Dynamics of nuclei in crystals

The phenomenon of the recoil-free resonant absorption of gamma rays is the result of the special dynamics of nuclei in solids. This fact was recognised by Mossbauer, who interpreted his apparently anomalous observations in terms of lattice dynamics of a similar nature to those associated with neutron scattering (Mossbauer, 1938). He found that the recoil momentum of the recoiling nucleus is shared by many nuclei of the crystal and thus the recoil energy is extremely small. This cooperative... 

Band theory also helps to understand the dynamics of electrons. In an ideal crystal, i.e. strictly periodic, the motion of an electron is not affected by the presence of nuclei and is therefore rectilinear and urriform. The velocity depends on the state... 

For the second example, cocoa butter was dynamically cooled from an initial liquid state at 42°C, under three cooling conditions. Just before the dynamic time was reached (the dynamic was first determined fw each of the three cooling rates), a sample was taken and put in the DSC FP900 apparatus, where it was submitted to an isothermal plateau at the last temperature it was taken. The complete thermal paths for the three cases considered are presented in Figure 9. For the three cases, a mixture of Forms IV and V crystallizes. The same crystal morphology as for the isothermal dynamic-static crystallization is observed, i.e., masses growing radially from nucleation centers. The number of nuclei decreases when the cooling rate is smaller. 

Evidence for an interfacial mechanism must necessarily be based upon the existence of an ice-liquid H20 interface. We postulate that the existence of a precritical embryonic ice crystal is possible. Consequently the 0°C environment permits the dynamic equilibrium between liquid H20 molecules (H20(1)) and nuclei (H20(t)), where i is the index of nuclei size. In particular ... 

NMR spectroscopists are also interested in nuclear spin relaxation times. The relaxation time measures the time required for an excited nucleus to return to the ground state. Two types of relaxation times are involved spin-lattice relaxation time Ti, the time constant for thermal equilibrium between the nuclei and crystal lattice, and spin-spin relaxation time Tz, the time constant for thermal equilibrium between nuclei themselves. Information on molecular dynamics can be obtained from these relaxation times. Generally, T Tz for low-viscosity liquids and T Tz for solids. A combination of information in molecular dynamics (from relaxation times), molecular structure (from spin-spin interaction), molecular identification (from resonance frequency and chemical shift), and spin density (from signal intensity) make the NMR an extremely versatile tool. 

The shell model has its origin in the Born theory of lattice dynamics, used in studies of the phonon dispersion curves in crystals.70,71 Although the Born theory includes the effects of polarization at each lattice site, it does not account for the short-range interactions between sites and, most importantly, neglects the effects of this interaction potential on the polarization behavior. The shell model, however, incorporates these short-range interactions.72,73 The earliest applications of the shell model, as with the Born model, were to analytical studies of phonon dispersion relations in solids.74 These early applications have been well reviewed elsewhere.71,75-77 In general, lattice dynamics applications of the shell model do not attempt to account for the dynamics of the nuclei and typically use analytical techniques to describe the statistical mechanics of the shells. Although the shell model continues to be used in this fashion,78 lattice dynamics applications are beyond the scope of this chapter. In recent decades, the shell model has come into widespread use as a model Hamiltonian for use in molecular dynamics simulations it is these applications of the shell model that are of interest to us here. 

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