A study of the phase transitions electronic structures and thermodynamic properties of mg2x x ge si and sn under high pressure

Djaballahc a Department of Physics, Faculty of Science, University of Batna, 05000, Batna, Algeria b Physics Department, Faculty of Science, University of M'sila, 28000, M'sila, Algeria

Original Article

A study of the phase transitions, electronic structures and

pressure

M Guezlanea, H Baazizb,*, Z Chari fib

, A Belgacem-Bouzidac, Y Djaballahc

a Department of Physics, Faculty of Science, University of Batna, 05000, Batna, Algeria

b Physics Department, Faculty of Science, University of M'sila, 28000, M'sila, Algeria

c Laboratoire d'
etude Physico-Chimique des Mat
eriaux, D
epartement de Physique, Facult
e des Sciences, Universit
e de Batna, Rue Chahid Boukhlouf, 05000,

Batna, Algeria

a r t i c l e i n f o

Article history:

Received 19 November 2016

Received in revised form

21 January 2017

Accepted 26 January 2017

Available online 6 February 2017

Keywords:

DFT

FP-LAPW

EV-GGA

Phase transitions

Thermodynamic

a b s t r a c t

In this work, we theoretically investigate phase transitions, electronic structures and thermodynamic properties of Mg2X (X¼ Ge, Si and Sn) under high pressures To reach this goal, the total energy has been calculated by using the full-potential linearized augmented plane wave (FP-LAPW) method with generalized gradient approximation (GGA), local density approximation (LDA) and EngeleVosko approximation (EV-GGA), which are based on the exchange-correlation energy optimization The fully relaxed structure parameters of Mg2X compounds are in good agreement with the available experi-mental data Our results demonstrate that the Mg2X compounds undergo two pressure-induced phase transitions The first one is from the cubic antifluorite (Fm3m) structure to the orthorhombic anticotunnite (Pnma) structure in the pressure range of 3.77e8.78 GPa (GGA) and 4.88e8.16 GPa (LDA) The second transition is from the orthorhombic anticotunnite structure to the hexagonal Ni2 In-type (P63mmc) structure in the pressure range of 10.41e29.77 GPa (GGA) and 8.89e63.45 GPa (LDA) All the structural parameters of the high pressure phases are analyzed in detail Only a small difference

in the structural parameters is observed at high pressures between the calculated and experimental results The electronic and thermodynamic properties are also analyzed and discussed The estab-lishment of the metallic state of the Mg2X (X ¼ Ge, Si and Sn) compounds at high pressure is confirmed

© 2017 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

1 Introduction

Among the silicides, Mg2Si is the only possible stoichiometric

compound in the MgeSi alloy as well as Mg2Sn and Mg2Ge These

compounds have attracted much attention in the last few years due

to their important properties Their relatively high melting points

(1358K [1], 1030 K[1]and 1390 K[2]for Mg2Si, Mg2Sn and

Mg2Ge, respectively) and high electrical conductivity make them

very useful for high thermoelectric material applications in the

temperature range of 500e800 K[3,4] The Mg2X (X¼ Ge, Si and Sn)

compounds as lightweight materials with high specific strengths

and high specific elastics modulus[5]were proposed to be suitable

materials for the automotive products and manufacturing pro-cesses, and due to the narrow energy gaps (Eg ~ 0.3e0.6 eV)[6]they can be used as an infrared detector in the wavelength range from 1.2

to 1.8mm [6] Finally, the non-toxic properties make them envi-ronmentally friendly[7] Under ambient conditions (the pressure below 0.1 MPa), the Mg2X (X ¼ Ge, Si and Sn) compounds are intermetallic with low densities (<2 g/cm3)[8]and crystallize in a face-centered cubic lattice They possess the antifluorite (Fm3m) CaF2type structure[9,10], which is a very interesting type of sem-iconducting materials forming the simplest metalesemiconductor hybrid material Some theoretical and experimental studies have been conducted to understand the physical properties of Mg2X (X¼ Ge, Si and Sn) in the last few years The structure and electronic properties of these semiconductors were reported by several groups [11e16] with different methods Some thermodynamic properties have also been studied[12,17,18]

* Corresponding author Fax: þ213 35556453.

E-mail address: baaziz_hakim@yahoo.fr (H Baaziz).

Peer review under responsibility of Vietnam National University, Hanoi.

Contents lists available atScienceDirect Journal of Science: Advanced Materials and Devices

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d

http://dx.doi.org/10.1016/j.jsamd.2017.01.005

2468-2179/© 2017 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license

Journal of Science: Advanced Materials and Devices 2 (2017) 105e114

The exploitation of the physical properties of any compound

requires focusing on the relationship between the pressure and the

structure In fact, the study of the material structure under

compression is a rapidly developing field and is receiving

increasing attention [19] In 1986, Mao et al [20] found

experi-mentally by the energy dispersive synchrotron X-ray diffraction

(EDXD) that Mg2Si undergoes a phase transition from the cubic

antifluorite structure to the anticotunnite structure under

pres-sures above 7.5 GPa at room temperature Recently, Hao et al.[21],

have reinvestigated the structural behavior of this semiconductor

under pressures up to 41.3 GPa They obtained twofirst order phase

transitions Thefirst transition occurs at pressures of about 7.5 GPa,

at which the cubic antifluorite (Fm3m) structure changes to the

orthorhombic anticotunnite (Pnma) structure The second one

oc-curs at higher pressures (of about 21.3 GPa), at which the

com-pound favors the hexagonal Ni2In-type P63mmc structure Due to

the absence of similar experimental results for the Mg2Sn and

Mg2Ge compounds, Yu et al.[16]have predicted the same phase

transition using the plane-wave pseudo-potential density

func-tional theory method Looking for the most stable structure of

Mg2X (X¼ Ge, Si and Sn), several other computational methods

have been adopted Most of these calculations are limited to zero

pressure, while the appliactions of the compound are often subject

to a higher pressure above ambient In literature, however, only a

few results under high pressure in the theoretical works have been

found Firstly, Kalarasse et al.[22]reportedfirst-principles’ studies

of the pressure effect using the full-potential linearized augmented

plane-wave method limited to the ambient structure and without

exceeding 5 GPa Secondly, Benhai Yu et al [23] obtained the

structural, electronic, elastic and thermodynamic properties of

magnesium silicide successfully using the first-principles

plane-wave pseudo-potential (PW-PP) method in combination with the

quasi-harmonic Debye model but also without exceeding the 8 GPa

Finally, Yu et al.[15,16]investigated the phase transitions of Mg2X

(X ¼ Ge, Si and Sn) and Huan et al.[14] for Mg2Si under high

pressures using thefirst-principles plane-wave method within the

pseudo-potential and generalized gradient approximations (GGA)

In this work, we have calculated the pressure and temperature

dependence of the thermodynamic properties of the MgeX

(X¼ Ge, Si and Sn) alloys with GIBBS2 program using the WIEN2K

data within the framework of the quasiharmonic approximation In

addition, the structural and electronic properties of their

stochio-metric compounds Mg2X (X¼ Ge, Si and Sn) have been investigated

by using thefirst principle calculations based on density functional

theory (DFT)[24,25]within the full-potential linearized augmented

plane wave (FP-LAPW) method

2 Computational details

The Mg2X (X¼ Ge, Si and Sn) compounds crystallize in a cubic

antifluorite structure at ambient conditions, the Mg and X (X ¼ Ge,

Si and Sn) atoms occupy the 8c (0.25, 0.25, 0.25) and the 4a (0, 0, 0)

Wyckoff sites, respectively At high pressure, it has been reported

experimentally [21] that Mg2Si undergoes two structural

trans-formations,firstly to the orthorhombic and then to the hexagonal

structures with a remarkable difference in the volume collapse

between thefirst and second transitions

The calculations have been performed using the FP-LAPW as

implemented in WIEN2K[26]code based on the very powerful

prediction method for the new materials properties (DFT) In this

FP-LAPW method, the unit cell of the three structures is

parti-tioned into non-overlapping muffin-tin spheres around the

atomic sites and an interstitial region We used the generalized

gradient approximation (GGA [27]) and the local density

approximation (LDA[25])eby Perdew et al-exchange-correlation

potential to treat the electroneelectron interaction In addition,

we have applied the EngeleVosko (EV-GGA[28]) scheme which proposes better electronic properties In order to achieve energy eigenvalues convergence, the wave functions in the interstitial region have been expanded in plane waves with a cut off of

Kmax ¼ 9/Rmt, where Rmt denotes the smallest atomic sphere radius and Kmaxgives the magnitude of the largest k-vector in the plane wave expansion The Rmtis taken to be 2.1e2 atomic units (a.u.) for Mg and X (X¼ Ge, Si and Sn) for all phases Brillouin-zone (BZ) integrations within the self-consistency cycles have been performed via a tetrahedron method, using 35k points for both phases in the IBZ The self-consistent iterations have been performed until the convergence in the energy reached about

104 Ry3 We have also used our results obtained by the GGA approximation for the thermodynamic properties the GIBBS2 [29]program

3 Results and discussion 3.1 Total energy calculation and high pressure structural transformation

We have determined the structural properties from the calcu-lation of the ground state energy as a function of the volume around the equilibrium The variations of the energy (E) with vol-ume (V) in three structures for the three compounds using GGA and LDA approximation are shown inFig 1 The calculated structural parameters from these three structures' types of Mg2X (X¼ Ge, Si, and Sn) are listed with the available experimental data and few other theoretical results inTable 1 The obtained lattice parameters

of the antifluorite structure using LDA are in excellent agreement with the experimental data and other theoretical results at 0 GPa, whereas the calculated parameters using GGA deviate with some proportions For the Mg2Si compound in the hexagonal Ni2In-type (P63mmc) structure our calculated value of c/a is about 1.3 using both GGA and LDA approximation in 0 GPa, and 1.27 in the tran-sition pressure, with the same value found in the prediction of the two other compounds Mg2Sn and Mg2Ge which is close to the other experimental and theoretical value 1.26, but a more evident discrepancy can be observed in the cell parameters at high pressure phases between our calculated results using GGA and LDA for the three compounds (Table 1) Using the plane-wave pseudo-potential density functional theory method, Yu et al.[15,16]and Huan et al [14]have found an overlapping curve of the EeV plot between the anticotunnite and Ni2In-type structures for all the Mg2X (X¼ Ge, Si and Sn) compounds, because of a groupesubgroup relation be-tween the anticotunnite (Pnma) and the Ni2In-type (P63/mmc) structures However, this overlap disappears in our results and the discrepancy became very clear, as can be explained by the higher precision of the full-potential method instead of the pseudo po-tential density functional theory method We notice here that there

is no accurate experimental data regarding the high pressure structural behavior available for Mg2Sn and Mg2Ge, and the only prediction results are obtained by Yu et al [16] In the present study, we can determine the actual transition point between the anticotunnite and the Ni2In-type structures from our EeV curves The transition pressures from the antifluorite phase to the anti-cotunnite phase and further to the Ni2In-type structure phase are listed inTable 2with the volume reduction for Mg2X (X¼ Si, Sn and Ge) compounds in comparison with the previous calculations and experimental data For all Mg2X (X¼ Ge, Si and Sn) compounds, we can notice that the bulk modulus increase with each transition, and decrease from LDA to GGA in the same phase This increase can be attributed to the increase in the bond strength between atoms under high pressures

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114 106

The relation between pressure and volume using LDA

approxi-mation for the different phases of the Mg2X (X¼ Ge, Si and Sn)

compounds is shown inFig 2 The two phase transitions can be

observed with a volume collapse synonym of a discontinuity in the

pressure These results indicate that these two transitions are

considered to be offirst-order due to the discontinuity of the

vol-ume at each one of them The Mg2X (X¼ Ge, Si and Sn) compounds

undergo two crystallographic transitions, the first one from the

antifluorite to anticotunnite phase, and the second one from

anticotunnite to the Ni2In-type structures phase For Mg2Si, thefirst

transition occurs at 8.78 GPa (GGA) and 8.16 GPA (LDA) with a

volume collapse of 11.99% (GGA) and 10.85% (LDA) This is very close

to the values of thefirst transition of Mg Ge with 12.29% (GGA) and

11.43% (LDA) volume collapse at 7.85 GPa (GGA) and 8.16 GPa (LDA), respectively For Mg2Ge, however, it is clearly higher: the first transition pressure occurs at 3.77 GPa (GGA) and 4.88 GPa (LDA) with a volume collapse of 8.15% (GGA) and 8.73% (LDA) This can be explained by the high compressibility of the Mg2Si and the Mg2Ge (54.1633 GPa and 46.2945 GPa respectively) with respect to that of the Mg2Sn (37.5718 GPa) in the ambient condition Those results are

in good agreement with the previous theoretical and experimental data[14e16,21] Our remaining results indicate that the second transition between the anticotunnite and Ni2In-type needs high pressures to occur for Mg2Si (22.9 GPa (GGA) and 22 GPa (LDA)) and even higher for Mg2Ge (29.77 GPa (GGA) and 63.45 GPa (LDA)) with

a significant volume collapse (18.61% (GGA) and 17.72% (LDA) for Fig 1 Calculated total energy as a function of unit-cell volume for three structures of Mg 2 X (X ¼ Ge, Si and Sn) compounds.

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114

Table 1

Calculated lattice parameters, bulk modulus, and DOS at E F using LDA and GGA, in comparison with the available previous calculations and the experimental data for Mg 2 X (X ¼ Ge, Si and Sn) in three phases.

Mg 2 Si-AF

Mg 2 Si-HEX

Mg 2 Si-AC

Mg 2 Sn-AF

Mg 2 Sn-HEX

Mg 2 Sn-AC

Mg 2 Ge-AF

Mg 2 Ge-HEX

Mg 2 Ge-AC

a PWPP Ref [11]

b Ref [21]

c Ref [30]

d Ref [31]

e FP-LAPW Ref [32]

f PWPP Ref [12]

g Ref [33]

h Ref [13]

i Ref [15]

j Ref [16]

k Ref [11]

Table 2

Calculated transition pressure and volume collapse using LDA and GGA, in comparison with the available previous calculations and the experimental data for Mg 2 X (X ¼ Ge, Si and Sn) compounds.

Antifluorite to Anticotunnite Anticotunnite to Ni 2 In-type

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114 108

the Mg2Si; 21.19% (GGA) and 33.03% (LDA) for Mg2Ge) However,

Mg2Sn has a lower pressure transition (10.41 GPa (GGA) and

8.89 GPa (LDA)) and a little less volume collapse compared with the

two other compounds (15.39% (GGA) and 12.10% (LDA)) Having

compared with the theoretical results[14e16], we have found that

for this prediction transition there is a rapprochement between

22 GPa (GGA), 24 GPa[14]and 28 GPa[15]for the pressure

tran-sition of Mg2Si, 10.41 GPa (GGA) and 18.40 GPa[16]for Mg2Sn, and

29.77 GPa (GGA) and 33.28 GPa[16]for Mg2Ge, with a small

in-crease The only big difference between these results is the second

phase transition of Mg2Ge at 63.45 GPa (LDA) with our GGA result

of 29.77 GPa This discrepancy can be attributed to the

non-existence of the hexagonal Ni2In-type (P63mmc) structure phase

for Mg2Ge

3.2 Band structure and density of states

We have computed the band structure and the total and partial

density of state (DOS) of Mg2X (X¼ Ge, Si and Sn) compounds in the

antifluorite (AF), anticotunite (AC) and hexagonal Ni2In-type (HEX)

structures using GGA, LDA and EV-GGA approximations to show

the pressure effects on these properties It was well known that the

simple form of GGA and LDA is not sufficiently flexible for

accu-rately reproducing both exchange-correlation energy and its charge

derivative They usually underestimate the energy gap [34,35]

That's why Engel and Vosko[28]by considering this shortcoming

constructed a new functional form of the GGA (called as EV-GGA),

which can provide a better band splitting and some other

properties depending to the accuracy of the exchange-correlation potential Fig 3 shows our calculated band structure and total density of state (TDOS) using the EV-GGA for Mg2X (X¼ Ge, Si and Sn) compounds in each phase The top of the valence band is

defined to be at zero energy which corresponds to the Fermi en-ergy The computed band gaps of these three compounds in the antifluorite phase structure using LDA, GGA and EV-GGA are listed

inTable 3 The band structure shows clearly that these materials are small indirect band gap (G-X) semiconductors [32] in ambient condition (0 GPa), with 0.676 eV,0.113 eV and 0.701 eV for Mg2Si,

Mg2Sn and Mg2Ge, respectively using the EV-GGA approximation These results are in good agreement with other studies[36], and more accurate than those obtained by Yu et al.[15,16]using the GGA approximation The total DOS of thisfirst phase can be divided into three groups The lowest energy groups are mainly dominated

by the s-X (X¼ Ge, Si and Sn) states for Mg2X compounds with a small contribution of the 3s-Mg and 3p-Mg bands The section between ~ 9 eV and 7 eV for Mg2Si and Mg2Sn, and between ~10 eV and 8 eV for Mg2Ge under the Fermi energy EF are dominated by the contribution of 4s-Ge, 3s-Si and 5s-Sn states with a tiny bonded contribution of 3s-Mg and 3p-Mg states The contribution of the p-X (X¼ Ge, Si and Sn) states are very small After a gap of ~2 eV for Mg2Si and Mg2Sn, and ~3 eV for Mg2Ge, we have found the second DOS group between5 eV and 0 eV asso-ciated with the p-X states interacting with the 3s and 3p states of thefirst and second Mg nearest neighbor The contribution of s-X bands is very small in this energy range The conduction band of

Mg X is mainly dominated by 3s-Mg, 3p-Mg and p-X states These Fig 2 Pressureevolume relations for the different phases of Mg 2 X (X ¼ Ge, Si and Sn) compounds.

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114

Fig 3 Electronic band structures and total density of states (TDOS) of Mg 2 X (X ¼ Ge, Si and Sn) compounds calculated using EVGGA.

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114 110

results show that the valence electrons are mainly around X,

although there is a little indication of a weak covalent bonding

between Mg and X With increasing pressure, the valence band

becomes wider and the conduction band penetrates down in the

valence band Thus, the value of DOS at EF(zero in our case)

in-creases The principal contribution to DOS near EFcome from

2p-Mg and p-X states for the anticotunite phase Going further with

the pressure, the bands become wider and the value of DOS at EF

tends to decrease in the hexagonal Ni2In-type phase, this

over-lapping band explains the metallization of the Mg2X compounds

3.3 Thermodynamic properties

Thermodynamic properties including heat capacity, thermal

conductivity, thermal expansion and the Grüneisen parameter are

fundamental features of materials They give interesting

informa-tion such as thermodynamic stability, interatomic interacinforma-tions,

anharmonicity of lattice vibrations and the utility of materials for

various applications

As we have mentioned, Mg2X (X¼ Ge, Si and Sn) compounds are

characterized by two phase transitions at high pressure, which can

be explained by the effect of temperature on these two transitions

and generally on the properties of each phase Therefore, it is very

important to study the thermodynamic properties and the effect of temperature on some structural parameters of these compounds in each phase (the heat capacity, the expansion coefficient, the Debye temperature, the bulk modulus and the relative variation in vol-ume) We started in Fig 4 with the effects of temperature and pressure on the bulk modulus B to get some information about the resistance to the contraction in each phase by plotting the variation

of B as a function of temperature for three different pressure values

0, 20 and 50 GPa using the GGA approximation In overall, for low temperatures between 0 and 100 K the bulk modulus appears constant especially at high pressure (50 GPa) in the three phases of

Mg2X (X¼ Ge, Si and Sn) compounds (a change of þ0.27% (for the

Mg2Ge hexagonal phase at 50 Gpa) to 2.81% (for the Mg2Ge Fig 3 (continued)

Table 3 Band gap of Mg 2 X (X ¼ Ge, Si and Sn) in the antifluorite phase.

GapG-X (eV)

Mg 2 Si 0.116 0.2218 0.676 0.6, 0.57 [14]

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114

hexagonal phase at 0 Gpa)) Above 100 K, bulk modulus decreases

linearly with increasing temperature up to 1000 K but differently

under each pressure The maximum percentage of changes clearly

seen from these results is about57.85% for Mg2Ge in the

hexag-onal phase structure under 0 GPa of pressure We note here that

increasing the pressure decreases clearly the influence of

temper-ature on the bulk modulus B Under zero-presure and at 0 K, the

antifluorite (AF) phase has the smallest bulk modulus B is lager in

the hexagonal (HEX) phase and then further increases in the

anti-cotunite (AC) phase for all Mg2X (X¼ Ge, Si and Sn) compounds

The order change between the antifluorite and the hexagonal

phases is observed at 390 K and 351 K for the Mg2Si and Mg2Ge

compounds, respectively Under a pressure of 20 GPa, a change of

order from AF-HEX-AC (with the smallest B value) to HEX-AF-AC

(with the highest B value) can be observed for Mg2Ge at about

784.5 K For Mg2Si, the change from AF-AC-HEX to AF-HEX-AC

occurs at about 633 K Only one change from AC-HEX to

AF-AC-HEX is observed under a pressure of 50 GPa for Mg2Ge at 906 K

Mg2Si always maintains the AF-AC-HEX arrangement under the

pressure of 50 GPa For Mg2Sn, the order is AF-HEX-AC, HEX-AC-AF

and HEX-AC-AF under pressures of 0, 20 and 50 GPa, respectively

without any temperature effects However the most noticeable

change under pressure effect is the behavior of the values of bulk

modulus in the antifluorite phase of Mg2Sn which increases with

pressure to exceed the value of the two other phases The calculated

volumetric thermal expansion coefficients (a) are plotted as a

function of temperature inFig 5under three pressures 0, 20, and

50 GPa For high pressures (20 and 50 GPa), a very fast expansion

can be clearly detected under 200e300 K, then it becomes very

slight until reaching a saturation value which depends for each

phase on the applied pressure Unlike these results, the alpha

co-efficients under 0 GPa for Mg2Ge and Mg2Si continue their

increasing value after 300 K, not like thefirst rate but with a clear

evolution The same behavior for Mg2Sn is observed but just in the antifluorite phase which causes the only transition observed be-tween the value of this coefficient under the temperature effect between the hexagonal and the antifluorite phases at 412 K The other remarkable result obtained from this curve is the great effect

of the pressure to this thermal expansion coefficient, which reduces its value ranges from between 10.5 105K1and 27 105K1 under 0 GPa to between 3.3 105K1and 4.6 105K1and between 1.8  105K1and 2.7 105 K1 under 20 GPa and

50 GPa respectively, which is a reduction of 60%e88% Another remark is regarding the structure which has the biggest value of the alpha coefficient at 0 GPa, it is always the hexagonal phase struc-ture except for Mg2Sn which is characterized by the increase of alpha in the antifluorite phase structure under the temperature effect at this pressure, which can be reviewed in result of the constant pressure heat capacity.Figs 6 and 7show our calculated constant volume heat capacity Cvand constant pressure heat ca-pacity Cpas a function of temperature for three different pressure values 0, 20, and 50 GPa using the GGA approximation At low temperature, both Cvand Cpincrease rapidly with temperature till

200 Ke300 K then this increase becomes lower for Cvto reach the saturation values given by Delong and Petit[37]Cv¼ 3nNAKBwhich corresponds to ~75 J/mol.K for Mg2X (X¼ Ge, Si and Sn) compounds

in all phases However, Cpcontinues increasing with temperature but slowly under 0 GPa with the same notice given for the alpha coefficient The results obtained for Debye temperature (qD) are plotted as a function of temperature under three different pressures

in Fig 8 The parameter qD increases clearly with pressure and decreases very slowly with temperature especially under high pressure We also added the variation of Gibbs energy (G) under temperature and pressure effects inFig 9, which shows the tran-sition phase and the weak effect of the temperature relative to the pressure on this energy (G)

Fig 4 Temperature and pressure effect on the bulk modulus B for Mg 2 X (X ¼ Ge, Si and Sn) compounds.

Fig 5 Temperature and pressure effects on the volumetric thermal expansion coefficients (a) for Mg X (X ¼ Ge, Si and Sn) compounds.

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114 112

Fig 7 Temperature and pressure effects on the constant pressure heat capacity C P for Mg 2 X (X ¼ Ge, Si and Sn) compounds.

Fig 8 Temperature and pressure effects on the Debye temperatureqD for Mg 2 X (X ¼ Ge, Si and Sn) compounds.

Fig 6 Temperature and pressure effects on the constant volume heat capacity C v for Mg 2 X (X ¼ Ge, Si and Sn) compounds.

¼ Ge, Si and Sn) compounds.

M Guezlane et al / Journal of Science: Advanced Materials and Devices 2 (2017) 105e114

4 Conclusion

We have performed the first principle calculations using the

full-potential linearized-augmented plane wave method

(FP-LAPW) to investigate the structural, electronic and thermodynamic

properties of Mg2X (X¼ Ge, Si and Sn) compounds for antifluorite,

anticotunite and hexagonal Ni2In type phases The

exchange-correlation potential has been treated using three different

ap-proximations of LDA, GGA and EV-GGA The obtained results for

equilibrium unit cell volumes and bulk modulus at zero pressure

are rather close to those reported in the literature At pressures

below 3 GPa, the Mg2X (X¼ Ge, Si and Sn) compounds maintain

their antifluorite structure with different bulk modulus values of

46.52 GPa, 54.16 GPa and 37.57 GPa for Mg2Ge, Mg2Si and Mg2Sn,

respectively At high pressures, these compounds undergo two

crystallographic phase transitions offirst-order nature to become

the hexagonal structure The density of state and the band structure

have been calculated by using EV-GGA for the Mg2X compounds in

all three phases, showing the metallic character for the two last

phases, which is in good agreement with the previous calculation

In addition, we have used GIBBS2 program to introduce the

tem-perature effect in these ab-initio results which allowed us to

calculate the constant volume and pressure heat capacity, Debye

temperature and the Gibbs free energy, as functions of temperature

and pressure

Acknowledgments

This work is supported by the Algerian University research

project (CNEPRU) under no D05620140014

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