Influence of the octahedral cation on the evolution of lattice phonons in metal halide double perovskites: Raman spectroscopic investigation of ${\mathrm{Cs}}_2{B}^{\prime }{B}^{″}{\mathrm{Cl}}_6$ ($B^{\prime }={\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x$; $B^{″}={\mathrm{Bi}}_{1-x}{\mathrm{In}}_x$)

Vibrational dynamics in halide double perovskites govern several key aspects including carrier recombination and transport properties. Here, we present comprehensive vibrational studies investigated through micro-Raman spectroscopy to understand how octahedral cation substitution in a wide range of metal halide double perovskites ${\mathrm{Cs}}_2{B}^{\prime }{B}^{″}{\mathrm{Cl}}_6$ ($B^{\prime }={\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x$; $B^{″}={\mathrm{Bi}}_{1-x}{\mathrm{In}}_x$) influence lattice vibrations. A significant enhancement in $F_{2g}$ mode intensity—a key factor in determining the cation ordering—is observed with ${\mathrm{Na}}^{+}$ substitution. In contrast to a generally observed trend, despite similar ionic sizes of ${\mathrm{Na}}^{+}$ and ${\mathrm{Bi}}^{3+}$, an increase in cationic ordering is observed as ${\mathrm{Na}}^{+}$ substitutes at ${\mathrm{Ag}}^{+}$ site in ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{Bi}{\mathrm{Cl}}_6$ and ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{In}{\mathrm{Cl}}_6$. The $F_{2g}$ mode intensity depends on $B^{\prime }$-site cationic ordering (${\mathrm{Ag}}^{+}$ or ${\mathrm{Na}}^{+}$), while its vibrational energy is governed by the $B^{″}$-site cations (${\mathrm{Bi}}^{3+}$ or ${\mathrm{In}}^{3+}$). The symmetric stretching vibrations depicted by $A_{1g}$ mode are mainly influenced by $\left[B^{3+}\text{−}{X}_6\right]$ octahedra. The reduction in the linewidth of symmetric-stretching LO phonon mode ($A_{1g}$) and the disappearance/diminishing of asymmetric-stretching vibrations ($E_{\mathrm{g}}$) further substantiates the improved cationic ordering. The changes in the vibrational mode intensities with $B^{\prime }$-site substitution (${\mathrm{Ag}}^{+}, {\mathrm{Na}}^{+}$) and the appearance of distinct octahedral modes with $B^{″}$-site substitution (${\mathrm{Bi}}^{3+}, {\mathrm{In}}^{3+}$) allow us to disseminate different octahedral contributions to the vibrational dynamics in the lattice. Further, the vibrational analyses on double perovskites with different choices of $B^{\prime }$ and $B^{″}$ cations and $X$ anion reveal the origin of asymmetric stretching ($E_{\mathrm{g}}$). This mode mainly prevails when sublattice distortions in the lattice exist. Thus, asymmetric-stretching mode can be a measure of sublattice distortion in the double perovskite, and a highly ordered system would exhibit very minimal or no asymmetric vibrations.

Figure 1

(a) Crystal structure of ${\mathrm{Cs}}_2{B}^{\prime }{B}^{″}{\mathrm{Cl}}_6$ double perovskite. (b) Variation of lattice constant with composition in ${\mathrm{Cs}}_2{B}^{\prime }{B}^{″}{\mathrm{Cl}}_6$ double perovskites ($B^{\prime }={\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x$ with $B^{″}=\mathrm{Bi}$ or In; $B^{″}={\mathrm{Bi}}_{1-x}{\mathrm{In}}_x$ with $B^{\prime }=\mathrm{Ag}$ or Na). Green open circle is the average lattice constant for $x=0.5$ in ${\mathrm{Cs}}_2\mathrm{Na}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$ from phase fractions.

Figure 2

XRD patterns and Rietveld refined plots for (a) ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{Bi}{\mathrm{Cl}}_6$, (b) ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{In}{\mathrm{Cl}}_6$, (c) ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$, and (d) ${\mathrm{Cs}}_2\mathrm{Na}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$ for $x=0$ to 1. Also see Fig. S1 for raw XRD plots [30].

Figure 3

Schematic representation of octahedral vibrational modes (superscript in the parentheses indicates degeneracy of the mode).

Figure 4

Raman spectra of (a), (b) ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{Bi}{\mathrm{Cl}}_6$ (c), (d) ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{In}{\mathrm{Cl}}_6$ for $x=0$ to 1. (b) and (d) are intensity contour plots of (a) and (c).

Figure 5

Variation of integrated intensities (a) and (b), vibrational energies (c) and (e), FWHM (d) and (f) of Raman modes with Na composition in ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{Bi}{\mathrm{Cl}}_6$ and ${\mathrm{Cs}}_2{\mathrm{Ag}}_{1-x}{\mathrm{Na}}_x\mathrm{In}{\mathrm{Cl}}_6$.

Figure 6

Raman spectra of (a) ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$ and (c) ${\mathrm{Cs}}_2\mathrm{Na}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$ for $x=0$ to 1. (b) and (d) shows the corresponding contour maps.

Figure 7

Variation of vibrational energies (a) and (c) and FWHM (b) and (d) of Raman modes with In composition in ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$ and ${\mathrm{Cs}}_2\mathrm{Na}{\mathrm{Bi}}_{1-x}{\mathrm{In}}_x{\mathrm{Cl}}_6$.

Figure 8

Raman spectra of double perovskites with different cation and anion combinations.