Montgomery method

The shape anisotropy also complicates efforts to determine the resistivity anisotropy. An extension of the Montgomery method must be employed for anisotropic materials (93). Such characterization has been carried out for Bi22Sr2 Ca 0 8Cu2O8+fi (94). 

The analysis of van der Pauw can be used for arbitrary electrode arrangements on thin samples of anisotropic materials of any shape and has been widely used in studies of conjugated polymers, where only small and irregular samples are available. Four electrodes are attached, as shown in Fig. 5.19(d). The resistance values Ry and R2 are measured as for the Montgomery method. The volume resistivity is then calculated from these values as... 

Similarly, one does not deviate much from 0(fi) with division in practice, although one can be faster asymptotically The only usual alternative to standard division is the Montgomery method, where the representation of residue classes by... 

Conductivity of single crystal samples cut into rectangular parallelepipeds 1.0 X 0.7 X 0.4 mm was measured by the Montgomery method (28) with contacts placed at four parallel edges of the samples. Single... 

The conductivity increases for pressures up to 4 kbar, then gradually decreases, as shown in Fig. 2.14 [ 125,126]. The data are consistent for both collinear four-probe and Montgomery methods. The increase in conductivity up to 4 kbar is reversible with pressure, whereas the decrease at higher pressures is not reversible. The pressure dependence of conductivity in potassium-doped oriented (CH). [124] is nearly identical to that obtained from iodine-doped material [125,126]. The inset in Fig. 2.14 shows the pressure dependence of the conductivity perpendicular to the chain axis. The initial increase in (HP) is attributed to enhanced interchain transport, whereas the decrease above 4 kbar is not understood. At 8 kbar, the anisotropy has decreased by a factor of 1.6, from 110 to 67, at room temperature. The pressure dependences parallel and perpendicular to the chain axis are identical, implying that the macroscopic conductivity in both directions is limited by interchain charge transport. 

Contacting was performed by mechanically pressing platinum contacts elastically on the film. By means of small screws, the pressure of the contacts could be adjusted. For the Montgomery method, this adjustment could be done for each of the contacts separately. Different sample holders were used for different sample sizes. For most of the conductivity experiments presented here, we used samples of 19 X 2 mm2 and 14 x 6 mm in size for the standard four-probe and Montgomery techniques, respectively. 

When samples have irregular shapes but are flat and uniform in thickness their conductivity can be measured by a modified four-electrode method, the van der Pauw technique, where small, point-like electrodes are placed arbitrarily at the periphery of the samples. Two measurements are performed with commuted current and voltage connections, and for calculation of the conductivity value, a correction factor, numerically calculated and published by van der Pauw, is needed. Another modification of the four-probe method, the Montgomery method, is similar to the van der Pauw method but is applied to anisotropic materials. This method allows the determination of the anisotropy ratio of investigated materials. 

F. Montgomery, S. Montgomery, and P. Stephens. Method of controlling porosity of well fluid blocking layers and corresponding acid soluble mineral fiber well facing product. Patent US 5222558, 1993. 

The physical properties of -hexane (see Table 3-2) that affect its transport and partitioning in the environment are water solubility of 9.5 mg/L log Kow (octanol/water partition coefficient), estimated as 3.29 Henry s law constant, 1.69 atm-m3 mol vapor pressure, 150 mm Hg at 25 °C and log Koc in the range of 2.90 to 3.61. As with many alkanes, experimental methods for the estimation of the Koc parameter are lacking, so that estimates must be made based on theoretical considerations (Montgomery 1991). 

TOA were determined, in the supernatant prepared as described by Hissett et al (25), by the method of Montgomery et al (26). The organic acids were esterified with acidified ethylene glycol. The esters were then reacted with hydroxylamine and the hydroxamic acids thus formed were converted to their ferric complexes and their concentrations were determined by optical density measurements at 500u. 

Ealick SE, Babu YS, Bugg CE, Erion MD, Guida WC, Montgomery JA, Secrist JA 3d. Application of crystallographic and modeling methods in the design of purine nucleoside phosphorylase inhibitors. PNAS USA 1991 88 11540-4. 

As a result, the formation of various national standards associations has led to the development of methods for coal evaluation. For example, the American Society for Testing and Materials (ASTM) has carried out uninterrupted work in this field for many decades, and investigations on the development of the standardization of methods for coal evaluation has occurred in all the major coal-producing countries (Montgomery, 1978 Patrick and Wilkinson, 1978). There are in addition to the ASTM, organizations for methods development and standardization that operate on a national level examples are the International Organization for Standardization (ISO) and the British Standards Institution (BS), which covers the analysis of coal under one standard number (BS 1016) (Table 1.2). 

A complete discussion of the large number of tests that are used for the evaluation of coal (and coal products) would fill several volumes (see, e.g., Ode, 1963 Karr, 1978, 1979 Montgomery, 1978 Zimmerman, 1979 Gluskoter et al., 1981 Smith and Smoot, 1990), and such detailed treatment is not the goal of this book. The focus is on a description, with some degree of detail, of the test methods in common use, as well as a critique of various procedures that are not obvious from the official descriptions of test methods and a description of pitfalls that can occur during application of a test method for coal analysis. 

Montgomery, W. J. 1978. In Analytical Methods for Coal and Coal Products, Vol. 1, C. K. Karr, Jr. (Editor). Academic Press, San Diego, CA, Chap. 6. 

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