Dislocation-Point Defects-Induced by X-Irradiation Interaction in Alkali Halide Crystals

Abstract

Strain-rate cycling tests under superposition of ultrasonic oscillation were carried out at 77–293 K for two kinds of samples: non-irradiated and X-ray-irradiated KBr single crystals. Point defects induced by X-ray irradiation have weak interaction with dislocation and act as obstacles to dislocation motion. Assuming that the defect is tetragonal, the interaction energy for the break-away of a dislocation from the defect has been obtained by fitting the Barnett model to experimental results. Then, the value of interaction energy was determined to be 0.81 eV for the crystal. This result is compared with it in other crystals (NaCl, NaBr, and KCl) by the X-irradiation.

1. Introduction

It is well known that alkali halide crystals are hardened by X-ray irradiation [1, 2, 3, 4]. The defect due to the radiation is electron-centre or hole-centre such as F-centre, V₂- or V₃-centre. Although the yield stress becomes large with the irradiation dose [5], the interaction between dislocation and the defect is not clearly established yet.

In this chapter, the dislocation-radiation defects interaction in KBr single crystals is described by analysing the data obtained by the combination method of strain-rate cycling tests and ultrasonic oscillation. Useful information on the interaction between a mobile dislocation and additive ions has been reported so far for alkali halide crystals during plastic deformation by the method [6, 7, 8], which can separate the effective stress due to the additions from that due to dislocation cuttings.

2. Experimental procedure

2.1 Preparation of samples

The samples were prepared by cleaving out of KBr single crystalline ingot, which was grown from the melt of superfine reagent powder by the Kyropoulos method in air, to the size of 5 × 5 × 15 mm³. The samples were annealed at 973 K for 20 h and were gradually cooled to room temperature at the rate of 40 K/h in order to reduce dislocation density as much as possible. The samples were exposed to X-ray (W-target, 30 kV, 20 mA) for 3 h on each of the pair wide surfaces at room temperature by Shimadzu XD-610. Namely, the total exposure time is 6 h.

2.2 Strain-rate cycling tests under superposition of ultrasonic oscillation

The experimental apparatus is schematically illustrated in Figure 1a, where the resonator composed of a vibrator and a horn with a resonant frequency of 20 kHz was attached to a testing machine (Shimadzu DSS-500). Figure 1b shows the main testing machine. The samples, which were fixed on a piezoelectric transducer, were compressed along <100> direction of the longest axis of a crystal and the ultrasonic oscillatory stress was intermittently superimposed by the resonator in the same direction as the compression. The amplitude of the oscillatory stress τ_v was monitored by the output voltage from the piezoelectric transducer. The strain of the specimen seems to be homogeneous, since the wavelength (152 mm [9]) for KBr is approximately 10 times as long as the length of the sample.

Figure 1.

Experimental apparatus: (a) schematic illustration of the apparatus, and (b) main testing machine.

The strain-rate cycling tests associated with ultrasonic oscillation are illustrated in Figure 2. Superposition of oscillatory stress τ_v causes a stress change (Δτ) during plastic deformation. When strain-rate cycling between the strain rates of ${\dot{\epsilon }}_1$ (1.1 × 10⁻⁵ s⁻¹) and ${\dot{\epsilon }}_2$ (5.5 × 10⁻⁵ s⁻¹) was conducted, keeping the stress amplitude constant at 77 K to room temperature, the stress increment due to the strain-rate cycling is Δτ′. The strain-rate sensitivity λ of flow stress was derived from the Δτ′ value (that is to say, λ = Δτ′/Δln$\dot{\epsilon }$ = Δτ′/ln(${\dot{\epsilon }}_2$/${\dot{\epsilon }}_1$)).

Figure 2.

Applied shear stress (τ_a) variation by the strain-rate cycling tests between the two strain rates, ${\dot{\epsilon }}_1$ (1.1 × 10⁻⁵ s⁻¹) and ${\dot{\epsilon }}_2$ (5.5 × 10⁻⁵ s⁻¹), off or on ultrasonic oscillatory shear stress (τ_v) due to the oscillation (20 kHz) during compression.

3. Results and discussion

3.1 X-ray-irradiated crystal

The sample was exposed to X-ray for 3 h on each of the pair wide surfaces at room temperature (i.e., total exposure time is 6 h) and was cleaved in four thin crystal plates (a)∼(d) at regular intervals (a thickness of about 1 mm) as illustrated in Figure 3. The concentration distribution of the F-centre (trapped electron) in the X-ray-irradiated crystal is shown for each plate in Figure 3. The abscissa “Distance from edge” of the figure represents the distance from the irradiated crystal surface of plate (a). The F-centre concentration, which was estimated from the Smakula formula [10], tends to decrease in the deep inside as against the surface of the sample. The average concentration of F-centres is 13 × 10¹⁶ cm⁻³ for the irradiated KBr crystal. However, F-centres or vacancies are so weak to interact with dislocation that they do not act as obstacles to dislocation motion, as described by Zakrevskii and Shul’diner [11]. This would be due to the isotropic defects around them in the crystal. Sirdeshmukh et al. also suggested that the radiation hardening is caused by the role of radiation-induced defects other than F-centres [12].

Figure 3.

Concentration distribution of F-centres in X-ray-irradiated KBr single crystal.

Figure 4 shows the absorption spectrum of the X-ray-irradiated KBr crystal. The colour centre has been reported for alkali halide [13, 14]. As can be seen in Figure 4, the peak of F-band (2.0 eV) is seen, and the peak of 4.7 eV is attributed to V₂-centre in the spectrum of X-irradiated KBr crystal. Since a hole-centre such as V₂-centre is considered to have not isotropic but tetragonal distortions, the irradiation-induced defects (V₂-centres) act as stronger obstacles to dislocation motion in comparison with F-centres or vacancies in the sample (the X-irradiated KBr crystal).

Figure 4.

Absorption spectrum of X-ray-irradiated KBr single crystal.

The radiation effect on stress–strain curve is shown in Figure 5 for KBr crystal at room temperature. The curves (a) and (b) in the figure represent nonirradiated and X-ray-irradiated samples, respectively. When the crystal is exposed to the X-irradiation, flow stress increases at a given strain and the radiation hardens the crystal. This is because X-ray-induced point defects obstruct dislocation motion.

Figure 5.

Stress versus strain curve for (a) non-irradiated and (b) X-ray-irradiated KBr single crystals at room temperature.

3.2 Effective stress (τ_p) due to X-ray-induced defects

The variations of Δτ and λ with shear strain ε are shown in Figure 6a and b for the non-irradiated KBr single crystal at 193 K. The oscillatory stress τ_v becomes large with output voltage, which is denoted in the legend of these figures, from the piezoelectric transducer. Δτ increases with the amplitude of τ_v and is almost constant independently of strain. λ tends to decrease with the stress amplitude, and the variation of it with τ_v is small at high amplitude. λ also increases with strain. This is due to the increase of the forest dislocation density with strain, since λ is proportional to the inverse of average length of dislocation segments.

Figure 6.

Strain versus (a) stress decrement (Δτ) due to superposition of oscillation and (b) strain-rate sensitivity (λ) of flow stress given by strain-rate cycling at 193 K and various stress amplitude, which were monitored by the output voltage from the piezoelectric transducer, for non-irradiated KBr single crystal.

The values of Δτ and λ at shear strains of 8, 12, 16, and 20% in Figure 6a and b are plotted in Figure 7 as the relative curve of λ versus Δτ at a given strain. Only one bending point is on each curve.

Figure 7.

Strain-rate sensitivity (λ) versus stress decrement (Δτ) at various strains for non-irradiated KBr single crystal at 193 K. the plotted points are obtained from Figure 6a and b.

The relation between λ and Δτ obtained by the above-mentioned method is shown in Figure 8a for the X-irradiated KBr single crystal at 183 K. Figure 8b corresponds to it for the irradiated KBr crystal at 203 K. The λ varies with Δτ like stair shape: the first plateau place ranges below the first bending point within low Δτ, and the second one extends from the second bending point within high Δτ. The λ decreases with Δτ between the two bending points. The value of Δτ at first bending point is referred to as τ_p in Figure 8b. λ_p denoted in the figure is introduced later. τ_p has been considered the effective stress due to the weak obstacles such as dopants when a dislocation begins to break-away from the dopants which lie on the dislocation with the help of thermal activation during plastic deformation of alkali halide doped with monovalent or divalent ions [6, 7, 8], because τ_p depends on temperature and on type and density of the obstacle [15, 16]. Although τ_p is not observed on the relative curve of λ versus Δτ for the nonirradiated crystal at 193 K in Figure 7, τ_p becomes to appear on the relative curve at nearly 193 K by irradiating the crystals with the X-ray, as shown in Figure 8(a) and (b). Therefore, the weak obstacles are considered the X-ray-induced defects here. Namely, the appearance of τ_p in this chapter represents the effective stress due to the defects such as V₂-centres referred in the previous section (i.e., Section 3.1).

Figure 8.

Strain-rate sensitivity (λ) versus stress decrement (Δτ) at (a) 183 K and (b) 203 K for X-ray- irradiated KBr single crystals.

3.3 Critical temperature (T_c) and Gibbs-free energy (G₀)

Figure 9 shows the dependence of τ_p on temperature for the sample (the X-irradiated KBr crystal). τ_p tends to decrease with increasing temperature and appears to be zero at the critical temperature T_c above 500 K. Figure 10 shows the relation between τ_p and activation volume V, which was obtained from kT/λ_p, for the thermally activated dislocation motion in the sample. k is the Boltzmann constant. λ_p is the difference between λ values at the first and second plateau places on the relative curve of λ versus Δτ (see Figure 8b) and has been regarded as the strain-rate sensitivity due to point defects [18] as expressed by the following Eq. (1).

Figure 9.

Dependence of τ_p on temperature for X-ray-irradiated KBr single crystals. The solid curve is given by numerical calculation (reproduced from Ref. [17] with permission from the publisher).

Figure 10.

Relation between τ_p and activation volume (V) for X-ray-irradiated KBr single crystals. The solid curve is given by numerical calculation (reproduced from Ref. [17] with permission from the publisher).

$${\lambda }_p=\frac{\mathit{kT}}{b{l}_{p}d}$$E1

where b is the magnitude of Burgers vector, l_p is the average spacing of point defects along dislocation, and d is the activation distance. The force-distance curve between dislocation and tetragonal defect was reported by Barnett and Nix [19]. Figures 9 and 10 reflect the interaction between dislocation and X-ray- induced defects. The solid curves in these figures were obtained on the assumption that the force-distance profile derived by Barnett and Nix (Barnett model) is appropriate for the interaction between dislocation and the radiation-induced defect in the X-irradiated KBr crystal. Each curve, which was given by numerical calculation with the parameters (τ_p0, T_c, and G₀) listed in Table 1, agrees with the data (solid circles in these figures) analysed in terms of λ versus Δτ for the samples. The critical temperature T_c at which τ_p is zero is about 660 K, and the τ_p0 value of τ_p at absolute zero is 0.67 MPa. G₀ (0.81 eV for the sample) is the Gibbs free energy for breaking away from the radiation-induced defect by dislocation at absolute zero.

Crystal	τp0 (MPa)	Tc (K)	G0 (eV)
X-Irr. NaCl	1.94	346	0.39 ± 0.09
X-Irr. NaBr	1.99	369	0.76
X-Irr. KCl	1.00	528	0.87 ± 0.19
X-Irr. KBr	0.67	660	0.81

Table 1.

Values of τ_p0, T_c, and G₀ for X-ray-irradiated single crystals [17, 20].

The values of τ_p0, T_c, and G₀ are also listed for the same X-ray-irradiated NaCl, NaBr, and KCl single crystals in Table 1. “X-ray-irradiated” is abbreviated to “X-Irr.” in the table. These values are derived on the basis of λ versus Δτ obtained by the above-mentioned method (i.e., the strain-rate cycling tests combined with ultrasonic oscillation). As for X-Irr. NaBr, the peak of V₂-centre is not clear in the absorption spectrum within the measurement [17]. In the spectrum, V₂-centre for X-Irr. NaCl and V₃-centre for X-Irr. KCl are seen as reported in the paper [20]. As given in Table 1, G₀ values are 0.39 ± 0.09, 0.76, and 0.87 ± 0.19 eV for X-Irr. NaCl, X-Irr. NaBr, and X-Irr. KCl, respectively. This suggests that the difference between longitudinal and transverse strains of distortion around the irradiation-induced defect, i.e. the tetragonality of defect, becomes large in the order of NaCl, NaBr, KBr, and KCl by the X-ray irradiation at room temperature.

4. Conclusion

The strain-rate cycling tests combined with ultrasonic oscillation were conducted for X-ray-irradiated KBr single crystals. Analysing the relation between λ and Δτ for two kinds of samples (non-irradiated and X-irradiated KBr crystals), the bending point τ_p within low Δτ is referred to the X-ray-induced defects in the sample. In addition, τ_p vs. T and τ_p vs. V curves reflect the interaction between dislocation and X-irradiated defects and further give the values of τ_p0, T_c, and G₀ for the sample. With regard to the same X-ray-irradiated NaCl, NaBr, and KCl crystals, the values of them have been obtained on the basis of τ_p vs. T or V curves by the mentioned method. G₀ values are 0.39 ± 0.09, 0.76, 0.87 ± 0.19, and 0.81 eV for X-Irr. NaCl, X-Irr. NaBr, X-Irr. KCl, and X-Irr. KBr, respectively. This suggests that the tetragonality around defect induced by the X-irradiation becomes large in the order of NaCl, NaBr, KBr, and KCl.

Acknowledgments

Dr. T. Ohgaku, as well as S. Matsumoto are acknowledged for his collaboration in the analysis on λ and Δτ data, as well as for his experimental assistance.

Conflict of interest

The author declares no conflict of interest.