Phonon lattice

MetaUic behavior is observed for those soHds that have partially filled bands (Fig. lb), that is, for materials that have their Fermi level within a band. Since the energy bands are delocalized throughout the crystal, electrons in partially filled bands are free to move in the presence of an electric field, and large conductivity results. Conduction in metals shows a decrease in conductivity at higher temperatures, since scattering mechanisms (lattice phonons, etc) are frozen out at lower temperatures, but become more important as the temperature is raised. 

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

In the crystal, the total number of vibrations is determined by the number of atoms per molecule, N, and the nmnber of molecules per primitive cell, Z, multiplied by the degrees of freedom of each atom 3ZN. In the case of a-Sg (Z =4, N =8) this gives a total of 96 vibrations ( ) which can be separated in (3N-6)—Z = 72 intramolecular or "internal" vibrations and 6Z = 24 intermo-lecular vibrations or lattice phonons ("external" vibrations). The total of the external vibrations consists of 3Z = 12 librational modes due to the molecular rotations, 3Z-3 = 9 translational modes, and 3 acoustic phonons, respectively. 

The density of states (DOS) of lattice phonons has been calculated by lattice dynamical methods [111]. The vibrational DOS of orthorhombic Ss up to about 500 cm has been determined by neutron scattering [121] and calculated by MD simulations of a flexible molecule model [118,122]. 

In materials with a band structure such as that sketched in Figure 4.8(b), the bottom point in the conduction band has a quite different wave vector from that of the top point in the valence band. These are called indirect-gap materials. Transitions at the gap photon energy are not allowed by the rule given in Equation (4.29), but they are still possible with the participation of lattice phonons. These transitions are called indirect transitions. The momentum conservation rule for indirect transitions can be written as... 

A fourth, often overlooked problem is most prominent in noble gas matrices which are notoriously poor heat sinks because only very low energy lattice phonons are available to accept molecular vibrational quanta. Hence, thermalization is very slow compared to solution, and the excess energy that may be imparted onto an incipient reactive intermediate in the process of its formation (e.g., from a precursor excited state) may therefore be dissipated in secondary chemical processes such as rearrangments or fragmentations, which may make it impossible to generate the primary reactive intermediate. Often, this problem can be alleviated by attaching alkyl groups that serve as internal heat sinks, but sometimes this is not acceptable for other reasons. 

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

Bulk crystalline radical ion salts and electron donor-electron acceptor charge transfer complexes have been shown to have room temperature d.c. conductivities up to 500 Scm-1 [457, 720, 721]. Tetrathiafiilvalene (TTF), tetraselenoful-valene (TST), and bis-ethyldithiotetrathiafulvalene (BEDT-TTF) have been the most commonly used electron donors, while tetracyano p-quinodimethane (TCNQ) and nickel 4,5-dimercapto-l,3-dithiol-2-thione Ni(dmit)2 have been the most commonly utilized electron acceptors (see Table 8). Metallic behavior in charge transfer complexes is believed to originate in the facile electron movements in the partially filled bands and in the interaction of the electrons with the vibrations of the atomic lattice (phonons). Lowering the temperature causes fewer lattice vibrations and increases the intermolecular orbital overlap and, hence, the conductivity. The good correlation obtained between the position of the maximum of the charge transfer absorption band (proportional to... 

That is, it appears that normal band conduction, with lattice-phonon, ionized-impurity, and possibly space-change (or localized-potential) (Podor,... 

Dislocations move when they are exposed to a stress field. At stresses lower than the critical shear stress, the conservative motion is quasi-viscous and is based on thermal activation that overcomes the obstacles which tend to pin the individual dislocations. At very high stresses, > t7crit, the dislocation velocity is limited by the (transverse) sound velocity. Damping processes are collisions with lattice phonons. 

For paramagnetic spin systems, there are two major processes of relaxation (55). One relaxation mode involves spin-flipping accompanied by lattice phonon creation and/or annihilation (spin-lattice relaxation), and the other mode is due to the mutual flipping of neighboring spins such that equilibrium between the spins is maintained (spin-spin relaxation). For the former mode of relaxation, th decreases with increasing temperature, and the latter relaxation mode, while in certain cases temperature dependent, becomes more important (th decreases) as the concentration of spins increases. 

On one level it is a quantum effect, and can be described in terms of photon—phonon scattering. The incident NIR beam is a source of photons, and the energy from the piezotransducer provides a source of lattice phonons that propagate through the crystal. As in all collision processes, the twin principles of conservation of momentum and conservation of energy apply. The momentum of a quantum particle is linked to its wavevector by hk. The energy is linked to its frequency by hjj. 

In considering the vibronic side-bands to be expected in the optical spectra when we augment the static crystal field model by including the electron-phonon interaction, we must know the frequencies and symmetries of the lattice phonons at various critical points in the phonon density of states. We shall be particularly interested in those critical points which occur at the symmetry points T, A and at the A line in the Brillouin zone. Using the method of factor group for crystals we have ... 

A.M. Kossevich, The Crystal Lattice (Phonons, Solitons, Dislocations), WILLEY-VCH Verlag Berlin GmbH, Berlin, 1999. 

Optical excitation of metals with intense femtosecond laser pulses can create extreme non-equilibrium conditions in the solid where the electronic system reaches several thousand degrees Kelvin on a sub-picosecond timescale, while the lattice (phonon) bath, stays fairly cold. As illustrated in Figure 3.22, photoexcited hot electrons may transiently attach to unoccupied adsorbate levels and this change in the electronic structure may induce vibrational motions of the adsorbate-substrate bond. For high excitation densities with femtosecond pulses, multiple excitation/deexcitation cycles can occur and may eventually lead to desorption of adsorbate molecules or reactions with co-adsorbed species. After 1-2 ps, the hot electron... 

In the second example BCS theory relates the appearance of a superconducting state to the breakdown of electromagnetic gauge symmetry by interaction with regular ionic lattice phonons and the creation of bosonic excitations. This theory cannot be extended to deal with high Tc ceramic superconductors and it correlates poorly with normal-state properties, such as the Hall effect, of known superconductors. It is therefore natural to look for alternative models that apply to all forms of superconductivity. 

The dimerization of 28 has also been studied by Prasad, who used Raman spectroscopy to monitor both changes in intermolecular vibrations and lattice phonon modes [73]. The Raman spectrum shows the disappearance of alkene stretches at 997, 1180, 1593, and 1625 cm-1 as expected, and the appearance of cyclobutane modes at 878,979, and 1001 cm-1. Phonon modes broadened as the reaction progressed, and bands around 15-40 cm-1 showed a shift in frequency. Between about 50 and 66% conversion it was difficult to define distinct bands, but after that point product bands grew in distinctly. This amalgamation behavior is good evidence for a homogeneous reaction mechanism. 

Experimental and theoretical studies of valence transitions are current topics with many open points. Different roles are expected for Coulomb or interchain interactions and coupling to molecular or lattice phonon in various systems. Direct solutions of models are one of several methods for studying the NIT. Magnetic, dielectric and thermal properties can be obtained exactly, albeit for finite systems of increasing size. Extrapolations to infinite chains require care and guidance from related analytical results. 

---