Thermal disordering

Rothberg L, Higashi G S, Allara D L and Garoff S 1987 Thermal disordering of Langmuir-Blodgett-films of cadmium stearate on sapphire Chem. Phys. Lett. 133 67-72... 

We can expect disorder to increase when a system is heated because the supply of energy increases the thermal motion of the molecules. Heating increases the thermal disorder, the disorder arising from the thermal motion of the molecules. We can also expect the entropy to increase when a given amount of matter spreads into a greater volume or is mixed with another substance. These processes disperse the molecules of the substance over a greater volume and increase the positional disorder, the disorder related to the locations of the molecules. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

That is, S —> 0 as T - 0. The perfect crystal part of this statement of the third law refers to a substance in which all the atoms are in a perfectly orderly array, and so there is no positional disorder. The T— 0 part of the statement implies the absence of thermal motion-—thermal disorder vanishes as the temperature approaches zero. As the temperature of a substance is raised from zero, more orientations become available to the molecules and their thermal disorder increases. Thus we can expect the entropy of any substance to he greater than zero above T = 0. 

Potassium nitrate dissolves readily in water, and its enthalpy of solution is +34.9 kj-niol. (a) Does the enthalpy of solution favor the dissolving process (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder ... 

If we have thermal disorder at room temperature (I do not know of any crystal for which this is not the case), then we can expect the following defect reaction relations ... 

Distortions of the First Kind and Thermal Disorder. In crystallography the best-known example for a lattice distortion of the first kind is the reduction of peak intensity from random temperature movement of the atoms. In materials science a frozen-in thermal disorder of nanostructures25 is observed as well. The result of this kind of disorder is a multiplicative26 attenuation of the scattering intensity by the Debye-Waller factor... 

We must warn on the fact that in Table IV, we have reported, for the liquid experimental and MD results, the frequencies corresponding to the maximum positions of the bending and stretching bands, which, because of thermal disorder, are quite broaden in addition the two sets of data present also librational and translational modes, not discussed here. 

The total number of imperfections per unit surface characterizes what may be termed the disorder of the crystal surface. Two parts should be distinguished in the disorder biographical disorder, which is retained at the absolute zero of temperature and depends on the method of preparation of the sample and on its entire preceding history and thermal disorder, which increases on heating and is superposed on the biographical disorder. ... 

If imperfections of some kind take part in adsorption as adsorption centers, then, as has been shown 106), a consideration of thermal disorder ... 

The surface imperfections being the centers of localization of free valencies may act as adsorption centers. In this case a real, but homogeneous surface may adsorb as an inhomogeneous one. This is because of thermal disorder on the surface of the crystal. 

N. Carroll, S.A. (2000) X-ray absorption spectroscopy of strontium coordination. I Static and thermal disorder in crysystalline, hydrated and precipitated solids and in aqueous solution. J. Coll. Interf. Sci. 222 184-198... 

The surface of real crystals are not perfect. At high temperatures thermal disorder will lead to a non-zero concentration of defects. At low temperatures, defects created at high temperatures may be frosen at the surface, defects in the bulk may extend to the surface. Also the orientation of the surface with respect to the crystal lattice may be oriented so that an atomically flat arrangement of the atoms is impossible. 

Nj and Oj in equation (2.4) represent the number of atoms in the jth shell and root-mean-square deviation of the interatomic distances over Rj which results both from static and dynamic (thermal) disordering effects respectively. The scattering amplitude, Fj(k) is given by... 

In view of the possibility that existing bands may simply be smeared out at room temperature by the thermal disorder in the liquid and the resulting fluctuations in the structure of the electron trap, Arai and Sauer (4) have determined the absorption spectrum of the solvated electron in ethanol at —78° C. No structure was observed, so that evidence is lacking for a transition to a second level, Is - 3p, even at the lower temperature. The absorption maximum was, however, found to be shifted from 7000 A. at 23 ° C. to 5800 A. at — 78 ° C. It is interesting to note that the half-width of the band remained the same, about 1.5 e.v., at the lower temperature. 

All of these hexafluorides are dimorphic, with a high-temperature, cubic form and an orthorhombic form, stable below the transition temperature (92). The cubic form corresponds to a body-centered arrangement of the spherical units, with very high thermal disorder of the molecules in the lattice, leading to a better approximation to a sphere. Recently, the structures of the cubic forms of molybdenum (93) and tungsten (94) hexafluorides have been studied using neutron powder data, with the profile-refinement method and Kubic Harmonic analysis. In both compounds the fluorine density is nonuniformly distributed in a spherical shell of radius equal to the M—F distance. Thus, rotation is not completely free, and there is some preferential orientation of fluorine atoms along the axial directions. The M—F distances are the same as in the gas phase and in the orthorhombic form. 

The technique of channeling-enhanced X-ray emission (CHEXE) has enabled cation site occupancies to be determined in various minerals, including transition metal ions in spinels and ferromagnesian silicates (Taftp, 1982 Taftp and Spence, 1982 Smyth and Taftp, 1982 McCormick etal., 1987). The method, which is based on relative intensities of X-ray peaks measured on crystals with diameters as small as 50 nm under the electron microscope, is particularly useful for determining site occupancies of minor elements with concentrations as low as 0.05 atom per cent in a structure. The most important criterion for the determination of element distribution in a mineral by this technique is that the cation sites should lie on alternating crystallographic planes. In order to make quantitative site population estimates, additional information is required, particularly the occupancy of at least one element in one of the sites or in another site that lines up with one of the sites of interest (McCormick et al., 1987). For example, cation site occupancies by CHEXE measurements have been determined from X-ray peak intensity ratios of Si to Ni, Mn, Cr and Fe in forsterite, as well as thermal disordering of these cations in heated olivines (Smyth and Taftp, 1982). 

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