)0 4975

Gruneisen parameter120574

204 2051

Debye temperature 120579119863

(K) 14467 14319

Entropy 119878 (Jmol K) 0 10355

the dominant contribution to the specific heat which is ameasure of degrees of freedom to absorb energy The specific

heats as a function of temperature at ambient pressure areshown in Figure 5(c) The plots show standard trend of heatcapacity and its highest value (sim48 Jmol K) is approximatelytwice of the value of 3119877 (=249 Jmol K) Here 119877 is universalgas constant The increased value in heat capacity may becorrelated to the fact that the large value of the magneticmoments corresponding to the higher value of temperaturebecomes ordered The Debye temperature as a function ofpressure is presented in Figure 5(d) at119879 = 0 500 and 1000KThe Debye temperature varies nonlinearly with the increasein pressure and separation of the curves increases with theincrease in temperature

34 Magnetic Properties Magnetic moments of interstitialregion atoms Dy and Ni total magnetic moment (119872

119872) and

total119872119872formula unit (119872

119872fu) for FeB CrB CsCl andNaCl

phases of DyNi are given in Table 4The interstitial magneticmoments in FeB CrB and CsCl phases are positive while itis negative for NaCl phase The magnetic behaviour of atomDy is nearly identical in all the phases of DyNi as its magneticmoments are obtained sim46 120583B The electronic configuration


600

400

200

00

minus200

minus400

minus6 minus4 minus2 0 2 4 6

Spin

Spin

TotDyNi

DO

S (s

tate

seV

)

Energy (eV)

(a)

150

100

50

00

minus50

minus100

DO

S (s

tate

seV

)

Energy (eV)

Dy-sDy-p

Dy-dDy-f


Spin

Spin

(b)

350

175

000

minus175

minus350

Ni-sNi-pNi-d


Spin

Spin

DO

S (s

tate

seV

)

Energy (eV)

(c)

Figure 4 Total and partial density of states for DyNi in FeB phase

Table 4 Magnetic moments of interstitial region atoms Dy and Nitotal magnetic moment (119872

119872) and total119872

119872formula unit (119872

119872fu)

for FeB CrB CsCl and NaCl phases of DyNi

Sites Magnetic moment (120583B)FeB CrB CsCl NaCl

Interstitial 030168 018221 005911 minus001504Atom Dy 463309 460257 466920 471424Atom Ni 001003 002365 006351 016738Total119872

1198721887416 934005 479181 486658

Total119872119872fu 471854 467002 479181 486658

of Dy is [Xe] 4f9 5d1 and 6s2 It seems that the magneticmoment of Dy is intimately related to the highly localized 4119891

electrons Similarly behaviour of atom Ni is identical in allfour phases The total magnetic moment per formula unitis sim47 120583B in all phases The total magnetic moment for thecomplete DyNi in FeB phase is found to be 1887 120583B inCrB phase it is 934 120583B while in CsCl and NaCl phases itis around 48 120583B The reason behind this is that FeB phasecontains 4 primitive cells per unit cell and CrB phase includes2 primitive cells per unit cell

4 Conclusions

Present paper includes ab initio study of the structuraland magnetic properties of DyNi alloy using FP-LAPWmethod The GGA is opted to perform all the calculations


00

04

08

12

16

0 100 200 300 400 500Temperature (K)

P = 0GPaP = 8GPaP = 16GPa

120572(105K

)

(a)

17

18

19

20

21

0 5 10 15 20

Gru

neise

n pa

ram

eter

Pressure (GPa)

T = 0KT = 500KT = 1000K

(b)

0

11

22

33

44

55

0 100 200 300 400 500Temperature (K)

Spec

ific h

eat (

Jmollowast

K)

C

Cp

(c)

137

154

171

188

205

0 5 10 15 20

Deb

ye te

mpe

ratu

re (K

)

Pressure (GPa)

T = 0KT = 500KT = 1000K

(d)

Figure 5 Thermodynamical parameters (a) thermal expansion coefficient 120572 (b) Gruneisen parameter (120574) (c) specific heats 119862V and 119862119901 and(d) Debye temperature 120579

119863

related to exchange-correlation functional The structuralphase transformations phase may enhance their physicalproperties The optimized results for equilibrium latticeconstants 119886119888 ratio for stabilisation of orthorhombic FeBphase unit cell volumes and bulk modulus and its firstorder pressure have been reported The electronic bandstructure and corresponding DOS plots showmetallic natureof DyNi in both the channels of spin Thermal expansion

coefficient 120572 specific heats 119862V and 119862119901 gruneisen parameter120574 Debye temperature 120579

119863 entropy 119878 and magnetic moments

of DyNi are reported Only available experimental data aboutDyNi are lattice constants The theoretical predictions onstructural electronic thermal and magnetic properties ofDyNi have been reported for the first time We expect thatour present communication will hopefully encourage theo-retical researchers and experimentalists to give their attention


to such technically imperative ferromagnetic intermetallicmaterials

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] G H Caoa Z Yua and A M Russell ldquoThe deformationbehavior of DyCu ductile intermetallic compound under com-pressionrdquoMaterials Science and Engineering A vol 528 no 24pp 7173ndash7177 2011

[2] N H Duc ldquoIntersublattice exchange coupling in the lantha-nide-transition metal intermetallicsrdquo in Handbook on thePhysics and Chemistry of Rare Earths K A Gschneidner Jr andL Eyring Eds vol 24 chapter 163 pp 339ndash398 CryogenicLabora Hanoi Vietnam 1997

[3] Y L Yaropolov A S Andreenko S A Nikitin S S AgafonovV P Glazkov and V N Verbetsky ldquoStructure and magneticproperties of RNi (R = Gd Tb Dy Sm) and R6M167Si3 (R= Ce Gd Tb M = Ni Co) hydridesrdquo Journal of Alloys andCompounds vol 509 no 2 pp S830ndashS834 2011

[4] R Mallik P L Paulose E V Sampathkumaran S Patil andV Nagarajan ldquoCoexistence of localized and (induced) itinerantmagnetism and heat-capacity anomalies in Gd

1minus119909Y119909Ni alloysrdquo

Physical Review B vol 55 no 13 pp 8369ndash8373 1997[5] P L Paulose S Patil R Mallik E V Sampathkumaran and

V Nagarajan ldquoNi3d-Gd4f correlation effects on the magneticbehaviour of GdNirdquo Physica B vol 223-224 no 1-4 pp 382ndash384 1996

[6] E Gratz G Hilscher H Sassik and V Sechovsky ldquoMagneticproperties and electrical resistivity of (Gd

119909La1minus119909

)Ni (0⩽x⩽1)rdquoJournal of Magnetism and Magnetic Materials vol 54-57 no 1pp 459ndash460 1986

[7] E Gratz and A Lindbaum ldquoAnomalous thermal expansion inGd-based intermetallicsrdquo Journal of Magnetism and MagneticMaterials vol 177-181 no 2 pp 1077ndash1078 1998

[8] D Paudyal YMudryk Y B Lee V K Pecharsky K AGschnei-dner Jr and B N Harmon ldquoUnderstanding the extraordinarymagnetoelastic behavior in GdNirdquo Physical Review B vol 78no 18 Article ID 184436 2008

[9] C A Poldy and K N R Taylor ldquoPossible influence of 3d stateson the stability of rare earth-rich rare earth-transition metalcompoundsrdquo Physica Status Solidi A vol 18 no 1 pp 123ndash1281973

[10] R E Walline and W E Wallace ldquoMagnetic and structuralcharacteristics of lanthanide-nickel compoundsrdquoThe Journal ofChemical Physics vol 41 no 6 pp 1587ndash1591 1964

[11] Y L Yaropolov V N Verbetsky A S Andreenko K OBerdyshev and S A Nikitin ldquoMagnetic properties of theintermetallic compounds RNi (R = Gd Tb Dy Sm) and theirhydridesrdquo Inorganic Materials vol 46 no 4 pp 364ndash371 2010

[12] N C Baenziger and J L Moriarty Jr ldquoGadolinium and dyspro-sium intermetallic phases IThe crystal structures of DyGa andGdPt and their related compoundsrdquoActa Crystallographica vol14 pp 946ndash947 1961

[13] S K Tripathy K G Suresh R Nirmala A K Nigam and SKMalik ldquoMagnetocaloric effect in the intermetallic compound

DyNirdquo Solid State Communications vol 134 no 5 pp 323ndash3272005

[14] P Kumar K G Suresh A K Nigam and O Gutfleisch ldquoLargereversible magnetocaloric effect in RNi compoundsrdquo Journal ofPhysics D vol 41 no 24 Article ID 245006 2008

[15] P J von Ronke D F Grangeia A Caldas and N A OliverialdquoInvestigations on magnetic refrigeration application to RNi

2

(R = Nd Gd Tb Dy Ho and Er)rdquo Journal of Applied Physicsvol 93 p 4055 2003

[16] R Mondal R Nirmala J Arout Chelvane and A K NigamldquoMagnetocaloric effect in the rare earth intermetallic com-pounds RCoNi (R =Gd Tb Dy and Ho)rdquo Journal of AppliedPhysics vol 113 p 17A930 2013

[17] P Hohenberg and W Kohn ldquoInhomogeneous electron gasrdquoPhysical Review vol 136 no 3B pp B864ndashB871 1964

[18] W Kohn and L J Sham ldquoSelf-consistent equations includingexchange and correlation effectsrdquo Physical Review vol 140 no4A pp A1133ndashA1138 1965

[19] P Blaha K Schwarz G K H Madsen D Kvasnicka and JLuitz WIEN2k an Augmented PlAne Wave Plus Local OrbitalsProgram for Calculating Crystal Properties ViennaUniversity ofTechnology Vienna Austria 2001

[20] J P Perdew K Burke andM Ernzerhof ldquoGeneralized gradientapproximation made simplerdquo Physical Review Letters vol 77no 18 pp 3865ndash3868 1996

[21] M A Blanco E Francisco and V Luana ldquoGIBBS isothermal-isobaric thermodynamics of solids from energy curves using aquasi-harmonic Debye modelComputer Physics Communica-tionsrdquo vol 158 no 1 pp 57ndash72 2004

[22] F D Murnaghan ldquoThe compressibility of media under extremepressuresrdquoProceedings of theNational Academy of Sciences of theUnited States of America vol 30 no 9 pp 244ndash247 1944

Submit your manuscripts athttpwwwhindawicom

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ThermodynamicsJournal of


Figure 1 Cell structure of DyNi in FeB phase

materials in magnetic refrigerators [14ndash16] Moreover thiscompound is also having peculiarities of the interaction withhydrogen and ability to absorb up to 3 atomsformula units(fu)

The goal of present communication is to report lackingbulk properties of DyNi using first principles study namelymagnetic electronic and structural properties The struc-tural studies of DyNi has been reported in FeB CrB CsCl andNaCl structures The effects of high pressure and high tem-perature on the electronic magnetic and thermal propertiesof the compound have also been reported Methodology ofthe study results and discussions and conclusions are givenin subsequent sections

2 Computational Methodology

In ground state DyNi crystallizes in orthorhombic structureof FeB with space group (62-Pnma) [6] The primitive cellstructure of DyNi in FeB phase is shown in Figure 1 Thestructure contains two pairs of Fe as well as Ni atoms

The DyNi has been investigated using full potentiallinear augmented plane wave (FP-LAPW)method within theframe work of density functional theory (DFT) [17 18] asimplemented in code Wien2k [19] The generalized gradientapproximation (GGA) for the exchange-correlation interac-tion given by Perdew Burke and Ernzerhof (PBE) [20] hasbeen used In thismethod the basis set inside eachmuffin-tinsphere is split into two parts core subset and valence subsetThe states under core region are treated as being sphericallysymmetric of the potential and are assumed to have a spher-ically symmetric charge density confined inside the muffin-tin spheres The valence part is treated within a potentialwhich is expanded into spherical harmonics up to 119897 = 4 Thevalence wave functions inside the spheres are expanded upto 119897max = 8 The energy convergence criterion of electronicself-consistency is chosen as 10minus4 Ry whereas charge conver-gence as 10minus3 eminus At ambient conditions DyNi crystallizes inorthorhombic FeB structure having space group 62-Pnma[21] The primitive cell structure of DyNi in FeB phase isshown in Figure 1 From the inspection of Figure 1 it indicatesthat the structure contains two pairs of Fe as well as Niatoms Each Dy atom is shared by four tetrahedral where Dyatoms are placed at the corners sharing by the corners and

Table 1 Lattice coordinates (119909 119910 119911) in FeB CrB CsCl and NaClphases of DyNi

Atoms Lattice coordinates119909 119910 119911

FeB phaseDy 0179 0250 0132Ni 0035 0250 0609

CrB phaseDy 0000 0146 0250Ni 0000 0440 0250

CsClNaCl phasesDy 0000 0000 0000Ni 0500 0500 0500

edges with other tetrahedral The calculations are made torelax the lattice coordinates for the atoms Dy and Ni in all thefour structures Atomic positions in four different structuresare given in Table 1 The energy that separates the valencestates from core states has been taken asminus60 RyThe 119896-pointswithin first Brillouin zone of the reciprocal space have beenchosen to be 2500 for DyNi in FeB structure

The electronic structure has also been computed usingPBE-GGA Since knowledge about thermodynamical prop-erties in the fabrication of modern devices is essentialtherefore the effects of temperature and pressure have alsobeen studied related to DyNi based on quasiharmonic Debyemodel as implemented in Gibbs Program [22]

Further rare earth intermetallics were generally foundto be crystallizing in three other crystal structures namelyCsCl NaCl and CrB Hence analysis of the stability of DyNiin these three phases has also been reported The 119896-pointswithin first Brillouin zone of the reciprocal space have beenchosen as 1331 1331 and 1000 respectively for CrB CsCl andNaCl phases

3 Results and Discussions

31 Structural Properties The total energy has been calcu-lated corresponding to different cell volumes of FeB CrBCsCl and NaCl phases of DyNi and fitted to the Murnaghanequation of state [15] During simulations it has been noticedthat the total energy and volume of the unit cell of FeB phaseare two times as compared to those of CrB phase while theyare four times of the total energy and volume of the unit cellof CsCl and NaCl phases The cause behind this is that theunit cell of FeB phase is made up of 4 primitive cells whileCrB phase contains 2 and CsCl and NaCl phases containsingle primitive cell In order to normalise the energy aswell as the volume of all four phases supercells have beengenerated for CrB phase and CsCl and NaCl phase of size of2times1times1 and 2times2times1 respectivelyThe results of the supercellcalculations are two and four times to their respective unitcells The four optimized plots are depicted in Figure 2 It isevident from this plot that ground state phase of DyNi is FeBstructure and its curve for CrB phase is found to be very closeto ground state The CsCl and NaCl optimization curve lies


650 850 1050 1250 1450

DyNi

FeBCrB

CsClNaCl

850 900 950 1000

Volume (Bohr3)

Volume (Bohr3)

Ener

gy +

109

513

(Ry) En

ergy

+ 1

0951

3 (R

y)

minus029

minus039

minus049

minus059

minus069

minus079

minus089

minus099

minus078

minus083

minus088

minus093

PT1 = 1839GPa

PT2 = 1407GPa





1198791= 1839GPa















0(GPa)



01198610

1198611015840

0119886 119887 119888




1198751198791



6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(a)

6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(b)




119875 = 0GPa119879 = 300K



0 4932


119901

(Jmol K)0 4975


204 2051


(K) 14467 14319

Entropy 119878 (Jmol K) 0 10355




119872) and





600

400

200

00

minus200

minus400


Spin

Spin

TotDyNi

DO

S (s

tate

seV

)

Energy (eV)

(a)

150

100

50

00

minus50

minus100

DO

S (s

tate

seV

)

Energy (eV)

Dy-sDy-p

Dy-dDy-f


Spin

Spin

(b)

350

175

000

minus175

minus350

Ni-sNi-pNi-d


Spin

Spin

DO

S (s

tate

seV

)

Energy (eV)

(c)



119872) and total119872


119872fu)




1198721887416 934005 479181 486658

Total119872119872fu 471854 467002 479181 486658



4 Conclusions



00

04

08

12

16

0 100 200 300 400 500Temperature (K)


120572(105K

)

(a)

17

18

19

20

21

0 5 10 15 20

Gru

neise

n pa

ram

eter

Pressure (GPa)

T = 0KT = 500KT = 1000K

(b)

0

11

22

33

44

55

0 100 200 300 400 500Temperature (K)

Spec

ific h

eat (

Jmollowast

K)

C

Cp

(c)

137

154

171

188

205

0 5 10 15 20

Deb

ye te

mpe

ratu

re (K

)

Pressure (GPa)

T = 0KT = 500KT = 1000K

(d)


119863









References









119909La1minus119909












2














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




650 850 1050 1250 1450

DyNi

FeBCrB

CsClNaCl

850 900 950 1000

Volume (Bohr3)

Volume (Bohr3)

Ener

gy +

109

513

(Ry) En

ergy

+ 1

0951

3 (R

y)

minus029

minus039

minus049

minus059

minus069

minus079

minus089

minus099

minus078

minus083

minus088

minus093

PT1 = 1839GPa

PT2 = 1407GPa





1198791= 1839GPa















0(GPa)



01198610

1198611015840

0119886 119887 119888




1198751198791



6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(a)

6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(b)




119875 = 0GPa119879 = 300K



0 4932


119901

(Jmol K)0 4975


204 2051


(K) 14467 14319

Entropy 119878 (Jmol K) 0 10355




119872) and





600

400

200

00

minus200

minus400


Spin

Spin

TotDyNi

DO

S (s

tate

seV

)

Energy (eV)

(a)

150

100

50

00

minus50

minus100

DO

S (s

tate

seV

)

Energy (eV)

Dy-sDy-p

Dy-dDy-f


Spin

Spin

(b)

350

175

000

minus175

minus350

Ni-sNi-pNi-d


Spin

Spin

DO

S (s

tate

seV

)

Energy (eV)

(c)



119872) and total119872


119872fu)




1198721887416 934005 479181 486658

Total119872119872fu 471854 467002 479181 486658



4 Conclusions



00

04

08

12

16

0 100 200 300 400 500Temperature (K)


120572(105K

)

(a)

17

18

19

20

21

0 5 10 15 20

Gru

neise

n pa

ram

eter

Pressure (GPa)

T = 0KT = 500KT = 1000K

(b)

0

11

22

33

44

55

0 100 200 300 400 500Temperature (K)

Spec

ific h

eat (

Jmollowast

K)

C

Cp

(c)

137

154

171

188

205

0 5 10 15 20

Deb

ye te

mpe

ratu

re (K

)

Pressure (GPa)

T = 0KT = 500KT = 1000K

(d)


119863









References









119909La1minus119909












2














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





0(GPa)



01198610

1198611015840

0119886 119887 119888




1198751198791



6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(a)

6

4

2

0

minus2

minus4

minus6

Ener

gy (e

V)

EF

R ΓΓ X M

(b)




119875 = 0GPa119879 = 300K



0 4932


119901

(Jmol K)0 4975


204 2051


(K) 14467 14319

Entropy 119878 (Jmol K) 0 10355




119872) and





600

400

200

00

minus200

minus400


Spin

Spin

TotDyNi

DO

S (s

tate

seV

)

Energy (eV)

(a)

150

100

50

00

minus50

minus100

DO

S (s

tate

seV

)

Energy (eV)

Dy-sDy-p

Dy-dDy-f


Spin

Spin

(b)

350

175

000

minus175

minus350

Ni-sNi-pNi-d


Spin

Spin

DO

S (s

tate

seV

)

Energy (eV)

(c)



119872) and total119872


119872fu)




1198721887416 934005 479181 486658

Total119872119872fu 471854 467002 479181 486658



4 Conclusions



00

04

08

12

16

0 100 200 300 400 500Temperature (K)


120572(105K

)

(a)

17

18

19

20

21

0 5 10 15 20

Gru

neise

n pa

ram

eter

Pressure (GPa)

T = 0KT = 500KT = 1000K

(b)

0

11

22

33

44

55

0 100 200 300 400 500Temperature (K)

Spec

ific h

eat (

Jmollowast

K)

C

Cp

(c)

137

154

171

188

205

0 5 10 15 20

Deb

ye te

mpe

ratu

re (K

)

Pressure (GPa)

T = 0KT = 500KT = 1000K

(d)


119863









References









119909La1minus119909












2














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




600

400

200

00

minus200

minus400


Spin

Spin

TotDyNi

DO

S (s

tate

seV

)

Energy (eV)

(a)

150

100

50

00

minus50

minus100

DO

S (s

tate

seV

)

Energy (eV)

Dy-sDy-p

Dy-dDy-f


Spin

Spin

(b)

350

175

000

minus175

minus350

Ni-sNi-pNi-d


Spin

Spin

DO

S (s

tate

seV

)

Energy (eV)

(c)



119872) and total119872


119872fu)




1198721887416 934005 479181 486658

Total119872119872fu 471854 467002 479181 486658



4 Conclusions



00

04

08

12

16

0 100 200 300 400 500Temperature (K)


120572(105K

)

(a)

17

18

19

20

21

0 5 10 15 20

Gru

neise

n pa

ram

eter

Pressure (GPa)

T = 0KT = 500KT = 1000K

(b)

0

11

22

33

44

55

0 100 200 300 400 500Temperature (K)

Spec

ific h

eat (

Jmollowast

K)

C

Cp

(c)

137

154

171

188

205

0 5 10 15 20

Deb

ye te

mpe

ratu

re (K

)

Pressure (GPa)

T = 0KT = 500KT = 1000K

(d)


119863









References









119909La1minus119909












2














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




00

04

08

12

16

0 100 200 300 400 500Temperature (K)


120572(105K

)

(a)

17

18

19

20

21

0 5 10 15 20

Gru

neise

n pa

ram

eter

Pressure (GPa)

T = 0KT = 500KT = 1000K

(b)

0

11

22

33

44

55

0 100 200 300 400 500Temperature (K)

Spec

ific h

eat (

Jmollowast

K)

C

Cp

(c)

137

154

171

188

205

0 5 10 15 20

Deb

ye te

mpe

ratu

re (K

)

Pressure (GPa)

T = 0KT = 500KT = 1000K

(d)


119863









References









119909La1minus119909












2














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







References









119909La1minus119909












2














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Research Article Theoretical Investigations of Structural ...to be crystallizing in three other...

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Transcript of Research Article Theoretical Investigations of Structural ...to be crystallizing in three other...