Adsorbate phases of H on ZnO $(10 \overline{1}0)$ surface as a function of temperature and pressure from first principles

Zinc oxide (ZnO) is a highly multifunctional material with unique properties and a wide range of applications. To understand atomic hydrogen adsorption on the thermodynamically stable $(10 \overline{1}0)$ surface at realistic H chemical potentials, we combine a first-principles cluster-expansion approach with {\em ab initio} atomistic thermodynamics. Our study reveals that at coverages below 6\%, H atoms adsorb exclusively on surface O. At higher coverages, H adsorbs also on Zn, but there is an excess of O-H over Zn-H at all coverages, except 50\% and 100\%. Due to an interplay of long- and short-range electrostatic interactions, neighboring O-H/Zn-H pairs form chains along surface -O-Zn- rows, with each chain anchored at the excess O-H, in a wide range of $(T,p_{\rm H_2})$. Our results offer a ``road map'' for H adsorption on the ZnO $(10 \overline{1}0)$ surface at various conditions, consolidating findings from previous experiments [1-4]. ---[1] Y. Wang {\em et al.}, PRL 95, (2005); [2] K. Ozawa and K. Mase, Phys. Stat. Sol. App. Mat. Sci. 207, (2010); [3] K. Ozawa and K. Mase, PRB 83, (2011); [4] J. Deinert {\em et al.}, PRB 91, (2015).