Frozen lattice

The presence of lattice coupling in direct dissociation complicates somewhat the definition of V and how V extracted from measurement should be compared to DFT calculations. There are two well defined limits for DFT calculations of V, for a frozen lattice (Ts = 0) and for the case where the lattice is fully relaxed at the transition state (Ts = oo). Since experiments are performed at finite Ts, the best V description is probably intermediate between these two extremes. 

A simple analogy between fast-ion conductors and zeolite synthesis can be drawn as follows. Assume the templates play the role of the frozen lattice in... 

The frozen-lattice trajectory of the gas atom is thus fixed by the orbit equati... 

Thus the time-dependent force exerted by the gas particle on the surface atom during its frozen-lattice trajectory is... 

Fig.3.2. Shown for two D/E ratios are the frequency components of the force exerted by the gas on the surface oscillator when the gas moves on the frozen lattice trajectory (3.15)., ...

The difference between (3.27,28) is that in obtaining (3.28) we have allowed the trajectory of the incident particle to "readjust" its motion during the collision event. This suggests that we can to some extent correct the results derived from (3.20) and (3.15) to remove the effects of the frozen-lattice assumption by a simple renormalization. That is, we could modify (3.26) [and (3.23)] by requiring that the results match the known impulsive limits. Equation (3.26) thus becomes... 

Fig. 10. Applied field dependence of the = 0 magnon energy gap in Tb—10%Ho demonstrating the validity of the frozen-lattice strain approximation as manifested by the minimum, but non-vanishing, of the gap energy at a held corresponding to the basal plane anisotropy held. Data taken with the field along the hard basal plane direction, except for the curves marked easy (axis) which show a linear increase of gap energy with field. The lines are theoretical curves. Different symbols are used to distinguish data taken at different temperatures. (After Nielsen et al. 1970b.)...

A comparison of the critical field, calculated within the frozen lattice model, in terms of the microscopic crystal field and magnetoelastic coefficients gives... 

The idea seems obvious. We could have traced it back to 1970 -although its origins are probably even older "If we can find the change in energy due to the static distortion of the lattice by the frozen lattice vibration, to second order in x, the calculation... 

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