Ab-initio investigations of the structural, electronic, magnetic and optical properties of Ca1-xEuxLiF3 fluoroperovskite

Computational Condensed Matter 21 (2019) e00432

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Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp

Review

Ab-initio investigations of the structural, electronic, magnetic and optical properties of Ca1-xEuxLiF3 fluoroperovskite Nada T. Mahmoud a, Jamil M. Khalifeh a, Ahmad A. Mousa b, * a b

Physics Department, The University of Jordan, 11942, Amman, Jordan Middle East University, 11831, Amman, Jordan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 June 2019 Received in revised form 19 August 2019 Accepted 26 August 2019

The electronic, magnetic, and optical properties of nonstoichiometric Fluoroperovskite Ca1-xEuxLiF3 alloys, where x ¼ 0, 0.25, 0.50, 0.75, 1.0, are investigated through the Density Functional Theory (DFT) by the full potential linearized augmented plane wave (FP-LAPW) method using mBJ and GGA approximations. Doping CaLiF3 alloy with rare earth Euþ2 generates the nonstoichiometric Ca1-xEuxLiF3 alloys and changes its original behavior from insulator to different properties of materials as we used the GGA and mBJ approximations. The total magnetic moment tends to increase by increasing Eu concentration with maximum local magnetic contributions on the Eu sites. The energy band gaps Eg for all concentrations are calculated. The mBJ approximation succeeded to enhance the value of Eg due to doping CaLiF3 by Euþ2 in Ca sites. The optical dielectric functions as well as their static values for all the above compounds are also investigated. Moreover, the absorption coefficient, reflectivity and refraction indices are calculated. All the optical calculations are found to agree well with the band structure calculations. © 2019 Elsevier B.V. All rights reserved.

Keywords: Fluoroperovskite Eu ions Optical properties Band-gap

Contents 1. 2. 3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Calculation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.1. Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2. Magnetic moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3. Band gap and density of states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4. Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1. Introduction Fluoroperovskite is a versatile material with cubic structure and space group Pm3m(221), with the general formula ABF3 [1], see Fig. 1. Its applications include lenses and semiconductor industry, solar cells, microelectronic and spintronic devices, superconductivity, magnetoresistance and ferroelectricity, [2e4].

* Corresponding author. E-mail address: [email protected] (A.A. Mousa). https://doi.org/10.1016/j.cocom.2019.e00432 2352-2143/© 2019 Elsevier B.V. All rights reserved.

Fluoroperovskites are very stable materials with wide band gaps, and they are considered as potential candidates for industrial applications [5e8]. The electronic and optical properties of XLiF3 (X ¼ Ca, Sr and Ba) fluoroperovskites were also studied using ab-initio method. Our results have shown the presence of a direct energy band-gap (G-G) [9]. Many recent studies are concerned with perovskites for their wide technological applications; all studies concentrated mainly on doping transition elements in A or B sites. A recent study investigated KMF3 (M ¼ Mn, Fe, Co, Ni) using FP-LAPW. They found that

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Fig. 1. Crystalline structures of CaLiF3. Table 1 Structure, optimized lattice constant a(Å) bulk modulus B(GPa) nonstoichiometric Ca1xEuxLiF3compounds. Compound

Space group

a(Å)

B(GPa)

CaLiF3

Pm3m(221)

78.803

Ca0.75 Eu0.25LiF3

P43m(123)

3.765 3.76a 3.661b 3.607c 3.800

78.532

Eu0. 5LiF3

P43m(123)

3.832

77.256

P43m(123)

3.861

76.483

Pm3m(221)

3.891

73.831

Ca0.

5

Ca0.25 Eu0. EuLiF3 a b c

Ref [9]. Ref [20]. Rrf [21].

75LiF3

the band gap increases through the 3d transition-metal series (Mn to Ni) [10]. Theoretical study of the structural, elastic, electronic and optical properties of XCaF3 (X ¼ K and Rb) were investigated by means of plane wave pseudo potential method within DFT; KCaF3 and RbCaF3 were considered ductile [11]. The electronic structure and magneto-optic properties of the Sr2GdReO6 double perovskite were investigated, the results indicated that this double perovskite may become an ideal candidate material for future spintronic applications [12]. Moreover, structural, electronic and magnetic properties of Sr2GdReO6 double perovskite are studied and the calculations predicted that Sr2GdReO6 is half-metallic, the ferromagnetic phase is found more favourable to occur [13]. Searching for new materials for spintronic applications has attracted the attention of scientist recently [14]; the electronic and magnetic properties of Co2Mn0.75(Gd, Eu)0.25Z(Z ¼ Si, Ge, Ga, Al) quaternary Heusler alloys are investigated and have shown half metallic behavior, when Z ¼ Si, Ge and metallic Z ¼ Ga, Al [15]. We achieved new properties of the Huesler alloy CoVSn when doped with Eu ions in Co sites; the new compounds are characterized by e new magnetic and optical properties, the rare Earth Euþ2 is considered as good optical and magnetic activator to certain compounds [16]. Inserting Eu ions changes the structural, electronic, magnetic, and optical properties of fluoroperovskite SrLiF3 compounds [17]. Here, we study the effects of inserting the rare earth Euþ2 into CaLiF3 on the properties of fluoroperovskite CaLiF3 compounds. Its electrical conductivity is found to increase to increase by doping A site by the rare earth element. Although no experimental data to form EuLiF3 has been successful until now, our computational study

Fig. 2. Crystalline structures of Ca1xEuxLiF3, (a) x ¼ 0.25, (b) x ¼ 0.50, (c) x ¼ 0.75, (d) x ¼ 1.

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3

Table 2 The magnetic moment (mB) of nonstoichiomic Ca1-xEuxLiF3 compounds, Mt calculated according GGA and mBJ. Compound

Ca

Eu

Li

F

Mt GGA

Mt mBJ

Ca0.75 Eu0.25LiF3

0.00429 0.00124

6.81718

0.00004

14.00002

13.73040

Ca0.

0.00449

6.87600

0.00080

28.00040

27.99240

Ca0.25 Eu0.75LiF3

0.02264

6.88043 6.87710

0.00873

42.00008

41.99980

EuLiF3

e

6.89859

0.00036

0.00202 0.00412 0.00002 0.00400 0.08870 0.00002 0.00614 0.00831 0.00402 0.01714

56.00000

56.00160

5

Eu0. 5LiF3

is carried out on this fluoroperovskite; new properties are achieved and considered as a major step towards solar cell technology. 2. Calculation method Our calculations are carried out on Ca1-xEuxLiF3 using DFT based on (FP-LAPW) method [18] as implemented in the WIEN2k package [19]. The exchange and correlation potential is used within the generalized gradient approximation (GGA) [20] and modified Becke-Johnson (mBJ) [21]. Fluoroperovskite CaLiF3 is cubic with space group Pm3m(221); Ca is located at (0, 0, 0), Li atoms at (0.5, 0.5, 0.5) and the three fluorine atoms are located at (0.5, 0.5, 0), (0.5, 0, 0.5), and (0, 0.5, 0.5), as shown in Fig. 1. Our calculations are performed using a (2  2  2) super cell with 24 atoms per unit cell. The cut off energy is 16 Ryd for the plane waves in the interstitial region and 169 Ryd for the potential itself. The expansion of wave function inside the muffin tins is taken up to lmax ¼ 10 and goes up to lmax ¼ 4, while the charge density Fourier expanded to Gmax ¼ 12. The core energy cutoff is taken as 6.0 Ryd. The Muffin tin radius (RMT) is taken 2.5 for Ca and Eu atoms, and 1.6 for Li and F atoms. The k-point sampling in the irreducible Brillouin Zone (BZ) is performed using (9  9  9) Monkhorst-pack grid. However, for the calculation of optical properties a dense k mesh is used (20  20  20). All structures are fully relaxed until the forces on the atoms are less than 1 mRy/a.u. The charge convergence test is taken with a tolerance of 0.0001 electron charge. The lattice constant is obtained by optimizing the structure using Murnghan equation of state [22]. The density of states (DOS) is calculated using the tetrahedron € chl corrections [23]. method with Blo

parameter. Fig. 2 shows different configuration structures for all concentrations. Bulk modulus B at zero pressure is calculated using equation of state (EOS). The calculated values are given in Table 1, the bulk modulus B for CaLiF3 value fits with previous theoretical and experimental values [9,24,and25]]. The bulk modulus decreases as the volume of the unit cell increases, in other words, the bulk modulus decreases as traversed from x ¼ 0 to x ¼ 1 concentrations due to the volume increase. 3.2. Magnetic moments The maximum local magnetic moment in the doped compounds is found in Eu sites. Table 2 shows the total magnetic moment for

3. Results and discussion 3.1. Structural properties The lattice constant of fluoroperovskite CaLiF3 is obtained by optimizing the structure using Murnghan equation of state and found equal to 3.765 Å in agreement with other studies (3.661 Å [24], 3.607 Å [25]) and with our previous calculations 3.76 Å [9]. The small difference between our current value and our previous value is due to (Kmax)2 as it was taken (7.5/RMT)2 and in this current work it is equal to (8/RMT)2. We increased (Kmax)2 values to improve the calculations for the super cell as well as the calculations for doped structures later on. The lattice constant of nonstoichiometric fluoroperovskite Ca1xEuxLiF3 alloys for selected concentrations (x ¼ 0.25, 0.50, 0.75 and 1.0) are calculated, see Table 1. The lattice constant increases with increasing Euþ2 concentration which is expected to occur; as Eu concentration increases the chemical nature changes and the atomic positions change in the lattice, these changes will affect the nearest neighbor’s distances, thus affect directly the lattice

Fig. 3. Band structure of CaLiF3, indirect (M- G) band gap (mBJ).

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Fig. 4. Electronic band structure for both spin channels (spin up and down) of Ca1xEuxLiF3 compounds (GGA) for: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.5, (d) x ¼ 0.75, (e) x ¼ 1.

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Fig. 4. (continued).

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Fig. 4. (continued).

Table 3 Band gaps (eV) in the minority spin channels and spin polarizations of Ca1xEuxLiF3 compounds using GGA and mBJ. Compound

Eg(eV) GGA

mBJ

Spin dn CaLiF3 Ca0.75 Eu0.25LiF3 Ca0. 5 Eu0. 5LiF3 Ca0.25 Eu0. 75LiF3 EuLiF3

(МG) (GG) (МG) (МG) (GG)

Spin up 6.559 6.629 6.775 6.964 7.231

(МG) (GG) (GG) (GG) e

the CaLiF3 and doped compounds as well as for their constituents. It is obvious that increasing Eu concentration will change the magnetic nature for the doped compounds resulting from 4f7 orbitals of Euþ2, which behaves as free atom with 7mB. Both GGA and mBJ approximations show the same results regarding the calculation of magnetic moment, which indicates that mBJ calculations does not affect the magnetism. For both approximations the maximum magnetic moment reaches 56 mB for x ¼ 1, which creates EuLiF3 fluoroperovskite. Eu ions are doped as Euþ2 (4f75d06s2) configuration, not as Euþ3 (4f65d16s2) configuration, since the ionic radius of Euþ2 is 1.17 Å which is comparable with that of Caþ2 (1.14 Å). Moreover, the charge number for both Eu and Ca ions is þ2, which is another reason why Euþ2 ions are favored to occupy Caþ2 sites [26]. The Curie temperature (TC) is the temperature at which certain magnetic materials undergo a sharp change in their magnetic properties and sometimes they lose their magnetic properties altogether. We calculated TC for EuLiF3 using the mean field approximation (MFA) according to:

Spin dn (МG) (GG) (МG) (GG) (GG)

6.559 0.908 0.719 0.862 e

Tc ¼

Spin up 8.202 7.298 7.981 7.883 9.284

2 DE 3KB

(МG) e e e (GG)

8.202 e e e 6.918

(1)

where; KB is the Boltzmann constant, and DE is the total energy difference between the antiferromagnetic phase and the ferromagnetic phase [27e29]. EuLiF3 has high Curie temperature equal to 631 K, which means the stable phase is the ferromagnetic.

3.3. Band gap and density of states The energetic properties are investigated for all compounds by calculating the energy band gap Eg as well as the DOS using GGA and mBJ approximations. CaLiF3 has indirect(МG) wide energy band gap Eg equals to 6.559 eV in both spin channels using GGA, which agrees with our previous study (6.6eV) [9], and with another previous value (6.63eV) [24]. On the other hand, energy band gap increases throughout our mBJ calculations (8.202eV). Our mBJ calculations are more precise and enhance the value of Eg as it is expected. Fig. 3 shows the band structure of CaLiF3 using mBJ and

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Fig. 5. Electronic band structure for minority spin channel (spin down) of Ca1xEuxLiF3 compounds (mBJ) for: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

7

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Fig. 5. (continued).

Table 4 Spin polarizations of Ca1xEuxLiF3 compounds using GGA and mBJ. Compound

Ca0.75 Eu0.25LiF3 Ca0. 5 Eu0. 5LiF3 Ca0.25 Eu0. 75LiF3 EuLiF3

Spin Polarization%

HM

GGA

mBJ

GGA

mBJ

e e e 100

100 100 100 e

No No No YES

YES YES YES e

mBJ approximation is found to improve the value of Eg Ref. [30]. In Fig. 6 the total (TDOS) and Local (LDOS) density of states are presented for all compounds 0  x  1 using mBJ, the sharp peak appearing at EF (doped compounds) in the spin up channel is attributed to the Eu ions which agrees with the band structure calculations. All density peaks were shifted to the right of EF, which pulls up towards conduction band as illustrated in the band structure. In Fig. 7, the GGA calculations of the density of state are presented. 3.4. Optical properties

Fig. 4(a) using GGA. It is clear in Fig. 3 that the bottom most bands are related to Li-2s and Ca-4s states at energies: 43, 39eV, respectively, while for Ca-p states at 19.7 eV, there are valences bands near Fermi level (EF) between 0.0 and 2.7 eV resulting from F-2p orbitals. The conduction band is essentially dominated by the Ca-3d. The calculated energy gaps for nonstoichiometric Ca1-xEuxLiF3 alloys using mBJ and GGA are displayed see Table 3. One can notice that the GGA calculations show new behavior of Eg which is spin dependent for x ¼ 0.25, 0.5, 0.75. The alloys show insulating behavior in the minority (down) spin channel and a semiconductor behavior in the majority (up) channel, see Fig. 4(bed). Inserting Euþ2 at Ca sites creates flat energy bands between EF and -1eV; these bands arise from 4f7 orbitals of Euþ2. In mBJ calculations the nonstoichiometric alloys show half metallic behavior: insulator in minority spin channel and metallic in majority spin channel with spin polarization 100, see Fig. 5 and Table 4. The energy band gap values in mBJ calculations tend to decrease as Eu concentrations increases till Ca ions are all replaced by Eu ions to create EuLiF3 which shows insulating behavior for both spin channels see Fig. 5e, in contrast EuLiF3 shows half metallic behavior using GGA Fig. 4e. In a recent calculation.

In this subsection, we investigate the dielectric function ε(u), where it includes two parts: real, ε1(u), and imaginary, ε2(u), parts. These two parts are calculated using the band structure of solids [31,32]. On the other hand, the refractive index, n(u), the extinction, k(u), and the absorption coefficients, I(u), and the reflectivity, R(u), are given as follows:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 ε21 ðuÞ þ ε22 ðuÞ þ ε1 ðuÞ  nðuÞ ¼ ½ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 ε21 ðuÞ þ ε22 ðuÞ  ε1 ðuÞ  kðuÞ ¼ ½ 2 IðuÞ ¼ RðuÞ ¼

1=2 pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2u ½ ε21 ðuÞ þ ε22 ðuÞ  ε1 ðuÞ

n þ ik  1 n þ ik þ 1

(2)

(3)

(4)

(5)

Figs. (8, 9) illustrate the imaginary and real parts of the dielectric

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Fig. 6. Total and local density of states DOS (state/eV) (MBJ) in: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

9

10

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Fig. 7. Total and local density of states DOS (state/eV) (GGA) in: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

function ε(u). In Fig. 8 the main peak in the spectrum of ε2(u) (using mBJ) is situated at 9.40eV, 9.84eV, 12.64eV, 11.14eV and 11.84eV as traversed from x ¼ 0 to x ¼ 1, respectively. These peaks are dominated by transitions from the F-2p band and the small contribution of Li-p state just below Fermi energy to the Ca-d state of the conduction band. All peaks are shifted to higher energies as Euþ2 concentration increases in agreement with band structure calculations. The static dielectric functions ε1(0) along xx direction are displayed in Table 5, the main peak occurs at 9.01eV, 8.39eV, 8.81eV, 9.34eV and 10.88eV for x ¼ 0 to x ¼ 1 in steps of 0.25, respectively, as seen in Fig. 9. Moreover, local peaks occur between 1eV and 4 eV

resulting from f-orbitals of Euþ2. The zeros of ε1(0) are found between energies 10eV and 15eV for the considered systems. The real part of the dielectric function, ε1(u), is characterized by minimum values at 11.12eV, 13.23eV, 13.32eV, 13.39eV, 13.42eV for the considered x concentrations as seen in Fig. 9. All spectra (absorption, refraction, reflectivity, extinction) are taken along xx direction, since all compounds have cubic structures; these spectra are presented in Figs. 10e13. The static refractive index n(0) increases with Eu concentration, this behavior is valid for both approximations, see Table 5 and Fig. 10. The refractive index reaches a maximum value (using mBJ) at energies 9.16eV, 8.34eV, 8.86eV, 9.53eV and 10.96eV with values about 1.78,

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11

Fig. 8. The imaginary part of the dielectric function ε2 (u) spectra of Ca1xEuxLiF3 compounds, using GGA and mBJ. (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

1,65, 1.55, 1.69 and 1.71, respectively for all considered systems, this means that increasing Euþ2 concentration will decrease the n(u) of the material, hence activating it optically. The static reflectivity, R(0), is calculated from the reflectivity spectra, see Fig. 11. The presence of Euþ2 in CaLiF3 modifies the spectra due to the f-orbitals of the rare earth element Eu. Fig. 12 presents the absorption spectra for all structures. The absorption resonance is shifted into higher energies. Table (5) contains the results of the optical absorption edge. CaLiF3 is considered as a light absorber, this behavior is still valid in the doped Ca1xEuxLiF3 compounds. The absorption edge slightly decreases, thus light absorbing efficiency increases, and still behaves as a light absorber to be used in solar cells and photovoltaics [33]. Fig. 13 displays the extinction coefficient. The local maxima of k(u) in Fig. 13, corresponding to the zeros of ε1(u), are 0.78, 0.74, 0.83, 0.97,1.01 at the corresponding energies 9.4eV, 11.09eV, 13.13eV, 12.79eV and 12.87eV, for all studied systems as shown in Fig. 9.

4. Conclusion We studied nonstoichiometric Ca1xEuxLiF3 alloys for discrete the concentrations x ¼ 0.25, 0.50, 0.75, 1.00 by inserting Euþ2 in CaLiF3 using DFT within FP-LAPW method, GGA and mBJ functionals. CaLiF3 compound has a wide indirect band gap(МG): 6.559eV and 8.202eV using GGA and mBJ, respectively. New electronic, magnetic and optical properties resulted by doping Eu atoms to create nonstoichiometric Ca1xEuxLiF3 compounds: a half metallic behavior is found using mBJ functional, in contrast GGA calculation shows semiconducting behavior in the majority spin channel (up) and insulator in the minority spin channel (down). The new stoichiometric EuLiF3 fluoroperovskite is the end of series systems (Ca1xEuxLiF3), which shows an insulating behavior (by means of mBJ) in both spin channels and half metallic behavior (by means of GGA), has favourable ferromagnetic phase with maximum value of magnetic moment 56mB and has high Curie temperature about 631 K. Our results show that Ca1xEuxLiF3

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Fig. 9. The real part of the dielectric function ε1 (u) spectra of Sr1xEuxLiF3 compounds, using GGA and mBJ. (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

Table 5 The real part of the dielectric function, ε1(u), the static refraction coefficient, n(0), reflectivity, R(0), and absorption edge, I(u), of Ca1xEuxLiF3 compounds using GGA and mBJ calculations. Compound

CaLiF3 Ca0.75 Eu0.25LiF3 Ca0.5 Eu0.5LiF3 Ca0.25 Eu0.75LiF3 EuLiF3

ε1 (u)

n(0)

R(0)

Absorption edge(eV)

GGA

mBJ

GGA

mBJ

GGA

mBJ

GGA

mBJ

1.6687 1.97012 2.2083 2.3633 2.3841

1.6873 1.5663 1.5079 2.0472 1.5962

1.3048 1.3942 1.4639 1.5530 1.2626

1.1459 1.2452 1.2299 1.4193 1.5392

0.0165 0.0264 0.0120 0.0454 0.0142

0.0026 0.0125 0.0365 0.0321 0.0468

6.4176 6.4266 6.9078 6.8927 6.8774

8.1333 7.7931 7.7412 7.7493 9.4019

N.T. Mahmoud et al. / Computational Condensed Matter 21 (2019) e00432

Fig. 10. The refractivity n(u) spectra of Ca1xEuxLiF3 compounds, using GGA and mBJ: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

13

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Fig. 11. The reflectivity spectra of Ca1xEuxLiF3 compounds using GGA and mBJ: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

N.T. Mahmoud et al. / Computational Condensed Matter 21 (2019) e00432

Fig. 12. The absorption spectra I(u) of Ca1xEuxLiF3 compounds using GGA and mBJ: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

15

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Fig. 13. The extinction spectra k(u), of Ca1xEuxLiF3compounds using GGA and mBJ: (a) x ¼ 0, (b) x ¼ 0.25, (c) x ¼ 0.50, (d) x ¼ 0.75, (e) x ¼ 1.

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