ΠΕΠΠ1
chemical science series
REACTIONS There are only two fundamental
considerations
in
IN THE studying
solid state reactions—transport
to the reac-
SOLID tion zone and the chemical reactions
themselves—but
STATE the fundamentals
lead to an infinite variety of specifics
DR. GIUSEPPE PARRAVANO, University of Michigan, Ann Arbor, Mich.
The establishment of chemical equilib rium in solids takes place by re arrangement of atoms or groups of atoms. This may involve the immedi ate neighborhood of each lattice point or it may occur over distances which are orders of magnitude larger than atomic dimensions. In the former in stance a transformation of the solid's crystal structure is produced, while in the latter case one has the formation of a chemically different solid. In both cases, w e may talk about solid state reactions in the sense that chemi cal bonds in the solid are broken and formed; that is, a chemical and geo metric reshuffling of the solid phase takes place. It is the task of solid state science to unravel all the phe nomena involved in the rearrangement
SCIENTIFIC FOCUS on solid state reac tions produces, among other things, an exciting array of solid state devices
of atoms in solids, so as to reach an understanding of solid state reaction mechanisms. These topics have been studied for a long time. Scientific curiosity on reactions in solids was sparked by the discovery that some solid state trans formations occurred very rapidly at low temperature, thus contradicting the old maxim, corpora non agunt nisi soluta. Only recently, however, has progress in the several areas of solid state chemistry and physics given new impetus to solid state reaction studies. From these, many variables of im portance to the behavior of reactions in solids have emerged. It is not pos sible to discuss all of them in this short presentation. I have therefore chosen to analyze the operation of but a few, selected somewhat arbitrarily according to the tastes of the writer and, hopefully, following the interests of the reader. First of all, one must realize the variety of transformations and reac
tions involving solids: phase changes in elements and chemical compounds, formation of metastable phases, and chemical reactions like reduction, oxi dation, and decomposition. Secondly, we must understand that the scientific task ahead involves several stages. One should be able to (a) distinguish and characterize the physicochemical nature of the different steps in the over-all transformation; (b) determine the important variables affecting each step; (c) relate mathematically the variables to each step's development in time and space; and (d) derive an over-all expression for describing the atomic changes in terms of macro scopic quantities. This is a formida ble task, indeed. We shall try to indi cate the main avenues currently being pursued toward its accomplishment. Nature of Solid State
Reactions
We may start our discussion con veniently b y briefly analyzing t h e MARCH
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METALLURGY. An Owens-Corning engineer makes a photomicrograph of a high temperature alloy. Solid state reac-
peculiarities of reactions in solids in the context of present knowledge about reactions in gases. A chemical reaction results from atomic and molecular collisions which occur according to definite statistical laws. As a consequence, a reaction among gaseous species takes place at a uniform rate throughout the reaction zone. To a large extent, the reacting system is independent of space coordinates and can be described mathematically with equations involving time only. In reactions with solids, the reactants are in general not initially mixed at the atomic level. They must therefore diffuse or penetrate into each other if a reaction is to start and propagate within the solid phase. Thus, spatial coordinates become a controlling element, and a complete description of the system requires the development of relationships between timerate or time-concentration and at least one spatial coordinate. It should be pointed out that this requirement is not typical of solid state reactions alone. It extends to other systems like flames, explosions, heterogeneous polymerizations, and catalytic homoheterogeneous reactions in general. A second characteristic of solid state reactions emerges from the realization 112
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tions are also important in ceramics, glass, polymers, catalysts, solid propellants, and many other fields
that, in principle at least, the reaction can be described as a movement of interphase boundaries. Thus, it becomes dependent upon the extent of the boundary, or the "degree of mixing" of reagents and products. The surface to volume ratio of the solids partaking in the reaction becomes an important variable, kinetically as well as thermodynamically; and this can be used to classify solid state reactions by the degree and scale of dispersion of the solid medium. We can, then, distinguish reactions among macroscopic single crystals and in polycrystalline aggregates (pellets, slabs, coarse or fine powders), gels, molecular complexes, and molecular dispersions. In the latter group are included free radical recombination in the solid and solid state polymerization, whose propagation step is quite unique. This will be discussed later. We recognize, thus, two fundamental processes in a solid state reaction: (a) the chemical reaction itself, during which the breaking of old chemical bonds and the formation of new bonds occur, resulting in production of a nucleus of a new phase ( nucleation ) ; and (b) the transport of matter to the reaction zone (growth of nuclei). The latter's contribution to the over-
all reaction can be vanishingly small depending upon the relative value of the distance to be traveled and the degree of dispersion of the reagents. Thus, solid state changes involving a phase transformation only, or requiring mass transport through molecularly thin or thick films of product will yield a different rate expression in each case. Active States of Solids Before analyzing solid state reaction kinetics in more detail, it would be instructive to review briefly some thermodynamic aspects of solids relative to their degree of division. There is a wealth of information in the literature on the effect of particle size on the chemical reactivity of solid aggregates. . The so-called active states of finely divided powders, gels, and highly porous materials with open structure and texture have been studied intensively with x-ray, thermochemical, magnetic, and gas phase equilibrium methods. The higher energy content of these states results from larger surface area (smaller particle dimensions), lattice distortions of several kinds (stretching and shrinking of the structure), combination of crystalline and amorphous
In discussing solid state reaction* kmetically it is desirable to distin guish between the transport of matter to the reaction zone and the chemical reaction itself. In doing so one must refer to diffusioniess transformation—a solid state change taking place without a change in composition—which comes about by development of a crystal lattice different from that of the matrix. Macroscopically, this can be described as a movement of a boundary between two crystal phases; microscopic ally, it is envisioned as a set of rotations and translations of the original crystal axes. In any case, the assumption is that a volume element of a new phase is formed, following which the nuclei grow into the original matrix by displacing a phase boundary.
regions, and completely amorphous structure. The well-known Thomson relation in E. = M. h p0 RTV gives the vapor pressure, p, in equi librium over a surface with a radius of curvature, r, of a solid of density, p, and molecular weight, M, as a function of the pressure in equilibrium over a flat surface, p 0 . This has been re peatedly used to account for the larger chemical reactivity of small particles. For example, when γ = 750 ergs per square centimeter, M = 18, ρ = 1,Τ=: 0° C , and r = 50 Α., then — = Po ρ 10; when τ = 5 Α., then — = 10 10 . Po These values correspond to an increase in the free energy of the system, —RT 1 In - , of 2.3 to 23 times. Ρ Lattice distortion effects can be determined by means of calculations based on the Madelung-Born lattice energy. These calculations give lat tice energy as a function of the dis tance between atoms in the solid; therefore they are suitable for com puting the increased energy of the solid due to variations of atomic dis
tances from their equilibrium values. By careful dehydration of M g ( O H ) 2 , various MgO samples have been pre pared with similar particle size but different degrees of lattice distortions (measured by x-ray intensity). It was found that such distortions in crease lattice energy by 1.7 kilocalories per mole. This value is consistent with energy values obtained by meas uring heats of solution. Similarly, the decomposition pressure of yFeOOH at 20° C. in equilibrium with the active form is found to be 2.5 χ 10~6 mm. Hg, while a value of 150 mm. Hg is obtained for the inactive form. The amorphous form of aF e 2 0 3 has an energy content of 13 kilocalories per mole above the energy content of the crystalline variety. These energy effects in particulate solid systems may manifest themselves in other phenomena. In a particulate nonmetallic solid of sufficiently small particle size, the distribution of electri cal charges throughout the particles can be affected by the particle size. Whenever this is of the same order of magnitude as the thickness of the space charge layer at the surface, the solid behaves electrically as if it were composed of surface only. As a con sequence, small particles may become
highly charged and have a strong tendency to repel each other. In ferromagnetic materials, if the particle size is of the same order of magnitude as that of the magnetic domains, the material is no longer ferromagnetic (Fe and F e 3 0 4 are examples). Fur thermore, ferrimagnetic behavior may be the result induced in a solid by surface effects. Kinetics: Reactions over Short Distances Having briefly reviewed the thermo dynamic aspects, we may now go on to discuss solid state kinetics. We have already recognized the two fun damental steps that characterize solid state changes, namely, the chemical reaction itself and the transport of matter to the reaction zone. Kinetically, ft would be desirable to dis tinguish them and to know the mecha nism of each. To do so requires refer ence to studies on diffusionless trans formation—that is, solid state changes occurring without compositional changes. These transformations evolve through development of a crystal lat tice different from that of the matrix. The phenomenon can be described MARCH
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macroscopically as a movement of the boundary between two crystal phases and microscopically as a set of rotations and translations of the original crystal axes. Examples of such transformations are those occurring between allotropie forms of elements and compounds, those which involve crystallization of a super-cooled liquid such as glass, the order-disorder changes in metal alloys, and the rearrangement of carbon atoms in the martensitic transformation in iron-carbon solid solutions. In the latter case, carbon does not have to travel farther than the atomic dimensions; therefore there is no change in local concentration. In all these cases, we can assume that a volume element of a new phase is formed and that there is subsequent growth of the nuclei into the original matrix by displacement of a phase boundary. The nuclei-forming mechanism is still very obscure. We are aware that different conditions for nucleation exist at the surface or in the interior of a solid, at grain boundaries, microcracks, or dislocations, and so on. For example, a reversible decomposition reaction cannot easily start in the interior of a perfect crystal, since products cannot escape rapidly and a local build-up of products will restore the original compound. On the other hand, products can escape easily from the surface of such crystals. Qualitatively one can visualize several conditions that may give rise to nuclei of a new phase in the interior or at the surface of a solid. Fluctuations in elastic and thermal energy may arise under the effect of stresses, and local deformations like those encountered in the "active" states may be produced. In fact it is well known that shearing stresses affect solid state transformation rates. Ordinary grinders may convert lead dioxide, manganese difluoride, calcium carbonate, and beryllium fluoride into their high pressure modifications. Under equilibrium conditions, these would require pressures up to 10,000 atmospheres at room temperature. It is not known whether this is an effect of stored strain energy or actual bond rupture, or both. Local temperature gradients may be formed. Fluctuations in atomic configuration may induce clusters of atoms or lattice defects with a spatial pattern resembling that of the product phase. Energy and entropy values for different types of nucleation, when 114
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SOLID STATE DEVICE. A Hughes Aircraft scientist observes growth of a synthetic ruby crystal which is to be used in experiments with a laser solid state device that emits a "coherent" light beam
known, would greatly help in classifying the various nuclei-forming processes. Theoretically the problem must be attacked first by finding out the probability of forming favorable configurations. This involves calculating entropy and energy changes corresponding to formation of the activated complex. Computation of the entropy is a relatively easy task, but the energy calculation is made difficult by anisotropic displacement of energy throughout a crystal lattice. This holds true even for a cubic one. We may obtain some help in the calculations from correlations with the elastic constants of the solid. A research program along these lines should produce an understanding and some control of the nucleation step. Several interesting problems are connected with control of the nucleation step in a solid state transformation. Consider, for example, the devitrification of glass. Here, nucleation generally occurs either at the surface or at some internal imperfection. The resulting crystals are coarse, oriented, and poorly connected, and marked de-
terioration of mechanical properties of the glass ensues. If, however, a large number of foreign nuclei are i n troduced, crystal growth can develop in a more orderly fashion around the added nuclei. Titania was one of the first materials to be dispersed in glass to control nuclei formation. Metals like gold, silver, copper, cerium, and platinum are also effective nucleation agents, when suitably dispersed in colloidal form in the glass phase. The resulting materials, known as glass ceramics, are characterized by completely random orientation of fine, uniformly sized grains; and they possess enhanced mechanical and electrical· properties. After a cluster of atoms in the solid has assumed the new configuration, more atoms must be added in order to form a stable nucleus. The basic step here is the movement of an atom from a cell of the original configuration to a cell of the nucleus phase. In a general fashion this is achieved by severing the bonds between the atom and its neighbors in the original con-
rather open structure for the activated complex. To overcome the resulting difficulty, it is advantageous to use solvents. In solution, the path of the transformation is changed, and the AVî that is needed is smaller. This is the situation that exists in the case of the synthesis of diamond from graphite. The synthesis has been successfully achieved by dissolving graphite in troilite ( FeS ). Not all solid state transformations follow this pattern. In martensitic type transformations we observe these facts: The propagation rate of the transformation is generally extremely high; the propagation follows preferred orientations; and it is facilitated by mechanical stresses. Probably the almost instantaneous propagation is the consequence of an energy chain, which results whenever the energy released during the repositioning of the atom is sufficient to activate a neighboring atom. In any event, these transformations must entail a low activation energy—very much lower than the sublimation energy. Intermediate SOLID PROPELLANTS. These hold promise for tiny precision instruments. Sperry Gyroscope technician inserts piece of solid propellant into gas generator for use in guided missile instruments
figuration. One may assume a simultaneous cutting of all of the original bonds of the atom in question. The atom then passes through a "gaseous" state at the interface. On the other hand it may happen that the old bonds are not completely broken before some of the new ones are formed. In the latter case one has a succession of activated complexes for each atomic addition. Experimental studies reveal that the former model applies to the transformation of monoclinic to rhombic sulfur. This is evident in that the activation energy for the transformation is close to the sublimation energy of sulfur—22.5 kilocalories per mole. But, in a sense, the question as to whether the atomic rearrangement involves complete isolation of the atom is without much significance—the atom will always be within the effect of the crystal's field. One may more properly discuss the degrees of freedom of the atom during the transition. Applying absolute rate theory to the growth of nuclei, at least to the extent of deriving relatively consistent data
on enthalpy and entropy, will prove helpful. As a first approximation, the activation energies can be used to indicate the type of mechanism involved. Transformations requiring an exchange of complexes such as Si0 4 = ; C0 3 = ? N 0 8 = , and Se 8 must occur by means of a complete isolation of the atomic group, and they would be expected to involve high activation energies. This expectation has been experimentally confirmed in several studies. On the other hand, transformations like graphite-to-diamond, which require bond hybridization only, should need smaller energies of activation. It might be interesting at this point to evaluate the interplay of thermodynamics and kinetics in phase transformations. In practice, the situation often arises wherein the phase obtained is stable only under high pressures. The pressure coefficient of the reaction rate is the volume change, AV*, taking place to form the activated complex. Since AV* is positive, high pressures retard the transformation. Generally, AV* is quite high ( 10 cc. per mole for diamond), indicating a
Cases
Presently, we know of solid state reactions whose mechanisms are in some respects intermediate between the previously discussed cases and those that are characterized by changes in chemical composition and mass transfer over large distances, to be discussed later. An example of the intermediate case is solid state polymerization. The initiation of the reaction occurs by the production of monomelic free radicals at the surface and at defects of various kinds. This has been shown conclusively, for example, for the solid state polymerization of acrylamide. Two types of propagation may be envisaged. If we regard the lattice of the monomer crystal as being composed of a series of tracks along which propagation takes place, then the monomer molecules should be located in such a way that, with small configurational changes, the addition reaction can occur. The configuration of the transition state is subjected to strict rules by the geometry and symmetry of the lattice, and one would expect this situation to be reflected in the configuration of the polymer. But indications are that this is not the major mechanism of propagation. The predominant mechanism involves formation of a boundary surMARCH
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magnesium, mercury, zinc, and cad mium with vinyl monomers (methylmethacrylate, acrylonitrile, acrylamide, methylacrylate) rapid polymerization occurs in the solid state at tempera tures from - 1 4 0 ° to - 1 0 0 ° C. These systems raise intriguing possibilities, since they show a low termination rate and low activation energy for chain growth. Some known results of this situation are the presence of "live" centers and an isotactic chain struc ture, at least for polymethylmethacryl ate, in the polymer formed. Reactions Involving Range Distances
I Solid state transformation accompanied by changes in composition in| volves a transfer of matter over large distances compared to atomic I dimensions. This transfer can be defined in a phenomenological way by Ρ charge, potential difference, flux, and conductance. To illustrate the t variation in potential, ior example, we may postulate the reaction A(solid) + B(solid) ~> AB(solkl) with the simplifying assumption that diffusing particles come only from A(solid). The variation in chemical potential, μΑ, of this substance in the solid system's three phases then falls into two limiting cases. Case I shows the limiting situation when the phase boundary processes are rapid, in this case, diffusion through the product AB is controlling the rate of the solid state reaction. Case II shows the other limiting situation, where phase boundary processes are not fast compared to diffusion through the product. The chemical potential gradient is smaller than in Case I, and A(solid) accumulates at the phase boundary between AB and B. In this case, the solid state reaction is slowed down until the situation reverts to Case I.
face between monomer and polymer. Propagation occurs when monomer and growing polymer chain contact each other across the boundary; and in this case a high monomer mobility in the solid state is needed. This mechanism seems to better explain the experimental data collected so far on this type of solid state reaction. Polymers with glassy and fibrous structures can be produced, and in 116
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both cases the solid polymer is amorphous. The interest in studies on these polymers lies, of course, in a desire to use the crystal lattice as a highly ordered matrix for inducing a regular pattern in the propagation. Hopefully, this should result in a crystalline polymer. Recently another type of solid state polymerization has been discovered. By mixing "molecular" dispersions of
Long
Whenever the solid state trans formation occurs with compositional changes, a step involving the transfer of matter over distances several orders of magnitude longer than atomic dis tances is present. The most fruitful description of transport phenomena in solids is obtained by expressing in a phenomenological fashion the relation among the quantities involved. The advantages of such a procedure are twofold. On the one hand it provides a frame of reference and a set of mathematical equations for describing the time and spatial sequence of the phenomena and for predicting their behavior. On the other, it serves as a basis for a finer, atomistic appraisal of the physicochemical events under lying the transfer of matter. Phenomenologically, solid state transport is defined by charge, poten tial difference, flux, and conductance. The charge represents the unit quan tity of material transported across the solid. The potential difference, or driving force, is the difference be tween the final and initial energy levels of the system. Since these po tentials are really tensors, the result ing chemical flow will also be a tensor; άμ and the diffusion coefficient, D = σ -r~ where σ, μ, and η are the chemical conductivity, potential, and concen tration, respectively, will be a function of direction. The relation between the reaction rate, as controlled by a mass trans port per unit area—or flux—J, and a potential, A, can be expressed as J = CA, where C is a measure of the con ductance of the system. It should be noted, however, that for purely chemi cal reactions (not involving spatial transport) serious departures from Ohm's law are encountered. The
potential of importance here may be due to electromotive force, stress, temperature, or thermodynamic activity. The contribution of the latter two potentials to the rate of solid state reactions has been the subject of many ^ investigations. However, this is not true of the first two, although such studies no doubt are desirable. For example, kinetic studies on the reaction among ionic solids, when they are under the influence of an electrical potential and when appreciable ionic conductivity exists, are of interest. Similarly, the effect of an elastic potential on the transport rate has not been clearly defined by means of critical and unequivocal experiments. It is well known that reaction rates at the surface termini of dislocations are enhanced. As a matter of fact, this effect is used to appraise dislocation densities in a solid. A dislocation is characterized by a line and a vector, which gives the extent and direction of the displacement of lattice planes brought about by the introduction of the dislocation into the crystal. Since the field around a dislocation is of an elastic nature, a quantitative study between stress and rate of reaction would be of interest. Furthermore, a dislocation, being a thermodynamically unstable defect, tends to emerge at the surface of a crystal. In so doing, the dislocation completes its displacement in a given plane and steps appear on the surface. The step width at a given point on the edge of the slip plane is equal to the component of the dislocation vector, b, lying in the slip plane normal to the edge. If the crystal is made to flow plastically, a new surface of area proportional to b 2 is produced, with a free energy yb 2 . Since this new surface contributes to the solid's reactivity, stresses above the critical shear stress of the solid should affect solid state reactivity. There is no doubt that as knowledge of the structure, energy, and interactions among dislocations progresses, a . whole new area of the chemistry of dislocations, grain boundaries, and plane defects will be uncovered. Historically, these developments will probably parallel similar developments that took place previously in the field of point defects in solids. It is worth noting at this point that the inverse effects of surface chemical reactions on the mechanical properties of solids are well known. Many of the experimental results on such
properties can be explained by the dislocation theory, since this is basic to both surface reactivity and plastic deformation of crystalline solids. In some cases differences in surface free energy may provide the only driving force for transport. Phenomena like sintering, polygonization, facet formation, pore shrinkage, and, in some instances, whisker growth, may be the result of a driving force of physical origin. Mechanistic
Description
Mechanistically, mass transport through a solid substance is described as a movement of carriers along a reaction path. This path is composed of a continuous array of free carriers from a source to a sink. Thus, the problem of understanding a solid state reaction includes a knowledge of the nature of carriers, their concentration per unit volume along the path, their speed, the mean distance traveled between collisions with other carriers, and the mean time interval elapsed between successive encounters. We also need information on the energy required to produce carriers for transport, since this energy controls the equilibrium concentration of
the carriers. In addition, once the carriers are free, energy may be needed to move them along the trail —the more so if the latter is rough and steep, leading to a high col. The point of departure of carriers as well as their final destination should also be known. These questions represent a multitude of problems, which have been completely solved for only a few solid state reactions. Carriers may be atoms, molecules, ions, or electrons, or a variety of possible associations among point defects, impurities, and lattice species. These "atomic clubs" are bound by coulomb or exchange interaction forces. Information on the nature of the carriers can be obtained by measuring diffusion coefficients, transport numbers, and ionic and electronic conductivities, as well as the dependence of these on temperature, partial pressures of metal and nonmetal (for a salt), and additions foreign to the host species. In the cases of several compounds, experiments on whether a given system follows the Nernst-Einstein relation between diffusion coefficients and ionic mobility have given a powerful insight on the nature of carriers and their concentration. For example, we know today that, in silver sulfide, sil-
GLASS CERAMICS. Dr. S. Donald Stookey, manager of Corning Glass' fundamental chemical research department, found that adding special ingredients to glass resulted in very hard, fine-grained Pyroceram, shown in cube form MARCH
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ver ions are far more mobile than sulfide ions. Thus, one expects that in the tarnishing of silver by sulfur, silver ions migrate across a film of silver sulfide to the outer surface. This has been confirmed by experiments. Similarly, we know that in uranium dioxide the diffusion of oxide ions is much faster than the diffusion of uranium ions. Therefore the latter control the transport rate in uranium dioxide. In general, the diffusion of metal ions dictates the rate of the process. The formation of spinels, ferrites, and chromites from the component oxides generally follows this mechanism. A rough idea of the rate of diffusional processes at a given temperature can be obtained by comparing the latter with the absolute melting temperature, T m , of the crystal (Tamman rule). In general, bulk diffusion becomes appreciable whenever the temperature during the investigation is higher than 0.5 T m , while diffusion along the surface sets in at much lower temperatures. There are, however, many exceptions to this rule. For example, diffusion in network structures, like oxygen in silica, probably occurs at a much lower rate than is suggested by their melting points. Sulfide films on copper exposed to polysulfide vapors are known to grow to a thickness of several thousand angstroms in a few seconds at room temperature. The rate of diffusion when developing a latent photographic image is of the same order of magnitude. * The available reaction paths go through the crystal interior, along the crystal surface, and through the surrounding gas or liquid phases. When bulk diffusion predominates, the relation between time and the amount of product distributed in a layer of constant cross section is parabolic. For example, in the reaction between contacting magnesium- and chromiumoxide pellets the weight increase of a layer of the spinel MgCr 2 0 4 , which forms between the two contacting pellets, varies linearly with the square root of time. In addition to this kinetic information, one may investigate the direction of movement of the boundaries between reagents and products. This can be done visually in those simple cases where the product has marked color, or by means of inert markers. In the instance of MgCr 2 0 4 , the spinel-magnesium oxide interface 118
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DR. GIUSEPPE PARRAVANO, a professor in the University of Michigan's chemical and metallurgical engineering department, received his doctorates in electrical engineering and chemistry at the University of Rome in 1940 and 1942, respectively. He was an Italo-American fellow and Elizabeth Proctor fellow at Princeton University in 1946 and 1947, and remained with that institution as a postdoctoral research associate until 1955. He also held a Privât docent at the University of Rome in 1954. After three years each with The Franklin Institute and the University of Notre Dame, he began his present association with Michigan in 1958. Dr. Parravano has written many papers on solid state reactions, heterogeneous catalysis, and other subjects. He is a member of ACS, AIChE, and Sigma XL grows preponderantly into the magnesium oxide pellet, indicating that the reaction is controlled by diffusion of the chromium species through the spinel layer. The fundamental mechanisms of bulk diffusion currently are under close scrutiny and extensive investigation. Surface diffusion plays an important role in crystal growth and adsorption but the details are poorly understood. One possible mechanism entails the motion of lattice steps on the crystal surface. Steps of random spacing and various heights, from monatomic up, are always present on crystal surfaces, and they are able to move and interact freely. Presently, there is a tendency to use the flow of surface steps to explain polygonization, facet formation, whisker growth, and under certain conditions, sintering. Diffusion along internal surfaces, such as grain boundaries, is even less well understood. There is also the possibility that transport of material through the gas phase provides a path during solid state reactions. Among the reacting systems in which gas phase transport is significant are the formation of NiCrL>04 from nickel and chromium oxides and of ZnALO.t from zinc and aluminum oxides. The present understanding of this type of mass transfer among solids is derived mainly from studies on the sintering rate be-
tween single crystals. The driving force here is given by differences in vapor pressure in different parts of the reacting system. The differences arise from thermal gradients, surface curvature, and chemical reactions between gaseous and condensed species. If evaporation is unhindered, the rate of transport is controlled by the rate of evaporation of the solid. But it may also be governed by diffusion of the evaporating species through a hydrodynamic boundary layer around the solid particle. This film originates in differences in concentration between the gaseous layer directly on the solid surface and the bulk of the gas phase. In contrast to the previous case, the rate of transport becomes in this instance an inverse function of the total pressure. Material transport involved in the welding together of single crystals of sodium chloride and zinc oxide follows this pattern. Apparently no experimental work investigating these effects in detail in chemically reacting systems has been done. It should be pointed out that a rate that is dependent on the partial pressure of one of the component species, but independent of the total pressure, indicates an entirely different reaction mechanism.
Conclusion The over-all kinetics of a solid state reaction results from a combination of factors: carriers, their source and sink, driving forces, and reaction paths. Obviously, a great variety of possibilities exists. It is the intriguing and challenging job of the research chemist to separate the various factors and clarify the nature of the entities involved. One should also look to neighboring areas of the physical chemistry of solids for help in suggesting new hypotheses and in planning critical and meaningful experiments. For example, the detailed understanding of the distribution of species in a chemically different matrix during the initial stages of reaction is lacking. Or one may ask a rather different question. Whenever solid bodies are brought in contact for reaction, how does the initial contact between maciOScopically and microscopically rough surfaces occur? Which mech anism takes care of establishing the contact at the atomic level on a large scale? There is recent evidence to show that whiskers growing between adjacent solid particles may provide
Λ
the initial contact, which can rapidly .extend to cover large areas of the particle surface. Also, solid state reactions occupy a central position in the exploration of the fascinating and largely unknown field of solid surfaces, their nature, composition, properties, and applica tions. Many are the questions still to be answered and problems to be formu^feted, and there is no doubt that the future of solid state science is ex citing, indeed. Our knowledge of re lictions and transport phenomena in solids is rapidly deepening, and it is providing us with a mastery over solid state changes that has never be fore been achieved. * Solid state science is producing to day an increasingly larger impact on "many areas of science and technology and exerting a great appeal to many scientists. This appeal will grow "stronger in future years, since richer rewards are awaiting scientists and engineers who will dedicate them selves to the nagging problems of the solid state.
menu: to color chemists
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SUGGESTED ADDITIONAL READING
de Boer, J. H., et al, editors, "Reactivity of Solids. Proceedings of the Fourth International Symposium on the Re activity of Solids," Elsevier Publishing Co., Amsterdam, 1961. Garner, W. E., editor, "Chemistry of the .^ Solid State," Academic Press, Inc., New York City, 1955. Hauffe, K., "Reaktionen in und an Festen Stoffen," Springer-Verlag, Berlin, 1955. Rees, A. L. C , "Chemistry of the Defect Solid State," Methuen and Co., Lon don, 1954 "Crystal Imperfections and the Chemical Reactivity of Solids," Discussion No. 28 of the Faraday Society, 1959 ".Molecular Mechanism of Rate Processes in Solids," Discussion No. 23 of the Faraday Society, 1957.
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DIRECTORY This section includes: CHEM ICALS EXCHANGE—Chemicals, Resins, Gums, Oils, Waxes, Pig ments, etc.; EQUIPMENT MART —New and Used Equipment, Instru ments; Facilities for Plant and Lab oratory; TECHNICAL SERVICES —Consultants ; Engineering, Testing, Professional Services.
SECTION
EQUIPMENT MART
Advertising Rates: Space rate is $50 per inch. Lower rates available on contract basis. An "inch" ad vertisement measures Vs" deep on one column. Additional space in even lineal inch units. Maximum space—4" per Directory per issue. Set ads due 21 days in advance of publication; plated ads, 17 days.
STAINLESS STEEL TANKS Available in the following sizes:
24" χ 48" 12" χ 24"
8/2 " x 18" 5/2 " x 8"
Type 304. 400 PSI. Air Force surplus. Big values. FREE FOLDER.
Illinois Mfg. & Supply Co. 1829 S. State, Chicago 16, III.
EQUIPMENT MART M E L - T E M P ® MEASURES CAPILLARY MELTING POINTS l§l l§j
· · • •
room temperature to 400°C 500°C with special thermometer rapid heating and cooling one to three samples
MEL-TEMP is an integrated capillary melting point apparatus whose heater is controlled by a variable transformer. Excellent viewing is provided by a built in light and a 6-power lens. The attrac tive gray hammertone base occupies
$
only 97 5 0
Includes vial m.p. capillaries and 0-400°C thermometer. f.o.b.
Cambridge
SPECIAL THERMOMETER 100-500°C in 1 C ° , fits MEL-TEMP, borosilicate glass, Helium filled, 76 mm imm. $7.50 each Pat'd. in U.S. „ and Canada
Write for Bulletin 60N
LABORATORY
DEVICES
TECHNICAL SERVICES
VISCOMETERS
All A.S.T.M. sizes and many special sizes
1. 2. 3. 4. 5· 6.
Cannon-Fenske Type in stock. Ubbelohde Type Opaque Type Cannon-Ubbelohde Type Semi-Micro Type Cannon-Zhukov Type
7.
D i l u t i o n T y p e (for intrinsic viscosity)
8. Shear Types 9. Asphalt Types Our 24th year of service.
ORGANIC MICROANALYSES H. W. Galbraith, Ph.D. P. 0 . Box 4187
UNPRECEDENTED SENSITIVITY
All calibrations double checked. Write for bulletin 20.
in trace element
CANNON INSTRUMENT COMPANY P.O.Box 812 State College,Pa.
Bench-Type
VACUUM FILTER
ASCO VACUUM GAUGE shockproof · accurate PIRANI-TYPE
GENERAL· D Y N A M I C S GENERAL· ATOMIC DIVISION
Two-piece c o n s t r u c t i o n
SCHWARZKOPF MICROANALYTICAL LABORATORY Complete Analysis of Orqanic Compounds. Results within one week.
New transistorized circuit and φ ^ ^ Zener diode stabilization insures top performance! Wide range, fine calibrations, and easy reading are attained with its wide scale, illuminated meter movement and dual reading scale, (.1 microns Hg. to 5000 microns Hg.). It is self-calibrating. A new transistorized circuit insures long, trouble-free use and Zener diode stabilization helps to insure accu racy to better than . 1 % . The gauge is shock resist ant to 8 g.'s and is made of strong polyester, shockproof case and mount. 115 V.—50-60 cycle opera tion. 6" wide χ SV2 " high χ 8!/2 " deep. Only $ 1 4 9 > Tube E x t r a $ 2 8
-
Elements, Functional Groups, Molecular Weights, Physical Constants, Spectra. Analysis of Boro-Fluoro, and Silicon Compounds Trace Analysis
MICROANALYTICAL RESEARCH 56-19 37th A v e . , Woodside 77, New York
Telephone: HAvemeyer 9-6248, 9-6223
Consultation JEOOCL
I N C O R P O R A T E
ARTHUR F. SMITH, INC.
Ο'
BERNARD L. OSER P h . D .
Director
WHERE EXPERIENCE C O U N T S
CHEMICALS EXCHANGE Sturdy and
G A S
CHROMATOGRAPHY THE KOFLER HOT BENCH
1 0 " high.
U.S. STONEWARE AKRON 9, OHIO
MARCH
Toxicology Pharmacology Nutrition Biochemistry Bacteriology
MELTING POINTS in SECONDS with
working capacity. Both sizes less than
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α/ηχί
Maurice Avenue at 58th St., Maspeth 78 New York City TWining 4-0800
simple design. Two sizes: 2 and 7 gal.
120
ctnd Research since 1922 \
5 ^ L
) 311 ALEXANDER ST., ROCHESTER 4. Ν. Υ. Write for literature on this and related items.
white | chemical | L , porcelain i f "
determinations
General Atomic Division of General Dynamics offers an activation analysis service for mak ing ultra-sensitive trace element determina tions accurately, quickly and economically. For information on $50 exploratory offer write Dept. 135, P.O. Box 608, San Diego 12, California.
SCINTILLATORS
NUCLEAR ENTERPRISES LTD. 550 Berry Street, Winnipeg 21, Mannitoba, Can.
Knoxville 21. Tenn. Founded 1950
P.O. BOX 6 8 , C A M B R I D G E 3 9 , M A S S .
NE 102 Highly efficient PLASTIC PHOSPHOR. As CAPILLARY IN NE 801 Continuous Flow Counter. As THIN FILAMENTS for solid three-dimensional detectors. As SHEETS or SLABS from thick nesses of 0.0002" up. NE 421 SLOW NEUTRON DETECTOR dis persed Lithium Fluoride containing 96% en riched Li 6 . NE 160 HIGH TEMPERATURE PHOSPHOR to150°C. New C A T A L O G U E on Scintillators and Nucleonic Instruments. Write
Dept. CEN
19,
19 H
1962
Range + 5 0 ° t o 2 6 0 ° C . Accuracy =b 1 ° C Request literature WILLIAM J . HACKER & C O . , I N C . P. O . Box 646 West Caldwell, N . J.
_
S u p p l i e s
l a n d FATTY ACID STANDARDS, ^
A P P L I E D S C I E N C E LABORATORIES, I N C . D e p t . C, B o x 1 4 0 State College, Penna.
