New Mechanism for the to ! Martensitic Transformation in Pure Titanium

sible supercells of and ! to determine the lattice strain exact energy barrier. The TB-NEB barrier is bounded Martensitic transformations are abundant in nature and are commonly used in engineering technologies [1]. Materials from steel to shape-memory alloys are governed by their underlying martensitic transformations [2]. The pressure driven hcp ! ! hexagonal transformation in pure titanium [3] has significant technological implications in the aerospace industry because ! phase formation lowers toughness and ductility. This transformation, first observed by Jamieson [4], has been extensively studied using static high-pressure [5] and shock-wave methods [6]. Because of experimental difficulties in directly observing martensitic transformation pathways, they are inferred from the orientation relationships between the initial and final phases. Such an approach may result in multiple transformation pathways for a given set of orientation relations, requiring one to guess the appropriate transformation pathway. Thus, despite several attempts, the pathway for this transformation is still unclear. We calculate the energy barrier for homogeneous transformation for different titanium ! ! transformation pathways. We systematically generate and sort possible ! ! pathways by their energy barriers. A new direct pathway emerges whose barrier is lower than any other pathway, remaining favorable in any nucleation model. Figure 1 shows our new low energy barrier pathway for the titanium ! ! transformation, called TAO-1 (‘‘titanium alpha to omega’’). This direct six-atom transformation proceeds without a metastable intermediate phase and has small shuffles and strains. The six atoms divide into a group of four atoms that shuffle by 0:63 A and two atoms by 0:42 A. Combining these shuffles with strains of exx 0:09, eyy 0:12, and ezz 0:02 produces a final ! cell from our cell. The original matrix is oriented relative to the ! matrix such that 0001 k 0 111 ! and 11 20 k 01 11 !. These orientation relations are seen in some experiments, but not in others [5,6,8]. Our pathway identification method matches (i) pos-