Lattice strains, applications

These techniques have very important applications to some of the micro-structural effects discussed previously in this chapter. For example, time-resolved measurements of the actual lattice strain at the impact surface will give direct information on rate of departure from ideal elastic impact conditions. Recall that the stress tensor depends on the elastic (lattice) strains (7.4). Measurements of the type described above give stress relaxation directly, without all of the interpretational assumptions required of elastic-precursor-decay studies. 

Figure 12. Application of the lattice strain model to Nb-Ta fractionation by clinopyroxene. The calculated is based on the...

The physical cause of this phenomenon (45) can be most easily explained by means of a one-dimensional chain with equal concentrations of the elements, as an analog to the three-dimensional alloy. The theoretical results can be extended to a three-dimensional system. They are only applicable to a true alloy if lattice strain effects are negligible. 

Raman Microspectroscopy. Raman spectra of small solids or small regions of solids can be obtained at a spatial resolution of about 1 J.m using a Raman microprobe. A widespread application is in the characterization of materials. For example, the Raman microprobe is used to measure lattice strain in semiconductors (30) and polymers (31,32), and to identify graphitic regions in diamond films (33). The microprobe has long been employed to identify fluid inclusions in minerals (34), and is increasingly popular for identification of inclusions in glass (qv) (35). 

Calculation of mean crystallite size, lattice strain and frequency distributions of crystallite sizes from the same XRD line-profiles used for crystallinity determinations. In addition to the application of the Scherrer equation, two single-line methods were used the variance method of Wilson (1963) (Akai and To th 1983 Nieto and Smchez-Navas 1994), and the Voigt method of Langford (1978) in combination with single-line Fourier analysis (Akai et al. 1996, 1997, 2000 Warr 1996 Jiang et al. 1997 Li et al. 

Pd alloys are preferred to pure palladium, which exhibits inadequate properties for membrane applications. Pd lattice can absorb large amounts of hydrogen with eonse-quent embrittlement of the metal. In fact, at atmospheric pressure and below 300°C, hydrogen in Pd co-exists under two hydride forms, phases a and p, with different lattice parameters, 0.3894 and 0.4025 nm, respectively. Transition between these two phases produces cyclic lattice strains that, at macroscopic level, are responsible for the embrittlement of the metal [4,14-16]. 

It has been found that adamantane crystallizes in a face-centered cubic lattice, which is extremely unusual for an organic compound. The molecule therefore should be completely free from both angle strain (since all carbon atoms are perfectly tetrahedral) and torsional strain (since all C—C bonds are perfectly staggered), making it a very stable compound and an excellent candidate for various applications, as wUl be discussed later. 

We will confine ourselves to those applications concerned with chemical analysis, although the Raman microprobe also enables the stress and strain imposed in a sample to be examined. Externally applied stress-induced changes in intramolecular distances of the lattice structures are reflected in changes in the Raman spectrum, so that the technique may be used, for example, to study the local stresses and strains in polymer fibre and ceramic fibre composite materials. 

This measures the likeness of two patterns, which is useful for pattern matching as we will see in the application of lattice parameter and strain measurements. 

The Cu-Co system is a particularly simple precipitation system in which a Corich /3 phase precipitates in a Cu-rich terminal a phase. The f.c.c. lattices of both phases are well matched in three dimensions, so that the precipitate interfaces are coherent with respect to either lattice as a reference structure and the interfacial energy is sufficiently isotropic so that they are almost spherical, as in Fig. 19.2. Both the interfacial energy and strain energy are therefore relatively low and the nucleation of the f3 phase is therefore relatively easy and occurs homogeneously. This system has been used to test the applicability of the classical nucleation theory (Section 19.1.1) [11, 12]. In this work, the experimental conditions under which... 

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