Ground state parameters,electronic properties and elastic constants of CaMg3:DFT study

H.Rkb-Djbri,Mnl M.Abus Slm,S.Dou,M.Drif,Y.Gurmit,S.Louhibi-Fsl

a Laboratory of Micro and Nanophysics(LaMiN),National Polytechnic School Oran,ENPO-MA,BP 1523,El M’Naouer,31000 Oran,Algeria

b Faculty of Nature and Life Sciences and Earth Sciences,Akli Mohand-Oulhadj University,10000 Bouira,Algeria

cDepartment of Applied Physics,Taflia Technical University,Tafila 66110,Jordan

dLaboratory of Materials and Electronic Systems,Mohamed El Bachir El Ibrahimi University of Bordj Bou Arreridj,Bordj BouArreridj 34000,Algeria

e Laboratoire des Matériaux Magnétiques,Département de Physique,Facultédes Sciences,UniversitéDjilali LIABES de Sidi-Bel-Abbès,Sidi Bel Abbes 22000,Algeria

Received 24 February 2020;received in revised form 4 June 2020;accepted 17 June 2020 Available online 18 September 2020

Abstract The present study aims to investigate the equation of state(EOS)parameters of CaMg3 inαReO3(D09),AlFe3(D03),Cu3Au(L12)and CuTi3(L60)structures,using full potential linear muffin-tin orbitals(FP-LMTO)approach based on the density functional theory(DFT).The local density approximation(LDA)and the generalized gradient approximation(GGA)were both applied for the exchange-correlation potential term.The calculated equation of state parameters at equilibrium,in general,agreed well with the available data of the literature.The calculations showed that under compression CaMg3 transforms from D03 to D09 at about 29.96GPa,and 25.1GPa using LDA and GGA,respectively.

Keywords:CaMg3 compound;Electronic properties;Phase transition;Elastic constants;FP-LMTO.

1.Introduction

Magnesium(Mg)is an abundant element in the world compared with other commonly used metals;it is one of the lightest among several commonly used structural metals.One of its major advantages is the low density,it is about one quarter that of steels and two thirds that of aluminum[1].Furthermore,Mg-based alloys,like the binary systems of Mg–Cu and Mg–Ca,have gained more attention in the last decade.These materials have several applications in engineering,especially in aerospace manufacturing field and automotive industry[2–6].The binary system of Mg-Ca is potentially used as biomaterial and has been a subject of research by many investigators in recent years[7],[8].

Zhou and Gong[8]have studied the electronic properties,mechanical moduli,chemical bonding and many other parameters of Mg-Ca system in different configurations.Their calculations showed that both BCC(AlFe3-type structure(D03))and FCC(Cu3Au-type structure(L12)phases of CaMg3are mechanically stable at equilibrium.Also,they investigated phase transition and found that both AlFe3-type structure(D03)and Cu3Au-type structure(L12)transform to the hexagonal close packed HCP-type structure(A3)at pressures around 29.47GPa and 26.44GPa,respectively.Actually,it is known that under the effect of hydrostatic compression,the crystal often transforms from the most energetic stable phase to another crystallographic configuration[9],[10].

Table 1Plane wave number NPLW,muffin-tin radius(RMT)(in a.u.)and the energy cut-off(in Ry)used in our calculation.

Groh[11]has investigated several physical,mechanical,and thermal properties of pure Calcium(Ca)and Mg–Ca binary system,in the framework of the second nearestneighbors modified embedded-atom method(MEAM).His results showed also that both AlFe3-type structure(D03)and Cu3Au-type structure(L12)of CaMg3are mechanically stable at equilibrium.

Furthermore,to the best of our knowledge,the CaMg3phases of Mg–Ca binary system is not synthesized until now,and it is very difficult to obtain the physical properties of all phases by using the experimental measurement.Under this situation,the first-principles calculations can be applied to compute various physical properties of different phases based on the crystal structural information.In order to further improve the properties of Mg-Ca alloys,a systematic investigation and accurate information on the mechanical properties of some other structures in binary Mg-Ca system is the prerequisite.In the present study,we investigate the equation of state(EOS)parameters,pressure-induced phase transition,elastic constants and electronic properties of CaMg3compound using first-principles total energy calculations in the framework of density functional theory(DFT),within both the local density approximation(LDA)[12]and the generalized gradient approximation(GGA)[13].

In Section 2 we introduce a brief description of the method used in this work.Then,we present,in Section 3 our obtained results of the structural parameters,high-pressure induced phase transitions,elastic constants as well as the electronic properties of CaMg3compound.Finally,a brief conclusion is given in Section 4.

2.Computational details

The chemical and physical properties of system are determined by the inter-atomic interactions,which can be described by the inter-atomic interaction potential.The calculations in the present work were made using the all-electron full potential linear muffin-tin orbital(FP-LMTO)augmented by a plane-wave basis(PLW)[14]within the framework of density functional theory(DFT).Unlike the previous LMTO methods,the present version treats both the interstitial regions and the core regions on the same footing[14].The exchange correlation energy of electrons is described using both the local density approximation(LDA)[12]and the generalized gradient approximation(GGA)as parameterized by Perdew et al.[13].

In FP-LMTO approach,the non-overlapping muffin tin spheres MTS potential is expanded in terms of spherical harmonics inside the spheres of radius RMTS,while in the interstitial region,the s,p and d basis functions are expanded in a number(NPLW)of plane waves determined automatically by the cut-off energies.The details of calculations are as follows:the charge density and the potential are represented inside the muffin-tin(MT)spheres by spherical harmonics up tolmax=6.The self-consistent calculations are considered to be converged when total energy of the system in stable within 10?4Ry,while self consistent convergence of forces was achieved to within 2×10?3Ry/bohr in ionic minimization.A total energy convergence tests are performed by varying both:plane waves’number PW and cut-off energyEcut.The number of plane waves(NPLW),total cutoff energies,and the muffin-tin radius(RMT)values used in our calculation for our material of interest are summarized in Table 1.

The structures with cubic symmetry(αReO3-type(D09),AlFe3-type(D03),which is described as cubic close packed(CCP)cell and Cu3Au-type(L12)which is described as an ordered CCP cell),have only one structural parameter(the lattice constanta)that is used to describe the unit cell,while the CuTi3-type(L60)having tetragonal symmetry,two structural parameters(aandc/aratio)are used to describe the unit cell.

The locations of atoms for each crystallographic configuration are also presented in Fig.1,while the positions of different atoms,as well as the space group for each of the considered structures of CaMg3are summarized in Table 2.From Fig.1,we can observe that the unit cell contains four molecules of CaMg3in D03structure,while in all other phases(D09,L12and L60)only one molecule was observed.

Table 2Location of different atoms and space group of each type of structure of CaMg3 compound.Pm?3m:Cubic Primitive(cP),Fm?3m:Face-centered cubic(FCC),P4/mmm:Tetragonal Primitive(tP).

Fig.1.Cubic and tetragonal crystal structures of CaMg3:Ca atoms in red,and Mg atoms in green.

From Fig.1,we can observe that in D03structure,the Ca atoms occupy the positions of the CCP structure and the Mg atoms fill all of the octahedral voids;while in L12structure the Ca atoms occupy the cell vertices,while the Mg atoms occupy the face centers.The L12structure is just that of cubic Perovskite(CaTiO3(E21))without the Titanium atoms,and replacing the atoms of Oxygen O per those of Magnesium Mg.

The L60structure(a=b=c)is a tetragonal distortion of L12structure(a=b=c),so whenc=a,the atoms are at the positions of a face centered cubic lattice,and with consequence L60structure becomes that of L12.

3.Results and discussion

3.1.Equation of state parameters

In order to investigate the ground state parameters,the total energy at different volumes(E-V)around the equilibrium one is usually determined[15]–[17],and this is how we obtained the structural parameters of different phases of CaMg3compound in the present work.These parameters can be also predicted fromab-initiocalculation of the pressure versus unit cell volume(P-V)data[18].The equilibrium lattice volumeV0,bulk modulusB0and the pressure derivative of the bulk modulusB0have been computed by minimizing the total energy by means of Murnaghan’s equation of state(EOS),which can be expressed as[15]:

Fig.2.Total energy versus volume for different structures of CaMg3 compound using LDA.

Fig.3.Total energy versus volume for different phases of CaMg3 compound using GGA.

In Eq.(1),E0is the energy of the ground state,corresponding to the equilibrium volumeV0,andB0(B0=?B/?P,atP=0)is the first pressure derivative of the bulk modulusB.The bulk modulusBdetermines the compressibility and is calculated using[16]:

In fact,the bulk modulusBis quantity that defines the strength of bonds in solids;it is a measure of the solid resistance to external deformation[15].

The variation of the total energy as a function of the unit cell volume was plotted in Figs.2 and 3 for different phases of CaMg3using LDA and the GGA,respectively.One can notice that CuTi3-type(L60),AlFe3-type(D03)and Cu3Autype(L12)structures have almost the same minimum energy,in both LDA and GGA,while the minimum energy ofαReO3-type(D09)structure is slightly higher in both approximations.Our results of the equilibrium structural parameters,bulk modulus and the pressure derivative of the bulk modulus of CaMg3in D03,L12,L60and B09structures are summarized in Table 3 together with those of the literature[8],[11].

From Table 3,we can see that the lattice constanta0of both AlFe3-type(D03)and Cu3Au-type(L12)configurations are in very good agreement compared to other theoretical results[8],[11].Our value(7.482?A)obtained with GGA for cubic AlFe3-type(D03)structure overestimates the theoretical value(7.48?A)reported by Zhou and Gong,using PPPAW(GGA)[8]by less than 0.03%,and underestimates the theoretical result(7.494?A)reported by Groh using(MEAM)[11]by about 0.16%;while our obtained value(4.775?A)of cubic Cu3Au-type(L12)phase underestimates the theoretical result(4.78?A)reported by Zhou and Gong[8]by about 0.1%,and overestimates the theoretical value(4.76?A)reported by Groh[11]by about 0.32%.

The calculated values of the bulk modulusB0of both D03and L12structures,as listed in Table 3,are slightly different from those obtained by other theoretical approaches[8],[11];where for example,our value(33.72GPa)obtained with GGA for D03structure overestimates the theoretical value(29.57GPa)reported by Zhou and Gong using PP-PAW(GGA)[8]by about 14%.To best of our knowledge,there are no other data existing in the literature on the structural parameters,bulk modulus and the pressure derivative of the bulk modulus for CaMg3compound in both L60and D09structures.Our findings regarding the structural parameters of CaMg3in both L60and D09structures phases perhaps can be used to predict most of the physical properties of this material.This is due to the fact that most of the physical quantities of compounds and alloys are related to the bonding of atoms,which is directly related to the structural parameters.

3.2.Structural phase transition

It is well known that high pressures influence crystal packing and electronic structure and as a result it plays an important role in materials properties,such as superconducting phenomenon,elastic properties,and structural phase transition[8].In order to get more information about the pressureinduced phase transition of crystals,we have to calculate the Gibbs free energiesGof different considered phases,which can expressed as follows[19]–[22]:

HereE,P,V,TandSsymbolize the total internal energy,pressure,volume,temperature,and entropy,respectively.Since the present calculations were performed atT=0K,the termTSbecomes null,and with consequence,the Gibbs free energy becomes equal to the enthalpyH[19–22]:H=E+PV.For CaMg3compound,the transition pressure(Pt)between AlFe3-type(D03)configuration andαReO3-type(D09)phase were calculated using the enthalpy difference as a function of the pressure with respect to D03structure.Using both LDA and GGA,the variation of the enthalpy differences as a function of pressure are plotted in Fig.4.

Fig.4.Variation of the enthalpy differencesH as a function of pressure for CaMg3 compound inαReO3 type(D09)phase using both LDA and GGA.The reference enthalpy in set for D03 phase.

The transition from AlFe3-type phase(D03)toαReO3-type(D09)may occur at pressures of 29.96GPa(from LDA calculations),and 25.1GPa(from GGA calculations)as shown on Fig.4.At these pressures the enthalpies of both structures become equal;and the enthalpy differences become null.Our results of the transition pressures(Pt)are in consistence with the results of Zhou and Gong[8],which found that both AlFe3-type structure(D03)and Cu3Au-type structure(L12)transform to the hexagonal close packed HCP-type structure(A3)at pressure of around 29.47GPa and 26.44GPa,respectively.

To best of our knowledge,there are no other data existing in the literature on the pressure-induced phase transition for CaMg3compound.Our fi ndings regarding the pressure phase transition of CaMg3compound may be used as a reference for future works.

Table 3Structural parameters(equilibrium lattice constants a and c/a ratio),bulk modulus B0 and the pressure derivatives of the bulk modulus B0’for D09,D03,L12 and L60 phases for CaMg3 compound.a-Ref.[8]using PP-PAW(GGA),b-Ref.[11]using modifeid embedded-atom method(MEAM).

3.3.Electronic properties

The electronic band structures of CaMg3compound in D03structure at the calculated equilibrium lattice constants along the high symmetry directions in the Brillouin zone are presented in Fig.5,using both LDA and GGA.One of the most important tools to investigate the electronic structure of a metallic material is the Fermi surface;which represents the surface of constant energy in k-space[23].The Fermi level(EF),the dashed line in Fig.5,was set to zero energy.It is noticed that the CaMg3in D03structure has a metallic behavior since a number of valance and conduction bands are overlapping at the Fermi level,and no band gaps exist.

Elastic constants,engineering moduli and several other related physical properties are directly related with the nature of atomic bonding in material,which can be analyzed and explained using both the total density of states(DOS)and the local density of states(LDOS)[24],[25].The electronic density of states(EDOS)elucidates the electronic features of materials(elements,compounds,alloys,etc.)[26],the total density of states(TDOS)and partial density of states(PDOS)of CaMg3in D03structure are calculated and presented in Fig.6.This fi gure shows that the lowest lying bands are due to mainly‘s’like states of Ca and do not contribute much to bonding.The valence bands in the energy range between 2eV,and 3eV are dominated by the maximum contribution of‘d’like states of Ca for GGA approximation,and between 4.5 and 5eV are dominated by the maximum contribution of‘d’like states of Ca using the LDA approximation.

Fig.5.Band structure of CaMg3 compound in D03 structure using both LDA and GGA approaches.

Fig.6.Density of states(TDOS and PDOS)of CaMg3 in D03 structure using both LDA and GGA.

Moreover,the DOS at Efof CaMg3in D03phase were calculated,they are to be around 0.469 and 0.454 using the LDA and GGA,respectively.Our obtained values agree well with the results of Zhou and Gong[8].The differences are around-0.061 and-0.076 using LDA and GGA,respectively.

Table 4Calculated Cij B,GV,GR,GH,E are all expressed in GPa,ν,A and G/B are without unity.Values with§are calculated using Cij of Ref.[8],while those with?are calculated using Cij of Ref.[11].

3.4.Elastic properties

3.4.1.Elastic constants,some aggregate moduli and Vickers hardness

The formation of solids is governed by the forces between the atoms,ions,and/or molecules,which are related to both the structural parameters of its crystal structure and to its chemical composition[27].The elastic properties play an important role in the structural stability and stiffness of materials.In cubic structures,as in the case of D03structure of CaMg3compound,there are three independent elastic stiffness constants,namely:C11,C12and C44,that were obtained in the present work by calculating the total energy as a function of strain[16],[28].The determination of the elastic constantsCijneeds the knowledge of the nature of the strain,which is expressed as follow[16]:

Applying this tensor strain modifies the total energy from its unstrained value to the following expression[16]:

whereE(0)is the energy of the unstrained lattice of unit cell volumeV0.

The identification ofC44is through the volume-conserving tetragonal strain tensor[16]:

The total energy is given as follow[16]

Our results of the elastic constants(C11,C12and C44)obtained from both LDA and GGA approximations are presented in Table 4.Except of two theoretical works based on DFT and MEAM,by Zhou and Gong[8]and Groh[11],respectively,there are no other theoretical or experimental values available,to the best of our knowledge,for the elastic constants of CaMg3in D03phase.Using the calculated values of the elastic constants,other elastic parameters can be calculated such as:bulk modulusB,Voigt,Reuss and Hill shear moduli(GV,GR,GH),Young’s modulusE,Poisson’s ratioν,anisotropy factorAand Pugh’s ratio(G/B)using the following equations[16],[28],[29]:

Our results of the elastic stiffness constantsCijand the other elastic parameters above obtained for D03phase of CaMg3phase using both LDA and GGA approximations are presented in Table 4.Except of two theoretical works based on DFT and MEAM,realized by Zhou and Gong[8]and Groh[11],respectively,to the best of our knowledge,there are no other theoretical or experimental values available for the elastic constants of CaMg3in D03phase.

A look on Table 4,shows that the calculated elastic constantsCijsatisfied elastic stability criteria:(C11-C12)>0,C11>0,C44>0,(C11+2C12)>0,C12

Another note,from Table 4,that our values of the elastic stiffness constantCijand other elastic moduli of CaMg3compound in D03structure are in excellent agreement with the results of Zhou and Gong[8]and Groh[11],except for C44,where for example,our value(29.77 GPa)of the bulk modulusBobtained with GGA overestimates the theoretical value(29.57?A)reported by Zhou and Gong[8]by around 0.68%.

The Poisson’s ratioνis small(usuallyv<0.1)for covalent materials,while for ionic materials,v is 0.25[33],[34].Therefore,in CaMg3compound in D03structure(wherev～0.20),a higher ionic contribution in an intra-atomic bonding is expected.

Young’s modulusEis an important indicator on elasticity;materials having higher values ofE,are more stiffer.Our obtained value ofEfor CaMg3compound in D03phase was found at around 55.94GPa using LDA,and 53.39GPa using GGA,respectively.These two values are slightly higher than the Young modulus(41.43GPa)reported by Daoud et al.[35]for MgCa in B2 phase.

On the other hand,the shear modulusG,which can be obtained from the measure of resistance to the reversible deformation under the applied shearing stress,plays a dominant role in predicting the hardness of the material[36].The Pugh’s ratioG/Bhas been extensively used as an empirical parameter to express the brittleness/ductility of materials[8].The critical value ofG/Bratio that separates the brittle/ductile behavior is 0.57(B/G=1.75);a largerG/Bvalue means more brittleness,and vice versa[8].It can be seen from Table 4 that our values ofG/Bratio obtained using both LDA and GGA for CaMg3compound in D03structure are in good agreement with the results of Zhou and Gong[8].The values ofG/Bratio are greater than 0.57,indicating the brittleness nature of CaMg3compound in D03phase.This conclusion was also confirmed from the values of the Poisson’s ratio(v～0.20)which is smaller than the critical valuev=0.26[16].It should be noted that,if we use the elastic stiffness constant Cijobtained by Groh[11],a value of～0.48 for the G/B ratio will be found.

Liu et al.[37]reported that the ductility is a shear-related mechanical property of material,it is associated with both the elastic constant C44and the density of states(DOS)at Fermi energy,while Daoud et al.[35]showed an anti-correlation between the elastic constant C44and the DOS at Fermi energy in MgCa intermetallic compound under compression.This anti-correlation perhaps explained by the fact that as the total DOS at Fermi level increases covalent/ionic behavior,gradually transformed into metallic behavior,thus turning the brittle phase into a ductile one[35].

The Vickers hardnessHVmeasurement is one of the most techniques used in the mechanical characterization of the materials[35].Like refractive index and density,hardness is a intrinsic property of the given crystal[36].The Vickers hardnessHV,the bulk modulusBand the shear modulusGare related by the empirical formula[35]:

Using our values of the bulk modulusBand the shear modulusGobtained from the LDA and GGA,the present results of the Vickers hardnessHVfor CaMg3compound in D03phase are:5.80 and 5.93GPa,respectively.These two values are slightly higher than the Vickers hardnessHV(4.82GPa)of MgCa intermetallic compound in B2 phase[35].As far as we know,there are no data available related to Vickers hardnessHVin the literature for CaMg3in D03phase,therefore our calculated values can be considered as prediction for this property for this material.

3.4.2.Elastic wave speeds and Debye temperature

The Debye temperatureθDparameter is related to many important physical properties of solids,such as specific heat and melting temperature[32].It is either measured from the elastic constants,or from the specific heat measurement[38].However,at low temperatures both methods give almost the same value ofθD,since at low temperature the vibrational excitations arise from acoustic modes only.The Debye temperatureθDmay be estimated from the average sound velocityvmby the following equation[16]:

wherehis Plank’s constant,kBBoltzmann’s constant,andVais the atomic volume.

Usually,the average sound velocityvmof the aggregate material can be calculated from the longitudinal(compressed)vland transverse(shear)vtsound velocities as follows[39],[40]

The crystal densityρis usually expressed in g/cm3(or in kg/m3);it is given as follow[41–43]

whereMis the molecular weight,usually expressed in 10?3kg,Zis the number of molecules per unit cell,NA(=6.022×1023mol?1)is the Avogadro’s number,whileVis the unit cell volume usually expressed in m3.For CaMg3compound in D03phase,the number of molecules per unit cellZwas taken equal to four,and the unit cell volumeVwas taken equal toa3,whileais lattice constant.Adachi[44]has mentioned that the lattice parameters are related to the pressure by Murnaghan equation of state,and they are influenced by the crystalline perfection,such as:impurities,stoichiometry,dislocations and surface damage.Table 5 summarize the results of the crystal densityρ,the average elastic wave velocityvm,the longitudinal wave velocityvland the transverse acoustic wave velocityvtas well as the Debye temperatureθDof CaMg3compound in D03phase,which could not be compared due to unavailability of the measured data.

A look on Table 5,the Debye temperatureθDof CaMg3in D03phase was found at around 393.44K using LDA,and 389.91K using GGA,respectively.Since the Debye temperatureθDcorrelates with the Young’s modulusEin cubic perovskite-type RBRh3(R are Sc,Y,La and Lu)materials[45],these two values ofθDare also slightly higher than the Debye temperatureθD(328.65K)reported by Daoud et al.[35]for MgCa in B2 phase.Although this rationalization may be useful for chemically related compounds,compounds that are significantly different in chemical nature perhaps should not be necessary expected to follow the same correlation.

Table 5Crystal densityρ,sound velocities vl,vt,vm Debye temperatureθD and the limiting angular vibrational frequencyωD for CaMg3 compound in D03 phase.Values with§are calculated using the data of Ref.[8],while those with?are calculated using the data of Ref.[11].

We have also calculated the Debye temperatureθDfor CaMg3in D03phase using a semi-empirical formula betweenθDand elastic constantsCijfirst proposed by Blackmann[46],and latter used by Siethoff and Ahlborn[47]after improvements for several crystals with different structures.This semiempirical formula can be written as[48]

whereais the lattice constant,Mis the atomic weight(for compounds,Mis the weighted arithmetical average of the masses of the species),andCB=3.89×1011×n–1/6h/kBis a model parameter.In this model parameter,h(=6.62617×10?34J.s),kB(=1.38062×10?23J.K?1)andnare Planck’s constant,Boltzmann’s constant and the number of atoms in the unit cell,respectively.More details can be found in Refs.[48].

Using Eq.(19),the Debye temperatureθDof CaMg3in D03phase was found at around 417.16K using LDA,and 408.91K using GGA,respectively.These two values ofθDare slightly higher than the values 393.44K(LDA)and 389.91K(GGA)obtained from Eq.(16).

From Debye temperature one can estimate the Debye cutoff frequency(the limiting angular vibrational frequency)ωDby the following expression[49]:

wherekBis Boltzmann’s constant,and?=h/2π,his Planck’s constant.

Substituting the values(393.44K,and 389.91K)of the Debye temperatureθD,obtained from the LDA and GGA,in Eq.(20),the present results of the limiting angular vibrational frequencyωDfor CaMg3compound in D03phase are:5.93×1013and 5.88×1013rad/s,respectively.These results as well as those calculated from the data of Refs.[8],[11]are also summarized in Table 5.

The same as in the case of the elastic constants and the structural parameters,the longitudinal,transverse and average sound velocities as well as the Debye temperature of our material of interest are in excellent agreement with those calculated using the data of Ref.[8]obtained from the same approach(DFT).To the best of our knowledge,there are no other theoretical or experimental data existing in the literature on the sound velocity,Debye temperature,and Debye cut-off frequency for CaMg3in D03structure.So,we think that our findings regarding these quantities can be used to predict and explain most of the physical properties of this material.

4.Conclusion

In this work,we have investigated the equilibrium structural parameters of CaMg3compound inαReO3-type(D09),AlFe3-type(D03),Cu3Au-type(L12)and CuTi3-type(L60)configurations using anab-initioFP-LMTO method,within both local density approximation(LDA),and generalized gradient approximation(GGA).At equilibrium our results for the EOS parameters,in general,agreed well with other data of the literature.

The results of the present work concerned with the possibility of phase transition at high pressure show that CaMg3transforms from AlFe3-type structure(D03)toαReO3-type(D09)at pressure of around 29.96GPa using LDA,and at around 25.1GPa using the GGA.

Both LDA and GGA approaches for the electronic band structures,the total density of states(TDOS)as well as the partial density of states(PDOS)showed that CaMg3in D03phase has a metallic behavior.

The elastic constants,Young’s modulus,shear modulus,Poisson’s ratio,index of ductility,Vickers hardness,sound velocities,Debye temperature,and the limiting angular vibrational frequency of CaMg3in D03phase were also reported.Our findings on the elastic constants were also in agreed well with other theoretical data of the literature.