  The ability to control carrier concentration based on the extent of Cu
solubility in the $\mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ alloy compound (where 0
$\leq$ x $\leq$ 1) makes $\mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ an interesting case
study in the field of thermoelectrics. While Cu clearly plays a role in this
process, it is unknown exactly how Cu incorporates into the
$\mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ crystal structure and how this affects the
carrier concentration. In this work, we use a combination of resonant energy
X-ray diffraction (REXD) experiments and density functional theory (DFT)
calculations to elucidate the nature of Cu incorporation into the
$\mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ structure. REXD across the $\mathrm{Cu_k}$
edge facilitates the characterization of Cu incorporation in the
$\mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ alloy and enables direct quantification of
anti-site defects. We find that Cu substitutes for Hg at a 2:1 ratio, wherein
Cu annihilates a vacancy and swaps with a Hg atom. DFT calculations confirm
this result and further reveal that the incorporation of Cu occurs
preferentially on one of the z = 1/4 or z = 3/4 planes before filling the other
plane. Furthermore, the amount of $\mathrm{Cu_{Hg}}$ anti-site defects
quantified by REXD was found to be directly proportional to the experimentally
measured hole concentration, indicating that the $\mathrm{Cu_{Hg}}$ defects are
the driving force for tuning carrier concentration in the
$\mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ alloy. The link uncovered here between crystal
structure, or more specifically anti-site defects, and carrier concentration
can be extended to similar cation-disordered material systems and will aid the
development of improved thermoelectric and other functional materials through
defect engineering.

Materials Science