Abstract We examine the equilibrium morphology of Al 2 Cu ( θ ′) precipitates in Al-Cu alloys using a phase field method with the parameters supplied by first-principles density functional theory (DFT) calculations. The phase field method employed allows for an interfacial energy that is highly anisotropic: there are missing high-energy orientations and corners on the Wulff shape. This high degree of anisotropic interfacial energy yields a plate-shaped equilibrium θ ′ precipitate in two-dimensions and a disk-like shape in three dimensions. Also, we consider the effects of a mismatch in elastic-moduli (elastic inhomogeneity) of Al and θ ′, elastic anisotropy, as well as tetragonal misfit strain anisotropy to gain a fuller picture of the elastic energy contributions to the morphology of θ ′ precipitates. Based on our phase-field modeling, the results show that the aspect ratio of the precipitate morphology with the anisotropy of interfacial and strain energies as given by DFT is significantly smaller than the aspect ratio observed in the experiment after long aging times (∼50 h). Specifically, the computed length (54 nm) is almost ten-times smaller than the length (∼580 nm) observed in the Al-Cu experiment with similar precipitate thickness (∼10 nm). Thus, we conclude that the experimental morphology after long aging times (∼50 h) is strongly influenced by the kinetics of precipitate growth.

中文翻译：

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Al-Cu合金中θ′析出的第一性原理/相场模拟

摘要 我们使用由第一性原理密度泛函理论 (DFT) 计算提供的参数，使用相场方法研究了 Al-Cu 合金中 Al 2 Cu ( θ ') 析出物的平衡形态。所采用的相场方法允许高度各向异性的界面能量：Wulff 形状上缺少高能量方向和拐角。这种高度的各向异性界面能产生了二维的板状平衡 θ ' 和三维的圆盘状。此外，我们考虑了 Al 和 θ ' 的弹性模量（弹性不均匀性）、弹性各向异性以及四方错配应变各向异性的失配的影响，以更全面地了解弹性能量对 θ ' 析出物形态的贡献. 基于我们的相场建模，结果表明，DFT 给出的具有界面能和应变能各向异性的析出物形态的纵横比显着小于长时间老化（~50 h）后实验中观察到的纵横比。具体而言，计算出的长度（54 nm）几乎比在具有相似沉淀厚度（~10 nm）的 Al-Cu 实验中观察到的长度（~580 nm）小十倍。因此，我们得出结论，长时间老化（~50 小时）后的实验形态受沉淀物生长动力学的强烈影响。计算出的长度 (54 nm) 几乎比在具有相似沉淀厚度 (~10 nm) 的 Al-Cu 实验中观察到的长度 (~580 nm) 小十倍。因此，我们得出结论，长时间老化（~50 小时）后的实验形态受沉淀物生长动力学的强烈影响。计算出的长度 (54 nm) 几乎比在具有相似沉淀厚度 (~10 nm) 的 Al-Cu 实验中观察到的长度 (~580 nm) 小十倍。因此，我们得出结论，长时间老化（~50 小时）后的实验形态受沉淀物生长动力学的强烈影响。