Anisotropic thermal expansion

Exploiting Anisotropic Thermal Expansion in Structure Solution. 171... 

Peak positions. Shifts in the positions of the peaks in an experimental powder XRD pattern may arise due to a number of instrumental factors. Furthermore, comparison of powder XRD patterns recorded at different temperatures may show differences in appearance (particularly in regions with significant peak overlap) as a result of anisotropic thermal expansion/contraction. This issue is particularly relevant when an experimental powder XRD pattern recorded at ambient temperature is compared with simulated powder XRD patterns for known crystal structures determined from single-crystal XRD data at low temperature. 

Fig. 7. Anisotropic thermal expansion of GdNij measured by x-ray powder diffraction (this work). The lines indicate the corresponding values of the isostructural YNij (nonmagnetic reference), scaled to coincide with GdNij at ISO K for allowing a direct comparison (the c/a ratio has not been scaled).

Fig. 9. Anisotropic thermal expansion of Gd2ln measured by x-ray powder diffraction (Gratz and Lindbaum 1998). The lines are the result of fitting Debye functions. The arrows indicate the two magnetic transitions at...

Fig. 11. Anisotropic thermal expansion of GdCuAl measured by x-ray powder diffraction (Andreev et al. 1999). The lines are extrapolations from the paramagnetic range. 7c and 7r indicate the magnetic ordering temperature and the second magnetic transition observed by Javorsky et al. (1998), respectively.

Fig. 28. Anisotropic thermal expansion of the orthorhombic FeB phase of GdCu obtained from neutron diffraction experiments on a bulk polycrystalline sample (Blanco et al. 1999). The lattice parameters (Ip) at 180 K are o = 7.I5 0.01 A, b = 4.527 0.008 A, c = 5.471 0.008 A.

Fig. 36. Anisotropic thermal expansion of the orthorhombic GdZn2, measured by x-ray powder diffraction (the data points have been extracted from Ohta et al. (1995)). The lines represent extrapolations of the lattice...

Kolb H.F. Rizzo, Growth of 1,3,5-Triamino-2,4,6-Trinitrobenzene (TATB). I. Anisotropic Thermal Expansion , Proplnts Expls 4 (1), 10-16(1979)... 

A ratchet mechanism is proposed to account for growth, in which the stresses generated by anisotropic thermal expansion of TNT are... 

Some kind of thermal shock loading is inevitable during service of FMs. In addition, most FMs have anisotropic thermal-expansion coefficients due to their unique architectures. In 2004, Koh and co-workers investigated the thermal shock resistance of Si3N4/BN FMs [29], They observed their excellent thermal shock resistance by measuring the retention of the flexural strength after thermal shock test, as shown in Fig. 1.17. The monolithic Si3N4 exhibited... 

It is worth pointing out that carbon fibre itself has anisotropic thermal expansion properties, and therefore this mismatch between the carbon fibres and the a-sialon matrix should be considered in both the radial and axial directions when carbon fibres are unidirectionally aligned in the composite. The thermal stress caused by thermal expansion differences between the carbon fibres and the matrix in the radial (cr) and axial (oa) directions can be estimated from the formulae (Chawla, 1993 Kerans and Parthasarathy, 1991) ... 

If metallic irranium is used as fuel, the modifications of the metal and their properties have to be taken into account (Table 11.4). The anisotropic thermal expansion of a-U leads to plastic deformations which restrict the use of metallic uranium considerably. Furthermore, by the difference in the density of a-U and j8-U the applica-... 

Most studies of the strength of glass ceramics have determined modulus of rupture as a function of crystal size (strength increases as crystal size decreases), volume fraction of crystalline phase (strength increases with the volume fraction of crystalline phase), and internal stresses generated either by the difference in thermal expansion between the crystalline phases and residual glass or by anisotropic thermal expansion of the crystalline phase (strength decreases as the difference or anisotropy increases). 

Displacement parameters of atoms are also expected to be different as the temperature of the powder diffraction experiment varies. Furthermore, it is also feasible that atomic positions may change due to generally anisotropic thermal expansion of crystal lattices. These considerations are in addition to the most obvious cause (different lattice parameters) preventing combined refinement using powder diffraction data collected at different temperatures. In general, material may also be polymorphic but this is not the case here, as was established in Chapter 6, sections 6.10 and 6.11. 

Table 13.2 Thermal expansion coefficients for some ceramic crystals with anisotropic thermal expansion behavior...

In their temperature studies Tashiro et al. [66,67] and Prosa et al. [69] noted strongly anisotropic thermal expansion of PHT, POT and PDoDT. Whereas the a-axis increases for the materials, the 6-axis increases initially above room temperamre but saturates and even decreases upon further heating. The expansion coefficient for the a-axis is large in the room temperamre range, of the order of 9 x 10 K for PHT and 1.4 X 10 K for PDoDT, but for both materials the expansion levels off as T, is approached. 

Scherrer rings of deliberately textured samples in another. one can make use of anisotropic thermal expansion to try and resolve different families of reflections at different temperatures. In the absence of such methods, overlap can only be reduced by recording the highest resolution data attainable for a given sample. 

II. 1.2b. 1.Thermal Expansion Thermal expansion of unidirectional SiC/RBSN composite is mainly a function of constituents volume fractions and measurement direction relative to the fiber, and is not affected by constituents porosity. Measurement of linear thermal expansion with temperature in nitrogen for the 1-D SiC/RBSN composites parallel and perpendicular to the fibers indicates a small amount of anisotropy (Fig. 5). This is attributed to small difference in thermal expansion coefficients of SiC fibers (4.2 x 10 ) and RBSN matrix (3.8 x 10 ) as well as anisotropic thermal expansion of carbon coating on SiC fibers. In the fiber direction, linear thermal expansion is controlled by the SiC fiber, and in the direction perpendicular to the fiber, it is controlled by the RBSN matrix. 

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