Temperature dependence crystalline defects

Lattice thermal conductivity data below 300 K for representative clathrates are summarized in Fig. 6.4 [35, 40 4], These data, for a representative number of compositions collected from both polycrystalline and single crystalline specimens, allow for a comparison of the effect of guest and framework composition on Kl. While some compositions have lattice thermal conductivities that are characteristic of glasses, others have Kl values that more closely resemble the typical temperature dependence of defect-free crystalline solids in which Umklapp processes [24] produce a monotonically decreasing Kl with increasing temperature above 10 K. 

An important result is also that many approximants of these quasicrystalline phases have similar conduction properties. For example the crystalline a-AlMnSi phase with a unit cell size of about 12 A and 138 atoms in the unit cell has a conductivity of about 300(Qcm) at low temperature [7,9]. The conductivity has the same defect and temperature dependence as that of the AlCuFe and AlPdMn icosahedral phase. There is, to our knowledge, no experimental result on the optical conductivity of this a-AlMnSi phase, but it is very likely that it is similar to that of AlCuFe and AlPdMn icosahedral phase. 

The temperature dependence of photodimer yield has been observed in flu-oro-4-methylcoumarin [63], Upon irradiation of crystalline samples (for 8 hr) at temperatures of 298, 323, and 363 K, the dimer yields are 3%, 10%, 20%, and 26%, respectively. The increase in dimer yield must be due to the greater population of the defect sites generated in the crystal as the temperature is increased. 

Therefore, the observed process (I) could be related to the cooperative dynamics of glycerol in the supercooled phase, while process (II) is most likely related to the crystalline phase of glycerol and is the result, similar to water, of the mobility of defects in the crystalline lattice [200]. The temperature dependence of the relaxation time for dehydrated glycerol is compared in Fig. 23 with those for the usual behavior of glycerol, which has absorbed some water from the atmosphere. 

The nature of plasticity is rupture and rearrangements of interatomic bonds which in crystalline objects involve peculiar mobile linear defects, referred to as dislocations. Temperature dependence of plasticity may significantly differ from that of Newtonian fluids. Under certain conditions (including the thermal ones) various molecular and ionic crystals, such as NaCl, AgCl, naphthalene, etc., reveal a behavior close to the plastic one. The values of x typically fall into the range between 10s and 109 N m 2. At the same time, plastic behavior is typical for various disperse structures, namely powders and pastes, including dry snow and sand. In this case the mechanism of plastic flow is a combination of acts involving the establishment and rupture of contacts between dispersed particles. Plastic object, in contrast to a liquid, maintains the acquired shape after removal of the stress. It is worth... 

The discussion of crystalline lattices has proceeded with the implicit assumption that every crystal is a perfect one. In reality, however, most crystals contain defects. As we have seen previously, whenever two or more gaseous ions combine to make a crystalline solid, the process is favored by enthalpy and a large amount of energy is released as the lattice enthalpy. At the same time, the process of crystallization is entropically unfavorable. If the enthalpy term is greater than the entropy term, the resulting lattice will approach that of a perfect crystal. However, whenever the entropy term is comparable in magnitude with the enthalpy of formation, the resulting solid will necessarily contain defects in its crystalline lattice. Because of the temperature dependence of the entropy term, the number of defects typically increases with temperature. 

Let us first consider dodecyl-cyanobyphenyl which shows two phase transitions at 48 °C (crystalline-semectic A) and at 58.5 °C (smectic A-isotropic). The analysis of the whole spectrum is reported in the original work [112] and we focus here only on the variation with temperature of the conformational structure of the dodecyl side chain which we hope to reveal with the study of the temperature-dependent vibrational spectrum in the 1420-1280 cm" range where defect modes are expected to occur. 

Figure 3-27. Liquid crystalline polyester with decamethylene spacers. Temperature-dependent infrared spectrum in the defect modes frequency range (see text). The spectra and shifted one from the other as in a tridimensional plot.

Because crystalline defects serve as scattering centers for conduction electrons in metals, increasing their number raises the resistivity (or lowers the conductivity). The concentration of these imperfections depends on temperature, composition, and the degree of cold work of a metal specimen. In fact, it has been observed experimentally that the total resistivity of a metal is the sum of the contributions from thermal vibrations, impurities, and plastic deformation—that is, the scattering mechanisms act independently of one another. This may be represented in mathematical form as follows ... 

The conductivity (or resistivity) of a semiconducting material, in addition to being dependent on electron and/or hole concentrations, is also a function of the charge carriers mobilities (Equation 18.13)—that is, the ease with which electrons and holes are transported through the crystal. Furthermore, magnitudes of electron and hole mobilities are influenced by the presence of those same crystalline defects that are responsible for the scattering of electrons in metals—thermal vibrations (i.e., temperature) and impurity... 

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