Kolmogorov–Johnson–Mehl–Avrami kinetics for non-isothermal phase transformations ruled by diffusional growth

We report on the functional form of the rate of the transformed volume fraction in non-isothermal phase transitions occurring by nucleation and diffusional growth. The microscopic growth rate is computed by solving the diffusion problem for time-dependent diffusion coefficient. The growth law is further employed in the Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory for describing the time dependence of the transformed volume at constant heating rate. It is demonstrated that the transformation rate separates in the product of volume fraction and actual temperature functions. In the framework of the KJMA approach this factorization is exact. It is also shown that for real systems (due to the high values of the reduced activation energies for nucleation and growth), the kinetics is in excellent agreement with the stretched exponential function appropriate for isothermal transformations.     

As2Se3 melt crystallization studied by quadratic approximation of nucleation and growth rate temperature dependence

The constant heating rate crystallization of As₂Se₃ undercooled melt was measured by the differential scanning calorimetry. The nonlinear regression analysis of conversion temperature dependence was performed in frame of the classical nucleation theory supposing the normal 3D growth. The parameters of temperature dependence of nucleation rate and growth rate were determined by three step process. First the simple parabolic model was used to estimate the maximum and width of nucleation/growth rate temperature dependence. Then the obtained parabolic curves were fitted by the theoretical ones. In the third step, the obtained parameters were used as zero estimates for nonlinear regression analysis of experimental data. The results obtained by using conversion degree α were compared with the results obtained by using the ?ln(1 ? α) transformed function. Although both treatments give comparable results the use of ?ln(1 ? α) input data is preferred due to better numerical stability of nonlinear regression treatment.     

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

Nucleation and crystal growth in Na2O · 2 CaO · 3 SiO2 glass: a DTA study

The non-isothermal devitrification of Na₂O · 2 CaO · 3 SiO₂ glass has been studied by differential thermal analysis in order to evaluate, from DTA curves, the temperature of maximum nucleation rate, T_m, and the activation energy values, E_c, for crystal growth.The temperature, T_m=580°C, is very close to the glass transition temperature, T_g=570°C, and the value of E_c=78 Kcal mole^?1 for the surface crystal growth is nearly the same as the value E_c=89 kcal mole^?1 for the bulk crystal growth; both are consistent with the activation energy for viscous flow. It is also pointed out that the nucleation rate—temperature curve and the crystallization rate—temperature curve are partially overlapped.     

最快结晶速率温度与结晶参数的关系

以经典的结晶速率与温度的关系为基础,对T_(c,max)与结晶参数的关系进行了研究.结果表明,T_(c,max)同平衡熔融温度(T_m)的比值仅与成核参数(φ)同扩散活化能(E_d)之比有关.高聚物的结晶过程可用二次成核模型近似.当结晶速率与温度的关系采用下式时 G=G_0exp[-E_d/RT-φT_m~2/T~2(T_m-T)]T_(c,max)与结晶参数的关系为 T_(c,max)=2/3T_m[1-(1+9α)~(1/2)cos(1/3)arccos1/(1+9α)~(3/2)+240°]或 α=φR/E_d=T_(c,max)(T_m-T_(c,max)~2/T_m?2(3T_(c,max)-2T_m)     

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

The homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. The whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m=3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids 160, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.     

Step-like change of the growth rate of primarily nucleated centres in the film formation of camphor

The theoretical time dependence of the surface coverage θ_f is derived for the case of film formation according to two-dimensional instantaneous nucleation and growth with a step-like change in the growth rate. By means of double potential step experiments it is shown that the experimental time dependence of θ_f for the formation of a camphor film can be described by the model considered.     

Equilibrium melting temperature and spherulitic growth rate of poly(phenylene sulfide)

The equilibrium melting temperature (T_m), through linear extrapolation method (HW) and nonlinear extrapolation method (MX) respectively, and the supercooling dependence of the spherulitic growth rate, in the context of the Lauritzen-Hoffman secondary nucleation theory, of poly(phenylene sulfide) (PPS) have been investigated by differential scanning calorimeter (DSC) and a polarized optical microscope (POM) equipped with a CSS450 shear hot stage. The results show that the T_m value obtained by MX method is more suitable for analyzing the regime transition behavior of PPS than that by HW method. And the regime I/II and II/III transitions can be really observed at T_X = 526 and T_X = 516 K, respectively, while analyzing the secondary nucleation theory of PPS by use of the T_m value obtained by MX method.     

Impact of plasticizers and tackifiers on the crystallization of isotactic poly(1-butene)

Crystallization of a semi-crystalline polyolefin in the presence of low molecular weight modifiers was quantified by differential scanning calorimetry and optical microscopy. The polyolefin was a commercial grade of isotactic poly(1-butene) (iPB). Two modifiers were used: an oligomeric plasticizer, designated HOAO, which decreased the glass transition temperature (T_g) of the system, and an oligomeric tackifier, designated HOCP, which increased T_g. Binary iPB/modifier blends containing 10% or 20% by weight of HOAO or HOCP were examined to determine how their addition affects T_g, while ternary iPB/HOAO/HOCP blends containing 10% or 20% by weight of total modifier were examined to determine the effects of dilution by using a ratio of HOAO to HOCP that matched the T_g of iPB. The addition of modifier decreased the nucleation rate, spherulitic crystal growth rate, and final crystallinity of each blend. However, only the nucleation rate showed a dependence on the type of modifier, with nucleation retarded more by HOCP than by HOAO. A Hoffman-Weeks analysis of the melting point as a function of crystallization temperature confirmed that the driving force for nucleation was reduced, and that the effect was larger for HOCP. An Avrami analysis of the bulk crystallization kinetics was consistent with these observations, as the Avrami exponents were in the range of 3-4.     

Parameters of the temperature dependence of the rate of magnetic relaxation of protons in water and its solutions including seawater

The results of measurements of the temperature dependence of the relaxation rate (1/T ₁) of protons in seawater with 35‰ salinity and salt solutions with different concentrations at temperatures from ?22°C to +120°C are presented. The possibility of approximating the temperature dependence of the magnetic relaxation rate by different functions in pure water, seawater, and solutions of the salts of the latter was studied. The parameters of this dependence and their variation under the influence of salt components are given. The least mean square deviation was obtained, and the best convergence was determined according to the statistical criteria for aqueous electrolytes of moderate concentrations for the function in the form of the sum of exponentials, in which the number of terms depended on the solution concentration. It is shown that the parameters of the thermal dependence of the relaxation rate represented by different functions can be used in combination for studying the dynamic properties of the solutions of low and moderate concentrations.     

Determining the nucleation rate from the dimer growth probability

A new method is proposed for the determination of the stationary one-component nucleation rate J with the help of data for the growth probability P2 of a dimer which is the smallest cluster of the nucleating phase. The method is based on an exact formula relating J and P2, and is readily applicable to computer simulations of nucleation. Using the method, the dependence of J on the supersaturation s is determined by kinetic Monte Carlo simulations of two-dimensional (2D) nucleation of monolayers on the (100) face of Kossel crystal. The change of J over nearly 11 orders of magnitude is followed and it is found that the classical nucleation theory overestimates the simulation J values by an s-dependent factor. The 2D nucleus size evaluated via the nucleation theorem is described satisfactorily by the classical Gibbs-Thomson equation and its corrected version accounting for the spinodal limit of 2D nucleation.     

Growth dynamics of CdTe nanoparticles in liquid and crystalline phases

Normally the size dependence of the chemical potential is used to explain the growth dynamics of semiconductor nanoparticles. Instead we show that very small CdTe nanoparticles continue to grow at high dilution, the growth rate is virtually independent of monomer concentration, nucleation continues after the growth of larger particles has saturated, and the growth rate has a much greater nonlinear dependence on particle size than predicted by theory. We suggest that nanoparticle growth is fast in the liquid phase and then saturates as the particles change phase from liquid to crystal at a threshold size which depends on the growth temperature and not the monomer concentration. The photoluminescence quantum efficiency becomes high when tellurium is depleted in the reaction solution giving a cadmium enriched surface.     

A study of homogeneous nucleation of ibuprofen in a flow chamber. Determination of the surface tension of critical nuclei

Homogeneous nucleation of ibuprofen vapor is studied in a nucleation flow chamber, a horizontal quartz tube equipped with an external heater. The area of the chamber where the nucleation proceeds most efficiently is determined, and the volume of this area is estimated. The temperature and supersaturation are determined and the homogeneous nucleation rate is calculated for this area. Saturation vapor pressure over liquid ibuprofen is measured in a temperature range of 353–383 K. Using an exact formula that has recently been derived for the nucleation rate based on the works by Kusaka, Reiss, as well as the Frenkel liquid-kinetics theory, surface tension and the radius of surface of tension of a critical nucleus σ= 25.9 mN/m and R _s = 1.6 nm, respectively, are calculated at 318 K. The measurement of the surface tension of an ibuprofen planar surface shows that, at 318 K, σ_∞ = 24.38 mN/m; i.e., σ is higher than σ_∞ by 6%. A critical nucleus is established as containing nearly 36 ibuprofen molecules.     

Low temperature structural transformation in T[Ni(CN)4]·xpyz with x=1,2; T=Mn,Co,Ni,Zn,Cd; pyz=pyrazine

The materials under study are pillared solids T[Ni(CN)₄]·xpyz with one and two (x=1,2) pyrazine (pyz) molecules and where T=Mn, Co, Ni, Zn, Cd. Stimulated by their structural features and potential role as prototype of porous solids for hydrogen storage, the structural stability under cryogenic conditions for this series of pillared solids was studied. At low temperature, in the 100-200 K range, the occurrence of a reversible structural transformation was found. For T=Mn, Co, Zn, Cd, with x=2, the structural transformation was observed to occur around 185 K, and the low temperature phase crystallizes with a monoclinic unit cell (space group Pc). This structure change results from certain charge redistribution on cooling within the involved ligands. For T=Ni with x=1, both the low and high temperature phases crystallize with unit cells of tetragonal symmetry, within the same space group but with a different unit cell volume. In this case the structure change is observed around 120 K. Above that temperature the rotational states for the pyrazine molecule are thermally excited and all the pyrazine molecules in the structure become equivalent. Under this condition the material structure is described using a smaller structural unit. The structural study using X-ray powder diffraction data was complemented with calorimetric and Raman spectroscopy measurements. For the low temperature phases the crystal structures were solved from Patterson methods and then refined using the Rietveld method.     

Study of solid state reactions in Nb/Al multilayer thin films

Solid state reactions of sputter-deposited Nb/Al multilayer thin films, with periodicities in the range 10–333 nm, have been studied by differential scanning calorimetry. The first phase to form upon annealing the films in NbAl₃. Constant-heating-rate calorimetric measurements show the presence of two peaks for the formation of this phase, while isothermal scans reveal that the first peak is associated with a nucleation and growth type transformation. The formation of NbAl₃ is thus interpreted as a two-stage process of nucleation and growth to coalescence (first peak) followed by growth until the consumption of one or both reactants (second peak).We thank NSF for support through DMR-9308651, K. Coffey, S. Vivekanand and B. Gadicharla for assistance and TA Instruments for the donation of a 1600°C furnace.     

Prediction of phase equilibria and thermodynamic properties of refrigerant/oil solutions

A method for estimation of the phase equilibrium, density, enthalpy, heat of vaporization and molecular weight of refrigerant/oil solutions (ROS) is proposed in this paper. The method is based on the theory of thermodynamic similarity, since refrigerant/oil solutions appear to be thermodynamically similar in the region of the refrigerant mass concentrations: 0.3≤w_R≤1.0. The initial information is the concentration dependence of the temperature of the normal boiling point, the concentration dependence of the density in very narrow temperature ranges, and the temperature dependence of the isobaric heat capacity of the liquid phase of the pure oil. On the basis of this information, the proposed method allows calculation of all the above-mentioned properties. Modeling of thermodynamic properties of the ROS requires data on pseudocritical properties and molar weight. Hence, the method of estimation of these properties is proposed.     

Membrane structure control of BTDA-TDI/MDI (P84) co-polyimide asymmetric membranes by wet-phase inversion process

The formation process and morphology of BTDA-TDI/MDI co-polyimide (P84, CAS#: 58698-66-1) asymmetric flat sheet membranes have been studied. Experimental results indicated that the weight ratio of H₂O and N-methyl-2-pyrrolidone (NMP, CAS#: 872-50-4) at cloud point curve (above critical point) was a constant (7.66/92.34 (w/w)) for the P84/NMP/H₂O system. For two different casting solutions (21 wt.% P84 in pure NMP; 15 wt.% P84 in H₂O/NMP: 6.0/94.0 (w/w)), the approaching ratio α strongly dominated the formation of finger-like structure rather than the viscosity of casting solution. The formation of finger-like structure in P84 co-polyimide asymmetric membranes was due to the hydrodynamically unstable viscous fingering developed when the casting solution was displaced by a polymer-lean phase. Three types of membrane morphologies, finger-like structure, transition structure and sponge-like structure can be expected with various approaching ratio α of casting solutions. The critical approaching ratio α^* was initially defined to describe the sharp change of membrane morphology from finger-like to sponge-like structure. The casting temperature also influenced the membrane morphology. For some casting solutions (e.g. 15 wt.% P84 in H₂O/NMP: 6.4/93.6 (w/w)), the membrane morphology changed from sponge-like to finger-like structure with an increase in casting temperature. Meanwhile, the critical approaching ratio α^* also increased with an increase in casting temperature.     

冷冻过程中胞内溶液均相成核温度的确定

为了研究冷冻过程中胞内溶液均相成核温度下降值与平衡凝固点下降值的关系, 提出了一种求解变组元系统成核温度的方法, 并联合细胞脱水方程, 进行了数值求解. 研究发现, 甘油-氯化钠-水三元系统的均相成核温度下降与平衡凝固点下降存在如下的线性关系: ⊿Th=1.17⊿Tm, 表明水溶液均相成核温度与溶质有关.     

Temperature effects for isothermal polymer crystallization kinetics

We adopt the cluster size distribution model to investigate the effect of temperature on homogeneous nucleation and crystal growth for isothermal polymer crystallization. The model includes the temperature effects of interfacial energy, nucleation rate, growth and dissociation rate coefficients, and equilibrium solubility. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different temperatures. The denucleation (Ostwald ripening effect) is also investigated by comparing moment and numerical solutions of the population balance equations. Agreement between the model results and temperature-sensitive experimental measurements for different polymer systems required strong temperature dependence for the crystal-melt interfacial energy.     

Bulk and solution crystallization kinetics of isotactic polybutene-1

The crystallization kinetics of an unfractionated sample of isotactic polybutene-1 have been studied from the melt and from dilute solutions in amyl acetate by the dilatometric method. The kinetics of bulk crystallization followed the Avrami equation for most of the transformation with a deviation towards the end of the crystallization process. The Avrami exponent is found to be temperature dependent with the value of n ≈ 3 at high undercooling (indicating a homogeneous nucleation process) and n ≈ 4 at lower undercooling (indicating a heterogeneous nucleation process). The temperature coefficients of the rate constants indicate a nucleation controlled process of crystallization.