The observed c/a lattice parameter of hcp solid solution Ag1-xZnx shows anomalous behavior in both epsilon (0.68<0.87) and eta (x>0.95) phases. We investigate the nature of these anomalies by performing ab initio exact muffin-tin orbitals total energy calculations for hcp Ag1-xZnx random alloys. The peculiar features in crystal structure and elastic constants are mapped out in detail, and where experimental data are available they excellently agree with the theoretical results. The sharp variation in c/a obtained for x=0.87 is explained by an almost zero resistance to c/a variations at constant volume, giving a deformation path with a very low energy barrier connecting the epsilon and eta phases. The rapid decrease of c/a in Zn-rich alloys, on the other hand, is found to have a band energy origin.
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