Crystallography of the Simple HCP/FCC System

Abstract

The edge-to-edge matching model has been used to predict the orientation relationships (ORs) between crystals that have simple hexagonal-close-packed (HCP) and face-centered-cubic (FCC) structures. Using the critical values for the interatomic spacing misfit along the matching directions and the d-value mismatch between matching planes, a total of seven ORs have been predicted for the most common HCP/FCC metallic systems. However, the ORs that appear more frequently in a particular system depend on the type of matching directions and the interatomic spacing misfit along these directions together with the d-value mismatch between the matching planes. The latter two are related to the lattice parameters of both phases. For example, in the Al/Ag2Al system, three ORs have been predicted. One is $$ {\left[ {11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}0} \right]}_{\gamma } //{\left[ {110} \right]}_{\alpha } $$ , (0002) γ 0.027 deg from $$ {\left( {\ifmmode\expandafter\bar\else\expandafter\=\fi{1}11} \right)}_{\alpha } $$ , which is consistent with the previously reported OR-1. The second is $$ {\left[ {11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}0} \right]}_{\gamma } //{\left[ {110} \right]}_{\alpha } ,\,{\left( {1\ifmmode\expandafter\bar\else\expandafter\=\fi{1}01} \right)}_{\gamma }\;0.8\,\deg $$ from $$ {\left( {\ifmmode\expandafter\bar\else\expandafter\=\fi{1}11} \right)}_{\alpha } $$ . Due to the larger mismatch values, this OR is not expected to occur frequently and has not been found experimentally to date. Another predicted OR is $$ {\left[ {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right]}_{\gamma } ||{\left[ {112} \right]}_{\alpha } ,\,{\left( {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right)}_{\gamma } 0.25\deg $$ from $$ {\left( {\ifmmode\expandafter\bar\else\expandafter\=\fi{2}20} \right)}_{\alpha } $$ . This OR is very close to the reported OR-1. Details of zigzag atom row matching and the principles and process of refining an OR using the Δg conditions are also discussed.