Jiří Málek

Kinetic analysis of crystallization processes in amorphous materials

Abstract Thermal analysis methods are widely used to study crystallization kinetics in amorphous solids. The experimental data is frequently interpreted in terms of the Johnson–Mehl–Avrami (JMA) nucleation-growth model. This paper discusses the limits of such an approach. A simple and convenient method is proposed to verify the applicability of the JMA model as well as the basic assumptions of kinetic analysis. It is shown that the two parameter autocatalytic model includes the JMA model and that is a plausible description of the crystallization kinetics. The main advantage of this model is its flexibility in describing quantitatively the kinetics of complex crystallization processes. The experimental data for crystallization of a chalcogenide glass and zirconia gel analyzed in this paper clearly demonstrate the rather complex nature of these processes. As a consequence, it is very difficult to explore the real mechanism of the crystallization unless some complementary studies are made.

A kinetic analysis of the curing reaction of an epoxy resin

Abstract The kinetics of a curing reaction under non-isothermal conditions using DSC is discussed. A simple, consistent method of kinetic analysis was applied. The method allows the correct determination of the most suitable kinetic model and the calculation of kinetic parameters. This method was used to study the kinetics of an epoxy resin based on diglycidyl ether of bisphenol A, cured by methyl tetrahydrophthalic anhydride with an accelerator. An activation energy of 73kJmol−1 was calculated and the autocatalytic kinetic model (Sestak-Berggren equation) was found to be the most covenient description of the studied curing process. The isothermal curves calculated for the kinetic parameters determined in non-isothermal conditions are in good agreement with experimental curves when the curing temperature Tc is above the maximum glass-transition temperature of the system, Tg∞ = 109°C. The influence of the vitrification phenomenon is discussed when Tc is below Tg∞. The temperature-time-transformation diagram of the studied epoxy system has been constructed and is discussed.

Kinetic analysis of solid-state processes

A simple method for kinetic analysis of solid-state processes has been developed. A criteria capable of classifying different processes is explored here with a view toward visualizing the complexity of solid-state kinetics. They provide a useful tool for the determination of the most suitable kinetic model. The method has been applied to the analysis of crystallization processes in amorphous ZrO 2 and RuO 2 . It is found that the crystallization kinetics of as-prepared sample exhibits a complex behavior under nonisothermal conditions. This is probably due to an overlapping of the nucleation- and crystal-growth processes at the beginning of crystallization. As a consequence, the Johnson–Mehl–Avrami nucleation-growth model cannot be applied. A two-parameter autocatalytic model provides a good description of the crystallization process under isothermal and nonisothermal conditions.

Diagnostic limits of phenomenological models of heterogeneous reactions and thermal analysis kinetics

Abstract Kinetic models of solid-state reactions are often based on a formal description of geometrically well defined bodies treated under strictly isothermal conditions; for real processes these prepositions are evidently incorrect. It can be equally useful to find an empirical function containing the smallest possible number of constants. In such a case the models of heterogeneous kinetics can be assumed as a distorted (fractal) case of the simpler homogeneous kinetics and mathematically treated by multiplying by an “accomodation” function. In addition, the conventional thermoanalytical (TA) studies apply intentionally the experimental conditions with constant heating and/or cooling where the models validity must again be investigated. The general method of kinetic data evaluation is proposed to include two-step evaluation: first, determining the activation energy, E , from a set of TA curves at different heating rates, and second, using the pre-established E to search for the reaction mechanism by analyzing the entire course of the single TA curve. In this respect the possibility of a simultaneous determination of all kinetic data is discussed. The computer method is recommended to be based on the evaluation of two specific functions available for a direct derivation from experimental data.

Viscosity of germanium sulfide melts

Abstract Viscosities of Ge x S 1− x melts (0.30⩽ x ⩽0.44) have been measured by penetration viscometry from 10 7 to 10 13 Pa s. The temperature dependence of equilibrium viscosities in this range can be expressed approximately by a simple Arrhenius equation. Both the heat capacity change at the glass transition and the activation energy of viscous flow monotonously increase with germanium content as predicted by the Adam–Gibbs theory. Therefore, the connectivity of the germanium–sulfur network is reduced due to decreasing concentration of sulfur which causes increasing fragility of the undercooled liquid. The glass transition temperature exhibits a maximum near the GeS 2 composition where heteropolar bonds are predominantly formed.

Rate-determining factors for structural relaxation in non-crystalline materials II. Normalized volume and enthalpy relaxation rate

Abstract The rate-determining factors for isothermal structural relaxation in non-crystalline materials are discussed. The normalized volume and enthalpy relaxation rate RF is defined and analyzed for the Tool–Narayanaswamy–Moynihan phenomenological model. It is shown that the temperature dependent RF is controlled mainly by the parameter (1−x)θ, where x is the non-linearity parameter and θ= Δ h ∗ /RT 2 g . Materials with higher values of parameter (1−x)θ (e.g. vinylic polymers) exhibit low relaxation rate. In contrast, high relaxation rate is expected for materials with low values of (1−x)θ (inorganic glasses). The applicability of this approach for the analysis of isothermal volume and enthalpy relaxation data is shown for arsenic sulfide glass, polystyrene, poly(vinyl acetate), poly(methyl methacrylate) and poly(vinyl chloride). The normalized enthalpy and volume relaxation rates for these materials agree well within the limits of experimental errors.

LAYERED VELOCITY MODELS OF THE WESTERN BOHEMIA REGION

A new robust and effective optimization algorithm – isometric algorithm – was used for the inversion of layered velocity models, with constant gradient in each layer, to find suitable 1-D models for the location of microearthquakes in the individual four subregions of the West Bohemian earthquake swarm region. Models which are considered as optimal yield the minimum sum of the absolute values of the travel-time residua in locating the whole group of earthquakes in the given subregion. The results obtained from the inversion of P and S waves and from P waves only are shown. For comparison, optimum homogeneous models derived by the grid search method, again using both P and S waves and P waves only, are given. The computations indicate that the models for the individual subregions differ from each other. For layered models the differences are more pronounced, as expected, in the upper parts, down to depths of about 5 km. In comparison with the subregions Nový Kostel and Plesná, the P and S wave velocities for subregion Lazy are relatively higher and the P and S velocities for subregion Klingenthal relatively lower. In the lower parts the differences are smaller and the velocities have practically identical gradients. The highest velocities were obtained for subregion Lazy and the lowest velocities for subregion Klingenthal, as well for the homogeneous models. The model that represents the whole swarm region was determined in a similar way. This model is compared with the previously published velocity-depth distribution, obtained from DSS profile VI/70 in the vicinity of the area under study.

New portable sensor system for rotational seismic motion measurements.

A new mechanical sensor system for recording the rotation of ground velocity has been constructed. It is based on measurements of differential motions between paired sensors mounted along the perimeter of a rigid (undeformable) disk. The elementary sensors creating the pairs are sensitive low-frequency geophones currently used in seismic exploration to record translational motions. The main features of the new rotational seismic sensor system are flat characteristics in the wide frequency range from 1 to 200 Hz and sensitivity limit of the order of 10(-8) rad/s. Notable advantages are small dimensions, portability, easy installation and operation in the field, and the possibility of calibrating the geophones in situ simultaneously with the measurement. An important feature of the instrument is that it provides records of translational seismic motions together with rotations, which allows many important seismological applications. We have used the new sensor system to record the vertical rotation velocity due to a small earthquake of M(L)=2.2, which occurred within the earthquake swarm in Western Bohemia in autumn 2008. We found good agreement of the rotation record with the transverse acceleration as predicted by theory. This measurement demonstrates that this device has a much wider application than just to prospecting measurements, for which it was originally designed.

Rate-determining factors for structural relaxation in non-crystalline materials I. Stabilization period of isothermal volume relaxation

Abstract The isothermal volume relaxation rate in non-crystalline materials is analyzed for the Tool–Naraynaswamy–Moynihan phenomenological model. It is demonstrated that the mathematical analysis of the inflectional slope of isothermal relaxation curve yields in a simple equation relating parameters of non-exponentiality, non-linearity, effective activation energy and the stabilization period of isothermal volume relaxation response. It can be expected that in non-crystalline materials with comparable non-linearity the temperature dependence of the stabilization period is controlled by the parameter θ= Δ h ∗ /RT 2 g . Materials with higher value of parameter θ (organic polymers) exhibit relatively low relaxation rate. In contrast, higher relaxation rate is expected for materials with low value of θ (inorganic glasses). The applicability of this approach for analysis of previously reported isothermal volume relaxation data of polyvinylacetate (PVA) and arsenic sulfide glass (As 2 S 3 ) is discussed.

Moment tensor inversion for two micro-earthquakes occurring inside the Háje gas storage facilities, Czech Republic

Broadband data from the Příbram seismological network was used to investigate the source of two earthquakes, with magnitudes Mw = 0.2 and 0.4 respectively, occurring in the period of October–November 2009 in the Háje natural gas storage area (Czech Republic). Both events were located inside the limits of the storage area and at depths similar to those of the underground caverns where the gas is stored. We applied an inversion technique using the software ISOLA for moment tensor retrieval in order to assess the source process of both events and recognize whether a significant isotropic component existed that could be interpreted as a possible cavern collapse. We also performed an uncertainty analysis so as to confirm the reliability of the focal mechanism solutions and we controlled the consistency between the inverted focal mechanisms and those calculated using the P-waves first motions. Our results showed that the nodal plane orientation, the centroid depth, and the magnitude remained stable. Furthermore, we calculated synthetic waveforms for collapse-type ruptures and compared them with the original records. The match between the synthetic and the original data was very poor supporting the interpretation of the shear character of the events. The combination of the inversion results, which indicated significant double-couple components and of the synthetic tests, which supported the inexistence of an isotropic component at the source, led to the conclusion that the possibility of rocks falling from the ceiling of the caverns or a cavern collapse is highly unlikely.