Solid-state reactions particle size

There have been few discussions of the specific problems inherent in the application of methods of curve matching to solid state reactions. It is probable that a degree of subjectivity frequently enters many decisions concerning identification of a best fit . It is not known, for example, (i) the accuracy with which data must be measured to enable a clear distinction to be made between obedience to alternative rate equations, (ii) the range of a within which results provide the most sensitive tests of possible equations, (iii) the form of test, i.e. f(a)—time, reduced time, etc. plots, which is most appropriate for confirmation of probable kinetic obediences and (iv) the minimum time intervals at which measurements must be made for use in kinetic analyses, the number of (a, t) values required. It is also important to know the influence of experimental errors in oto, t0, particle size distributions, temperature variations, etc., on kinetic analyses and distinguishability. A critical survey of quantitative aspects of curve fitting, concerned particularly with the reactions of solids, has not yet been provided [490]. 

If a precipitate is allowed to undergo Ostwald ripening, or is sintered, or is caused to enter into a solid state reaction of some kind, it will often develop into a distribution which has a size limit to its growth. That is, there is a maximum, or minimum limit (and sometimes both) which the particle distribution approaches. The distribution remains continuous as it approaches that limit. The log-probability plot then has the form shown in 5.8.2. on the next page. 

The examples illustrate the strong points of XRD for catalyst studies XRD identifies crystallographic phases, if desired under in situ conditions, and can be used to monitor the kinetics of solid state reactions such as reduction, oxidation, sulfidation, carburization or nitridation that are used in the activation of catalysts. In addition, careful analysis of diffraction line shapes or - more common but less accurate-simple determination of the line broadening gives information on particle size. 

When mixtures of substances are investigated, e.g. in solid state reactions, the mixture should be completely homogeneous and of uniform particle size. Smaller particle size, i.e. higher ratio surface area/volume, are important for such types of reaction ... 

Solid-State Reactions of Iron Compounds. Black iron oxides obtained from the Laux process (see below) or other processes may be calcined in rotary kilns with an oxidizing atmosphere under countercurrent flow to produce a wide range of different red colors, depending on the starting material. The pigments are ground to the desired particle size in pendular mills, pin mills, or jet mills, depending on their hardness and intended use. 

For unsupported catalysts, where particle sizes are typically an order of magnitude larger than those for supported catalysts, the mobility of various species in the bulk structure may be of interest when considering how the bulk structure and composition are reflected in the surface properties of the particle. In addition, bulk mobility is an important consideration in the understanding of solid state reactions and phenomena such as sintering. 

This route is the solid state reaction at temperatures above 1100 °C of a mixture of BaC03 and Ti02 - together with modifiers . The calcination is followed by comminution to reduce the particle size to approximately 1 /an. 

Reaction kinetics may be determined for a fixed-bed reactor, provided measurements are performed under conditions comparable to those that prevail in the fluidized-bed reactor (for example the same solids composition and particle-size distribution, and the same activity state) [98] However, the kinetic parameters can also be determined directly by measurements in a bench-scale fluidized-bed apparatus [99]... 

Solid-state reactions 100% yield, stoichiometric reaction, highly crystalline products Most thermodynamically stable phases are obtained, low surface area, particle size is difficult to control... 

FIGURE 5.23 Solid state reaction between silica and BaCOg, showing (a) time dependence, (b) particle size dependence, and (c) temperature dependence of reaction. From Jander [28]. 

In contrast to solid-state reactions, solution-based soft chemical methods are expected to yield chemically homogeneous and phase-pure products with narrow particle size distribution and low crystallization temperatures. 

There are certain essential differences between solid state reactions and reactions involving gaseous or liquid phases. In the latter case, the kinetic motion of the reactant molecules ensures that they are available to one another for reaction under conditions which can be defined by statistical laws. Solid state reactions occur between apparently regular crystal lattices, in which the kinetic motion is very restricted and depends on the presence of lattice defects. Interaction can only occur at points of contact between the reacting phases and is therefore dependent on particle size and particle size distribution. The factors which govern the rate of a solid state reaction are (/) the rate of the boundary phase processes which lead to the consumption of the original lattices, and (ii) the rate of particle transfer through the product layer. 

More detailed studies demonstrate that crystalline Al2(W04)3 is produced from the direct solid-state reaction between crystalline WO3 and the alumina support and occurs by the migration of alumina to the WO3 particles at these elevated temperatures. The initial transformation of the surface tungsten-oxide phase to crystalline WO3 particles at elevated temperatures, when the alumina surface area decreases, reveals that the tungsten-oxide species are not miscible in the alumina support and are actually diffusing away from the alumina support. Thus, it appears that the surface tungsten oxide-alumina mixed oxide forms an "immiscible oxide system" because of the inability of the alumina support to accommodate the large charge and size of the cation. More recent Raman studies... 

The ceramic material obtained by this method (sample C) is compared to those obtained by solid state reactions using either a carbonate (A) or nitrate (B) as the source of barium. Micrographs for the three samples are shown in Figure 1. Note that sample C is homogeneous with a particle size of about 1 micron whereas about 100 and 20 micron particle sizes are observed for samples A and B respectively. Resistivity measurements on the same set of samples, were performed using a standard four-probe method with silver paint contacts in an exchange gas cryostat with a Si-diode thermometer. A Tc of 91K with a transition width of 0.5K is observed for sample C whereas samples B and A exhibit widths of 2 and IK respectively. The Meissner effect was observed to be 35, 65 and 50% for samples A, B and C respectively. 

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