Effect of Ultrasonic Processing on Mechanical and Structural Properties of Ge:Na Plates of Ge:Na Plates

4.4.5.1. Changes in the Vickers Microhardness

Measurements of Vickers microhardness were carried out at a load of 25 g and a holding time under a load of 9 s. Indenter was installed in the central part of the selected crystallite area of at least 10 cm² in size, since, as is known [37], to increase the accuracy of measurements on polycrystalline materials, it is necessary to conduct measurements on the crystallite of the largest possible area and to install the indenter on as much distance as possible from the crystallite edges.

As shown by the measurements, the average Vickers microhardness in polycrystalline plates before and after their ultrasonic treatment was 690 kg/mm² and 720 kg/mm², respectively, i.e. the microhardness increased after this treatment by 4.35 %. We note that the maximum Vickers measured on the (111) plane of the Ge single crystal (which plane is most favorable for these measurements) is 746 kg/mm², i.e. only 3.5 % higher than that measured by us on a crystallite with a randomly chosen crystallographic orientation. This testifies to the fact that, as a result of ultrasonic treatment of polycrystalline plates, the degree of their "looseness" becomes insignificant.

4.4.5.2. Changes in the Density, Porosity and Etch Pits Density

The evaluation of the change in the plate density resulted from the ultrasonic processing was carried out on a plate in the form of an elongated rectangle with one pointed smaller

side. The rectangular part of the plate had a length of 160.00 mm and a width of 116.90 mm. Taking into account the triangular part of the plate, its total length was 196.70 mm. The thickness of the plate was 11.00 mm. Thus, the initial (i.e., before the ultrasonic processing) volume of the plate was 229.34 cm³.

It was found that after the ultrasonic processing at optimum values of the frequency and power of mechanical vibrations, and also with the optimal treatment time (which was chosen so that the release of gas bubbles from the plates ceased completely), the linear dimensions of the plate were reduced: the length and width of the rectangular part by 0.25 mm and 0.20 mm, respectively, and the total length (taking into account the triangular part) – by 0.30 mm. Thus, the volume of the plate after ultrasonic processing also decreased and became 228.60 cm³. The weight of the plate after its ultrasonic processing remained unchanged and amounted to 1210.00 g. Hence, we obtain that, as a result of ultrasonic processing, the volume of the plate decreased by ΔV = 0.74 cm³, and the density ρ, respectively, increased from the value of 5.276 g/cm³ to 5.293 g/cm³, i.e. by Δρ = 0.017 g/cm³. According to reference data, the density of Ge single crystals is 5.327 g/cm³ at 25 °C, i.е. only by 0.64 % exceeds the density of polycrystalline plates processed by ultrasound. It is easy to calculate that in the case of untreated Ge plates, this difference is greater by one and a half times.

The porosity of the untreated plates relative to the treated plates was evaluated by the formula

Р = (ρtr-ρuntr)/ρtr = ∆ρ/ρtr,

where ρuntr and ρtr are the density of initial (untreated) and ultrasound-treated plates, respectively. It turned out that P ≈ 0.32 %.

Let us estimate how this value agrees with the amount of hydrogen in the untreated plates, measured by the high-temperature extraction method (see Section 4.4.4.1). For such estimation, suppose that the pores in such plates are completely filled with hydrogen (which, of course, not necessarily implemented in practice).

The total volume of pores in the plate is 0.32 % of 229.34 cm³, i.e. about 0.73 cm³. Since the weight of 1 m³ of hydrogen is 90 g, this volume may be occupied by about 6.5ꞏ10^-5 g or 1.9ꞏ10¹⁹ molecules of hydrogen. Such an amount of hydrogen, located in a plate of 229.34 cm³ in volume, corresponds to the fact that the concentration of hydrogen atoms in the plate is 1.6ꞏ10¹⁷ at/cm³. Taking into account the accuracy of measurements of the plate density, evaluative character of calculations made, and also the fact that the complete filling of pores with hydrogen is unlikely, we can assume that this value does not conflict with the concentration of hydrogen in the ultrasound-treated plates 2.73ꞏ10¹⁶ cm^-3 measured by the high-temperature extraction method.

Note that, at first glance, it may seem that the reduction in porosity and the increase of microhardness resulted from ultrasonic treatment are small and cannot significantly affect the strength of the plates. However, studies of some other solids, even less brittle than Ge, had shown the importance of even small decreases in porosity [38]. In particular, it was

revealed that a decrease in the porosity by 3 % leads to an increase in the strength of some types of steel up to 20 %.

It can be assumed that in the raw material from which germanium crystals are grown, namely, in zone-refined germanium, which, in contrast to polycrystalline plates, consists of small grains, the mechanism of hydrogen storage is not the same as in the plates. Most likely, due to other conditions for the solidification of zone-refined germanium, hydrogen is located at numerous grain boundaries and, as indicated above, the ultrasonic treatment used could not release it from this position.

As was indicated above, we observed an intense release of bubbles from the plates during their ultrasonic treatment (Fig. 4.6). According to our estimations, the diameter of the bubbles ranged from 0.1 mm to 0.4 mm. Based on the above amount of hydrogen released from the plate, it is easy to estimate that the number of the released bubbles was on the order of several hundred thousand.

Note that the bubbles were released most intensively from the middle part of the plate along its direction of growth, from which it can be concluded that just this region of plate is most defective. This result agrees with our previous observations [39] that in the plates grown by the horizontal directional crystallization, the mechanical stresses are maximal in the middle region of the plates along the growth direction. Fig. 4.8 shows the distribution of the etch pits density over the surface of the optical germanium plate 330×150×20 mm in size measured before (a) and after (b) the ultrasonic processing of the plate. The dimensional diagrams were obtained by the automated method for determining the etch pits density [39] using a computerized calculations of the etch pits density in 384 points over the surface of the crystal plate. As seen, in both cases the etch pits density is maximal in the middle region of the plates along the growth direction. The fact that cracking of the as-grown plates during their machining occurs, if at all, just in half along the plate length is consistent with the fact that, as it was shown previously [40] in optical germanium crystals the dislocation density correlates with the value of thermoelastic stress. On the other hand, removing mechanical stress (in our case, by ultrasonic processing) results in the release of energy which leads to dislocation multiplication, provided that the value of this released energy exceeds the energy cost of making dislocations. Just for this reason the density of dislocations in the middle part of the plate increases after the ultrasonic processing (Fig. 4.8b) in comparison with the density of dislocations in as-grown plates (Fig. 4.8a).

In the Raman spectrum of germanium, the maximum of the TO phonon peak due to the optical vibrations of the Ge-Ge bonds is located at a frequency of approximately 300 cm^-1 [41]. As our experiments showed (Fig. 4.7b), as a result of ultrasonic processing of the optical germanium plate, this peak shifted from 301.9 cm^-1 (before processing) to 303.6 cm^-1 (after processing) (see curves 1 and 2, respectively). The half-width of the peak remained practically unchanged (6.6 cm^-1 and 7.0 cm^-1, respectively). Note that similar displacement was observed as a result of uniaxial [42] or hydrostatic [43] compression, which caused a decrease in the interatomic distances of the crystal lattice.

Fig. 4.8. The dimensional diagrams of distribution of etch pits density over the surface of the same optical germanium plate before (a) and after (b) its ultrasonic processing. The numbers along the horizontal axes indicate the geometric dimensions of plate in cm, the numbers along the vertical axis – etching pits density in cm^-2.

4.4.5.3. Changes in the Plate Structure Revealed from Raman Spectroscopy and X-ray Diffractometry Data

Note by the way, that, as it was shown theoretically [44] for the intermetallic alloys, the introduction of hydrogen atoms into the pores of the alloy with a hexagonal structure was accompanied by a significant (by 10-27 %) increase in the volume of the crystal lattice, although the lattice type did not change.

Fig. 4.9 presents X-ray diffraction patterns of the untreated plate (curve 1) and of the same plate after ultrasonic processing (curve 2) measured on the automated X-ray diffractometer HZG-4 with doublet Kα1 and Kα2 radiation of the Co-anode using a special preset holder of the sample allowing for an independent movement along the ω axis (coaxial to the 2θ axis of the goniometer) and φ axis (perpendicular to the surface of the specimen, defines the angle of rotation of the sample around its axis). In the experiment, the axis φ was installed perpendicular to the main axis of the goniometer (perpendicular to the ω and 2θ axes).

It was found that, as a result of ultrasonic processing, the lattice parameter of the sample is decreased from 5.667 Å to 5.649 Å.

Thus, the Raman spectroscopic and X-ray diffractometric data presented in this section for the untreated and ultrasound-treated plates, are in complete agreement with the observed decrease in the plate volume resulted from their ultrasonic treatment, set forth above in Section 4.4.5.2. The reason for this decrease may be a decrease in the amount (or complete elimination) of hydrogen-containing pores in the crystal lattice of germanium, as well as a decrease in the lattice volume. Both of these processes lead to hardening of Ge:Na plates.

The observed changes in the parameters of polycrystalline Ge:Na plates resulted from their ultrasonic processing are summarized in Table 4.5.

Fig. 4.9. X-ray diffraction pattern from the Ge:Na sample before (1) an after (2) ultrasonic processing.

Table 4.5. The changes in the parameters of polycrystalline Ge:Na plates resulted from their ultrasonic processing.

Parameter Before ultrasonic processing

After ultrasonic processing

Hydrogen content, сm^-3 1.9ꞏ10¹⁷ 2.7ꞏ10¹⁶

Vickers microhardness, кg/mm² 690 720

Density, g/сm³ 5.276 5.293

Lattice parameter, Å 5.667 5.649

4.4.6. Fracture Toughness and Possible Causes for Increasing the Plates Strength