
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12190-1
10.1016/j.heliyon.2024.e36159
e36159
Research Article
Insight into the electronic, elastic, structural, thermal, and optical characteristics of potassium magnesium fluoride KMgF3 with isotropic external stress
Sahar M. Sana Ullah a
Zaidi S. M. Junaid b
Ashraf Muhammad Towqeer c
Hashim Muhammad c
Khan M. Ijaz ijazkhan4123@gmail.com
d⁎
a Department of Mechanical, Industrial, and Energy Systems, University of Sargodha, Sargodha, 40100, Pakistan
b Department of Physics and Mathematics, Faculty of Sciences, Superior University, Lahore, 54000, Pakistan
c Institute of Physics, The Islamia University, Bahawalpur, Pakistan
d Institute of Mechanical and Manufacturing Engineering, Khwaja Fareed UEIT, Rahim Yar Khan, Pakistan
⁎ Corresponding author. ijazkhan4123@gmail.com
12 8 2024
15 9 2024
12 8 2024
10 17 e3615927 11 2023
1 7 2024
11 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
The demand for increasingly fine detail in optical lithography for semiconductors necessitates the use of lower-wavelength lithographic light. This drives the need for lenses in optical lithography steppers made of vacuum ultraviolet-transparent (VUV-transparent) materials. In this work, the density functional theory (DFT) study of potassium magnesium fluoride KMgF3 is presented. Total energy was calculated with correlation functional generalized gradient approximation (GGA). The ground state quantities such as bulk modulus and lattice parameters have been evaluated. The material's cubic structure is scrutinized under various stress levels (0–100 GPa), revealing that KMgF3 starts to deform at 128 GPa. The C11, C12, and C44 independent elastic constants were used to analyze the structural stability of the KMgF3. The densities of states and electronic band structures have also been computed. According to electronic calculations, when stress is applied to KMgF3, the band gap increases for all values of stress (0–100 GPa). Mechanical parameters, including elastic constants and ratios, indicate the material's remarkable ductility and stability. Phonon density of states and thermal characteristics exhibit shifts and variations with increasing stress, providing insights into the material's behaviour below its melting point. The thermodynamic properties of KMgF3, such as enthalpy, free energy, entropy, heat capacity, and Debye temperatures at various temperatures ranging from 0 K to 1000 K, have also been examined to explore their basic properties. These findings contribute to a comprehensive understanding of KMgF3, opening avenues for its application in advanced technologies, particularly in the realms of semiconductors and optoelectronics.

Keywords

First-principles calculation
Stress effect
Optical properties
Thermodynamic properties
Elastic properties
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pmc1 Introduction

Increasingly fine detail is required for optical lithography in semiconductors due to technological demands, which calls for lower wavelength lithographic light. Therefore, optical lithography steppers need lenses made of vacuum ultraviolet-transparent (VUV-transparent) materials [1]. Several perovskite structures are used in optical, electrical, and other solid-state devices, making them generally intriguing materials for dielectric investigations. Because they lack birefringence, which makes lens design challenging, the ternary compounds in the Fluoro perovskites group, with the general formula ABF3 (where A and B stand for alkali metals and alkaline earth metals, respectively), have recently attracted some attention in light of their potential use as lens materials [2]. Additionally, low transmission and the difficulties of material manufacturing and polishing due to fracture or the hygroscopic nature of the materials are potential issues with using optical materials for the UV and VUV areas [3]. Since KMgF3 does not have these issues, it will be a good optical material for the UV and VUV regions and play a bigger role in the development of the next generation of lithographic technology [4].

Shakeel et al. [5] worked on detailed electronic and optical properties of KMgF3 with induced stress from 0 to 50 GPa. With the increase in stress 0–50 GPa the cell volume, and lattice parameter were decreased while the band gap was increased. The high rate of absorption coefficient and optical conductivity was found with the increase in stress. Cui et al. [6] found the structural parameters of cubic KMgF3 and claimed high stability in their simulation results. Neupane et al. [7] also performed simulation work on KMgF3 to find its structural and electronic behaviour. Their calculated bandgap was 7.2 eV which represented the insulating behaviour of the material. The structural, electronic, elastic, and dielectric properties of cubic KMgF3 were examined by Pilania et al. [8], and his coworkers. Syrotyuk et al. [9] worked on band gap measurement through their simulation work on KMgF3. They also found that there is an increase in band gap with the increase in stress from 0 to 30 GPa.

The main aim of this work is to analyze in detail the electronic, structural, mechanical, optical, and thermal properties of material KMgF3. We are presenting a comprehensive detailed analysis of KMgF3 mechanical and thermal properties which has never been explained previously. The reported literature still lacks a detailed analysis of thermal characteristics.

2 Computational methodology

This study uses the Material Studio setup to thoroughly examine the fundamental, elastic, mechanical, electrical, and optical characteristics of KMgF3. The complete computer study is carried out utilizing a CASTEP program [[10], [11], [12]], resulting in the use of the plane wave pseudopotential approach and the concepts of density functional theory (DFT). A Perdew-Burke-Ernzerhof (PBE) relationship of exchange parameterization devised a generalized gradient approximation (PBE-GGA) technique to take electron transfers into account [[12], [13], [14]]. A cubic KMgF3 structure alongside the space group pm-3m (221) is used in the GGA calculations. A supercell structure at the dimensions 2 × 2 × 1 is taken into consideration, and a limit energy of 340 eV is applied to depict the electron-ion connection through an ultrasoft pseudopotential [10,15] while subjecting it to various stress capacities of 0, 20, 40, 60, 80 and 100 GPa, as shown in Fig. 1 (a). A precise depiction of electronic wave functions is made possible by using the plane wave function as a set of bases. The mixing technique utilized is Pulay, and the MPG with 2 × 2 × 2 k-points is chosen for the Brillouin zone integration. A self-consistent field (SCF) limitation is set at 1 × 10−6 eV/atom, while the band energy range is set to 1 × 10−5 eV. According to the investigation, KMgF3's cubic structure starts to deform at 128 GPa of stress.Fig. 1 Supercell of KMgF3.

Fig. 1

3 Results and discussion

3.1 Geometrical optimization

To reach the minimum energy state to ensure phase stability, the material's shape must be optimized. The geometry of the material is precisely shown in Fig. 1 (a), which shows the supercell's atoms in their exact placements. As shown in Fig. 2, which further explains variation in lattice parameters, as well as the corresponding volume shifts under stress, the amounts of lattice constants and the volume of the unit cell, have been adjusted and recorded at various levels of stress (0, 20, 40, 60, 80, and 100 GPa). This was done to investigate the impact of stress on the material. The material's lattice constant decreases from 4.0935 to 3.4306 Å as applied stress rises (0–100 GPa). Within the material, this diminution, which is a sign of more intense atomic interactions, intensifies and becomes more apparent. As a result, the unit cell's volume dropped about 68.5953 to 40.3752 Å3, directly in reaction to the decrease in the lattice parameters' values. Essentially, the compression brought on by the pressure forces the atoms to move closer together, resulting in a lower unit cell volume. Our estimated results are quite accurate and fit within acceptable ranges when compared to the findings of prior research in the peer-reviewed literature, confirming the validity and dependability of our calculations. There is no published information regarding the experimental or even theoretical values of this alloy especially related to thermodynamics properties. Our computed structural characteristics for alloys may serve as a guide for researchers conducting more research. The cubic nature of the compound is verified by the relations as t=RA+RO2(RB+RO), where RA = radius of potassium = 1.38 Å, RB = radius of magnesium = 0.72 Å, and Ro = radius of fluoride = 1.33 Å. By using the above values, the value of t is 0.937, which is close to 1 which shows the cubic perovskite structure of the compound under study.Fig. 2 Unit cell lattice parameters and volume were plotted as a function of stress for KMgF3.

Fig. 2

3.2 Elastic and mechanical properties

To comprehend and characterize the mechanical behaviour, strength, and durability of materials, the constants for elasticity (C11, C12, and C44) are crucial [16,17]. They are essential for the choice of materials, for improving designs, and for forecasting how materials will react with external forces. The mechanical industry heavily depends on having a solid understanding and ability to measure the constants of elasticity of the stress being applied in response to any material. Studying mechanical parameters can help us understand the mechanical nature of forces applied to alloys. These constants may be used to describe the anisotropic character, bonding features among neighbouring atomic planes, ductile/brittleness, and structural stability. The cubic crystal's elasticity is described by the three distinct elastic constants C11, C12, and C44. The least overall energy, as an outcome of volume-preserving strains, that results in symmetry interruption has been utilized to calculate these elastic constants [17]. Following inequality relations are the necessary conditions for a compound to be stable cubically, (C11 – C12) > 0, C11 > 0, C44 > 0, C12 < B < C11, (C11 + 2C12) > 0 [18]. In Fig. 3 and Table 2, it can be seen that the above conditions are fulfilled for all stress values from 0 to 100 GPa.Fig. 3 Elastic constants C11, C12 and C44 versus stress on KMgF3.

Fig. 3

Table 1 Lattice parameter ao(Å), band gap ΔE (eV), Elastic constants C11, C12, C44, Young’s Modulus (E), Bulk Modulus (B), shear Modulus (G), and Poisson's ratio (υ) at 0 GPa.

Table 1	ao(Å)	ΔE(eV)	C11	C12	C44	E	B	υ	
GGA (present work)	4.0935	6.78	106.51	33.78	35.93	89.7101	58.0289	0.2423	
(Theoretical)
(reported work)	4.068 [5]	7.27 (LDA) [19]	132.56 [8]	43.31 [8]	48.86 [8]	126.3 [20]	59.25 [5]	0.208 [20]	
4.032 [6]	7.8 [21]							
4.065 [7]								
4.040 [8]								
Experimental (reported work)	4.006 [20]	12.4 [22]	132 [23]	39.6 [24]	48.5 [24]		71.2 [25]		
3.993 [26]		138 [27]	43.6 [28]	49.8 [28]				
3.983 [29]								
3.999, 4.064 [30]								

Table 2 Values of elastic constants for KMgF3.

Table 2Stress (GPa)	C11	C12	C44	
0	106.513	33.787	35.935	
20	267.218	76.545	56.867	
40	373.086	102.249	62.149	
60	488.669	166.452	85.725	
80	585.628	209.169	102.679	
100	678.776	247.442	113.683	

About their space group number, a collection of distortion types is then provided for energy and stress. Initial input parameters include the absolute Lagrangian and the quantity of deformed structures. It was necessary to develop and optimize input files for each distorted structure. Following that, a given Lagrangian strain's second derivative is determined using WIEN2K's polynomial fitting process [31]. Table 2 provides the computed elastic constants for PGMs-alloys at zero pressure. Mechanically stability standards are expressed as follows for cubic crystals:

It can be concluded that the alloys addressed in this study are stable by obtaining values for elastic constants. There is a lack of published information on the elastic constants, either theoretical or experimental, for these alloys. As a result, the results we present in this research may serve as a starting point for other investigations. The fluctuation in C11, C12, and C44 with the force exerted is seen in Fig. 3. M. S. Alam et al. [32] explained properly the variation in elastic properties as a function of pressure. From Fig. 3, it is quite clear that the elastic constant C11 is more sensitive to C12 and C44 with variation to applied stress. At nearly 20 GPa where the two linear lines meet, there is variation in C11.

The linear outcome is displayed in C12 and C44. The change in elastic constants is due to structural distortion, anisotropic effects, and electronic structural change. It is important to calculate mechanical properties such as Young's modulus (E) [33], Bulk modulus (B) [34], Shear modulus (G) [33], Anisotropic component (A) [13], Poisson's ratio (υ) [33,35], Cauchy pressure (CP) [36], and Frantsevich ratio (G/B) at various stress (0, 20, 40, 60, 80, and 100 GPa) to assess the firmness or stability of KMgF3. The different elastic properties at 0 GPa are also compared with previous literature in Table 1. These properties are calculated by combining the results of elastic constant calculations. The fluctuation of KMgF3's bulk modulus (B), shear modulus (G), along Young's modulus (E) with increasing stress applied within the range of 0–100 GPa is shown in Fig. 4 (a). The computed values of a Frantsevich ratio (G/B) are below the crucial threshold of 0.57, underlining the material's capacity to tolerate substantial deformation without resorting to brittle failure, which strengthens our conclusions. In our results, the Frantsevich ratio greater than 0.57 was found for stress 0 GPa condition while 20–100 GPa the ductile response was found [37,38].Fig. 4 (a) Elastic moduli, (b) Frantsevich ratio, Poisson ratio, and anisotropic factor, (c) Pugh ratio, and (d) Cauchy Pressure of KMgF3 plotted versus applied stress.

Fig. 4

Another significant mechanical measure that may be used to assess a material's ductility or brittleness is the Poisson's ratio (υ) [33]. A value of υ < 0.26 denotes brittle behaviour, whereas υ > 0.26 denotes ductile behaviour. As seen in Fig. 4 (b), our results demonstrate ductile behaviour when stress is increased, with estimated υ values exceeding the limit of 0.26. Furthermore, an anisotropic factor (A) denotes the directional characteristics that define the amount of anisotropy and aids in determining if a material is anisotropic or isotropic if an amount of A = 1 denotes an isotropic material and otherwise anisotropic [39]. By recognizing and examining the anisotropic component (A), we may better understand how the material behaves and make decisions about how it will function in practical situations. According to our calculations, the material's reaction to the applied stress- or deformation may vary depending on the exact direction or orientation on which it has been measured due to the anisotropic nature noticed, as seen in Fig. 4 (b). The change of the Pugh's ratio (B/G) [40], Frantsevich ratio (G/B) [41], and anisotropy are shown in Fig. 4 (c). Pugh's ratio (B/G) undoubtedly evaluates the plastic behaviour, particularly the brittleness, and ductility. Pugh's criteria state that a material is brittle if its Pugh's ratio is less than 1.75 and ductile if it is greater than 1.75. As seen in Fig. 4 (c), this material exhibits significant ductility across the full stress range of 20–100 GPa while at 0 GPa brittle behaviour was observed. By using the Cauchy pressure (CP), Fig. 4 (d) helps us better grasp whether a material is ductile or brittle. In contrast to brittleness, ductility is denoted by a positive CP and brittleness by a negative CP [42].

The material's persistent ductile behaviour is convincingly indicated by the constantly positive CP values over the full stress range of 0–100 GPa. Furthermore, it is interesting that the CP values show an increasing trend as the stress magnitudes increase, indicating a stronger predisposition towards ductile behaviour. These results offer compelling proof of the material's inherent ductility and its capacity to sustain rising stress levels. Overall, a thorough examination of KMgF3's mechanical characteristics and elastic constants reveals the material's remarkable ductility and mechanical stability over a wide range of stresses.

3.3 Electronic characteristics

Valence and conduction bands were constructed to analyze the conduction mechanism in KMgF3 with varying stress conditions at 0, 20, 40, 60, 80, and 100 GPa values shown in Fig. 5. In our estimated calculations about a 54 % increase in band gap was found with varying stress. The selected material band gap calculations represented highly insulating behaviour with varying applied stress. The shown Fig. 5 (a) represents a band gap value of 6.78 eV which is higher than a diamond. At 20 GPa the band gap is increased to 8.40 eV and on further increasing stress up to 40 GPa band gap is increased to 9.50 eV which is greater than quartz and glass. The increase in bandgap is due to distortion in lattice constant which may increase bond length and bond angle which push the density of states away from the fermi level, resulting in an increase in the bandgap.Fig. 5 Band structure of KMgF3 at (a) 0 GPa, (b) 20 GPa, (c) 40 GPa, (d) 60 GPa, (e) 80 GPa, and (f) 100 GPa, (g) The band gap plotted as a function of stress.

Fig. 5

At 60, 80, and 100 GPa bandgaps are found up to 10.43, 10.46, and 10.47 eV respectively, one can readily see there is no significant increase in band gap shown in Fig. 5(d–h). On further increase in the stress may redistribute the density of states which does not further increase the bandgap.

Fig. 6 indicates the PDOS of KMgF3 potassium (K), magnesium (Mg), and fluorine (F) atoms. The major contribution of potassium p-state, magnesium p-states, and fluorine s, p states for the formation of the valence band is clearly shown in Fig. 6(a–f). The conduction band formation is due to p-states of potassium (K) and magnesium (Mg) and the s-state of magnesium shown by Fig. 6(a–f). The expansion in the band gap can be seen from Fig. 5, Fig. 6. The merged plot of the total density of states at different stress conditions of 0, 20, 40, 60, 80, and 100 GPa is shown in Fig. 7. The calculated results showed that by applying stress the total density of states is expanding in both valence and conduction bands. The increase in band gap with applying stress can be seen in Fig. 7.Fig. 6 (a–f): Partial density of states (PDOS) of KMgF3.

Fig. 6

Fig. 7 Total density of states (TDOS) of KMgF3.

Fig. 7

3.4 Thermodynamic properties

For thermal applications, understanding a material's thermal behaviour is essential and plays an integral part from an application perspective [16,43]. Below their melting point, various materials have intriguing properties. We have examined the free energy (E), Debye temperature, specific heat at constant volumes (Cv) with zero pressure, and entropy (S) of pure KMgF3 at 0, 20, 40, 60, 80, and 100 GPa which can be seen in Fig. 8. In enthalpy vs Temperature plot shown in Fig. 8(a) one can readily see the enthalpy values are low at high stressed conditions. By applying stress, the enthalpy energy becomes less due to volume change and electronic state changes as previously shown in Fig. 2, Fig. 5. The values of free energies were found high with respect to temperature for higher stressed conditions, especially at 100 GPa. The higher rate of free energy shown in simulated results has a greater ability to do work. Furthermore, the less values of entropy were found for higher stressed conditions shown in Fig. 8(c). The heat capacity was also simulated shown in Fig. 8(d) which shows that at 0 GPa higher energy is required to increase the temp as compared to 100 GPa. As Debye temperature represents the average phonon energy in the lattice. Fig. 8(f) shows that the average phonon lattice energy is higher for higher stressed conditions.Fig. 8 (a) Enthalpy, (b) free energy, (c) entropy, (d) heat capacity, and (e) Debye temperature at 0, 20, 40, 60, 80, and 100 GPa plotted as a function of temperature.

Fig. 8

These quantities are connected to the following relationships [17,44,45];(1) ΔF=3nNkβT∫0ωmaxln{2sinhℏω2kβT}g(ω)dω

(2) ΔE=3nNℏ2∫0ωmaxωcoth(ℏω2kβT)g(ω)dω

(3) S=3nNKβ∫0ωmax[ℏω2kβTcothℏω2kβT−ln{2sinhℏω2kβT}]g(ω)dω

(4) Cv=3nkβT∫0ωmax(ℏω2kβT)2csch2(ℏω2kβT)g(ω)dω

where ‘ω’ is phonon frequency with its maximum value ‘ωmax’ and ‘g(ω)’ is the normalized phonon density of states.

The density of the state associated with phonons is related to electron excitation, and electron excitation is important for electronic characteristics. The density of states of phonons is intimately related to the thermodynamic properties. Fig. 9, Fig. 10 show the phonon DOS for KMgF3 at 0–100 GPa. In Fig. 9, one can readily see the frequency of phonon density of states is shifting towards a higher value with the increase in stress from 0 to 100 GPa. The presence of imaginary phonon modes around 20 GPa, when the elastic characteristics become anomalous, points to a possible correlation with a structural transition in KMgF3. This would suggest that KMgF3 experiences a phase transition or a major crystal structural shift at this pressure, which would impact its stability and modify its elastic behaviour. Imaginary phonon modes are generally indicative of phase transitions and dynamic instability in the crystal lattice. Thus, the observed anomaly is probably a sign that KMgF3 is going through a similar transition. One can readily see here The imaginary phonons are starting to initiate at 20 GPa and on further increase in stress these imaginary phonons are also increasing shown in Fig. 9(b–f). The thermal properties of KMgF3 are not so much covered in the literature. Therefore, our findings might be useful for future research.Fig. 9 Phonon frequencies at 0, 20, 40, 60, 80 and 100 GPa.

Fig. 9

Fig. 10 Phonon density of states vs frequency (THz).

Fig. 10

3.5 Optical properties

A thorough investigation of the complex interactions between light and matter is required for the entire analysis of optical behaviour. This investigation explores the intricate electron transitions between the valence and conduction bands, which have a major influence on the recombination rate [15]. With an emphasis on efficiency and performance, this knowledge holds enormous promise for the development of next-generation materials, notably in the field of solar and optoelectronic applications [40], by carefully examining the optical characteristics, such as the complicated dielectric function and derived parameters like the reflectivity, extinction coefficient, refractive index, and absorption coefficient [46].

These variables offer important insights into how different stress levels from 0 to 100 GPa affect a material's response. Researchers open new doors for material design and production by elucidating the complexities of these optical features, paving the way for the creation of cutting-edge technologies. As the stress level rises from 0 to 100 GPa, the absorption edge in the spectrum shown in Fig. 11 (a) experiences a strong blue shift, which is defined by a movement of the absorption peaks towards higher energies, producing sharper and more prominent peaks. The term "threshold energy" describes the amount of electromagnetic radiation that causes a substance to absorb quickly [47]. In conclusion, the band gap narrows, the state densities approach one another, and the material becomes absorbent to a larger variety of electromagnetic spectrum wavelengths as a result of applied stress. One can readily see from Fig. 5 (g) that there is an increase in bandgap from 0 to 60 GPa, but at 80 and 100 GPa there is no significant increase in the band gap, and from Fig. 11 (a) the intensities of absorption are increasing at 80 and 100 GPa.Fig. 11 Optical properties of KMgF3.

Fig. 11

The reflection of photoconductivity, which follows the same pattern as the absorption spectra, is optical conductivity, or σ(ω). The Fig. 11 (b), contains the conductivity plots of KMgF3 with increasing energy of applied electromagnetic waves. This finding lends additional support to the idea that as stress levels rise, the material's photon absorptivity increases, as shown by the increased optical conductivity and the ensuing absorption behaviour [14,48].

Dielectric functions expose the complicated behaviour of dielectric materials in reaction to electric fields, including optical and electronic properties, and unravel their interaction with waves [49]. The material's ability to store and transmit energy is characterized by the real component, whilst its absorption and dissipation properties are shown by the imaginary component [50]. Another important parameter that describes how much energy is lost when light travels through a substance is the loss function. On the other hand, reflection offers a sizable transmittance that greatly increases absorption.

Notable insights are shown in Fig. 11(d and e), which shows the loss function and reflectivity curves under applied stress. It is noticeable that when the applied stress rises, the material shows less loss, which denotes less energy loss. Moreover, the reflectivity curves disclose a fascinating pattern, as the applied stress increases reflectivity rises, demonstrating a higher proportion of incident light being reflected. The maximum reflectivity was found in the range of 50–60 eV. The refractive index, which affects how fast, far, and how light is refracted in a material [51], is depicted in Fig. 7 (f) at various stress levels of 0–100 GPa. At 0 GPa, the refractive index reaches its maximum value, which is 2.3 eV. We discovered that absorption and the refractive index had an inverse relationship after taking into account the optical study discussed above that was computed against stress levels ranging from 0 to 100 GPa. The same thing holds for reflectivity, loss function, and absorption. The design of next-generation innovative materials for photovoltaics and optoelectronics, with an emphasis on increasing efficiency and performance, appears promising in light of these discoveries.

4 Conclusion

KMgF3's structural, electrical, elastic, mechanical, thermal, and optical characteristics have been thoroughly investigated. A supercell of 2 × 2 × 1 dimensions was considered in account for finding physical properties with varying applied stress 0, 20, 40, 60, 80, and 100 GPa. It is found that the lattice parameter is decreased by up to 16 % and lattice volume is exponentially decreased by up to 41 % with varying stress values of 0–100 GPa. The mechanical ratios represent the ductile nature of the selected material. The electronic bandgap of the material is increased by about 54 % with the applied stress. A linear increment is observed from 0 to 60 GPa while from 60 to 100 GPa there is no significant increase in bandgap. In valence band formation p-states of potassium “K” and s, p-states of fluorine “F” are found to play a significant role. The enthalpy, entropy, and heat capacity are found to decrease with applying stress, while free energy and Debye temperature are found to increase. The absorption of the electromagnetic waves is found between 50 and 60 eV which is in the ultraviolet region.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

M. Sana Ullah Sahar: Visualization, Data curation. S. M. Junaid Zaidi: Writing – original draft, Validation. Muhammad Towqeer Ashraf: Project administration. Muhammad Hashim: Project administration. M. Ijaz Khan: Writing – review & editing, Software, Project administration, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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