In situ X-ray diffraction study of the formation of TiSi2-C49 phase from Ti-Si multilayers on Si(100)

Circumventing Thermodynamic Constraints in Nucleation-Controlled Crystallization of Al2TiO5-Based Chemical Vapor Deposition Coatings

“…53,56 Indeed, in most crystallization processes, nucleation will proceed so fast compared to the growth stage that the entire process may practically be regarded as a (pseudo)-first-order transformation limited primarily to diffusion. 54,57 However, during circumstances where the role of nucleation becomes significant or even rate-determining, the lack of a saturated nucleation rate, especially at the earliest stages of crystallization, may strongly affect the physical meaning of K. 53 Therefore, one should be careful of using K as a parameter in any further interpretation of, for example, activation energies. Instead, an expression for the apparent activation energy representative of the entire crystallization process, E a app , can be derived by noting that the time t x required to reach a certain crystalline volume fraction, for example, t 0.05 , t 0.50 , and t 0.99 , frequently follows an Arrhenius-like relationship 58−62…”

“…Assuming that the adsorption coefficient is negligible in the coatingswhich usually is the case among thin films and coatingsand that no significant change in texturing occurs throughout the phase transformation, the diffracted Bragg intensity I can, at any given time t , be treated according to , where V t denotes the volume fraction transformed of the crystalline phase in the analyzed sample. Because V t is enclosed in [0, 1], unity-based normalization of the obtained intensity data must be made from the equation where I t norm is the total gross counts at t , I 0 is the background intensity, and I ∞ is the constant gross counts at the end of the run period. By convention, I ∞ is defined as the I 0.99 level, that is, where 99% of the crystallization has been completed.…”

“…Although K is a constant related to the overall crystallization rate, it is essential to note that it is not a “true” rate constant in the strictest sense because it simultaneously incorporates the rates from nucleation and growth . In other words, K does not truly represent any proper elementary step under the first-order mechanism of crystallization, which the JMAK equation and classical nucleation theory regularly assume. , Indeed, in most crystallization processes, nucleation will proceed so fast compared to the growth stage that the entire process may practically be regarded as a (pseudo)-first-order transformation limited primarily to diffusion. , However, during circumstances where the role of nucleation becomes significant or even rate-determining, the lack of a saturated nucleation rate, especially at the earliest stages of crystallization, may strongly affect the physical meaning of K . Therefore, one should be careful of using K as a parameter in any further interpretation of, for example, activation energies.…”

“…Assuming that the adsorption coefficient is negligible in the coatingswhich usually is the case among thin films and coatings 29 and that no significant change in texturing occurs throughout the phase transformation, 53 the diffracted Bragg intensity I can, at any given time t, be treated according to 53,54 l…”