Cubic to tetragonal transformations

Fig. 10.31. Schematic illustration of deformation gradients in different wells for the cubic to tetragonal transformation that satisfy the rank-one connection condition (adapted from Ball and James (1992)).

Cubic-to-tetragonal transformation in rare earth dicarbide solid solutions... 

The solid solution LaAg Ini- crystallizes with a CsCl type stmcture (Balster et al., 1975). This pseudobinary system undergoes a martensitic (displacive) crystal structure transition. At low temperature the X-ray powder patterns of polycrystalline samples show line splitting corresponding to a cubic-to-tetragonal transformation. The indium concentration 1 - x and thus the electron count per formula unit has a large influence on the transition temperature. This structural phase transition is revealed also in the temperature dependence of the electrical resistivity. For indium concentrations above 5% the curves show a pronounced hysteresis behavior. 

Only few direct pressure syntheses have been reported. LiTiMF6 phases (M = Mn—Ni) were prepared from respective binary fluorides at T = 700-1200°C and 15-70 kbar [27]. The products crystallized in Na2SiF6 and PbSb206 type structures. On the other hand, pressure induced phase transitions are common, e.g. KMnF3 transforms from cubic to tetragonal symmetry. However, in contrast to oxide containing perovkites, the transition temperature rises with increasing pressure [28]. 

The cubic compound UInAu2 with Heusler structure was studied by Besnus et al. (1987). The lattice parameter a = 696.9 pm indicates a U-U spacing of 493 pm. ThInAu2, like the compounds of the REInAu2 series with light rare earths (Besnus et al. 1986), undergoes a structural transformation from cubic to tetragonal symmetry below 190 K (a = 707.0 pm at 300 K). 

The cubic-to-tetragonal phase transformation temperature of various binary dicarbide solid solutions have been measured (McColm et al. 1973, Adachi et al. 1974,1976, 1978, Loe et al. 1976). A typical example is shown in fig. 13. 

As in the mixed rare earth dicarbide systems, the rare earth dicarbides also form a solid solution with uranium dicarbide and there exists a composition dependence of the cubic-to-tetragonal phase transformation for the UC2-LaC2 or the UC2 CeC2 solid solutions (McColm et al. 1972), as well as for the UC2-GdC2 solid solution (Wallace et al. 1964). 

The BOg octahedra can not only deform but may also tilt and rotate along their fourfold or twofold axes, giving rise to different superstmctures or modulated structures. Besides, there is a strong dependence of structural symmetry on temperature at lower temperatures, numerous modifications or structural distortions from the ideal perovskite stmcture exist [43—45], and all of these causes lower the symmetry of the structure from cubic to tetragonal, orthorhombic, rhombohedral, or monoclinic. A lowering in symmetry will introduce different orientation variants (twins) and translation variants (antiphase boundaries). Stmctures with a lower symmetry, derived from the cubic structure by tilting and/or deformation of the BOg octahedra, become stable such that one (or several) phase transformation(s) may take place. 

Diffusionless phase transformations do not require the net transport of atoms across a phase boundary. For example, phase transformations involving a change in spin or magnetic moment or certain changes in crystal structure or symmetry do not require diffusional fluxes. Examples of such processes include the martensitic transformation in steel or certain cubic-to-tetragonal phase transformations. 

Guo Q, Zhao Y, Mao WL et al (2008) Cubic to tetragonal phase transformation in cold-compressed Pd nanocubes. Nano Letters 8 972-975... 

Most R-H systems exhibit a second phase transformation P —> y in the interval RH2-RH3. The y-phase possesses an hep structure, but with a bigger unit cell than the metal because of symmetry loss due to an off-center displacement of the H atoms occupying the T and O sites (see sect. 3). Those exhibiting only one (a —> P) transformation are the two divalent lanthanides Eu and Yb, Sc (too small to incorporate a third H atom under normal pressure conditions) as well as the systems La-H, Ce-H and Pr-H, with a big enough unit cell to permit a complete occupation of the O sites in the P-phase. The latter, however, exhibit second-order transformations with slight cubic-to-tetragonal deformations of the host lattice. 

Since these substances are isostructural, solid solution formation is easy across the whole series, and the hardness of 50 mol % alloys, Lno.5Lno.5C2, can be considered alongside the observed depression of the cubic-to-tetragonal phase transformation on cooling. It has been shown that the depression in transformation temperature, AT), is related to cell volume difference AV and the shear modulus G for such solid solutions when the dicarbide of smaller cell volume is considered as the solvent and the dicarbide of larger cell volume is dissolved in it the relationship is... 

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