Thermal parameters, tetragonal

Polymorphism. Many crystalline polyolefins, particularly polymers of a-olefins with linear alkyl groups, can exist in several polymorphic modifications. The type of polymorph depends on crystallisa tion conditions. Isotactic PB can exist in five crystal forms form I (twinned hexagonal), form II (tetragonal), form III (orthorhombic), form P (untwinned hexagonal), and form IP (37—39). The crystal stmctures and thermal parameters of the first three forms are given in Table 3. Form II is formed when a PB resin crystallises from the melt. Over time, it is spontaneously transformed into the thermodynamically stable form I at room temperature, the transition takes about one week to complete. Forms P, IP, and III of PB are rare they can be formed when the polymer crystallises from solution at low temperature or under pressure (38). Syndiotactic PB exists in two crystalline forms, I and II (35). Form I comes into shape during crystallisation from the melt (very slow process) and form II is produced by stretching form-1 crystalline specimens (35). 

Although correlation between parameters is a function of the data structure and has nothing to do with deficiencies in the model, it has implications for both the choice of the model and the design of the experiment. EVANS described his experiences with the determination of the crystal structure of tetragonal barium titanate (BaTiOa). The problem was ample in that it involved only three atomic positional parameters (one for Ti and two for 0), plus nine thermal parameters. There was considerable interest in the details of the structure because of the ferroelectric properties of the material. The proposed model was essentially a simple cubic arrangement of atoms, but with Ti displaced slightly from the center of an octahedron. By ordinary x-ray standards, this distortion (which was expected to be on the order of 0.15 A) could be measured with a standard error of 0.01-0.02 A if... 

Table I. Atomic Positional and Thermal Parameters for the Tetragonal (P4/mmm) Compounds YBa2Cu306, YBa2Cu307 3(15, and La gBa gCusOy 33<4>...

For crystalline PbZrOs, which has tetragonal (Ittima) symmetry and 40 atoms per unit cell, the real-space refinement method resulted in a practically identical structure as the Rietveld method did [11] (Fig. 5). The only difference was that the thermal parameter of Pb refined by the PDF method was appreciably smaller and more realistic than that by the Rietveld method. Thus for a perfectly periodic system, the PDF method is at least equivalent to the Rietveld method. While it is obviously more convenient to use the Rietveld method for determining the lattice constants, the atomic position within the... 

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. 

The salt undergoes a crystalline transition from tetragonal to cubic at 412 K AH for the transition is 2.49 kJ mol-1. The temperature dependence of the lattice parameters and thermal expansion coefficient has been carefully studied.100... 

The crystal structure of zirconia and the catalytic properties of SZ generally depend on the synthesis method and thermal treatment adopted. In particular zirconia crystallises in three different polymorphs characterised by monoclinic, tetragonal and cubic symmetry. Among them only the tetragonal SZ phase displays significant catalytic properties [5-7]. Unfortunately, the synthesis of the pure tetragonal polymorph is difiBcult and, in the absence of promoted oxides [8], it could be stabilised only through an accurate control of the synthesis parameters, with particular attention to the thermal treatments. 

The thermal expansion and compressibility of rhombohedral NaN3 and tetragonal KN3 are highly anisotropic. The largest values in both cases are perpendicular to the azide axis, suggesting that ionic forces within the azide layers are stronger than those between the layers. The results of Parsons and Yoffe [85] also indicate that the lattice parameters increase linearly with temperature between 300 and 600°K. 

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