Diffusion-controlled Growth Kinetics Research Articles

Out-of-phase thermomechanical fatigue of a single crystal Ni-base superalloy

The present work studies the out-of-phase thermomechanical fatigue (OP-TMF) behavior of the precisely oriented [001] single crystal Ni-base superalloy ERBO/1 (CMSX-4 type). The OP-TMF tests are performed between minimum and maximum temperatures of 1023 and 1223 K and a cyclic mechanical strain amplitude of ±0.5 %. In accordance with previous findings, the present study confirmed that isothermal low cycle fatigue (LCF) tests at 1023 and 1223 K show significantly longer fatigue lives than the OP-TMF tests, specimens with rougher surfaces fail earlier than polished specimens and deformation bands and cracks form in the specimen surface. Two new results were obtained: First, when comparing OP-TMF cycles with fast cooling (tensile part of cycle) and fast vs. slow heating (compressive part of cycle) one finds that the slower heating/compressive cycle is more damaging. Second, analytical scanning electron microscopy of the flanks of an OP-TMF crack allows to study the diffusion-controlled growth kinetics of the oxide and the underlying zone, which is depleted by the oxide forming elements. These results are discussed in the light of the microstructural, mechanical and chemical results of the present study considering previous work on OP-TMF of superalloy single crystals (SXs).

Precipitate growth kinetics under inhomogeneous concentration fields using a phase-field model

We investigate precipitation dynamics in the presence of a local solute gradient using phase-field simulations. During the homogenization heat treatment of the solidified Inconel 718 alloy, high Nb concentration within the Laves phases or at the core of the secondary arms results in Nb diffusion into the $\ensuremath{\gamma}$ matrix. The volume fraction and spatial distribution of precipitation during subsequent annealing can be controlled by tailoring the Nb concentration gradient in the matrix during homogenization. We use a surrogate Ni-Fe-Nb alloy for Inconel 718 to explore the growth dynamics of $\ensuremath{\delta}$ precipitates related to the local Nb concentration levels. The simulations indicate that in the presence of a Nb concentration gradient the growth rate of $\ensuremath{\delta}$ precipitates is higher than in a matrix of uniform average Nb concentration. The higher growth rate is a result of the higher local thermodynamic driving force at the interface between the solute-rich matrix and the $\ensuremath{\delta}$ interface. We propose a phenomenological model to describe the diffusion-controlled growth kinetics of the $\ensuremath{\delta}$ phase under a solute concentration gradient.

Intermetallic growth kinetics and microstructure evolution in Al-Cu-Al metal-matrix composite processed by high pressure torsion

Constrained high pressure torsion and subsequent annealing was used to fabricate Al-Cu-Al metal-matrix multilayered composite. The composite has a heterogeneous structure consisting of a plastic aluminum matrix and hard intermetallic inclusions with a gradient decrease of layer thickness from the center to periphery of the sample. Intermetallic growth kinetics was retrieved from precise X-ray phase analysis using a narrow parallel X-ray beam of increased intensity. It was found that the growth of Al2Cu phase at temperatures from 150 °C to 210 °C can be fitted by t1/2 time relation, indicating to the bulk diffusion-controlled growth kinetics. The growth activation energy of Al2Cu was calculated to be 0.48 eV.

Insight into the effect of Ti-addition on diffusion-controlled growth and texture of Nb3Sn intermetallic superconductor phase

The alloying of Ti with Cu(Sn) and Nb significantly increases the grain boundary diffusion-controlled growth kinetics of Nb3Sn accompanied with a decrease in the activation energy in the Cu(5.5 at.% Sn, Ti)/Nb and Cu(5.5 at.% Sn)/Nb(Ti) diffusion couples. In either case, the β-(Ti,Nb) precipitates form at the grain boundaries of Nb3Sn. On the other hand, the ternary intermetallic phase, Nb3Sn2Ti3, is present in the interior of the Nb3Sn phase matrix only when Ti is added to Nb. The pinning forces on the grain boundaries of Nb3Sn exhorted by the β-(Ti,Nb) precipitates and related microstructure refinement results in an enhanced growth kinetics of the product phase, Nb3Sn. The addition of 0.5 at.% Ti to Cu(Sn) has a stronger influence on the growth kinetics and the activation energy for the growth of Nb3Sn compared to 3 at.% Ti to Nb owing to a higher fraction of smaller and equiaxed grains with high angle grain boundaries of Nb3Sn. The Ti-free Nb3Sn phase layer grows with a weak texture, a commonly observed behavior in other material systems for the product phases grown by diffusion-controlled mechanism in the interdiffusion zone. On the contrary, a very strong crystallographic texture of the Ti-containing product phase, Nb3Sn, is reported that has a unique pattern depending on the orientation of the adjacent Nb or Nb(Ti) grains. The Cu atoms segregate to the grain boundaries of Nb3Sn over a distance of ∼2–5 nm with a depletion of Nb.

Formation and growth of Cu–Al IMCs and their effect on electrical property of electroplated Cu/Al laminar composites

Cu/Al laminar composite was prepared by dipping Zn layer and then electroplating Cu thick layer on pure Al sheet. During annealing the Cu/Al composites at temperature from 473 to 673 K, the Cu/Al interfacial diffusion and reaction and its kinetics and also the electrical resistivity of the composites were studied. The results show that no Cu–Al IMC layer is observable as the composites are annealed at 473 K for time till 360 h, indicating that the Zn intermediate layer can effectively suppress the Cu/Al interfacial diffusion. However, as the composites are annealed at 573 K and above, Zn atoms in the Zn layer dissolve into the Cu layer. Tri-layered reaction product of CuAl2/CuAl/Cu9Al4 then forms from the Al side to the Cu side. The IMC layer follows the diffusion-controlled growth kinetics. Electrical resistivity of the Cu/Al composites increases with the increase of the annealing temperature and time.

Role of Ti on growth, morphology and microtexture evolution of A15-based V3Ga superconductor by bronze technique

We report a rare experimental evidence of an exceptional increase in grain-boundary diffusion-controlled growth kinetics of product phase by grain-refinement due to minor alloying. Ti-addition during growth of V3Ga superconductor by coupling V and Cu(Ga)-solid solution by bronze process increases the critical current density (Jc) significantly. In this manuscript, the exact role of Ti-addition is studied based on systematic and quantitative diffusion-couple experiments that mimic the bronze-method. Metallurgical aspects like microstructural features and growth mechanism are assessed critically. Results are compared when Ti is added either to V or Cu(Ga) and to both for a fixed Ga content. Ti-addition to Cu(Ga) compared to V increases growth kinetics of V3Ga more significantly. Quantitative EPMA-analysis indicates that a mixture of Ti-free and Ti-containing V3Ga phase grows when Ti is added to V. Small precipitates grow along with Ti-containing V3Ga when Ti is added only to Cu(Ga). TEM-study indicates that these precipitates are rich in V and Ti. Much finer grains found in the precipitate-containing region lead to higher growth kinetics due to grain-boundary diffusion. EBSD-analysis shows equiaxed grains and relatively random in orientation because of alloying. This study indicates that Ti-addition to Cu(Ga) is most effective considering metallurgical aspects that influence Jc.

Non-classical nuclei and growth kinetics of Cr precipitates in FeCr alloys during ageing

In this manuscript, we have quantitatively calculated the thermodynamic properties of the critical nuclei of Cr precipitates in FeCr alloys. The concentration profiles of the critical nuclei and nucleation energy barriers were predicted by the constrained shrinking dimer dynamics method. It is found that Cr concentration distribution in the critical nuclei strongly depends on the overall Cr concentration as well as on the temperature. The critical nuclei are non-classical because the concentration in the nuclei is smaller than the thermodynamic equilibrium value. These results are in agreement with atomic probe observation. The growth kinetics of both classical and non-classical nuclei was investigated by the phase-field approach. The simulations of critical nucleus evolution showed a number of interesting phenomena: (1) a critical classical nucleus first shrinks toward its non-classical nucleus and then grows; (2) a non-classical nucleus has much slower growth kinetics at its earlier growth stage compared to the diffusion-controlled growth kinetics and (3) a critical classical nucleus grows faster at the earlier growth stage than does a non-classical nucleus. All of these results demonstrate that it is critical to introduce the correct critical nuclei in order to correctly capture the kinetics of precipitation.

Soft impingement in diffusion-controlled growth of binary alloys: moving boundary effect in one-dimensional system

The impact of soft impingement on the kinetics of diffusion-controlled growth of binary alloys is investigated. An analytical approach is developed which takes into account the process of island growth, that is the time dependence of the position of the nucleus/parent phase interface. The concentration profile, the growth law, and the kinetics of the fraction of transformed phase are computed and compared with those attained for point islands. At odd with the point island approach the local kinetics of growth depends on initial supersaturation. On the other hand, the whole transformation kinetics is in good agreement with that of the point island model with an Avrami exponent close to the theoretical value n = 0.5. The concentration profile is well described by a polynomial function in the whole spatial domain, with an exception for the initial stage of the phase separation. The effect of the spatial distribution of the nuclei on the kinetics is also studied in the model case of hard-core correlation among nuclei.

Electrochemical Study of Copper in Room Temperature Protic Ionic Liquids Ethylammonium Nitrate and Triethylammonium Methylsulfonate

Electrochemical reduction of Cu(II) and electrodeposition of copper were studied in two room temperature protic ionic liquids (PILs), ethylammonium nitrate and triethylammonium methylsulfonate by using voltammetric techniques. The results provided evidence that slow disproportionation of Cu(I) occurred in the PILs. Images obtained by scanning electron microscopy revealed that electrodeposition of Cu nanoparticles and crystalline thin films onto glassy carbon and indium tin oxide electrodes occurred via two distinctly different, potential-dependent pathways: (i) disproportionation of Cu(I), at mild potentials in the range of 0.48 to 0.03 V vs. Fc0/+, and (ii) electroreduction of Cu(I), at potentials lower than 0.03 V vs. Fc0/+. The electrodeposition mechanisms were examined by using chronoamperometry and were found to be governed by instantaneous nucleation and diffusion-controlled growth kinetics.

Impact of soft impingement on the kinetics of diffusion-controlled growth of immiscible alloys

The effect of the soft impingement mechanism on the kinetics of diffusion-controlled phase transitions of binary alloys is investigated. Soft impingement arises from the interference of the diffusional fields and implies a different morphology of the product phase when compared to that attained in the case of genuine impingement. Mean field rate equations for nucleus radius and supersaturation are coupled with the mass balance equation in terms of the geometrical parameter (time dependent) which defines the soft impingement process. The kinetics is studied as a function of the initial supersaturation and it is compared with that attained in the case of genuine impingement. Solutions of the kinetics are obtained in the model case of time dependent supersaturation which scales according to Ham’s law and in the case of simultaneous nucleation. The phase transformation of immiscible alloys in one-dimensional system is also investigated. In this case and for point islands, the exact solution of the kinetics is obtained and allows one to gain an insight into the validity of the Kolmogorov–Johnson–Mehl–Avrami model and Avrami’s exponent for one-dimensional growths.

2D Nucleation and Growth Phenomena in UPD of Cd on Ag(111) and Ag(100)

Underpotential deposition (UPD) of Cd on Ag single crystal substrates has been studied by in situ scanning tunneling microscopy (STM) and electrochemical measurements. On Ag(111) the UPD process starts with formation of an expanded adlayer. This adlayer transforms by 2D nucleation and growth to a condensed Cd monolayer, which is unstable and at long polarization times undergoes changes involving surface alloy formation phenomena. In contrast to Ag(111), on Ag(100) a formation of a condensed monolayer by 2D nucleation and growth has been observed at relatively high underpotentials. The growth rate of 2D clusters extracted from the in situ STM images indicates a surface diffusion-controlled growth kinetics. At lower underpotentials the UPD of Cd on both substrates involves a significant surface alloy formation, which is reflected in the surface topography changes observed during the anodic stripping.

Dolostones from Grand Cayman, British West Indies

ABSTRACT Pervasively dolomitized Tertiary strata on Grand Cayman are dominated by heterogeneous dolostones that are composed of both low-Ca calcium dolomite (LCD 55 mol % CaCO3). Homogeneous dolostones, formed of either LCD or HCD, are rare. Some dolostones contain dolomite crystals that are characterized by oscillatory zones (1-10 µm thick) of LCD and HCD, whereas others have rims of LCD surrounding cores of HCD. In some dolostones, bioclasts formed of LCD are embedded in a matrix of HCD. An 1‰ 18O difference between the LCD and HCD can be attributed to the natural covariance that exists between the 18O and mol % CaCO3 in dolomite. There are no significant differences in the 87Sr/86Sr ratios of the LCD and HCD. There is no consistent vertical or lateral pattern to the distribution of LCD and HCD in the Cayman dolostones even in closely spaced sampling sites. Such variability is more consistent with growth of individual dolomite crystals being controlled by processes that operated around the surfaces of individual crystals rather than by large-scale changes in the dolomitizing fluids. This interpretation is consistent with the development of oscillatory zoning, which is attributed to precipitation of different phases or minerals from the same parent fluid because of competition between interface-controlled and diffusion-controlled growth kinetics. Dolomitization of the Tertiary strata on Grand Cayman was probably mediated by seawater or modified seawater. Nevertheless, small-scale intrinsic factors controlled the incorporation of Ca in the dolomite lattice and, accordingly, the geochemical parameters that are intimately linked to the mol % CaCO3. These small-scale intrinsic controls must be factored into any model to explain the formation of Tertiary island dolostones.

Formation and growth of interfacial intermetallic layers in eutectic Sn-Ag solder and its composite solder joints

Single shear lap joints were made by soldering two Cu substrates with eutectic Sn-Ag solder, and its composite solders containing FeSn/FeSn2 or Ni3Sn2 intermetallic particles introduced by an in-situ method. Ageing of solder joints was performed at 70, 100, 120, 150, 180 °C for 1400 h. The growth of the interfacial intermetallic compound (IMC) layers was characterized assuming diffusion-controlled growth kinetics. Effects of such FeSn/FeSn2 and Ni3Sn4 particulates on the IMC layer growth rate were extensively characterized. Composite solder joints in the fabricated condition formed thinner IMC layers compared to the corresponding non-composite solder joints. The Cu6Sn5 IMC layer grew faster at temperatures above 120 °C (T/T m=0.8), while growing slower at temperatures below 120 °C in composite solder joints. In-situ introduced FeSn/FeSn2 and Ni3Sn4 particle reinforcements in composite solder joints proved effective in reducing the overall growth of the interfacial Cu6Sn5 IMC layer only at lower temperatures. Composite solder joints exhibited slower growth of the Cu3Sn layer during ageing at all temperatures used in this study. Two different regions having different activation energies depending on the temperature were identified for the growth of Cu6Sn5 and Cu3Sn IMC layers. © 2000 Kluwer Academic Publishers

Calorimetric determination of NiAl 3-growth kinetics in sputter-deposited Ni/Al diffusion couples

Ni/Al multilayer films with 1:3 molar ratio and periodicities in the range 640–2000 nm were prepared by sputter deposition, and investigated by differential scanning calorimetry and X-ray diffraction. X-ray diffraction showed that only NiAl 3 formed in the reaction of these films. The calorimetry measurements were analyzed using one-dimensional diffusion-controlled growth kinetics. The activation energies so obtained were in the range 1.64–1.76 eV, and the pre-exponential factors were (5–50)×10 −4 m 2s −1. These kinetic growth parameters were extracted from the calorimetry data using a variety of analysis methods applied to constant-heating-rate calorimetry data. Good agreement was found among the results of the various methods. The present paper, in addition to providing the kinetic parameters for the growth of nickel trialuminide in these Ni/Al films, demonstrates the general utility of multilayer films and calorimetric methods in the determination of the growth kinetics of intermetallic phases in diffusion couples.

Dendritic growth velocities of the intermetallic compounds Ni 2TiAl, NiTi, Ni 3Sn, Ni 3Sn 2 and FeAl

The dendritic growth velocities of melts of several ordered intermetallic compounds were measured during rapid solidification. Bulk melt undercoolings were achieved by the application of the electromagnetic levitation and the glass fluxing technique. The results obtained on Ni 2TiAl, NiTi, Ni 3Sn, Ni 3Sn 2 and FeAl allow comparisons with respect to the dependence of the crystal growth behaviour on the complexity of the superlattice structure and on the predominant type of bonding. Disorder trapping in FeAl was strongly indicated by the observation of large growth velocities up to 7 m s −1, whereas all other investigated alloys solidified chemically ordered even at deep undercoolings up to 300 K. A dendrite growth model was applied to analyse the experimental data. The results reveal the diffusion-controlled growth kinetics of ordered intermetallic compounds in contrast to collision-limited growth conditions in pure metals and solid solutions.

Kinetics of diffusion-controlled growth of fayalite

The rate of growth of fayalite (Fe2SiO4) has been measured at one atmosphere total pressure, temperatures from 1000° to 1120° C, and oxygen fugacities controlled by CO/CO2 gas-mixing from 10-9.9 to 10-13.0atm, chosen to span the fayalite stability field. The fine-grained polycrystalline fayalite layer was formed by reacting the oxides FeO or Fe3O4 with a thin slice of single-crystal quartz. The rate of growth of the fayalite increases with increasing temperature and decreasing oxygen fugacity, and is consistent with a parabolic rate law, indicating that the growth rate is controlled by diffusion through the fayalite. Microstructural observations and platinum marker experiments suggest that the reaction phase is formed at the quartz-fayalite interface, and is therefore controlled by the diffusion of iron and oxygen. The parabolic rate constant was analyzed in terms of the oxide activity gradient to yield mean chemical diffusivities for the rate-limiting ionic species, assuming bulk transport through the fayalite layer. Given that iron diffusion in olivine polycrystals occurs either by lattice diffusion, which shows a positive dependence on oxygen activity, or by grain boundary diffusion, which would result in growth rates significantly faster than we observe, we conclude that the diffusivities derived in this study represent oxygen diffusion. However, since oxygen lattice diffusion in fayalite has been established to be much slower than our measurements, it is likely that the transport path for oxygen is along the grain boundaries. Thus, the mean grain boundary diffusivity of oxygen in fayalite % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmirayaara% aaaa!36CE! $$\bar D$$ O (m2 s-1), using the measured grain size of 0.25 μm, is then given by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaieYdg9frVeeu0dXdh9vqqj-hEiea0d% j9q8arFj0dir-hbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9% q8qr0xc9Fve9Fve9qapdbaqaaeGaciGaaiaabeqaamaabaabaaGcba% GabmirayaaraWaa0baaSqaaGqaaiaa-9eaaeaaieGacaGFNbGaa4Ny% aaaakiaahccacqaH0oazcqGH9aqpcaaIXaGaaiOlaiaaikdacaaI4a% Gaey41aqRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGc% caWGMbWaa0baaSqaaiaa-9eadaWgaaadbaGaa8Nmaaqabaaaleaacq% GHsislcaaIWaGaaiOlaiaaigdacaaI3aaaaOGaaCiiaiaadwgadaah% aaWcbeqaaiabgkHiTiaaiwdacaaI0aGaaGimaiaac+cacaWGsbGaam% ivaaaaaaa!5790! $$\bar D_O^{gb} {\mathbf{ }}\delta = 1.28 \times 10^{ - 3} f_{O_2 }^{ - 0.17} {\mathbf{ }}e^{ - 540/RT} $$ , where δ is the grain boundary width (in m), and the activation energy is in kJ/mol. Assuming δ=10-9 m (Ricoult and Kohlstedt 1983), the oxygen grain boundary diffusivities are about a factor of 30 × slower than those reported by Watson (1986) for Fo90 olivine.

Initial Stages of Epitaxial Growth of GaAs on (100) Silicon

ABSTRACTDirect observations of early stages of growth of GaAs on (100)Si are presented. Cross sectional TEM and plan view SEM images show three dimensional island growth, for growth above 300°C. Island size, island spacing, surface morphology and stacking fault defect spacing all decrease with substrate temperaturefor fixed Ga and As2 fluxes. Below 300C, 7nm thick films are uniform. Diffusion-controlled growth kinetics are inferred.