Solid-State Phase Transformations and Reactions

Abstract

In Chapters 14 and 15, we discussed grain boundaries (GBs) and phase boundaries (PBs), respectively. Those two chapters described the interfaces and crystal defects. In Chapter 24, we then examined how the movement of GBs can lead to sintering, grain growth, and densification. In the present chapter, we examine how the movement of PBs leads to transformations and reactions. Some examples of reactions involving the movement of a PB are given in Table 25.1: Not all of these are solid-state reactions.

1 People and history

Schmalzried, Hermann (1932–). An exception to the rule. Formerly a postdoctoral student with Carl Wagner, Hermann has been a mentor and inspiration to many of the current generation of researchers in the field of solid-state reactions in ceramic systems and is profusely thanked by the authors.

Wagner, Carl (1901–1977). He was born in Leipzig and died in Göttingen. He wrote the seminal text with Schottky and laid the foundations for understanding corrosion and reactions between oxides.

2 Exercises

• 25.1 Two cubes (400 m long on each side) of NiO and Al₂O₃ are reacted at 1,600°C. Assuming that the reaction takes place without significant movement of electrons or oxygen and that a reaction layer is produced that is 100 m thick, what are the respective thicknesses of the remaining NiO and Al₂O₃?

• 25.2 Given the densities of some of the polymorphs of SiO₂, should it be possible to convert -cristobalite to some of the other forms by applying pressure? Briefly explain the reasoning behind your answer and indicate to which of the four forms, if any, the transformation might occur.

• 25.3 Calcium carbonate (CaCO₃) exists in two polymorphic forms: calcite and aragonite. The standard state enthalpy of calcite is −1,207.37 kJ/mol, and that of aragonite is −1,207.74 kJ/mol. The entropies of aragonite and calcite under the same conditions are 88 J mol⁻¹ K⁻¹ and 91.7 J mol⁻¹ K⁻¹, respectively. What is the stable polymorph at 25°C and 1 atm? Is there a temperature above which the other polymorph would be the equilibrium phase? If so, what is that temperature? If not, why not?

• 25.4 You want to prepare a sample of mullite by reacting alumina and silica powders. If the activation energy is 210 kJ/mol and the reaction is 10% complete at 1,400°C, how long would it take to convert 50% to mullite at 1,400°C and at 1,500°C? How do you determine that 50% has indeed been converted?

• 25.5 You place two perfect crystals of alumina and magnesia in contact with flat (0001) and (111) surfaces in contact. What orientation do you choose to produce the fast reaction when you heat these to 1,400°C for 1 h? You make the assumption that oxygen does not move during this heat treatment, but this cannot be strictly true. Explain.

• 25.6 You react two samples of alumina and magnesia at 1,400°C for 1 h. This time the MgO is a perfect single crystal, but the alumina is 100-nm grain size polycrystalline material. Does the reaction proceed more quickly or more slowly on average?

• 25.7 Explain the geometry of the precipitates in Figure 25.5 and the defects they contain.

• 25.8 Consider Figure 25.13. What can you determine about the activation energies involved and the diffusion processes?

• 25.9 Consider Figure 25.21. How do you explain the experimental observations in the images in view of the phase diagram and other factors you know about these materials?

• 25.10 Consider Figure 25.24. What can you determine about the energies involved in this reaction?

• 25.11 Imagine the particle in Figure 25.7 growing as the sample is internally reduced. Discuss the diffusion of point defects that must occur.

• 25.12 Draw a schematic to show six atomic planes of Fe₂O₃ and six of NiFe₂O₄ aligned with (0001) and parallel to (111). Label them as if they were hexagonal close-packed (hcp) and face-centered cubic (fcc) crystals and suggest how the hematite might grow in the spinel by exsolution.

• 25.13 Draw a nucleus of the particle of the type shown in Figure 25.5, and then draw it again as it begins to grow. Thereby, suggest when and how the twins might form.

• 25.14 Consider Figure 25.10. Which surface of the sapphire is reacting the fastest, and why do you think this is so?

• 25.15 Determine equation 25.5 for yourself and suggest reasonable values for each of the variables and “constants” for the case of water penetrating through a layer of slip.

• 25.16 A layer of MgO reacts with a layer of Al₂O₃ such that only the cations move. By considering Figure 25.12, show that the spinel grows into the sapphire faster than into the periclase.

• 25.17 Consider equation 25.12 and Figure 25.15. What can you deduce about the average diffusion coefficient?

• 25.18 Consider Figure 25.18B. Explain quantitatively why the spinel nucleates where the grain boundary (GB) meets the substrate surface.

• 25.19 Consider Figure 25.20. Are the three straight lines consistent with one another? (Is T the only factor that is different in the three experiments?)

• 25.20 Consider Figure 25.24. What can you deduce about the dissolution of sapphire in silicate glass?