Short-range ordering

Amorphous carbon is a carbon material without long-range crystalline order. Short-range order exists, but with deviations of the inter-atomic distances and/or inter-bonding angles with respect to the graphite lattice as well as to the diamond lattice. 

No order Short-range order Long-range order Perfect order... 

J. Keller and J. M. Ziman, Long range order, short range order and energy gaps, J. Noncryst. Solids, 8-10, 111-21 (1972). 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Figure Al.3.28. Examples of disorder (a) perfeet erystal, (b) eompositional disorder, (e) positional disorder whieh retains the short-range order and (d) no long-range or short-range order.

The details of the second-order energy depend on the fonn of exchange perturbation tiieory used. Most known results are numerical. However, there are some connnon features that can be described qualitatively. The short-range mduction and dispersion energies appear in a non-expanded fonn and the differences between these and their multipole expansion counterparts are called penetration tenns. 

Onsager L and Kaufman B 1949 Orystal statistics III. Short range order in a binary Ising lattice Phys. Rev. 65 1244... 

The integral under the heat capacity curve is an energy (or enthalpy as the case may be) and is more or less independent of the details of the model. The quasi-chemical treatment improved the heat capacity curve, making it sharper and narrower than the mean-field result, but it still remained finite at the critical point. Further improvements were made by Bethe with a second approximation, and by Kirkwood (1938). Figure A2.5.21 compares the various theoretical calculations [6]. These modifications lead to somewhat lower values of the critical temperature, which could be related to a flattening of the coexistence curve. Moreover, and perhaps more important, they show that a short-range order persists to higher temperatures, as it must because of the preference for unlike pairs the excess heat capacity shows a discontinuity, but it does not drop to zero as mean-field theories predict. Unfortunately these improvements are still analytic and in the vicinity of the critical point still yield a parabolic coexistence curve and a finite heat capacity just as the mean-field treatments do. 

Equation (A3.3.57) must be supplied with appropriate initial conditions describing the system prior to the onset of phase separation. The initial post-quench state is characterized by the order parameter fluctuations characteristic of the pre-quench initial temperature T.. The role of these fluctuations has been described in detail m [23]. Flowever, again using the renomialization group arguments, any initial short-range correlations should be irrelevant, and one can take the initial conditions to represent a completely disordered state at J = xj. For example, one can choose the white noise fomi (i /(,t,0)v (,t, 0)) = q8(.t -. ), where ( ) represents an... 

The major role of TOF-SARS and SARIS is as surface structure analysis teclmiques which are capable of probing the positions of all elements with an accuracy of <0.1 A. They are sensitive to short-range order, i.e. individual interatomic spacings that are <10 A. They provide a direct measure of the interatomic distances in the first and subsurface layers and a measure of surface periodicity in real space. One of its most important applications is the direct determination of hydrogen adsorption sites by recoiling spectrometry [12, 4T ]. Most other surface structure teclmiques do not detect hydrogen, with the possible exception of He atom scattering and vibrational spectroscopy. 

Short-range order parameter a Standard enthalpy of activa- m... 

Some materials that are atomically ordered also develop a sHp-iaduced anisotropy as a result of plastic deformation. The origin is thought to be identical to that of thermomagnetic anisotropy, ie, short-range directional order, except that the order is brought on by deformation rather than by heat treatment ia a field (3,4). 

The short-range order in a material is important in determining optoelectronic properties. For instance, x-ray and electron diffraction experiments performed on amorphous siHcon (i -Si) and germanium (a-Ge) have revealed that the nearest neighbor environments are approximately the same as those found in their crystalline counterparts (6) photoemission experiments performed on i -Si show that the DOS in valence and conduction bands are virtually identical to the corresponding crystal with the exception that the singularities (associated with periodicity) present in the latter are smeared out in the former. 

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