Grain-Boundaries

Grain boundaries as barriers to dislocation motion are discussed in various text books (for example, Meyers and Chawla, 1998). The discussions either take the position that the dislocations form at the grain centers and become blocked by the dislocations of the boundaries, or that the dislocations originate at the boundaries and block one another within the grains. Here, a third view will be taken which seems more likely to this author. It is a more macroscopic 

Stresses can can be concentrated by various mechanisms. Perhaps the most simple of these is the one used by Zener (1946) to explain the grain size dependence of the yield stresses of polycrystals. This is the case of the shear crack which was studied by Inglis (1913). Consider a penny-shaped plane region in an elastic material of diameter, D, on which slip occurs freely and which has a radius of curvature, p at its edge. Then the shear stress concentration factor at its edge will be = (D/p)1/2.The shear stress needed to cause plastic shear is given by a proportionality constant, a times the elastic shear modulus, 

Therefore, in a polycrystal, the macroscopic stress needed general plastic deformation is  

There is a large literature discussing the effects of grain boundaries on plastic deformation. The essential effects for clean boundaries have just been discussed, but there are many additional effects when the boundaries are contaminated with impurities and precipitates. All this will not be discussed further here. Books that have differing viewpoints on grain boundary effects are Baker (1983), and Meyers and Chawla (1998). 

Grain boundaries (and boundaries between phases) are elements of the microstructure of crystalline solids, being characterized by their number, shape, and topological arrangement. The microstructure is a non-equilibrium property. In the next section we discuss grain boundaries. 

Inspection of the atomistic structure of a grain boundary (GB) reveals that ions in the GB region can exist in very different 

Much work has been invested in understanding and reducing the grain boundary proton resistance, especially with regard to the effects of A-site nonstoichiometry and impurities. We shall not treat this here but just mention that, somewhat surprisingly, the grain boundary resistance disappeared 

Real crystals differ from ideal crystals in that they are composed of mosaic blocks, i.e. small crystallites. Typical values of their sizes lie in the range of some 100 up to some 1000 lattice constants. They are tilted relative to one another by a few minutes of arc (Fig. 4.6). The intersection of two of these blocks forms a so called small-angle grain boundary. This is known from the maxima in X-ray diffraction spectra their widths for an ideal crystal should theoretically be only a few seconds of arc. In reality, one measures instead values of at least one minute of arc, due to the distribution of orientations of the mosaic blocks. 

The grain boundaries are thus a third type of extended defect. They can be considered to be a row of dislocations which are formed between neighbouring crystallites or mosaic blocks. 

An interface is a plane which joins two semi-infinite solids. Interfaces between two crystals exhibit some of the characteristic features of surfaces, such as the broken bonds suffered by the atoms on either side of the interface plane, and the tendency of atoms to rearrange themselves to restore their bonding enviroiunent. We can classify interfaces in two categories those between two crystals of the same type, and those between two crystals of different types. The first type are referred to as grain boundaries, because they usually occur between two finite-size crystals (grains), in solids that are composed of many small crystallites. The second type are referred to as hetero-interfaces. We discuss some of the basic features of grain boundaries and hetero-interfaces next. 

For an industrial catalyst, energy dispersive X-ray analysis. X-ray powder diffraction, optical microscopy and Mossbauer spectroscopy show that part of the A1 and Ca atoms are dissolved in the magnetite lattice [15, 27, 28, 38-43]. The lattice constant of the magnetite phase of an industrial catalyst is 8.377 kX [15]. The lines in the X-ray powder diffractions diagram are broadened [15] the broadening is independent of particle size [15]. 

From the Mossbauer spectrum [27, 44,45] and the X-ray power diffraction diagram [39] of the unreduced catalyst, it has been estimated that 85% of the A1 in the unreduced catalyst is dissolved in the magnetite. Evidence for the dissolution of K[41,46], Mg[41,46], V[41], Si[41], W[46], and Mo[46] in the magnetite has been reported. However, due to the large size of only a small amount of K is found in the magnetite phase of the industrial catalyst. 

Additional information on the structure of the magnetite phase comes from the study of catalyst models, in particular of (Fe, Al) solid solutions. Mossbauer spectroscopic studies of Fe304 [47] and of unstochiometric Fe-spinels [44] have been reported. 

The grain boundary regions may constitute about 7% of the volume of the unreduced catalyst [46], and may contain much higher concentrations of promoter [14, 52] than the magnetite. The phases detected in the grain bound- 

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Figure Bl.17.9. A CoSi grain boundary as visualized in a spherical-aberration-corrected TEM (Haider et a/ 1998). (a) Individual images recorded at different defocus with and without correction of C(b) CTFs in the case of the uncorrected TEM at higher defocus (c) CTF for the corrected TEM at only 14 nm underfocus. Pictures by courtesy of M Haider and Elsevier.

From polarization curves the protectiveness of a passive film in a certain environment can be estimated from the passive current density in figure C2.8.4 which reflects the layer s resistance to ion transport tlirough the film, and chemical dissolution of the film. It is clear that a variety of factors can influence ion transport tlirough the film, such as the film s chemical composition, stmcture, number of grain boundaries and the extent of flaws and pores. The protectiveness and stability of passive films has, for instance, been based on percolation arguments [67, 681, stmctural arguments [69], ion/defect mobility [56, 57] and charge distribution [70, 71]. 

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

Because densification occurs via tire shrinkage of tliennodynamically unstable pores, densification and microstmcture development can be assessed on tire basis of tire dihedral angle, 0, fonned as a result of tire surface energy balance between tire two solid-vapour and one solid-solid interface at tire pore-grain boundary intersection [, 78, 79 and 80],... 

Figure C2.11.7. An illustration of tlie equilibrium dihedral angle, 0, fonned by tlie balance of interfacial energies at a pore-grain boundary intersection during solid-state sintering.

Kingery WD and Francois B 1965 The sintering of crystaiiine oxides, i. interactions between grains boundaries and pores Sintering and Related Phenomena ed G C Kuczynski, N A Hooton and C F Gibbon (New York Gordon and Breach) pp 471-98... 

Extended defects range from well characterized dislocations to grain boundaries, interfaces, stacking faults, etch pits, D-defects, misfit dislocations (common in epitaxial growth), blisters induced by H or He implantation etc. Microscopic studies of such defects are very difficult, and crystal growers use years of experience and trial-and-error teclmiques to avoid or control them. Some extended defects can change in unpredictable ways upon heat treatments. Others become gettering centres for transition metals, a phenomenon which can be desirable or not, but is always difficult to control. Extended defects are sometimes cleverly used. For example, the smart-cut process relies on the controlled implantation of H followed by heat treatments to create blisters. This allows a thin layer of clean material to be lifted from a bulk wafer [261. 

If tlie level(s) associated witli tlie defect are deep, tliey become electron-hole recombination centres. The result is a (sometimes dramatic) reduction in carrier lifetimes. Such an effect is often associated witli tlie presence of transition metal impurities or certain extended defects in tlie material. For example, substitutional Au is used to make fast switches in Si. Many point defects have deep levels in tlie gap, such as vacancies or transition metals. In addition, complexes, precipitates and extended defects are often associated witli recombination centres. The presence of grain boundaries, dislocation tangles and metallic precipitates in poly-Si photovoltaic devices are major factors which reduce tlieir efficiency. 

Fig. 3. An overview of atomistic mechanisms involved in electroceramic components and the corresponding uses (a) ferroelectric domains capacitors and piezoelectrics, PTC thermistors (b) electronic conduction NTC thermistor (c) insulators and substrates (d) surface conduction humidity sensors (e) ferrimagnetic domains ferrite hard and soft magnets, magnetic tape (f) metal—semiconductor transition critical temperature NTC thermistor (g) ionic conduction gas sensors and batteries and (h) grain boundary phenomena varistors, boundary layer capacitors, PTC thermistors.

The commercial sintered spinel and M-type ferrites have a porosity of 2—15 vol % and a grain size in the range of 1—10 ]lni. In addition, these materials usually contain up to about 1 wt % of a second phase, eg, CaO + Si02 on grain boundaries, originating from impurities or sinter aids. 

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