Ab initio investigation of the physical properties of Tl based chloroperovskites TlXCl₃ (X = Ca and Cd)

Scintillators are widely used as a radiation detector. An efficient scintillator is the one that has high density, high effective atomic number Z_eff, excellent energy resolution, high light output, and hardness of radiation and can grow easily in large dimensions with low cost.¹ There is recently a trend in the development of scintillators for various technological applications, such as in the field of material science, medical diagnostics, and high energy physics.^2–4 Widespread applications of scintillators, like oil well logging, medical imaging, home land security, and experiments of high energy physics, have driven researchers to discover new scintillators with better efficiency.^5,6 Due to their cost-effective and easy synthesis, multicolor emission, high photoluminescence quantum yields (PLQYs), wide bandgap, and excellent optical and charge carrier characteristics, halide perovskites have become common among scintillating materials.⁷ These characteristics make halide based perovskites ideal for engineering devices such as solar cells, light-emitting diodes (LEDs), photo-detector lasers, topological insulators, and even superconductors.^8–11 Ternary chloride perovskites have a broad range of applications among halide perovskite compounds due to wide bandgap and maximum valued optical absorption coefficients and having bright photoluminescence of narrow band, low exciton binding energies, and long-range carrier diffusion.^12,13 Due to these properties, such materials are widely examined theoretically as well as experimentally.^14–16 Ephraim Babu et al. reported CsCaCl₃ as a better self-activated scintillator.¹⁷ For the production of optical and optoelectronic products, structural and optoelectronic properties of CsPbM₃ (M = Cl, Br, and I) are addressed.¹⁸ 

To the best of our knowledge, there is no theoretical evidence on the study of Tl-based chloride perovskites despite interest in the study of chloroperovskites for different applications. The ternary Tl-based chloride perovskites are crystallized in the cubic perovskite type structure with chemical composition ABX₃ where A represents thallium (Tl), B is the metal cation, and X is the chlorine (Cl) atom. Recently, Yutaka Fujimoto et al. synthesized TlCdCl₃ by using the Bridgman technique while studying photoluminescence and scintillation properties and found that because of its high effective atomic number (Z_eff) and density, it presents excellent detection efficiency for g-rays and x rays. Reasonable scintillation properties in the crystal were shown, such as adequate light production for a photon-counting measurement and quick principal decay time (45 ns and 170 ns).¹⁹ Fujimoto et al.²⁰ also reported TlMgCl₃ as a dominant candidate for the detection of x rays and gamma rays because of its large effective atomic number. In an experimental study of TlCaCl₃,²¹ researchers found that crystal emission spectra under x-ray excitation show broadband spans in the range of 350 nm–550 nm with a maximum emission of 425 nm. The calculated scintillation properties showed that, in various applications, TlCaCl₃ can be a better option for x-ray and g-ray detection. Due to the presence of thallium in its chemical structure, these compounds have received interest, which enhances the effective atomic number that leads to excellent detection efficiency.²² The single crystal growth of these compounds is less challenging because of their cubic structure, which makes them interesting candidates for technological applications. In the current work, we have investigated structural, elastic, and electronic properties as well as optical behavior of TlXCl₃ (X = Ca and Cd) by using generalized gradient approximation (GGA).

In this report, the structural, elastic, and electronic properties and optical behavior of the compounds are evaluated by performing first-principles calculation using the full potential linearized augmented plane wave (FP-LAPW) method,²³ as applied in the WIEN2K code.²⁴ To examine the exchange correlation effect, generalized gradient approximation (GGA)²⁵ is issued to perform calculations. Using Murnaghan’s state equation, structural parameters are studied by adjusting the energy against the volume.²⁶ Because of this analysis, the RMT value is selected in such a way that from the center, no charge leakage occurs and the total energy is assured. The RMT values for Tl, Ca, and Cd are 2.5, 2.42, and 2.5, respectively, while the RMT values for Cl in TlCaCl₃ and TlCdCl₃ are 2.42 and 2.7, respectively. In spherical harmonics, the wave function inside muffin tin spheres is extended to I_max = 10, while K points are taken to be 1500 and G_max is 12. The energy difference between the core band and valence band is taken as −6 Ry.

In this section, we report the structural parameters of TlXCl₃ (Ca and Cd). The conventional unit cell of the cubic crystal structure comprises of one molecule having space group Pm-3m 221. The Tl atom is located at (0, 0, 0) and X = Ca and Cd is located at (0.5, 0.5, 0.5), while three Cl atoms are positioned at (0.5, 0, 0), (0, 0.5, 0), and (0, 0, 0.5) sites of the Wyckoff coordinate, respectively, as presented in Fig. 1.

The crystal structure of all the studied compounds belongs to the cubic family, as presented in Fig. 1. The stability of this structure is checked by plotting the changes in total energy as a function of volume, as shown in Fig. 2. This plot is then fitted with the Murnaghan equation of state, and the values of equilibrium lattice constants were found for each compound, as listed in Table I. The energy vs volume relation is depicted in Fig. 2.

Since the experimental and theoretical results related the ground state lattice constants of these compounds are not available, we endorse our findings on the basis of the reported lattice constant of TlMnCl₃.²⁷ In the case of our compound, Tl and Cl atoms are the same, as studied in Ref. 27, and the only difference is in the metal cation. As the radius of the third atom increases, the lattice constant should increase. The ionic radii of Ca⁺² and Cd⁺² are larger than those of Mn⁺²; therefore, our compounds have a large value of lattice constants, as compared to the TlMnCl₃, which is reported as 4.83 A⁰. We can also compare our results with similar systems. The ab initio investigation of TlXF₃ (X = Ca, Cd, Hg, and Mg)²⁸ reports the decreasing behavior in measured lattice constants as Ca is replaced by Cd. The same movement is perceived in the present work, except F is replaced by Cl, where the lattice constant reduces from 5.40 A⁰ for TlCaCl₃ to 5.26 A⁰ for TlCdCl₃.

The bulk modulus (B_o) at zero pressure is calculated by fitting pressure–volume data to the third-order Birch equation of state,²⁶ listed in Table I. The bulk modulus decreases as the volume of unit cell increases. However, TlCdCl₃ shows more hardness than TlCaCl₃. There is an agreement with the previous study of Tl based halide perovskites reported in Ref. 27.

The elastic constants Cij are central and necessary for unfolding the mechanical behavior of compounds. They help us to understand the response of the materials under the macroscopic stress. These constants offer a relation between the dynamical and mechanical response of crystals and explain in what way a compound experiences stress deformation and regains its original position after removal of stress.²⁹ For the cubic system, there are three independent elastic constants, C₁₁, C₁₂, and C₄₄. These constants carry important information about the stability of the structure, bonding nature among adjoining atomic planes, and anisotropic behavior. The measured values of C_ij are presented in Table I. The positive values of Cij fulfill the Born–Haun criteria,³⁰ C₁₁ > 0, C₄₄ > 0, (C₁₁–C₁₂) > 0, (C₁₁ + 2C₁₂) > 0, and C₁₂ < B < C₁₁, for cubic crystals.

The following relation is used to calculate the bulk modulus:

In Table I, the anisotropy factor A, Young’s modulus E, Poisson’s ratio ν, and Pugh’s index ratio B/G are given by using the following relations:³¹ 

with B/G ratio materials classified as ductile or brittle.³² The material will exhibit brittle nature if B/G is less than 1.75, otherwise the material will be ductile.³³ According to Pugh’s criteria, both the compounds have shown ductility. The value of Poisson’s ratio (v) also defines the ductile and brittle behavior of the material. The material will show ductility if the value of v is larger than 0.26, else it is brittle. Our results are presented in Table I again to ensure that both TlCaCl₃ and TlCdCl₃ have ductile nature. The anisotropy factor A is given in Table I. This factor is equal to 1 for isotropic materials, and the value other than 1 characterizes a measure of anisotropy. The values for TlCaCl₃ and TlCdCl₃ are 0.41 and 0.42, respectively. These results evidently reveal that both compounds are anisotropic.

In solid state physics, the electronic band structure of a solid defines the range of energy levels that electrons may have within it as well as the range of energy that they may not have (called bandgaps or prohibited bands). The energy band structure investigations are very useful for the understanding of the electronic and optical properties of a material. The electronic properties of these compounds can be depicted through band structures and density of states. The electronic behavior of TlXCl₃ (X = Ca and Cd) is investigated by using GGA. The bandgap profiles of both compounds are shown in Fig. 3 in such a manner that high symmetry points in BZ are labeled by alphabetic letters and the Fermi level is represented by the dashed line, whereas the energy value spans over the range −10 eV to 10 eV. The measured values of bandgap from the band profile for TlCaCl₃ and TlCdCl₃ are 3.7 eV and 1.8 eV, respectively. It reveals that the bandgap reduces from TlCaCl₃ to TlCdCl₃. Due to the small value of electro-negativity of Ca, it tends to make a stronger bond, as compared to Cd. That is why, TlCaCl3 has a large bandgap because it is created by the Cd-d states above the Fermi level, as compared to TlCdCl3. Such a trend of decreasing bandgap is also reported in Refs. 28 and 34. It can be seen from the band profile that conduction bands are lower and transferred near to the Fermi level when Ca is replaced by Cd in TlXCl3 (X = Ca and Cd). This reality is because of the rising number of electrons in the respective band and accumulation of states near the Fermi level. The nature of bandgap is determined by the analysis of the location of maxima of valence band and minima of conduction band. Figure 3 reveals that valence band maxima lie at M and conduction band minima coincide at the X symmetry point and hence present indirect band nature, while TlCdCl3 has also indirect band nature as its valence band maxima and conduction band minima coincide at M-X symmetry points.

To further elaborate the electronic structure, the contribution of different states is studied. The contribution of partial and total density of states for TlXCl₃ (X = Ca and Cd) is shown in Fig. 4(a). Figure 4 reveals that the valence band of TlCaCl₃ is mainly composed of the Cl – p state. However, in the conduction band, the d state of Ca has a major contribution, while the upper part of this band is due to Tl states. Similarly, the contribution of different states of TlCdCl₃ is depicted in Fig. 4(b), which shows that the peaks occurring in the valence region are basically due to the Tl atom to which the Cd-d state shows major contribution, while states of Cl have negligible contribution. On the other hand, in the conduction band, only small peaks are observed due to the Tl p-state.

The optical properties provide valuable information about the compound’s internal structure. All the optical properties of TlXCl₃ (X = Ca and Cd) are measured by applying the GGA method. In a complex dielectric function, a complete explanation of how any material responds to the incident light is given by the following equation:³⁵ 

where ɛ₁ and ɛ₂ represent the real and imaginary parts of the dielectric function, respectively, evaluated by the following equations:

The real part of the dielectric feature ε₁(w) provides us with details about a material’s electronic polarizability. The frequency dependent limit ε₁(0) is a very important parameter and shows an inverse relation with the electronic bandgap, as depicted in Figs. 5(a)–5(h). From Figs. 5(a)–5(h), we found that the values ofε₁(0) are 3.4 and 4.0 for TlCaCl₃ and TlCdCl₃, respectively. The spectrum reveals that the calculated value of ε₁(0) increases as Ca is replaced by Cd and presents the inverse relation to the bandgap. A similar trend in the calculated values of ε₁(0) is also discussed in Refs. 28 and 34.

The imaginary part of the function has a direct relation with the spectrum of optical absorption. As it is the sum of all the transitions between the valence and conduction bands, it gives the information about a solid’s electronic band structure.³⁶ Hence, we computed the imaginary part of the dielectric function for TlXCl₃ (X = Ca and Cd) on the basis of the evaluated band structure. The imaginary part of the dielectric function for understudy compounds is evaluated up to incident photons of 30 eV, as displayed in Figs. 5(b)–5(i). In the imaginary part ε₂ (ω), the threshold energy values of dielectric functions relate to electronic bandgaps occurred at 3.52 eV and 1.86 eV for TlCaCl₃ and TlCdCl₃, respectively. The spectrum reveals that the absorption edge moves toward lower energy values as going from Ca to Cd. This behavior is in line with the bandgap, as shown in Fig. 3. The curves grow quickly beyond absorption edges, leading to an increase in the number of points contributing to absorption. Maximum absorption peaks that arise due to inter-band transitions are observed at 8.7 eV and 5.7 eV for TlCaCl₃ and TlCdCl₃, respectively, as presented in Figs. 5(b)–5(i). For the measurement of other optical parameters, such as refractive index, extinction coefficient, reflectivity and absorption coefficient, and optical conductivity, the complex dielectric function provides a framework.

It is possible to determine the refractive index and coefficient of extinction using the following expressions:³⁷ 

The refractive index and extinction coefficient for TlXCl₃ (X = Ca and Cd) are shown in Figs. 5(c)–5(j). We find from Figs. 5(c)–5(j) that refractive indices follow similar behavior that of the real part of the dielectric function. From the spectrum, the values of refractive index at zero frequency (static refractive index) observed for TlCaCl₃ and TlCdCl₃ are 1.8 and 2.0, respectively. It is obvious from Figs. 5(c)–5(j) that the value of refractive index for both compounds enhances from the zero frequency limit reaches to the peak value of 2.6 observed at 4.6 eV for TlCaCl₃ and 2.7 at 4.7 eV for TlCdCl₃. The interaction of electrons with incident photons reduces the speed of photons, which allows the values of refractive indices to surpass 1. The photon interaction increases as Z_eff enhances in the order Ca (Z = 20) < Cd (Z = 48) with an increase in the atomic number. Thus, TlCaCl₃ has a small refractive index value, as compared to TlCdCl₃. A similar trend is also reported in Refs. 28 and 34. The spectrum also reveals optically isotropic behavior of studied materials because both compounds have a constant refractive index at a low energy range. The spectrum of extinction coefficient has the same character as that of the imaginary part of the dielectric function, as shown in Figs. 5(d)–5(k). Maxima of the extinction coefficient are found to be 1.5 at 8.8 eV and 1.7 at 6.13 eV for TlCaCl₃ and TlCdCl₃, respectively.

In the following expression, the real and imaginary parts of the refractive index are used to determine the optical reflectivity:

From Figs. 5(e)–5(l) we find zero frequency reflectivity of 8.6% and 10% for TlCaCl₃ and TlCdCl₃, respectively.

The absorption coefficient and optical conductivity are calculated by the following relations:

The absorption coefficient is determined by the light energy absorbed in unit length per unit incident energy.³⁸ The absorption coefficients for TlXCl₃ (Ca and Cd) are presented in Figs. 5(g)–5(n). The peaks of absorption coefficient are correlated with the inter-band transitions on the electronic band spectrum at different high symmetry points. The maximum absorption coefficient is noted to be about 196 at 14.8 eV for TlCaCl₃ and 177.3 at 15 eV for TlCdCl₃. Overall absorption is observed in the range of 2.8 eV–30 eV. TlCaCl₃ is a high band compound having high absorption power used in optoelectronic devices. These compounds are optically isotropic and exhibit anisotropic behavior mechanically, hence proven themselves as potential candidates for scintillator applications. The optical conductivity has the same feature similar to the absorption coefficient, as shown in Figs. 5(f)–5(m). The spectrum of optical conductivity reveals that TlCaCl₃ shows the maximum optical conductivity as the maximum value peak is observed at 8.7 eV. TlCaCl₃ and TlCdF₃ compounds are optically conductive in the low energy region; however, some peaks for TlCaCl₃ are also observed for high energy photons. It is also evident from Figs. 5(f)–5(m) that the optical conductivity spectrum moves to the low energy range by replacing the cation Ca with Cd, which corresponds to a small bandgap.

In summary, we find that lattice constants and ground state energy reduce as metallic ion changes from Ca to Cd. The bulk modulus also varies from Ca to Cd, and by the comparison of bulk modulus, TlCdCl₃ shows more hardness than TlCaCl₃. The B/G ratio shows that both compounds are ductile in nature. The measured value of Poisson’s ratio also confirms their ductile behavior. Analyses of results have shown that both compounds have wide and indirect bandgap nature. The fundamental bandgap occurs at M-X symmetry points. Band profiles reveal that energy bands depress when Ca is replaced by Cd. We also conclude that both the compounds are optically isotropic and the peak of all the optical spectra shifts toward low energies going from Ca to Cd. The presence of the Tl atom and optical isotropic nature of these materials prove themselves promising candidates for scintillation.

The authors declare that they have no competing.

The data that support the findings of this study are available from the corresponding author upon reasonable request.