Defect clustering in Fe- and Al-substituted ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

Atomistic simulation techniques are used to investigate the effect of Fe and Al dopant substitution in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. Interatomic potentials that were previously developed for the oxide are employed, which correctly reproduce the orthorhombic crystal structure. From the calculated defect energies, values of the binding energies are derived for various dopant-oxygen interstitial clusters on the Cu(1) basal plane. The cluster configurations considered range in size from the simple dimer, containing two dopant ions, to large clusters containing up to seven dopant ions. The results indicate a strong tendency towards cluster formation, rather than a random distribution of defect species. This leads to an increase in the Fe (or Al) site coordination with oxygen. Ion displacements following lattice relaxation about the dopants are also examined. We calculate significant off-center displacement of both Fe and Al ions and find a lengthening of the bond with the apex oxygen, O(4). Our results are in line with recent neutron-diffraction and x-ray-absorption studies that find evidence for defect clustering in doped samples.