Lattice instability

Boyer L L 1985 Theory of melting based on lattice instabilities Phase Trans. 5 1 Cotteril R M J 1980 The physics of melting J. Crystal Growth 48 582... 

In Sec. 2 the effective mass equation is introduced and the band structure is discussed with a special emphasis on an Aharonov-Bohm effect. Optical absorption spectra are discussed in Sec. 3. A lattice instability, in particular induced by a magnetic field perpendicular to the tube axis, is discussed in Sec. 4 and magnetic properties of ensembles of CNTs are discussed in Sec. 5. 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

L.R. Testardi and T. B. Bateman, Lattice instability of high-transition-temperature... 

The SSH model (Eq. (3.2)) is, essentially, the model used by Peierls for his discussion of the electron-lattice instability [33]. Its ground state is characterized by a non-zero expectation value of the operator. 

Fig. 38. ID model of metal surface reconstruction. The coupling between discrete phonon modes (dashed line) and the electron-hole pair continuum (hatched) produces lattice instability.

The strength of the lattice instability near the Fermi vector depends on the magnitude of the electron-phonon coupling and on the phase space available for electron-hole pair excitation around 2kf. Thus, a reconstructive surface phase transition has to fulfill the following requirements in order to be ascribed to an electronically driven lattice instability ... 

In the Slater-type mode, oxygen atoms oscillate with the largest relative amplitude. As a result, we find that the criterion of the FE lattice instability in totally oxygen isotope-exchanged STO and KTO is ... 

It has now become apparent that f-band superconductors can be understood in a normal way, like d-band ones" we have just to think about density of states, bandwidth lattice unstabilities and electron correlations to interpret it. This was clearly summarized by Smith after the discovery of superconductivity of Pa and Am. Superconductivity of Am is made by the J = 0 ground state of its six 5 f electrons as was stressed by Johansson , this could also be the case for stabilized trivalent europium metal. The importance of lattice instabilities (like in A-15 high Tc superconductors) was put forward by Fournier who showed that the very large 6T/8p slope for U was mainly due to a very targe change in the electron-phonon coupling associated with the low temperature phase transition. 

Conradson, S.D.. I.D. Raistrick, and A.R. Bishop Axial-Oxygen-Centered Lattice Instabilities and High-Temperatnre Superconductivity, Science, 1394 (June 15, 1990). 

International Conference on Stripes, Lattice Instabilities and High Tc Superconductivity, edited by A. Bianconi andN. L. Saini, J. Supercond. 10, no.4 (1997) Lattice effect in High Tc superconductors edited by Y. Bar-Yam, T. Egami, J. Mustre de Leon and A. R. Bishop (World Scientific, Singapore 1992)... 

Bungaro C, Rabe KM (2002) Lattice instabilities of PbZrQs/PbTlQs [1 1] superlattices from first principles. Phys Rev B 65 224106... 

The local lattice instability by the hole-doping has been smdied by the molecular orbital cluster method [15]. In this method a part of a solid, cluster , is embedded in a model potential that mimics the crystal environment and the molecular orbital calculation is only performed on the cluster. The advantage of this method is that strong-electron correlation is systematically handled. However, the cluster size is rather limited, thus, a care must be taken whether it really reflects the bulk property. 

It is generally agreed that thermally induced vibrations of atoms in solids play a major role in melting [2.144]. The simple vibrational model of Linde-mann predicts a lattice instability when the root-mean-square amplitude of the thermal vibrations reaches a certain fraction / of the next neighbor distances. However, the Lindemann constant/varies considerably for different substances because lattice anharmonicity and soft modes are not considered, thus limiting the predictive power of such a law. Furthermore, Born proposed the collapse of the crystal lattice to occur when one of the effective elastic shear moduli vanishes [2.138], Experimentally, it is found instead that the shear modulus as a function of dilatation is not reduced to zero at Tm and would vanish at temperatures far above Tm for a wide range of different substances [2.145]... 

The present treatment concentrates on the electron phonon interaction as the most fundamental aspect of a Peierls lattice instability. For this purpose the Frbhlich Hamiltonian is the simplest relevant model. We calculate the ion displacement correlation for the Incommensurate Model (Eq. (2), i. e. complex a ) including thermodynamic fluctuations of the ion positions. 

Extended Defects, Lattice Instabilities and Non-Stoichiometry Amorphous Semiconductors. 

Both the high-Tc copper oxides and the molecular charge transfer salts give evidence of lattice instabilities,which may have a bearing on the occurrence and mechanism of the superconductivity. 

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