# Unravelling the Influence of the Local Structure on the Ultralow Thermal Conductivity of the Bismuthinite–Aikinite Series, Cu1–x □ x Pb1–x Bi1+x S3

## TL;DR

This paper explores how local structural changes in a copper-rich mineral series affect its ultralow thermal conductivity.

## Contribution

The study reveals how local cation and vacancy disorder influence phonon transport and thermal conductivity in a crystal series.

## Key findings

- Intermediate compositions crystallize in the krupkaite structure, not the aikinite structure.
- Copper-rich and copper-poor regions form due to non-statistical cation and vacancy disordering.
- Lattice softening and phonon scattering are linked to local structural features like Pb2+–Cu+ distances.

## Abstract

Understanding the relationship between crystal structure,
bonding
and thermal transport is critical for the discovery of materials with
ultralow thermal conductivities. Materials in the bismuthinite–aikinite
series, Cu1–x
□
x
Pb1–x
Bi1+x
S3 (0 ≤ x ≤
1), in which a Bi3+ cation and a vacancy (□) are
progressively substituted by a Pb2+ and a Cu+ cation, exhibit ultralow thermal conductivities (∼0.5 W m−1K–1 for x <
1). Here, we investigate the effect of decreasing the Pb2+ and Cu+ content on the crystal structure and properties
of Cu1–x
□
x
Pb1–x
Bi1+x
S3 (x = 0, 0.33, 0.6 and 0.83).
These materials exhibit two-channel thermal transport, with non-propagating
phonons being the dominant contribution. Neutron diffraction data
reveal that intermediate compositions crystallize in the krupkaite
structure (x = 0.5, P21
ma), instead of the end-member aikinite structure
(x = 0, Pnma). Pair distribution
function (PDF) analysis reveals that the disordering of vacancies
and cations deviates significantly from that expected for a statistical
distribution and that, at a local level, copper-rich and copper-poor
regions occur. Reducing the Pb2+ and Cu+ content
results in lattice softening, which may be attributed to the increased
concentration of vacancies in copper-poor regions. Moreover, the persistence
of short Pb2+–Cu+ distances in the copper-rich
regions is likely to facilitate the cooperative interaction between
lone pairs and rattling Cu+ cations that leads to phonon
scattering. These findings provide crucial insights into the effect
of the local structure on the phonon transport and highlight the potential
of local-structure design to achieve high thermoelectric performance
in crystalline solids.