THE CRYSTALLOGRAPHY OF THE BCC TO HCP (ORTHOHEXAGONAL) MARTENSITIC TRANSFORMATION IN DILUTE Zr-Nb ALLOYS: Part I: Lattice Strain and Lattice Invariant Shear

The Bain strain (homogenous strain or lattice strain), the inhomogeneous shear (LIS) and the rigid body rotation in relation with the martensitic transformation in Zr-2.5%Nb alloy has been calculated. The homogeneous lattice strain has been uniquely determined by invoking Lomer’s criterion and the minimum distortion criterion. Both the minimum strain energy and the minimum distortion considerations lead to the same type of Bain strain and lattice correspondence. A systematic study has been carried out to identify the possible lattice invariant shears (LIS) which meet the IPS condition for both slip type and twin type shears. Mathematical and graphical methods have been employed to determine the slip and the twin systems which qualify as the LIS from amongst the possible deformation systems of the hcp structure. In this manner, the most frequently observed H H H H H H > < > < > < 3 1 1 2 } 21 1 1 { ; 3 1 1 2 } 112 2 { ; 3 1 1 2 } 101 1 { slip systems and the H H H H > < > < 11 1 0 } 2 1 01 { ; 3 5 41 } 101 1 { twin systems have been found to qualify as the LIS.