Isochronal Conditions Research Articles

Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions.

Period function monotonicity of planar vector fields

In this paper, we study planar differential systems possessing a center at the origin. We introduce functional conditions for centers and obtain sufficient conditions for monotonicity of period function and isochronicity of the center of systems of ODE reducible to the equation x ⋅ ⋅ = f ( x , x ⋅ ) . These criteria are applied to obtain sufficient conditions for isochronicity of some special important systems.

Applicability of Johnson-Mehl-Avrami model to crystallization kinetics of Zr 60Al 15Ni 25 bulk amorphous alloy

The applicability of Johnson-Mehl-Avrami(JMA) model to the crystallization kinetics of Zr 60Al 15Ni 25 bulk amorphous alloy is investigated by differential scanning calorimetry(DSC) under isochronal and isothermal conditions. A criterion x m, at which a defined function z( x) exhibits the maximum value, is introduced to check the validity of JMA model to the kinetics analysis. The value of x m has a constant of 0.632 for JMA model. It is found that the values of x m at different isothermal annealing temperatures (743, 748, 753 and 758 K) are almost near 0.632, which indicates that the isothermal crystallization kinetics can be modeled by JMA equation. However, the values of x m at different heating rates (10, 20, 30 and 40 K/min) are about 0.52, implying that JMA model is not valid to the isochronal crystallization kinetics. The reason why the JMA model is not valid to the isochronal crystallization kinetics is discussed.

Application of fractional calculus to the modeling of the complex rheological behavior of polymers: From the glass transition to flow behavior. I. The theoretical model

AbstractA model based on the concept of fractional calculus is proposed for the description of the dynamic elastic modulus (E* = E′ + iE″, where E* is the complex modulus, E′ is the storage modulus, or real part of the complex modulus, and E″ is the loss modulus, or imaginary part of the complex modulus) under isothermal and isochronal conditions for amorphous polymers, including both the glass transition process and the flow behavior. The differential equations obtained for this model, which we call the extended fractional Zener model (EFZM), have differential and/or integral operators of fractional order between 0 and 1. The application of the Fourier transform to the fractional equation of the EFZM, the association of their parameters to the relaxation times of the cooperative or noncooperative molecular movements of polymer chains, and the isothermal and isochronal diagrams of E′ and tan δ = E″/E′ were evaluated. These theoretical diagrams were typical curves that clearly showed the glass‐transition (α‐relaxation) and flow behavior. The EFZM will enable us to analyze the complex rheological behavior of amorphous polymers. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Recrystallization of pure copper investigated by calorimetry and microhardness

The recrystallization of cold rolled copper has been investigated using both differential scanning calorimetry (DSC) and Vickers microhardness techniques. The activation energy of the recrystallization process has been determined by microhardness and by DSC under isochronal conditions. The DSC results have been analyzed using models developed by Kissinger, Ozawa and Boswell. In addition, the recrystallized fraction, as a function of temperature, has been determined from the DSC analysis and compared to that obtained by microhardness measurements.

Influence of phase transformation on the low temperature dielectric measurements in 1-cyanoadamantane

Dielectric measurements have been performed on the supercooled plastic crystal phase of cyanoadamantane under isothermal and isochronal conditions in the temperature range [170-250 K], each experiment with a new sample. The measurements performed in the course of isotherms allowed us to emphasize the effects of the transformations close to the glass transition temperature leading to a change in the dynamic behavior of the compound. The temperature dependence of the dielectric relaxation times exhibits an Arrhenius evolution on the whole metastable domain and gives at the calorimetric glass transition temperature a value of 1 s, i.e., two orders of magnitude lower than the usual value [tau(T(g)) congruent with 100 s]. These results indicate that the Vogel-Fulcher-Tammann behavior observed with other techniques does not appear in the Brillouin zone center (q=0) and that the glass transition for this glass former is not associated with the freezing out of the tumbling motion of individual molecular dipoles but to the freezing out of fluctuations of an antiferroelectric local ordering.

Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.

Isochronicity of analytic systems via Urabe's criterion

A method for studying isochronous oscillations in some systems of ODE reducible to the equation is described. It is applied to obtain the necessary and sufficient conditions for isochronicity of a cubic two-dimensional autonomous system depending on six parameters. For all isochronous systems in this family the Urabe function is explicitly constructed.

Formation of icosahedral phase in Zr 65Al 7.5Ni 10Cu 12.5Ag 5 metallic glass

Two Zr 65Al 7.5Ni 10Cu 12.5Ag 5 amorphous specimens were prepared from the mother ingots with different solidification microstructures. Observation by high-resolution electron microscopy (HREM) revealed that there existed numerous nano-sized short-range order regions (SRORs) in the as-cast specimens although their amorphous nature had been verified by X-ray diffraction (XRD). The average size of the SRORs decreased significantly as the solidification microstructure of the mother ingot became finer. The transformation from amorphous to icosahedral phase (I-phase) in the Zr 65Al 7.5Ni 10Cu 12.5Ag 5 metallic glass was systematically investigated by differential scanning calorimetry (DSC) under isochronal and isothermal conditions. The results indicated that the transformation kinetics slightly changed, and that the formation of I-phase was triggered by the growth of those SRORs as the pre-existing embryos. It was strongly suggested that the atomic configuration of the unit structure in the metallic glasses showed an icosahedron-like one.

PERIODIC CONSTANTS AND TIME-ANGLE DIFFERENCE OF ISOCHRONOUS CENTERS FOR COMPLEX ANALYTIC SYSTEMS

By introducing a concept of the time-angle difference for planar complex analytic systems, two recursive formulas of the function of the time-angle difference and period constants of complex isochronous centers can be given. Using these results to a class of real cubic system, the first five period constants and the isochronous center conditions of the origin are obtained. One open problem posed by [Cairo et al., 1999] is proved.

A new experimental approach for isochronous mass measurements of short-lived exotic nuclei with the FRS-ESR facility

Projectile fragments separated in flight with the FRS have been injected into the storage ring ESR. Operating the ESR in the isochronous mode has enabled high-resolution mass measurements of short-lived isotopes. Already in our pilot experiments the Isochronous Mass Spectrometry (IMS) has provided accurate results for a restricted isotope range in the neighborhood of a selected isotope characterized by the best isochronous condition. In the present experiment this restriction has been overcome by precise external magnetic rigidity determination (1.5·10–4) at the dispersive midplane of the FRS. In this way the mass resolving power for neutron-rich fission fragments covering a large mass-over-charge ratio in one spectrum has been improved by up to one order of magnitude and the accuracy by more than a factor of two.

Modeling non-isothermal austenite to ferrite transformation in low carbon steels

Austenite to ferrite transformation has significant commercial importance due to its effect on the final microstructure and properties of steel. In the present work, austenite to ferrite transformation has been studied by dilatation method under isochronal conditions. The experimental data for a wide range of cooling rates have been accurately modeled by the quasi-isothermal model, in conjunction with a functional relationship between the cooling rate and the apparent activation energy. Furthermore, the mechanistic significance of the observed functional relationship has been explained.

Kinetics of crystallization in amorphous Se 73.2Te 21.1Sb 5.7 under isochronal conditions: Effect of heating rate on the activation energy

The kinetics of crystallization in a-Se 73.2Te 21.1Sb 5.7 were determined at different heating rates (2–99 K/min) using differential scanning calorimetric (DSC) technique. It is evident from this study that the effective activation energy associated with crystallization, E c in a-Se 73.2Te 21.1Sb 5.7 is not constant but heating rate dependent. Attempt is made to explain this variation in terms of recent theoretical models based on the concept of variable effective activation energy. Using isoconversional method, the temperature dependence of E c was determined. It is shown here that the apparent variation of E c with the heating rate is a result of this temperature dependence. It is also shown that the JMA-based models (Kissinger model etc.) which assume constant effective activation energy show clear deviation from linearity giving at least two values of effective activation energy.

Algorithmic derivation of isochronicity conditions

This paper is concerned with obtaining the conditions under which the origin is an isochronous centre for certain planar polynomial systems. The necessity of these conditions is proved using a computer implementation of an algorithm first proposed by I.I. Pleshkan. Their sufficiency is then proved using various methods.

Characterisation and structure development of Ni 64Cu 9Fe 8P 19 glass forming alloy at elevated temperatures

Nickel–copper–iron–phosphorus Ni 64Cu 9Fe 8P 19 alloy was prepared using 99.95 wt.% Ni, 99.95 wt.% Cu, 99.95 wt.% Fe and the Ni–P master alloy. The precursors were melted in the arc furnace under argon gettered protective atmosphere. Then the alloy was induction melted in quartz tubes under vacuum (10 −2 bar) and quenched in water to obtain ingot of 10 mm diameter. The primary microstructure of the ingot was investigated by the use of light microscope. The Ni 64Cu 9Fe 8P 19 alloy was cast using melt spinning. The ribbon in the as cast state was characterised with use of transmission electron microscope (TEM) and X-ray diffraction (XRD). Differential thermal analysis (DTA) of the melt-spun ribbon was made to determine the thermal stability and glass forming ability of the alloy. The pieces of ribbon were heated to different temperatures and annealed during 1 h then characterised with use of the Mössbauer spectroscopy and the X-ray diffraction to see the change of the microstructure after heating to elevated temperatures. It has been found that the devitrification sequence consists of progressive formation of the (Ni, Fe, Cu) 3P phase and (Ni, Fe, Cu)-FCC phase. The temperature range of the sequence is determined under isochronal conditions.

Comments on “Modeling the isochronal crystallization kinetics” by S.S. Sahay, K. Krishnan [Physica B 348 (2004) 310

Satyam and Kirshnan proposed an unsuitable methodology of modeling the isochronal crystallization kinetics, assuming that there is a log-linear relationship between heating rate and the effective activation energy due to the increase in free energy under isochronal condition. In the present communication we have tested the above methodology, and provided a reasonable interpretation for the corresponding isochronal crystallization kinetics, in terms of a recently proposed analytical phase transformation model.

Cerebellum and M1 interaction during early learning of timed motor sequences

We used positron emission tomography (PET) to examine within-day learning of timed motor sequences. The results of this experiment are novel in showing an interaction between cerebellum and primary motor cortex (M1) during learning that appears to be mediated by the dentate nucleus (DN) and in demonstrating that activity in these regions is directly related to performance. Subjects were scanned during learning (LRN) across three blocks of practice and during isochronous (ISO) and perceptual (PER) baseline conditions. CBF was compared across blocks of learning and between the LRN and baseline conditions. Results demonstrated an interaction between the cerebellum and M1 such that earlier, poorer performance was associated with greater activity in the cerebellar hemispheres and later, better performance was associated with greater activity in M1. Inter-regional correlation analyses confirmed that as CBF in the cerebellum decreases, blood flow in M1 increases. Importantly, these analyses also revealed that activity in cerebellar cortex was positively correlated with activity in right DN and that DN activity was negatively correlated with blood flow in M1. Activity in the cerebellar hemispheres early in learning is likely related to error correction mechanisms which optimize movement kinematics resulting in improved performance. Concurrent DN activity may be related to encoding of this information and DN output to M1 may play a role in consolidation processes that lay down motor memories. Increased activity in M1 later in learning may reflect strengthening of synaptic connections associated with changes in motor maps that are characteristic of learning in both animals and humans.

Resistivity models of the phase transformation of amorphous Al78W22 thin films under isothermal and isochronal conditions

The phase transformation and crystallization kinetics of amorphous Al78W22 thin films under isothermal and isochronal conditions was examined by continuous in situ electrical resistance measurements. Sample preparation was performed by magnetron co-deposition. The resistivity of the samples was monitored during isothermal annealing at 803, 813, and 823 K, i.e. at temperatures at which the crystalline phase starts to develop. The temperature dependence of the resistivity ϱ(T ) was estimated from the isochronal measurements, while the volume fraction of the crystalline phase ϱ(x,t) was established by using the isothermal measurements and general two-phase resistivity models for this system. Combinations of these two approaches were used to model the variation of the resistivity during the cooling cycles. The activation energy for crystallization and the reaction order were determined within the framework of the JMA theory. The results indicate that the crystallization mechanism is a diffusion-controlled process with quenched-in nuclei during non-isothermal heating, whereas it is a diffusion-controlled process with steady-state nucleation during isothermal heating.

Stress relaxation and viscosity of a bulk Pd40Cu30Ni10P20 metallic glass under isochronous heating conditions

Isochronous relaxation of tensile stresses is measured in a bulk Pd40Cu30Ni10P20 metallic glass in the initial state and after certain thermal treatments. The results of measurements are used to find the energy spectrum of irreversible structural relaxation, from which the temperature dependence of shear viscosity is then calculated. This dependence is also found independently from measurements of creep in the same glass. The calculated viscosity is shown to agree well with the experimental data.

Crystallization kinetics of Zr60Al15Ni25bulk glassy alloy

The crystallization kinetics of Zr60Al15Ni25 bulk glassy alloy under isochronal and isothermal conditions has been investigated by differential scanning calorimetry (DSC). The microstructure of as-cast Zr60Al15Ni25 bulk glassy alloy is observed by high-resolution electron microscopy (HREM). It is found that there exist nanocrystals with a size of about 7 nm in the glassy matrix, which are not observed in the XRD image. The results of Kissinger analysis show that the effective activation energies for glass transition (457 kJ/mol) and crystallization (345 kJ/mol) are high, indicating that it has large thermal stability against crystallization. The crystallization of Zr60Al15Ni25 bulk glassy alloy under isothermal annealing can be modeled by the Johnson-Mehl-Avami equation. The crystallization kinetics parameters show that the isothermal crystallization starts from the growth of the pre-existing nanocrystals and the crystallization process is diffusion-controlled.