Phase transformations computer simulation

Figure 18. Computer-simulated phase-shifted exponential FID and its Fourier transforms, (a) time domain signal, e" cos(o)t-< ) (b) cosi FT (c) sine FT (d) sguare of the modulus FT (e) modulus FT.

Metallurgists originally, and now materials scientists (as well as solid-state chemists) have used erystallographic methods, certainly, for the determination of the structures of intermetallic compounds, but also for such subsidiary parepistemes as the study of the orientation relationships involved in phase transformations, and the study of preferred orientations, alias texture (statistically preferential alignment of the crystal axes of the individual grains in a polycrystalline assembly) however, those who pursue such concerns are not members of the aristocracy The study of texture both by X-ray diffraction and by computer simulation has become a huge sub-subsidiary field, very recently marked by the publication of a major book (Kocks el al. 1998). 

The complexity of the physical properties of liquid water is largely determined by the presence of a three-dimensional hydrogen bond (HB) network [1]. The HB s undergo continuous transformations that occur on ultrafast timescales. The molecular vibrations are especially sensitive to the presence of the HB network. For example, the spectrum of the OH-stretch vibrational mode is substantially broadened and shifted towards lower frequencies if the OH-group is involved in the HB. Therefore, the microscopic structure and the dynamics of water are expected to manifest themselves in the IR vibrational spectrum, and, therefore, can be studied by methods of ultrafast infrared spectroscopy. It has been shown in a number of ultrafast spectroscopic experiments and computer simulations that dephasing dynamics of the OH-stretch vibrations of water molecules in the liquid phase occurs on sub-picosecond timescales [2-14],... 

The atomic density of the hex phase is about 20% higher than that of the 1 x 1 phase. As could be demonstrated by scanning tunneling microscopy (STM) (49), during the CO-induced hex — 1 x 1 transformation, these additional atoms are squeezed out from the surface layer, on top of which they are aggregating to new small I x 1 patches, a result which could also be successfully modeled by computer simulations (50). 

In a given work computer simulations devoted to study of nanostructure of abovementioned cryogenic amorphous phases of ice, mechanisms of their transformations, and properties to accumulate methane and hydrogen was realized within the theoretical concepts thermo field dynamics [5] and quantum-field chemistry [6-9]. We developed two models of nanostructures corresponding to HDA-ice and LDA-ice, respectively. Some computations of energetic barriers locking molecules CH4 and H2 inside of amorphous ice were fulfilled. 

The presence of several structural phase transformations in glassy Ge02 suggests the respective structural changes in the melt, which is already partially confirmed by both experimental study [117] and computer simulation study [118]. 

We hope to have demonstrated that computer simulation of transport and transformation processes on digitally reconstructed multi-phase media can be beneficial to practical chemical engineering applications. We believe that as chemical engineering becomes more product-oriented, the need to model phenomena that control material microstructure formation will gain in importance. We hope that this chapter will provide a useful starting point for those who wish to familiarize themselves with the relevant computational techniques. 

FIGURE 27.7 Computer simulations of microstructures of (a-d) PZT and (e-h) SrTiOs thin-film cross sections illustrating microstructural evolution at various times during the transformation to the perovskite state. Lighter colors associated with intermediate phase darker colors associated with the perovskite phase. 

The potential of Eq. (1) with parameters determined in Refs. [10, 11] was thoroughly tested in computer simulations of silica polymorphs. In Ref. [10], the structural parameters and bulk modulus of cc-quartz, a-cristobalite, coesite, and stishovite obtained from molecular dynamics computer simulations were found to be in good agreement with the experimental data. The a to / structural phase transition of quartz at 850 K ha.s also been successfully reproduced [12]. The vibrational properties computed with the same potential for these four polymorphs of crystalline silica only approximately reproduce the experimental data [9]. Even better results were reported in Ref. [5] where parameters of the two-body potential Eq. (1) were taken from Ref. [11]. It was found that the calculated static structures of silica polymorphs are in excellent agreement with experiments. In particular, with the pressure - volume equation of state for a -quartz, cristobalite, and stishovite, the pressure-induced amorphization transformation in a -quartz and the thermally induced a — j3 transformation in cristobalite are well reproduced by the model. However, the calculated vibrational spectra were only in fair agreement with experiments. 

Some fundamental aspects of the nucleation process have been investigated by molecular dynamics (MD) methods. In a recent review [44] the advantages and limitations of molecular cluster models in simulating the dynamics of nucleation and phase changes have been discussed. In this approach, molecular dynamic simulations are correlated with experimental nucleation rates extracted from electron diffraction patterns of molecular supersonic jets. The dynamics of freezing of ammonia, CCI4 and water, and the phase transformations of t-butyl chloride have been analysed. A useful feature of the MD computational... 

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