Solid-state reactions barrier

It is noteworthy that it is the lower cross-over temperature T 2 that is usually measured. The above simple analysis shows that this temperature is determined by the intermolecular vibration frequencies rather than by the properties of the gas-phase reaction complex or by the static barrier. It is not surprising then, that in most solid state reactions the observed value of T 2 is of order of the Debye temperature of the crystal. Although the result (2.77a) has been obtained in the approximation < ojo, the leading exponential term turns out to be exact for arbitrary cu [Benderskii et al. 1990, 1991a]. It is instructive to compare (2.77a) with (2.27) and see that friction slows tunneling down, while the q mode promotes it. 

Eor analysis of emitted particles, solid state surface barrier detectors (SBD) are used inside the scattering chamber to measure the number and energy of the reaction products. Stopper foils are used to prevent scattered projectiles from reaching the detector. Depth profiles can be obtained from the energy spectra, because reaction products emitted in deeper layers have less energy than reaction products emitted from the surface. The concentration in the corresponding layer can be determined from the intensity of reaction products with a certain energy. 

Recently, RBS has been used to study the metal-silicon reactions induced by both a CW laser and an electron beam (53). Uniform, large area, single phase silicides were formed by adjusting the beam power level to induce a solid state reaction. Under certain conditions metastable mixed-phase systems were also obtained. RBS could non-destructively determine the stoichiometry of the phases formed without additional standards. AES and SIMS have also been used in the study of metal silicides. These applications and other points of interest in the fabrication, characterization and application of metal-semiconductor Schottky barrier junctions have been reviewed recently by Sharma and Gupta (54). 

The current status of the models of fluctuational and deformational preparation of the chemical reaction barrier is discussed in the Section 3. Section 4 is dedicated to the quantitative description of H-atom transfer reactions. Section 5 describes heavy-particle transfer models for solids, conceptually linked with developing notions about the mechanism of low-temperature solid-state chemical reactions. Section 6 is dedicated to the macrokinetic peculiarities of solid-state reactions in the region of the rate constant low-temperature plateau, in particular to the emergence of non-thermal critical effects determined by the development of energetic chains. 

The evaluation made in the preceding section shows the possibility of a natural explanation of the regulation of low-temperature solid-state reactions in a model accounting for barrier parameter oscillations resulting from intermolecular vibrations. A consistent analysis of such a model is required. A mathematical body used for this purpose is, conceptually, close to the common theory of nonradiative transitions, but unlike the latter it enables us to exceed the limits of the one-dimensional Franck-Condon approximation which is inapplicable in treatment of heavy-particle transfer. 

Thus, expression (59) enables us to describe the solid-state reaction rate constant dependence on the parameters of the potential barrier and medium properties in a wide temperature range, from liquid helium temperatures when the reaction runs by a tunneling mechanism to high temperatures (naturally, not exceeding the melting point) when the transition is of the activation type. 

Glass formation by mechanical alloying of elemental crystalline powders can be considered a special form of solid-state interdiifusion reaction. The basic principles of such a reaction [3.15] are described in Fig. 3.4. As is well known, the thermodynamic stable state of a system is determined by a minimum in the free enthalpy G. In metallic systems, the free enthalpy of the equilibrium crystalline state Gx is always lower than that of the amorphous state Ga below the melting temperature. The amorphous state is a metastable state, i.e., an energy barrier prevents the amorphous phase from spontaneous crystallization. To form an amorphous metal by a solid-state reaction, it is necessary to establish first a crystalline initial state with a high free enthalpy G0 (Fig. 3.4). Depending on the formation process, this initial state can be achieved, for example, by... 

Reactions between solids are slow because of the high barrier to the diffusion of atoms. Conventional solid-state reactions involve high temperatures, but methods including vapor transport can be used to accelerate the reaction. 

Reactions between two solids are analogous to the oxidation of a metal, because the product of the reaction separates the two reactants. Further reaction is dependent on the transport of material across this barrier. As with oxidation, cracking, porosity and volume mismatch can all help in this. In this section, the case when a coherent layer forms between the two reactants will be considered. The mechanism of the reaction may depend on whether electron transport is possible in the intermediate phase, and the rate of reaction will be controlled by the rate of diffusion of the slowest species. To illustrate the problems encountered a typical solid-state reaction, the formation of oxide spinels, is described. 

There are many obstacles involved in making a kinetic study of even the simplest of solid-state reactions ( ). In most solid-state reactions the impenetrable barrier to obtaining satisfactory rate data is the analysis of the products. This difficulty arises because conventional solvent and chemical separation techniques are not applicable. Another experimental difficulty arises from the fact that knowledge of the defect type and concentration must be known before any quantitative interpretation may be developed as to how the defect state affects solid-state reactions. Care must be taken at all times to keep the entire investigation within the boundary conditions set up by the methods used to investigate the data. 

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