Kinetics of surface area changes in glasslike carbon: reanalysis of the data
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I. INTRODUCTION In studying the kinetics of growth of the pores in a glasslike carbon material (GC), Lachter et al.1 derived an average activation energy of 75 + 3.6 kcal/mol using small-angle scattering measurements of the radius of gyration Rg. However, this activation energy is quite different from that obtained by Bose and Bragg,2 6 4 + 1 0 kcal/mol derived from the kinetics of decreases in surface area of the pores in glasslike carbon samples similar to those investigated by the aforementioned authors. The purpose of the present article is to apply the porecoarsening analysis to Bose and Bragg's surface area data,2 assuming the pores are spherical as a close approximation. In this reexamination of the data it is necessary to correct for the total time of isothermal heat treatments since Bose and Bragg's data were not corrected for the transient time required to heat the sample to the desired heat treatment temperature (HTT). The annealing times, HTt, were measured from the point after HTT was reached, and hence Bose and Bragg's HTt's were underestimated.
II. PORE-COARSENING THEORY Lachter et al.1 showed that the Lifshitz, Slyozov, and Wagner theory3'4 of bulk diffusion with controlled second-stage growth of precipitates can be successfully applied to describe the pore growth kinetics in an annealed glasslike carbon material. If Rg is the radius of gyration of the pores at time / and Rgo the radius of gyration extrapolated to time t0 = 0 at a given temperature T, then the changes in pore size can be written in the form 846
J. Mater. Res. 2 (6), Nov/Dec 1987
http://journals.cambridge.org
t
9vkR where y is the interfacial energy between matrix and solute species (in this instance, vacancies), D is their diffusion coefficient, Co is their equilibrium solubility, is their molar volume, v is their stoichiometric factor or weight fraction, A: is a pore shape factor, and R is the gas constant. In this equation D = Z>oexp( — AH/RT), where AH is the activation energy characterizing the pore-coarsening process. Lachter et al.5 showed that the shape of the pores in GC samples can be modeled as ellipsoids of revolution that are randomly oriented in the matrix material with axial ratios ranging between 0.94 and 1.16. The pores can the be assumed as roughly spherical in shape and the surface area can be related to the radius of gyration through the relation Sv = 3/k 'Rg, where k' is a pore shape factor of the order of unity, not necessarily equal to k above. Thus Eq. (1) can be rewritten as
T[(3/Sv)3-(3/SvJ3] or, equivalently, T[(3/S1)3-(3/SvJ3] K{t-t0)
(2)
_L
wheieK = k'K. For notation clarity T is the heat treatment temperature HTT and t is the heat treatment time HTt in all the above equations. According to Eq. (2), isothermal curves of (3/Sv)3 plotted versus t will have a slope K(D/T). According to Eq. (3), a graph of the logarithm of the slope thus derived times the corresponding
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=KD(t-t0)
© 1987 Materials Research Society
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