MSE 2022
Lecture
28.09.2022
Difficult phase diagrams: using crystallographic information to understand phase equilibria
AL

Prof. Dr. Andreas Leineweber

Technische Universität Bergakademie Freiberg

Leineweber, A. (Speaker)¹; Becker, H.²; Fabrichnaya, O.²; Kriegel, M.J.²; Martin, S.²
¹Technische Universität Bergakademie Freiberg; ²TU Bergakademie Freiberg
Vorschau
18 Min. Untertitel (CC)

Fundamental basis for the understanding of the heat-treatment behaviour of a particular multicomponent system is the bulk thermodynamic properties of the system. These bulk thermodynamic properties can typically be modelled using the CALPHAD (CALculation of PHAse Diagram) method by formulating the composition-, temperature- and possibly pressure-dependent Gibbs energy functions of the relevant phases occurring in the system. Thereby, the crystallographic information of these phases is relevant for multiple reasons: (i) The crystal structure determined experimentally is typically the basis for the sublattice model formulated for a phase within the compound-energy formalism and thus the physical basis in particular for the modelling of its configurational entropy. (ii) Sublattice occupancies and compositions (especially in equilibrium with other phases) determined by crystal structure analysis can be valuable information for assessing thermodynamic parameters of a phase.
Own experience in trying to review crystallographic information from the literature and own experiments for consideration upon thermodynamic modelling has taught some lessons that all this is not always a straightforward process:
(a) There are often multiple ways to arrive at a structure model, which is compatible with diffraction data, and preference of a specific way is often influenced by the crystallographer’s preferences in setting up such models. Determination of atomistic structure chemical features are often the main motivation for crystal structure analysis, and the desire to produce a model suitable for use within the compound energy formalism.
(b) The crystallographer’s preferences and experimental limitations during structure analysis sometimes even lead to apparently contradicting structure models with differing unit cells and space groups, suggesting the presence of more phases than present in reality. Assessing literature in this respect is a particular challenge as it requires finding out whether diffraction information available is really contradictory and whether it really require existence of multiple phases. This requires identification of the common and differing features of the structure models which critically have to be against available diffraction information. Moreover, it has to be critically assessed whether some low-symmetry state really constitute an equilibrium state besides some high-symmetry state, since there are erroneous ways to conclude symmetry breaking.
(c) Even the observation of truly distinct crystal structure should not be taken as definite sign for existence of truly differing phases as the material having such structures may not be in true thermal equilibrium with any other phases.
Examples can be presented from the authors’ activities in the Nb-Cr, Cu-Sn, Fe-Al and Fe-Al-Si systems.

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