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Showing papers on "Crystallization published in 1990"


Journal ArticleDOI
16 Nov 1990-Science
TL;DR: This result represents an experimental demonstration of chiral symmetry breaking or total spontaneous resolution on a macroscopic level brought about by autocatalysis and competition between L- and D-crystals.
Abstract: Sodium chlorate (NaClO3) crystals are optically active although the molecules of the compound are not chiral. When crystallized from an aqueous solution while the solution is not stirred, statistically equal numbers of levo (L) and dextro (D) NaClO3 crystals were found. When the solution was stirred, however, almost all of the NaClO3 crystals (99.7 percent) in a particular sample had the same chirality, either levo or dextro. This result represents an experimental demonstration of chiral symmetry breaking or total spontaneous resolution on a macroscopic level brought about by autocatalysis and competition between L- and D-crystals.

774 citations


Journal ArticleDOI
TL;DR: In this paper, a method for mounting single crystals in macromolecular crystallographic studies is described in which the crystal is suspended in a thin film, formed from a mixture of the crystallization buffer and a hydrophilic viscous material, confined within a thin-wire loop by surface tension.
Abstract: A method for mounting single crystals in macromolecular crystallographic studies is described in which the crystal is suspended in a thin film. The film is formed from a mixture of the crystallization buffer and a hydrophilic viscous material, confined within a thin-wire loop by surface tension. Compared with conventional crystal mounting methods, this method greatly simplifies and speeds the mounting procedure, is well suited to shock freezing and to optical monitoring of the crystals, deforms fragile crystals less and gives a lower and more uniform background in the X-ray diffraction patterns.

375 citations


Patent
06 Aug 1990
TL;DR: In this paper, a very thin discontinuous film of a nucleating site forming material over the amorphous Si prior to rapid thermal anneal is used to reduce the temperature of polycrystalline Si to a temperature range from 550° C to 650° C.
Abstract: The 700° C./4 min. rapid thermal anneal described in the prior art for converting amorphous Si to polycrystalline Si can be reduced to a temperature range of from 550° C. to 650° C. This is accomplished by depositing a very thin discontinuous film of a nucleating site forming material over the amorphous Si prior to rapid thermal anneal. Furthermore, by selectively depositing the material in a pattern, only that amorphous Si beneath the deposited pattern is caused to crystallize during annealing, while the remaining areas of amorphous Si remain in the amorphous state.

306 citations



Journal ArticleDOI
01 Jun 1990
TL;DR: Computer simulations of melting, crystallization, glass transition, and annealing for a model system of 864 Lennard-Jones atoms under a periodic boundary condition are carried out using constant-pressure molec ular dynamics techniques with temperature control to characterize the glass's stability.
Abstract: Computer simulations of melting, crystallization, glass transition, and annealing for a model system of 864 Lennard-Jones LJ atoms under a periodic boundary condition are carried out using constant-pressure molec ular dynamics techniques with temperature control. When an fcc crystal of LJ atoms is heated, melting occurs; however, an LJ liquid, when quenched slowly, crystallizes into layers with stacking faults. Each layer forms a two-dimensional, close-packed structure with occasional point defects but without dislocations. When the quench rate is high enough, an LJ liquid transforms into a disordered structure without a discontinuous change in volume. The dependence of the glass transi tion on the quench rate is determined by examining macroscopically observable physical features. Several microscopic structure parameters are introduced to ana lyze, at the atomic level, the structures of glasses pro duced by different quench rates. When annealed, a glass made with a low enough quench rate is stable against crystallization. Identifying the number of atoms in the system having local icosahedral symmetry is a prom ising method of characterizing the glass's stability. The microscopic structural changes in the annealing pro cesses are presented in the companion video to this paper.

292 citations


Journal ArticleDOI
TL;DR: Differential scanning calorimetry was used to determine the phase transitions of dried and rehumidified amorphous lactose, sucrose, and a mixture of sucrose and Amioca.
Abstract: Differential scanning calorimetry was used to determine the phase transitions of dried and rehumidified amorphous lactose, sucrose, and a mixture of sucrose and Amioca. Glass-transition, crystallization, and melting temperatures decreased with increasing moisture content. The time to crystallization of amorphous lactose held isothermally above the glass-transition temperature decreased as the temperature was increased. Isothermal crystallization time of lactose was a function of the temperature difference between the holding temperature and the glass-transition temperature independently of moisture content. Amorphous biological materials are metastable showing temperature, moisture content, and time-dependent phase transitions that affect their drying behavior, stickiness, storage stability, and quality.

288 citations


01 Jan 1990
TL;DR: In this paper, the authors determined glass transition, crystallization, and melting temperatures of amorphous lactose, sucrose, and a gelatinized mixture of sucrose (80%) and Amioca (20%) as a function of moisture content and determined the temperature dependence of the crystallization time with use of differential scanning calorimetry.
Abstract: The purpose of this study was to determine glass-transition, crystallization, and melting temperatures of amorphous lactose, sucrose, and a gelatinized mixture of sucrose (80%) and Amioca (20%) as a function of moisture content and to determine the temperature dependence of the crystallization time with use of differential scanning calorimetry

282 citations



Journal ArticleDOI
TL;DR: In this article, the influence of α,ω-dicarboxylates on the morphology of calcite crystals grown from supersaturated bicarbonate solutions was studied by optical and scanning electron microscopy.
Abstract: The influence of a range of α,ω-dicarboxylates on the morphology of calcite crystals grown from supersaturated bicarbonate solutions was studied by optical and scanning electron microscopy. At Ca/malonate ≈ 3, spindle-shaped crystals elongated along the c axis and with curved {1text-decoration:overline10} prismatic faces were formed. This effect was reduced with increasing chain length. The unsaturated derivative, maleate, was intermediate in potency compared with the saturated malonate and succinate compounds. In contrast, the trans isomer, fumarate, had minimal morphological effect. Functionalization of the lower chain acids had a marked influence on crystal morphology. Crystals grown in the presence of aspartate (α-aminosuccinate) exhibited well defined {1text-decoration:overline10} prismatic faces at Ca/additive = 17, whilst γ-carboxyglutamate had a pronounced effect at ratios as high as 85. The stabilization of the {1text-decoration:overline10} faces of calcite by αω-dicarboxylate binding is described in terms of electrostatic, geometric and stereochemical recognition at the crystal/additive interface.

207 citations


Book
30 Nov 1990
TL;DR: In this article, the authors introduce the concept of membrane separations and detailed theories for separating a moving bed from a pack of columns, and compare them with a simulated moving bed separator.
Abstract: Preface. 1. Introduction. Part I: Crystallization. 2. Crystallization and Precipitation from Solution - Equilibrium Analysis. 3. Nucleation and Crystal Growth. 4. Population Balances and Crystal Size Distributions. 5. Crystallization from the Melt. Part II: Sorption and Chromatography. 6. Basics of Sorption in Packed Columns. 7. Linear Theories of Sorption and Chromatography. 8. Non-Linear Theories and Packed Bed Adsorption Systems. 9. Ion Exchange. 10. Moving Bed and Simulated Moving Bed Sorption Separations. 11. Electrophoretic Separation Methods. Part III: Membranes. 12. Introduction to Membrane Separations. 13. Detailed Theories for Membrane Separations. Part IV: Selection and Sequencing. 14. Selection and Sequencing of Separations. Appendix: Answers to Selected Problems. Index.

205 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that melting occurred in the explosive reactions of films with an atomic concentration ratio of 3Al:1Ni and that the propensity of multilayer films to undergo explosive reactions is dependent on the modulation length of the film as well as on the ambient temperature.
Abstract: Self‐propagating explosive reactions, with a reaction front speed of about 4 m/s, have been observed in free‐standing polycrystalline Al/Ni multilayer thin films. The resultant phases and microstructures are compared with those obtained by conventional thermal annealing. We show evidence which indicates that melting occurred in the explosive reactions of films with an atomic concentration ratio of 3Al:1Ni. It is also observed that the propensity of multilayer films to undergo explosive reactions is dependent on the modulation length of the film as well as on the ambient temperature. These observations are interpreted with a simple model based on the rate balance between the rates of heat generation and heat dissipation.

Journal ArticleDOI
TL;DR: In this article, the first reported crystalamorphous phase transition induced by ball-milling in a pure element: a silicon powder is presented, and the influence of the ballmilling conditions on the dynamic equilibrium between the crystalline and the amorphous phases has been studied.
Abstract: We present an experimental study of the first reported crystalamorphous phase transition induced by ball-milling in a pure element: a silicon powder. Scanning electron microscope observations show some particular spherical particles with smooth shapes. Only minor contamination with iron and chromium (less than or equal to 0.2 at.%) has been determined by chemical EDX microanalyses. The analyses of the X-ray patterns reveal the coexistence of silicon microcrystallites and an amorphous phase. Transmission electron microscope investigations (selected area diffraction patterns) show that such mixing is on the micrometer scale. The various enthalpic evolutions which have been studied by differential scanning calorimetry experiments reveal three major contributions which may be successively interpreted starting from room temperature up to 725°C as a release of the strain energy (exothermic event), followed by an equilibration between the in situ differential scanning calorimetry annealed silicon crystallites and the amorphous phase (endothermic effect), and subsequently by the crystallization of the amorphous phase (exothermic contribution). The influence of the ball-milling conditions on the dynamic equilibrium between the crystalline and the amorphous phases has been studied.

Journal ArticleDOI
TL;DR: The two-level-system (TLS) model was proposed by Anderson et al. as discussed by the authors to describe the dynamics of low-temperature glassy systems, and it has been widely used in chemistry, physics, and materials science.
Abstract: Amorphous materials at low temperature have markedly different physical and thermal properties from crystals.' For example, the specific heats of crystals obey the Debye P law at low temperatures2 and the thermal conductivity also follows the same P temperature dependen~e .~ Many of these properties can be calculated because crystals have long-range spatial and orientational order.4 Twenty years ago, specific heat measurements on disordered materials revealed significant deviations from the Debye law at approximately 1 K.5-8 Measurements of thermal conductivity5y9 and dielectric responselOJ1 also deviated from crystalline behavior. These observations showed that the dynamics of ordered and disordered systems must be fundamentally different. Although ordered crystals are commonly found in nature, many other naturally occurring complex systems, such as proteins, are inherently disordered.12 Furthermore, many artificial materials, such as polymeric solids and amorphous semiconductors, are glasses. Therefore, understanding the microscopic behavior of the glassy state has been and continues to be13-15 an important problem in chemistry, physics, and materials science. Glasses are systems in which there is no translational or rotational order. More important, unlike a crystal, a glass is not in thermodynamic equilibrium. At low temperature, the equilibrium state of a substance like ethanol is crystalline. A glass is formed by rapid cooling, which traps the material in the glassy state. Thermodynamically the material should be a crystal, but kinetics prevent the system from finding the global potential minimum; Le., the kinetics at low temperature make the time scale for crystallization essentially infinitely long. Dynamics in simple crystals involve fast fluctuations about an equilibrium structure.16 In conlocal structures as well as time evolution of the nonequilibrium local structures them~e1ves.l~ Glass dynamics can occur through essentially all time scales from femtoseconds, to kiloseconds, and perhaps longer.lgZ0 Many concepts that are useful in describing dynamics in crystals cannot be extended to the amorphous state, e.g., translational symmetry, which gives rise to phonon bands and fast phonon fluctuations, providing a separation of time scales for a variety of processes.z1 In crystals at low temperatures, only the acoustic phonons are thermally excited. The phonon dispersion is well described by the Debye density of ~ t a t e s , ~ J ~ and this means that the distribution of fluctuation rates is known. A glass also has modes that are equivalent to a crystal's phonons. Even at low temperatures, however, there is a major contribution to the dynamical properties of glasses from the evolution of local structures, and it is these "extra" dynamics that make glasses fundamentally different from crystals. The anomalous heat capacities found in glasses show a term linear in temperature which is not present in crystals. This is true in such diverse substances as silicates and ceramics as well as poly(methy1 methacrylate) and Lexan polymer^.^-^>^^ In addition, heat capacities are time dependent; the heat capacity increases as time i n c r e a ~ e s . ~ ~ J ~ ~ ~ ~ ~ Thermal conductivity, which varies as P in crystals, varies as P? The phonon mean free path in a glass is substantially less than in the corresponding crystal, and a variation in the velocity of sound with temperature is seen in amorphous syst e m ~ . ~ ~ Many theoretical models have been developed to account for the various observations. The models invoke defect-induced scattering,26 localized electronic states,27 and defect and particle diffusionz8 to explain aspects of the observed behaviors. The two-level-system (TLS) model proposed independently by Anderson et al.29 and Phillips30 has been the most widely used, and it is frequently the point of departure in discussing the properties of low-temperature glasses. The TLS model postulates that, in an amorphous material, some atoms or molecules (or groups of atoms or molecules) can reside in not just one but two potential minima of the local structure potential surface (Figure 1). Each side of the double-well potential represents a distinct local structure of the glass. This is a simplified representation of what is almost certainly a complex multidimensional potential surface. At low temperatures, transitions from one side of the double well to the other represent changes in the local structure. Transitions occur by phonon-assisted tunneling. To model the complex distribution of local structures and transition rates, the TLS model states that there

Journal ArticleDOI
TL;DR: In this article, a plot of the DTA peak height versus nucleation temperature closely resembles the classical nucleation rate curve for lithium disilicate glass whose maximum is at 453 C.
Abstract: The crystallization of lithium disilicate (Li2O+2SiO2) glass nucleated at various temperatures was studied by differential thermal analysis (DTA). A plot of the DTA crystallization peak height versus nucleation temperature closely resembles the classical nucleation rate curve for lithium disilicate glass whose maximum is at 453 C. The glass becomes saturated with internal nuclei when heated at 453 C for 10 h. The activation energy for crystallization and the heat of crystallization are independent of the concentration of nuclei and are 249 + or - 10 and 67 + or - 3 kJ/mol, respectively. The Avrami exponent, n, depends strongly on the concentration of nuclei in the glass.

Journal Article
TL;DR: In this article, the CSE parameterization of the position of Ymax as a function of T, TL and T suggested by Dearnley (1983) provides a potentially useful model that requires further testing.
Abstract: Natural systems provide time-controlled experiments on scales unreachable in the laboratory, and with complexities unapproachable by computer experiments. Since temperature (undercooling) cannot be directly scaled with time, in situ crystallization experiments provide information unavailable by other means. The kinetics of crystallization in simple silicate systems have been studied extensively for glass ceramic systems (e.g. Uhlmann, 1982; James, 1982), but predictive models for nucleation behavior, in particular, remain inadequate. Part of the problem in creating models of nucleation lies in the difficulty of experimentally isolating the nucleation process; crystal growth measurements are more accessible experimentally, and for this reason crystal growth is better understood (e.g. Dowty, 1980; Kirkpatrick, 1981; James, 1982; Baronnet, 1984). However, predictive models of crystal growth (e.g. Lasaga, 1982) require accurate models for the temperature and compositional dependence of both the thermodynamic and kinetic driving forces for crystallization, information that is currently limited. The CSE parameterization of the position of Ymax as a function of T, TL and T suggested by Dearnley (1983) provides a potentially useful model that requires further testing. Similarly, application of the adiabatic nucleation model of Meyer (1986) to simple systems suggests that the position of Tmax relative to TL has an approximately constant value of 0.55-0.60 (exceptions are low DSf minerals such as albite and quartz). Additionally, while experimental crystallization rate data is a necessary link between processes in natural melts and numerical models, experimental growth rate data is confined to simple systems and conditions of moderately large undercooling, while growth rate estimates in complex natural systems suggest that under most conditions, undercoolings remain very small. Quantitative textural studies of dikes suggest a pronounced dependence of growth rate on total crystallization time (e.g. Ikeda, 1977), which is in turn related to effective undercooling, a function of both total dike width and distance from the dike margin. By analogy, minimum crystallization rates may be estimated from programmed cooling experiments if a temperature interval of crystallization is assumed. Growth rates determined in this way show the same relationship between growth rate and total crystallization time seen in the dike studies, reflecting a systematic relationship between growth rate and cooling rate (effective undercooling) for plagioclase in basaltic systems. While the data are not available for other mineral systems, there is no reason to believe that similar patterns would not exist for other silicate minerals (i.e., the similarity in dendritic olivine growth rates estimated by Fowler et al.,1989, using fractal analysis to the growth rates of plagioclase under conditions of rapid cooling estimated from programmed cooling rate experiments). Analysis of measured crystal size frequencies provides a means of extracting effective (bulk) kinetic information from geologic systems that can help to constrain the dynamic feedback between physical models of magmatic systems and rates of chemical change.

Journal ArticleDOI
TL;DR: In this paper, a study of microstructures and crystallization of the electroless Ni-P deposits containing 11.3 to 23.0 at% P obtained from acidic nickel sulphate baths with sodium hypophosphite as a reducing agent by means of differential scanning calorimetry, X-ray diffractometry and hot stage transmission electron microscopy.
Abstract: A study has been made of microstructures and crystallization of the electroless Ni-P deposits containing 11.3 to 23.0 at% P obtained from acidic nickel sulphate baths with sodium hypophosphite as a reducing agent by means of differential scanning calorimetry, X-ray diffractometry and hot stage transmission electron microscopy. The deposits containing low phosphorus content of 11.3 at% could be represented as an fcc Ni-P solid solution of 5 to 10 nm microcrystallites, whereas the deposits containing high phosphorus content were amorphous. The crystallization process of amorphous Ni-P solution involved more than one intermediate phases; precrystallized nickel or off-stoichiometric Ni3(P, Ni) or Ni5(P, Ni)2 phase in which some phosphorus sites are replaced by nickel atoms. The final equilibrium phases were bct Ni3P and fcc nickel crystals regardless of phosphorus content. The amorphous phase containing 20 to 22 at% phosphorus was the most stable among the amorphous Ni-P alloys.


Journal ArticleDOI
TL;DR: In this paper, the many structures of bulk niobium pentoxide can be grouped into the low-temperature and hightemperature forms, with the latter being more ordered and the crystallization behavior, however, is influenced by starting materials, impurities, and interactions with another component.

Journal ArticleDOI
TL;DR: In this paper, the sequence of phase transformations induced in the Zr-Al binary system by mechanical alloying of mixed Zr and Al powders was studied by transmission electron microscopy and by x-ray diffraction measurements.
Abstract: We have studied the sequence of phase transformations induced in the Zr-Al binary system by mechanical alloying of mixed Zr and Al powders. The structure of these materials has been studied by transmission electron microscopy and by x-ray diffraction measurements. Three different metastable phases have been found experimentally with variation of the initial composition xAl: (1) a nanocrystalline supersaturated solid solution of alpha-Zr for xAl<=0.15, (2) an amorphous phase for 0.15

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the silicidation process of the Ni/a-Si:H system on a fused silica substrate mainly by in situ electric resistance measurement.
Abstract: We have investigated the silicidation process of the Ni/a-Si:H system on a fused silica substrate mainly by in situ electric resistance measurement. A rise of the resistance is observed in the temperature range of 480–510°C of the resistance curve at a heating rate of 2 K/min. The results of the RBS measurements and the XRD measurements show that the rise of the resistance originates from the diffusion of Ni from the NiSi2 layer to a-Si:H film, and that the a-Si:H crystallizes during the diffusion. Noting that the crystallization temperature of a-Si:H film is higher than 700°C, the present crystallization occurs at a much lower temperature. It is suggested that this low-temperature crystallization is induced by heterogeneous nucleation, where the NiSi2 becomes the nucleus for Si crystallization.

Journal ArticleDOI
TL;DR: In this paper, the ion-beam-induced epitaxial crystallization (IBIEC) and planar amorphization of amorphous Si (a-Si) layers onto single-crystal Si substrates is reviewed.

Journal ArticleDOI
TL;DR: In this paper, the freezing phase transition in a binary suspension of colloidal hard spheres of diameter ratio α = 0.61 was studied by light scattering and scanning electron microscopy, which consisted of sterically stabilized poly(methyl methacrylate) spheres of diameters about 670 and 407 nm suspended in a near refractive indexed matched suspension medium composed of carbon disulphide and cis−decalin.
Abstract: The freezing phase transition in a binary suspension of colloidal hard spheres of diameter ratio α=0.61 was studied by light scattering and scanning electron microscopy. The suspensions consisted of sterically stabilized poly(methyl methacrylate) spheres of diameters about 670 and 407 nm suspended in a near refractive indexed matched suspension medium composed of carbon disulphide and cis‐decalin. With increasing volume fraction, binary suspensions of number fraction of larger component A xA>0.43 crystallized to give irregularly stacked close packed crystals containing almost entirely component A. As the number fraction xA decreased, the rate of crystallization decreased. Suspensions of xA≊0.28 remained amorphous and showed glassy behavior. Suspensions of xA≊0.057 showed a complex sequence of phase behavior with coexistence of crystals of component B, the ordered binary alloy phase AB13, and a binary fluid. In suspensions with xA<0.057, the only solid phase observed was irregularly stacked close packed cr...

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the evolution of the homogeneous nucleation rate, work of nucleus formation, and critical nucleus size along different expansion paths for the model system phenanthrene-carbon dioxide.
Abstract: When a supercritical solution is rapidly expanded, large solute supersaturations can be attained, and small particles are formed. The evolution of the homogeneous nucleation rate, work of nucleus formation, and critical nucleus size along different expansion paths is investigated here for the model system phenanthrene-carbon dioxide. Nucleation rates are the result of the competition among solvent expansion, cooling due to depressurization, and high supersaturation. Although supersaturations can reach very high values (> 106), relatively flat nucleation rate profiles result due to cooling and expansion. For an interfacial tension of 0.02 N/m, computed nucleation rates never exceed 104 s−1 · cm−3. A substantial fraction of the maximum nucleation rate is attained with partial decompression to pressures above 1 bar.

Journal ArticleDOI
TL;DR: In this article, a NiTi intermetallic compound was cold rolled at room temperature by 30% and 60% thickness reductions, and microstructures were studied by means of transmission electron microscopy (TEM).
Abstract: A NiTi intermetallic compound was cold rolled at room temperature by 30% and 60% thickness reductions, and microstructures were studied by means of transmission electron microscopy (TEM). In the cold-rolled samples we observed both a phase of nanometer-sized crystals and an amorphous phase. A substantially high dislocation density, 1013 to 1014/cm2, was evident in the transition region between crystalline and amorphous phases. A simple estimate of the elastic energy arising from this dislocation density is of the same order as the crystallization energy, suggesting that dislocation accumulation is a major driving force for amorphization in cold-rolled NiTi.

20 Jun 1990
TL;DR: In this paper, a kinetic equation of non-isothermal crystamzation was derived by extending Avrami's equation to the nonisothermal situation more crystallization information can be obtained from this kinetic equation.
Abstract: A kinetic equation of non-isothermal crystamzation was derived by extending Avrami’s equation to the non-isothermal situation More crystallization information can be obtained from this kinetic equation The curves of non-isothermal and isothermal crystallizations were analysed and compared for poly (ethylene terephthalate) (PET), and the results were discussed

Journal ArticleDOI
01 Feb 1990-Polymer
TL;DR: In this article, the authors measured dissolved oxygen permeability, water content, crystalline structure, crystallinity, and density of silk fibroin membrane as a function of immersion time of the membrane in 50 vol% aqueous methanol solution.

Journal ArticleDOI
TL;DR: In this paper, a method for applying zirconia barrier coatings using a solgel method is described, and the coatings of 8 wt % yttria-stabilized ZIRconia are applied by spin coating a solution containing zirconsium alkoxides and yttrium acetate on to stainless steel substrates.
Abstract: A method for applying zirconia barrier coatings using a sol-gel method is described. The coatings of 8 wt % yttria-stabilized zirconia are applied by spin coating a solution containing zirconium alkoxides and yttrium acetate on to stainless steel substrates. Crystallization of the films was observed for thermal treatments in the range 750 to 1050° C. Excellent adhesion at the interface, due to significant coating-substrate interfacial reactions, indicates that this sol-gel route is a feasible method for applying zirconia coatings.

Journal ArticleDOI
TL;DR: In this article, it was shown that glycerol monostearate-amylose complexes reveal the presence of at least two thermally distinct metastable forms, which implies a definite connection between thermal properties and the supermolecular organization of these materials.

Journal ArticleDOI
TL;DR: In this article, a hydrogenated amorphous Si-C alloy film (a-Si1−xCx:H with x = 0.29) was prepared by glow discharge decomposition of a silane and ethylene gas mixture, and a detailed investigation of the IR absorption was undertaken in the range from 400 to 4000 cm−1 for both the as-deposited (Ts = 250°C) and annealed (up to 1200°C).

Journal ArticleDOI
01 Mar 1990-Polymer
TL;DR: In this article, an improved formulation for the nucleation rate j of a generalized sequential process is presented, where activation energy for chain sliding diffusion within crystals is introduced, and the topological nature of linear chains is formulated by introducing activation energy.