Abstract The Pt 3 Hf compound plays a decisive role in strengthening Pt–Hf alloy systems. Evaluating the stacking fault, dislocation dissociation, and twinning mechanisms in Pt 3 Hf 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 Pt 3 Hf 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 $$a\left\langle {1\bar{1}0} \right\rangle$$ a 1 1 ¯ 0 superdislocation will dissociate into two collinear $${a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1 ¯ 0 superpartial dislocations. The $${a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1 ¯ 0 dislocation could further dissociate into a $${a \mathord{\left/ {\vphantom {a 6}} \right. \kern-0pt} 6}\left\langle {\bar{1}\bar{1}2} \right\rangle$$ a / 6 1 ¯ 1 ¯ 2 Shockley dislocation and a $${a \mathord{\left/ {\vphantom {a 3}} \right. \kern-0pt} 3}\left\langle {2\bar{1}\bar{1}} \right\rangle$$ a / 3 2 1 ¯ 1 ¯ super-Shockley dislocation connected by a SISF, which results in an APB → SISF transformation. The study also discovered that Pt 3 Hf exhibits normal yield behavior, although the cross-slip of a $${a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1 ¯ 0 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 $${a \mathord{\left/ {\vphantom {a 2}} \right. \kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1 ¯ 0 dislocation slipping may change from the {111} planes to the {100} planes. Graphical abstract

中文翻译：

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Pt3Hf 化合物中的堆垛层错、位错解离和孪晶：DFT 研究

摘要 Pt 3 Hf 化合物在强化 Pt-Hf 合金体系方面起着决定性作用。评估 Pt 3 Hf 中的堆垛层错、位错解离和孪生机制是了解其塑性行为的第一步。在这项工作中，广义堆垛层错能 (GSFE)，包括复杂堆垛层错 (CSF)、超晶格本征堆垛层错 (SISF) 和反相边界 (APB) 能量，使用第一性原理计算进行计算。在将 Pt 3 Hf 纳入 Peierls-Nabarro 模型后，基于 GSFE 讨论了 Pt 3 Hf 的位错解离、变形孪晶和屈服行为。我们发现(111)APB的不稳定堆垛层错能(γus)低于SISF和(010)APB，这意味着 (111)APB 生成所需的能量势垒和临界应力低于 (010)APB 形成所需的那些。这个结果表明 $$a\left\langle {1\bar{1}0} \right\rangle$$ 一个 1 ¯ 0 超位错将解离成两个共线的 $${a \mathord{\left/ {\ vphantom {a 2}} \right。\kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1 ¯ 0 超偏位错。$${a \mathord{\left/ {\vphantom {a 2}} \right。\kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1¯ 0 位错可以进一步分解为 $${a \mathord{\left/ { \vphantom {a 6}} \对。\kern-0pt} 6}\left\langle {\bar{1}\bar{1}2} \right\rangle$$ a / 6 1 ¯ 1 ¯ 2 肖克利位错和 $${a \mathord{\左/ {\vphantom {a 3}} \right。\kern-0pt} 3}\left\langle {2\bar{1}\bar{1}} \right\rangle$$ a / 3 2 1 ¯ 1 ¯ 超肖克利位错由 SISF 连接，导致APB → SISF 转换。该研究还发现 Pt 3 Hf 表现出正常的屈服行为，尽管 $${a \mathord{\left/ {\vphantom {a 2}} \right 的交叉滑移。\kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1¯ 0 错位不被禁止，并且满足异常屈服准则。此外，据观察，APB 形成的能量势垒和临界应力随着压力的增加而增加，并随着温度的升高而降低。当温度升至 1400 K 以上时，$${a \mathord{\left/ {\vphantom {a 2}} \right。\kern-0pt} 2}\left\langle {1\bar{1}0} \right\rangle$$ a / 2 1 1 ¯ 0 位错滑移可能从{111}面变为{100}面。图形概要