Value Of Growth Exponent Research Articles

Promoting effects of alternating current and input power on grain growth behavior of cubic ZrO2 polycrystals

AbstractThe grain growth behavior during an AC flash event was examined in 8 mol% yttria‐stabilized cubic zirconia (8Y‐CSZ) polycrystals. The effects of current/power densities on the grain growth behavior were investigated in 8Y‐CSZ samples with different specific surface areas at a constant sample temperature and applied field strength. The grain growth rate of flash‐treated 8Y‐CSZ was 300 times faster than that of heat‐treated 8Y‐CSZ at the same sample temperature in the absence of an electric current/field, suggesting that the promoted grain growth cannot be ascribed only to a thermal effect but also to an athermal effect occurring during the AC flash event. Moreover, the grain growth during the flash treatment strongly depends on the applied current/power densities and grain size; in particular, the grain growth showed enhancements with increasing applied current/power densities and for relatively small grain sizes. This result suggests that the grain boundary diffusivity of cations, which are regarded as the rate‐controlling species for grain growth, could be accelerated by tuning the current/power densities during the flash event. The grain growth mechanism was characterized using a grain growth exponent (n) value of 4.8 for the flash treatment at high current/power densities and using a conventional value of n = 3 under normal heat treatment conditions. The dependence of the grain growth behavior on the AC current/power density suggests that because the cation diffusivity is accelerated due to the formation of numerous point defects during the AC flash event, the grain growth mechanism might depend on the current/power densities and differ from that of conventional grain growth.

Synthesis, growth kinetics and ultra-sensitive performance of electrospun WO3 nanofibers for NO2 detection

WO3 nanofibers are fabricated as NO2 sensing materials by a simple electrospinning technique followed with calcination treatment. The obtained WO3 nanofibers are constructed by nanograins located along the 1 D direction. The growth kinetics of WO3 nanograins in individual nanofibers are studied by varying calcination temperatures and times. The calculated growth exponent value (n = 2.90) suggests that WO3 nanograins growth in nanofibers is developed by lattice diffusion in the pore control scheme. Subsequently, NO2 sensing performance of the as-synthesized WO3 nanofibers is evaluated, which shows excellent performance for NO2 detection at 200 °C, including high response (12.523) and fast response/recovery times (11 s/26 s) to 1 ppm NO2. Moreover, the WO3 sensor displays excellent anti-interference ability toward several interfering gases. The stability of the WO3 sensor is further confirmed by 14 days of continuous testing. Compared with previously reported works, the WO3 sensor still demonstrates outstanding gas sensing properties due to its unique advantages such as 1D nanofibrous structures, high BET surface area, and rich oxygen vacancies.

Determination of growth exponent for percolating clusters of various lattices

A computer simulation experiment has been carried out near the critical region of percolation clusters of various lattices. This certain growth exponent/spreading velocity exponent has been determined by put on the scaling theory on this percolating cluster near the critical region (i.e., P = Pc ). This exponent is named in a different way in not the same context. Owing to this enormous usage of this exponent to the real physical system, we focus our attention to find this exponent. The value of this exponent is determined for the normal conducting lattices like square, triangular & honey comb and superconducting Ortho I phase & Ortho II phase for different lattice dimensions. From the experiment it is detected that, if the concentration of the site occupancy increases, the spreading velocity or the value of growth exponent is also increases naturally. All the values are found to be less than one, indicating large spreading nature or growth nature physically as per the scaling laws. From our experiments it is found to be the exponent values fall between 0.2 and 0.5 for all lattice dimensions irrespective of lattice type.

Surface scaling behaviour of size-selected Ag-nanocluster film growing under subsequent shadowing process

Surface morphology of size-selected silver nanocluster films grown by dc magnetron sputtering has been investigated by means of an atomic force microscopy (AFM). From the height-height correlation functions obtained from corresponding AFM images, the scaling exponents are calculated and two types of growth regimes have been observed. In the first regime, the growth exponent is found to be β1 = 0.26 ± 0.01 close to the Kardar–Parisi–Zhang growth exponent, while in the second growth regime shadowing effect plays dominant role which gives the growth exponent value β2 = 0.85 ± 0.15. On the other hand for the whole deposition regime, the roughness exponent value is found to be constant around α = 0.76 ± 0.02. UV–Vis spectroscopy measurement suggests how the average reflectance of the film surface changes with different growth times.

A Comparative Study of Kinetic Models Regarding Bainitic Transformation Behavior in Carburized Case Hardening Steel 20MnCr5

Isothermal bainite transformation kinetics have been carried out and evaluated for the case hardening steel 20MnCr5 with the carbon content ranging between 0.2 and 0.8 wt pct in a wide span of isothermal temperatures. Multiple austenitization temperatures were chosen to investigate the effect of austenitic grain coarsening on the effect of transformation kinetics. Three well-known transformation kinetic equations were evaluated on more than 60 transformation curves, the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation, the Austin–Rickett (AR) equation, as well as an autocatalytic (AC) model proposed by van Bohemen. In terms of fit quality, the AR kinetic is superior, although all models show a good accordance with experimental data. The results demonstrate that the interpretability of overall activation energies can be highly ambiguous. Also, an increase for the growth exponent of JMAK/AR equations was found with a scatter of values between 1.5–4.5 and 2.0–6.0, respectively. This finding demonstrates that the value of the growth exponent cannot be interpreted in terms of growth dimension of the bainitic subunits. Furthermore, the kinetic model on a diffusionless approach was evaluated, and the activation energies were compared to work from van Bohemen. Due to the consideration of the grain size on the delay of transformation a surprisingly constant OAE was evaluated for every alloy irrespective of the austenitization temperature. Also, found OAE values are close to findings by van Bohemen with approx. 190 to 200 kJ/mol. Finally, an exponential dependency of the autocatalytic factor with respect to carbon content was proposed.

Dynamical universality classes of simple growth and lattice gas models

Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar–Parisi–Zhang (KPZ) for nonlinear, or the Edwards–Wilkinson class for linear surface growth. The autocorrelation functions of the heights and the dimer lattice gas variables are determined with high precision. Parallel random-sequential (RS) and two-sub-lattice stochastic dynamics (SCA) have been compared. The latter causes a constant correlation in the long time limit, but after subtracting it one can find the same height functions as in case of RS. On the other hand the ordered update alters the dynamics of the lattice gas variables, by increasing (decreasing) the memory effects for nonlinear (linear) models with respect to RS. Additionally, we support the KPZ ansatz and the Kallabis–Krug conjecture in dimensions and provide a precise growth exponent value . We show the emergence of finite size corrections, which occur long before the steady state roughness is reached.

Synthesis of CdS thin films at room temperature by RF-magnetron sputtering and study of its structural, electrical, optical and morphology properties

Thin films of cadmium sulfide (CdS) have been deposited at room temperature by using RF-magnetron sputtering at various deposition times. Films were systematically investigated using variety of techniques such as low angle XRD, UV–Visible spectroscopy, Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDAX), atomic force microscopy (AFM), transmission electron microscopy (TEM), four probe Van der Pauw method etc. Low angle XRD and TEM analysis revealed that films are polycrystalline having constant average crystalline size. EDAX revealed the formation of nearly stoichiometric CdS films. Surface morphology of CdS films examined using SEM shows the formation of smooth, continuous and dense films without defects such as cracks, pinholes, and protrusion. RMS roughness estimated using AFM increases with increase in deposition time. The optical studies showed decrease in band gap with increase in deposition time. The photodetector fabricated using RF sputtered CdS film show an excellent photo-response. Estimated value of growth exponent β was found ~0.53 which suggests uncorrelated growth of CdS films by RF sputtering. The uncorrelated growth of CdS was further confirmed by Monte-Carlo simulation.

Effect of Nano-TiO2 particles on growth of interfacial Cu6Sn5 and Cu3Sn layers in Sn[sbnd]3.0Ag[sbnd]0.5Cu[sbnd]xTiO2 solder joints

In this study, the effect of nano-TiO2 particles additive on the growth of interfacial Cu6Sn5 and Cu3Sn intermetallic compound (IMC) layers between Sn3.0Ag0.5CuxTiO2 solder and Cu substrate was investigated under different isothermal aging temperatures of 120 °C, 150 °C, and 190 °C. Scanning electron microscopy (SEM) was adopted to observe the morphological evolution of interfacial IMC layers. The composition and phase of the IMCs were identified by energy-dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD), respectively. Results show that the morphology of the Cu6Sn5 transformed from scalloped to plate-like after solid-state aging, while that of the Cu3Sn phase remains the layer-type. Nano-TiO2 particles have a strong influence on the growth of both the Cu6Sn5 and Cu3Sn IMC layers. The thickness of Cu3Sn layer increases promptly with aging temperature and time, while that of Cu6Sn5 layer increases slowly. This might be due to the Cu3Sn grows at the expense of Cu6Sn5 layer. The growth exponent value of the Cu6Sn5 layer ranges from 0.52 to 0.8, while that of the Cu3Sn ranges from 0.45 to 0.64. The addition of nano-TiO2 significantly affected the Cu6Sn5 layer growth, but very little influence on the growth of Cu3Sn layer, especially at the low aging temperature. The activation energies for the Cu6Sn5 and Cu3Sn layers are the range of 14.91 kJ/mol to 20.95 kJ/mol and 85.51 kJ/mol to 86.23 kJ/mol, respectively. Adding 0.1 wt% nano-TiO2 to Sn3.0Ag0.5Cu solder exhibits the smallest growth rate for both the two IMC layers and gives the most prominent effect in suppressing IMC growth. Based on the theory of adsorption, grain boundary pinning is one of the most important mechanisms for regarding the Cu6Sn5 and Cu3Sn growth when nano-TiO2 is added.

Grain growth kinetics for B2O3-doped ZnO ceramics

Abstract Grain growth kinetics in 0.1 to 2 mol % B2O3-added ZnO ceramics was studied by using a simplified phenomenological grain growth kinetics equation Gn = K0 · t · exp(-Q/RT) together with the physical properties of sintered samples. The samples, prepared by conventional ceramics processing techniques, were sintered at temperatures between 1050 to 1250 °C for 1, 2, 3, 5 and 10 hours in air. The kinetic grain growth exponent value (n) and the activation energy for the grain growth of the 0.1 mol % B2O3-doped ZnO ceramics were found to be 2.8 and 332 kJ/mol, respectively. By increasing B2O3 content to 1 mol %, the grain growth exponent value (n) and the activation energy decreased to 2 and 238 kJ/mol, respectively. The XRD study revealed the presence of a second phase, Zn3B2O6 formed when the B2O3 content was > 1 mol %. The formation of Zn3B2O6 phase gave rise to an increase of the grain growth kinetic exponent and the grain growth activation energy. The kinetic grain growth exponent value (n) and the activation energy for the grain growth of the 2 mol % B2O3-doped ZnO ceramics were found to be 3 and 307 kJ/mol, respectively. This can be attributed to the second particle drag (pinning) mechanism in the liquid phase sintering.

Kinetic identification and experimental validation of continuous plug flow crystallisation

This paper investigates the suitability of a number of potential crystallisation models to best describe the experimentally observed behaviour of the antisolvent crystallisation of benzoic acid from aqueous ethanol solution using water as an antisolvent, in a continuous plug flow crystalliser. The system is modelled using a population balance model incorporating nucleation and growth kinetics. Three separate population balance models have been assessed using a variety of growth models (size-independent growth, growth rate dispersion through random fluctuation growth, and constant crystal growth). The prediction from the growth rate dispersion model with constant crystal growth kinetics shows good agreement with the experimental results. In this model, growth rate is described by a normal power law of the absolute supersaturation and the value of growth exponent was estimated as 1.09. The value of the exponent in the expression that describes the relationship between the coefficient of variation of the growth activity distribution and supersaturation is estimated to be 0.09 and as a result this would indicate that there is a weak dependence on supersaturation. The same model was then validated at different residence times and the results demonstrate good agreement between the simulated and experimental results. Estimated parameters were then utilised to simulate the evolution of weighted mean crystal size and crystal size distribution, with residence times under a different supersaturation condition.

Dynamic scaling of swift heavy ion induced surface restructuring of BaF2 thin film

Dynamic scaling of swift heavy ions induced cracks in the nanodimensional BaF2 thin films is studied using 100MeV Au+8 ions at different ion fluences. Atomic force micrographs show that, up to a fluence of 1×1012 ions/cm2, the surface morphology is almost unchanged from virgin film, but thereafter, the formation of cracks is seen. The dimensions and density of the cracks is found to increase with increase in ion fluence. Dynamic scaling of surfaces demonstrates that the surface roughness exponent (α) values are in the range of 0.2–0.5. The growth exponent values are found to be β=0.10±0.03 and 1.1±0.1 for continuous and cracked surfaces, respectively. Shift of X-ray diffraction peaks after irradiation indicates contribution of tensile stress in the crack evolution with ion fluence.

Effect of Heat Treatment on Grain Growth of Beta Titanium Alloy

One of the disadvantages of β-Ti alloys is rapidgrain coarsening at elevated temperatures due to accelerated diffusion in the βphase region. Microstructural stability of β-Ti alloys would depend on theirability to maintain refined grains or microstructures at high temperatures. Thebeta grain growth kinetics of a newly designed beta titanium alloy has beensystematically investigated in this research. The grain growth exponent (n) value is at the range of 0.1-0.2,about 0.1 at low temperatures and about 0.2 at high temperatures over 950°C. Itis lower than other beta titanium alloys. The reason of lower n values can be investigated in the viewof the solute and the diffusivity in the titanium matrix.

3D MС Simulation of Grain Growth Kinetics and the Zener Limit in Polycrystals

Large scale Potts model Monte Carlo simulation was carried on 3-dimensional square lattices of 1003 and 2003 sizes using the Metropolis algorithm to study grain growth behavior. Simulations were carried out to investigate both growth kinetics as well as the Zener limit in two-phase polycrystals inhibited in growth by second phase particles of single-voxel size. Initially the matrices were run to 10,000 Monte Carlo steps (MCS) to check the growth kinetics in both single phase and two-phase poly-crystals. Grain growth exponent values obtained as a result have shown to be highest (~ 0.4) for mono-phase materials while the value decreases with addition of second phase particles. Subsequently the matrices were run to stagnation in the presence of second phase particles of volume fractions ranging from 0.001to 0.1. Results obtained have shown a cube root dependence of the limiting grain size over the particle volume fraction thus reinforcing earlier 3D simulation efforts. It was observed that there was not much difference in the values of either growth kinetics or the Zener limit between 1003 and 2003 sized matrices, although the results improved mildly with size.

Crystallization And Grain Growth Behavior Of La2O3-doped Yttria-stabilized Zirconia

The effect of La2O3 addition on the microstructure and grain growth behavior of yttria-stabilized zirconia (8YSZ) was investigated. To this end, 8YSZ was doped with 1-15 wt% La2O3 by means of colloidal processing, and then sintered at 1550 °C for 1 h. XRD results identified a dissolution limit of 5 wt% La2O3 in 8YSZ, the insoluble La2O3 at higher concentrations reacting with ZrO2 during sintering to form a secondary La2Zr2O7 phase. Both undoped and La2O3-doped 8YSZ specimens were annealed at 1400, 1500, and 1600 °C for 10, 50, and 100 h to induce grain growth. Grain growth measurement results showed that an increase in annealing temperature and holding time caused to grain growth in all specimens. Excessive grain growth was observed in the case of the undoped, and 1-5 wt% La2O3-doped 8YSZ specimens; however, the grain growth in 10 and 15 wt% La2O3-doped 8YSZ was inhibited by the formation of a pyrochloric La2Zr2O7 secondary phase around the grains and grain boundaries of 8YSZ. Grain growth exponent (n) and activation energy (Q) values for grain growth of undoped 8YSZ were obtained as 3, and 358 kJ/mol, respectively, while 15 wt% La2O3 containing specimens had a grain growth exponent of 3, and activation energy of 413 kJ/mol. These results indicate that grain growth rate can be controlled by the addition of 10 or 15 wt% La2O3. Copyright © 2014 VBRI press.

Effect of temperature on grain growth kinetics of high strength Ti–2Al–9.2Mo–2Fe alloy

Abstract Grain growth behaviors of a beta titanium alloy (Ti–2Al–9.2Mo–2Fe) have been systematically investigated for various temperatures. Quantitative evaluations of the grain growth kinetics over a wide range of temperatures from 820 °C to 1000 °C have been performed. The results showed that the isothermal grain growth kinetics followed the normal growth behavior. The solution-treated alloy at lower temperatures (820–900 °C) exhibited a good uniformity of the grain size. It showed a poor uniformity of the grain size due to the abnormal grain growth at higher temperatures (950–1000 °C). The grain growth exponent values ( n ) were at the range of 0.1–0.2, about 0.1 at lower temperatures and about 0.2 at higher temperatures. They were lower than other beta titanium alloys. The lower exponent values ( n ) and the higher activation energy ( Q ) can be attributed to the solute drag effect and the high Mo content with low diffusivity in Ti matrix.

Sintering behavior and non-linear properties of ZnO varistors processed in microwave electric and magnetic fields at 2.45 GHz

A study of the densification behavior and grain growth mechanisms of ZnO-based varistors composed of 98mol.% ZnO–2mol.% (Bi2O3, Sb2O3, Co3O4, MnO2) has been carried out. The pressed samples were sintered in microwave electric (E) and magnetic (H) fields using a single-mode cavity of 2.45GHz. The effect of the sintering temperature (900–1200°C), holding time (5–120min) and sintering mode (E, H) on the microstructure and electrical properties of the sintered varistor samples were investigated. The grain growth kinetics was studied using the simplified phenomenological equation Gn=kte(−Q/RT). The grain growth exponent (n) and apparent activation energy (Q) values were estimated for both electric and magnetic heating modes and were found to be n=3.06–3.27, Q=206–214kJmol−1, respectively. The lower value of n estimated in the E field was attributed to a volume diffusion mechanism, whereas the higher n value in the H field sintering was correlated mainly to a combined effect of volume and surface diffusion processes. Samples sintered in the H and E fields showed high final densities. Moreover, the ones sintered in the H field presented slightly higher density values and bigger grains for all sintering temperatures than E field heated ones. The optimal sintering conditions were achieved at 1100°C for a 5min soaking time for both H and E field processed samples, where respectively densities of 99.2±0.5% theoretical density (TD) and 98.3±0.5% TD along with grain size values of G=7.2±0.36μm and G=6.6±0.33μm were obtained. Regarding the electrical properties, breakdown voltage values as high as 500–570Vmm−1 were obtained, together with high non-linear coefficients α=29–39 and low leakage currents (Jl≈5×10−3mAcm−2), respectively, for E and H field sintered varistor samples. Moreover, samples sintered in an H field systematically exhibited higher breakdown voltage values compared to the ones sintered in the E field. This was attributed to an improved coupling between the H field and the present dopants within the ZnO matrix, this latter being mostly semiconductive, thus leading to an enhanced reactivity and improved properties of the electrostatic barrier.

Formation and modifications of nanostructures of tin oxide by SHI irradiation

We deposited thin films of tin oxide (SnO2) by the thermal evaporation method on quartz and Si substrates. The as-deposited films were irradiated using 100 Mev Ag ions at different fluences ranging from 1×1012 to 1×1013 ions/cm2. Pristine and irradiated films were characterized for surface topographical study using atomic force microscopy. Pristine films on both types of substrates (Si and Quartz) are featureless. Irradiation at the lowest fluence (1×1012 ions/cm2) induces the nanostructures at the surface and higher fluence irradiations change the shape and size of these nanostructures. The value of roughness and growth exponent, as evaluated from power spectral density analysis, indicates that the formation of nanostructures is mainly due to the swift heavy ion-induced surface diffusion process. We have tried to explain the results in the framework of the thermal spike model.

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G I and G II using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = − 1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G I since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.

Swift heavy ion-induced surface nanopatterning of indium oxide films

In this study, indium oxide films are deposited by electron-beam evaporation and thermally annealed at 600°C in an oxygen atmosphere to form stoichiometric In2O3 films with a high transparency. They are then irradiated with 120 MeV Ag ions with different fluences (i.e. 1×1011, 1×1012 and 1×1013 ions/cm2). The morphology of the films as a function of fluence is studied by atomic force microscopy and the root mean square roughness values are obtained. The pristine film consists of uniformly-sized particles distributed over the sample surface. On irradiation with 1×1011 ions/cm2, fragmentation of these particles takes place. These fragmented particles start to agglomerate and align slightly in a particular direction at a fluence of 1×1012 ions/cm2. Morphology is further confirmed by scanning electron microscopy. A two-dimensional power spectral density analysis has been done to elucidate the topographical changes due to varying ion fluences. The growth exponent value of α>1 suggests that the growth is governed by surface diffusion.

Sintering behavior of Zn–Pr–Co–Mn–O varistor ceramics

Sintering and grain growth of Pr 6O 11-based ZnO varistors were investigated in detail over a range of temperature and holding time. The grain growth kinetics in the Zn–Pr–Co–Mn–O system was studied using the simplified phenomenological grain growth kinetics equation: G n − G 0 n = K 0 t exp (− Q/ RT) together with the physical properties of the sintered samples. From 1050 °C to 1300 °C, the grain growth exponent value ( n) and the apparent activation energy for this system were found to be approximately 3.7 and 306 ± 61 kJ/mol respectively. Highly densified ceramics sintered at 1300 °C for 4 h were obtained, reaching about 96% of theoretical density (TD = 5.78 g/cm 3). These values are compared with those obtained for Bi 2O 3-based ZnO varistors. The maximum nonlinear exponent ( α = 54.7) was obtained at a sintering temperature of 1275 °C.