Integration rate constant, crystal

As stated above, expression (9) for the rate constant of transition in Einstein s crystal was first calculated analytically by the method of the straight search in the pioneer works of Pekar [1] and Kun and Rhys [2]. Their analytic expression remains till now the unique exact expression for multi-phonon transition probability in the time unit. Then, there appeared different methods that permit to derive the integral expressions for the rate constant in the general case of the phonon frequencies dispersion the operator calculation method [5], the method of generating polynomial [6], and the method of density matrix [7]. The detailed consideration of these methods was made in the Perlin s review [9],... 

The integral in the expression (20) can be calculated exactly only in the absence of the frequency dispersion of the phonons, i.e. for Einstein s model of the crystal cos — a>. Then, the expression for the rate constant of multiphonon transition results from the formula (20) ... 

The spectrum represented in Fig. 2 has been recorded with the flat quarz crystal (2d = 0.236013 nm) as a monochromator. A scanning rate has been O.25deg.20- min, the value of an integrator time constant refers to 16 s. 

Incorporation of components in a growing facet involves ion adsorption at the surface, dehydration of lattice ions, surface diffusion to favored sites, integration into the crystal, as well as the opposing process of ion dissolution. Different facet types will have different reaction rate constants, and the alteration of the thickness of the boundary layer can affect the growth rate to produce different growth morphologies. 

There exists a considerable literature on CVD (2) but relatively few attempts have been made to combine chemical and physical rate processes to give a complete representation of the deposition process. Most CVD studies have focused on demonstrating the growth of a particular material or crystal structure. However, the combined analysis is necessary in order to design CVD reactors where it is possible to deposit thin films of constant thickness and uniformity across an entire wafer. This is particularly important in the realization of submicron feature sizes for Very Large Scale Integrated Circuits. The further development of devices based on III-V compounds also depends on CVD reactor design improvements since the composition and thus the electronic properties of these materials vary considerably with process conditions. 

The crystal phases in the glass-ceramics were determined by XRD analysis. All instruments were precisely and identically set to ensure a high precision to obtain the integral peak area. The microstructure of the fresh fractured cross section of the glass-ceramics was observed by SEM. The thermal expansion coefficient (TEC) was calculated from room temperature to 500 °C at a heating rate of 5°C/min in the dilatometry analyser (NETZSCH, DIL402PC). The flexural strength was determined in a 3-point bend test at a constant strain ratio of 0.5mm/min. 

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