# Ab Initio Investigation of Interfacial and Grain Boundary Properties of Metals and Alloys

**Time: **
Tue 2023-05-23 10.00

**Location: **
F3, Lindstedtsvägen 26 & 28, Stockholm

**Language: **
English

**Subject area: **
Materials Science and Engineering

**Doctoral student: **
Changle Li
, Egenskaper, Applied Materials Physics

**Opponent: **
Prof. Dr. Hongbin Zhang, Technische Universität Darmstadt

**Supervisor: **
Professor Levente Vitos, Egenskaper, Tillämpad fysik; Dr Song Lu, Egenskaper

## Abstract

Phase interface (IF) and grain boundary (GB) are both common yet critical planar defects influencing the mechanical and physical properties of polycrystalline materials. Due to the complex nature of IFs and GBs in terms of structure and chemistry, determining the accurate excess energies associated with these defects is challenging for both experimental measurements and theoretical simulations. In this thesis, using first-principles methods, I make efforts towards establishing an efficient and robust model for predicting the IF and GB properties in elemental metals and complex multi-component alloys including the temperature and composition dependences.

First I focus on the temperature dependent interfacial energy (IFE) for Cu-Co alloys. IFE plays a critical role in determining the nucleation and precipitate coarsening thermodynamics and kinetics. I start with assessing the phase diagram of Cu-Co alloys by ab initio calculations, which is used for establishing the composition-temperature relationship of precipitates and matrix. Calculations of the physical and thermodynamic properties for the ferromagnetic (FM) and paramagnetic (PM) $\ce{Cu}_{1-x}\ce{Co}_{x}$ solid solutions are performed using the exact muffin-tin orbital (EMTO) method in combination with the coherent potential approximation (CPA) for dealing chemical and magnetic randomness. This study demonstrates that the equilibrium volumes and magnetic states are crucial for a quantitative description of the thermodynamics of the Cu-Co system at temperatures up to 1400 K. The predicted ab initio Cu-Co phase diagram is in good agreement with the measurements and CALPHAD data. Then, the composition and magnetic dependent IFEs for a coherent $\ce{Cu}_{1-x}\ce{Co}_{x}$/$\ce{Cu}_{x}\ce{Co}_{1-x}$ interface are investigated at various magnetic states including FM, PM, and the mixed PM+FM states to account for the magnetic state change at different temperatures. Then, I translate the composition dependence of the IFE to the temperature dependence. The obtained results are in reasonable agreement with those obtained by experiments and thermodynamic calculations. The first part of the thesis provides an ab initio database for the IFEs in Cu-Co system and emphasizes the importance of understanding and properly describing various physical and thermodynamic quantities in different materials modeling approaches.

The second focus of this thesis is on grain boundary energy (GBE). We calculate the GBEs for ten face-centered cubic (fcc) and seven body-centered cubic (bcc) metals. Various types of symmetric tilt GB structures ranging from twin boundary up to $\Sigma$19 coincident site lattice (CSL) boundaries are studied using the Vienna Ab initio Simulation Package (VASP). Ab initio results show a correlation between the GBEs of the same grain boundary structure in different fcc and bcc metals. Importantly, I show that the correlation factor is best determined by the ratio of the low-index surface energy. By using this correlation, the general GBEs of fcc and bcc metals are predicted at 0 K. Furthermore, using the Foiles's method, which assumes that the general GBE has a similar temperature dependence as the elastic modulus $c_{44}$, the general GBEs at elevated temperatures are predicted. The so obtained theoretical results show a good agreement with the available experimental data. Finally, the proposed method for predicting the general GBEs is applied to complex multicomponent alloys (austinite Fe-Cr-Ni and ferritic Fe-Cr alloys), yielding a parameterized prediction of the composition and temperature dependent GBE. After examining two common experimental methods used for determining the general GBEs, it is concluded that the two sets of experimental GBEs for fcc metals agree well with each other, while for bcc metals they correspond to different grain boundary structures and differ by a factor of 2. This part of the thesis introduces an effective and robust model for predicting the general GBEs of metals and alloys, facilitating grain boundary engineering for advanced alloy design.

The third focus is on alloying GB segregation in complex alloys. Manganese (Mn) and Nickel (Ni) segregation behaviors at bcc Fe-Cr grain boundaries are investigated. In this segregation study, three GB structures, namely, $\Sigma$3(111), $\Sigma$9(114), and $\Sigma$11(332), are considered. First, a systematic comparison of the theoretical segregation energies for Mn and Ni solutes in pure Fe GBs is conducted between VASP and EMTO calculations. The EMTO results agree reasonably with VASP and previous theoretical data, indicating a reliable potential for capturing the solute segregation behaviors. Next, the Mn and Ni segregation energies at bcc Fe-Cr solid solution GBs are determined at various concentrations of the matrix and at the FM and PM states to account for the temperature effects on the magnetic state using the EMTO-CPA method. Strong magnetic effects on the segregation energy are observed. Particularly, it is found that the magnetic states of Mn atoms depend strongly on local chemical and structural environment, which has a remarkable effect on the segregation energy. It is found that Mn and Ni show different segregation tendencies at FM and PM states. This part of the thesis puts forward an attempt to investigate the solute segregation properties in complex solid solutions as compared to pure metal or dilute alloys, and improves our understanding of GB segregation in engineering alloys, like steels.