Parallelepiped samples

Pd4oCu4oP2o, Pd5oCu3oP2o, and Pd6oCu2oP20 alloys were measured by resonant ultrasound spectroscopy (RUS). In this technique, the spectrum of mechanical resonances for a parallelepiped sample is measured and compared with a theoretical spectrum calculated for a given set of elastic constants. The true set of elastic constants is calculated by a recursive regression method that matches the two spectra [28,29]. 

Fig.l, Change of the reflected signal with scanning of a sample as parallelepiped with internal apertures. 1 - sample Ks 1 2 - sample iNs 2 3 -difference of the reflected signals 4 - difference of the reflected signals after mathematical processing. The area from 12 up to 14 corresponds to an additional aperture (defect). 

The potential influence of shape on the correct design of laboratory test-pieces has been discussed in detail by Romanski. Samples of iron in the form of discs, cylinders, plates or parallelepipeds, and of a wide range of areas, were sulphidised under controlled conditions. The parabolic rate constant could be expressed in terms of the area A of the samples by... 

We demonstrate the procedure with an experiment conducted on a Bentheimer sandstone sample. For simplicity, we use a relatively thin sample and resolve only the two in-plane spatial coordinates. The sample is a rectangular parallelepiped shape having a length of 50 mm extending in the z direction, width 25 mm along the z2 direction and thickness 5 mm in the z3 direction. The sample was sealed laterally with epoxy and mounted in Plexiglass end-plates with O-rings and tube... 

The calculation was similar to that made for the problem of three-dimensional heat transmission and uniform heat generation in a rectangular parallelepiped (3) with the surfaces maintained at ambient temperature. By solving the parallelepiped equation with appropriate values, it can be shown that the temperature distribution over the sample cross section is approximately parabolic, with the maximum temperature at the center (7). (Figure 17 gives a graphical presentation of this solution.) This leads to the conclusion that the average temperature is approximately 63.5% of the maximum temperature. 

Let us assume that the oxide sample exists in the form of a parallelepiped. The solution to Fick s second law under the given boundary conditions gives for the change in time of the integral number of vacancies wv... 

In experiments with liquid solutions laser beam was focused inside the parallelepiped or cylindrical quvettes. The beam had the minimal cross section diameter not lower then 0.2 mm. In experiments with solid samples the beam was stretched in one direction by means of cylindrical lens, so the ellipse projected on a surface had dimensions of about 2x0.2 mm2. In such conditions the density of exciting light power did not excite 65 W/cm2 for the experiments with liquids and was at least 10 times smaller for the... 

A sample cell—normally parallelepiped in shape with a standard length of 1 cm and made of glass for the VIS region or quartz (or fused silica) for the UV region. The cell has an opening for inserting the sample and a stopper to prevent evaporation. 

The factors that are included when calculating the intensity of a powder diffraction peak in a Bragg-Brentano geometry for a pure sample, composed of three-dimensional crystallites with a parallelepiped form, are the structure factor Fhkl 2=l/ TS )l2, the multiplicity factor, mm, the Lorentz polarization factor, LP(0), the absorption factor, A, the temperature factor, D(0), and the particle-size broadening factor, Bp(0). Then, the line intensity of a powder x-ray diffraction pattern is given by [20-22,24-26]... 

An example of a joint density function gA (r, R) is shown in Fig. 12. The sample is a Bentheimer sandstone in a rectangular parallelepiped shape 50 mm long extending in the -direction, 25 mm wide along the x-direction, and 5 mm thick in the y-direction. The average volumetric flow rate of the water was 1.5 ml min-1 along the -direction. The sample is located between the two spikes resulting from free water present in the end caps of the core holder. 

The experimental flow system is taken to be a rectangular parallelepiped of dimensions z, , z2o, and z3 , with a known porosity experimental domain. A fluid is introduced at the injection or entrance face Sent, located at z = 0, at a constant flow rate that is assumed to be known. The fluid, on average, flows through the medium in the positive z, direction, although local heterogeneities in the sample will cause the velocity field to vary in both the z2 and z3 directions. No fluid is allowed to enter or leave the porous matrix through the sides, Snf, and all of the fluid is even-... 

Figure 6-3a). In the general case of a pure homogeneous strain, the cube is transformed into a rectangular parallelepiped (Figure 6-3b). The dimensions of the parallelepiped are A, /I2 and /L3 in the three principal axes, where the are called the principal extension ratios. Choosing the coordinate axes for the chain to coincide with the principal axes of strain for the sample, then... 

It can happen that the structure of a data set is such that a standard two-way table (objects versus variables) is not enough to describe it. Let us suppose that the same analyses have been performed at different sampling sites on different days. A third way needs to be added to adequately represent the data set, which can be imagined as a parallelepiped of size IXJXK, where I is the number of sampling sites (objects), / is the number of variables, and K is the number of sampling times (conditions). " ... 

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... 

Consider as an example of the use of Eq. 1.3 a clay sample containing oethit CTjstals (parallelepipeds) with the dimensions 160 x 26 x 6.5 nmT nce the mass density of goethite is 4.37 x 10 kg crystallographic specific surface area of these crystals is... 

In Method 5B, the method of test for the higher density materials is similar but the sample size, although still a parallelepiped, is reduced to 40 mm square sides for the load-bearing surfaces with a width-to-thickness ratio of 4 1. The area of the load-bearing surface should not be less than 1600 mm", The specimen is compressed at a rate of 5 mm minute, and a preflexing procedure is carried out whereby the sample is compressed to the specified strain three times before the stress is determined on the fourth cycle. 

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