A study of the phase transitions, electronic structures and thermodynamic properties of Mg2X (X = Ge, Si and Sn) under high pressure

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 coef ﬁ cien[r]

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Original Article

A study of the phase transitions, electronic structures and

thermodynamic properties of Mg2X (X ¼ Ge, Si and Sn) under high

pressure

M Guezlanea, H Baazizb,*, Z Chariﬁb, A Belgacem-Bouzidac, Y Djaballahc aDepartment of Physics, Faculty of Science, University of Batna, 05000, Batna, Algeria

bPhysics Department, Faculty of Science, University of M'sila, 28000, M'sila, Algeria

cLaboratoire d'etude Physico-Chimique des Materiaux, Departement de Physique, Faculte des Sciences, Universite 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 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 (X¼Ge, 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 (X¼Ge, 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 ¼Ge, 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 (X¼Ge, 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:ỵ213 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

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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 (X¼Ge, 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 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 GPa Finally, Yu et al.[15,16]investigated the phase transitions of Mg2X (X ¼Ge, 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 (X¼Ge, 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 (X¼Ge, 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 (X¼Ge, Si and Sn) compounds crystallize in a cubic antifluorite structure at ambient conditions, the Mg and X (X¼Ge, 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 (X¼Ge, Si and Sn) for all phases Brillouin-zone (BZ) integrations within the self-consistency cycles have been performed via a tetrahedron method, using 35kpoints 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 The calculated structural parameters from these three structures' types of Mg2X (X¼Ge, Si, and Sn) are listed with the available experimental data and few other theoretical results inTable The obtained lattice parameters of the antiﬂuorite structure using LDA are in excellent agreement with the experimental data and other theoretical results at 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 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 (X¼Ge, 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 (X¼Si, Sn and Ge) compounds in comparison with the previous calculations and experimental data For all Mg2X (X¼Ge, 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 (2017) 105e114

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The relation between pressure and volume using LDA approxi-mation for the different phases of the Mg2X (X¼Ge, Si and Sn) compounds is shown inFig 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 (X¼Ge, 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 Mg2Ge with 12.29% (GGA) and

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Table

Calculated lattice parameters, bulk modulus, and DOS at EFusing LDA and GGA, in comparison with the available previous calculations and the experimental data for Mg2X

(X¼Ge, Si and Sn) in three phases

This work Others Exp

GGA LDA

Mg2Si-AF

a0(Å) 6.369 6.262 6.09a, 6.26e, 6.29f 6.338g, 6.35h

B (GPa) 54.16 56.55 59.2a, 58.3e, 56.2f 46.3

e55.0a Mg2Si-HEX

0 GPa 22.9 GPa GPa 22 GPa

a0(Å) 4.651 4.38 4.567 4.309 4.162i 4.166b

c0(Å) 6.046 5.57 5.937 5.601 5.25i 5.287b

c0/a0 1.3 1.27 1.3 1.27 1.261i 1.269b

B(GPa) 55.6236 e 59.4477 e 56.07i 163.83b

Mg2Si-AC

0 GPa 8.78 GPa GPa 8.16 GPa

a0(Å) 6.985 6.89 6.862 6.80 6.595i 6.035b

b0(Å) 4.191 4.13 4.117 4.08 3.995i 4.591b

c0(Å) 8.102 7.99 7.960 7.89 7.734i 6.784b

B(GPa) 57.3325 e 60.5048 e 56.48i 102.65b

Mg2Sn-AF

a0(Å) 6.827 6.675 6.694j 6.759d,6.765b, 6.762e, 6.761f

B(GPa) 37.5718 43.5460 44.74j 41.2k

Mg2Sn-HEX

a0(Å) 4.996 4.826 4.866 4.769 V0(Å)¼66.49j

c0(Å) 6.495 6.129 6.327 6.057

c0/a0 1.3 1.27 1.3 1.27

B(GPa) 38.2066 e 45.7508 e 46.05j

Mg2Sn-AC

a0(Å) 7.488 7.49 7.325 7.306 V0(Å)¼69.21j

b0(Å) 4.493 4.49 4.395 4.384

c0(Å) 8.687 8.69 8.497 8.475

B(GPa) 46.2965 50.809 e 45.91j

Mg2Ge-AF

a0(Å) 6.431 6.295 6.12a, 6.286e, 6.31f, 6.423c 6.393g,6.378b, 6.393e, 6.445f

B(GPa) 46.2945 52.7659 57.6a, 55.9e, 55.1f 44.0

e54.7a Mg2Ge-HEX

a0(Å) 4.730 4.372 4.658 4.067 V0(Å)¼57.45j

c0(Å) 6.148 5.553 6.055 5.165

c0/a0 1.3 1.27 1.3 1.27

B(GPa) 46.5224 53.4534 51.74j

Mg2Ge-AC

a0(Å) 7.076 6.946 6.919 6.822 V0(Å)¼59.54j

b0(Å) 4.246 4.168 4.151 4.093

c0(Å) 8.208 8.058 8.026 7.913

B(GPa) 49.3302 e 61.3158 e 54.97j

aPWPP Ref.[11]. bRef.[21]. c Ref.[30]. d Ref.[31]. eFP-LAPW Ref.[32]. f PWPP Ref.[12]. gRef.[33]. hRef.[13]. iRef.[15]. jRef.[16]. kRef.[11].

Table

Calculated transition pressure and volume collapse using LDA and GGA, in comparison with the available previous calculations and the experimental data for Mg2X (X¼Ge, Si

and Sn) compounds

Antiﬂuorite to Anticotunnite Anticotunnite to Ni2In-type

Present Work Theory Experiment[21] Present Work Theory Experiment[21]

GGA LDA GGA LDA

Mg2Si PT(GPa) 8.78 8.16 8.38[15] 7.5e10.4 22.9 22 28.84[15] 21.3e37.8 DV (%) 11.99 10.85 7.53[15] ~12 18.61 17.72 3.66[15] ~3.0 Mg2Sn PT(GPa) 3.77 4.88 5.26[16] e 10.41 8.89 18.40[16] e

DV (%) 8.15 8.73 7.43[16] e 15.39 12.10 3.11[16] e

Mg2Ge PT(GPa) 7.85 8.16 8.71[16] e 29.77 63.45 33.28[16] e DV (%) 12.29 11.43 6.82[16] e 21.19 33.03 3.12[16] e

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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 (X¼Ge, 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 sufficientlyflexible 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

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Fig 3.Electronic band structures and total density of states (TDOS) of Mg2X (X¼Ge, Si and Sn) compounds calculated using EVGGA

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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 (X¼Ge, 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 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 and 100 K the bulk modulus appears constant especially at high pressure (50 GPa) in the three phases of Mg2X (X¼Ge, Si and Sn) compounds (a change ofỵ0.27% (for the Mg2Ge hexagonal phase at 50 Gpa) to 2.81% (for the Mg2Ge Fig 3.(continued)

Table

Band gap of Mg2X (X¼Ge, Si and Sn) in the antiﬂuorite phase

GapG-X (eV)

Our work Other results[36]

LDA GGA EV-GGA

Mg2Ge 0.097 0.168 0.701 0.7

Mg2Si 0.116 0.2218 0.676 0.6, 0.57[14]

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hexagonal phase at 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 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 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 (X¼Ge, 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 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 10.5105K1and 27105K1 under GPa to between 3.3105K1and 4.6105K1and between 1.8 105 K1 and 2.7105 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 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 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]Cv¼3nNAKBwhich corresponds to ~75 J/mol.K for Mg2X (X¼Ge, Si and Sn) compounds in all phases However, Cpcontinues increasing with temperature but slowly under 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 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 Mg2X (X¼Ge, Si and Sn) compounds

Fig 5.Temperature and pressure effects on the volumetric thermal expansion coefﬁcients (a) for Mg2X (X¼Ge, Si and Sn) compounds

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Fig 7.Temperature and pressure effects on the constant pressure heat capacity CPfor Mg2X (X¼Ge, Si and Sn) compounds

Fig 8.Temperature and pressure effects on the Debye temperatureqDfor Mg2X (X¼Ge, Si and Sn) compounds Fig 6.Temperature and pressure effects on the constant volume heat capacity Cvfor Mg2X (X¼Ge, Si and Sn) compounds

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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 (X¼Ge, 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 GPa, the Mg2X (X¼Ge, 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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