Calculation of the cyclic hardening curves of fatigued FCC monocrystals using a two-phase model

The cyclic hardening curve of fatigued fcc monocrystals shows a maximum of the stress amplitude if the plastic resolved shear strain amplitude γ_ap exceeds the threshold value γ_M for the formation of persistent slip bands (PSBs). Using a simple two-phase model the typical shape of the cyclic hardening curve will be calculated for lower γ_ap values. The calculation takes into account the fact that the PSB formation starts already at a „nucleation stress”︁ amplitude τ_n below the maximum stress amplitude τ_am. Qualitatively the maximum of the cyclic hardening curve follows from the superposition of cyclic hardening of the matrix volume and of volume growth of the „soft”︁ PSB phase between the nucleation cycle number N_n and the saturation cycle number N_s.     

Effect of the defect structure character in calcite single crystals on X-ray diffraction

The paper presents experimental results for the dependence of the integral intensity of anomalous transmission T_i and Laue reflection R_i of X-rays on the structural quality of calcite single crystals as obtained by a two-crystal spectrometer. The relation between X-ray dynamic and kinetic scattering as a function of the sample thickness, densities of perfect dislocations in perfect CaCO₃ crystals and of atom-vacancy complexes in calcite crystals with „background”︁ has been found. Distortions due to perfect grown-in dislocations in calcite are shown to exceed those produced in crystals with „background”︁. The latter appear to be more X-ray transparent. A comparison with results of twin layer thickening experiments on CaCO₃ crystals of different qualities again points to the different nature of these distortions. In CaCO₃ crystals with the dislocation density of up to 2 × × 10³ cm⁻², the X-ray scattering, in our experiments, was consistent with the dynamic diffraction theory, while at higher dislocation densities, the X-ray scattering markedly differs from it.     

Modification of the smectic B phase by the aid of dielectric relaxation

The analysis of the dielectric relaxation data in the liquid crystalline S_B phase allow to classify the substances into two groups: S_B phases which are similar to the low or high temperature modifications. The experimental results are correlated to the recently discussed „heaxtic”︁ and „solid like”︁ S_B modifications.     

Temperature and Strain Rate Effects on Work-Hardening of KCl Single Crystals

The influence of temperature and strain rate on work hardening of a KCl crystal has been investigated. Using the experimental data on flow stress relaxation, the activation “volume” for dislocation motion and internal counteracting stresses have been calculated in the temperature range of 300 to 40 K. Estimation has been carried out for the variation of a number of mobile dislocations ϱ₂/ϱ₁, when the strain rate is changed by a factor of four.     

Mesoscopic and microscopic aspects of the PSB formation mechanism in fatigued FCC monocrystals

Persistent zones of plastic strain localization (PSBs) can be observed in fatigued fee monocrystals above the “nucleation cycle number” N_n and the “nucleation stress” amplitude τ_n, respectively. They follow after temporary strain localizations existing at N < N_n and being discernible by oscillations of the relative shape of the hysteresis loops (V_H) or by strain bursts. Using a simple rheological model the frequency of internal stresses of mesoscopic wave length (“mesoscopic stresses”) was determined for Ni monocrystals fatigued at four different plastic strain amplitudes up to N_n. A “mesoscopic threshold stress” τ* has been found to be exceeded within the whole volume of the dislocation-dense regions (DRs) at N ≧ N_n. By comparison of τ* with the stress for the operation of Frank-Read sources of the segment lengths l₀ at the border of the DRs, it might be assumed that above N_n and τ_n respectively a mechanism of dislocation sources acts, compensating the high annihilation rate of movable dislocations in the zones of strain localization. In so doing the formation of persistent zones of strain localization becomes possible, in which the “ladder-like” dislocation structure of the final PSBs develops successively.     

X-Ray topographic characterization of α-Fe2O3 single crystals obtained by chemical transport with TeCl4

The method of Lang is used to study the defect structure of „as-grown”︁ hematite crystals obtained by chemical transport with TeCl₄. The presence of twin boundaries, dislocations and crystallites built in the platelet matrices is established. Considerable differences in density and distribution of the crystal disturbances are observed with samples grown under the same experimental conditions. In some cases the real structure is found to be nearly perfect.     

Defect structure in nickel single crystals in dependence on the cyclic deformation prehistory

The development of the dislocation structure in nickel single crystals push-pull fatigued at room temperature is investigated for different deformation types using electrical resistivity measurements and results of TEM observations. The dislocation density in the bundles of the matrix is higher after changing the strain amplitude from region A to region B (CD_AB-type) of the cyclic stress-strain curve (N_dB ≈︁ 1.6 ≈︁ 10¹⁵ m⁻²) than after virginal deformation in region B (VD_B-type) especially at higher strain amplitudes (N_dB ≈︁ 0.75 ≈︁ 10¹⁵ m⁻²). Increasing the strain amplitude within region B (CD_BB-type) does not change N_dB. The farther development of the matrix structure after reaching the v_H-minimum during the VD_B-type of deformation suggests the action of the „formation and dissolution”︁ – mechanism, whereas the CD_BB-type causes the „cord”︁-mechanism of the PSB nucleation.     

Special features of optical strength change in melt-grown NaCl crystals

The variation of the CO₂-laser pulse induced breakdown threshold has been studied experimentally in melt-grown NaCl crystals. An increase of the optical strength (up to two order of magnitude) is observed from the „top”︁ towards „bottom”︁ of the large diameter crystal boules, i.e. in the direction in which the impurities are driven away. The dependence of the threshold with the Ca²⁺ concentration demonstrates a complicated character of the effect of the impurity content on the optical strength of sodium chloride.     

A method for the determination of the cyclic stress-strain curve of presistent slip bands in fatigued single crystals

Single crystals of pure nickel oriented for single slip were fatigued at constant total strain amplitude (ε_at) at room temperature. The dependence of the saturation resolved shear stress amplitudes (τ_as) on the saturation plastic resolved shear strain amplitudes (γ_aps) (cyclic stress-strain curve — CSSC) was determined. In the plateau range of the CSSC the volume fraction f of persistent slip bands (PSBs) was found to be linearly related to γ_aps. The reduction of the total strain amplitude after saturation in the plateau range of the CSSC leads to the so-called secondary CSSC with a slope n > 0 in the log-log plot. From the secondary CSSC the ”︁true”︁ cyclic stress-strain curve of the PSB-volume (PSB-CSSC) can be determined. The method is based on the two assumptions that firstly the PSB-groups (or ”︁macrobands”︁) penetrate the whole cross-section of the specimen and secondly the volume fraction of PSBs in the secondary range of the CSSC remains constant.     

On the recrystallization of metals in the emission electron microscope

By the emission electron microscope a high-contrast picture of grain structure is obtained with thermal or photoelectric release of electrons. The „memory effect”︁ (MORLIN , TREMMEL ) marks the individual steps of the grain boundary movement through volume expansion or thermal etching when releasing electrons by electrons or ions. The existence of an oxide layer on the surface of e.g. molybdenum and tungsten is starting the recrystallization and influencing the recrystallization temperature. Oxide layers are formed in selected areas corresponding to the distribution of surface seeds and the oxygen bombardment. Carbon atoms accumulate preferably at the grain boundaries as carbides, so decorating the crystallites in forming mixed crystals. – It may be assumed that the carbon solved in tungsten and molybdenum fixes the dislocations at the grain boundaries. In contradiction to all theories of secondary recrystallization „ring crystals”︁ are formed.     

Effect of structural relaxation on helium diffusion and solubility in vitreous B2O3

Helium permeation, diffusion, and solubility in vitreous B₂O₃ were measured as a function of thermal history and as a function of time at constant temperature. Volume relaxation measurements were also made on similar specimens. The correspondence between the effective relaxation times for gas mobility and molar volume suggests that the changes observed in both properties results from the same changes in the glass structure. This relaxation mechanism is described by the expression τ′ = 10^?4 exp(-18 000/RT), where τ′ is in seconds and the activation energy is in cal/mole. It is concluded that helium mobility is a function of the molar volume of the glass.     

Zur thermisch aktivierten Basisgleitung von Antimoneinkristallen

It is found that the basal slip in antimony single crystals is a thermally activated process. The activation volume, the thermal component of applied stress, and the enthalpy of activation ΔH₀ of the dislocation movement were determined from differential constant strain-rate tests, stress relaxation experiments, and differential temperature tests. It may be concluded that a diffusion controlled mechanism like the nonconservative movement of jogs is rate controlling.     

Über P.B.C.-Vektoren und ihre Bedeutung für das Kristallwachstum,speziell beim Silicium

It is shown, how to obtain some general points of view for crystal growth by the P.B.C.-method. Thereby the conception „Richtkraft”︁ is proposed allowing to compare different crystalline systems, especially concerning the chance of growing crystals low in dislocation density.     

Effect of Stressed State Type on Work Hardening and Evolution of Dislocation Structure in Magnesium Single Crystals

The type of stressed state (compression, simple shear) is shown to effect the parameters of a work hardening curve for Mg single crystals under basic slip. The electron-microscopic results for the dislocation structure are indicative of the fact that work hardening at stage A of the work hardening curve is connected with the basis-basis dislocation interaction, while the to-B-stage transition and a rapid growth of strain stress are due to the interaction between basic dislocations and “forest” dislocations in the {101 0} {112 0} systems, the latter dislocations arising from the stress relaxation in the primary slip system.     

Deformation mechanism and dislocation structure of high-purity molybdenum single crystals at low temperatures

High purity molybdenum single crystals were deformed in tension and compression along the symmetric double slip orientation [110] in the temperature range from 300 K down to 0.5 K with strain rates between 10⁻³ and 10⁻⁵ s⁻¹. The activation volume was measured by stress relaxation tests. The dislocation structure of the deformed crystals (T → 1.85 K) was examined by high voltage electron microscopy. It was established that the low temperature increase of the critical shear stress exhibits three distinct temperature regimes with different temperature dependences. These non-uniformities are discussed in terms of recently developed theories of kink-pair formation and kink-kink interactions on screw dislocations in bcc metals. The HVEM observations suggest that the mobility of screw dislocations at very low temperatures should be determined by the combined effects of the PEIERLS barriers and the jog dragging.     

Dependence of positron capture rate on dislocation density in solid solutions of KCl—KBr

Generally well-annealed alkali halide crystals exhibit three lifetime components. τ₁ arises due to annihilation with anion and τ₂ due to Bloch Ps. The origin of τ₃ is not well understood. Positron lifetime and etching techniques have been performed on solid solutions of KCl_100−xBr_x with mole % of x = 0.0, 15, 30, 37, 50, 70, and 100. The positron lifetime spectra have been analysed to resolve into three components. The positron capture rate K₃ for the longest lived component and the dislocation density shows a non-linear variation with composition. The positron capture rate varies linearly with the dislocation density of the samples. The origin of τ₃ is identified as due to positronium formation in the dislocations present in the samples. The trapping probability per dislocation has been estimated to be 2.2 × 10⁻¹²/s.     

On the delay of thermally activated motion of pyramidal dislocations in zinc

The effect of shear stress and temperature on the delay time, t_i, of thermally activated motion of dislocations in the {112 2} 〈112 3〉 slip system in Zn single crystals is studied. The delay is associated with a higher density of crystal defects at the initial path of dislocation motion.     

Results of texture simulation in b.c.c. materials

Rolling textures of b.c.c. polycrystals are simulated by the „full constraint”︁ (FC)- and the „relaxed constraint”︁ (RC)-Taylor model, by the FC-model with glide asymmetry in {112}〈111〉slip systems included, by a combination of FC- and RC-model, and by this combination with glide asymmetry included, respectively. Several cases of activated slip system families have been investigated. Simulation results are compared qualitatively with experimental ones.     

Correlation between different parameters of plastic deformation in doped NaCl crystals

The yield stress (τ_y), the microhardness (H) and the dislocation mobility in the stress field of a concentrated load (γ) were measured in NaCl: Ca and NaCl: Pb single crystals within the temperature interval 77–673 K. It was shown that there was a good correlation between the concentration changes of τ_y, H and γ for NaCl:Ca crystals. Such clear results were absent for NaCl:Pb single crystals. An anomaly of τ_y at 77 K was revealed for these crystals; it was not followed by the H anomaly. In conclusion it was stated that the impurity hardening was connected with the increasing of dislocation mobility but such a parameter did not determine the temperature hardening.