Shift of lines in phase diagrams for nanograined materials

Abstract

If one adds the atoms of a second component B to a one-component polycrystal A, they distribute between bulk and grain boundaries (GBs) and form a solid solution (A). If the amount of B exceeds the solubility limit in (A), the particles of a second phase appear and start to grow, and the concentration of B in (A) remains constant and equal to the solubility limit. However, the equilibrium solubility in the GBs is usually much higher than in the bulk. Therefore, the overall solubility of B in a polycrystal (A) would be higher than in a single-crystal (A). Thus, the solubility lines in the phase diagrams should shift with decreasing grain size. We measured the solubility of Mn and Co in the zinc oxide with grain size of about 20 nm and compared with that in the ZnO single-crystals. At 500°C, the overall solubility increases from 2 to 33 at.% Co and from 2 to 28 at.% Mn. Temperature dependences of the solubility shift for the grain size of 20, 100 and 1,000 nm were calculated using the published data from the papers devoted to the investigations of ferromagnetism in doped ZnO. The quantitative estimation leads to the conclusion that, close to the bulk solubility limit, the thickness of a Co- and Mn-enriched layer in GBs is several monolayers and at least two monolayers in the free surfaces.