Isothermal crystallization experiments were performed on the halozeotype CZX-1 with 2D temperatureand time-resolved synchrotron X-ray diffraction (TtXRD) and differential scanning calorimetry (DSC). These crystallization experiments demonstrate that the fundamental materials property, the velocity of the phase boundary of the crystallization front, v pb , can be recovered from the Kolmogorov Johnson and Mehl and Avrami (KJMA) model of phase-boundary controlled reactions by introducing the sample volume into the KJMA rate expression. An additional corrective term is required if the sample volume of the crystallization measurement is anisotropic. The concurrent disappearance of the melt and appearance of the crystalline phase demonstrate that no intermediates exist in the crystallization pathway. The velocity of the phase boundary approaches 0 as the glass transition (T g ≈ 30°C) is approached and at about 10°below melting point (T m = 173°C). The velocity of the phase boundary reaches a maximum of 30 μm s −1 at 135°C. Single or near-single crystals are grown under conditions where the v pb is much greater than the rate of nucleation.
Crystal growth and viscous relaxation
are known to be activated processes, albeit inadequately described
by transition state theories. By considering a transition zone and
accounting for the Kauzmann-type temperature dependence of configurational
entropy we here develop transition zone theory (TZT). Entropic and
enthalpic activation probabilities scale with the cooperativity of
the reactant, and the attempt frequency prefactor (k
B
T/h) is scaled by a
characteristic phonon wavelength equal to twice the lattice constant
for crystal growth, and the speed of sound squared for viscous relaxation.
TZT accurately describes the temperature-dependent crystal growth
rates and viscosity of diverse materials over the entire temperature
ranges T
g to T
m and T
g to T
c, respectively, and affords a detailed mechanistic understanding
of condensed matter reactions similar to that afforded to molecular
chemistry by the Eyring equation.
A series of simulations was performed to enable interpretation of the material and physical significance of the parameters defined in the Kolmogorov, Johnson and Mehl, and Avrami (KJMA) rate expression commonly used to describe phase boundary controlled reactions of condensed matter. The parameters k, n, and t 0 are shown to be highly correlated, which if unaccounted for seriously challenge mechanistic interpretation. It is demonstrated that rate measurements exhibit an intrinsic uncertainty without precise knowledge of the location and orientation of nucleation with respect to the free volume into which it grows. More significantly, it is demonstrated that the KJMA rate constant k is highly dependent on sample size. However, under the simulated conditions of slow nucleation relative to crystal growth, sample volume and sample anisotropy correction affords a means to eliminate the experimental condition dependence of the KJMA rate constant, k, producing the material-specific parameter, the velocity of the phase boundary, v pb .
A set of new data analysis software tools have been developed for the study of structural dynamics of materials using coherent scattering and photon correlation techniques. The new software tools can readily process high-throughput, multidimensional data, enabling studies of slow and fast dynamics of materials using X-ray Speckle Visibility Spectroscopy and Xray Photon Correlation Spectroscopy techniques. They support a wide range of user expertise, from novice to developer, and are available in Scikit-beam python package which is available at https://github.com/scikit-beam/scikit-beam.
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