Thermal Dehydration of Crystalline Hydrates Microscopic Studies and Introductory Experiments to the Kinetics of Solid-state Reactions Haruhiko Tanaka and Nobuyoshi Koga Faculty of School Education, Hiroshima University, Shinonome, Minami-ku, Hiroshima 734, Japan Andrew K. Galwey School of Chemistry, The Queen's University of Belfast, Belfast, BT9 5AG, Northern Ireland Kinetic correlations are the cloth from which molecular mechanistic models are fashioned.
Comparisons and contrasts are essential ingredients in effective teachinp: is an indisoensable heln in - nersnective . . meaningful communication. The present article describes ~ O U the use of microsconv in studies of a representative .D of solid-state reactibis, the dehydrations of crystalline hydrates. These direct observations complement the well-established and easily understood pattern of kinetic behavior t h a t i s characteristic of t h i s type of reaction. The subject has some technological importance, i s of considerable intrinsic interest hut often i s not included in general undergraduate courses of chemical kinetics. Accordingly, we present here: First a short, hut general, account of the factors that have been identified as controlling the specialized pattern of behavior that is exhibited by the decompositions of solids. The theory is developed from reaction models that are based on microscopic observational evidence. Second, and referring directly to some of the reactions from which these models were developed originally, we describe particular experimental systems that are suitable for introductory and far more advanced microscopic studies in the laboratory. I t is a well-established practice in the subject to use microscopic observations of the textural changes that accompany reaction to complement kinetic conclusions in the formulation of reaction mechanisms. Theory of Solid-state Reactions The essential feature of many solid-state reactions i s that the chemical change occurs preferentially within a reaction interface. This is a thin contact zone joining the reactant and oroduct. a schematic reoresentation of the probable stnicture of a typical interface is shown in Figure 1. As reaction proceeds. this interface ~romessivelvadvances into unEhanged 'reactant, thereby &creasing the amount of product present. The expulsion of a product during reaction, for example the water volatilized from a hvdrate, is accompanied bv a contraction because the resid"al solid occupiis a smafler volume than the crystal from which i t was derived. Reaction usually yields a residue that is microcrystalline and is penetrated by a system of cracks t h a t provide escape routes for the water evolved. Under the microscope such material usually is recognizably distinct from the reactant and, therefore, the disposition of product and the progress of chemical change can be observed directly. We describe below the kinetic information that can be deduced from such observations.
Figure 1. A schematic representation of the section of an active interface at the boundary of a growth nucleus. Reaction occurs preferentially here possibly due to local strain or due to promotion by temporarily retained water vapor (13). Kinetics of Solid-state Decomposition Selected solid-state decompositions, including dehydrations, have been identified a s relatively simple reactions and have been accepted a s model systems that are useful in establishing the theorv of the subiect. There is ~ e n e r a l agreement I 1 4 that chem~calcbnnye occurs ,ilmosr exclunirrl\~n.ithinth? intrllnrial lone Ftg. 1 . p0S;ihly :is il cons e q k n c e of strain a t the plane of contact getween the crystalline reactant and product phases. I t follows, therefore, that the initiation of reaction a t a site where an interface does not already exist may be relatively difficult. This is termed "nucleation" (5).Nucleation is the series of steps that together culminate in the generation of a product particle embedded in the reactant and around which is formed a n active advancing interface a t which chemical change proceeds. Nucleation usually (perhaps almost invariably) occurs a t a crystal surface, probably a t sites of imperfection such as superficial damage, dislocations, impurities, etc. Once established, the reaction interface advances into unchanged reactant. Nucleus growth, a reaction proceeding through the three-dimensional growth of nuclei is portrayed in Figure 2. The kinetic behavior during such isot h e r m a l nucleation-and-growth r e a c t i o n s i s a characteristically sigrnoid shaped a-time curve (a is the fractional reaction). Initially the reaction rate is very small, during the induction period to nucleation. Once growth nuclei are established there is advance with expansion of the active contact zone during the acceleratory period of reaction. For the three-dimensional example illustrated, Figure 2, during the early period of growth there is the development of Volume 72 Number 3 March 1995
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The Kinetics of Nucleation Nucleation rates ( 1 4 )often are considered from the assumption that it is a first order process occurring a t No potential sites. Thus, the number of growthnuclei active a t time t is given by N = Noll- expl-kNtut)l
which is the exponential nucleation law. If kN is large then all possible nuclei are generated rapidly a t the commencement of reaction,N=No: the instantaneous nucleation law. If kN is small then the initial rate of nucleus formation is constant and N = N&,t
Fiaure 2. Diaarammatic remesentation of the three-dimensional in a~~, crvstal. The reaction start mav be delaved before acce eralory proo-ct formaton o-r ng growln of n~cle. Afteroverlap of n-c e tne nterface m grales lowaro me crfsla center by a contracting envelope model. o = r- h h of - nucl; ~
~~~
hemispherical aggregates of product crystallites. Continued growth results in acceleration to a reaction rate maximum around which nuclei begin to overlap so that interface e x p a n s i o n becomes progressively curtailed. Thereafter, the rate becomes deceleratory in the approach to completion. Here, the interface becomes coherent and migrates inward toward the center of the particle in the form of a contracting envelope. Rates of this type of reaction are proportional directly to the area of the active interface. Consequently, the kinetic expressions describing such behavior are hased on the geometric pattern of interface development. In the formulation of a mechanism describing such reactions i t is necessary, therefore, to consider two aspects of the chemistry.
.
First, a rate equation that satisfactorily represents the kinetics la-time) data may be identified and this may be used to characterize the reaction geometry. It is always important . to support the conclusions from this approach by independent microscopic observations,the subject of the present paper. Second, it is necessary to identify the bond redistribution steps participating in the chemical changes of the reaction interface. Elucidation afthese steps may be based on diverse and sometimes indirect evidence based an microscopic observations, stoichiometry, crystallographic considerations including topotaxy, activation energy magnitude, etc. ~
~
Concentration terms usually are not relevant to the kinetic analyses of reactions of solids. In this respect these heterogeneous processes differ fundamentally from chemical change in homogeneous phases. In crystals the reactivities of all equivalent species are not equal and the probability of reaction of a particular entity increases markedly on the arrival of a migrating reaction interface. Rate Equations Systematic accounts of the derivation of those rate equations that have found application to solid-state decompositions, including dehydrations have been given (1-9).These are hased on an integration that aggregates quantitatively the growth of all the nuclei developed from the nucleation laws considered. A general mathematical treatment is not possible because the individual participating processes (nucleation and growth) are functionally distinct. Insight into the subject and the development of appropriate kinetic expressions has, however, been achieved through consideration of the following aspects of behavior.
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which is the linear nucleation law. Acceleratory nucleation ~ : power nualso has been described where N = ( k ~ t )the cleation law.
Journal of Chemical Education
The Kinetics of Nucleus Growth For manv decom~ositionsi t has been demonstrated experimentaliy that the linear rate of interface advance is constant and the radius a t time t of a mowth nucleus appearing a t time to is r = k& - to)
This law is applicable to most of the reactions described below a s being suitable for laboratory experiments. In other systems where water loss involves diffusive escape, the effective rate of advance is deceleratory and (3, 7). r= Ih& - toll112
Nucleus Dimensions Figure 2 portrays a reaction in which there are equal rates of growth in three dimensions (;h = 3), yielding hemispherical nuclei. Nuclei may, however, grow in a smaller number of dimensions. Where the crystal structure i s strongly laminar or t h e reactant i s composed of thin Table 1. Physico-Chemical Meaning of the Value of n in the Avrami-Erofe'ev Equation
Nucleation Rate Behavior p pre-exsist
0
Acceleratory
O+1
Constant
1
Deceleratory
p
