The structural, electronic, elastic and optical properties of CsYx I(1 − x)(Y = F, Cl, Br) are investigated using full potential linearized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA). The ground state properties such as lattice constant (ao) and bulk modulus (K) have been calculated. The mechanical properties including Poisson’s ratio (σ), Young’s modulus (E), anisotropy factor (A) and shear modulus (G) were also calculated. The results of these calculations are comparable with the reported experimental and theoretical values. The ductility of CsYx I(1 − x) was analyzed using Pugh’s rule (B/G ratio) and Cauchy’s pressure (C12−C44). Our results revealed that CsF is the most ductile among the CsYxI(1 − x)(Y = F, Cl, Br) compounds. The incremental addition of lighter halogens (Yx) slightly weakens the strength of ionic bond in CsYxI(1 − x). Moreover, the optical transitions were found to be direct for binary and ternary CsYxI(1 − x). We hope that this study will be helpful in designing binary and ternary Cs halides for optoelectronic applications.
In solid-state physics, alkali halide crystals play a prominent role. The wide applications of mixed crystals in optical, electronic and optoelectronic devices evoked considerable interest and motivated researchers to perform extensive investigations [1, 2]. The compounds formed by alkali halides are considered to be a prototype of ionic compounds. The mixed crystals of alkali halides are of disordered substitutional type. They are insulators and crystallize in two types of crystal structures, i.e. body centered cubic and face centered cubic structure [3, 4]. Alkali halides are colored materials when exposed to radiation or impurity doping and thus they are used as detectors due to their strong scintillation effect . Alkali halides are interesting materials in terms of their optical properties and often serve to test new theories .
The physical properties of alkali halides (or mixed alkali halides) have been reviewed by Sirdeshmukh et al. . The difference in atomic sizes between mixed crystals causes local stresses in lattice and changes crystal properties, particularly lattice parameter [8, 9]. Recently, several established studies about the absorption spectrum, thermo luminescence, X-ray diffraction, spin-electron resonance, etc., on mixed crystals have been published [10, 11].
The alkali halides usually crystallize in two different phases, i.e. NaCl (B1) and CsCl (B2) phase. The space group of NaCl is Fm3m having coordination number of six and containing four atoms per cell, while CsCl belongs to the space group Pm3m having coordination number of eight and two atoms per unit cell. At high temperature, CsCl structure transforms to NaCl structure, i.e. B1 phase. At elevated pressure, Rb halides, K halides and NaCl get converted into the CsCI phase .
The interest in the high pressure properties of alkali halides has been restored in the diamond cell technology . Cesium halides studies have been carried out to search for the band-overlap metallization which occurs at pressures in the Mbar range. Unexpected phase transformations to tetragonal and orthorhombic structures in the quest of metallization have been observed experimentally and theoretically [14–16].
The absorption spectra of alkali halides contain a large number of peaks which continue to the far ultraviolet region . For example, the emission spectra of heavy metals doped cesium halides are caused by Jahn-Teller effect. The ionic nature (strong or weak) depends on the difference in electronegativity and varies when either of the materials is changed at standard temperature and pressure. Most of the cesium halides crystallize in the BCC form in which both alkali metals and halides have a coordination number of six [18, 19].
Cesium halides CsX (X = F, Cl, Br, I) are inorganic ionic solids and are valuable as radiation detectors or infrared (IR) optical materials in nuclear physics and fuel container technology . Halide structured cesium fluoride (CsF) is used in organic synthesis as a source of fluoride ions . Single crystal of the salt is transparent in deep infrared region and can be used as windows of cells .
The chemical bonding and simple morphology of Cs-based halides have made them the preferred choice in several innovative experiments and various theories. Debye’s theory of specific heats, Grüneisen’s theory of thermal expansion, Born’s theory of cohesion, Kellermann’s lattice dynamics and Lowdin’s very first application of quantum mechanics to crystal elasticity were tested on the alkali halides [23−25].
In this study, we have investigated the structural, elastic, electronic and optical properties of CsYx I(1 − x)(Y = F, Cl, Br) using GGA and EV-GGA methods. Although the structural and optoelectronic properties of binary alkali halides have been investigated, there are few reports regarding the theoretical study of mixed Cs-based halides. In this study, the calculated values of different parameters such as ductility, band gap, structural and electronic properties of binary and ternary CsYxI(1 − x)(Y = F, Cl, Br) have been compared and discussed.
2 Computational method
We have used the FP-LAPW method within the generalized gradient approximation (GGA)  and Engel-Vosko generalized gradient approximation (EV-GGA)  as implemented in Wien2k code  to investigate CsYx I(1 − x)(Y = F, Cl, Br). Band gaps and electronic dispersion curves are usually underestimated by GGA. In FP-LAPW method, the unit cell is divided into atomic (muffin-tin) spheres and interstitial regions. Inside the muffin-tin sphere, the wave function is expanded in spherical harmonics and the maximum value of l for wave function expansion is taken as lmax = 10. Plane-waves basis set is used for expansion of wave function, charge density and potential in the interstitial regions. The calculations are performed using a mesh of 1000 k-points in the Brillouin zone (BZ).
3 Results and discussion
3.1 Structural properties
To obtain the structural parameters for all concentrations (0 ⩽ x ⩽1), optimization of CsYxI1 − x(Y = F, Cl and Br) alloys at the ground state energy was carried out using Birch Murnaghan’s equation of state . As an example, the optimized structures of CsBr and CsBr0.25I0.75 are given in Fig. 1.
The variation in the unit cell volume optimizes the unit cell energy to the ground state energy of the system as shown in Fig. 2.
Lighter halogens (F, Cl and Br) were doped in CsI. The calculated structural properties such as the lattice constant (ao), bulk modulus (K), and energy at equilibrium state (Eo) for both B1 and B2 phases are shown in Table 1 and Table 2.
Structural parameters of CsFxI1 − x, CsClxI1 − x and Cs BrxI1 − x in B1 phase.
|Compound||a [Å]||K [GPa]||E0|
|GGA||Exp.||Other method||GGA||Exp.||Other method|
|CsI||7.69||7.52||5.459 ||8.72||7 .30 ||−29815.72|
|CsBr||7.25||7.23 ||9.83||10.45 ||−20791.45|
Structural parameters of CsFxI1 − x, CsClxI1 − x and CsBrxI1 − x in B2 phase.
|Compound||a [Å]||K [GPa]||E0|
|GGA||Exp.||Other method||GGA||Exp.||Other method|
|CsI||4.51||4.57  4.51 ||4.64  4.52 ||10.19||11.9 ||12.21  9.02 ||−29815.72|
|CsF||3.59||3 ||2.99 ||35.57||59.17 ||−15778.65|
|Cs Cl||4.08||4.091 ||4.11  3.934 ||17.95||22.9 ||12.58 ||−16501.67|
|CsBr||4.26||4.23  4.28 ||4.27  4.069 ||15.45||15.6  17.9 ||16.5  13.01 ||−20791.45|
As can be seen, the lattice constant exhibits inverse relationship with the dopant concentration. The bulk modulus (K) shows a random variation with increasing doping concentration (x) of halogens. However, for each doping element, the bulk modulus is smaller at x = 0 and greater at x = 1. In addition, the lattice constant (a0) and bulk modulus (K) of the materials are in fair agreement with experimental data. Variations of the lattice constant (a0) and bulk modulus (K) are also plotted vs. concentration (x). Bulk modulus (K) is proportional to crystal rigidity i.e. the larger its value the more rigid is the crystal.
3.2 Elastic properties
Elastic properties of a material can better explain the behavior of a solid under an applied stress. The stability of a material and its stiffness purely depend on elastic properties. These fundamental properties of a solid can be calculated provided we have stress tensor parameters. Knowing the elastic constants, one can calculate bulk modulus K, Young’s modulus E, Poisson’s ratio σ, shear modulus G, anisotropy factor A and other physical properties. To describe mechanical properties of cubic compounds CsY (Y = F, Cl, Br and I) we only need to calculate three elastic constants C11, C12 and C44.
The elastic and structural parameters of alkali halides are listed in Table 3. It can be seen that the materials show a mix behavior of properties of cubic compounds in both phases. Binary compounds of Cs halides exist in CsCl structure except CsF which exists in NaCl structure at normal conditions. The available experimental and theoretical data concern only the normal phases, in general. We have also calculated the elastic properties of the compounds in other phases i.e. CsCl, CsBr and CsI in FCC structural phase and CsF in BCC phase. Elastically stable cubic structures must satisfy the following relations :
The Elastic constants and mechanical properties of alkali halides.
|CsCl)||42.33 42.6c||−0.02 1.3c||3.952 10.9c||14.099||8.35||20.920||0.25||0.19||1.69||−3.97|
|CsBr||28.32 30.97a 30b||7.36 9.03a 7.8b||12.95 7.5a 7.56b||14.348||11.90||27.965||0.18||1.24||1.21||−5.59|
|CsI||33.98 24.34a 24.6b||−1.21 6.36a 6.7b||6.89 6.32a 6.24b||10.523||10.14||23.030||0.14||0.39||1.04||−8.10|
The data presented in the Table do not show isotropic behavior which means that the structures are anisotropic . Following equations are used to compute the elastic properties E, G, A, K and σ, etc.:
Young’s modulus (E) tells us about the stiffness of materials. The greater the value of (E), the stiffer is the material. From Table 3, it is evident that CsF in B1 phase is stiffer (E = 50.149) as compared to other compounds in both phases. Using elastic constants Cij, Cauchy’s pressure C12–C44, the ratio (K/G) Pugh’s index of ductility and Poisson’s ratio σ we obtain a good prediction of stiffness and ductility. The negative value of Cauchy’s pressure represents brittleness, while the positive means that the material is ductile . From Table 3, only CsF in B2 phase has positive Cauchy’s value, while it is negative for all other compounds. Similarly, the higher the ratio K/G, the more ductile is the material and vice versa. The critical value that separates ductility from brittleness is 1.75 . CsF in B2 phase and CsBr in B1 phase have this ratio greater than the critical value while for other compounds it is smaller. Poisson’s ratio σ is another method to calculate brittleness and ductility of a compound. For a compound to be ductile, the value of its Poisson’s ratio must be greater than 0.26, while the one smaller than this value represents the brittle nature . The CsBr in B1 phase, and CsF in B2 phase have σ value larger than 0.26 which shows their ductile nature.
3.3 Electronic properties
The energies difference between valence and conduction band determines the electronic properties of materials. Band structures of all binary and their ternary alloys, calculated using two different methods for the compounds in our study; Wu-Cohen GGA and Engel-Vasco (EV) GGA using 1000 k-points grid during DFT simulation, are presented in Fig. 4 to Fig. 7.
The calculated band gap values for binary compounds and their ternary alloys in B1 phase are tabulated in Table 4, while for B2 phase are presented in Table 5 along with experimental and other theoretically calculated values. Most of the band structures of the binary and ternary alloys are direct band gap. The results obtained using Wu-Cohen GGA and EV-GGA for binary compounds reveal that the band gap (Eg) is smaller for rock salt phase of cesium halides than B2 phase, while for CsCl band gap in B1 phase is larger than B2 only in EV-GGA scheme. Similarly, the band gap calculated for binary cesium halides using Wu-Cohen GGA is smaller than EV-GGA except for CsI (B1 phase). Band gap is larger as EV-GGA method has been used for B2 phase. This increase is also observed in the case of all ternary alloys in both phases calculated using EV-GGA method. Furthermore, the increase in band gap is proportional to the dopant concentration in all cases and phases.
Energy band gaps for F, Cl and Br doped CsI in rock salt (B1) phase for (0 ⩽ x ⩽ 1).
|Eg [eV]||Eg [eV]||Eg [eV]|
Energy band gaps for F, Cl and Br doped CsI in B2 phase for (0 ⩽ x ⩽ 1).
|Eg [eV]||Eg [eV]||Eg [eV]||Eg [eV]|
|CsI||3.8744||5.0283||6.2  6.50 ||3.91  3.97 |
|CsCl||5.2493||5.2247||7.90 ||5.27 |
|CsBr||4.3900||5.8385||7.30 ||4.56 |
3.4 Density of states
Density of states (DOS) is an important tool to determine different electronic states, dielectric function, reflectivity and band structure of solids.
In Fig. 8, total and partial density of states are given at all concentrations (0 ⩽ x ⩽ 1) and in both phases of CsYx I (1 − x) (Y = F, Cl, Br) using Wu-Cohen GGA scheme. In the figure of binary compounds and ternary alloys of B1 and B2 phases, mixed d-states of all the elements contribute in a very small proportion in conduction band, whereas far region of conduction band is upheld by Cs f-state with a very minute contribution. Fluorine p-state gives a separate peak in all compounds and in both phases (binary as well as ternary) in the valence band near Fermi level. The second sharp peak in the valence band region of CsCl and CsBr corresponds to the halogen p-state, excluding fluorine. The third peak at the lower energy side of valence band is purely the contribution of Cs p-state. In the density of states plot, overall behavior of all compounds is the same for both phases shown in Fig. 8. This behavior is attributed to the overlapping of energy states to form a ternary alloy.
3.5 Electron density
To assess the probability of identifying the specific location of electrons and to obtain information about the nature of bonds among the atoms of a molecule, electron density calculations are important. In the present work, the electron density has been calculated in CsYxI1 − x(Y = Br, F and Cl) in rock salt phase as well as CsCl structure using the generalized gradient approximation (GGA) method. The bonding nature is ionic in which charge transfer between the anion and cation occurs.
The first column in both figures represents CsI with increasing concentration (x = 0.25, 0.50, 0.75 and 1) of halogens in the order of F, Cl and Br, respectively. From the plots of these compounds it is revealed that the boding nature is mostly ionic since there is a strong localization of the charge around the anion side. The contour plots are expressed in the units of electrons per unit cell. It is observed that doping of lighter halogens produced slightly covalent character in binary compounds which are pure ionic in nature. In B1 phase of CsF, the covalent character is strong as compared to other binary Cs halides because fluorine is the smallest halogen atom while the ternary alloys, CsF.75I.25 and CsCl.75I.25 show the most covalent character out of all in B1 phase. The rest of all binary compounds and ternary alloys are ionic in both phases.
3.6 Optical properties
The dielectric functions for CsYxI1 − x in the energy range of 0 eV to 40 eV are presented in Fig. 11 and Fig. 12 showing the real ε1(ω) and imaginary ε2(ω) parts for all concentrations in B1 and B2 structure.
In the left panel of Fig. 11 and Fig. 12, ε1 (ω) is the real part while in the right panel of the figures, imaginary part ε2(ω) is shown. The positive value of the real part at low frequency is the static part of the dielectric constant. After reaching the maximum value, the dielectric constant decreases with frequency and some peaks with negative values appear. This corresponds to the metallic region of materials that exhibit negative values of ε1(ω). From Fig. 12 it is noted that different peaks appear in the spectra of the compounds and the alloys. The transition of electrons from the occupied states of the valence band to the unoccupied states of the conduction band causes the appearance of the peaks.
In CsFxI1 − x with B1 phase at x = 0 the real part ε1(ω) is positive for all energy ranges but is negative in the energy ranges of 7.52 eV to 8.79 eV and 14.12 eV to 17.47 eV which gives maximum peak 5.31 at energy 4.74 eV. The imaginary part ε2(ω) indicates two peaks: the maximum peak 5.30 at energy 7.28 eV and second 4.28 at 5.97 eV. As the concentration of lighter halogens was increased, the maximum peak decreases in both real and imaginary parts of dielectric function. This reflects that the behavior of the material has shifted from lower to higher energy values as the dopant concentration is increased. This is observed in both real and imaginary parts of dielectric function. Reflectivity is the ratio of the reflected power to the incident power of the material. The reflectivity (R) is plotted for CsYxI1 − x for concentrations x (0 ⩽ x ⩽ 1) as shown in the Fig. 13.
Binary CsI (B1) reflectivity is maximum in energy range from 5 eV to 10 eV (0.29) and from 15 eV to 20 eV (0.38) and it decreases at high energy. Fluorine doped CsI peak diminishes with increasing concentration x = from 0 to 1. Furthermore, no significant peak changes are observed in the range of 15 eV to 20 eV. By chlorine doping into CsI, the peak reduces in a similar way with increasing concentration while slight increase is observed in the range of 15 eV to 20 eV. The reflectivity at x = 0.25, 0.50, 0.75 and 1 is given as 0.33, 0.34, 0.37 and 0.47, respectively. Slight peaks change from 0.28 to 0.23 is observed in bromine doping in the range of 5 eV to 10 eV. The observed changes are very clear in the second set of peaks from 0.29 to 0.37 with bromine doping for x equal to 0, 0.25, 0.5, 0.75, and 1.0.
In B2 structure of CsI, maximum reflectivity (0.38) is found in the energy range from 5 eV to 10 eV and the second set of two peaks with reflectivity of 0.35 is located in 15 eV to 20 eV energy range. Fluorine doping with x = 0.25, 0.50, 0.75 and 1 in the range of 15 eV to 20 eV changes the peaks to 0.39, 0.41, 0.45 and 0.48, respectively, whereas the peak in the range of 5 eV to 10 eV decreases from 0.37 to 0.17. For chlorine doping, two peaks in the energy range 5 eV to 10 eV are evident which shift from 0.28 and 0.30 at x = 0.25 to 0.24 and 0.25 at x = 1 (CsCl). Two more intense peaks in the energy range of 15 eV to 20 eV change from 0.39 and 0.35 at x = 0.25 to 0.49 and 0.39 at x = 1. These clearly indicate that increasing dopant concentration results in larger peaks but at higher photon energies. Finally, in case of bromine, two peaks in the range of 5 eV to 10 eV decrease with increasing dopant concentration from 0.29 and 0.32 at x = 0.25 to 0.25 and 0.29 at x = 1. The peaks observed in the range of 15 eV to 20 eV increase from 0.39 and 0.36 at x = 0.25 to 0.44 and 0.39 at x = 1.
3.7 Optical conductivity
The electron transportation in a material can be observed by optical conductivity (σ). In Fig. 14, optical conductivity of CsYxI1 − x at different concentrations for both B1 and B2 structures is presented.
The conductivity changes in the range of 4 eV to 40 eV for all compounds with different concentrations. It is observed that for BCC phase optical conductivity shifts to higher energy with increasing concentration, whereas in FCC structure, one of the two peaks gets smaller.
In binary CsI (B1), two peaks of 5080 Ω–1⋅cm–1 and 5577 Ω−1⋅cm−1 are located, respectively, at 7.26 eV and 13.89 eV. Finally, the conductivity decreases and approaches to zero at 39 eV. The decreasing behavior in the peak values of optical conductivity is observed when the halogens are doped at concentrations x = 0.25, 0.5, 0.75 and 1.
The optical conductivity for B2 phase of CsYxI1 − x is also shown Fig. 14. The highest peak is found for pure CsI (6222 Ω−1⋅cm−1) at 7.7 eV, while there is a set of three peaks (4860 Ω−1⋅cm−1) lying in energy range of 12 eV to 14.5 eV. By fluorine doping in B2 phase CsI, the first peak shifts from 6222 Ω−1⋅cm−1 to 3459 Ω−1⋅cm−1, when the concentration varies from x = 0 to 1, while the second peak increases as concentration increases, i.e. from 4860 Ω−1⋅cm−1 to 9099 Ω−1⋅cm−1 at x changing from 0 to 1. Introduction of chlorine (Cl) caused that the plot of optical conductivity shows three major peaks, two in the energy range of 6 eV to 10 eV, while the third one lies between 12 eV and 14 eV. The very first peak keeps decreasing with increasing Cl content, while the second one decreases till x = 0.75 and then starts to increase for x = 1 (CsCl). The third peak increases with Cl concentration and has the highest value of 7803 Ω−1⋅cm−1 at x = 1 (CsCl) at energy of 13.6 eV. After addition of bromine (Br), CsI shows three major peaks. Two of them are in the energy range of 6 eV to 9 eV, while the third one is in the range of 11.5 eV to 12.5 eV. The first peak decreases with an increase in Br concentration. The second peak is of the same height as that of the first one but it gradually increases from 5521 Ω−1⋅cm−1to 5821 Ω−1⋅cm−1 (CsBr). The third peak keeps increasing till it attains a maximum value of optical conductivity (7346 Ω−1⋅cm−1) at 12.2 eV for CsBr (B2) phase.
The GGA, EV-GGA potentials were applied to study the bonding nature and optoelectronic properties of CsYxI1 − x compounds. In cubic phase, the structural properties and density of states (DOS) have been calculated for further theoretical and experimental investigations. It is worth noting that our calculated structural properties for CsYxI1 − x compounds match well with available experimental data, better than other theoretical results. From the structural properties, it has been demonstrated that bulk modulus decreases in both B1 and B2 phases and is responsible for low compressibility and high hardness.
The bonding analysis and electron density revealed that most of binary and ternary halides of Cs are ionic except for few showing a minute contribution of covalent bonding. High absorption peaks and reflectivity are observed in the visible and ultraviolet (UV) region of the energy spectrum. CsCl in B1 phase shows the highest reflectivity among all others. This study can be helpful in designing these materials for devices such as Bragg’s reflectors, optical and optoelectronic devices working in UV region of spectrum.
The authors acknowledge the support from the Institute of Chemical Sciences, University of Peshawar, Department of Physics University of Peshawar and Islamia College University Peshawar for providing research facilities.
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