Effect of dislocation densities

Blum A. E., Yund R. A., and Lasaga A. C. (1990) The effect of dislocation density on the dissolution rate of quartz. Geochim. Cosmochim. Acta 54, 283 —297. 

Table II. Effect of Dislocation Densities on Reaction Rates...

Blank J (1993) An experimental study of the behavior of carbon dioxide in rhyolitic melt. PhD Dissertation, California Institute of Technology, Pasadena Blum AE, Yund RA, Lasaga AC (1990) The effect of dislocation density on the dissolution of albite. Geochim Cosmochirm Acta 54 283-297... 

The effect of dislocations has also been studied by Bloembergen and Rowland 106) in cold-worked copper (Cu and Cu resonances), and also the effect of alloying in Al-Zn alloys (Al resonance) by Rowland 107). Otsuka and Kawamura 108) have studied the NMR of 1" in KI, Na in NaCl-NaBr mixed crystals, and Br in KBr-NaBr mixed crystals and have estimated dislocation densities in these materials. 

The effect of dislocation line oscillations on the probability of its separation from the defect was accounted for by Natsik [211, 212], who has considered the following model A dislocation line moves in the slipping plane under the action of the one-axis stress. The dislocation is characterized by the linear mass density p and tension coefficient C. Pinning in A and B sites is considered to be rigid, and the dislocation detachment from the defect located in the zero point is considered (Figure 21). At a li, I2 < d [d is... 

This relation, established in 1963 by Krivoglaz [KRI 63, KRI 69], is the fundamental equation for describing the expression of the total intensity racted by a crystal containing a concentration c of dislocations. As you can see, this intensity corresponds to the one diffracted by a ciystal free of any dislocations multiplied by a factor (e ) smaller than 1 and that decreases when T increases, and hence when the dislocation density increases (see equation [5.29]). This generic form of the effect of dislocations on the diffracted intensity is similar to the one describing the effect of temperature, which actually corresponds to variations in atomic mobility and therefore to a certain form of atom displacements with respect to their reference position. 

Using Eq. 11, we can compare the effect of dissolution at dislocations to the overall dissolution rate. For instance, one predicts that the critical dislocation density pc at which the dissolution rate due to dislocations and to the dislocation-free surface become equal is pc 2.109, 3.109, and 10locm-2 for quartz, calcite, and rutile, respectively. These values compare well with experimental data and calculations of Blum and Lasage (1987) for quartz. Obviously, the effect of dislocation on the overall rate of dissolution become significant only lor very high dislocation densities. 

Possible explanations for the small effect of dislocations on dissolution rates, even at very high dislocation densities, are that (1) in contrast to intuitive... 

Calculations of this type are carried out for fee, bcc, rock salt, and hep crystal structures and applied to precursor decay in single-crystal copper, tungsten, NaCl, and LiF [17]. The calculations show that the initial mobile dislocation densities necessary to obtain the measured rapid precursor decay in all cases are two or three orders of magnitude greater than initially present in the crystals. Herrmann et al. [18] show how dislocation multiplication combined with nonlinear elastic response can give some explanation for this effect. 

The shock-induced micromechanical response of <100>-loaded single crystal copper is investigated [18] for values of (WohL) from 0 to 10. The latter value results in W 10 Wg at y = 0.01. No distinction is made between total and mobile dislocation densities. These calculations show that rapid dislocation multiplication behind the elastic shock front results in a decrease in longitudinal stress, which is communicated to the shock front by nonlinear elastic effects [pc,/po > V, (7.20)]. While this is an important result, later recovery experiments by Vorthman and Duvall [19] show that shock compression does not result in a significant increase in residual dislocation density in LiF. Hence, the micromechanical interpretation of precursor decay provided by Herrmann et al. [18] remains unresolved with existing recovery experiments. 

Champion and Rohde [42] investigate the effects of shock-wave amplitude and duration on the Rockwell C hardness [41] and microstructure of Hadfield steel over the pressure range of 0.4-48 GPa (pulse duration of 0.065 s, 0.230 ls, and 2.2 ps). The results are shown in Fig. 7.8. In addition to the very pronounced effeet of pulse duration on hardness shown in Fig. 7.8, postshoek electron microscope observations indicate that it is the final dislocation density and not the specific microstructure that is important in determining the hardness. 

In a detailed study the dissolution kinetics of shock-modified rutile in hydrofluoric acid were carefully studied by Casey and co-workers [88C01], Based on the defect studies of the previous sections in which quantitative measures of point and line defects were obtained, dissolution rates were measured on the as-shocked as well as on shocked and subsequently annealed powders. At each of the annealing temperatures of 200, 245, 330, 475, 675, 850, and 1000 °C, the defects were characterized. It was observed that the dissolution rates varied by only a factor of 2 in the most extreme case. Such a small effect was surprising given the very large dislocation densities in the samples. It was concluded that the dissolution rates were not controlled by the dislocations as had been previously proposed. 

The above data relate to very pure iron samples with low dislocation densities. In real steels the trapping effects result in much lower apparent diffusivities, which are dependent on the metallurgical state of the steel, as well as its chemical composition. Typical values for the apparent diffusion coefficient of hydrogen in high-strength alloy steel at room temperature are in the region of 10" mVs. 

Each new layer is populated by adding the particles in rows that are uniformly spaced along the y axis that is, by changing the density of misfit dislocations. The grouping of atoms into 2D clusters is an important effect that is excluded by this approach. However, the effects of this type of clustering can be inferred from these results. Since the chemical potential of the film material is fx=dE/dN, the tangent to this curve is ... 

The effect of on the dislocation density is shown in Fig. 3.46. It can be concluded that there is an optimum P, or Tas (TLp.) ( = 617 °C) for growing low dislocation density (less than 500 cm crystals (at the time this work was carried out, the dislocation density of commercial GaAs with the highest quality was more than 2 x lO cm" ). Above and below this... 

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