Solving the disordered structure of β-Cu_2-xSe using the three-dimensional difference pair distribution function.

Area of Science:

• Materials Science
• Solid-State Physics
• Crystallography

Background:

• High-performing thermoelectric materials often possess atomic disorder, complicating structure-property relationship analysis.
• Copper selenide (Cu_2-xSe) is a cost-effective, non-toxic thermoelectric material with unusual transport properties near its phase transition.
• The crystal structure of the low-temperature β-Cu_2-xSe phase has remained unsolved since 1936, hindering property understanding.

Purpose of the Study:

• To elucidate the complex crystal structure of β-Cu_2-xSe.
• To establish a method for solving structures with partial dimensionality disorder.
• To understand the link between the atomic structure and thermoelectric properties of Cu_2-xSe.

Main Methods:

• Utilized three-dimensional difference pair distribution function (3D-ΔPDF) analysis on diffuse single-crystal X-ray scattering data.
• Solved the structure of the ordered layers within β-Cu_2-xSe.
• Identified two distinct stacking disorder modes.

Main Results:

• Demonstrated that β-Cu_2-xSe exhibits two-dimensional order and three-dimensional disorder.
• Determined the ordered layer structure and characterized the stacking disorder.
• The average structure, derived from Bragg crystallography, possesses higher symmetry than the actual local structure.

Conclusions:

• The study presents a novel approach to solving crystal structures with partial dimensionality disorder, generalizing the Patterson method.
• The unique structural characteristics of β-Cu_2-xSe, with its layered order and stacking disorder, are crucial for its thermoelectric performance.
• This work highlights the significant divergence between local atomic structure and average structure in determining material properties, particularly for thermoelectrics.