M. Z. Butt

Solid-solution hardening in dilute alloys

Abstract Models of solid-solution hardening based on an assumed random dispersion of solute atoms account inadequately for the observed temperature and concentration dependence of the cross of relatively dilute alloys. This is shown to be a consequence of the neglect of Cottrell atmospheres, formation of which implies an above-nominal solute content near dislocations, and results in a mode of yielding akin to that occurring in concentrated alloys. On applying the model of solid-solution hardening used by Butt and Feltham [ Acta metall. 26 , 167 (1978)] with concentrated alloys to available data on several dilute cadmium and magnesium-based solid solutions, good agreement is obtained.

On the temperature dependence of the flow stress of metals and solid solutions

The linear correlation between the logarithm of the CRSS, or of the yield stress in the case of polycrystals, and temperature, frequently encountered in representations of experimental data on metals and solid solutions, is shown to be consistent with the requirements of models in which kink-pair formation processes control the migration of dislocations.

Kinetics of flow stress in crystals with high intrinsic lattice friction

A relatively simple theoretical model, based on the concept of kink-pair mode of escape of screw dislocations trapped in Peierls valleys, has been developed to account for the observed temperature dependence of the critical resolved shear stress (CRSS), τ, and of the associated activation volume, v, in crystals with high intrinsic lattice friction at rather low temperatures. In this model, the CRSS varies with temperature T as τ1/2 = A–BT, and the associated activation volume v depends on temperature T as v −1 = C–DT, where A, B, C and D are positive constants. Moreover, the activation volume v is found to be a function of τ such that vτ1/2 is constant for a given slip system. Data analysis of the temperature dependence of the CRSS of W, α-Fe, Cr and V metal crystals shows excellent agreement between theory and experiment in both regime III (low temperature or high stress) and regime II (intermediate temperature/stress). However, the predicted temperature and stress dependence of the activation volume are borne out by experiment in regime II, but lack quantitative agreement in regime III. On the other hand, the CRSS of CdTe crystals at low temperatures (T ≤ 200 K) is determined by the Peierls mechanism, whereas the weak temperature dependence of the CRSS above 200 K is probably governed by the breakaway of edge dislocation segments from arrays of pinning points due to localized defects in the crystal.

Grain growth in copper and alpha-brasses

The wires of 99.999% copper and alpha-brasses containing 12, 20, 30 and 35 at % Zn have been annealed in vacuum for 30 to 240 min at 873, 923, 973 and 1023 K. The grain-growth data obtained are well encompassed by the relationD2, —D02, =Kt exp(-H/kT), whereD is the instantaneous mean grain diameter at the time,t, of isothermal anneal andD0 refers to the initial mean grain diameter. In alpha-brasses the activation energy for grain-boundary self-diffusion,H, and the pre-exponential factor,K, depends on the zinc concentration,c, asH = (H0 — 1.1c) eV andK =K0 exp(-10.7c) cm2 sec−1. The values ofH0 andK0, referred to the base metal are respectively 0.87 eV and 3.0 × 10−4 cm2 sec−1, which are in good agreement with those (0.85 eV and 3.6 × 10−4 cm2 sec−1) found for copper.

Plastic flow in b c c solid solutions

Available data on the temperature dependence of the CRSS of potassium, sodium, niobium, tantalum and of several binary bcc alloys are examined with reference to the kink-pair process of dislocation movement described by Butt and Feltham [1]. The model is found to account for the observations on the pure metals; equally the temperature and concentration dependence of the CRSS of the alloys are encompassed by it when the alloy-atom pinning of edge dislocations becomes strong enough to render the latter less mobile under stress than the screws.

A comparative study of the stress relaxation in aged and un-aged high-purity aluminium polycrystals

Stress relaxation in 99.996% aluminium polycrystals of average grain-diameter 0.30, 0.42 and 0.51 mm, annealed at 500°C and aged for six months at room temperature, has been studied as a function of initial stress level from which relaxation at constant strain was allowed to start. Data were also obtained with annealed but un-aged aluminium specimens of the same purity and grain size for comparison. The grain size has no notable effect on the strength parameters and stress-relaxation rate in both aged and un-aged aluminium. The room-temperature ageing causes significant increase in the yield stress, while tensile strength and fracture stress remain un-effected. The intrinsic height of the thermally-activable energy barrier (1.64 eV) evaluated for aged aluminium is comparable with that (1.94 eV) for un-aged aluminium, and is of the order of magnitude for recovery processes. In aged specimens, the relaxation rate at a given stress level is 30% larger and associated activation volume is accordingly smaller than that in un-aged specimens. This is most probably due to the diffusion of vacancies and/or residual gaseous and metallic impurity atoms to the cores of edge dislocations in aged specimens.

Characterization of laser-produced plasma ions of various metals and their effect on the optical properties of the CR-39 polymer

The laser-produced plasma (LPP) ions of various metals (Mo, Ni, Cu, Ti and Zn) was implanted in CR-39 polymer, and their influence on its optical properties was investigated. The plasma of these metals was produced using 200 shots of a Q-switched Nd:YAG pulsed laser in a vacuum of 10−3 Torr. The CR-39 specimens were exposed to LPP ions (flux: F=8.01×109−22.14×109 ions/m2, average energy: E av=52−297 keV) emitted along the normal to the metal surface in each case. Both F and E av were found to be a function of the room temperature Debye–Waller thermal parameter B and increase with increase in B-value. The structural behavior of virgin and implanted specimens was investigated using a ultra violet (UV)–visible spectrophotometer. The value of disorder content (Urbach energy E u) was found to lie in the range of 0.287–0.377 eV. The optical band gap energy (E g) for indirect transition decreased on implantation with metallic LPP ions, whereas such a variation in the case of direct transition was negligible. It was observed that E g for indirect transition increases with the increase in E u, whereas the dependence of E g for direct transition on E u was negligible.

Investigation of the compositional modulations in copper-aluminium alloys

The main object of the present work was to analyse the τ/T data of Demirskiy et al. referred to above, together with that obtained by Koppenaal and Fine and Basinski et al. with copper single crystals of high structural perfection and purity containing 0.01 to 14 at% aluminium, within the frame work of the kink-pair formation (KPF) model of solid-solution hardening, various parameters of which have been found to be of diagnostic value in elucidating the mode of solute distribution in the Cu-Zn, Cu-Mn and Al-Mg alloys

Solid-solution hardening in dilute and concentrated alloys

Abstract Numerical analysis of the temperature dependence of the critical resolved shear stress of several binary copper-based alloy single crystals containing 0·11 to 7·6 at.% Mn, 0·01 to 14·0 at.% Al, 0·5 to 8·0 at.% Ge and 5 to 30 at.% Zn, has been carried out in terms of the kink-pair formation model of solid-solution hardening. Several solute atoms are found to be involved in the unit activation process not only in concentrated alloys but also in dilute ones. A single mechanism of solution hardening, which involves the interaction between a dislocation and many solute atoms, is therefore operative in all the alloys referred to above.

Analysis of temperature and concentration dependence of flow stress in KCl–KBr single crystals with special reference to solute distribution

Available data on the temperature and concentration dependence of critical resolved shear stress (CRSS) of KCl–KBr solid-solution crystals containing 9, 17, 27 and 45 mol% KBr in the temperature range 77–230 K have been analyzed within the framework of the kink-pair nucleation model of plastic flow in solid- solution crystals. It is found that CRSS τ decreases with increasing temperature T in accordance with the model relation lnτ = A − BT, where A and B are positive constants. The CRSS τ at a given temperature depends on solute concentration c as τ ∝ cp , where exponent p has a value between 0.33 and 0.57 as temperature T rises from 0 to 230 K. The model parameter W o, i.e. binding energy between the edge-dislocation segment L o involved in the unit activation process and the solute atoms close to it (T → 0 K), which is inversely proportional to B, increases with solute concentration c monotonically as W o ∝ c 0.33 up to a critical value c m = 35 mol% KBr, which is in reasonable agreement with the model prediction W o ∝ c 0.25. However, W o decreases with an increase in c beyond c m, which indicates somewhat ordered distribution of solute in the host lattice of concentrated KCl–KBr solid solutions with c > c m.