Materials Science in Semiconductor Processing 40 (2015) 676–684

Contents lists available at ScienceDirect

Materials Science in Semiconductor Processing

http://d1369-80

n CorrE-m

journal homepage: www.elsevier.com/locate/matsci

Mechanical and electronic properties of Ca1�xMgxO alloys

Qingyang Fan a, Changchun Chai a, Qun Wei b,n, Yintang Yang a, Liping Qiao a, Yinbo Zhao a,Peikun Zhou c, Mengjiang Xing d, Junqin Zhang a, Ronghui Yao b

a State Key Discipline Laboratory of Wide BandGap Semiconductor Technology, School of Microelectronics, Xidian University, Xi'an 710071, PR Chinab School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, PR Chinac Faculty of Science, University of Paris-Sud, Paris 91400, Franced Faculty of Information Engineering & Automation, Kunming University of Science and Technology, Kunming 650051, PR China

a r t i c l e i n f o

Article history:Received 27 May 2015Received in revised form30 June 2015Accepted 14 July 2015

Keywords:Ca1�xMgxO alloysFirst principles calculationsMechanical propertiesElectronic structures

x.doi.org/10.1016/j.mssp.2015.07.03501/& 2015 Elsevier Ltd. All rights reserved.

esponding author. Fax: þ86 29 88202507.ail address: weiaqun@163.com (Q. Wei).

a b s t r a c t

The structural, mechanical, elastics anisotropy and electronic properties of Ca1�xMgxO in the cubicstructure are investigated using density functional theory calculations. The lattice parameters, elasticconstants and elastic modulus are in excellent agreement with the experimental and others theoreticaldata. The sound velocities and the Debye temperatures are calculated for all the Ca1�xMgxO alloys usingthe calculated elastic constants and elastic modulus. The elastic anisotropy are characterized by calcu-lating several different anisotropic indexes and describing the three dimensional surface constructions.Finally, electronic structure studies show that Ca1�xMgxO alloys are direct band gap semiconductors.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Recently, the alkaline earth oxides MO (M¼Be, Mg, Ca, Sr, Ba)have gained more and more attentions due to their various uniquephysical and chemical properties and potential technological ap-plications [1–5]. There have been a large number of research pa-pers related to MgO [6–12] and CaO [12–20]. Duffy et al. [6] havefound that MgO is stable in the B1 (NaCl) phase up to 230 GPa byexperiment. The temperature dependence of the elastic propertiesof MgO has been investigated by Isaak et al. [9] at ambient pres-sure. Karkietal et al. [11] have investigated the structural and op-tical properties of MgO up to 150 GPa based on the first-principlespseudo-potential method. They found that MgO has the high an-isotropy in its elastic properties. The structural, electronic andmechanical properties of alkalin earth metal oxides MO (M¼Be,Mg, Ca, Sr, Ba) in the cubic (B1, B2 (CsCl) and B3 (Zinc Blende))phases and in the B4 (wurtzite) phase are studied by Cinthia [12].They found that the energy band gap values increase in the orderBeO4MgO4CaO4SrO4BaO, and the Debye temperatures ofMO follow the same order.

Jeanloz et al. [13] have reported a pressure induced phasetransition of CaO from B1 to B2 phase around 60 GPa at roomtemperature by the diamond-anvil cell experiment and the shock

wave experiment; where as the theoretically predicted values arearound 55 GPa [14,15], and the B2 phase can be stable up to atleast 135 GPa [16,17]. Speziale et al. [18] have studied the highpressure elasticity of CaO up to 25.2 GPa and 65.2 GPa by thesingle crystal Brillouin scattering and the X-ray diffraction method,respectively. Naeemullah et al. [19] have also calculated structural,electronic and optical properties of CaO1�xSx (x¼0.25, 0.50, 0.75;S¼S, Se, Te). Baltache et al. [20] have analyzed the structural,elastic and electronic properties of the three alkaline earth oxides,namely MgO, CaO and SrO by using the FP-LAPW method.

It is preferable to combine two compounds with differentphysical properties in order to obtain a new material with inter-mediate properties. Semiconductor alloys are known for theirimportant technological applications, especially in the manu-facture of electronic and electro-optical devices. Direct band gapmaterials have high absorption power and therefore optically ac-tive. The present work is basically carried out to get direct bandgap alloys including Ca0.75Mg0.25O, Ca0.5Mg0.5O and Ca0.25Mg0.75Ofrom the binary compounds (CaO and MgO). In this paper, thestructural, mechanical, elastics anisotropy and electronic proper-ties of Ca1�xMgxO (x¼0.25, 0.50, 0.75) in the cubic structure areinvestigated systematically using density functional theory (DFT)calculations. To the best of our knowledge, no experimental ortheoretical investigations of these ternary alloys have been re-ported in the literatures so far.

Fig. 1. Unit cell crystal structures of Ca1�xMgxO, the red, blue, and black spheres represent Ca, Mg and O atoms, respectively. (a) CaO; (b) Ca0.75Mg0.25O; (c) Ca0.5Mg0.5O; (d)Ca0.25Mg0.75O; (e) MgO. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684 677

Table 2Calculated results of lattice constants for Ca1�xMgxO alloys with experimental andtheoretical data.

x a (Å)

Ca1�xMgxO Present Exp. Other calculations

WC PBE PBEsol LDA

0.0 4.77 4.81 4.77 4.71 4.81a 4.71b, 4.81b, 4.77c, 4.86d,4.761e, 4.838f, 4.843g,

4.714h

0.25 4.68 4.73 4.68 4.620.5 4.57 4.61 4.56 4.500.75 4.44 4.47 .43 4.371.0 4.28 4.29 4.27 4.21 4.213i,

4.20j,4.212k

4.241g, 4.22l, 4.20d,4.259j 4.167h, 4.19m,

4.165n, 4.25o

a Ref. [17].b Ref. [47].c Ref. [19].d Ref. [48].e Ref. [49].f Ref. [50].g Ref. [12].h Ref. [8].i Ref. [51].j

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684678

2. Theoretical method

The first principles calculations for investigating the stability,elastic properties, hardness and Debye temperature of Ca1�xMgxOalloys are based on DFT [21,22], which is implemented in CASTEPcode [23]. In our calculations, the structural optimization andproperty predictions of the Ca1�xMgxO alloys were performedusing the DFT with the generalized gradient approximation (GGA)parameterized by Perdew, Burke and Ernzerrof (PBE) [24], Wu andCohen (WC) [25], PBEsol [26] and the local density approximation(LDA) [27,28]. Ultrasoft pseudo potentials were used to characterthe interactions between ionic core and valence electrons. In thestructure calculation, a plane-wave basis set with energy cut-off420 eV is used. The Vanderbilt ultrasoft pseudopotential was usedin present work. The special k-point method proposed by Mon-khorst–Pack [29] was used to character energy integration in thefirst irreducible Brillouin zone [30], the k-point mesh was adopted8�8�8 for all compounds. The valence electron structures of Ca,Mg and O are 4s2, 3s2 and 2s22p4, respectively. The Broyden–Fletcher–Goldfarb–Shanno [31] minimization scheme was used ingeometry optimization. The self-consistent convergence of thetotal energy is 5�10�6 eV/atom; the maximum force on the atomis 0.01 eV/Å, the maximum ionic displacement within 5�10�4 Åand the maximum stress within 0.02 GPa.

Ref. [52].k Ref. [53].l Ref. [54].m Ref. [7].n Ref. [20].o Ref. [11].

3. Results and discussion

The crystal structures of Ca1�xMgxO (x¼0.0, 0.25, 0.50, 0.75,1.0) are shown in Fig. 1. In a conventional cell, CaO have 8-atoms (4Ca atoms and 4 O atoms). The optimized lattice parameter of a is4.81 Å. The atomic positions in the ordered alloy Ca1�xMgxO arelisted in Table 1. The calculated values of lattice parameters forCa1�xMgxO with experimental and theoretical data are listed inTable 2. From Table 2, it can be seen that the calculated values oflattice parameters for CaO and MgO are in excellent agreementwith experimental and theoretical values. For the ternary alloys atx¼0.25, 0.5, 0.75, there are no experimental or theoretical datagiven in the literature. Equilibrium lattice parameters versuscomposition x along with Vegard's rule are shown in Fig. 2(a).From Table 2 and Fig. 2(a), it can be seen that the lattice para-meters of Ca1�xMgxO decrease with the composition x.

Calculated single crystal elastic constants Cij, bulk modulus B,shear modulus G for Ca1-xMgxO are showed in Table 3. From Ta-ble 3, we found that our calculation results of CaO and MgO are inexcellent agreement with the experimental or previous theoreticaldata. Bulk modulus B and shear modulus G are calculated by theVoigt–Reuss–Hill approximation [32–34]. It is known that theVoigt bound, which is achieved by the average polycrystalline

Table 1Atomic position for Ca1�xMgxO alloys.

Concentration (x) Atom Atomic positions

0.0 Ca (0, 0, 0), (0, 0.5, 0.5), (0.5 ,0, 0.5), (0.5, 0.5, 0)O (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5), (0.5, 0.5, 0.5)

0.25 Ca (0, 0, 0), (0, 0.5, 0.5), (0.5 ,0, 0.5)O (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5), (0.5, 0.5, 0.5)Mg (0.5, 0.5, 0)

0.5 Ca (0, 0, 0), (0, 0.5, 0.5)O (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5), (0.5, 0.5, 0.5)Mg (0.5, 0, 0.5), (0.5, 0.5, 0)

0.75 Ca (0, 0, 0)O (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5), (0.5, 0.5, 0.5)Mg (0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)

1.0 O (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5), (0.5, 0.5, 0.5)Mg (0, 0, 0), (0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)

modulus based on the assumption of uniform strain throughout apolycrystalline, is the upper limit of the actual effective modulus[32], while the Reuss bound achieved by assuming a uniformstress and is the lower limit of the actual effective modulus [33].The arithmetic average of Voigt and Reuss bounds is termed as theVoigt–Reuss–Hill approximations [34]:

G G G12

, 1R V= ( + ) ( )

B B B12

, 2R V= ( + ) ( )

where subscript V denotes the Voigt bound, R denotes the Reussbound. From Table 3, it reveals that CaO has the bulk modulus of111 GPa within GGA, which is smaller than that of MgO (145 GPa),and the calculated elastic modulus are in good agreement with thereported experimental and theoretical values (see Table 3).Young's modulus and Poisson's ratio are important for technolo-gical and engineering applications. The larger value of E means thematerial is stiffer. Young's modulus E and Poisson's ratio v areobtained by the following formulas [34]:

EBG

B G9

3 3=

+ ( )

B GB G

3 22 3 4

ν = −( + ) ( )

Young's modulus of CaO is 188 GPa, which is much smaller thanMgO (271 GPa). The Poisson's ratio v provides more informationabout the characteristics of the bonding forces than any of theother elastic constants. The Poisson's ratio v of CaO is 0.218 withGGA, slightly greater than Ca0.5Mg0.5O (0.217). From Table 3, wecan find that all the elastic constants and elastic modulus increasewith the composition x, whereas Poisson's ratio v decreases withthe composition x.

According to Pugh [35], a smaller B/G value (B/Go1.75) for a

4.2

4.3

4.4

4.5

4.6

4.7

4.8

0.00 0.25 0.50 0.75 1.003.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

Latti

ce c

onst

ants

(A° )

PBE PBEsol WC LDA

Composition (x)

PBE PBEsol WC LDA

Ban

d ga

p (e

V)

Fig. 2. Lattice constants and band gap of Ca1�xMgxO as a function of composition x.

Table 3Calculated results of elastics constants and elastics modulus for Ca1�xMgxO alloys.

x C11 C12 C44 B G B/G E v

0.0 215 59 76 111 77 1.442 188 0.218227a 65 87 119 85 1.399 206 0.221221b 57 80

0.25 218 62 82 113 79 1.430 192 0.2170.5 226 68 90 120 86 1.395 208 0.2100.75 241 77 107 131 96 1.365 231 0.2061.0 262 90 132 145 114 1.272 271 0.189

297a 100 152 166 128 1.297 305 0.252297b 95 156

a Ref. [12].b Ref. [55].

Fig. 3. Anisotropy factors of Ca1�xMgxO as

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684 679

solid represents a brittle manner while a larger B/G value (B/G41.75) usually means a ductile manner. Moreover, Poisson'sratio v is consistent with B/G, which refers to ductile compoundsusually with a larger Poisson's ratio v (v40.26) [36]. The value ofB/G is smaller than 1.75 and value of v is smaller than 0.26 forCa1�xMgxO in Table 3, which shows that Ca1�xMgxO (x¼0.0, 0.25,0.50, 0.75, 1.0) is brittle. B/G value and Poisson's ratio v decreasewith the composition x.

As an important parameter which is closely concerned with thepossibility of inducing micro-cracks in materials, the elastic ani-sotropy of a crystal can be described by the shear anisotropicfactors and the universal anisotropic index AU. The shear aniso-tropic factors provide a measure of the degree of anisotropy in thebonding between atoms in different planes. The shear anisotropic

a function of pressure, (a) A1; (b) AU.

Fig. 4. The elastic anisotropy of Poisson's ratio, shear modulus, and Young's mod-ulus for Ca1�xMgxO (x¼0.0, 0.25, 0.5, 0.75, 1.0).

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684680

factor for the {100} shear plane between〈011〉and〈010〉di-rections is [37,38]:

AC

C C C4

2,

51

44

11 33 13=

+ − ( )

for the {010} shear plane between〈101〉and〈001〉directions itis [37,38]:

AC

C C C4

2,

62

55

22 33 23=

+ − ( )

for the {001} shear plane between〈110〉and〈010〉directions itis [37,38]:

AC

C C C4

2 73

66

11 22 12=

+ − ( )

For an isotropic crystal the factors A1, A2, and A3 must be 1.0,while any value smaller or larger than 1.0 is a measure of theelastic anisotropy possessed by the crystal. The universal elasticanisotropy index AU and the percent anisotropy for a crystal withany symmetry are expressed as follow [39,40]:

AGG

BB

5 6,8

U V

R

V

R= + −

( )

AU¼0 means the isotropy to the solid. The deviation of AU fromzero defines the extent of single crystal anisotropy and accountsfor both the shear and the bulk contributions unlike all other ex-isting anisotropy measures. The calculated shear anisotropic fac-tors A1 and universal anisotropic index AU of the Ca1�xMgxO areshown in Fig. 3. A1(CaO)¼0.974 represents the less elastic aniso-tropic, A1(MgO)¼1.535 represents the larger elastic anisotropic.From Fig. 3(a) and (b), it is evident that the higher the compositionx, the greater the AU and A1.

It is well known that the anisotropy of elasticity is an importantimplication in engineering science and crystal physics. The direc-tional dependence of anisotropy was calculated using the ELAM[41,42] code. The calculated Poisson's ratio, shear modulus andYoung's modulus along different directions as well as the projec-tions in different planes are shown in Fig. 4. Since Ca1�xMgxO arein the cubic crystal system, and also due to the fact that the data inthe xy, xz, and yz plane are the same, we only present the xy planein Fig. 4. The solid line represents the maximum value and dashline represents the minimum value. Fig. 4(a)–(c) displays the 2Drepresentation of Poisson's ratio, shear modulus and Young'smodulus in the xy plane for Ca1�xMgxO, respectively. The max-imum value of CaO is 0.23 and the minimum value is 0.21, whilethe maximum value of MgO is 0.33 and the minimum value is 0.05.The greater the ratio of the maximum value and the minimumvalue for Poisson's ratio v, the greater the anisotropy. We foundthat by calculating the vmax/vmin(CaO)¼1.095, vmax/vmin(MgO)¼6.600, which indicates that MgO has the larger anisotropy, this isin consistent with previous discussions. From Fig. 4, it is clearlyshown that, as the pressure becomes larger, anisotropy also larger.The surface in each of graphs represents the magnitude of E alongdifferent orientations. For an isotropic system, the 3D directionaldependence would exhibits a spherical shape, while the deviationdegree from the spherical shape reflects the content of anisotropy[43]. The 3D figures of the Young's modulus for Ca1�xMgxO areshown in Fig. 5. From Fig. 5, we can see that the 3D figures of theYoung's modulus for cubic CaO have almost no deviation in shapefrom the sphere, which indicates that the Young's modulus for thisconsidered cubic structure compound show very little anisotropy.We can draw an obvious conclusion from Fig. 5 that MgO has themost obviously anisotropy.

The phase velocities of pure transverse and longitudinal modesof the Ca1�xMgxO compounds can be calculated from the single

crystal elastic constants following the procedure of Brugger [44].The sound velocities are determined by the symmetry of thecrystal and propagation direction. The pure transverse and long-itudinal modes can only be found for [001], [110] and [111] di-rections in a cubic crystal and the sound propagating modes inother directions are the quasi-transverse or quasi-longitudinalwaves. In the principal directions, the acoustic velocities in a cubiccrystal can be expressed by:

v C100 / , 9l 11 ρ[ ] = ( )

v v C010 001 / , 10t t1 2 44 ρ[ ] = [ ] = ( )

v C C C110 2 /2 , 11l 11 12 44 ρ[ ] = ( + + ) ( )

Fig. 5. The surface constructions of Young's modulus (E) for (a) CaO; (b) Ca0.75Mg0.25O; (c) Ca0.5Mg0.5O; (d) Ca0.25Mg0.75O; (e) MgO. For all graphs, the units are in GPa.

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684 681

v C C110 / , 12t1 11 12 ρ[ ] = ( − ) ( )

v C001 / , 13t2 44 ρ[ ] = ( )

v C C C111 2 4 /3 , 14l 11 12 44 ρ[ ] = ( + + ) ( )

v v C C C112 /3 . 15t t1 2 11 12 44 ρ[ ] = = ( − + ) ( )

where ρ is the density of Ca1�xMgxO alloys; vl is the longitudinalsound velocity; vt1 and vt2 refer to the first transverse mode andthe second transverse mode, respectively. As a fundamentalparameter for the materials' thermodynamic properties, Debye

Table 4The density (in g/cm3), anisotropic sound velocities (in m/s), average sound velocity (in m/s) and the Debye temperature (in K) for Ca1�xMgxO.

Compounds CaO Ca0.75Mg0.25O Ca0.50Mg0.50O Ca0.25Mg0.75O MgO

ρ 3.346 3.278 3.269 3.295 3.383[111] [111]vl 7966 8223 8580 9125 9776

v112 t1,2[ ] 4808 4868 5029 5236 5473

[110] [110]vl 7979 8183 8515 8985 9104

v110 t1[ ] 6828 6787 6952 7055 7130

[001] vt2 4766 5002 5247 5699 6246[100] [100]vl 8016 8061 8315 8552 8800

[010] vt1 4766 5002 5247 5699 6246[001] vt2 4766 5002 5247 5699 6246

vp 7991 8161 8473 8866 9370vs 4797 4909 5129 5398 5805vm 5307 5429 5669 5963 6401ΘD 658 685 734 797 891

-4

-2

0

2

4

6

8

Ener

gy (e

V)

-4

-2

0

2

4

6

8

Ener

gy (e

V)

-4

-2

0

2

4

6

8

Ener

gy (e

V)

-4

-2

0

2

4

6

8

Ener

gy (e

V)

Γ F Q Z Γ Γ F Q Z Γ

Γ F Q Z Γ X R M Γ R

Fig. 6. Band structure of Ca1�xMgxO alloys at various concentrations (x¼0.25, 0.50, 0.75, 1.0). (a) Ca0.75Mg0.25O; (b) Ca0.5Mg0.5O; (c) Ca0.25Mg0.75O; (d) MgO.

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684682

temperature ΘD is related to specific heat, thermal expansion andelastic constants. The Debye temperature can be estimated fromthe average sound velocity by the following equation based onelastic constant evaluations [45]:

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

hk

n NM

v34

,16

DA

m

13

Θπ

ρ=

( )

where h is the Planck constant, respectively; NA is the Avogadronumber, M is the molecular weight, and ρ is the density. Theaverage sound velocity vm can be calculated as follows [46]:

⎡⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤⎦⎥⎥v

v v

13

2 1,

17m

t l3 3

13

= +( )

−

⎡⎣⎢⎛⎝⎜

⎞⎠⎟

⎤⎦⎥v B

G43

/ ,18

l

12

ρ= +( )

v G/ . 19t ρ= ( )

where B and G are bulk modulus and shear modulus, respectively.vl is the longitudinal velocity and vt is the transverse sound

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684 683

velocity. The calculated sound velocities in the directions forCa1�xMgxO alloys and the calculated results of Debye tempera-tures are listed in Table 4. It is obvious that the alloy with a small

Table 5The calculated band gap for Ca1�xMgxO alloys together with experimentallymeasured and other theoretical calculations.

x Present Exp. Other calculations

Ca1�xMgxO WC PBE PBEsol LDA

0.0 3.530 3.647 3.518 3.437 6.25a 3.67b, 3.44b, 3.46c

0.25 3.439 3.311 3.344 3.6800.5 3.186 3.106 3.173 3.4580.75 3.343 3.323 3.414 3.6691.0 4.245 4.261 4.264 4.764 7.83d 5.00e, 4.43f, 7.64g

a Ref. [56].b Ref. [57]-GGA, LDA.c Ref. [58]-LDA.d Ref. [59].e Ref. [20]-LDA.f Ref. [12]-GGA.g Ref. [60]-HF.

-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 150

1

2

3

4

5

O-s O-p Ca-s Ca-p Ca-d

Den

sity

of s

tate

s (el

ectro

ns/e

V)

Energy (eV)

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 150

1

2

3

4

5 O-s O-p Mg-s Mg-p Ca-s Ca-p Ca-d

Den

sity

of s

tate

s (el

ectro

ns/e

V)

Energy (eV)

-45 -40 -35 -30 -25 -20 -10

1

2

3

4

5

Den

sity

of s

tate

s (el

ectro

ns/e

V)

Energ

Fig. 7. Density of states of Ca1�xMgxO alloys at various concentrations (x¼0.25, 0.50,

density and large elastic constants has large sound velocities. FromTable 4, it can be clearly seen that the Debye temperatureincreasing with the composition x. When composition x increasesfrom 0.0 to 1.0, the Debye temperature changes from 658 to 891 K.

The knowledge of band gap is crucial for the development ofefficient optoelectronic devices. Fig. 2(b) shows the band gaps as afunction of composition x for Ca1�xMgxO. As can been seen, thecalculated band gaps show a nonlinear variation with concentra-tion x. The band structure calculations for Ca1�xMgxO (x¼0.0, 0.25,0.5, 0.75, 1.0) are carried out using the calculated lattice constantswithin LDA, as shown in Fig. 6. It can be seen from the binary bandstructures that both the valence band maximum (VBM) and theconduction band minimum (CBM) locates at the Γ point, resultingin direct band gap compounds. It is well known that the materialswith the indirect band gap are optically inactive due to the phononpartaking in interband transitions. Therefore, their applications arelimited compared to the direct band gap materials. The bandstructure of Ca1�xMgxO (x¼0.25, 0.5, 0.75) are all direct band gap,so this is a certain convenience for their application. Table 5 liststhe calculated band gap within GGA and LDA for Ca1�xMgxO, to-gether with experimental and theoretical data. From Table 5, we

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 150

1

2

3

4

5 O-s O-p Mg-s Mg-p Ca-s Ca-p Ca-d

Den

sity

of s

tate

s (el

ectro

ns/e

V)

Energy (eV)

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 150

1

2

3

4

5 O-s O-p Mg-s Mg-p Ca-s Ca-p Ca-d

)Ve /snortc ele(

s etats foyt isne

D

Energy (eV)

5 -10 -5 0 5 10 15y (eV)

O-s O-p Mg-s Mg-p

0.75, 1.0). (a) CaO; (b) Ca0.75Mg0.25O; (c) Ca0.5Mg0.5O: (d) Ca0.5Mg0.75O; (e) MgO.

Q. Fan et al. / Materials Science in Semiconductor Processing 40 (2015) 676–684684

can see that our calculated band gap for CaO and MgO are rea-sonable compared with previous studies. It is known that thecalculated band gap by DFT are usually underestimated by 30–50%,the true band gap must be larger than the calculated results.Partial density of states of Ca1�xMgxO alloys at various con-centrations (x¼0.0, 0.25, 0.50, 0.75, 1.0) are shown in Fig. 7. ForCaO, the valence band formations are mainly due to Ca-s, Ca-p andO-p with minor contribution of O-s while Ca-d has the significantcontributor in conduction band formation. But for MgO, the va-lence band formation is mainly due to O-s, O-p and Mg-p withminor contribution of Mg-s while Mg-s and Mg-p has the sig-nificant contributor in conduction band formation. In the case ofthe ternary alloy at x ¼0.25, 0.5 and 0.75 the valence band ismainly due to O-s, O-p, Mg-p and Ca-s, and conduction bands aremainly due to Mg-s, Mg-p and Ca-d.

4. Conclusions

We have performed first principles calculations to investigatethe structural, elastic constants, elastic modulus, elastic anisotropyproperties, anisotropy of acoustic velocities, Debye temperature,and electronic structures of Ca1�xMgxO alloys. The B/G shows thatCa1�xMgxO (x¼0.0, 0.25, 0.50, 0.75, 1.0) is brittle. AU, A1, Poisson'sratio, shear modulus and Young's modulus calculations showCa1�xMgxO have elastic anisotropies. The composition x increasingfrom 0.0 to 1.0, the Debye temperature goes from 658 to 891 K. Thedegree of the Debye temperature for the considered Ca1�xMgxOalloys follows the order CaOoCa0.75Mg0.25OoCa0.5Mg0.5OoCa0.25Mg0.75OoMgO. The analysis on the electronicstructures shows that the present work is carried out to get directband gap alloys Ca0.75Mg0.25O, Ca0.5Mg0.5O and Ca0.25Mg0.75O.

Acknowledgments

This work was supported by the State Key Program of NationalNatural Science of China (Grant Nos. 61234006, 61334002), Na-tional Natural Science Foundation of China (No. 61474089).

References

[1] G.A. Slack, S.B. Austerman, J. Appl. Phys. 42 (1971) 4713.[2] B. Salamatinia, I. Hashemixadeh, Z.A. Ahamad, Iran. J. Chem. Chem. Eng. 32

(2013) 113.[3] P.A. Tellex, J.R. Waldron, J. Opt. Soc. Am. 45 (1955) 19.[4] Y. Tatekawa, K. Nakatani, H. Ishii, Surg. Today 26 (1996) 68.[5] J.A. Ober, D.E. Polyak, Mineral Yearbook 2007, Strontium, U.S.G. Survey (Ed.),

2008.[6] T.H. Duffy, R.J. Hemley, H.K. Mao, Phys. Rev. Lett. 74 (1995) 1371.[7] K.J. Chang, M.L. Cohen, Phys. Rev. B 30 (1984) 4774.

[8] M.J. Mehl, R.E. Cohen, H. Krakauer, J. Geophys. Res. 93 (1988) 8009.[9] D.G. Isaak, O.L. Anderson, T. Goto, Phys. Chem. Miner. 16 (1989) 704.[10] E.H. Bogardus, J. Appl. Phys. 36 (1965) 2504.[11] B.B. Karki, L. Stixrude, S.J. Clark, M.C. Warren, G. Acland, J. Crain, Am. Mineral.

82 (1997) 51.[12] A.J. Cinthia, G.S. Priyanga, R. Rajeswarapalanichamy, K. Iyakutti, J. Phys. Chem.

Solids 79 (2015) 23.[13] R. Jeanloz, T.J. Ahrens, H.K. Mao, P.M. Bell, Science 206 (1979) 829.[14] G. Kalpana, B. Palanivel, M. Rajagopalan, Phys. Rev. B 52 (1995) 4.[15] M.J. Mehl, R.J. Hemley, L.L. Boyer, Phys. Rev. B 33 (1986) 8685.[16] J.F. Mammone, H.K. Mao, P.M. Bell, Geophys. Res. Lett. 8 (1981) 140.[17] P. Pichet, H.K. Mao, P.M. Bell, J. Geophys. Res. 93 (1988) 15279.[18] S. Speziale, S.R. Shieh, T.S. Duffy, J. Geophy. Res. B 111 (2006) 02203.[19] Naeemullah, G. Murtaza, R. Khenata, A. Safeer, Z.A. Alahmed, S.Bin Omran,

Comput. Mater. Sci. 91 (2014) 43.[20] H. Baltache, R. Khenata, M. Sahnoun, M. Driz, B. Abbar, B. Bouhafs, Physica B

344 (2004) 334.[21] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864.[22] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133.[23] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I.J. Probert, K. Refson, M.

C. Payne, Z. Kristallogr. 220 (2005) 567.[24] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.[25] Z. Wu, Phys. Rev. B 73 (2006) 235116.[26] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.

A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100 (2008) 136406.[27] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566.[28] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048.[29] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188.[30] J. Moukhorst, J.D. Pack, Phys. Rev. B 54 (1996) 16533.[31] B.G. Pfrommer, M. Côté, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997)

233.[32] W. Voigt, Lehrburch der Kristallphysik, Teubner, Leipzig, 1928.[33] A. Reuss, Angew. Z. Math. Mech. 9 (1929) 49.[34] R. Hill, Proc. Phys. Soc. Lond. 65 (1952) 349.[35] S.F. Pugh, Philos. Mag. 45 (1954) 823.[36] J.J. Lewandowski, W.H. Wang, A.L. Greer, Philos. Mag. Lett. 85 (2005) 77.[37] D. Connétable, O. Thomas, Phys. Rev. B 79 (2009) 094101.[38] Q.Y. Fan, Q. Wei, H.Y. Yan, M.G. Zhang, Z.X. Zhang, J.Q. Zhang, D.Y. Zhang,

Comput. Mater. Sci. 85 (2014) 80.[39] S.I. Ranganathan, M. Ostoja-Starzewski, Phys. Rev. Lett. 101 (2008) 055504.[40] J. Feng, B. Xiao, R. Zhou, W. Pan, D.R. Clarke, Acta Mater. 60 (2012) 3380.[41] A. Marmier, Z.A.D. Lethbridge, R.I. Walton, C.W. Smith, S.C. Parker, K.E. Evans,

Comput. Phys. Commun. 181 (2010) 2102.[42] Q.Y. Fan, Q. Wei, C.C. Chai, H.Y. Yan, M.G. Zhang, Z.Z. Lin, Z.X. Zhang, J.Q. Zhang,

D.Y. Zhang, J. Phys. Chem. Solids 79 (2015) 89.[43] W.C. Hu, Y. Liu, D.J. Li, X.Q. Zeng, C.S. Xu, Comput. Mater. Sci. 83 (2014) 27.[44] K.J. Brugger, Appl. Phys. 36 (1965) 768.[45] O.L.J. Anderson, Phys. Chem. Solids 24 (1963) 909.[46] K.B. Panda, K.S. Ravi, Comput. Mater. Sci. 35 (2006) 134.[47] M. Dadsetani, H. Doosti, Comput. Mater. Sci. 45 (2009) 315.[48] M.P. Habas, R. Dovesi, A. Lichanot, J. Phys.: Condens. Matter 10 (1998) 6897.[49] Y. Duan, L. Qin, G. Tang, L. Shi, Eur. Phys. J. B 66 (2008) 201.[50] B.B. Karki, J. Crain, J. Geophys. Res. 103 (1998) 12405.[51] Y. Fei, Am. Mineral. 84 (1999) 272.[52] R.W.G. Wyckoff, Crystal Structure, Wiley, New York (1963), p. 88.[53] S. Spezial, C.S. Zha, T.S. Duffy, R.J. Hemley, H.K. Mao, J. Geophys. Res. 106

(2001) 515.[54] J. Yamashita, S. Asano, J. Phys. Soc. Jpn. 52 (1983) 3506.[55] H. Zang, M.S.T. Bukowinsky, Phys. Rev. B 44 (1991) 2495.[56] B. Ulrici, W. Ulrici, N.N. Kovalev, Phys. Solid State 17 (1976) 2305.[57] E.L. Albuquerque, M.S. Vasconcelos, J. Phys: Conf. Ser. 100 (2008) 042006.[58] R. Khenata, M. Sahnoun, H. Baltache, M. Rérat, D. Rached, M. Driz, B. Bouhafs,

Physica B 371 (2006) 12.[59] R.C. Whited, C.J. Flaten, W.C. Walker, Solid State Commun. 13 (1973) 1903.[60] R. Pandey, J.E. Jaffe, A.B. Kunz, Phys. Rev. B 43 (1991) 9228.