Solid-state reactions diffusion

The solid state reactions at low-heating temperatures have their own characteristics. There are four steps in a typical solid state reaction diffusion, reaction, nucleation, and growth. At low heating temperatures, any step can be the rate determining step of solid state reaction. By means of this method, many new compounds have been synthesized. In recent years, much progress has been made in the preparation of nanomaterials by solid state reactions at ambient temperatures. 

A small particle size of the reactant powders provides a high contact surface area for initiation of the solid state reaction diffusion paths are shorter, leading to more efficient completion of the reaction. Porosity is easily eliminated if the initial pores are very small. A narrow size... 

The loss of the guest molecules corresponds to endothermic processes with low enthalpic values ( AH(jec l3-30 KJ rool l). The rate constants for such processes were evaluated for each compound at several temperatures, by fitting isothermal TG curves to different kinetic physical mechanisms of solid state reactions (diffusion, nucle-ation, growth, nucleation-growth and homogeneous)The kinetic parameters (Ko, Ea) were calculated from an Arrenhius plot of the rate constants. The declathration physical mechanisms were assigned on the basis of agreement between these calculated kinetic parameter and those determined from non-isothermal TG curves by mean of Coats--Redfern method. 

The application of RBS is mostly limited to materials applications, where concentrations of elements are fairly high. RBS is specifically well suited to the study of thin film stmctures. The NMP is usefiil in studying lateral inliomogeneities in these layers [30] as, for example, in cases where the solid state reaction of elements in the surface layers occur at specific locations on the surfaces. Other aspects, such as lateral diffusion, can also be studied in tluee-dimensions. 

Koenig U and Schultze J W 1992 Solid State Ion. DIffus. Reactions 53-56 255... 

An example of a journal hovering between broad and narrow spectrum is Journal of Alloys and Compounds, subtitled an interdiciplinary journal of materials science and solid-state chemistry and physics. One which is more restrictively focused is Journal of Nuclear Materials (which I edited for its first 25 years). Ceramics has a range of journals, of which the most substantial is Journal of the American Ceramic Society. Ceramics International is an example of an international journal in the field, while Journal of the European Ceramic Society is a rather unusual instance of a periodical with a continental remit. More specialised journals include Solid State Ionics Diffusion and Reactions, and a new Journal of Electroceramics, started in 1997. 

G. Schulz, M. Martin. Computer simulations of pattern formation in ionconducting systems. Solid State Ionics, Diffusion and Reactions 101-103AM,... 

Fej04 . A similar correspondence between theory and practice has been found for growth of Fej04 by the solid state reactions from FeO and Fe, , between 600 and 1 200°C. The growth rate of FeO is within 10% of the theoretical rate expected from Fe lattice diffusion, calculated according to the Wagner theory . 

In this case, we have given both the starting conditions and those of the intermediate stage of solid state reaction. It should be clear that A reacts with B, and vice versa. Thus, a phase boundary is formed at the interface of the bulk of each particle, i.e.- between A and AB, and between B and AB. The phase boundary, AB, then grows outward as shown above. Once the phase boundary is established, then each reacting specie must diffuse through the phase AB to reach its opposite phase boundary in order to react. That is- A must difiuse through AB to the phase boundary... 

However, this is not how it occurs in Nature. We have presented the above concept because it is easier to understand than the actual conditions which occur. Thus, the overall solid state reaction is dependent upon the rate of diffusion of the two (2) species. These two rates may, or may not, be the same. The reason that A and/or B do not react in the middle, i.e.- the phase AB, is that AB has a certain ordered structure which probably differs from either A or B. But there is a more important reason which is not easily illustrated in any diagram. 

We find that this solid state reaction is very slow, even at 800 °C., and occurs at the interface of the two types of particles. The reaction is slow because it is diffusion-limited. What is happening is that since the silica-network is three-dimensionally bound, the only reaction that occurs is caused by the difiusion of Ba2+ atoms within the network, as shown in the following ... 

Note that diffusion occurs only in one direction because the silica-tetrahedra are not free to move. What is actually happening is that the three-dimensional network of tetrahedra is being rearranged to form cmother structure. This illustrates the fact that the actual structure and composition of the two reacting species are the major factor in determining the nature and speed of the solid state reaction. 

The BaO is produced in the form of very small particles of nearly atomic proportions which react immediately to form the silicate. Actually, the rate of reaction is proportional to the number of nuclei produced per unit vdlume. A nucleus is a point where atoms or ions have reacted and begun the formation of the product structure. In the case of the BaO reaction, the number of nuclei formed per unit of time is small and formation of the structure is diffusion limited. In the case of BaCOa decomposition, the atomic-proportioned BaO reacts nearly as fast as it is formed so that the number of nuclei per unit volume is enormously increased. It is thus apparent that if we wish to increase solid state reaction rates, one way to do so is to use a decomposition reaction to supply the reacting species, we will further address this type of reaction later on in our discussion. 

We have already dealt with two of these. Section 2 dealt with formation of a phase boundary while we have just completed Section 4 concerning nuclei growth as related to a phase boundary. We will consider diffusion mechanisms in nuclei and diffusion-controlled solid state reactions at a later part of this chapter. 

We are now ready to consider some soUd state reactions that relate more directly to the real world. These include the tarnishing reaction and Pick s Laws of Diffusion. Both of these scientific areas have been rigorously studied because of their importcmce in revealing how diffusion mechanisms are related to everyday solid state reactions which occur on a daily basis. 

Ba2+wlll be very fast while the silicate ion will diffuse very slow (if at all). Because of the vast differences in the types of diffusing species, there is no reason to expect all of them to diffuse at the same rate, particularly when we compare electrons and vacancies. Actually, this aspect of solid state reaction has been studied in great detcdl and the Kirchendall Effect deals with this aspect. 

There are three (4) types of diffusion-controlled reactions possible for heterogeneous solid state reactions, viz-... 

For phase-boundary controlled reactions, the situation differs somewhat. Diffusion of species is fast but the reaction is slow so that the dlfiusing species pile up. That is, the reaction to rearrange the structure is slow in relation to the arrival of the diffusing ions or atoms. TTius, a phaseboundary (difference in structure) focus exists which controls the overall rate of solid state reaction. This rate may be described by ... 

Here, we find it necessary to be able to measure the progress of a solid state reaction. If we can do so, then we can determine the type of diffusion involved. If - log (In(l-x)) is plotted against In t, one obtains a value for the slope, m, of the line which allows cleissification of the most likely diffusion process. Of course, one must be sure that the solid state reaction is primarily diffusion-limited. Otherwise, the analysis does not hold. 

Let us now turn to diffusion in the general case, without worrying about the exact mechanism or the rates of diffusion of the various species. As an example to illustrate how we would analyze a diffusion-limited solid state reaction, we use the general equation describing formation of a compound with spinel (cubic) structure and stoichiometry ... 

In this mechanism where Da 2+ Db3+, transport of external oxygen gas is involved in the overall solid state reaction, accompanied by electronic charge diffusion. 

It should be clear, by examining 4.8.9. carefully, that a number of possibilities exist for the diffusion of reacting species through spinel during the solid state reaction used to form it. Which of these is more likely will depend upon the exact nature of A" as well as that of B". 

Note that the ions given in 4.8.10. cancel out in the equations, and that only the overall solid state reaction remains. However, it has been determined that diffusion is limited by ... 

The overall reaction mechanisms are diffusion-controlled, and the total solid state reaction can be summarized as follows ... 

The only conclusion that we can draw is that diffusion-controlled solid state reactions tend to produce mixtures of compounds, the relative ratio of which is related to their thermod5rnamic stability at the reaction temperature. Obviously then, if we change the temperature of reaction, we would expect to see somewhat different mixtures of compounds produced. 

It should be clear by comparing the examples for calcium silicate and barium silicate that one cannot predict how the diffusion-controlled solid state reactions will proceed since they are predicated upon the relative thermodsmamic stability of the compounds formed in each separate phase. 

The series of diffusion-controlled reactions are for the case of the solid state reaction between BaO Si02 as given in 4.9.16. above. These solid... 

Note that aU of these methods attempt to bypass the dependence of the solid state reaction upon diffusion. But, using a gaseous reactant may not be practical in all cases. And. sometimes it is hard to find a flux which does not interfere with the reaction. A flux is defined as follows ... 

The very fine particles of nearly atomic proportions react almost immediately. Because the BaO product hcis an extremely large surface area, the solid state reaction Is not diffusion limited. In the last method (see 4.9.18.), we might use a precipitated product to use as the basis to form the desired compound. We might precipitate ... 

If a solid state reaction is diffusion-limited, if is unlikely that we can obtain 100% of any product, and will alwa obtain a mixture of compounds whose relative ratio will depend upon their thermod3mamic stability at the firing temperature. 

Several different types of species, including various solid state defects, diffuse and form a phase boimdaty of reaction, which may further react to form specific compositions. 

Although we have covered mechanisms relating to solid state reactions, the formation and growth of nuclei and the rate of their growth in both heterogeneous and homogeneous solids, and the diffusion processes thereby associated, there exist still other processes zifter the particles have formed. These include sequences in particle growth, once the particles have formed. Such sequences include ... 

Given that Gd.203 reacts with AI2O3 to form GdA103, draw a diagram showing the reaction conditions, the phase boundary formed and the diffusion conditions likely to prevail in the solid state reaction. 

Sintering of particles occurs when one heats a system of particles to an elevated temperature. It Is caused by an interaction of particle surfaces whereby the surfaces fuse together and form a solid mass. It Is related to a solid state reaction In that sintering is governed by diffusion processes, but no solid state reaction, or change of composition or state, takes place. The best way to illustrate this phenomenon is to use pore growth as an example. 

With the exception of single-crystal transmission work, most solids are too opaque to permit the conventional use of ultraviolet/visible (UV/VIS) electronic spectroscopy. As a result, such work must be performed through the use of diffuse reflection techniques [8-10]. Important work has been conducted in which UV/VIS spectroscopy has been used to study the reaction pathways of various solid state reactions. Other applications have been made in the fields of color measurement and color matching, areas which can be of considerable importance when applied to the coloring agents used in formulations. 

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