Interpolation of equation-of-state data

Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation. Methods. We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines. Results. The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum $lg P$ difference lies in the range from $10^{-9}$ to $10^{-4}$, and $\Gamma_1$ difference varies from $10^{-9}$ to $10^{-3}$. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at $T \sim 1.5\cdot 10^3 - 10^5$ K. The best precision is achieved at higher temperatures, $T>10^5$ K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.Comment: Accepted for publication in A&

Polarization reversal and jump-like domain wall motion in stoichiometric LiTaO 3 produced by vapor transport equilibration

The polarization reversal and domain structure evolution has been studied in stoichiometric lithium tantalate prepared by vapor transport equilibration process. The first in situ visualization of domain kinetics has demonstrated the jump-like motion of few strictly oriented plane domain walls, which leads to short isolated current pulses in the switching current data. The proposed model of jump-like domain wall motion caused by interaction with pinning centers representing the areas with increased value of the threshold field is based on the effect of retardation of bulk screening. The derived formulas were applied successfully for analysis of the field dependence of the total switching time. The durations of wall jumps and wall stays (rest times) extracted from the switching current data are analyzed separately. The deceleration of the wall motion velocity during jump is controlled by the trail of residual depolarization field produced by bound charges and screening charges in the area behind the wall. The duration of the rest time is governed by the bulk screening of residual depolarization field. The value of Hurst exponent 0.75 obtained by fractal analysis of the switching current data has confirmed the essential influence of prehistory on the domain wall motion. The measurements of the coercive field by switching in bipolar triangular pulses in wide range of the field ramp rate have allowed us to extract the record low value of coercive field 60 V/mm for quasi-static polarization reversal. © 2012 American Institute of Physics

Fatigue effect in ferroelectric crystals: Growth of the frozen domains

The model of the fatigue effect during cyclic switching caused by growth of the frozen domain area with charged domain walls has been proposed. It was claimed on the basis of the previous experimental results that for switching in increasing field the frozen domain area started to grow at the given sub-threshold field value and stopped at the threshold field. The influence of the shape and frequency of the field pulses used for cyclic switching has been considered. The uniaxial ferroelectric stoichiometric lithium tantalate single crystals produced by vapor transport equilibration with record low value of coercive field have been chosen as a model material for experimental verification of the model. The formation of the charged domain walls as a result of cyclic switching has been revealed by analysis of the domain images obtained by optical and Raman confocal microscopy. It has been shown that the fatigue degree is equal to the fraction of the frozen domain area. The experimental dependence of the switched charge on the cycle number has been successfully fitted by modified Kolmogorov-Avrami formula. The experimentally observed frequency independence of fatigue profile for rectangular pulses and frequency dependence for triangular pulses has been explained by proposed model. © 2012 American Institute of Physics

Equation of state SAHA-S meets stellar evolution code CESAM2k

We present an example of an interpolation code of the SAHA-S equation of state that has been adapted for use in the stellar evolution code CESAM2k. The aim is to provide the necessary data and numerical procedures for its implementation in a stellar code. A technical problem is the discrepancy between the sets of thermodynamic quantities provided by the SAHA-S equation of state and those necessary in the CESAM2k computations. Moreover, the independent variables in a practical equation of state (like SAHA-S) are temperature and density, whereas for modelling calculations the variables temperature and pressure are preferable. Specifically for the CESAM2k code, some additional quantities and their derivatives must be provided. To provide the bridge between the equation of state and stellar modelling, we prepare auxiliary tables of the quantities that are demanded in CESAM2k. Then we use cubic spline interpolation to provide both smoothness and a good approximation of the necessary derivatives. Using the B-form of spline representation provides us with an efficient algorithm for three-dimensional interpolation. The table of B-spline coefficients provided can be directly used during stellar model calculations together with the module of cubic spline interpolation. This implementation of the SAHA-S equation of state in the CESAM2k stellar structure and evolution code has been tested on a solar model evolved to the present. A comparison with other equations of state is briefly discussed. The choice of a regular net of mesh points for specific primary quantities in the SAHA-S equation of state, together with accurate and consistently smooth tabulated values, provides an effective algorithm of interpolation in modelling calculations. The proposed module of interpolation procedures can be easily adopted in other evolution codes.Comment: 8 pages, 5 figure

Synthesis and characterisation of nanocrystalline ZrN PVD coatings on AISI 430 stainless steel

The nanocrystalline films of zirconium nitride have been synthesized using ion-plasma vacuum-arc deposition technique in combination with high-frequency discharge (RF) on AISI 430 stainless steel at 150oC. Structure examinations X-ray fluorescent analysis (XRF), X-ray diffraction analysis (XRD), scanning electron microscopy (SEM) with microanalysis (EDS), and transmission electron microscopy (TEM), nanoidentation method – were performed to study phase and chemical composition, surface morphology, microstructure and nanohardness of coatings. The developed technology provided low-temperature coatings synthesis, minimized discharge breakdown decreasing formation of macroparticles (MPs) and allowed to deposit ZrN coatings with hardness variation 26.6…31.5 GPa. It was revealed that ZrN single-phase coatings of cubic modification with finecrystalline grains of 20 nm in size were formed

Reduction of some cyclic derivatives of diphenic acid with sodium borane in alcohols

Reduction of heptamerous cyclic imides with sodium borane has been carried out for the first time by the example of some imides of diphenic acid. In this case for the first time amides of 2'-hydroxymethylxenyl-2-carboxylic acid which are potentially valued bioactive compounds were obtained. It was shown that the nature of substituent at nitrogen atom influences the reaction products yields and composition. The reduction of diphenic acid anhydride with sodium borane in simple alcohols occurs with the formation of reduction products - 7H-dibenzyl[c,e] oxepin-5-on (36...46 %) as well as products of diphenic acid alcoholysis-monoester (29...36 %). In this case the nature of alcohol influences weakly reaction products rati