Skip to main content
NCBI home page
ACS Omega logoLink to ACS Omega
. 2022 Dec 15;7(51):47662–47670. doi: 10.1021/acsomega.2c04631

Structural, Electronic and Optical Properties of Titanium Based Fluoro-Perovskites MTiF3 (M = Rb and Cs) via Density Functional Theory Computation

Abdullah †, Umar Ayaz Khan †,*, Sajid Khan ‡, Sara J Ahmed §, Naimat Ullah Khan ∥, Hamid Ullah ⊥, Shehla Naz †, Lamia Ben Farhat #, Mongi Amami #,, Vineet Tirth ∇,○, Abid Zaman ⧫,*
PMCID: PMC9798396  PMID: 36591182

Abstract

graphic file with name ao2c04631_0009.jpg

This study reports the theoretical investigations on the structural, electronic, and optical properties of titanium-based fluoro-perovskites MTiF3 (M = Cs and Rb) using density functional theory. The impact of on-site Coulomb interactions is considered, and calculations are performed in generalized gradient approximation with the Hubbard U term (GGA + U). The ground state parameters, such as lattice constants, bulk modulus, and pressure derivatives of bulk modulus, were found. These compounds are found stable in cubic perovskite structures having lattice constants of 4.30 and 4.38 Å for RbTiF3 and CsTiF3, respectively. Analysis of elastic properties shows that both of the compounds are ductile in nature. According to the band structure profile, the examined compounds have a half-metallic character, exhibiting conducting behavior in the spin-up configuration and nonconducting behavior in the spin-down configuration. The ferromagnetic nature is conformed from the study of its magnetic moments. The optical behaviors such as reflectivity, absorption, refraction, and conductivity of the cubic phase of MTiF3 (M = Rb and Cs) are studied in the energy range of 0–40 eV.

Introduction

Today is the era of science and technology. Scientists across the globe are working on smart materials for various potential applications. Spintronic devices are constructed from half-metallic materials (HMs).1 The nature of HMs depends upon the spin orientation, showing metallic characteristics for one spin orientation while exhibiting semiconductor behavior in the opposite spin channel.2 In simple words, it can be stated that HM is a material in which a band gap is absent for one type of spin direction while a band gap is present in the opposite spin orientation. The presence of a band gap in the case of any one spin orientation indicates that the material is 100% spin-polarized at the Fermi level.3 The spin-polarized current in the HM ferromagnetic materials can be utilized for the construction of magnetic random-access memories, giant magnetoresistance, and in tunneling magnetoresistance devices as a spin injector.4−6 The polarization induced at the Fermi level of a material due to spin orientation can be calculated using7

graphic file with name ao2c04631_m001.jpg

where the symbols N↑(Ef)∧N↓(Ef) represents the electronic density of states at the Fermi level. Firstly, HM was reported in the Mn-based Heusler alloys in 1983 by de-Groot et al.8 Since the discovery of HM, the half-metallic characteristics of different materials, such as transition metal oxide and dilute magnetic semiconductors, have been investigated theoretically,9−13 while few experimental studies have also been also performed.14,15 The unique properties of spin up and spin down of HM have led scientists to construct a new type of device where standard microelectronics are combined with spin-dependent effects such as magnetic sensors and volatile magnetic random access memories.16

Recently, perovskites with the general formula ABF3, where A and B are metallic cations with different sizes, have been investigated to explore further suitable HM materials. Complex alkali metal fluorides are studied intensively by researchers due to their extended applications as a fluorinating agent and as a catalyst in organofluorochemical chemistry.17,18 Moreover, fluoro-perovskite has considerable applications in photoluminescence, high-temperature superconductors, colossal magnetoresistivity, and piezoelectricity.19−22 The most cubic fluoroperovskites are reported to be mechanically stable and elastically anisotropic with desired magnetic, elastic, and electronic properties. These perovskites can be transferred from cubic to other crystal structures.23−27 It is reported that stable fluoroperovskites are formed from the combination of fluorine and inorganic or organic and transition metals.28

Looking into the device applications, we are motivated to present a detailed study on structural, elastic, and half metallicity in the Rb-based perovskite MTiF3 (X = Cs and Rb).

To carry out this theoretical study, generalized gradient approximation (GGA–PBE)29−31 and GGA with the Hubbard U term (GGA + U) have been used, as these are efficient in general to calculate most properties under the umbrella of the FP-LAPW method and in particular the electronic properties. This theoretical work will cover the lack of data on these important materials, and in the future, this study will be used as a reference for experimental and theoretical work as well.

Results and Discussion

Structural Properties

Titanium-based fluoro-perovskites MTiF3 (Rb and Cs) have a cubic structure with space group pm3̅m 221. The unit cell contains five atoms. One atom of Rb/Cs, one atom of Ti, and three atoms of fluorine. The atom M is located at (0, 0, 0), Ti(0.5, 0.5, 0.5), and F at (0, 0.5, 0.5). The unit cell structure is presented in Figure 1. To obtain the ground state stable position and other lattice parameters such as the lattice constant and Bulk modulus optimization has been performed for these compounds. The computed values are listed in Table 1. Table 1 shows that with increasing lattice constant, the bulk modulus decreased because, with increasing lattice constant, the atomic radius increases and electronegativity decreases. The obtained energy verse volume curve has been plotted in Figure 2. The degree of curviness shows the extent of stability. The electronic structures of RbTiF3 and CsTiF3 are optimized in nonmagnetic (NM), ferromagnetic (FM), and antiFM (AFM) states. The energies released during optimization at minimum volume are computed for NM, FM, and AFM states. The FM states are more favorable than the AFM and NM states, as shown in Figure 2.

Figure 1.

Figure 1

Open in a new tab

Sample unit cell structure of (a) RbTiF3 and (b) CsTiF3.

Table 1. Computed Structural Parameters for RbTiF3 and CsTiF3.

structural parameters RbTiF3 CsTiF3
lattice constant (ao) 4.3 4.38
bulk modulus (B0) 66.74 64.23
volume at the ground state (V0) 536.75 568.7
bulk modulus derivative B′ 4.8 4.00
ground state energy (E0) –8270.46 –17888.06
tolerance factor 0.95 0.96
octahedral factor (μ) 0.45 0.47
formation energy –5.242 eV/atom –3.662 eV/atom
Open in a new tab

Figure 2.

Figure 2

Open in a new tab

Optimized plots of RbTiF3 and CsTiF3 in (a) NM, (b) FM, and (c) AFMphase.

Octahedral factor (μ) and tolerance factor (τ) are evaluated from the atomic radii of atoms for these titanium-based fluoro-perovskites, MTiF3 (M = Rb and Cs), to determine the structural stability.

graphic file with name ao2c04631_m002.jpg 1
graphic file with name ao2c04631_m003.jpg 2

In the abovementioned equations rA, rB, and rX are the ionic radii of MTiF3 respectively. For cubic perovskites, the value of octahedral factor (μ) is in the range of 0.44 < μ < 0.90, and the tolerance factor (τ) value is in the range of 0.8 < τ < 1.0. The value of τ and μ is listed in Table 1, and the abovementioned range shows the stable cubic perovskite structure of these materials.32

The formation energy of compounds determines the formation and thermodynamic stability of compounds. It can be determined by using the following relation

graphic file with name ao2c04631_m004.jpg 3

In the abovementioned equation, ΔHf is the formation energy Etot is the total energy of the compound, and μA, μB, and μx are the chemical potential of M, Ti, and F, respectively. The calculated values of ΔHf are listed in Table 1. The negative value of these compounds shows that they are thermodynamically stable and can be synthesized in a laboratory.

Phonopy

For making a real device, material stability is very important. To see the potential applications of CsTiF3 and RbTiF3, we have carried out the phonon dispersion to check their stability. For observing the stability, the calculated phonon band spectrum along the high symmetry directions (W–L−Γ–X–W–K) of the Brillouin zone are plotted as shown in Figure 3. Generally, real and imaginary frequencies express stable and unstable phonon structures due to positive and negative signs of the frequencies, respectively. The computed spectra exhibit positive frequencies that express structural stability, as displayed in Figure 3. Our results are in analogy to Cs2InBiX6 (X = Cl, Br, and I), Cs2InSbX6 (X = Cl, Br, and I), AlGaX2 (X = As, and Sb), SrBaSn, and many more.33−37

Figure 3.

Figure 3

Open in a new tab

Calculated phonon Dispersion curves of (a) CsTiF3 and (b) RbTiF3.

Electronic Properties

In this sub-section, we are presenting the electronic structure of compounds under study from the perspective of the band structure and density of states. The band structure of these compounds is displayed in Figure 4 for both spin-up and spin-down configurations. From the displayed figure it can be seen that in the spin-up configuration of these compounds, there is no gap between the valance band (VB) and conduction bands (CB). They are overlapped with one another across the Fermi level and show a metallic nature in this configuration. Though in spin down configuration, there is an indirect gap (R−Γ) present between the VB and CB, showing the nonmetallic nature of this configuration. Thus, overall, these compounds show a half-metallic nature.

Figure 4.

Figure 4

Open in a new tab

Calculated band structures for (a) RbTiF3 and (b) CsTiF3.

The total and partial densities of states are studied to explore insights into the electronic structure. The obtained graph for the total and partial density of states (TDOS and PDOS) is shown in Figure 5. These graphs follow the band structure result and indicate the half-metallic nature of compounds under study. From Figure 5, it is clear that the graph can be divided into three regions. The first region is from −9 to 5 eV; the second region is from −1 eV to 1 eV, and the third region is from 2 to 7 eV. In the first region of the spin-up configuration, the F-p states show a higher contribution, and in the second region, the Ti-d states are more dominant. The M-p and M-d states, along with Ti-d states, have active participation in the third region. Similarly, in the case of the spin-down configuration in region 1 and region 3, the contributions of the atoms are the same as they have in spin up, but in the second region, there is no contribution from any atom, showing a gap between valence and CBs.

Figure 5.

Figure 5

Open in a new tab

Calculated TDOS and PDOS for (a) RbTiF3 and (b) CsTiF3.

Magnetic Properties

The magnetic properties of any material can be explored through its electronic configuration. We can determine the total magnetization from the valance electron by using the relation38 Mt = (Zt-18) μB, where Mt is the total magnetization, Zt is the no. of valance electrons, and μB is the Bohr magneton. The electronic configuration of compounds under study is [Rb] 5s1, [F] 2s2 2p5, and [Ti] 3d2 4s2. From their electronic configuration, it can be observed that these have unpaired electrons due to which they have some sort of magnetization. The partial and total magnetic moments are computed for the determination of the magnetic nature. The calculated magnetic moments are listed in Table 2. From the table, it is clear that Ti atoms have the main role in magnetization. As titanium has more unpaired electrons due to it having more magnetization as compared to others. The value of total magnetic for MTiF3 (M = Rb and Cs) is an integer indicating its FM and the half-metallic nature.39,40

Table 2. Here mint, m*1, m*2, m*3, and mtot Represent Interstitial Magnetic Moment, Magnetic Moment of Rb/Cs, Magnetic Moment of Ti Atoms, Magnetic Moment of Fluorine, and Total Magnetic Moment in Bohar Magneton (μB), Respectively.

magnetic parameters RbTiF3 CsTiF3
mint 0.489 0.21
m*1 0.004 0.0020
m*2 1.52 1.77
m*3 0.0031 0.02
mtot 2.00 2.00
Open in a new tab

Moreover, we have calculated the energy difference (ΔE = EAFM – EFM) to calculate the Curie temperature (TC). The ΔE for RbTiF3 and CsTiF3 are estimated to be 300 and 200 meV, respectively. The positive ΔE value exhibit that the FM states are more favorable. To ensure the stability in the FM state, we have calculated the Tc using the classical Heisenberg model (Inline graphic, KB is the Boltzmann constant, and n is the number of Ti atoms).41 The TC values are computed to be 580 and 387 K for RbTiF3 and CsTiF3, respectively.

Elastic Properties

Any material’s stability, stiffness, and hardness may be analyzed from the observation of the changes in elastic responses under pressure.42 Elastic constants determine this ground-state behavior of the material. For the compounds under investigation, MTiF3 (M = Rb and Cs), the elastic constant is calculated by using the IR-Elast package within the wien2k code listed in Table 2. For these cubic compounds, the three self-sufficient elastic constants fulfill the mechanical stability criteria (C11 > 0, C44 > 0, C12–C44 > 0, and B > 0) verifying that compounds are mechanically stable.43 Other elastic parameters like shear modulus, Young modulus, Poisson ratio, anisotropic factor, and Kleinman parameter can be calculated from the elastic constants.

We can measure the stiffness and compressibility of material through two well-known modules, that is the shear (G) and bulk (B). B determines the resistance of the material to fracture, while G measures opposition to plastic deformation.44 These two parameters can be computed through the following equations.45

graphic file with name ao2c04631_m006.jpg 4
graphic file with name ao2c04631_m007.jpg 5
graphic file with name ao2c04631_m008.jpg 6
graphic file with name ao2c04631_m009.jpg 7

The evaluated values of shear modulus (G) and bulk modulus (B) are listed in Table 3. The value of B and G is greater for RbTiF3 than CsTiF3.

Table 3. Computed Elastic Constants, Bulk Modulus (B), Anisotropy Factor (A), Poisson’s Ratio (ν), Bulk Modulus (B), Young’s Modulus (E), Shear Modulus (G), and Pugh’s Ratio (B/G).

compounds C11 C12 C44 B A G E ν B/G
  Generalized Gradient Approximation (GGA)
RbTiF3 114.91 36.0 18.40 62.3 0.4 1.7 5.0 0.69 36.64
CsTiF3 96.37 37.33 19.07 57 0.6 0.5 1.5 0.74 114
Open in a new tab

Cauchy pressure’s Cp (C12–C44) and Pugh’s ratio (B/G) distinguish between the brittle and ductile natures of the material. The positive (negative) value of Cauchy pressure verifies its ductile (brittle) nature. Meanwhile, the value of Pugh’s ratio greater(less) than 1.75 declares the ductile (brittle) nature. The value of Cp is positive, and B/G values are greater than 1.75 for RbTiF3 than for CsTiF3, indicating that both materials are ductile.46

To examine the possible microcracks within materials, the imperative parameter elastic anisotropic factor (A) is used. It indicates the degree of anisotropy of materials. By using the following equation, it can be determined.

graphic file with name ao2c04631_m010.jpg 8

For isotropic materials, the value of the anisotropic factor is 1 (unity); else, the material will be anisotropic.47 For RbTiF3 than CsTiF3, the values of A are not unity showing the anisotropic nature. Furthermore, CsTiF3 shows more anisotropy than RbTiF3.

Poisson’s ratio describes the bonding nature of materials. The materials will possess a central force if Poisson’s ratio is in the range of 0.25–0.5; else, the force between atoms will be directional.48 It can be calculated through the following relation

graphic file with name ao2c04631_m011.jpg 9

The obtained value of Poisson’s ratio confirms the directional force between the atoms of the material.

Optical properties

The optical properties of a material can be predicted by analyzing its electronic arrangement and the behavior of photon energy. High-energy photons, when interacting with the material’s surface, expose the internal behavior of the material. On the basis of the optical behavior of the material, it can be suggested that the material is suitable or not for the optoelectronic industry.49 Optical behaviors such as reflectivity, absorption, refraction, and conductivity of the cubic phase of MTiF3 (M = Rb and Cs) are studied in the energy range of 0–40 eV. These characteristics are interlinked with one another and also frequency-dependent. These behaviors can be determined from the complex dielectric function ε(ω).

graphic file with name ao2c04631_m012.jpg 10

ε1(ω) and ε2(ω) is the real and imaginary parts of the dielectric function, respectively. ε1(ω) describes the polarizability of the material. The curve of ε1(ω), presented in Figure 6a, shows that the zero-frequency value [ε1(0)] for RbTiF3 and CsTiF3 is 15 and 18.6, respectively. The curve after ε1(0) decreases, and again, for increasing energy, the peaks reached a maximum of 4.1 at 7.6 eV for RbTiF3 and 4.5 at 8.7 eV for CsTiF3. Beyond these points, the curve decreases with some variation and reaches a negative value at energies between 16 and 9 eV. The negative value expresses the metallic nature of the material because, at this region, the material reflects the total incident photons.50 The imaginary component of dielectric function ε2(ω) gives the optical absorption and optical band-gap of a material. The obtained spectra of ε2(ω) for materials under study are presented in Figure 6b. The threshold energy of the imaginary part starts from 4.5 to 4.7 eV for CsTiF3 and RbTiF3 and reaches maximum peaks of 3.9 on 19 eV for RbTiF3 and for CaTiF3, attaining a peak value of 3.8 on 8 eV.

Figure 6.

Figure 6

Open in a new tab

(a) Energy vs real part of dielectric function (b) energy vs imaginary part of the dielectric function.

The optical behavior of a compound can be explained on the basis of the absorption spectrum in response to incident photons. The imaginary part of the dielectric function ε2(ω) provides the absorption characteristics of the target medium. We can deduce the energy of excitonic peaks corresponding to peaks which lie in the absorption spectrum. From Figure 6b, one can locate the low-energy exciton peaks at 5.9 and 8 eV for CsTiF3, while for RbTiF3, peaks are found at 6 and 9 eV. These peaks lie in the ultraviolet part of the electromagnetic spectrum.51,52

The refractive index is an important optical parameter describing the absorption and dispersion of incident photons. Previous studies reveal that for denser media, the value of the refractive index will be large.53 The obtained curve of refractive index as a function of energy for both compounds is displayed in Figure 7a. A similar trend was found between the curves of ε1(ω) and n(ω). The zero-frequency n(0) is found 4.1 and 4.5 for RbTiF3 and CsTiF3, respectively. By increasing the photon energy, the n(ω) gains a maximum value of 2.07 at 7 eV for RbTiF3 and 2.2 at 8.7 eV for CsTiF3. The reflectivity R(ω) is the impactful parameter describing the ability of the material to reflect the optical radiation. The calculated spectra for reflectivity are presented in Figure 7c. The material shows a maximum reflectivity of 0.37 at 19.3 eV and 0.33 at 16 eV for RbTiF3 and CsTiF3.

Figure 7.

Figure 7

Open in a new tab

(a) Energy vs refractive index, (b) energy vs absorption coefficient, (c) energy vs reflectivity, and (d) energy vs optical coefficient of RbTiF3 and CsTiF3.

The absorption I(ω) and conductivity σ(ω) spectra are shown in Figure 7b,d. The absorption spectra indicate that both compounds have the absorption power of photons in the energy range of 5–30 eV and 35–40 eV. The maximum peaks of absorption were found at 288 cm–1 at 19.3 eV for RbTiF3 and 267 cm–1 at 34.8 for CsTiF3. The absorption power of RbTiF3 is greater than that of CsTiF3. Conductivity spectra similar to the absorption spectra show high conduction at the above-stated ranges. The maximum conductivity was found at 9499 Ω–1 cm–1 at 19.3 eV and 8956 Ω–1 cm–1 at 34.8 eV for RbTiF3 and CsTiF3, respectively. The materials, which are highly transparent in the visible region and exhibit EM wave absorption properties in the high-frequency millimeter-wave region, exhibit ferromagnetism, and our result correlates with the literature.40

Conclusions

Titanium-based fluoroperovskite compounds MTiF3 (M = Cs and Rb) are studied using Wien2K in the general framework of density functional theory. The calculation of structural, electronic, and optical properties is carried out with the GGA + U approach. It is found that both compounds are structurally and dynamically stable in the cubic phase due to positive phonon frequencies. The half-metallic nature is observed, such that the metallic character in the spin-up state and the nonmetallic character in the spin-down state with an indirect band gap (R−Γ) were observed for both compounds. The FM nature of compounds is confirmed by their magnetic moments. The various optical properties are explored in the wide energy range of 0–40 eV. Both compounds show significant absorption in the intermediate energy range, and sharp absorption peaks are observed around 35 eV. The phonon structural stability is observed from phonon dispersion.

Computational Model

The first principle calculations are performed through the FP-LAPW technique54 incorporated in the Wien2k code within spin-polarized density functional theory.55 The impact of on-site Coulomb interactions is considered, and simulations are carried out in GGA with the Hubbard U term (GGA + U).56 The energy-volume curve is adjusted for the investigation of structural parameters by using Murnaghan’s state equation.31 Energy gap-6Ry is taken between the valance and core orbital. Furthermore, G-max is taken at 12, the cut-off l-max value is 10, the K-point value is 2000, and the RK max value is selected at 5. The elastic parameters are studied using elastic constants determined through the IR-Elast package designed by Jamal.57 Optical parameters that are studied from the frequency depended on a complex dielectric function. Additionally, we have calculated the phonon spectra to check the stability of the CsTiF3 and RbTiF3. We have adopted the EDIFF = 10–6 eV in order to minimize the error to the maximum possible extent. The phonon spectra are calculated with the finite difference method with a supercell size of 5 × 5 × 2 and analyzed with the phonopy code58 using VASP59 as a calculator.

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61421, Asir, Kingdom of Saudi Arabia, for funding this work through the Large Groups Project under grant number RGP.2/140/43. The authors are thankful to Al-Mustaqbal University College (grant no.: MUC-G-0322) for their support.

The authors declare no competing financial interest.

References

  1. Žutić I.; Fabian J.; Sarma S. D. Spintronics: Fundamentals and applications. Rev. Mod. Phys. 2004, 76, 323. 10.48550/arXiv.cond-mat/0405528. [DOI] [Google Scholar]
  2. Wolf S. A.; Awschalom D. D.; Buhrman R. A.; Daughton J. M.; von Molnár V. S.; Roukes M. L.; Chtchelkanova A. Y.; Treger D. M. Spintronics: a spin-based electronics vision for the future. Science 2001, 294, 1488–1495. 10.1126/science.1065389. [DOI] [PubMed] [Google Scholar]
  3. Wang K. L.; Alzate J. G.; Khalili Amiri P. K. Low-power non-volatile spintronic memory: STT-RAM and beyond. J. Phys. D: Appl. Phys. 2013, 46, 074003. 10.1088/0022-3727/46/7/074003. [DOI] [Google Scholar]
  4. Lee H.; Ebrahimi F.; Amiri P. K.; Wang K. L. Low-power, high-density spintronic programmable logic with voltage-gated spin Hall effect in magnetic tunnel junctions. IEEE Magn. Lett. 2016, 7, 1–5. 10.1109/lmag.2016.2538742. [DOI] [Google Scholar]
  5. Zhao W.; Belhaire E.; Chappert C.; Mazoyer P.. Spintronic device based non-volatile low standby power SRAM. IEEE Computer Society Annual Symposium on VLSIIEEE, 2008; pp 40–45.
  6. Nikolaev K.; Kolbo P.; Pokhil T.; Peng X.; Chen Y.; Ambrose T.; Mryasov O. “All-Heusler alloy” current-perpendicular-to-plane giant magnetoresistance. Appl. Phys. Lett. 2009, 94, 222501. 10.1063/1.3126962. [DOI] [Google Scholar]
  7. Sakuraba Y.; Hattori A. M.; Oogane M.; Ando Y.; Kato H.; Sakuma A.; Miyazaki T.; Kubota H. Giant tunneling magnetoresistance in Co2MnSi/Al-O/Co2MnSi magnetic tunnel junctions. Appl. Phys. Lett. 2006, 88, 192508. 10.1063/1.2202724. [DOI] [Google Scholar]
  8. Tsunegi S.; Sakuraba Y.; Oogane M.; Takanashi K.; Ando Y. Large tunnel magnetoresistance in magnetic tunnel junctions using a Co2MnSi Heusler alloy electrode and a MgO barrier. Appl. Phys. Lett. 2008, 93, 112506. 10.1063/1.2987516. [DOI] [Google Scholar]
  9. Ishikawa T.; Marukame T.; Kijima H.; Matsuda K. I.; Uemura T.; Arita M.; Yamamoto M. Spin-dependent tunneling characteristics of fully epitaxial magnetic tunneling junctions with a full-Heusler alloy Co2MnSi thin film and a MgO tunnel barrier. Appl. Phys. Lett. 2006, 89, 192505. 10.1063/1.2378397. [DOI] [Google Scholar]
  10. Wang Y.; Zheng J.; Ni Z.; Fei R.; Liu Q.; Quhe R.; Xu C.; Zhou J.; Gao J.; Lu J. Half-metallic silicene and germanene nanoribbons: towards high-performance spintronics device. Nano 2012, 07, 1250037. 10.1142/s1793292012500373. [DOI] [Google Scholar]
  11. Liu H. X.; Honda Y.; Taira T.; Matsuda K. I.; Arita M.; Uemura T.; Yamamoto M. Giant tunneling magnetoresistance in epitaxial Co2MnSi/MgO/Co2MnSi magnetic tunnel junctions by half-metallicity of Co2MnSi and coherent tunneling. Appl. Phys. Lett. 2012, 101, 132418. 10.1063/1.4755773. [DOI] [Google Scholar]
  12. Wei J. Y. T.; Yeh N. C.; Vasquez R. P.; Gupta A. Tunneling evidence of half-metallicity in epitaxial films of ferromagnetic perovskite manganites and ferrimagnetic magnetite. J. Appl. Phys. 1998, 83, 7366–7368. 10.1063/1.367799. [DOI] [Google Scholar]
  13. Ram M.; Saxena A.; Aly A. E.; Shankar A. Half-metallicity in new Heusler alloys Mn2ScZ (Z = Si, Ge, Sn). RSC Adv. 2020, 10, 7661–7670. 10.1039/c9ra09303f. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Park J. H.; Kwon S. K.; Min B. I. Half-metallic antiferromagnetic double perovskites:LaAVRuO6(A=Ca,Sr, and Ba). Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 174401. 10.1103/physrevb.65.174401. [DOI] [Google Scholar]
  15. Galanakis I.; Şaşıoğlu E. High TC half-metallic fully-compensated ferrimagnetic Heusler compounds. Appl. Phys. Lett. 2011, 99, 052509. 10.1063/1.3619844. [DOI] [Google Scholar]
  16. Wang Z.; Jing Q.; Zhang M.; Dong X.; Pan S.; Yang Z. A new 12L-hexagonal perovskite Cs4Mg3CaF12: structural transition derived from the partial substitution of Mg2+with Ca2+. RSC Adv. 2014, 4, 54194–54198. 10.1039/c4ra07819e. [DOI] [Google Scholar]
  17. Yin W. J.; Yang J. H.; Kang J.; Yan Y.; Wei S. H. Halide perovskite materials for solar cells: a theoretical review. J. Mater. Chem. A 2015, 3, 8926–8942. 10.1039/c4ta05033a. [DOI] [Google Scholar]
  18. Edwardson P. J.; Boyer L. L.; Newman R. L.; Fox D. H.; Hardy J. R.; Flocken J. W.; Guenther R. A.; Mei W. Ferroelectricity in perovskitelikeNaCaF3predictedab initio. Phys. Rev. B: Condens. Matter Mater. Phys. 1989, 39, 9738. 10.1103/physrevb.39.9738. [DOI] [PubMed] [Google Scholar]
  19. Boyer L. L.; Mehl M. J.; Mei W. N.; Duan C. G.; Flocken J. W.; Guenther R. A.; Edwardson P. J.. Predicted properties of NaCaF 3. In AIP Conference Proceedings; American Institute of Physics, 2000; Vol. 535, No. (1), , pp 364–371).
  20. Duan C.-G.; Mei W. N.; Liu J.; Yin W.-G.; Hardy J. R.; Smith R. W.; Mehl M. J.; Boyer L. L. Electronic properties of NaCdF 3: A first-principles prediction. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 033102. 10.1103/physrevb.69.033102. [DOI] [Google Scholar]
  21. Benkabou M. H.; Harmel M.; Haddou A.; Yakoubi A.; Baki N.; Ahmed R.; Al-Douri Y.; Syrotyuk S. V.; Khachai M. R.; Khenata R.; Voon C. H.; Johan M. R. Structural, electronic, optical and thermodynamic investigations of NaXF 3 (X = Ca and Sr): First-principles calculations. Chin. J. Phys. 2018, 56, 131–144. 10.1016/j.cjph.2017.12.008. [DOI] [Google Scholar]
  22. Bhalla A. S.; Guo R.; Roy R. The perovskite structure-a review of its role in ceramic science and technology. Mater. Res. Innovations 2000, 4, 3–26. 10.1007/s100190000062. [DOI] [Google Scholar]
  23. Arora G.; Ahuja G.; Ahuja U. Electronic and elastic properties of ternary fluoro-perovskite RbCaF3. J. Phys. Conf. Ser. 2021, 1849, 012032. 10.1088/1742-6596/1849/1/012032. [DOI] [Google Scholar]
  24. Tian L.; Hu Z.; Liu X.; Liu Z.; Guo P.; Xu B.; Xue Q.; Yip H.-L.; Huang F.; Cao Y. Fluoro- and Amino-Functionalized Conjugated Polymers as Electron Transport Materials for Perovskite Solar Cells with Improved Efficiency and Stability. ACS Appl. Mater. Interfaces 2019, 11, 5289–5297. 10.1021/acsami.8b19036. [DOI] [PubMed] [Google Scholar]
  25. Turner G.Global Renewable Energy Market Outlook 2013; Bloom. New Energy Financ., 2013; Vol. 26, p 506. [Google Scholar]
  26. Mahmoud N. T.; Khalifeh J. M.; Mousa A. A. Effects of rare earth element Eu on structural, electronic, magnetic, and optical properties of fluoroperovskite compounds SrLiF3: First principles calculations. Phys. B Condens. Matter 2019, 564, 37–44. 10.1016/j.physb.2019.03.028. [DOI] [Google Scholar]
  27. Lufaso M. W.; Woodward P. M. Prediction of the crystal structures of perovskites using the software program SPuDS. Sect. B Struct. Sci. 2001, 57, 725–738. 10.1107/s0108768101015282. [DOI] [PubMed] [Google Scholar]
  28. Mubarak A.; Al-Omari S. First-principles calculations of two cubic fluoropervskite compounds: RbFeF3 and RbNiF3. J. Magn. Magn. Mater. 2015, 382, 211–218. 10.1016/j.jmmm.2015.01.073. [DOI] [Google Scholar]
  29. Levy M. R.Crystal structure and defect property predictions in ceramic materials. Doctoral Dissertation, University of London, 2005. [Google Scholar]
  30. Blaha P.; Schwarz K.; Madsen G.; Kvasnicka D.; Luitz J.; Laskowsk R.; Tran F.; Marks L.. Wien2k An Augmented Plane Wave Plus Local Orbital Program for Calculating the Crystal Properties; Vienna University of Technology: Austria, 2001. [Google Scholar]
  31. Perdew J. P.; Burke K.; Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. 10.1103/physrevlett.77.3865. [DOI] [PubMed] [Google Scholar]
  32. Bartel C. J.; Sutton C.; Goldsmith B. R.; Ouyang R.; Musgrave C. B.; Ghiringhelli L. M.; Scheffler M. New tolerance factor to predict the stability of perovskite oxides and halides. Sci. Adv. 2019, 5, eaav0693 10.1126/sciadv.aav0693. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Iqbal M. W.; Asghar M.; Noor N. A.; Ullah H.; Zahid T.; Aftab S.; Mahmood A. Analysis of ternary AlGaX2(X = As, Sb) compounds for opto-electronic and renewable energy devices using density functional theory. Phys. Scr. 2021, 96, 125706. 10.1088/1402-4896/ac2024. [DOI] [Google Scholar]
  34. Michel K. H.; Verberck B. Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 224301. 10.1103/physrevb.80.224301. [DOI] [Google Scholar]
  35. Alam M.; Waheed H. S.; Ullah H.; Iqbal M. W.; Shin Y.-H.; Iqbal Khan M. J.; Elsaeedy H. I.; Neffati R. Optoelectronics properties of Janus SnSSe monolayer for solar cells applications. Phys. Rev. B Condens. Matter 2022, 625, 413487. 10.1016/j.physb.2021.413487. [DOI] [Google Scholar]
  36. Yan J. A.; Ruan W. Y.; Chou M. Y. Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene: Density-functional perturbation theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 125401. 10.1103/physrevb.77.125401. [DOI] [Google Scholar]
  37. Khandy S. A.; Islam I.; Kaur K.; Ali A. M.; Abd El-Rehim A. F. Effect of Strain on the Electronic Structure and Phonon Stability of SrBaSn Half Heusler Alloy. Molecules 2022, 27, 3785. 10.3390/molecules27123785. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Galanakis I.; Mavropoulos P.; Dederichs P. H. Electronic structure and Slater-Pauling behaviour in half-metallic Heusler alloys calculated from first principles. J. Phys. D Appl. Phys. 2006, 39, 765. 10.1088/0022-3727/39/5/s01. [DOI] [Google Scholar]
  39. Dar S. A.Osmium Containing Double Perovskite Ba 2 XOsO 6 (X= Mg, Zn, Cd): Important Candidates for Half-Metallic Ferromagnetic and Spintronic Applications. In Perovskite Materials, Devices and Integration; Intech Open, 2019. [Google Scholar]
  40. Tokoro H.; Nakabayashi K.; Nagashima S.; Song Q.; Yoshikiyo M.; Ohkoshi S. I. Optical Properties of Epsilon Iron Oxide Nanoparticles in the Millimeter- and Terahertz-Wave Regions. Bull. Chem. Soc. Jpn. 2022, 95, 538–552. 10.1246/bcsj.20210406. [DOI] [Google Scholar]
  41. Wang X.; Cheng Z.; Wang J.; Liu G. A full spectrum of spintronic properties demonstrated by a C1b-type Heusler compound Mn2Sn subjected to strain engineering. J. Mater. Chem. C 2016, 4, 8535–8544. 10.1039/c6tc02526a. [DOI] [Google Scholar]
  42. Tripathi M. N.; Saha A.; Singh S. Structural, elastic, electronic and optical properties of lead-free halide double perovskite Cs2AgBiX6 (X = Cl, Br, and I). Mater. Res. Express. 2019, 6, 115517. 10.1088/2053-1591/ab48ba. [DOI] [Google Scholar]
  43. Glazer A. M. WINOPTACT: a computer program to calculate optical rotatory power and refractive indices from crystal structure data. J. Appl. Crystallogr. 2002, 35, 652. 10.1107/s0021889802013997. [DOI] [Google Scholar]
  44. Ghebouli B.; Ghebouli M. A.; Bouhemadou A.; Fatmi M.; Khenata R.; Rached D.; Ouahrani T.; Bin-Omran S. Theoretical prediction of the structural, elastic, electronic, optical and thermal properties of the cubic perovskites CsXF3 (X = Ca, Sr and Hg) under pressure effect. Solid State Sci. 2012, 14, 903–913. 10.1016/j.solidstatesciences.2012.04.019. [DOI] [Google Scholar]
  45. Khandy S. A.; Gupta D. C. Structural, elastic and thermo-electronic properties of paramagnetic perovskite PbTaO3. RSC Adv. 2016, 6, 48009–48015. 10.1039/c6ra10468a. [DOI] [Google Scholar]
  46. Pugh S. F. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Lond. Edinb. Dublin Philos. Mag. J. Sci. 1954, 45, 823–843. 10.1080/14786440808520496. [DOI] [Google Scholar]
  47. Yang Y.; Lu H.; Yu C.; Chen J. M. First-principles calculations of mechanical properties of TiC and TiN. J. Alloys Compd. 2009, 485, 542–547. 10.1016/j.jallcom.2009.06.023. [DOI] [Google Scholar]
  48. Gupta Y.; Sinha M. M.; Verma S. S. First-principles investigation on the electronic, mechanical and lattice dynamical properties of novel AlNiX (X= As and Sb) half-Heusler alloys. Mater. Today Commun. 2021, 26, 101885. 10.1016/j.mtcomm.2020.101885. [DOI] [Google Scholar]
  49. Amudhavalli A.; Rajeswarapalanichamy R.; Iyakutti K.; Kushwaha A. K. First principles study of structural and optoelectronic properties of Li based half Heusler alloys. Comput. Condens. Matter 2018, 14, 55–66. 10.1016/j.cocom.2018.01.002. [DOI] [Google Scholar]
  50. Jamil M. T.; Ahmad J.; Bukhari S. H.; Sultan T.; Akhter M. Y.; Ahmad H.; Murtaza G. Effect on structural and optical properties of Zn-substituted cobalt ferrite CoFe2O4. J. Ovonic Res. 2017, 13, 45–53. [Google Scholar]
  51. Xu L.; Liu G.; Xiang H.; Wang R.; Shan Q.; Yuan S.; Cai B.; Li Z.; Li W.; Zhang S.; Zeng H. Charge-carrier dynamics and regulation strategies in perovskite light-emitting diodes: From materials to devices. Appl. Phys. Rev. 2022, 9, 021308. 10.1063/5.0080087. [DOI] [Google Scholar]
  52. Ullah S. S.; Farooq M.; Din H. U.; Alam Q.; Idrees M.; Bilal M.; Amin B. First principles study of electronic and optical properties and photocatalytic performance of GaN-SiS van der Waals heterostructure. RSC Adv. 2021, 11, 32996–33003. 10.1039/d1ra06011b. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Lal M.; Kapila S. Structural, electronic, optical and mechanical properties of CsCaCl3 and KCdF3 cubic perovskites. Int. J. Mater. Sci. 2017, 12, 137–147. [Google Scholar]
  54. Perdew J. P.; Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244. 10.1103/physrevb.45.13244. [DOI] [PubMed] [Google Scholar]
  55. Nair S.; Deshpande M.; Shah V.; Ghaisas S.; Jadkar S. Cs2TlBiI6: a new lead-free halide double perovskite with direct band gap. J. Phys. Condens. Matter 2019, 31, 445902. 10.1088/1361-648x/ab32a5. [DOI] [PubMed] [Google Scholar]
  56. Singh D. J.; Nordstrom L.. Planewaves, Pseudopotentials, and the LAPW method; Springer Science & Business Media, 2006. [Google Scholar]
  57. Murnaghan F. D. The compressibility of media under extreme pressures. Proc. Natl. Acad. Sci. 1944, 30, 244–247. 10.1073/pnas.30.9.244. [DOI] [PMC free article] [PubMed] [Google Scholar]
  58. Togo A.; Tanaka I. First principles phonon calculations in materials science. Scr. Mater. 2015, 108, 1–5. 10.1016/j.scriptamat.2015.07.021. [DOI] [Google Scholar]
  59. Paier J.; Marsman M.; Kresse G. Dielectric properties and excitons for extended systems from hybrid functionals. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 121201. 10.1103/physrevb.78.121201. [DOI] [PubMed] [Google Scholar]

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES