Burgers vector, determination

Thus, because of these empirical correlations, it may be possible, at least in principle, to estimate quantitatively the stress, temperature, and perhaps the strain-rate of a naturally deformed rock from measurements of dislocation density, subgrain size, and dynamically recrystallized grain size, together with Burgers vector determinations. However, these estimates will be questionable unless certain conditions are fulfilled. Some of the more important of these conditions will now be discussed before considering specific examples of the application of microstructural observations to tectonic problems. 

Dislocations can be imaged and their Burgers vectors determined by using transmission electron microscopy. This technique has shown that many dislocations have a Burgers vector that is less than the repeat distance of the structure. These are called partial dislocations. 

Most of the dislocations in specimen after high-temperature tests are associated in sub-boundaries. The parallel sub-boundary dislocations are situated at equal distance from each other. It follows from results of the Burgers vector determinations... 

Figures 3.89 and 3.90 show twist boundaries in SiAlON and in sapphire ceramics, respectively. In Fig. 3.89, both tilt and twist boundaries are indicated. Rows of parallel and more complex dislocations are observed. These dislocation structures are periodic. The Burgers vector determined for the dislocations are of type b = a/3 (110). The experimental results show that these twist boundaries are stable without an amorphous grain-boundary phase. It appears, according to the experimental results, that boundaries with low L misorientation possess relatively low energies and, therefore, are formed favorably during a sintering process.

Fig. 22. (a) Basis vectors in the (010) plane, (b) Burgers vector determination by a circuit around the tile representing the core of a metadislocation with six associated phason halfplanes. 

The Burgers vectors, glide plane and ine direction of the dislocations studied in this paper are given in table 1. Included in this table are also the results for the Peierls stresses as calculated here and, for comparison, those determined previously [6] with a different interatomic interaction model [16]. In the following we give for each of the three Burgers vectors under consideration a short description of the results. 

Figure 3.3 Determination of the Burgers vector of an edge dislocation (a) a circuit around an edge dislocation and (b) the corresponding circuit in a perfect crystal. The vector linking the finishing atom to the starting atom in (b) is the Burgers vector of the dislocation.

The Burgers vector of a screw dislocation can be determined in exactly the same way as an edge dislocation, following the FS/RH (perfect crystal) convention. A closed Burgers circuit is completed in a clockwise direction around the dislocation (Fig. 3.7a). An identical circuit in both direction and number of steps is completed in a perfect crystal (Fig. 3.7b). This will not close. The vector needed to close the circuit in the perfect crystal, running from the finish atom to the start atom, is the... 

Sketch an edge dislocation formed by the insertion of extra material parallel to a cube edge in fluorite, CaF2, and use the FS/RH convention to determine the Burgers vector. (The fluorite structure is given in Supplementary Material SI and drawn in Fig. 4.7a.)... 

Note that the sign of the final expression in Eq. 13.33 must be consistent with the convention for determining the Burgers vector (see the text following Eq. 11.1). 

Consider the reactions between parallel dislocations given below. In each case write the Burgers vector of the product dislocation and determine whether the reaction is energetically favorable. 

The Burgers vectors of the loops are easily determined using the g b = 0 and g b X u invisibility criteria (Section 5.6). We consider some examples in foils normal to an a-axis. First, most of the dislocations are out-of-contrast in DF images with g = (XX)3 at = 0, as shown in Figure 9.9(a), indicating that b = j. Second, dislocation loops with these Burgers... 

The dislocation microstructures that develop during creep with stresses in the range 15 < a < 110 MPa at temperatures from 1,400 to 1,600°C were studied in detail by Darot and Gueguen (1981) on the optical microscope scale using the dislocation decoration technique as modified by Jaoul et al. (1979). However, TEM was used to determine Burgers vectors by application of the g-b = 0 and g-bxu = 0 invisibility criteria (Section 5.6). 

If the flow law (strain-rate c as a function of stress a and temperature T) is known from rheological measurements, then the stress estimated from the microstructure can be used to constrain the (e, T)-regime. The strain-rate (or equivalent viscosity) can be estimated if the temperature is constrained by the mineral assemblages that are present. Conversely, the temperature can be estimated if it is assumed that e is in the range 10 -10 s . The (e, 7 )-regime may also be constrained by the Burgers vectors if the predominant slip system has been experimentally determined as a function of e and T and if these observations can be extrapolated to geological conditions. 

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