含掺杂剂的原子尺度相场建模：具有分数占位的随机自洽谐波近似
Atomic-scale phase-field modeling with dopants: Stochastic self-consistent harmonic approximation with fractional site occupancy
AI总结：
研究将相场概念扩展到原子尺度，基于随机自洽谐波近似理论制定原子系统自由能，通过计算自由能导数获化学势，成功再现银在铜中的分布及晶格膨胀，还研究了晶界掺杂剂偏析，可识别偏析位点并可视化原子尺度图案形成。
AI中文摘要：
相场建模在预测材料中的图案形成方面取得了巨大成功，如铁电畴的形成。然而，传统相场建模基于连续介质力学，无法直接应用于由化学势驱动的原子尺度图案形成，如掺杂剂偏析和空位有序化。本文通过在随机自洽谐波近似（SSCHA）理论中制定原子系统的自由能，将相场概念扩展到原子尺度，以允许分数占位。该方法能够直接计算自由能相对于占位的导数，从而获得化学势，成功再现了块状铜中的银分布以及由此产生的晶格膨胀。此外，还将该方法应用于研究掺杂银原子的Σ5(310)[001]铜晶界周围的掺杂剂偏析。发现银原子优先在晶界三角形图案的顶点偏析。随着掺杂剂数量的增加，多余的银原子先在顶点附近偏析，然后在三角形图案的底部位置偏析。本研究将相场概念扩展到离散原子系统，能够识别优先的掺杂剂偏析位点，从而可视化原子尺度的图案形成。
英文摘要：
Phase-field modeling has achieved great success in predicting pattern formation in materials, such as the formation of ferroelectric domains. However, because it is typically based on continuum mechanics, conventional phase-field modeling cannot be straightforwardly applied to atomic-scale pattern formation, such as dopant segregation and vacancy ordering, which are driven by chemical potentials. Here, we extend the phase-field concept to the atomic scale by formulating the free energy of atomic systems within stochastic self-consistent harmonic approximation (SSCHA) theory to allow fractional site occupations. Our methodology enables us to directly calculate the derivative of the free energy with respect to site occupation and thereby obtain the chemical potential, successfully reproducing Ag distributions in bulk Cu as well as the resulting lattice expansion. Furthermore, we applied our methodology to investigate dopant segregation around a Σ5(310)[001] Cu grain boundary doped with Ag atoms. We found that Ag atoms preferentially segregate at the vertices of the triangular motif of a grain boundary. As the number of dopants increases, excess Ag atoms segregate near the vertices and then at the bottom sites of the triangular motif. This study extends the phase-field concept to discrete atomic systems, enabling the identification of preferential dopant-segregation sites and thereby visualizing atomic-scale pattern formation.
