The Thermodynamics of Short Range Order

Abstract

In many important phase transformations in minerals transformation occurs by way of modulated structures. This is true in the case of the plagioclase feldspars and potassium feldspar, and an excellent example of modulated structures is found in the transformation of cordierite. Knowledge of the general characteristics of these microstructures has long been available from electron microscopy but a proper understanding of their origins in terms of the interaction between different possible ordering schemes, and between ordering and displacement modes is only now becoming available. Current advances in understanding in this field are due primarily to the application of symmetry principles as contained in group theory. In this chapter these principles will be discussed in some detail and then used to elucidate a number of the more important examples of short range interactions and ordering in modulated mineral structures. The analysis begins with an account of the origin of simple incommensurate structures in minerals. These can best be understood in terms of interaction of two different structures in a short range distribution. From this point the analysis proceeds to a consideration of the interaction of three or more components and deals in detail with the interaction between local ordering and two displacement waves. This effect, which may be described as a triple product interaction, or three component interaction, gives rise to a very important third order term in the Landau free energy expansion, and results in a phase transformation of first order character. The triple product interaction is observed in both potassium feldspar and cordierite and both examples will be discussed in some detail in this chapter. It is relevant to note that the theory which is discussed in this chapter is not simply relevant in the case of modulated mineral structures. Some of the best examples of the triple product interaction occur in martensitic transformations in alloys, and examples of two component interactions leading to incommensurate structures are legion in both organic and inorganic materials.