Sampling length

DOS and, concomitantly, on p [63-66], and, (iv) the temporal features of TOF signals, notably the universality of non-dispersive signals at variable sample length and electric field, and the transition to dispersive transport which, remarkably, does not bear out universality [67]. 

In Equations 2 and 3, Ei and Ef are strains at point I in the initial and final collection rate areas, Is is the starting point and Ir is the rate transition point, Ti and Tf are the initial and final collection rates in sec/point, C is the crosshead speed in lnches/sec, and L is the sample length in inches. 

Sample Length l.OOOin Sample Width 0.750in... 

Now consider the finite sampling systematic error. As discussed in Sect. 6.4.1, the fractional bias error in free energy is related to both the sample size and entropy difference 5e N exp(-AS/kB). With intermediates defined so that the entropy difference for each substage is the same (i.e., AS/n), the sampling length Ni required to reach a prescribed level of accuracy is the same for all stages, and satisfies... 

Among these techniques, the capacitance dilatometer method may be very sensitive. The change in the sample length produces a capacitance change between the two electrodes of a capacitor one plate of the capacitor is kept in a fixed position while the other is fixed onto one end of the sample. At the maximum elongation of the sample, the two capacitor plates are practically in contact. When the sample contracts the capacitance varies as 1 /AL. One of the main difficulties in this measurement is the realization of a dilatation-free support. 

This interferometric dilatometer consists of a rather simple and small Michelson interferometer, in which the two arms are parallel, and of a 4He cryostat, in which the sample to be measured is hold. The sample is cooled to 4 K, and data are taken during the warm up of the cryostat. The optical path difference between the two arms depends on the sample length hence a variation of the sample length determines an interference signal. The Michelson interferometer consists of a He-Ne stabilized laser (A = 0.6328 xm), two cube corner prisms, a beam splitter, three mirrors and a silicon photodiode detector placed in the focal plane of a 25 mm focal length biconvex lens (see Fig. 13.1). 

The total optical path difference between the two arms of the interferometer, for a sample length of about 50 mm, is of the order of 10 mm or less, minimizing the systematic error due to laser frequency fluctuations. To reduce the thermal effects on the interferometer assembly, the interferometer support plate is stabilized to a temperature slightly higher than room temperature and insulated from air currents by a polystyrene foam shield. The temperature variation of the interferometer support is kept below 0.1 K. 

Since the distance between the zeroes, in terms of sample length variation, is A/4, the total contraction of the sample is AL = N A/4, where N is the total number of zero crossing. The resolution of the system is basically A/4, but it could be improved with an evaluation of fractions of a fringe. 

DMT A measurements were made with a Polymer Labs instrument. Samples were clamped in the single cantilever mode in a frame of 22 mm using 6 mm clamps with 0.5 mm faces. The sample length between the clamps was 8 mm. Measurements were performed at a frequency of 1 Hz, a strain amplitude of 0.063 mm and a heating rate of 5 K.min . Clamping was checked by monitoring the strain amplitude on an oscilloscope. The measurements were carried out in air. Values of the temperature of maximum mechanical loss, T (tan 5max). were reproducible to 2 K. 

Fig. 25 Comparison of the predictions of various models for current injection from a metal electrode into a hopping system featuring a Gaussian DOS of variance a = 15 meV as a function of the electric field at different temperatures. The ID continuum and the 3D master equation model have been developed by van der Holst et al. [127]. The calculations based upon the Burin-Ramer and the Arkhipov et al. models are taken from [175] and [170] respectively. Parameters are the sample length L, the intersite separation a and the injection barrierA. From [127] with permission. Copyright (2009) by the American Institute of Physics...

The sample length is at least twice either of the other two dimensions (valid for samples used in this work). 

The same assumptions apply for gas generation as for heat generation—that the sample is isotropic, that the gas generation rate does not vary with time or location in tne radiation area, and that the sample length is more than twice either of the other dimensions. 

In the laboratory experiments, DOC monolith samples (length 7.5 cm, diameter 1.4 cm) with rather thin catalyst layer coating ( 25 pm) were employed to minimize the internal diffusion effects. The samples were placed into a thermostat to suppress the formation of temperature-gradients along the channels. In the course of each experiment, the temperature of the inlet gas and the monolith sample was increased at a constant rate of /min within the range of 300-800 K. The exhaust gases at the inlet of the converter were simulated by synthetic gas mixtures with defined compositions and flow rates (cf. individual figure captions all gas mixtures contained 6% C02 and 6% H20). 

Yet another check of convergence in MD simulations, as alluded to in Section 3.5, is to ensure that the sampling length is longer than the autocorrelation decay time for a particular property by several multiples of that time. In practice, this analysis is performed with less regularity than is the simple monitoring of individual property values. 

Fig. 19. Magnetostriction measured at 0.06T forTb0.27Dyo.73(CoxFei x)2 thin films (1 1 ) as-deposited (2 2 ) annealed at 150°C (3 3 ) annealed at 250°C. Solid lines represent by,2(i.y%2), dashed lines h (A ). The measuring direction along the sample length is indicated. After Due et al. (2000a, 2000c),...

Although traditionally the thermodynamic treatment of the deformation of elastomers has been centered on the force, the alternative condition of keeping the force (or tension) constant and recording the sample length as a function of temperature at constant pressure is even simpler 23,271. 

Table 1.4 reports values of the modulus of elasticity, or Young s modulus. This is another mechanical property which represents the stiffness of the material, or its resistance to elastic strain. More precisely, Young s modulus is the stress required to produce a unit strain by changing sample length. Table 1.4 shows that the modulus is considerably higher in the carbides and nitrides than in the metals, with values resembling those of the ceramic materials. Diamond, again, is special. 

Fig. 40. Temperature dependence of the nominal stress at constant sample length 1 for the l.c.

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