Role of entropy in anistropy of grain boundary segregation

Abstract

From the viewpoint of existence of linear dependence between entropy and enthalpy of grain boundary segregation, the meaning of the entropy term is discussed. It is suggested that negative values of segregation entropy for silicon segregation at individual grain boundaries in α‐iron reflect an ‘ordering’ tendency of the interfaces due to the presence of silicon. On the other hand, positive values of segregation entropy suggest a ‘disordering’ of the structure of these grain boundaries by segregation of carbon and mainly of phosphorus. The effect of ‘disordering’ is especially high for special grain boundaries with compact intrinsic structure, resulting in high values of segregation entropy. The slope of the dependence of enthalpy on entropy of solute segregation at different grain boundaries can be considered as a compensation temperature. Its existence implies that an anisotropy of grain boundary chemical composition will possess a qualitatively different character above and under this temperature. This anisotropy measured above the compensation temperature will be characterized by high values of grain boundary concentration for special boundaries as compared to general boundaries. © 1998 John Wiley & Sons, Ltd.

Solute segregation at grain boundaries

“…The value A/tp ~ = -33 kJ/mol determined from these model calculations is in very good agreement with the value -34.3 kJ/mol found by Erhart and Grabke [51] for phosphorus segregation in polycrystaUine u-Fe. The use of maximum values of grain boundary segregation for determination of "more realistic" values of parameters AH ~ and AS ~ was found to be very sensitive to the random presence of a single grain boundary exhibiting large segregation effects at the fracture surface [53]. Another reasonable description of grain boundary segregation in polycrystals seems to be the use of a spectrum of grain boundary free energies [54][55][56].…”

“…Besides for the polycrystalline Fe-and Ni-doped W base alloy [37] already mentioned above, Eqs. (1) and (2) have been used to correlate the temperature dependences of grain boundary composition of well-characterized grain boundaries in an Fe-3.55 at.% Si alloy [39,[44][45][46][47], and in a Ni-rich Ni3AI(B) [38]. The respective values of segregation enthalpies AH ~ and entropies AS ~ determined in these studies at individual grain boundaries are compiled in Table 3.…”

“…Thus, the question arises about the physical meaning of the quantities A/t ~ and AS ~ determined in this way. In order to find a relationship between A/~ ~ and AS ~ and the corresponding values of segregation enthalpies and entropies, respectively, for individual grain boundaries, Lej~ek [53] modeled polycrystalline fracture surfaces from the boundaries of known segregation behavior and found that this relationship is very complex. Only if the arithmetic average of the boundary concentration is equal (or close) to the geometric average, the values of AH ~ and AS ~ represent the arithmetic averages of AHt ~ and AS ~ of individual grain boundaries.…”

Effect of Grain Size on Grain Boundary Segregation Thermodynamics of Phosphorus in Interstitial-Free and 2.25Cr-1Mo Steels

“…The closer to zero is the segregation entropy, the higher the segregation enthalpy is. The unified linear relationship between the segregation entropy and enthalpy can be expressed as: Lejček et al [6][7][8]24] analyzed the grain boundary segregation data from many Fe-based alloy systems. The involved segregating impurity elements mainly include phosphorus, sulfur, tin, silicon, antimony and so on.…”

“…Lejcek et al [4][5][6][7][8] gathered numbers of experimental results from the literatures and analyzed in detail the thermodynamics of grain boundary segregation of several solute/impurity elements. A key discovery of their work is that a linear relationship between segregation entropies and enthalpies of solute atoms exists in multiple alloy systems.…”