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Journal of Magnesium and Alloys 2 (2014) 349e356www.elsevier.com/journals/journal-of-magnesium-and-alloys/2213-9567

Full length article

First principle study of structural, electronic and thermodynamic behaviorof ternary intermetallic compound: CeMgTl

R.P. Singh*

Department of Physics, S.S.V. Degree College, Affiliated to C.C.S. University-Meerut, Hapur, U.P. India

Received 23 August 2014; revised 20 October 2014; accepted 21 October 2014

Available online 4 December 2014

Abstract

To study the structural, electronic and thermodynamic behavior of CeMgTl, full-potential linear augmented plane wave plus local orbital (FP-LAPWþ lo)method has been used. The lattice parameters (a0, c0), bulkmodulus (B0) and its first order pressure derivative (B00) have been calculatedfor CeMgTl. Band structure and density of states histograms depicts that “5d” orbital electrons of Tl have dominant character in the electroniccontribution to CeMgTl. Impact of the temperature and pressure on unit cell volume, bulk modulus, Debye temperature, Grüneisen parameter,specific heat and thermal expansion coefficient (a) have been studied in wide temperature range (0e300 K) and pressure range (0e15 GPa).Copyright 2014, National Engineering Research Center forMagnesiumAlloys of China, Chongqing University. Production and hosting by ElsevierB.V. All rights reserved.

Keywords: Intermetallics; Structural properties; Electronic structure; Thermodynamic properties

1. Introduction

Ceriumemagnesiumethallium (CeMgTl) is a 1:1:1 stoi-chiometry isotypic intermetallic compound belonging toREMgX (RE ¼ elements from rare earth group, X ¼ 13thgroup element) like compounds viz. GdMgIn and GdMgGa)[1]. CeMgTl crystallizes in hexagonal ZrNiAl type (P-62m)structure. REMgX intermetallics are formed by replacing latetransition element (T ) with light main group element viz. Li,Mg etc [1e3] in the equiatomic intermetallics RETX(RE ¼ rare earth element; T ¼ late transition element;X ¼ main group element) which have potential applications inthe sensors, random access memories etc [4].

REMgTl may be the one of superior alternate of RETX fromfuture aspects of applications. So far hereCeMgTl is taken underconsideration from REMgX compounds for the study. Also

* Tel.: þ91 9411901677; fax: þ91 122 2306645.E-mail address: [email protected].

Peer review under responsibility of National Engineering Research Center

for Magnesium Alloys of China, Chongqing University.

http://dx.doi.org/10.1016/j.jma.2014.10.004.

2213-9567/Copyright 2014, National Engineering Research Center for Magnesium Alloys of China, Cho

CeMgTl and other REMgX intermetallic compounds have beensynthesized successfully and some structural, magnetic studieshave been made by R. Kraft et al. [5e7]. But these studiesprovide a very little information on CeMgTl compound and tobest our knowledge no more experimental/theoretical study hasbeen made on CeMgTl. Thus, the motivation for the presentwork is to discuss and give more information on structural andelectronic properties along with thermodynamic behavior ofunit cell volume (V), Bulk modulus (B), Debye temperature(qD), Grüneisen parameter (g), specific heat (CV) and thermalexpansion coefficient (a) for CeMgTl under pressure and tem-perature. This work will help in further understanding andcontrolling the material properties under stress, and also pro-vides reference data for the future experimental/theoreticalwork on this notable material.

2. Computational approach

Structural, electronic and thermodynamical calculationsbased on density functional theory (DFT) implemented inWIEN2k and Gibbs2 package have been [8,9] investigated for

ngqing University. Production and hosting by Elsevier B.V. All rights reserved.

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Fig. 1. Unit cell structure of CeMgTl generated by Xcrysden.

350 R.P. Singh / Journal of Magnesium and Alloys 2 (2014) 349e356

CeMgTl intermetallic compound. The advanced FP-LAPW þ lo method [10,11] has been used to linearize theenergies which is highly accurate technique based on DFT. Forstructural and electronic properties, we have used generalizedgradient approximation (GGA) [12]. The k and E convergenceare checked by increasing the number of k points and theenergy convergence criteria. In the irreducible part of theBrillouin zone, 12 � 12 � 18 k points were used to calculatethe total and partial density of states and Fermi energy ofCeMgTl is found to be 0.3742 eV.

Quasi-harmonic Debye model implemented in Gibbspackage [9,13,14] has been used to calculate thermo-dynamical behavior of CeMgTl. In quasi-harmonic Debyemodel the non equilibrium Gibbs function G* (V; P, T ) is inthe form of

G*ðV ;P;TÞ ¼ EðVÞ þPV þAvib½qðVÞ;TÞ ð1ÞHere E(V) is total energy per unit cell of CeMgTl, PV

denotes the constant hydrostatic pressure, q(V) is the Debyetemperature, and Avib is the vibration term which can beexpressed using Debye model of the phonon density of statesas [14]

Avib

�q;T

�¼ nkT

�9q

8Tþ 3 ln

�1� e�q=T

��D

�q

T

��ð2Þ

Here, n is the number of atoms per unit formula unit, D(q/T ) is the Debye integral. For an isotropic solid, q can beexpressed as [14]

qD ¼ Zk

�6pV1=2n

�1=3f

s

! ffiffiffiffiffiBsM

rð3Þ

Here, M is molecular weight per unit cell and Bs is theadiabatic bulk modulus, which is nearly equal to staticcompressibility given by

Bs ¼ B�V

�¼ V d

2EV

dV2ð4Þ

and f (s) is given by

f

s

!¼"3

(2

�2ð1þsÞ3ð1�2sÞ

�3=2þ�

1þs3ð1�sÞ

�3=2)�1#1=3ð5Þ

The non-equilibrium Gibbs functions as a function of (V; P,T ) is minimized with respect to volume V:�vG*ðV ;P;TÞ

vV

�P;T

¼ 0 ð6Þ

By solving the above equation with respect to volume V,one can obtain the thermal equation of state (EOS) V (P, T ).The specific heat at constant volume and pressure (CV, Cp)and thermal expansion coefficient a by using the expressions[14]:

Cv ¼ 3nk�4D

�q

T

�� 3q=Teq=T � 1

�ð7Þ

S¼ nk�4D

�q

T

�� 3 ln

�eq=T � 1

��ð8Þ

a¼ gCvBTV

ð9Þ

Cp ¼ Cv1þ agT ð10Þ

Here g represents the Grüneisen parameter, expressed as

g¼�dln qðVÞdln V

ð11Þ

3. Results and discussion

3.1. Structural properties

Unit cell structure of CeMgTl generated by “Xcrysden”package [15] has been shown in Fig. 1 which shows thehexagonal structure with lattice parameters (a ¼ 7.741 Å,c ¼ 4.737 Å) [7]. The bulk properties of a crystalline materialcan accordingly be determined by calculating the total energyas a function of unit cell volume. Structural properties viz.lattice parameter (a0, c0), bulk modulus (B0) and its first orderpressure derivative (B0

0) are calculated by fitting the totalenergy according to the BircheMurnaghan's equation of state[16,17] given by:

Etotal¼E0 V

!þ B0V0B00B00�1

"B0

�1�V0

V

�þ�V0V

�B00

�1#

ð12Þwhere, and are the energy and volume at equilibrium. and arethe equilibrium bulk modulus and its first order pressurederivative.

Fig. 2. Total energy as a function of unit cell volume for CeMgTl with GGA approximation.

351R.P. Singh / Journal of Magnesium and Alloys 2 (2014) 349e356

The energy vs. volume (obtained using optimizationmethod) curve for CeMgTl has been shown in Fig. 2 withdisplaying equilibrium volume (V0), bulk modulus (B), pres-sure derivative of bulk modulus (BP) and minimum energy(E0). The shape of energy vs volume curve shows good relaxedoptimization of CeMgTl. The calculated lattice parameters(a0, c0), bulk modulus and its first order pressure derivative arealso shown in Table 1 in which a0, c0 show good agreementwith experimental values [7].

Table 1

Lattice constant, a0, c0 (Å), Bulk modulus, B0 (GPa), Pressure derivative ofbulk modulus, B0

0 (GPa) equilibrium condition (at 0 K) for CeMgTl usingGGA.

Compounds a0 c0 B0 B00

CeMgTl 7.753 4.747 48.78 4.55

Expt. [12] 7.741 4.737 e e

Fig. 3. Contour plots of the total valence charge density in 3-dimentional (100)

plane for CeMgTl.

3.2. Electronic properties

The charge density calculations are necessary to determinethe character of chemical bonds between the constituent

Fig. 4. (a) Electron dispersion curves along high symmetry direction in the

Brillouin zone for CeMgTl.


elements. In order to investigate the charge distribution andalso the nature of chemical bonding, we have calculated theelectronic charge density for CeMgTl. The contour plots ofcharge density have been shown in Fig. 3. From Fig. 3, it

Fig. 5. (i) Calculated total density of states for (a) CeMgTl (b) Ce, Mg and Tl (ii)

orbital (f) Mg-“s”, “p” orbital (g) Tl-“s”, “p” orbital (h) Tl-“d” orbital.

appears that the LaeTl bond is typically ionic, this is becausethere is no much bonding charge to link the La and Tl atomsand almost spherically symmetric around each atom. Again,no bonding charge is found to link between LaeMg and

partial density of states for (c) Ce-“s”, “p” orbital (d)Ce-“d” orbital (e) Ce-“f”


TleMg. Thus, LaeMg and TleMg bonds also have completeionic character. The ionic character is a consequence ofmetallic character, indicating that CeMgTl is a metallicmaterial.

The results on the electronic behavior of CeMgTl havebeen shown in terms of energy bands and total, partial densityof states. The calculated band structure of CeMgTl along thehigh symmetry directions G, M, K and A in the Brillouin zone

Fig. 6. (i) Temperature induced variation in (a) volume, V (c) Bulk modulus, B (e) D

modulus, B (f) Debye temperature.

have been shown in Fig. 4. It can be seen from Fig. 4 that thereis no band gap is found at the Fermi level as valence andconduction bands overlap significantly near the Fermi level, asa result, CeMgTl exhibit the metallic character.

The total density of states (TDOS) plots for CeMgTl, Ce,Mg, and Tl have been shown in Fig. 5(a) and (b). The partialdensity of states (PDOS) have been displayed in (i) Fig. 5(c)for Ce-s, p (ii) Fig. 5(d) for Ce-d (iii) Fig. 5(e) for Ce-f (iv)

ebye temperature, qD (ii) pressure induced variation in (b) volume, V (d) Bulk


Fig. 5(f) for Mg-s, p (v) Fig. 5(g) for Tl-s, p and (vi) Fig. 5(h)for Tl-d orbitals respectively. The dotted lines in all DOSFig. 5(a)e(h) at 0 eV show the Fermi level. It is clear fromFig. 5(a) that most of the DOS lie in the energy rangeapproximately between �11.0 eV and 0 eV. The states whichlie at around �11.0 eV are due to Tl atom (see blue line

Fig. 7. (i) Temperature induced variation in (a) Debye temperature, qD (c) Grüneis

Debye temperature, qD (d) Grüneisen parameter, g and (f) specific heat, CV.

contribution in Fig. 5(b)). An interesting feature of the DOS ofCeMgTl is the strong hybridization between Ce-p and Mg-sstates at about �7.0 eV below Fermi level. Hybridizationalso exists between Ce-p and Mg-p states at around �1.0 eV.Furthermore, since large difference is existed between theenergies of Ce-p and Tl-s, d states. Thus, no hybridization is

en parameter, g and (e) specific heat, CV (ii) Pressure induced variation in (b)


found between Ce-p and Tl-s, d states. Some Ce-d, f states areempty above the Fermi level for the conduction (see Fig. 5(d),(e)). In overall DOS Figures, it is clear that Tl-d states havedominant character in contribution to electronic conduction inCeMgTl.

3.3. Thermodynamic properties

The effect of temperature and pressure on unit cell volume(V), Bulk modulus (B), Debye temperature (qD), Grüneisenparameter (g), specific heat (CV) and thermal expansion co-efficient (a) for CeMgTl have been studied using Quasi-harmonic Debye model in a wide temperature range0e300 K and pressure range 0e15 GPa at different temper-atures (0 K, 75 K, 150 K, 225 K and 300 K). The results oneffect of temperature and pressures have been shown in Figs. 6and 7.

Fig. 6(a) and (b) depict that unit cell volume (V) increaseswith temperature but decreases with pressure. Unit cellvolume increases with temperature due to the expansion ofits dimensions with temperature. Unit cell volume, V de-creases with pressure as dimensions of unit cell are com-pressed with increasing the pressure. The bulk modulus (B)is a material property indicating the degree of resistance of amaterial to compression. Larger the bulk modulus, greater isthe degree of resistance. Fig. 6(c) and (d) show that bulkmodulus, B decreases with increasing the temperature butincreases with increasing the pressure. This change in bulkmodulus is caused by change in unit cell volume with tem-perature and pressure. This also shows that degree of resis-tance of CeMgTl decrease with increasing the temperaturebut increase with increasing the pressure. Debye temperatureis related to the maximum thermal vibration frequency of asolid. The variation of Debye temperature with temperatureand pressure reflects the fact that the thermal vibration fre-quency of the particles changes with pressure and tempera-ture. It can be seen from Fig. 6(e) and (f) that Debyetemperature, qD decreases slowly with increasing the tem-perature and increase with increasing the pressure rapidly.The slow variation in qD with temperature reflects smalleffect of temperature on qD while rapidly variation in qD withpressure shows good impact of pressure on qD. In case ofCeMgTl, the variation of Debye temperature, qD with tem-perature and pressure reflects the fact that the thermal vi-bration frequency of the particles changes slowly withtemperature but changes rapidly with pressure.

The Grüneisen parameter could describe the alteration invibration of a crystal lattice based on the increase or decreasein volume as a result of temperature or pressure. Fig. 7(a) and(b) shows the variation in Grüneisen parameter with tem-perature and pressure. It can be seen from these Figures thatGrüneisen parameter increase with temperature but decreasewith pressure rapidly. Grüneisen parameter increases almostmonotonously with temperature, indicating that temperaturehas no significant effect on Grüneisen parameter. The tem-perature and pressure dependent behavior of the calculatedheat capacity at constant volume (CV) has been shown in

Fig. 7(c) and (d). One can see from Fig. 7(c) that CV in-creases with the temperature up to T z 150 K (followsDebye T3 law) and at temperature, T > 150 approaches aconstant value (DulongePetit limit), indicating that temper-ature has more impact on the heat capacity. Fig. 7(d) in-dicates that pressure has opposite influences on the heatcapacity, CV and the effect of temperature on the heat ca-pacity is more significant than that of pressure. Fig. 7(e)shows the variation of thermal expansion coefficient, a as afunction of temperature. The thermal expansion coefficient(a) increases rapidly especially at temperature below 150 K,whereas it gradually tends to a slow increase at higher tem-peratures. Fig. 7(f) shows that thermal expansion coefficient,a decrease slowly with pressure, indicating small impact ofpressure on thermal expansion coefficient, a. Furthermore, Itcan be observed from temperature dependent thermodynamiccharacteristics (Fig. 6(a), (c), (e)) and ((b), (d), (f)) thattemperature has negligible effect on V, B, qD, g and a in thetemperature range 0e50 K.

4. Conclusions

Full potential linearize potential augmented plane wavemethod using generalized gradient approximation (GGA) andquasiharmonic Debye model has been used to study thestructural, electronic and thermodynamic properties ofCeMgTl isotypic intermetallic compound. The calculated lat-tice parameters are consistent with experimental/theoreticalvalues. Ionic character is dominant on CeMgTl which isconsequence of metallic character. The bands are found to beoverlap at Fermi level, indicating metallic character ofCeMgTl. In DOS, Tl-d orbital electrons are found to bedominant character. The bulk modulus, B found to be de-creases with increasing the temperature but increase withincreasing the pressure, indicating degree of resistance ofCeMgTl decrease with increasing the temperature but increasewith increasing the pressure. Temperature has found to besmall impact on B, qD, g but good impact on CV and a intemperature range T < 150 K. Pressure has found to be highimpact on B, qD, and small impact on g, CV and a.

References

[1] F. Canepa, M.L. Fornasini, F. Merlo, M. Napoletano, M. Pani, J. Alloys

Compd. 12 (2000) 312.

[2] A. Czybulka, G. Steinberg, H.U. Schuster, Z. Natur-forsch. 34b (1979)

1057.

[3] G. Steinberg, H.U. Schuster, Z. Natur-forsch. 34b (1979) 1165.

[4] C. Falser, F.G. Fecher, B. Balke, Chem. Int. Ed. 46 (2007) 668.

[5] R. Kraft, M. Valldor, R. Pottgen, Z. Natur-forsch. 58b (2003) 827.

[6] R. Kraft, M. Valldor, D. Kurowski, R.D. Hoffmann, R. Pottgen, Z. Natur-

forsch. 59b (2004) 513.

[7] R. Kraft, R. Pottgen, Z. Natur-forsch. 60b (2005) 265.

[8] P. Blaha, K. Schwarg, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k,

an Augmented Plane Wave Plus Local Orbitals Program for Calculating

Crystal Properties, Technical University, Wien, Austria, 2001, ISBN 3-

9501031-1-2.

[9] M.A. Blanco, E. Francisco, V. Lua~na, Comput. Phys. Commun. 158(2004) 57.

http://refhub.elsevier.com/S2213-9567(14)00064-4/sref1http://refhub.elsevier.com/S2213-9567(14)00064-4/sref1http://refhub.elsevier.com/S2213-9567(14)00064-4/sref2http://refhub.elsevier.com/S2213-9567(14)00064-4/sref2http://refhub.elsevier.com/S2213-9567(14)00064-4/sref3http://refhub.elsevier.com/S2213-9567(14)00064-4/sref4http://refhub.elsevier.com/S2213-9567(14)00064-4/sref5http://refhub.elsevier.com/S2213-9567(14)00064-4/sref6http://refhub.elsevier.com/S2213-9567(14)00064-4/sref6http://refhub.elsevier.com/S2213-9567(14)00064-4/sref7http://refhub.elsevier.com/S2213-9567(14)00064-4/sref8http://refhub.elsevier.com/S2213-9567(14)00064-4/sref8http://refhub.elsevier.com/S2213-9567(14)00064-4/sref8http://refhub.elsevier.com/S2213-9567(14)00064-4/sref8http://refhub.elsevier.com/S2213-9567(14)00064-4/sref9http://refhub.elsevier.com/S2213-9567(14)00064-4/sref9http://refhub.elsevier.com/S2213-9567(14)00064-4/sref9


[10] K. Schwarz, P. Blaha, Comput. Mater. Sci. 28 (2003) 259.

[11] G.K.H. Madsen, P. Blaha, K. Schwarz, E. Sj€ostedt, L. Nordstr€om, Phys.

Rev. B 64 (2001) 195134.

[12] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 3244.

[13] A. Otero-de-la-Roza, D. Abbasi-P�erez, V. Lua~na, Comput. Phys. Com-mun. 182 (10) (2011) 2232.

[14] M. Flrez, J.M. Recio, E. Francisco, M.A. Blanco, A.M. Pends, Phys. Rev.

B 66 (2002) 144112.

[15] A. Kokalj, Comput. Mater. Sci. 28 (2003) 155.

[16] F. Birch, Phys. Rev. 71 (1947) 809.

[17] F.D. Murnaghan, Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244.

http://refhub.elsevier.com/S2213-9567(14)00064-4/sref10http://refhub.elsevier.com/S2213-9567(14)00064-4/sref11http://refhub.elsevier.com/S2213-9567(14)00064-4/sref11http://refhub.elsevier.com/S2213-9567(14)00064-4/sref11http://refhub.elsevier.com/S2213-9567(14)00064-4/sref11http://refhub.elsevier.com/S2213-9567(14)00064-4/sref12http://refhub.elsevier.com/S2213-9567(14)00064-4/sref13http://refhub.elsevier.com/S2213-9567(14)00064-4/sref13http://refhub.elsevier.com/S2213-9567(14)00064-4/sref13http://refhub.elsevier.com/S2213-9567(14)00064-4/sref13http://refhub.elsevier.com/S2213-9567(14)00064-4/sref14http://refhub.elsevier.com/S2213-9567(14)00064-4/sref14http://refhub.elsevier.com/S2213-9567(14)00064-4/sref15http://refhub.elsevier.com/S2213-9567(14)00064-4/sref16http://refhub.elsevier.com/S2213-9567(14)00064-4/sref17

First principle study of structural, electronic and thermodynamic behavior of ternary intermetallic compound: CeMgTl1. Introduction2. Computational approach3. Results and discussion3.1. Structural properties3.2. Electronic properties3.3. Thermodynamic properties

4. ConclusionsReferences

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