Size and Shape of the Sample

The earliest work was done for hard disks and spheres, with no longer range forces. In that case there is no direct effect due to interactions with distant (but correlated) parts of the periodic system. There is nevertheless some dependence of the results on the size and shape of the periodic sample. This arises in various ways, which of course also persist for systems with other forces. For example, the number of particles within any of the periodic boxes is fixed at N. This is a serious constraint on the density fluctuations for small N, and will lead to errors in the resulting thermodynamic averages, in particular to a diminished entropy. (For mixtures, the concentration fluctuations are similarly constrained, and this could be a still more severe problem.) With small samples the range of structural fluctuations may be similarly constrained. This will clearly be the case if significant interparticle configurational correlations have a 

When N-dependent errors are feared, one procedure has been to do the Monte Carlo work for several sample sizes N, afterwards extrapolating to the large-system limit (l/N- 0). This extrapolation (of intensive thermodynamic or structural quantities, such as U/N or g2) has usually been done linearly in 1/N (cf. Card and Valleau, Rasaiah et but that is not entirely 

Happily it is frequently true that these sources of error are quantitatively unimportant for the problem at hand and can be ignored. It is good practice to test this supposition by carrying out at least a few MC runs with a sample size noticeably different from that adopted for the bulk of the investigation. 

Of course, the box size puts an upper limit on the range of particle correlations that can be investigated. For example, as an upper limit, no information may be obtained on pair correlation functions for pair separations greater than half the box length. (If the correlations are still strong at such separations, however, the sample size is probably too small to give reliable thermodynamic results.) 

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The type of heating equipment and the size and shape of the sample holders as well as the material from which they are made (platinum crucibles specified) all have some influence on the rate of heating of the sample and the range of temperatures to which it is exposed. The crucibles used are 10 to 20 mL in capacity, of specified size, with deep-fitting lids, and there are two procedures for determination of volatile matter. 

Some of the factors involved in choosing a particular nondestructive evaluation technique are the primary reason or objective, the type of flaw to be detected, the size and orientation of the flaw, the location of the flaw in the sample, the size and shape of the sample and the nature of the sample. It is also necessary to know the type of flaws that are acceptable or unacceptable in the sense that flaws may be deleterious or nondeleter-ious. The size, type, orientation and location of the flaws determine whether they are acceptable or unacceptable as per the code, or standard given by American Society of Mechanical Engineers Pressure Vessel Code, American Welding Society Structural Welding Code or any other applicable code or standard. 

The material and the size and shape of the sample container, as well as the disposition of the sample within it, may all influence the rate of decomposition. TG equipment is well suited to studies of the influences of controlled pressures of gases (including volatile products) on reaction rates. 

The basics of photoacoustic spectroscopy (PAS) are described in Chapter 5. PAS is useful for examining highly absorbing samples that are difficult to analyze by other IR techniques. Minor or even no sample preparation is required here. The size and shape of the sample are not critical. PA spectra can be obtained from a wide variety of samples such as powders, polymer pellets, viscous glues, single crystals, and single fibres. 

The net-peak intensity /,meas can be determined by fitting the experimental spectra using nonlinear least squares fitting (Janssens et al. 1996, 2000). The self-absorption factor A,-depends on the matrix composition and on geometrical factors (size and shape of the sample). 

An apparent mass loss is caused by the upper flowing stream of gas in the vicinity of the sample holder. The upper flowing stream can be reduced by changing the configuration of the sample holder (see Section 2.2.1). It is also important that the size and shape of the sample crucible are adjusted appropriately. In some cases, it is recommended that a small hole is made in the crucible (Figure 3.6). 

The major advantages of WPS compared to screen printing or plasma spraying are the low-cost fabrication, the flexibility concerning size and shape of the samples to be coated, and the easy integration into an industrial process chain. 

The choice of the best conditions for a combustion can sometimes be made easier by preliminary observation of the reaction in a bomb fitted with a window. This is particularly true of the combustion of rigid inorganic materials (in oxygen or fluorine) where there exists considerable scope for variations in the size and shape of the sample and its method of support. Nuttall, Frisch, and Hubbard have described an inexpensive combustion vessel of similar dimensions to a normal bomb but made from thick-walled Pyrex pipe. A more elaborate window-bomb, in which the combustion of metals, carbides, and borides has been observed, contains a... 

The main characteristics of PAS are collected in Table 1.22. The major benefit of PAS is that, to a large extent, the general features of the spectrum are independent of the sample morphology. This is in contrast to other IR sampling techniques for solids such as diffuse reflectance, for which particle size and shape of the sample are critical. 

Frequently, the size and shape of the sample has been found to affect detonation results, which imposes an additional hardship on the operator of this test or upon the statistics-minded analyst. Peaks or sharp edges of the specimen may create intensified energy areas during impact, which then may... 

After crosslinking, the treated porous preforms are subjected to a hydrolysis process to revert the crosslinked silyl HA-CTA to hydrophilic, crosslinked HA. The hydrolysis procedure involves placing the treated preforms in a solution of NaCl in ethanol. The precise procedure depends on the size and shape of the sample and is simply performed long enough to ensure full hydrolysis. Zhang and James confirmed that the hydrolysis procedure reverted the silyl HA-CTA back to native HA using FTIR [80], and later studies confirmed full hydrolysis of the preforms using XPS [83]. 

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