First principle study of optoelectronic and mechanical properties of lead-free double perovskites Cs₂SeX₆ (X = Cl, Br, I)

Figures & data

Figure 1. (Left) Ground state structural optimizations (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆. (Right) Crystalline structure of Cs₂SeX₆ (X = Cl, Br and I).

Table 1. Various calculated parameters, for instance, lattice constant a_o (Å), bulk modulus B_o (GPa), formation energy H_f (eV), electronic bandgap E_g (eV) and tolerance factor (T_f) of Cs₂SeX₆ (X = Cl, Br, I).

Parameters	Cs2SeCl6	Cs2SeBr6	Cs2SeI6
ao (Å)	10.70	11.37	12.31
Bo (GPa)	23.63	22.13	18.80
Hf (eV)	−1.55	−1.40	−1.35
Eg (eV)	3.10 (W-L)	2.64 (W-L)	1.15 (Γ-L)
Tf	0.97	0.98	1.0

Figure 2. The phonon dispersion plots of (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆, respectively.

Figure 3. Electronic band structure of (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆.

Figure 4. Total DOS and partial DOS of (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆.

Table 2. The calculated elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus B (GPa), shear modulus G (GPa), Young modulus E (GPa), Pugh’s ratio (B/G), Poisson ratio (υ), anisotropy factor (A), Kienman parameter (ξ), Lams constant (μ and λ), sound velocities V_ℓ, V_t and V (Km/s), Debye temperature _D (K), melting temperature T_m (K), hardness H_a (GPa) and minimum thermal conductivity K_min (Wm⁻¹K⁻¹) of Cs₂SeX₆ (X = Cl, Br, I).

Parameters	Cs2SeCl6	Cs2SeBr6	Cs2SeI6
C11 (GPa)	26.1	24.2	21.0
C12 (GPa)	22.4	21.1	19.20
C44 (GPa)	4.2	3.3	2.5
B (GPa)	23.63	22.13	19.80
G (GPa)	3.02	2.43	1.66
E (GPa)	8.69	7.05	4.85
B/G	7.81	9.08	11.9
υ	0.43	0.44	0.46
A	2.07	2.12	2.78
ξ	0.90	0.91	0.94
μ (GPa)	3.02	2.43	1.66
λ (GPa)	21.14	20.50	18.69
Vℓ (km s^−1)	3.025	2.61	2.364
Vt (km s^−1)	1.000	0.808	0.649
V (km s^−1)	1.137	0.921	0.740
D (K)	104.7	79.8	59.2
Tm (K)	700.3	675.0	671.1
Ha (GPa)	1.7	1.2	0.59
Kmin (Wm^−1K^−1)	0.105	0.078	0.058

Table 3. The calculated bandgap E_g (eV), static dielectric constant ε₁ (0), static refractive index n (0) and reflectivity R (0) of Cs₂SeX₆ (X = Cl, Br, I).

Compounds	Cs2SeCl6	Cs2SeBr6	Cs2SeI6
Eg (eV)	3.10	2.64	1.15
ε1 (0)	3.59	4.13	6.17
n (0)	1.89	2.03	2.48
R (0)	0.095	0.115	0.181

Figure 5. (a) Real part of dielectric constant ε₁ (ω), (b) imaginary part of dielectric constant ε₂ (ω), (c) absorption coefficient α (ω) and (d) refractive index n (ω) of Cs₂SeX₆ (X = Cl, Br, I).

Figure 6. (a) Reflectivity R (ω), (b) optical loss factor L (ω) of Cs₂SeX₆ (X = Cl, Br, I).