Entropy: A controversy between experiment and calculations in grain boundary segregation

Grain boundary segregation is one of the crucial phenomena affecting the properties of the materials and their technological applications. However, 50 years since starting its intensive study, there still remain open questions and controversies related to this phenomenon. Probably, the most serious uncertainty consists in understanding the segregation entropy. While this term seems to result directly from experimental studies of temperature dependence of chemical composition of grain boundaries, it is mostly neglected in theoretical calculations. This negligence arises from the fact that most of the first-principles calculations are performed at the temperature of 0 K and, therefore, the segregation entropy is usually not evaluated. Consequently, it is supposed that its contribution at enhanced temperatures is negligible which is supported by scarce calculations of the vibrational entropy of grain boundary segregation. Another question discussed presently between theoreticians on one hand and experimenters on the other hand deals with physical meaning of the values of the thermodynamic quantities determined from the average grain boundary concentration.This paper summarizes the present knowledge on the segregation entropy in metallic hosts and documents some issues in which the segregation entropy plays important and irreplaceable role. These issues are represented by the enthalpy–entropy compensation effect, by the method of prediction of grain boundary segregation and by comparison of calculated results and experimental or predicted data. The role of the entropy is also crucial in the recently discussed cases of the entropy-dominated and entropy-driven grain boundary segregation. Finally, collective processes related to grain boundaries – grain boundary migration and intergranular fracture – are discussed suggesting that these processes, based on coordinated behavior of numerous neighbor atoms in the grain boundary core, will be better characterized by average values of characteristic quantities rather than by the values of these quantities for individual sites.