First-principles study of energy and atomic solubility of twinning-associated boundaries in hexagonal metals

Twinning-associated boundaries (TB), {101¯n} coherent twin boundaries (CTB) and the coherent basal-prismatic (CBP) boundary in six hexagonal metals (Cd, Zn, Mg, Zr, Ti and Be) are studied using first-principles density function theory, with the focus on the structural character of TB and the solute's solubility at TB. Regarding the structure and energy of TB, the formation of TB is associated with the creation of an excess volume. All six metals show positive excess volume associated with (101¯1) and (101¯3) CTB, but the excess volume associated with (101¯2) CTB and CBP can be positive or negative, depending on the metal. The (101¯2) CTB has higher excess energy than (101¯1) and (101¯3) CTB for metals with c/a<8/3 , but lower for metals with c/a>8/3. More interestingly, CBP has lower excess energy than (101¯2) CTB for all metals. This is consistent with the recent finding concerning the pure-shuffle nucleation mechanism of (101¯2) twins. To understand solubility at TB, the solubility of solute atoms in Mg, Ti and Zr is calculated for solute positions in bulk, (101¯2) CTB and CBP boundaries. In general, solute atoms have better solubility at CTB and CBP than in bulk. Interestingly, the solubility of solute atoms changes linearly with normal strain at CBP, increasing with normal strain for solute atoms with a greater metallic radius than the matrix, and decreasing with normal strain for solute atoms with a smaller metallic radius than the matrix. This suggests that the distribution of solute atoms in bulk, CTB and CPB boundaries varies with stress state and, in turn, affects the mobility of TB.