Crystallization of Whitlockite from a Glass in the System CaOP 2 O 5 SiO 2 MgO Ana L. Oliveira, José M. Oliveira, Rui N. Correia, Maria H. V. Fernandes, Jorge R. Frade * Departamento de Engenharia Cera ˆmica e do Vidro, Universidade de Aveiro, 3810 Aveiro, Portugal The kinetics of crystallization of a glass with composition 30SiO 2 24.14P 2 O 5 28.61CaO17.25MgO (wt%) was studied with variable temperature, by differential thermal analysis. These results were interpreted according to revised theo- retical models which describe the dependence of fraction crystallized on temperature and on the heating rate, and the dependence of the peak temperature on the rate of change in temperature. These models emphasize the differ- ences in crystallization behavior between ‘‘as-prepared’’ glass samples, and the corresponding previously nucleated samples. These differences in behavior suggest that the ki- netics of crystallization comprises a nucleation stage at tem- peratures of about 730°C, and particle growth for tempera- tures higher than 800°C. The temperature dependence of the fraction crystallized corresponds to a very high value of activation energy for growth (≈763 kJ/mol), but this is still lower than the activation energy evaluated from the tem- perature dependence of viscosity. I. Introduction T HE kinetics of crystallization must be properly understood to obtain glass-ceramic materials with controlled micro- structure and properties. These studies are usually based on the dependence of fraction reacted on time and/or temperature, and this may be evaluated under isothermal conditions or with vari- able temperature. Experiments performed with variable tem- perature require much less time than what is needed to perform several isothermal experiments for different temperatures and times. This is possible because crystallization is exothermic and changes in fraction crystallization can thus be evaluated in real time by differential thermal analysis (DTA) or differential scanning calorimetry (DSC). Sound theoretical models are also needed to interpret experi- mental data obtained with variable temperature. These models describe the dependence of fraction crystallized on temperature and on the rate of change in temperature for a variety of dif- ferent mechanisms. However, designing materials with con- trolled fractions crystallized requires several parameters such as the activation energy and preexponential factor, for describ- ing the temperature dependence, and an exponent n for describ- ing the effects of the rate of change in temperature. This ex- ponent n depends on the dimensionality of particle growth, and also on the controlling mechanisms (diffusion control or phase boundary controlled growth). It is thus sometimes difficult to attribute a physicochemical meaning to every fitting parameter obtained from DTA or DSC results. The meaning of the activation energy obtained by fitting is not always straightforward, especially because this may com- prise contributions of nucleation (E g ) and growth (E n ). In ad- dition, most theoretical models are based on assuming that the rates of nucleation and growth follow the Arrhenius law, which may fail in real cases. For example, the growth rate tends to vanish on approaching the melting temperature (after reaching a peak). This effect is accounted for by a classical model for the growth rate with phase boundary control 1 U  U 0 exp[-E g /(RT )]{1 - exp[G/(RT )]} (1) where U 0 is a preexponential factor, E g is an activation energy for transport across the interface, R is the perfect gas constant, T is absolute temperature, and G is the transformation free energy. The factor 1 - exp[G/(RT )] drops to zero at the melting temperature, due to the temperature dependence of G  H - TS, and the growth rate thus vanishes in iden- tical conditions. On the other hand, one may expect |G| << RT at sufficiently low temperatures, and in this case Eq. (1) re- duces to a typical Arrhenius law U ≈ U 0 exp[-E g /(RT )], as assumed by most models proposed to describe the temperature dependence of fraction crystallized with variable temperature. The nucleation rate usually reaches a peak at even lower temperature, and a classical model can be written 2 I  I 0 exp[-E N /(RT )] exp[-W * /(kT )] (2) where I 0 is the preexponential factor, E N is a typical activation energy for nucleation (kinetic barrier), W * is the Gibbs free energy to form the nucleus, and k is the Boltzmann constant. The thermodynamic barrier W * varies with G -2 , and tends to increase rapidly on approaching the melting temperature. At sufficiently low temperatures one expects W * /(kT ) << 1, and a simpler Arrhenius law can also be assumed for the nucleation rate I ≈ I 0 exp[-E N /(RT )]. The experimental conditions must be carefully planned to avoid exceeding the growth rate peak temperature, and thus to be able to assume that the Arrhenius law is nearly true. For example, experiments performed with low heating rates might ensure that high fractions crystallized are attained before reach- ing the growth peak temperature. Avoiding the nucleation peak is less critical, and relatively simple models can be obtained at least for the following cases: Case A—when the nucleation peak occurs at temperatures which are lower than required for the onset of growth, the growth rate being described by the Arrhenius law for the entire temperature range (Fig. 1). Case B—for simultaneous nucleation and growth in a tem- perature range where the nucleation rate and growth rate are both described by Arrhenius laws. Case A comprises stages of nucleation and growth, and these stages can be separately adjusted by changing suitable experi- mental variables. For example, the number of nuclei formed during an isothermal nucleation stage will increase with time, prior to the onset of growth; this will be referred to as case A1 as shown in Fig. 1. Alternatively, the number of nuclei formed with variable temperature will increase with decreasing heating rate for temperatures lower than the onset of crystallization; 3 this corresponds to case A2 in Fig. 1. In cases A1 and A2 the nucleation rate vanishes before W. C. LaCourse—contributing editor Manuscript No. 190960. Received June 2, 1997; approved December 1, 1997. * Member, American Ceramic Society. J. Am. Ceram. Soc., 81 [12] 3270–76 (1998) J ournal 3270