In this work we re-assess experimental data for grain boundary (GB) segregation of P in bcc Fe with thermodynamic and statistical methods. The data are based on Auger-Electron-Spectroscopy (AES) measurements which have provided P GB concentrations for various bulk contents and temperatures for ferrite. While in the previous investigations of this system a single-site McLean equation was used to extract segregation enthalpy and entropy, we employ multi-site segregation models as suggested by atomistic simulations. We use a recently introduced methodology based on inter-atomic potentials to calculate the segregation energy spectrum, as well as vibrational entropy and solute-solute interactions of P in polycrystalline Fe, thereby obtaining a three-dimensional distribution of energy, entropy and interactions. Using this trivariate distribution we predict P GB concentrations and compare them to the experimental measurements. Furthermore, we calibrate the parameters of physical models of increasing complexity to the experimental data with an inverse modeling approach based on Bayesian inference. While it is not possible to seamlessly link the results from AES to atomistic modeling, our investigation provides significant new insights for thermodynamic modeling of GB segregation. The vibrational entropy deduced from experiment differs from physics based atomistic simulations even when taking the spectral nature of energy, entropy and interactions into account. However, the correlations of the quantities are in good agreement when considering the trivariate model. Our investigation highlights the need for new and more accurate experimental datasets of GB segregation.

中文翻译：

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Fe-P 系统的晶界偏析：原子建模和贝叶斯推理的见解


在这项工作中，我们使用热力学和统计方法重新评估了 bcc Fe 中 P 晶界 (GB) 偏析的实验数据。这些数据基于俄歇电子能谱 (AES) 测量，该测量提供了不同体积含量的 P GB 浓度和铁氧体的温度。虽然在该系统的先前研究中使用单点麦克莱恩方程来提取分离焓和熵，但我们采用原子模拟所建议的多点分离模型。我们采用最近推出的基于原子间势的方法来计算多晶Fe中P的偏析能谱、振动熵和溶质-溶质相互作用，从而获得能量、熵和相互作用的三维分布。使用这个三变量分布，我们预测 P GB 浓度并将其与实验测量值进行比较。此外，我们使用基于贝叶斯推理的逆向建模方法，根据实验数据校准日益复杂的物理模型的参数。虽然不可能将 AES 的结果无缝链接到原子建模，但我们的研究为 GB 分离的热力学建模提供了重要的新见解。即使考虑到能量、熵和相互作用的光谱性质，从实验推导出来的振动熵也不同于基于物理学的原子模拟。然而，在考虑三变量模型时，数量的相关性非常一致。我们的调查强调需要新的、更准确的 GB 分离实验数据集。