Analytical Calculation of Solidification of a Melt in a Mold

The mathematical method of investigation of the process of crystallization of a molten metal in a two-dimensional mold has been developed using the variational formulation of the problem with determination of the velocity of motion of the crystallization front and the solidified-metal thickness at any instant of time.     

Simulation of the thermal state of a billet from casting to rolling

A mathematical model is given for the thermal treatment of a billet for rolling, in which the crystallization, cooling, and reheating are considered as stages in a single process.     

Mechanical properties of uniaxially oriented syndiotactic polystyrene

Syndiotactic polystyrene has been oriented by uniaxially drawing at temperatures near the glass transition temperature, starting with amorphous material produced by quenching from the melt. The hot drawing process involves concurrent crystallization and orientation. Increasing crystallinity by itself does not affect the mechanical properties to any large extent. The orientation process is shown to substantially increase the strength and modulus in the draw direction. The anisotropy of mechanical properties is compared to mathematical models: the modulus using Arridge's model for oriented block copolymers, and the tensile strength using both the Hill-von Mises yield criterion and a modified fiber composite analog.     

On the kinetics of crystallization of silicalite I

It has been shown that the linear rate of crystal growth of silicalite I is constant during the stationary crystallization stage and independent of the crystal size. With rising temperature of crystallization, the linear rate of crystal growth increases significantly and the crystal habit changes. By means of the activation energy data for the linear crystal growth, the linear growth rate has been proposed to be the limiting step of the crystallization process.     

用差示扫描量热法研究Mg65Cu25Gd10块体非晶合金的晶化动力学

通过铜模吸铸法得到Mg65Cu25Gd10块体非晶舍金，用差示扫描量热仪（DSC）研究其晶化动力学和玻璃转变行为，玻璃转变温度Tg，晶化起始温度Tx，晶化峰值温度Tp都与加热速率有关，通过Kissinger方程可以得到表面激活能，发现晶化初始激活能Ex小于峰值激活能Ep，表明形核过程比生长过程容易，讨论了此非晶舍金的玻璃形成能力，根据JMA方程非等温模型研究了晶化动力学，Avrami参数表明在不同温度下的晶化机制是不同的．     

一水柠檬酸降温结晶工艺研究

针对影响一水柠檬酸降温结晶的各个控制点进行研究,并对结晶工艺参数进行优化,采用优化后的降温结晶工艺可以得到颗粒较大且均匀的一水柠檬酸晶体。     

Function space theory of dynamic nucleation during solidification at high cooling rates

An analytical theory is proposed to study the dynamic nucleation of crystals from melt at very high cooling rates (10⁻⁶ to 10⁻¹² °K/sec). The mathematical framework is found to be isomorphic with the function space theory, wave and matrix mechanics, which enables application of various approximate methods of the latter disciplines. In principle, the mathematical apparatus and concepts of function space and wave mechanics can be utilized to study the time varying nucleation process. The Arrhenius law has been used to extrapolate the self-diffusion coefficient as a function of temperature above the melting point than those below. Since, applicability of Arrhenius equation at very high degrees of supercooling is not known and has to be substituted with appropriate constitutive relationship based on free volume theory of transport, the conclusion derived from the present analysis will not be unique with respect to the certainty of crystallization during the solidification process.     

HDPE材料冷却过程的结晶动力学模型及其微分方程

根据高密度聚乙烯(HDPE)高聚物冷却时结晶和晶体分解两种动力学趋势相互竞争的观点,建立了HDPE材料冷却结晶的物理模型,引入了结晶过程中的物质结构参数概念。从模型推导出了描述该结晶过程的微分方程,并将其转换成熟知的Ricatti方程来求得解析解。模型中参数可以由实验来确定,方程中的温度变化本身是时间的一般函数,故在应用中可以不必区分结晶系统是否等温。     

Two-stage crystallization kinetics equation and nonisothermal crystallization analyses for PTEG and filled PTEG

A novel modified Avrami model considering both primary and secondary crystallization has been presented to extract the kinetic behavior of these two crystallization stages in nonisothermal crystallization process of polymers. Nonisothermal crystallization kinetics of poly(trimethylene terephthalate)–poly(ethylene glycol) segmented copolyesters (PTEG) has been investigated by differential scanning calorimetry. The crystallization rate constants and Avrami exponents at various cooling rates were obtained from the analyses for neat PTEG and multiwalled carbon nanotube (MWNT) filled PTEG. Secondary crystallization displays a lower-dimensional crystal growth compared with primary crystallization and the results of kinetics analyses are consistent with morphology study. The MWNTs introduced into PTEG matrix take the role of effective nucleating agents during composites crystallization and can expedite the process of crystallization of the matrix by providing more nucleation sites to the crystallizing phase.     

Mathematical models of heat transport in processes to obtain refractory single crystals

Simplified mathematical models are considered for horizontal and vertical directional crystallization methods, as are programs to compute the process on an electronic computer, and the regularities disclosed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 2, pp. 359–363, February, 1981.     

Progress of Pharmaceutical Continuous Crystallization

Crystallization is an important unit operation in the pharmaceutical industry. At present, most pharmaceutical crystallization processes are performed in batches. However, due to product variability from batch to batch and to the low productivity of batch crystallization, continuous crystallization is gaining increasing attention. In the past few years, progress has been made to allow the products of continuous crystallization to meet different requirements. This review summarizes the progress in pharmaceutical continuous crystallization from a product engineering perspective. The advantages and disadvantages of different types of continuous crystallization are compared, with the main difference between the two main types of crystallizers being their difference in residence time distribution. Approaches that use continuous crystallization to meet different quality requirements are summarized. Continuous crystallization has advantages in terms of size and morphology control. However, it also has the problem of a process yield that may be lower than that of a batch process, especially in the production of chirality crystals. Finally, different control strategies are compared.     

Crystallization kinetics of Zr-33 at % Ni amorphous alloy

The amorphous to crystalline transition in Zr-33 at% Ni amorphous alloy has been found to occur by polymorphic crystallization. The product of the cyrstallization process has been identified as the equilibrium Zr₂Ni intermetallic phase. The kinetics of crystallization have been studied independently using differential scanning calorimetry (DSC) and transmission electron microscopy. The activation energy of crystallization has been evaluated by isothermal and continuous heating in DSC. The isothermal anneals have revealed that the crystallization follows the Johnson-Mehl-Avrami kinetics with an Avrami exponent close to 4. The microstructural changes accompanying crystallization have been studied for an interpretation of the Avrami exponent. The nucleation and growth rates of crystals have been estimated at different temperatures in order to determine the activation energies of the two processes. It has been found that nucleation is thermally activated and growth is interface controlled.     

Development and validation of a two-dimensional population balance model for a supercritical CO2 antisolvent batch crystallization process

In this study, a two-dimensional population balance model with solvent removal kinetics has been developed to predict the dynamic behavior of carbamazepine form II crystals produced by a supercritical CO₂ antisolvent batch crystallization process. The model was simulated and validated using experimental crystal size distribution data (CSD). The model was able to accurately predict the behavior of CSD with a change in process operating conditions. The model was also applied to study the time evolution of aspect ratio, average crystal length, and solute concentration in the solution. Finally, solvent removal kinetics were modeled to evaluate the solvent content and drying temperature of the drying gas during the solvent removal process. The developed mathematical model and the presented results suggest the ability of the discussed approach to make suitable model predictions, which can significantly reduce the number of experimental trials required for process design, optimization, and control.     

PET/有机蒙脱土纳米复合材料等温结晶动力学过程研究

用DSC方法研究了具有反应活性的有机蒙脱土与聚对苯二甲酸乙二酯（PET）原位聚合和熔融共混后的两种插层复合材料的等温结晶行为。结果表明，有机蒙脱土起异机成核作用，使PET的结晶过程更加复杂，对聚合样由于有机处理剂参与PET链的反应，特殊的结构有利于成核过程，但对总的结晶速率有一定影响，结晶速率的提高程度依赖于有机蒙脱土的添加量；有机蒙脱土使共混样品的结晶速率大大加快。     

Isothermal Crystallization Kinetics of an Amorphous CuTi Alloy

Isothermal crystallization kinetics ofCu_(40)Ti_(60)amorphous alloy has been studied usingdifferential scanning calorimetry(DSC).Bothas-quenched and pre-annealed ribbons were inves-tigated.For crystallization of as-quenched amor-phous ribbon in Ar,it was found that the kineticsfollows Johnson-Mehl-Avrami equation withmean Avrami exponent n=2.58,which indicatesthat crystallization of amorphous Cu_(40)Ti_(60)is athree-dimensional diffusion controlled growth pro-cess with constant nucleation rate,i.e.,primarycrystallization process.The primary phase is thetetragonal CuTi_2.The as-quenched amorphousribbons were also crystallized in air,the results re-veal that oxidation has no significant influence oncrystallization kinetics of amorphous Cu_(40)Ti_(60).The results of crystallization of pre-annealed rib-bons show a decreasing tendency of Avrami expo-nent with increasing pre-anneal time.The localactivation energy and local Avrami exponent dur-ing crystallization process of as-quenched amor-phous alloy were also examined.     

Numerical simulation of the crystallization front inversion in oxide single crystals grown from melt using the Czochralski method

The process of pulling a Czochralski grown oxide single crystal out from melt has been numerically simulated for the first time from the moment of seeding until attaining a stationary growth regime. It is established that the phase boundary inversion at the lateral (shouldering) growth stage is a rather complicated process accompanied by intense oscillations of the crystallization rate. Diagrams illustrating variations of the crystal shape during this process are presented.     

PET固相缩聚装置切片及粉尘结晶行为分析

采用差示扫描量热(DSC)方法研究了聚对苯二甲酸乙二酯(PET)固相缩聚工艺过程中切片及粉尘的结晶熔融及降温结晶行为,研究表明,切片与粉尘呈现出不同的结晶行为,切片随工艺过程的进行,特性黏度增加,降温结晶能力减弱;而粉尘特性黏度增加的幅度更大,降温结晶能力增强;预结晶及结晶粉尘因摩擦形成了更高熔融温度(267.5℃)下的结晶;高的无机杂质的浓度,促进了粉尘的降温结晶成核;粉尘高的结晶能力,易造成后产品加工过程形成结晶斑点。     

Nucleation control in polymer crystallization: structural and morphological probes in different length- and time-scales for selection processes

Thermodynamically, polymer crystallization is a first-order transition that involves overcoming an energy barrier. Building a molecular kinetic model that links this macroscopic concept with experimental observations has been and still remains a difficult issue. It requires a physical picture that can show how a three-dimensionally random linear macromolecule is converted to a chain-folded crystalline state despite the loss of entropy in the process. There are a number of dynamic molecular pathways during polymer crystallization, and previous analytical models have used a 'mean-field' approach. In polymer crystallization, every macromolecule has to go through several selection processes on different length- and time-scales. In this article, we try to identify these selection processes and lay down some basic principles of polymer crystallization. Experimental observations on stem configurations, helical conformations, crystal structures, fold lengths, global macromolecular conformations and lamellar single-crystal morphologies have been used as probes to identify these selection processes.     

Kinetics of devitrification (crystallization) of amorphous titanium

In this paper the behaviour of amorphous titanium (62.0% Ti, 25.0% Ni, 9.0% Cu and 4.0% Si) has been investigated by differential scanning calorimetry (DSC). It has been shown that the crystallization process takes place throughout three distinct stages within the temperature interval 713–788 K; three exothermic thermal effects, depending upon the heating rate have been noticed as well. It has also been proved that, at room temperature and in hydrogen atmosphere, amorphous titanium sorbs hydrogen and liberates the same at temperatures exceeding 473 K, showing an exothermic thermal effect. During the performed research, the activation energy of crystallization, a factor of frequency, rate constants, as well as a half-time of reaction and heat of crystallization, have been determined.     

Crystal formation at the surface of the subliming layer in the vacuum sublimation of ice

It has been established that the temperature or corresponding pressure gradient created by radiant heating is the motive force of the sublimation process. A reduction of temperature at the phase interface causes the crystallization (desublimation) of migrating vapor molecules on the surface. The branchlike growth of the crystals is accompanied by the eventual separation and entrainment of the individual branches, which characterizes the molar-molecular sublimation process.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 5, pp. 794–803, November, 1968.