Applied Thermodynamics: Grain Boundary Segregation

Atomistic Assessment of Solute-Solute Interactions during Grain Boundary Segregation

Grain boundary solute segregation is becoming increasingly common as a means of stabilizing nanocrystalline alloys. Thermodynamic models for grain boundary segregation have recently revealed the need for spectral information, i.e., the full distribution of environments available at the grain boundary during segregation, in order to capture the essential physics of the problem for complex systems like nanocrystalline materials. However, there has been only one proposed method of extending spectral segregation models beyond the dilute limit, and it is based on simple, fitted parameters that are not atomistically informed. In this work, we present a physically motived atomistic method to measure the full distribution of solute-solute interaction energies at the grain boundaries in a polycrystalline environment. We then cast the results into a simple thermodynamic model, analyze the Al(Mg) system as a case study, and demonstrate strong agreement with physically rigorous hybrid Monte Carlo/molecular statics simulations. This approach provides a means of rapidly measuring key interactions for non-dilute grain boundary segregation for any system with an interatomic potential.

Diffusion of strontium implanted in glassy carbon

Glassy carbon has properties making it attractive as a containment material for radioactive waste. In this study, the diffusivity of the radiological important fission product, strontium, is measured. Two hundred kiloelectronvolt strontium ions were implanted at room temperature. The implanted samples were either annealed isochronally for 1 h up to 900°C or by increasing the temperature linearly up to 648°C. The Sr profiles were determined by Rutherford backscattering spectrometry (RBS). The isochronally annealed samples showed Fickian diffusion at 300°C ( D  = 6.7 × 10 −19  m 2  s −1 ) with segregation occurring at the higher temperatures. Raman spectroscopy indicated a link between damage annealing and the onset of segregation. During increasing temperature, the system is dynamic with diffusion taking place. An equation to determine diffusion coefficients for ramped heating was derived. Fickian diffusion occurred with an activation energy of 1.97 eV for 414–454°C, and from 458 to 558°C, it was 0.184 eV. At higher temperatures, a segregation of the strontium towards the surface was observed. A calculation of the heat of segregation of Sr in carbon supports this segregation. The results show that the in situ RBS measurements with a linear increase in temperature give additional information compared with the conventional isochronal annealing.

The Significance of Entropy in Grain Boundary Segregation

The role of entropy in materials science is demonstrated in this report in order to establish its importance for the example of solute segregation at the grain boundaries of bcc iron. We show that substantial differences in grain boundary chemistry arise if their composition is calculated with or without consideration of the entropic term. Another example which clearly documents the necessity of implementing the entropic term in materials science is the enthalpy-entropy compensation effect. Entropy also plays a decisive role in the anisotropy of grain boundary segregation and in interface characterization. The consequences of the ambiguous determination of grain boundary segregation on the prediction of materials behavior are also briefly discussed. All the mentioned examples prove the importance of entropy in the quantification of grain boundary segregation and consequently of other materials properties.

Interstitial and substitutional solute segregation at individual grain boundaries of α-iron: data revisited

Theoretical calculations (usually density-functional-theory methods performed at 0 K) confirm the formerly assumed substitutional phosphorus segregation in α-iron. In contrast, the enthalpy-entropy compensation effect predicts that phosphorus should segregate interstitially. To resolve this discrepancy, we recalculated the values of the segregation enthalpy and entropy for the interstitial segregation of phosphorus according to the Guttmann model of segregation in multicomponent systems. This recalculation is based on earlier measured experimental data and shows that only slight changes in the values of the standard enthalpy and entropy of phosphorus, carbon and silicon segregation are obtained. Consequently, all dependences constructed previously remain qualitatively the same. By thermodynamic considerations based on the enthalpy-entropy compensation effect we quantitatively show that there is an alteration of the position of phosphorus at grain boundaries in α-Fe with increasing temperature: while substitutional segregation is preferred at 0 K, interstitial segregation occurs at temperatures of practical interest.