Sample thickness, measurements

Examination of oven-aged samples has demonstrated that substantial degradation is limited to the outer surface (34), ie, the oxidation process is diffusion limited. Consistent with this conclusion is the observation that oxidation rates are dependent on sample thickness (32). Impact property measurements by high speed puncture tests have shown that the critical thickness of the degraded layer at which surface fracture changes from ductile to brittle is about 0.2 mm. Removal of the degraded layer restores ductiHty (34). Effects of embrittled surface thickness on impact have been studied using ABS coated with styrene—acrylonitrile copolymer (35). 

Nature Two samples were selected from different locations in a plastic-film sheet and measured for thickness. The thickness of the respective samples was measured at 10 close but equally spaced points in each of the samples. It was of interest to compare the average thickness of the respective samples to detect whether they were significantly different. That is, was there a significant variation in thickness between locations ... 

From a modehng standpoint statisticians would define this problem as a two-population test oihypothesis. They would define the respective sample sheets as two populations from which 10 sample thickness determinations were measured for each. 

Application. Two samples were selected from different locations in a plastic-film sheet. The thickness of the respective samples was measured at 10 close hut equally spaced points. 

None, except there are techniques that measure sample thickness... 

The thickness of a film influences the interference of light waves reflected from the front and back of the film, and hence the reflectance. The thickness of an absorbing film can, therefore, be measured only as long as there is still a contribution of from the back of the film to the reflectance of the sample. Typical measurable thicknesses of metallic layers are <50 nm. 

Given limits to the time resolution with which wave profiles can be detected and the existence of rate-dependent phenomena, finite sample thicknesses are required. To maintain a state of uniaxial strain, measurements must be completed before unloading waves arrive from lateral surfaces. Accordingly, larger loading diameters permit the use of thicker samples, and smaller loading diameters require the use of measurement devices with short time resolution. 

SE is present only in sufficiently thick films of P3BT. If the sample is too thin, i.e., its OD at 625 nm is less than 0.6, then SE is not observed and only PA is present in this case. Figure 7-22 illustrates this situation, depicting two normalized transient PM decays measured at exactly the same experimental conditions, except for the samples thickness. Gain can be observed in the thicker film (see Fig. 7-22a), but no gain is present in the thinner film (see Fig. 7-22b). 

Cliff and Lorimer (1975) used this equation to form the basis for X-ray microanalysis of thin foils, where the constant kAB contains all the factors needed to correct for atomic number differences. kAB varies with operating voltage, but is independent of sample thickness and composition if the two intensities are measured simultaneously. Its value can be determined experimentally with accuracy, using specimens of known composition. The value of kAB can be determined by calculation more rapidly, but with less accuracy. 

For concentrated or bulk samples a transmission experiment is both the simplest and the most effective. In essence, one measures the X-ray intensities incident and transmitted through a thin and uniform film of the material. Careful analysis of signal-to-noise ratio considerations indicates that optimal results are obtained when the sample thickness is of the order of 2.5 absorption lengths. Since in this case a simple Beer s law applies, the data are usually plotted as In(7//0) versus E. The intensities are measured using ionization chambers in conjunction with high-gain electrometers (see Fig. 11). 

Precise thickness measurements by TEM require sections transverse to the basal lamellar surface. Conversely, only lamellae that can be identified as untilted "edge-on" or "flat-on" in AFM images are suitable for thickness analysis. The average thickness obtained by these techniques is based on sampling microscopic areas and will only be correct if the morphology is uniform in the sample. Micrographs taken from different areas of the specimen are usually studied, and statistical analysis of histograms used for quantitative analysis [255,256]. 

Multiple scattering means that a photon is at least scattered twice inside the sample. The phenomenon changes the measured small-angle scattering. In practice, multiple scattering can effectively be reduced by decreasing the sample thickness. 

The optimum sample thickness for PET of a mass density pp r=l-35 g/cm3 in transmission geometry thus is topt,PET = 1 /Ppet 1 mm. If measured in reflection, the PET sample should be at least 3 mm thick. 

Example Suppose one wants to measure the thermal conductivity of a solid (k). To do this, one needs to measure the heat flux (q), the thickness of the sample (d), and the temperature difference across the sample (AT). Each measurement has some error. The heat flux (q) may be the rate of electrical heat input (< ) divided by the area (A), and both quantities are measured to some tolerance. The thickness of the sample is measured with some accuracy, and the temperatures are probably measured with a thermocouple to some accuracy. These measurements are combined, however, to obtain the thermal conductivity, and it is desired to know the error in the thermal conductivity. The formula is... 

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