High temperature lattice expansions

Of the various high temperature lattice expansion formalisms advanced, Handy s was the most pertinent to wavelet analysis. As recognized in his original study, the use of a moments representation is very relevant to the space (translation) - scale, wavelet reconstruction of a function. One of the principal objectives of this work is to present this within the important class of problems corresponding to one dimensional (for simplicity), rational... 

The above formalism mimics the (approximate) high temperature lattice expansion analysis of Bender and Sharp (1981) and Handy (1981). These works involve an adhoc modeling of the corresponding continuum problem, combined with Pade related techniques for recovering the continuum limit. In contrast, the e-perturbation scalet analysis yields a similar structmre however, it is exact. 

Buta et al. (2001) tested the Monte Carlo approach for the lattice cluster theory to derive the thermodynamic properties of binary polymer blends. They considered the two polymers to have the same polymerization indices, i.e., M = 40, 50, or 100. The results confirm that this lattice cluster theory had a higher accuracy compared to the Flory-Huggins theory and the Guggenheim s random mixing approximation. However, some predictions for the specific heat were found to be inaccurate because of the low order cutoff of the high temperature perturbative expansion. 

Fig. 240. Cu(HCOO)2 -4H20. Temperature dependence of l/fC, and 1/ 2- Measuring points experimental solid lines high temperature series expansion solution to the Heisenberg two-dimensional antiferromagnetic lattice with J/hc=-54cm, g =2.34, gj =2.04. The calculated X T and values have been corrected for TIP=120 10" ...

Figure A2.3.29 Calculation of the critical temperature and the critical exponent y for the magnetic susceptibility of Ising lattices in different dimensions from high-temperature expansions.

Figure 3.3. Equilibrium linear susceptibility (x/Xiso) versus temperature for an infinite spherical sample on a simple cubic lattice. The dotted lines are the results for independent spins, while the solid lines show the results for parallel and random anisotropy calculated with thermodynamic perturbation theory, as well as for Ising spins calculated with an ordinary high-temperature expansions. We notice in this case that the linear susceptibility for systems with random anisotropy is the same as for isotropic spins calculated with an ordinary high-temperature expansion. The dipolar interaction strength is hj = a/2a = 0.004.

Yasuda, I. and Hishinuma, M., Lattice expansion of acceptor-doped lanthanum chromites under high-temperature reducing atmospheres, Electrochemistry 68, 2000, 526. 

The pressure inside the heated chamber may also vary as a result of the local density changes produced by thermal expansion or phase changes resulting from the heating. For example NaCl may expand, melt, and thereby increase the local pressure, while pyrophyllite, a layer-lattice-type aluminum silicate, may transform into a denser assembly of coesite and kyanite, thereby reducing the local pressure. It follows that experimental results in high-pressure, high-temperature work must be interpreted with care. 

Two types of transformations can be very broadly distinguished. The first is the formation of a solid solution, in which solute atoms are inserted into vacancies (lattice sites or interstitial sites) or substitute for a solvent atom on a particular sublattice. Many types of synthetic processes can result in this type of transformation, including ion-exchange reactions, intercalation reactions, alloy solidification processes, and the high-temperature ceramic method. Of these, ion exchange, intercalation, and other so-called soft chemical (chimie douce) reactions produce no stmctural changes except, perhaps, an expansion or contraction of the lattice to accommodate the new species. They are said to be under topotactic, or topochemical, control. 

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