The Measurement of Grain Boundary Geometry

Valerie Randle

• Editorial: CRC Press
• Año: 2017
• ISBN:
  9781351409872
• Edición: 1
• Categoría: Ciencias físicas
• Categoría: Historia y práctica de la ciencia

As the selection of material for particular engineering properties becomes increasingly important in keeping costs down, methods for evaluating material properties also become more relevant. One such method examines the geometry of grain boundaries, which reveals much about the properties of the material.Studying material properties from their geometrical measurements, The Measurement of Grain Boundary Geometry provides a framework for a specialized application of electron microscopy for metals and alloys and, by extension, for ceramics, minerals, and semiconductors. The book presents an overview of the developments in the theory of grain boundary geometry and its practical applications in material engineering. It also covers the tunneling electron microscope (TEM), experimental aspects of data collection, data processing, and examples from actual investigations. Each step of the analysis process is clearly described, from data collection through processing, analysis, representation, and display to applications. The book also includes a glossary of terms.Exploring both the experimental and analytical aspects of the subject, this practical reference guide is essential for researchers and students involved in material properties, whether in physics, materials science, metallurgy, or physical chemistry.

1

Introduction

1.1 Significance of Grain Boundaries in Polycrystals

The surface where two dissimilarly oriented crystals (grains) meet constitutes a grain boundary; thus at the most simple level a grain boundary (GB) is a crystallographic discontinuity. The GB width is on average less than two atomic diameters, which is sufficiently small for attractive forces to act across it, therefore the component grains in polycrystals remain united across GBs. However, GBs are far from being just inert surfaces which demarcate changes in orientation. The following important phenomena are influenced by GBs:

1. Phenomena directly resulting from movement (migration, sliding) of the GB itself (Aust and Rutter, 1959), e.g. recrystallisation (Berger et al, 1988), grain growth (Randle and Ralph, 1988a), creep (Ralph, 1980);

2. Transport phenomena e.g. solute segregation (Bouchet and Priester, 1987) or corrosion (Palumbo and Aust, 1990a);

2. Chemical reactions e.g. precipitation (Ainsley et al, 1979) and other phase transformations (Harase et al, 1990);

3. Mechanical properties e.g. strength and toughness (Wyrzykowski and Grabski, 1986; Lim and Watanbe, 1990);

4. Electrical properties (Nakamichi, 1990) e.g. with respect to dopants in semiconductors (Maurice et al, 1985);

5. Magnetic properties e.g. ‘magnetic annealing’ (Watanabe et al, 1990).

In other words GBs are active structural elements in crystalline materials, including some polymeric materials (Martin and Thomas, 1991). To illustrate this point further it is only necessary to compare the physical, chemical and mechanical properties of a polycrystalline material with those of the same material in single crystal form. The most well-known example is that of a single crystal turbine blade which performs far better under stress at high temperatures than its polycrystalline counterpart because grain boundary sliding (creep) is eliminated (Ralph, 1980, 1988).

It follows logically from the recognition of GBs as structural components that in general the behaviour of polycrystals cannot be considered to depend only upon the properties of an aggregate of individual grains; the macroscopic properties of polycrystals are governed by both grains and grain boundaries (Kurzydlowski, 1990). It is only recently that the relative importance, relationship and possible synergy between these two microstructural elements has been considered and has led to the proposal of a more physically relevant length scale in polycrystals which consists of grain clusters having a particular type of GB in common (Nichols et al, 1991a,b). There are methods available for the quantification of this clustering, also known as a ‘mesostructure’ (Adams et al, 1987), which measure the amount of ‘orientation coherence’ (Zhao, Adams and Morris, 1988).

The importance of GBs in the parent polycrystal can be further illustrated by the special cases of nanocrystalline materials and polycrystals which are essentially two-dimensional. Nanocrystalline materials typically have a grain size of lOnm or less (Gleiter, 1985). Hence they approach the upper bound of the relative proportions of grains and GBs in the material; for a grain size of 2nm the volume fraction occupied by grains and boundaries is equivalent, i.e. 50% each compared to a 0.3% volume fraction of GBs for a grain size of 1μm (Palumbo et al, 1990). The large grain boundary component modifies material properties, for example with respect to saturation magnetisation of α-iron. ‘Two-dimensional’ polycrystals could be either deposited on a substrate as a thin film (Grovenor et al, 1984) or rapidly solidified as a ribbon (Watanabe et al, 1989). Their properties are modified with respect to bulk polycrystals. One reason for this is the major role of surface effects when the GBs extend from the top to the bottom of the material.

1.2 Grain Boundary Structure and Special’ Boundaries

The principal physical feature which characterises the structure of a GB is its porosity or excess free volume (Qian et al, 1987) and associated short and long range elastic strain fields (Sutton and Vitek, 1983) compared to the lattice. Figure 1.1 is a simple schematic model for a GB which shows the ‘width’ of the GB region and some adsorbed species (segregants) in the GB. It is principally this excess free volume and the associated stress fields which confer upon GBs properties which are different from the lattice. For example, GBs have a greater propensity for segregation, diffusion, strain and defect accommodation, and various kinds of nucleation phenomena compared to the lattice. Values for specific parameters may vary by up to an order of magnitude or more. For example, figure 1.2 summarises comparisons between lattice and GB self diffusion coefficients (Gust et al, 1985).

Figure 1.1 Schematic diagram of a GB between grains A and B where atoms are denoted by spheres. The dark spheres are segregant elements which can act as incipient precipitates (IP). θ is the angle of misorientation between common directions in grains A and B (see chapter 2) (Murr et al, 1990).

There is a further division between classes of GBs themselves, rather than between GBs and the lattice, based on their properties. Frequently in the literature this division is denoted by describing boundaries as either general or special (Priester, 1989). General (also called random) boundaries are characterised by having average values for specific parameters such as diffusivity, mobility, energy, etc. By contrast special boundaries exhibit behaviour or have values for specific parameters which are very different to the average ones associated with random boundaries. These differences are directly related to the structure of the GB, and one important factor which confers special properties at certain GBs is particularly low excess free volume.

Figure 1.2 Graph showing a comparison of GB self-diffusion D_b and lattice self-diffusion D for a range of homologous temperatures T_m/T (Gust et al, 1985).

The significance of special GBs is that their properties are usually beneficial to the overall properties of the polycrystal, or could be exploited to be so. Appreciation of this fact has led to a great deal of research activity to elucidate precisely the structure of ‘special’ GBs and how the proportion of GBs with special properties could be maximised. The term ‘grain boundary engineering (or design)’ has been used in this context (Watanabe, 1984, 1988). For example, a fairly well studied area is how GB cavitation may be improved by manipulation of GB statistics (Lim and Raj, 1984a; Palumbo and Aust, 1990a; Field and Adams, 1992). However, the complete relationship between GB structure and properties is far from clear, and its clarification is one of the goals of research on GBs.

The term ‘GB structure’ implies a detailed knowledge of the atomic positions contributed by each grain at the GB (as in figure 1.1) in addition to the defect structure, chemistry, etc. Measurement of these parameters is only feasible on a small scale. Consequently studies of GBs in polycrystals is usually considered in terms of the overall GB geometry based on the crystallographic relationships between abutting grains rather than a detailed description of actual atomic positions at the interface and their interactions. This simplified geometrical approach is justifiable because the crystallographic relationship between abutting grains at a GB contributes the major part of the structure. Furthermore, and this is an important point, if statistically significant quantities of data are to be generated, crystallographic parameters are far more experimentally accessible and interpretable than those which involve invesigations on an atomic level. This is particularly true in the light of experimental techniques which have been developed in recent years for rapid crystallographic analysis such as electron back-scatter diffraction (EBSD) in a scanning electron microscope (SEM) (Dingley, 1981; Dingley and Randle, 1992; Randle 1992c). The purpose of this book is to describe in detail the whole approach to large-scale investigations of GB geometry, from theoretical aspects through data measurement, processing, representation, display, interpretation and application.

1.3 Development of Techniques for Measurement and Analysis of Grain Boundary Geometry

The input data for the measurement of GB geometry is a combination of crystallographic and spatial information. In other words we need to know how the grains in a polycrystal fit together, i.e. which are contiguous, to be able to compute GB geometries. Furthermore the interpretation of these data is enhanced if we have other information about the local environment. Hence the essential experimental requirements are to be able to perform diffraction from selected regions which are less than the grain size and (usually) to be able to image these regions of the microstructure. To measure the orientation of the GB plane itself in addition to the misorientation requires additional spatial information. The most suitable technique for analysis of GB geometry is one which utilises electron microscopy so that diffraction and imaging can both be carried out in situ.

Until a few years ago, investigations which concerned the geometry of GBs were performed in the transmission electron microscope (TEM) but usually restricted to experiments on specially fabricated bicrystals (Goodhew et al, 1978; Forwood and Clarebrough, 1992). Few experiments were performed with the objective of collecting statistically significant quantities of data from polycrystals due to the labour intensity of the data acquisition. This was because the TEM route involved the somewhat tedious preparation of thin foil specimens, which (unless the grain size was very small) only allowed a small number of GBs to be analysed per foil. An alternative route, selected area channelling (SAC) in the scanning electron microscope (SEM), could be used on bulk specimens (Joy, 1975). However, specimen preparation was also difficult for this technique and the spatial resolution was about 10μm, which precluded application to very small grains or subgrains.

In the last few years there have been great improvements both in the experimental techniques available and the software for on-line interrogation of diffraction patterns. Currently, the raw data for GB geometrical analyses can be measured and processed on-line semi-automatically both in the TEM and in the SEM (Schwarzer, 1990). The principal technique for crystallographic analysis in the SEM, which has been implemented during the last decade and is now superceding SAC, is electron back-scatter diffraction (EBSD). This technique has a spatial resolution of 200nm, is performed on specimens prepared by simple metallographic techniques and allows particularly rapid and convenient collection and analysis of data. It is largely because of developments in experimental techniques that the study of GB geometries in polycrystals, and their subsequent relationship with the properties of both the constituent grains and the GBs themselves, has been able to broaden into an area of major research activity.

In addition to the instrumental and software developments to measure GB geometry which were mentioned in section 1.2, the methods by which GB geometrical parameters can be manipulated and represented are becoming increasingly sophisticated (Field et al, 1991). This is in response to the need to analyse and interpret the large quantities of data which can now be generated, which is a result of increased research activity in this area. The task of presentation of GB geometrical data is complex because frequently several statistical parameters as well as spatial information need to be incorporated into the data output. In other words both the local environment and crystallography of individual GBs have been probed concurrently. Furthermore, for a more complete description of the microstructure, these data can be united with parallel information - crystallographic and spatial - about the constituent grains themselves in addition to the GBs.

1.4 Scope of This Book

The aim of this book is to provide a comprehensive guide to all the stages of data collection and analysis connected with GB geometry in cubic polycrystals. It will be of particular value to the experimentalist or anyone who requires a state-of-the-art overview of the field of GB geometry research. The title of the book refers specifically to GB geometry: there are other aspects of GB structure and structure/property relationships which are not covered in detail in this book but nonetheless contribute information about GB structure. These topics include high resolution electron microscopy (HREM) (Merkle and Smith, 1987), studies of dislocation interactions with GBs including dislocation spreading/dissociation (Swiatnicki et al, 1986), modelling or simulation of GB structure (Pond and Vitek, 1977; Balluffi et al, 1987), the measurement of any GB properties such as diffusion, energy, etc (McLean, 1973; Balluffi, 1982) and GB geometry in non-cubic materials (Bleris et al, 1982; Grimmer, 1989).

The central theme of this book is the collection and analysis of orientation data relating both to adjoining grains and to the plane of the GB itself. Measurement of both of these parameters is accessible in the SEM. However, where a finer probe size is required than can be generated in the SEM, e.g. for subgrains or cold-worked structures, the same parameters can be obtained in the TEM. The important point to be made here is that measurement of the GB geometrical parameters is rapid (especially for the misorientation), accurate and does not require extremely specialised equipment or skills, yet can provide valuable information about GB structure. This information can, if required, be combined with other microstructural data, e.g. that concerning properties. More detailed studies of GBs would include mapping of the atomic positions at the boundary, defect structure analysis, chemical species profiles and computer simulations; however, resources and labour intensity render such studies unfeasible except on a small scale. By contrast, stastistically significant quantities of GB geometrical data can be generated readily using modern experimental techniques and methodologies. Hence the geometrical route offers the op...