Pore growth kinetics in heat-treated glass-like carbons
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Stephen Spooner National Center for Small Angle Scattering Research, Oak Ridge National Laboratory, Oak Ridge, Tennessee 34830 (Received 16 June 1986; accepted 7 October 1986) The kinetics of changes in void size during annealing of glass-like carbons in the temperature range 1000°-2800 °C for times up to 150 h were studied using small-angle x-ray scattering determinations of the radius of gyration Rg. The results show that Rg ranged from 9 A at 1000 °C to about 24 A at 2800 °C. A pore coarsening analysis and a superimposition kinetic analysis applied to Rg gave activation energies of 76 + 4 kcal/mole and 74 + 9 kcal/mole, respectively, which are associated with migration of vacancies within graphitic layers in the matrix material.
I. INTRODUCTION
II. PORE COARSENING THEORY
It is well known that glass-like carbon (GC) gives a strong small-angle x-ray scattering (SAXS), 1 and the radius of gyration Rg increases with the heat treatment temperature.2 However, heretofore no attempt has been made to characterize the shape of the pores in GC, except to note that they are slit shaped,3 and there have been no systematic studies of the kinetics of pore coarsening using measurements of pore size. The results of a preliminary investigation by Hoyt and Bragg4 showed that, approximately, Rg increased linearly as the cube root of the time, but this work did not take into account the need to correct the data for nonkinetic changes that occur when the temperature is increased stepwise, nor were corrections made for the added intensity component resulting from density fluctuations within the matrix of the carbon material.2 Although they investigated the kinetics of changes in the internal surface area of the pores in GC, Bose and Bragg's studies5 of the closed pore structures on both soft and hard carbons fell short of investigating the temperature/time changes of pore size as they are related to the radius of gyration Rg. In a previous paper Henry et al.6 monitored the shape and the size of the pores in GC materials as they are affected by both heat treatment time HTt (0-150 h) and heat treatment temperature HTT (1000°-2800 °C). These authors also characterized the nonkinetic changes occuring in the same GC samples.7 It is intended in the present work to obtain an effective activation energy governing the growth of the pores in the same GC samples, by measurements of Rg as a function of heat treatment time HTt for different temperatures HTT.
Hoyt and Bragg3 suggested that the pore coarsening in GC materials can be likened to the steady-state particle coarsening in alloy systems where the process is controlled by volume diffusion driven by the reduction of interfacial area between particles and matrix. In this instance, vacancies play the role of solute atoms in the usual case. Consider the Lifshitz, Slyozov, and Wagner (LSW) theory8'9 of bulk diffusion with controlled second-stage growth of precipitates in a supersaturated alloy system. It is equivalent to a steady-state precipitate coarsening governed by the equation
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