Vacancy-solute Complexes Research Articles

The effect of grain boundary segregation of boron in cast alloy 718 on HAZ microfissuring—A SIMS analysis

Secondary ion mass spectroscopy (SIMS) has been used to examine grain boundary segregation in cast alloy 718. The relationship between the boron segregation and the microfissuring tendency in heat affected zones (HAZ) around electron beam welds is discussed in this study. It is concluded that two types of segregation, namely equilibrium and non-equilibrium segregation, occurred during the homogenization heat treatment of the base material. Water quenching after the homogenization treatment inhibited non-equilibrium segregation of boron and other trace elements owing to insufficient time for diffusion of solute-vacancy complexes to occur. Intermediate cooling rates such as air cooling enhanced both non-equilibrium and equilibrium segregation, since equilibrium segregation occurred during holding at the heat treatment temperature. The value of net segregation produced by a combination of equilibrium segregation and non-equilibrium segregation varied with temperature in a U-shape. The nature of the grain boundary in the cast alloy was examined by using an electron backscattered diffraction (EBSD) technique and it was found that 93% of the grain boundaries were of the random type (Σ > 49). The weldability of this alloy was found to be closely related to the grain boundary segregation of boron, i.e. the variation of HAZ total crack length (TCL) with pre-welding heat treatment temperatures has a trend similar to that of boron segregation with temperature after air cooling. Mechanisms for the effect of boron on HAZ microfissuring have been proposed.

Non-isothermal short-range-ordering by excess vacancies in αCu−Zn alloys

The kinetics short-range-order (SRO) in quenched Cu-30 at.% Zn, Cu-25 at. %Zn and Cu-20 at. %Zn was investigated by differential scanning calorimetry (DSC). It was evidenced a growing atomic mobility with increasing Zn content. From the DSC traces it is inferred that ordering is established in one stage, assisted by excess vacancies. As the quenching temperature increases considerable reordering occurs during cooling from the quenching temperature. The variation in the SRO non-isothermal behaviour with quenching temperature and composition is interpreted in terms of the atomic mobility and the degree of disorder together with the concentration of vacancies retained by quenching. Activation energies which control the mean life of vacancies and those which control the ordering rate were very similar, indicating that the mobility of vacancies is highly effective in generating SRO. Such activation energies are somewhat lower than the effective energies which control the kinetics of the process obtained from the DSC traces, suggesting that the presence of solute-vacancy complexes may be important as the Zn concentration increases. This feature was confirmed by an estimation of the solute-vacancy binding energy. It was also inferred that divacancy formation is unlikely in the alloys under study.

Non-equilibrium segregation of solutes to grain boundary

Mechanisms for the non-equilibrium segregation of solutes to static grain boundary duringcooling (quenching-induced segregation) and to moving grain boundary during recrystallization (moving-induced segregation) are proposed. For quenching-induced segregation, in consideration of the local equilibrium among vacancies, solute atoms and vacancy-solute atom complexes, as well as the influence of equilibrium grain-boundary segregation, the theoretical dynamic formulae for this non-equilibrium segregation have been derived on the basis of the vacancy-dragging mechanism

Non-equilibrium segregation of solute to grain boundary

Mechanisms for the non-equilibrium segregation of solutes to static grain boundary during cooling (quenching-induced segregation) and to moving grain boundary during recrystallization (moving-induced segregation) are proposed. For quenching-induced segregation, in consideration of the local equilibrium among vacancies, solute atoms and vacancy-solute atom complexes, as well as the influence of equilibrium grain-boundary segregation, the theoretical dynamic formulae for this non-equilibrium segregation have been derived on the basis of the vacancy-dragging mechanism. Theoretical calculations have been carried out for the non-equilibrium segregation of boron to austenitic grain boundaries during isothermal holding and continuous cooling after heating at high temperature; the results agree well with those obtained from experiments. The model has also successfully explained the different behaviours of boron segregation during cooling in α-Fe and in γ-Fe. For moving-induced segregation, based on the interaction between dislocations and the moving boundaries during recrystallization, a dislocation relaxation and widening grain-boundary mechanism of solute segregation on moving boundaries is proposed. Applying this model, we have calculated the boron segregation on moving boundaries during recrystallization in Fe-3% Si alloy; the results of these calculations agree with experimental results.

Vacancy concentration in strain ageing of substitutional f c c alloys

The relation between vacancy concentration, C v and tensile plastic strain, ɛ, has been constantly expressed as C v ∞ ɛ m . To take into account the grain-size effect, we have recently proposed that C∞ ɛβv ∞ϱm, where ϱm is the mobile dislocation density. With the conventional expression that ϱm d −n , where d is the average grain size, the strain and grain-size dependence of vacancy concentration appears to be C v ∞ ɛβγ d -nγ. This equation has proved effective in rationalizing the onset strain, ɛc, and stress amplitude, Δσ, of flow instability associated with the Portevin-LeChatelier effect of substitutional f c c alloys, where ɛc and Δσ are described by $$\dot \varepsilon \propto \varepsilon _c^{\beta (1/2 + \gamma )} d^{ - n(1/2 + \gamma )} T^{ - 1} exp( - Q/kT)$$ and $$\Delta \sigma \propto \left[ {\dot \varepsilon ^{ - 1} \varepsilon _c^{\beta (1/2 + \gamma )} d^{ - n(1/2 + \gamma )} T^{ - 1} exp( - Q/kT)} \right]^{2/3} $$ in which $$\Delta \sigma \gamma \propto \left[ {\varepsilon ^{\beta \gamma } d^{ - n\gamma } t_a T^{ - 1} exp( - Q/kT)} \right]^{2/3} $$ , T, Q and k are the strain rate, temperature, Boltzmann constant and activation energy for solute migration, respectively. Using the same concept, we have obtained $$\Delta \sigma \gamma \propto \left[ {\varepsilon ^{\beta \gamma } d^{ - n\gamma } t_a T^{ - 1} exp( - Q/kT)} \right]^{2/3} $$ to rationalize the increment of stress drop, Δσγ, observed at the instant of reloading after a static ageing time of t a. By adopting the above three equations, the strain-ageing data of two Al-Mg alloys in this study reveal that the vacancy concentration which is responsible for strain ageing is lower than the reported data from electrical resistivity measurements. This result is in agreement with the idea of migration of a vacancy-solute complex which has been proposed in the literature.

Kinetics of short-range ordering in αCu-Al alloys

The ordering behaviour in quenched αCu-Al was investigated by differential scanning calorimetry (DSC) under rising temperature conditions and by electron diffraction. It was found that the ordering processes can be better explained in terms of a homogeneous short-range order (SRO) model rather than a heterogeneous disperse order (DO) model as previously interpreted for the same type of experiments. The DSC traces indicate that the ordering takes place in two stages: the stage 1 ordering at lower temperatures is associated with the migration of excess vacancies and the stage 2 ordering at higher temperatures is associated with the migration of equilibrium vacancies. At higher temperatures, a marked surge of energy absorption occurs (stage 3) which is attributed to the destruction of order. For furnace-cooled alloys, only stage 3 appears. The relative dominance of stages 1 and 2 is influenced by the quenching temperature, the quench rate, the density of vacancy sinks and the sample shape before quenching. A relationship describing the overall SRO kinetics for both stages together, in terms of either the reacted fraction or the first SRO parameter, is proposed. A method for evaluating boundary values for this parameter is developed, making use of the features displayed by the DSC thermograms. The mobility of the vacancies, which controls their life-time and the short-range ordering rate, was evaluated by computing frequency factors and activation energies. Values for activation energies controlling the short-range ordering rate are somewhat smaller than the effective values obtained for stage 1 from the DSC traces, suggesting that the presence of solute-vacancy complexes may be important mainly as the aluminium concentration increases. From estimations of solute-vacancy and divacancy binding energies, it is inferred that divacancy formation is unlikely in the alloys under study. Process frequency factor values are in very good agreement with those calculated for a short-range order state developed during two-stage ordering by a vacancy mechanism. A flow diagram of the factors controlling the fractional increase of short-range order during anisothermal experiments is proposed.

Age-Hardening characteristics of an AlMgSi Alloy

Age-hardening behaviour of an AIMgSi alloy was followed by hardness measurements during isochronal and isothermal ageing. The alloy is found to age-harden during natural ageing at room temperature after quenching from the solid solution temperature. The alloy exhibits peak hardness by artificial ageing at 200 °C for 2 hours. Isothermal ageing curves indicated that the rate of hardness increase at early stages of ageing, is dependent upon the ageing temperature in a manner which obeys an Arrhenius-type equation. An activation energy of 0.95±0.05 eV was calculated from the Arrhenius plot of the results. This activation energy shows that the process responsible for hardness increase in the early stages of ageing may be controlled by the migration of solute-vacancy complexes.

Pressure dependence of the hyperfine field of a Cd probe in a relaxed trivacancy complex in Ni

Perturbed \ensuremath{\gamma}-\ensuremath{\gamma} angular-correlation experiments were carried out using extremely dilute $^{111}\mathrm{Cd}$ probes to measure the pressure dependence of the magnetic hyperfine field at a vacancy-solute complex in Ni in which the Cd probe is relaxed to the center of a tetrahedron of vacancies. The pressure dependence of the hyperfine field of the defect-free substitutional site was found to be ${\mathit{dH}}_{\mathrm{hf}}$/dp=-0.038(6) kG/kbar, which agrees with a previous measurement. The pressure dependence of the hyperfine field associated with the vacancy complex was found to be ${\mathit{dH}}_{\mathrm{hf}}$/dp=-0.023(4) kG/kbar. Results are not found to be consistent with a simple picture of the hyperfine-field-production mechanism obtained from recent first-principles calculations.

A method of determining the diffusion coefficient of vacancy-solute atom complexes during the segregation to grain boundaries

A new method of determining the diffusion coefficient of vacancy-solute atom complexes by measuring the critical time for non-equilibrium grain boundary segregation of solute atoms was established in this work. For a sample cooled quickly enough from a high temperature to a lower temperature and isothermally held there, the critical time is defined to be the holding time of the sample at the lower temperature required for the level of segregation to reach a maximum. According to this method, the Arrhenius parameters of the diffusion of vacancy-boron atom complexes in a B-doped Fe-28 at. % Ni alloy were determined to be 10.0 · 10 −5 m 2/s for the pre-exponential factor and 0.94 eV for the activation energy. As a by-product of this work the numerical constant δ was determined to be 0.48 for the diffusion of vacancy-boron atom complexes in the above alloy.

Short-range ordering by excess and thermal vacancies during linear heating experiments in α-CuAl alloys

The ordering behaviour in quenched α-CuAl was investigated by differential scanning calorimetry (DSC) under increasing temperature conditions. It was found that the ordering processes can be better explained in terms of an homogeneous short-range order (SRO) model rather than a heterogeneous disperse order model as previously interpreted for the same types of experiment. The DSC traces indicate that the ordering takes place in two stages; stage 1 ordering at low temperatures is associated with the migration of excess vacancies and stage 2 ordering at high temperatures is by the migration of equilibrium vacancies. The relative dominance of each stage is influenced by the quenching temperature, the quench rate, the density of vacancy sinks and the sample shape before quenching. A relationship describing the overall SRO kinetics for both stages together in terms of either the reacted fraction, or the first SRO parameter was proposed. A method for evaluating boundary values for this parameter was developed, making use of the features displayed by the DSC thermograms. The mobility of vacancies, which controls their lifetime and short-range ordering rate, was evaluated by computing frequency factors and activation energies. The resulting values for activation energies controlling the short-range ordering rate were somewhat smaller than the effective values obtained for stage 1 from the DSC traces, suggesting that the presence of vacancy-solute complexes may be important especially as the aluminium concentration increases. From estimations of vacancy-solute and divacancy binding energies, it was inferred that divacancy formation is unlikely in the alloys under study. The process frequency factor values were in very good agreement with those calculated for an SRO state developed during two-stage ordering by a vacancy mechanism.

A new kinetic model for non-equilibrium grain boundary segregation

The author proposes a new kinetic model for non-equilibrium grain boundary segregation. The model is based on three assumptions: that non-equilibrium grain boundary segregation is caused by diffusion of solute-vacancy complexes to the grain boundary; that the grain boundary is a sink for the complexes; and that the grain boundary and grain dimensions are sufficiently large.

A Mechanism for Solute Segregation to Grain Boundaries

ABSTRACTBased an the local equilibrium among vacancies, solute atans and vacancy-solute atom complexes, a mechanism for solute segregation to grain boundaries is suggested for a alloy system with binding energy of complex S≫kT. A set of dynamic equations for grain boundary segregation is ived, which can describe both equilibrium and nonequilibrium segregations, as the effect of the equilibrium segregation is taken into account in the bonndary condition. Theoretical calculation is made by computer for boron segregation at austenite grain boundaries as functions of isothermal holding time, cooling rate and quenching teaperature, which agree well with experimental results.

Overview no. 63 Non-equilibrium grain boundary segregation of boron in austenitic stainless steel—III. Computer simulations

A computer model has been developed to simulate non-equilibrium grain boundary segregation. The model is based on simultaneous diffusion of free vacancies, free solute atoms and vacancy-solute complexes while maintaining local equilibrium between these three entities. The driving force for segregation is the change in equilibrium vacancy concentration during cooling. A sufficient condition for grain boundary enrichment to occur is that complexes are more mobile than free solute atoms. The simulations showed that the amount and width of segregation should be strongly dependent on 1. (i) the heat treatment temperature and cooling rate, 2. (ii) the solute concentration, 3. (iii) the binding energy of complexes 4. (iv) the vacancy formation energy and 5. (v) the mobility of solute atoms and complexes. The maximum boundary enrichment occurs at some intermediate cooling rate. Higher mobilities, higher starting temperatures and smaller grain sizes require higher cooling rates to give maximum enrichment. The model was applied to the system boron-austenite. Good agreement between experimental results and simulations was achieved. The diffusion coefficients for boron and vacancy-boron complexes in austenite were estimated at D B = 2.10 −7 exp [ −1.15( ev kT ] and D VB = 2.10 −7 exp [ −1.15( ev kT ] ( m 2/s ) respectively.

Serrated yielding in an Al—3wt% Mg alloy with trace additions of indium, cadmium and tin

The occurrence of serrations in the stress-strain curve is a common phenomenon exhibited by several solidsolution alloys over certain ranges of temperature and strain rate. Dynamic strain ageing due to the migration of solute atoms to the dislocations is considered to be a possible mechanism for the onset of serrations [1]. The generation of vacancies during plastic deformation enhances the diffusivity of substitutional solute atoms and leads to a critical strain for the onset of serrations; the latter is usually found to increase with increasing strain rate and decreasing temperature. The activation energy for dynamic strain ageing can be determined by studying the temperature dependence of the critical strain for a fixed strain rate. The measured value of the activation energy has been attributed to that for the migration of the solutevacancy complex and has been employed for the estimation of the solUte-vacancy binding energy [2, 3]. Several investigations have been reported on the serrated yielding of binary and complex AI-Mg alloys and the measured values of the migration energy lie in the range 0.27 to 0.66eV [3-8]. Annealing studies on alloys containing a supersaturation of vacancies, obtained by quenching from an elevated temperature, can be used for the estimation of the migration energy of vacancies. The addition of trace elements to binary alloys can cause a marked change in the annealing characteristics of vacancies. There is ample experimental evidence to show that vacancy migration in A1-Zn, A1-Cu and A1-Ag alloys is retarded by the presence of small amounts of ternary elements; this method has been used for deducing the solute-vacancy binding energy

The creation and annihilation of vacancy-solute complexes during irradiation of Ni(In) and Ni(Au) crystals

The displacement of solute atoms from normal lattice sites, which results from the trapping of irradiation-induced defects by the solute atoms, can be determined in ion channeling studies by measuring the yield of reaction products resulting from ion-solute collisions. In the present investigation, the backscattering of 1.5 MeV 4He ions from Ni crystals containing ≈ 0.1 at % In or Au was used to monitor the fraction f ds 〈 lmn〉 of solute atoms displaced into various ⩽lmn> channels following 4He ion irradiations and annealing treatments. Also, the rate at which the channeled ions were dechanneled in the Ni host lattice served as a simultaneous measure of the total irradiation-induced defect concentration. Subsequent to 35 K irradiations, annealing in the range ≈ 250–400 K produced appreciable displacements of both In and Au atoms from their normal lattice sites with f ds 〈100〉 > f ds 〈110〉 > f ds 〈111〉 . There were also a peaking of solute atom yield for angular scans through a 〈100〉 direction. The displacements are believed to arise from the trapping of vacancies at the solute atoms, thus forming relatively simple vacancy-interstitial solute atom complexes. These vacancy-solute complexes remain quite stable up to approximately 600 K and then break up in the region 600–750 K. In addition, the vacancy-solute complexes can be annihilated during irradiations at 80 K where only interstitials are mobile. The results provide strong evidence for the formation of tetravacancy-solute atom complexes in which an interstitial solute atom is surrounded by a tetrahedron of four vacancies. In such a complex the solute atom is displaced into the centre of the 〈100〉 channel, i.e. into a tetrahedral lattice site. Trivacancy-interstitial solute atom complexes, in which the solute atom is at the centre of a triangle of three nearest-neighbour vacancies in a {111} plane, may also be present.

A channelling study of vacancy-solute complexes in Al-0.04 at.% Sn

Ion channelling measurements in an Al-0.04 at.% Sn crystal have shown that the Sn atoms trap irradiation induced vacancies to create trivacancy-Sn, tetravacancy-Sn and hexavacancy-Sn complexes. The Sn atoms in these complexes occupy interstitial positions at the centre of a triangle of nearest neighbour vacancies, at the tetrahedral site and at the octahedral site respectively. Quantitative measurements were made of (i) the growth of these complexes caused by vacancy trapping at 200K following 35K irradiation, and (ii) the decay of these complexes caused by self-interstitial trapping during irradiation at 70K.

Modification on near-surface precipitation in AlGE alloy by ion irradiation

A model including precipitate dissolution and solute segregation is used to explain the changes in precipitate distribution during 100 keV Al + ion irradiation of AlGe alloy. It is found by TEM that Ge precipitates in the peak damage region i.e. <100 nm from the surface are destroyed by prolonged irradiation to doses greater than 28 dpa, whereas precipitates near the tail of the damage profile i.e. 100–250 nm from the surface, continue to grow. SIMS has shown that the dissolution of near-surface precipitates is accompanied by segregation of Ge to depths below the damage peak, indicating that Ge segregates down defect gradients. The results show that solute segregation is an important factor in determining precipitate stability. It is thought that the reversal in precipitate behaviour from growth to dissolution occurs because the solute depletion in the matrix near the surface reduces the solute arrival rate at the precipitate sufficiently for recoil dissolution to determine the precipitate behaviour. A preliminary study on low temperature irradiation of AlGe shows that Ge solute re-distribution rate is limited by the concentration and mobility of vacancy-solute complexes, and not by the rate of precipitate dissolution.

Defect-solute interactions and radiation-induced segregation in Ni(Si) and Ni(Ge) alloys

The electronic structure of a solute is shown to play an important role in dictating the nature of its interactions with vacancies and interstitials in a solid. Contrary to usual expectations, the solute-vacancy binding energies are relatively large in Ni(Si) and Ni(Ge) systems. This indicates that, aside from the contribution of mixed dumbbells, the formation and migration of mobile vacancy-solute complexes can give rise to solute enrichment at sinks in these alloys. Calculations show that the defect-solute binding energies account for the segregation and precipitation behavior observed in Ni(Si) and Ni(Ge). (FS)

Positron studies of mercury-indium alloys

Ratios of coincidence counting rates of annihilation gammas at 0 and 10m rad were measured for 16 atomic percentages of indium in liquid mercury. Theory of trapping of positrons at solute atoms and solute-vacancy complexes is applied. Complete angular correlation measurements for 14.3, 25, 35, and 50 atomic percentages of indium were also made and showed possible effects of solute-vacancy complexes on the smearing of the angular correlation distributions.

The role of quenched-in vacancies in the ageing of nimonic alloys

Diffusion controlled coarsening theory has been applied to the resistance maximum observed during the ageing of two Nimonic alloys (PE16 and 80A). The position of the resistance maximum is shown to be strongly dependent on the rate of loss of the quenched-in vacancy supersaturation. In both alloys the principal vacancy sink is the dislocation network. The kinetics of vacancy loss have been modified to include the effect of solute-vacancy complexes in the diffusive process. Estimates are made of the efficiency of the retention of the vacancies quenched-in at the solution treatment temperature and these are shown to be in good agreement with the observed values of the vacancy supersaturation in these alloys.