THEORETICAL INVESTIGATION OF THE STRUCTURAL, ELECTRONIC, AND MECHANICAL PROPERTIES OF THE MAGNESIUM-BASED FLUOROPEROVSKITE COMPOUNDS XMgF3 (X= Ga, Al, In)

Abstract

Ab initio investigations of the Mg-based fluoroperovskite XMgF3 (X = Ga, Al and In) compounds were calculated by using the full-potential linearized augmented plane wave method. The various physical properties were computed using the WIEN2k code. The structural parameters of these compounds agreed with previous predictions within acceptable limits.This study revealed that GaMgF3 and InMgF3 compounds were anisotropic, ductile, and mechanically stable, while GaMgF3 was found to be more rigid and less compressible than InMgF3. Furthermore, it was shown that the third compound investigated, AlMgF3, was mechanically unstable. The electronic band structure of AlMgF3 and InMgF3 was of a semiconductor with an indirect (M - X) band gap with an energy of 2.49 eV and 2.98 eV, respectively, while GaMgF3 was found to be an insulator with a direct (X-X) band gap with and energy of 3.86 eV. We found that the bonding force between the atoms was mostly ionic with just a little covalent nature. The understanding of these compounds gained from these computations can be applied in the design of electronic devices.

Headnote

ABSTRACT: Ab initio investigations of the Mg-based fluoroperovskite XMgF3 (X = Ga, Al and In) compounds were calculated by using the full-potential linearized augmented plane wave method. The various physical properties were computed using the WIEN2k code. The structural parameters of these compounds agreed with previous predictions within acceptable limits.This study revealed that GaMgF3 and InMgF3 compounds were anisotropic, ductile, and mechanically stable, while GaMgF3 was found to be more rigid and less compressible than InMgF3. Furthermore, it was shown that the third compound investigated, AlMgF3, was mechanically unstable. The electronic band structure of AlMgF3 and InMgF3 was of a semiconductor with an indirect (M - X) band gap with an energy of 2.49 eV and 2.98 eV, respectively, while GaMgF3 was found to be an insulator with a direct (X-X) band gap with and energy of 3.86 eV. We found that the bonding force between the atoms was mostly ionic with just a little covalent nature. The understanding of these compounds gained from these computations can be applied in the design of electronic devices.

Keywords: Electronic properties; Fluoroperovskites; GGA approximation; Mechanical properties; Structural properties.

(ProQuest: ... denotes formulae omitted.)

1. INTRODUCTION

Cubic perovskite compounds have received a great deal of attention due to their massive use in technology. Many groups of perovskite crystals, including fluoroperovskites (ABF3), oxideperovskites (ABO3), and nitrideperovskites (ABN3), are found on earth. A stable fluoroperovskite is generated by the concoction of fluorine, organic or inorganic, and a transition metal (TM).1 Owing to the importance of their technical applications in lenses and the semiconductor industry, there has been a focus of interest on the structural, electronic, and elastic properties of the fluoroperovskites.2 Cubic perovskite compounds are usually preferred for the manufacture of lenses because the birefringence which occurs with most lens materials does not occur with them. Fluoroperovskites, with the structure of ABF3, are one of the customary perovskite structures. The elements A and B are alkaline metals (Li - Cs), and alkaline earth metals (Be - Ba), respectively. The perovskite crystal family is a vast area for investigating other physical properties, such as giant magnetoresistance,3 an almost zero temperature resistivity coefficient,4 and being a laser source.5 Based on their chemical composition, these compounds may be expected to have various significant physical properties, ranging from semiconduction to magnetic and superconduction properties.6,7 The fluoroperovskites have a wide band-gap energy. Because of their short absorption edges, they have a high potential as window materials in the ultraviolet (UV) and vacuum-ultraviolet (VUV) wavelength regions.8,9 Husain et al. reported for the first time on the structural, electronic, and mechanical properties of cubic fluoroperovskites, (ZnXF3, X = Y, Bi) using the density functional theory (DFT). It was observed that both of the compounds had a narrow band gap, were structurally stable, and were mechanically ductile.10 Khan et al. investigated theoretically the thallium (Tl)-based fluoroperovskite compounds TlXF3 (X = Ca, Cd, Hg, and Mg) and concluded that due to their wide band gap, in the insulator range, these compounds can be used as a scintillation detectors.11 To the best of our knowledge, there have been insufficient experimental and theoretical studies devoted to the basic structural, electronic, and mechanical properties of XMgF3 compounds, where X = gallium (Ga), aluminum (Al), and indium (In). Among these compounds GaMgF3 was found to be an insulator electronically and was predicted to have Auger-Free luminescence (AFL), while AlMgF3 and InMgF3 were considered to have a semiconducting nature. The aim of the present research was to investigate systematically the structural, electronic, and elastic properties of XMgF3 (X = Ga, Al and In) using the full-potential linearized augmented plane wave (FP-LAPW) method.

2.METHOD OF CALCULATIONS

For this study we used a methodology based on the density functional theory (DFT)12 and the approach of the FP-LAPW method13 to solve the Kohn-Sham equations as implemented in the WIEN2k code.14 For many body problems, this approach is a universal quantum mechanical method and has proven to be one of the most reliable methods for determining physical properties. The generalized gradient approximation-developed by Perdew, Burke, and Ernzerhof-(GGA-PBE)15 was used for estimating the potential for exchange-correlation. The valence and core electrons were considered as semi- and completely relativistic, respectively.

The compound's unit cell was subdivided into two regions where the first was the interstitial zone. In this zone the plane wave was generated with the cutoff value of Kmax = 8.0/Rmt in order to achieve convergence eigen values. The Kmax and Rmt are the largest K vector of the expansion of the plane wave and the smallest radius of the non-overlapping atomic spheres, respectively. The Rmt for the atoms X= Ga, Al, and In are 2.5 for each one, and 1.77, 1.76, and 1.8 for Mg in the cases of AlMgF3, GaMgF3, and InMgF3, respectively. The corresponding values for F are 1.86, 1.85, and 1.89 atomic units (a.u.) on going from Al to Ga and In, respectively.

The second region is the non-overlapping muffin-tin spheres, in which the spherical-harmonic wave generates around and within lmax = 14. The lattice constants for each compound are determined using Murnaghan's equation of states16 to minimize the total energy of the unit cell with respect to its volume.

3.1 Structural properties: We evaluated the structural properties of the Mg-based fluoroperovskite compounds XMgF3 (X= Ga, Al and In) in the ideal 0 K and 0 GPa cubic unit cell. Such compounds with a Pm-3m space group have the Wyckoff atomic positions at (0, 0, 0) for X, (0.5, 0.5, 0.5) for Mg, and (0.5, 0.5, 0) for F as shown in Figure 1.

The structural properties, such as the lattice constants, the bulk modulus, the pressure derivative of the bulk modulus, the ground state energy, and the ground state volume, were calculated for the first time using first principles (ab initio) as shown in Table 1.

The higher bulk modulus and absolute value of the cohesive energy suggest a high crystal rigidity. Thus, AlMgF3 can be assumed to be harder and less compressible than GaMgF3 and InMgF3 based on the B0 values as shown in Table 1.

The volume optimization method was used to analyze the structural properties of XMgF3 (X = Ga, Al, and In). The volume optimization was conducted on each compound by reducing the unit cell's total energy with respect to the unit cell volume and was made to fit by the state equation of Birch-Murnaghan as shown in Figures 2A-2C.

From Figures 2A-2C it can be seen that energy of the unit cell at first decreases with the increase of the unit cell volume to a point where the system's minimum energy is obtained, which is the system's ground state energy Eo. The volume at this minimal energy is considered to be the ground state or optimum cell volume. After this optimized stage, the unit cell energy increases with the further increases in the unit cell volume and the system becomes un-relaxed again.

The energy of the unit cell was minimized by performing the volume optimization of the unit cell volume as shown in Figures 2A-2C.

3.2Electronic properties: The electronic properties of the compounds GaMgF^, AlMgF3, and InMgF3 were examined at 0 K and 0 GPa using the electronic band structure and the full and partial state density spectrum as shown in Figures 3A-3C and 4A-4C.

From Figures 3A-3C, one can consider that both AlMgF3 and InMgF3 have a semiconducting nature while GaMgF3 has a combination of insulators. The maxima of the valence and the minima of the conduction bands of AlMgF3 and InMgF3 were located at the M and X symmetry levels, respectively. Such bands create an indirect (M-X) band gap that has been found to be 0.49 eV for the former and 2.98 eV for the later compounds. Furthermore for GaMgF3, both the valence band maxima and the conduction band minima lie at the same X symmetry points which form a direct (XX) band gap of 3.86 eV This gap in the energy band may serve as a reference for future research.

The total and partial state densities (TDOS and PDOS) of the compounds being studied were within the energy range of -7 to 7 eV as illustrated in Figures 4A-4C. The dominant hybridization in the TDOS valence band was linked to the F s-p states with a minor contribution from the X d-state (where X= Ga, Al, and In). The valence zone of the compounds was characterized by two bands. The first band near the Fermi scale was due to the hybridization of the d-state of X together with the p-state of F. In this region, the bonding states are connected to the spin-up X-d-state. The second band was linked to the actions of the d-state of X and the d-state of Mg with a major contribution from the p-state of F. The main contributions in the conduction band were from the s- and p-states of the X atom, the s- and d-states of the Mg atom, and the p-state of the F atom.

It should also be noted that the Mg atoms are positioned in XMgF3 at the middle. The octahedrons of the MgF6 bonds are formed because six F ions surround the central Mg atom. The transfer of electrons from the Mg atom to the F atom is due to the difference in the electro-negativity of these atoms. This difference in electronegativity induces an attraction between the positively charged Mg atom and the negatively charged F atoms in the octahedron, and produces a dipole moment. The electrons are positioned in MgF6 to partly fill the d-state of the Mg atom, while the pstate of the F atoms states is complete, which establishes the covalent Mg-F bond. The densities of electron charges along the (110) plane of the XMgF3 compounds, GaMgF3, AlMgF3, and InMgF3, are shown in Figures 5A-5C. Within the sphere, the form of Mg and X is not fully spherical, which shows that the d-state of the Mg is partially filled. It is known that the contours of the Mg-F bond are not completely isolated and that although the bond has some partially covalent characteristics it is mainly ionic in nature. In contrast however, the X-MgF6 bond is strictly ionic since the X and MgF6 contours are completely separated. One can infer that the compound XMgF3 has some covalent bonding but is mainly ionic.

3.3Mechanical properties: The elastic constant parameters (Cij) were utilized to define the degree of the compound's reaction to the exerted macroscopic stress. These constants establish a connection between the mechanical and dynamic actions of the compound. In cubic arrangement crystals, three distinct elastic constants, Cu, Cj2, and C44, are needed to measure the mechanical properties such as stability and rigidity. The Cij values determined for the three compounds studied are shown in Table 2.

A compound can be described as mechanically stable when the restriction formulas in a cubic structure [(Cjj+2Cj2)/3; C44> 0; (Cn-C^)> 2; C^< B< Cļļ] are attained.17 The uniaxial deformation along the (100) direction and the pure shear deformation on the (100) crystal plane are denoted by C11 and C44. The calculated unidirectional elastic Cu is higher than C44 for all of our compounds XMgF^ (X = Ga, Al and In). These compounds show a lower resistance to pure shear deformation compared with their resistance to unidirectional compression. From the measured C44 values it can be concluded that GaMgF3 is stiffer than AlMgF3 and InMgF3. To the best of our knowledge, there are no reported Cij values in the literature for XMgF3 (X= Ga, Al and In) with which we can compare our findings,.

The constant elastic anisotropy (A) is an important parameter in engineering science that describes the induction of microcracks in materials.18

... (1)

This constant has been used to overcome the elastic anisotropy and to evaluate the degree. A compound is classified as isotropic where A = 1. Otherwise, it is known as anisotropic elastically. The present compounds can be classified as anisotropic based on the calculated A values in Table 2 which shows that InMgF3 is more anisotropic than GaMgF3 and AlMgF3.

Table 2 also displays the elastic moduli results, such as the Young's modulus (E). The equations for the various factors are:

... (2)

... (3)

... (4)

... (5)

... (6)

The estimated B0 values are in agreement, calculated by both the elastic constants and the state equation of Birch-Murnaghan. This may be due to the accuracy of the measurements of the elastic constants. The resistance to plastic dislocation and the degree of stiffness can be inferred, from the shear and Young's moduli, respectively. The measured values of G and E for AlMgF3 were found to be higher than those for GaMgF3 and InMgF3 indicating that AlMgF3 is stiffer than the other two.

A compound can be defined as ductile when Cauchy's pressure (Cjj-C^) has a positive value and Poisson's ratio (v) and Pugh's index ductility (B/G) are higher than the critical values (vcrit = 0.26 and B / Gcrit = 1.75, respectively).19-21 Similar work by Mubarak found that the Ag-based fluoroperovskite compounds AgMF^ (M = Co and Ni) were ductile and mechanically stable.22 Therefore, both GaMgF3 and InMgF3 can be considered to be ductile compounds according to the measurement values of the ductile parameters of the Poisson's ratio (v) and the Pugh's index ductility (B/G).

Poisson's ratio can also be used to obtain the details on the bonding force behavior between atoms. The measured values of v for the present compounds were located between the lower and upper limit values of the central force solids (0.25-0.5) indicating that the interatomic forces between the atoms are central.

4.CONCLUSIONS

The density functional theory with the GGA-PBE exchange correlation was used to examine the structural, electronic, and mechanical properties of XMgF3 (X= Ga, Al, In). All the properties were calculated for the first time for these compounds and we are confident about the accuracy of the calculations. For the structural properties, the lattice constants, the bulk modulus, the ground state energy, and the ground state volume were investigated. AlMgF3 and InMgF3 were found to have a semiconducting nature with an indirect (M-Х) band gap of 0.49 eV for AlMgF3 and 2.98 eV for InMgF3, respectively, while GaMgF3 was found to be an insulator with a direct (X-Х) band gap of 3.86. All the compounds were found to be anisotropic with GaMgF3 and InMgF3 being ductile compounds and AlMgF3 showing stiffness. The bonding force between the atoms was found to be predominantly ionic with only a little covalent nature. Our investigations indicate that compounds of this type can be used to create strong state electronic devices.

References

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