**2. Combination method of strain-rate cycling tests and the Blaha effect measurement**

Specimens used in this work were seven kinds of single crystals: NaCl doped with Li+ , K+ , Rb+ , Cs+ , F<sup>−</sup>, Br<sup>−</sup> or I<sup>−</sup> ions separately. Each concentration of the dopants was 0.5 mol% in the melt. The specimens were prepared by cleaving the single crystalline ingots, which were grown by the Kyropoulos method [55] in air, to the size of 5 × 5 × 15 mm3 . Furthermore, they were kept immediately below the melting point for 24 h and were gradually cooled to room temperature at a rate of 40 K h<sup>−</sup><sup>1</sup> . This heat treatment was carried out for the purpose of reducing dislocation density as much as possible.

The schematic illustration of apparatus is shown in **Figure 1**. A resonator composed of a vibrator and a horn was attached to the testing machine, INSTRON Type 4465. The specimens were lightly fixed on a piezoelectric transducer and then cooled down to a test temperature. Each specimen was held at the test temperature for 30 min prior to the following test. The specimens were deformed by compression along the <100> axis at 77 K up to the room temperature, and the ultrasonic oscillatory stress was intermittently superimposed for 1 or 2 min by the resonator in the same direction as the compression. The temperature measurements of specimens were conducted by heater controlled using thermocouples of Ni-55%Cu vs. Cu. As for the tests at 77 K, the specimen was immersed in the liquid nitrogen. The stability of temperature during the test was kept within 2 K. The resonant frequency was 20 kHz from a multifunction synthesizer and the amplitude of the oscillatory

**Figure 1.**

*Schematic block diagram of apparatus system.*

*Electron Crystallography*

tion density below 104

cm<sup>−</sup><sup>2</sup>

number of investigations have been conducted by the separation of the flow stress into effective and internal stresses on the basis of the temperature dependence of yield stress, the strain rate dependence of flow stress, and the stress relaxation. Yield stress depends on dislocation velocity, dislocation density, and multiplication of dislocations [30]. On the other hand, the effect of heat treatment on the microhardness is almost insensitive to the change of atomic order of point defects in a specimen. As for direct observations, electron microscopy provides the information on dislocation motion for a thin specimen but not for bulk, and also light scattering method is useful only for a transparent specimen. X-ray topography is the lack of resolution in the photograph, so that the specimen is limited to the low disloca-

of the dislocation which breaks away from the weak obstacles between two forest dislocations by vibration [31]. Stress relaxation tests are generally assumed that internal structure of crystals does not change, i.e., dislocation density and internal stress are constant. Above-mentioned methods cannot provide the information on

In this chapter, the study on interaction between a dislocation and dopant ions is made by the strain-rate cycling tests during the Blaha effect measurement. The original method (strain-rate cycling tests associated with the Blaha effect measurement) is different from above-mentioned ones and would be possible to clear up it. The Blaha effect is the phenomenon that static flow stress decreases when an ultrasonic oscillatory stress is superimposed during plastic deformation [32]. Ohgaku and Takeuchi [33, 34] reported that the strain-rate cycling under the application of oscillation can separate the contributions arising from the interaction between a dislocation and dopant ions and from the dislocations themselves during plastic deformation at room temperature. Using ionic single crystals of KCl doped with Br<sup>−</sup> (0.5, 1.0, and 2.0 mol%) or I<sup>−</sup> (0.2, 0.5, and 1.0 mol%) [35] and of NaCl doped with Br<sup>−</sup> (0.1, 0.5, and 1.0 mol%) [36], they discussed temperature dependence of the effective stress due to monovalent dopants (i.e., Br<sup>−</sup> or I<sup>−</sup>) and found that the measurement of strain-rate sensitivity under the ultrasonic oscillatory stress provides useful information on a mobile dislocation-the dopant ions interaction [35, 36]. The information on the dislocation motion breaking-away from dopant ions [37–40] and also X-irradiation induced defects [41] with the ultrasonic oscillatory stress has been successively provided by the original method, which seemed to separate the contributions arising from the dislocation-the point defects interaction and from

dislocation-obstacles interaction in bulk during plastic deformation.

dislocations themselves during plastic deformation of crystals.

The Blaha effect was found by Blaha and Langenecker when the ultrasonic oscillatory stress of 800 kHz was superimposed during plastic deformation of Zn single crystals. The same phenomenon as Zn crystals has been also observed in many metals (e.g., [42–44]). Since this phenomenon has a significance as an industrial purpose, it has been widely made to apply to the plastic working technique: wire drawing, deep drawing, rolling, and another metal forming

The strain-rate cycling tests associated with ultrasonic oscillation were carried out here for NaCl single crystals doped with various monovalent ions separately. The monovalent ion is considered to have isotropic strain in the alkali halide crystal because its size is different from the substituted ion of the host crystal. Dopant ions are expected to cause the hardening due to the dislocation motion hindered by the defects around them at low temperature. Its force-distance profile between a dislocation and an atomic defect is expressed by Cottrell and Bilby [54]. This chapter refers to the energy supplied by the thermal fluctuations, when the dopant ions are overcome by a dislocation with the help of thermal activation during plastic deformation of crystals. This is estimated from the dependence of the effective stress

. Internal friction measurements concern the motion

**90**

techniques (e.g., [45–53]).

#### **Figure 2.**

*Explanatory diagram of a change in applied shear stress,* τa*, for the strain-rate cycling test between the strain rates,* ε̇ 1 *(2.2 × 10<sup>−</sup><sup>5</sup> s<sup>−</sup><sup>1</sup> ) and* ε̇ 2 *(1.1 × 10<sup>−</sup><sup>4</sup> s<sup>−</sup><sup>1</sup> ), under superposition of ultrasonic oscillatory shear stress,* τ*v.*

stress was monitored by the output voltage from the piezoelectric transducer set between a specimen and the support rod, which was observed by an a.c. voltmeter or an oscilloscope. Since the wavelength, which is 226 mm on the basis of calculating from the data of ref. [56], is 15 times as long as the length of specimen, the strain of specimen is supposed to be homogeneous.

Strain-rate cycling tests made between the crosshead speeds of 10 and 50 μm min<sup>−</sup><sup>1</sup> were performed within the temperatures. The strain-rate cycling test associated with the ultrasonic oscillation is illustrated in **Figure 2**. Superposition of oscillatory stress (*τ*v) causes a stress drop (Δ*τ*) during plastic deformation. When the strain-rate cycling between strain-rates of ε̇ 1 (2.2 × 10<sup>−</sup><sup>5</sup> s<sup>−</sup><sup>1</sup> ) and ε̇ 2 (1.1 × 10<sup>−</sup><sup>4</sup> s<sup>−</sup><sup>1</sup> ) was carried out keeping the stress amplitude of *τ*v constant, the variation of stress due to the strain-rate cycling is Δ*τ*'. The strain-rate sensitivity (Δ*τ*'/Δlnε) of the flow stress, which is given by ̇ Δ*τ*'/1.609, was used as a measurement of the strain-rate sensitivity (*λ* = Δ*τ*'/Δlnε). Slip system for rock-salt structure ̇ such as NaCl crystal is {110} <11\_ 0> so that shear stress (*τ*) and shear strain (*ε*) calculated for the slip system were used in this study.
