Chemo-Structural Disorder in the kagomé spin $S$ = 1/2 systems ZnCu${}_3$(OH)${}_6$Cl${}_2$ and YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]

By single crystal diffraction we characterize the chemo-structural disorder introduced by Zn-Cu site mixing in the kagomé spin $S$-1/2 systems herbertsmithite ZnCu${}_3$(OH)${}_6$Cl${}_2$ and YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]. For an untwinned single crystal of herbertsmithite of composition Zn${}_{0.95(1)}$Cu${}_{2.99(3)}$O${}_{5.9(1)}$H${}_{5.8(1)}$Cl${}_2$ we find substitution by Cu of the Zn atoms in the layers separating the kagomé layers as well as substantial Zn substitution for Cu in the kagomé layers. In YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$] site mixing disorder is present for intermediate $x$. Analogous to the Cl homologous system in crystals with $x=1\mathrm{/}3$ disorder is absent and a low-temperature structural transition emerges driven by strong magneto-phonon coupling as a release of frustration. Apart from this structural anomaly we find the physical properties of these crystals unchanged compared to intermediate $x$ and closely resembling the Cl homologue where long-range magnetic order was observed.