Specimen displacement

Fig. 8. Apparent torsional modulus (period"2 in arbitrary units) measured at various end loads. Specimen correctly aligned 9 Specimen displaced at one end by 2 microns, parallel to its thin dimension, x Specimen displaced at one end by 10 microns.

The extrapolation fimction cos 9 is best if the flat sample effect is the principal error, while cos 0/sin0 for specimen displacement error. Using this latter fimction, it can be shown that... 

The fifth parameter characterizes specimen displacement, s, from the goniometer axis and it is expressed as... 

Figure 2.41. The differences between the observed and calculated 20 values plotted as a function of 20 without (open circles) and with (filled triangles) specimen displacement correction. The corresponding values of the unit cell parameters and the specimen displacement parameter are indicated on the plot. The material belongs to the tetragonal crystal system.

The specimen displacement parameter usually varies from sample to sample and it usually takes up some of the effects of sample transparency. For a properly aligned goniometer, the zero shift error should be negligible. Even if the goniometer is misaligned, the zero shift correction should remain sample independent. 

The effect of a specimen displacement at right angles to the incident beam [Fig, 1 l-3(b)] is to shift the lines from A to C and from B to D. When Ay is small, AC is very nearly equal to BD and so, to a good approximation, no error in S is introduced by a right-angle displacement. 

The total error in S due to specimen displacement in some direction inclined to the incident beam is therefore given by Eq. (11 -6). This error in S causes an error in the computed value of Inasmuch as we are considering the various errors one at a time, we can now put the radius error AR equal to zero, so that Eq. (11-4) becomes... 

SPE 95] SPERLING Z., Specimen displacement error in focusing systems . Powder Diffr., vol. 10, p. 278-281,1995. 

Thickness, temperature. Specimen displacement,t displacement record... 

CF experiments are hindered by several common factors. Aggressive environments are difficult to contain at a constant condition, and hinder precise measurements of specimen displacement, load, and crack size. CF is influenced by many interactive mechanical, chemical, and microstructured variables that must be factored into experimental design. It is often necessary to investigate slow-rate deformation and cracking phenomena in a realistic time experiments must be conducted for one day to one year or more. CF damage is localized at surface slip structure and near the crack tip high resolution observations are not generally available and behavior must be interpreted from indirect measurements. 

Refinement strategy Refined global parameters and sequence of refinement Refined phase-specific parameters and sequence of refinement Parameter constraints Fixed parameters Specimen displacement, background type and number of coefficients Scale factors, lattice parameters, peak shape type and parameters, site occupancies, preferred orientation correction Limits on lattice parameter shift, peak shape parameters Atomic positions, atomic displacement parameters... 

In the first step, C3S (M3) and C4AF were identified as major phases. Both phases were included in a first refinement cycle. Phase-specific parameters that were varied were the phase scale factors, lattice parameters and a Lorentzian peak-broadening parameter. To constrain parameter variation and prevent parameter drift, hard limits were placed on the variation intervals e.g. for lattice parameters a 1% variation from the literature values was allowed. The refined global variables were a specimen displacement error and a background polynomial of two coefficients and a 1/X term. The results of this first refinement round are shown in Figure 4.17a. The graph shows that the majority of diffraction peaks has been matched however, the difference curve clearly shows that many smaller peaks are not or not fully accounted for. 

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