# Theoretical Exploration of the Physical-Chemical Properties of Divalent (np 2) Cation Mixing in Double Cs2AgBiBr6 Perovskite

## TL;DR

This paper explores how mixing different cations in a lead-free perovskite material affects its stability and electronic properties.

## Contribution

The study introduces a theoretical framework for optimizing lead-free perovskites using heterovalent substitution to enhance optoelectronic performance.

## Key findings

- Mixed-halide perovskites show high structural flexibility and entropy-driven stabilization.
- Larger cations reduce octahedral distortions and promote lattice symmetry.
- Sn- and Pb-rich compositions are energetically favored for better stability.

## Abstract

Lead-free halide double perovskites have emerged as promising
alternatives
to conventional lead-based materials for photovoltaic applications,
as they combine environmental compatibility with structural stability.
However, their indirect band gaps limit optoelectronic performance,
motivating compositional and structural optimization to achieve higher
efficiency. In this work, we used density functional theory calculations
to investigate complex mixed-halide double perovskites with general
composition Cs2Ag
x
Bi
x

B

y

B'
z
Br6, where B,B′ = Ge, Sn, or Pb. By coupling
electronic-structure calculations with high-throughput stress-tensor
optimizations across thousands of configurations, we identified the
energetic and structural principles governing their stability and
electronic properties. The results revealed a narrow energy distribution,
indicating high structural flexibility and entropy-driven stabilization.
Substitutional trends are dictated by ionic size, with larger cations
reducing octahedral distortions and promoting lattice symmetry. Although
all ternary mixtures exhibited positive excess energies, Sn- and Pb-rich
compositions were energetically favored. The decomposition of the
bond energy consistently linked the strength of the metal-halide interaction
to the stability of the lattice, with increasing Ag content weakening
the overall bonding. In particular, partial substitution of Ge, Sn,
or Pb at the B-site of pristine Cs2AgBiBr6 enhanced electronic transitions and induced nonlinear bowing
effects, demonstrating heterovalent substitution as an effective strategy
for tuning stability and optoelectronic performance in lead-free perovskite
absorbers.