Stacking fault, dislocation dissociation, and twinning in Pt₃Hf compounds: a DFT study

The Pt₃Hf compound plays a decisive role in strengthening Pt–Hf alloy systems. Evaluating the stacking fault, dislocation dissociation, and twinning mechanisms in Pt₃Hf is the first step in understanding its plastic behavior. In this work, the generalized stacking fault energies (GSFE), including the complex stacking fault (CSF), the superlattice intrinsic stacking fault (SISF), and the antiphase boundary (APB) energies, are calculated using first-principles calculations. The dislocation dissociation, deformation twinning, and yield behavior of Pt₃Hf are discussed based on GSFE after their incorporation into the Peierls-Nabarro model. We found that the unstable stacking fault energy (γ_us) of (111)APB is lower than that of SISF and (010) APB, implying that the energy barrier and critical stress required for (111)APB generation are lower than those required for (010)APB formation. This result indicates that the \(a\left\langle {1\bar{1}0} \right\rangle\) superdislocation will dissociate into two collinear \({a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle\) superpartial dislocations. The \({a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle\) dislocation could further dissociate into a \({a \mathord{\left/ {\vphantom {a 6}} \right. \kern-0pt} 6}\left\langle {\bar{1}\bar{1}2} \right\rangle\) Shockley dislocation and a \({a \mathord{\left/ {\vphantom {a 3}} \right. \kern-0pt} 3}\left\langle {2\bar{1}\bar{1}} \right\rangle\) super-Shockley dislocation connected by a SISF, which results in an APB → SISF transformation. The study also discovered that Pt₃Hf exhibits normal yield behavior, although the cross-slip of a \({a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle\) dislocation is not forbidden, and the anomalous yield criterion is satisfied. Moreover, it is observed that the energy barrier and critical stress for APB formation increases with increasing pressure and decreases as the temperature is elevated. When the temperature rises above 1400 K, the \({a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle\) dislocation slipping may change from the {111} planes to the {100} planes.