Lattice parameter distortion

Homogeneous alloys of metals with atoms of similar radius are substitutional alloys. For example, in brass, zinc atoms readily replace copper atoms in the crystalline lattice, because they are nearly the same size (Fig. 16.41). However, the presence of the substituted atoms changes the lattice parameters and distorts the local electronic structure. This distortion lowers the electrical and thermal conductivity of the host metal, but it also increases hardness and strength. Coinage alloys are usually substitutional alloys. They are selected for durability—a coin must last for at least 3 years—and electrical resistance so that genuine coins can be identified by vending machines. 

Crystal Structure and Lattice Parameters (nm) Orthorhombic, a = 0.283, b = 0.554, c = 1.1470 Cr3C2 is an intermediate carbide having carbon chains with C-C distance approximately 0.165 nm running through distorted metal lattice where the Cr atoms are at the corners of trigonal prisms and the carbon atoms in the center of the prisms.i li" ... 

TABLE 6.4. Comparison of Thin-Film and Single-Crystal CuGaS2 Lattice Parameters (a and c), c/a, and the Distortion Parameter x ... 

The 220/204 reflections and the 312/116 reflections were split, which is consistent with the tetragonal distortion of the crystal lattice49 (Fig. 6.15). Lattice parameters a and c were calculated from X-ray d spacings according to Eq. 6.5,... 

Some examples of direct measurement of the crystal distortion during the reaction by optical and electron microscopy, IR absorption, and x-ray diffraction have been reported (see references in Ref. 311). The observed (anisotropic) changes in lattice parameters have been used for calculating the kinetic parameters of the transformations. For some reactions, it was possible to follow by x-ray diffraction the change in lattice parameters and also in atomic coordinates, so the relaxation could be observed at atomic level. 

Figure 7. Lattice parameter measurement for NiO at -170°C, which has a rhomboherdal distortion. The best fit (shown at right) gives a=2.9522 A and a=60.05°.

A mismatch in the lattice parameters of materials on both sides of an interface results in strain that is released by lattice distortions and dislocations next to the interface. Understanding the release mechanisms of the strain is crucial in order to tune the properties of the interface. 

Jahn—Teller distortion associated with the Mn + ion. The variation in lattice parameter, 3o, with chemical composition in Lii+ ,]V[n2-/)2 is shown in Figure 12a (after ref 157) its variation is given by 3o = 8.4560 - 0.21746X. 

Subsequently the transition has been called the Verwey transition and the transition temperature the Verwey temperature Ty. Verwey also guessed that, below Ty, the mobile electrons order as Fe on [110] rows and Fe on [llO] rows of B-site cations to produce a distortion to orthorhombic symmetry with lattice parameters approximately y/2 + 6)ao X (V2 - 6)ao x ao, where 5 is a small fraction and ao is the cubic lattice parameter. Although Bickford was able to confirm that Fc304 is magnetically orthorhombic at temperatures T < Ty, it is now known that the low-temperature structure is in fact monoclinic with lattice parameters V2ao x y/lz x 2ao and that the electronic ordering is more complex than originally proposed by Verwey. 

Using X-ray spectrometry, De la Fuente et al. (1999) measured the thermal dependence of the a and c lattice parameters in a Er32/Lu 10)40 superlattice. Again, strong single-ion CEF contributions, originating from the Er/Lu interfaces, were observed in the volume and tetragonal distortions. Their analysis reveals also important contributions caused by epitaxial misfit. 

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