Precursor decay

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. 

Kumar and Clifton [31] have shock loaded <100)-oriented LiF single crystals of high purity. The peak longitudinal stress is approximately 0.3 GPa. Estimates of dislocation velocity are in agreement with those of Flinn et al. [30] when extrapolated to the appropriate shear stress. From measurement of precursor decay, inferred dislocation densities are found to be two to three times larger than the dislocation densities in the recovered samples. 

To answer questions regarding dislocation multiplication in Mg-doped LiF single crystals, Vorthman and Duvall [19] describe soft-recovery experiments on <100)-oriented crystals shock loaded above the critical shear stress necessary for rapid precursor decay. Postshock analysis of the samples indicate that the dislocation density in recovered samples is not significantly greater than the preshock value. The predicted dislocation density (using precursor-decay analysis) is not observed. It is found, however, that the critical shear stress, above which the precursor amplitude decays rapidly, corresponds to the shear stress required to disturb grown-in dislocations which make up subgrain boundaries. 

Introduction of the surface-nucleation mechanism in numerical computation of elastic-plastic wave evolution leads to enhanced precursor attenuation in thin specimens, but not in thicker ones. Inclusion of dislocation nucleation at subgrain boundaries indicates that a relatively low concentration of subgrain boundaries ( 2/mm) and nucleation density (10"-10 m ) is sufficient to obtain predicted precursor decay rates which are comparable to those obtained from the experiments. These experiments are only slightly above the threshold necessary to produce enhanced elastic-precursor decay. 

These techniques have very important applications to some of the micro-structural effects discussed previously in this chapter. For example, time-resolved measurements of the actual lattice strain at the impact surface will give direct information on rate of departure from ideal elastic impact conditions. Recall that the stress tensor depends on the elastic (lattice) strains (7.4). Measurements of the type described above give stress relaxation directly, without all of the interpretational assumptions required of elastic-precursor-decay studies. 

G. Meir and R.J. Clifton, Effects of Dislocation Generation at Surfaces and Subgrain Boundaries in Precursor Decay in High-Purity LiF, J. Appl. Phys. 59, 124-148 (1986). 

J.N. Johnson, O.E. Jones, and T.E. Michaels, Dislocation Dynamics and Single-Crystal Constitutive Relations Shock-Wave Propagation and Precursor Decay, J. Appl. Phys. 41, 2330-2339 (1970). 

J.R. Asay and Y.M. Gupta, Effect of Impurity Clustering on Elastic Precursor Decay in LiF, J. Appl. Phys. 43, 2220-2223 (1972). 

The thorough and persistent work on precursor decay (the dependence of Hugoniot elastic limit on propagation distance) of Duvall s Washington State University group was successful in demonstrating that precursor attenuation was due to both stress relaxation and hydrodynamic attenuation. Typical data on crystalline LiF is shown in Fig. 2.7. Observed plastic strain... 

Fig. 2.7. Elastic precursor decay in which elastic waves are observed to decrease in amplitude with propagation distance is a typical behavior. The data of this figure describe the behavior of crystalline LiF samples of different yield strengths (after Asay et al. [72A02]).

Fig. 3.9. Comparison of exact concentration histories for species A, oc(t), with pseudo-stationary-state form (broken curves) showing the influence of the precursor decay rate constant c when the uncatalysed reaction rate is relatively large, k = i (a) s= 10 3 (b) = 10 2 (c) e= 10 1 ...

As with previous assessments (e.g. Carter, 2000), the quantity D(Oj-NO) was used as the main criterion of model performance. This quantity is defined as D(03-NO)t = [Oajt -[NO]t - ([Osjo - PMO]o), where [03]o [NO]o, and [Osh, [NO]t are the concentrations of O3 and NO at the beginning of the run, and at time t , respectively. As described in detail previously (e.g., Carter and Lurmann, 1991, Carter et al, 1995a, Carter, 2000), D(Os-NO) is an indicator of the ability of the mechanism to simulate the chemical processes fliat cause O3 formation, giving a useful measure, even when O3 is suppressed by the presence of excess NO. In addition, use of this measure allows a direct comparison wifli die SAPRC-99 published results. The precursor decay rate and formation of die carbonyl products and PAN were also used as criteria of model praformance. 

The formation and evolution of multiple waves becomes more complicated when chemical reactions or phase transitions occur. Volume decreasing phase transformations cause the pressure at point B in Figure 2 and Figure 7 to decrease with time. This common phenomenon is known as elastic precursor decay in elastic-plastic wave system. [9] The timescale for this pressure decay depends primarily on the timescale for the chemical reaction or phase transition that gives rise to the 2" wave. 

The last step in the equation follows from the fact that each precursor decay yields one neutron, so that... 

Delayed neutron precursors decay by beta decay. Which ONE reaction below is an example of beta decay ... 

The decay constant, X, is the average precursor decay rate. The inverse of the decay constant, = l/X, is the mean precursor generation time, Individual precursor generation times are weighted by the appropriate values of summed and divided by the total delayed neutron fraction to obtain t. 

The values in parentheses are cumulative yields in atoms per 100 fissions. The quantity of I present in a fission product mixture will increase slowly with time after irradiation has ceased as the I precursors decay. The peak activity is not reached for several months. 

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