J.W. Christian

Bio: J.W. Christian is an academic researcher from University of Oxford. The author has contributed to research in topics: Crystal & Nucleation. The author has an hindex of 10, co-authored 16 publications receiving 8273 citations.

CHAPTER 11 – Theory of Thermally Activated Growth

Abstract: This chapter is concerned with the descriptive theory of growth in condensed phases. The chapter begins by considering the type of growth that is controlled by processes in the immediate vicinity of the interface. It may be supposed that there is a negligible change in volume and no change in composition as the boundary moves, this is almost true for many transformations, and even in interface controlled precipitation processes, the boundary conditions of the diffusion equation may be such that the composition gradients can be ignored. The distinction between stepped and continuous growth is sometimes made on the basis of the diffuseness of the interface such as the degree of atomic disorder and the extent of the transition region, rather than on grounds of the singularity of surface free energy.

Chapter 9 - Diffusion in the Solid State

Abstract: This chapter begins with a discussion of diffusion with a statement of Fick's law that is the analogue for material flow of Fourier's law for heat flow by conduction. Fick's equation retains its significance since experimental results are almost always presented in the form of diffusion coefficients defined by reference to it. A general account of diffusion can be developed without reference to the actual mechanism of atomic migration, but the more detailed theories depend on this mechanism. The chapter considers an assembly containing two or more kinds of different atoms. “Chemical” diffusion takes place when this assembly is not in equilibrium with respect to distribution of the different atomic species and “Tracer” diffusion presents a situation in which the assembly is in equilibrium, except for the distribution of two components that differ from each other in an insignificant manner (as far as the diffusion problem is concerned). In addition to this the chapter also discusses the effect of plastic deformation on diffusion rate.

CHAPTER 2 – Formal Geometry of Crystal Lattices

Abstract: This chapter explains the formal geometry of crystal lattices. Amorphous and quasi-crystalline forms of solids have been investigated in recent years but most solid metals are crystalline and some appreciation of crystallography is essential to a study of metallic transformations. The ideal crystal is classified by considering the symmetry properties of the atomic arrangement. The symmetry properties of the lattice are much more restricted, and there are only fourteen Bravais lattices, obtained from relations among the vectors a i . Instead of the primitive unit cell, it is often convenient to use a larger unit cell that illustrates the symmetry of the lattice positions. The scientific concept of a crystal has evolved gradually from the original classification by external shape to modern views on the internal atomic arrangement. The development of X-ray methods enabled the structure of a crystal to be investigated on a finer scale. The ideal crystal may be regarded as the repetition in three dimensions of some unit of structure, within which the position of each atom is specified exactly by a set of spatial coordinates.

CHAPTER 8 – Polycrystalline Aggregates

Abstract: A one-phase assembly is in true thermodynamical equilibrium only when it forms a single crystal, the exterior surface of which has the shape giving the minimum energy. Very large single crystals can often be grown by a suitable technique, but macroscopic specimens usually consist of a compact polycrystalline mass. The crystals are allotriomorphic—that is, their limiting surfaces are not regular and do not display the symmetry of the internal structure. In a single-phase assembly, neighbouring crystals differ only in the orientations of their respective lattices, it is then usual to refer to the individual crystals as the grains of the structure and the regions over which the lattice orientation changes are the grain boundaries. In a one-phase assembly, the orientations of the grains may be completely random, or there may be a preferred orientation induced by mechanical deformation or thermal treatment. A polycrystalline mass at high temperatures is able to reduce its grain boundary energy, and hence its total free energy, by atomic movements over relatively short distances.

CHAPTER 5 – The Structure of Real Metals

Abstract: This chapter discusses the approximate models of the structure of ideal solids. It considers the properties of point defects with the assumptions that the vast majority of the atoms present in a real crystal lie in regions of good crystal, so that it can be justified to treat this real crystal as an ideal crystal with a distribution of defects. The concept of a defect implies that a localized region of the actual crystal can be associated unambiguously with a corresponding region of the ideal crystal. The justification for this assumption is that it accords with experimental evidence; for example, the chapter may cite the way in which the ideal structure may be inferred from X-ray diffraction experiments on real crystals. Although the two sets of atoms may not have identical mean positions, the differences can be described by small (elastic) displacements, and it is always possible to establish a unique one to one correspondence between the atoms of the two crystals. Regions of crystal where this local correspondence is possible are called “good” crystal; the remaining regions of “bad” crystal may be considered to be localized defects in the structure.

Mechanical Behavior of Materials

Abstract: A balanced mechanics-materials approach and coverage of the latest developments in biomaterials and electronic materials, the new edition of this popular text is the most thorough and modern book available for upper-level undergraduate courses on the mechanical behavior of materials To ensure that the student gains a thorough understanding the authors present the fundamental mechanisms that operate at micro- and nano-meter level across a wide-range of materials, in a way that is mathematically simple and requires no extensive knowledge of materials This integrated approach provides a conceptual presentation that shows how the microstructure of a material controls its mechanical behavior, and this is reinforced through extensive use of micrographs and illustrations New worked examples and exercises help the student test their understanding Further resources for this title, including lecture slides of select illustrations and solutions for exercises, are available online at wwwcambridgeorg/97800521866758

Fine phase mixtures as minimizers of energy

Abstract: Solid-solid phase transformations often lead to certain characteristic microstructural features involving fine mixtures of the phases. In martensitic transformations one such feature is a plane interface which separates one homogeneous phase, austenite, from a very fine mixture of twins of the other phase, martensite. In quartz crystals held in a temperature gradient near the α-β transformation temperature, the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature. In this paper we explore a theoretical approach to these fine phase mixtures based on the minimization of free energy.