Velocity transformation

Speed of transformation = velocity of lattice vibrations through crystal (essentially independent of temperature) transformation con occur at temperatures os low os 4 K. 

Eqs. 7.22 and 7.24 represent the velocities due to screw rotation for the observer in Fig. 7.9, which corresponds to the laboratory observation. Eq. 7.25 is equivalent to Eq. 7.24 for a solution that does not incorporate the effect of channel width on the z-direction velocity. For a wide channel it is the z velocity expected at the center of the channel where x = FK/2 and is generally considered to hold across the whole channel. The laboratory and transformed velocities will predict very different shear rates in the channel, as will be shown in the section below relating to energy dissipation and temperature estimation. Finally, it is emphasized that as a consequence of this simplified screw rotation theory, the rotation-induced flow in the channel is reduced to two components x-direction flow, which pushes the fluid toward the outlet, and z-direction flow, which tends to carry the fluid back to the inlet. Equations 7.26 and 7.27 are the velocities for pressure-driven flow and are only a function of the screw geometry, viscosity, and pressure gradient. 

To conclude this chapter, which has been devoted to the growth of thick films, the sequence of optical microscopy images as a function of time corresponding to a /7-NPNN/glass film is shown. The time evolution is illustrated in Fig. 5.18 revealing the transformation in ambient conditions. The mean transformation velocity at ambient conditions along the directions defined by the fibres is 6.0 0.4 xm h . ... 

By taking the Laplace transform of eqn. (290) and then multiplying throughout by the initial velocity u(0) and finally taking an ensemble average, the Laplace transformed velocity autocorrelation function is [490]... 

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

The mobility of a macromolecule, constrained by other macromolecules, can be also calculated as (5.1). In the linear approximation, the zeroth normal co-ordinates of the macromolecule (equation (4.1), at z/jj = 0) define diffusive mobility of macromolecule. The one-sided Fourier transform velocity correlation function is determined by expression (4.15), so that we can write down the Fourier transform... 

By monitoring films of different thickness we found that orientational order is even more enhanced in the thinnest films, indicating that the BOO is higher in proximity of the substrate. Consistently, we found that the transformation velocity into the ordinary liquid is slower at lower thicknesses, which indicates a correlation between the degree of orientational order and the kinetic stability of the MROL phase. 

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