Mechanism of crystal structure transformations. Part 3. - Factors affecting the anatase-rutile transformation

The particle size and crystallite size of anatase increase markedly in the region of the crystal structure transformation. The unit cell of anatase seems to expand prior to the transformation to rutile. This expansion has been attributed to a displacive transformation of the type defined by Buerger. Smaller particle size and larger surface area seem to favour the transformation. The kinetics of the transformation of anatase prepared by the hydrolysis of titanium sulphate have been studied at different temperatures and are found to be considerably different from the kinetics of the transformation of pure anatase. The transformation becomes immeasurably slow below ∼695 ± 10°C compared to ∼610°C for pure anatase. An induction period is observed in the transformation of anatase obtained from sulphate hydrolysis and the duration decreases with increase in temperature. The activation energy is ∼120 kcal/mole, a value higher than that for the pure anatase-rutile transformation. The results have been interpreted in terms of the relative rates of nucleation and propagation processes. The activation energy for the nucleation process seems to be much larger than for the propagation process. The kinetics of the transformation of anatase samples doped with different amounts of sulphate ion impurity have also been studied and the transformation is found to be progressively decelerated with increase in the impurity concentration. The energy of activation for the transformation appears to increase progressively with increase in impurity concentration.

Steady laminar flow with suction or injection and heat transfer through porous pipe

Following the method due to Bhatnagar (P. L.) [Jour. Ind. Inst. Sic., 1968, 1, 50, 1], we have discussed in this paper the problem of suction and injection and that of heat transfer for a viscous, incompressible fluid through a porous pipe of uniform circular cross-section, the wall of the pipe being maintained at constant temperature. The method utilises some important properties of differential equations and some transformations that enable the solution of the two-point boundary value and eigenvalue problems without using trial and error method. In fact, each integration provides us with a solution for a suction parameter and a Reynolds number without imposing the conditions of smallness on them. Investigations on non-Newtonian fluids and on other bounding geometries will be published elsewhere.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

An exact analysis of free vibrations of simply-supported viscoelastic plates

In this paper an exact three-dimensional analysis for free vibrations of a class of simply-supported viscoelastic rectangular plates is given. The characteristic equation defining the eigenvalues is of closed form. Some numerical results are presented for standard linear solids. Results from thin plate and Mindlin theories are also given for the purpose of comparison.

Free convection heat transfer between vertical parallel plates

A new mathematical model for the solution of the problem of free convection heat transfer between vertical parallel flat isothermal plates under isothermal boundary conditions, has been presented. The set of boundary layer equations used in the model are transformed to nonlinear coupled differential equations by similarity type variables as obtained by Ostrach for vertical flat plates in an infinite fluid medium. By utilising a parameter ηw* to represent the outer boundary, the governing differential equations are solved numerically for parametric values of Pr = 0.733. 2 and 3, and ηw* = 0.1, 0.5, 1, 2, 3, 4, ... and 8.0. The velocity and temperature profiles are presented. Results indicate that ηw* can effectively classify the system into (1) thin layers where conduction predominates, (2) intermediate layers and (3) thick layers whose results can be predicted by the solutions for vertical flat plates in infinite fluid medium. Heat transfer correlations are presented for the 3 categories. Several experimental and analytical results available in the literature agree with the present correlations.

Free-to-bound and bound exciton transitions at isoelectronic impurities: GaP(Zn,O)

We show, for sufficiently high temperatures and sufficiently weak majority-carrier binding energies, that the dominant radiative transition at an isoelectronic acceptor (donor) in p-type (n-type) material consists of the recombination of singly trapped minority carriers (bound by central-cell forces) with free majority carriers attracted by a Coulomb interaction. There are two reasons why the radiative recombination rate of the free-to-bound process is greater than the bound exciton process, which dominates at lower temperatures: (i) The population of free majority-carrier states greatly exceeds that of exciton states at higher temperatures, and (ii) the oscillator strength of the free-to-bound transition is greatly enhanced by the Coulomb attraction between the free carrier and the charged isoelectronic impurity. This enhancement is important for isoelectronic centers and is easily calculable from existing exciton models. We show that the free carrier attracted by a Coulomb interaction can be viewed as a continuum excited state of the bound exciton. When we apply the results of our calculations to the GaP(Zn, O) system, we find that the major part of the room-temperature luminescence from nearest-neighbor isoelectronic Zn-O complexes results from free-to-bound recombination and not exciton recombination as has been thought previously. Recent experiments on impulse excitation of luminescence in GaP(Zn, O) are reevaluated in the light of our calculations and are shown to be consistent with a strong free-to-bound transition. For deep isoelectronic centers with weakly bound majority carriers, we predict an overwhelming dominance of the free-to-bound process at 300°K.

Free energy of mixing of divalent basic oxides with silica

An expression derived for the free energy of mixing of a divalent basic oxide (MO) with SiO2 based on a model of silicate structure, takes into account the distribution of O2- (from MO) into the silica network, the mixing of silicate ions with O2- and the enthalpy of mixing. The resulting expression is ΔGmix=RT{N11n (2N1-N)2/4N1(1-N)+N21n N 2-N/1-N}, where N={(β+N1)-√(β+N 1)2-8βN1N2}/2β β=characteristic constant for the system N1=mol fraction of silica N2=mol fraction of MO. For the proper choice of β, calculated values of the activity of MO for the system PbO-SiO2, MnO-SiO2, FeO-SiO2 and CaO-SiO2 are in good agreement with experiment. The model predicts that the activity of the basic oxide decreases with increase in temperature.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Profligate Descent : The Cultural Transformations of Evolutionary Narrative

This dissertation traces a set of historical transformations the Darwinian evolutionary narrative has undergone toward the end of the twentieth century, especially as reflected in Anglo-American popular science books and novels. The study has three objectives. First, it seeks to understand the organizing logic of evolutionary narratives and the role that assumptions about gender and sexuality play in that logic. Second, it asks what kinds of cultural anxieties evolutionary theory raises and how evolutionary narratives negotiate them. Third, it examines the possibilities and limits of narrative transformation both as a historical phenomenon and as a theoretical question. This interdisciplinary dissertation is situated at the intersection of science studies, cultural studies, literary studies, and gender studies. Its understanding of science as a cultural practice that both emerges from and contributes to cultural expectations and institutional structures follows the tradition of science studies. Its focus on the question of popular appeal and the mechanisms of cultural change arises from cultural studies. Its view of narrative as a structural phenomenon is grounded in literary studies in general and feminist narrative theory in particular. Its understanding of gender and sexuality as implicated in discourses of epistemic authority builds on the view of gender and sexuality as contingent cultural categories central to gender studies. The primary material consists of over 25 British and American popular science books and novels, published roughly between 1990 and 2005. In order to highlight historical transformations, these texts are read in the context of Darwin s The Origin of Species and The Descent of Man, on the one hand, and such sociobiological classics as E. O. Wilson s On Human Nature and Richard Dawkins s The Selfish Gene, on the other. The research method combines feminist narrative analysis with cultural and historical contextualization, emphasizing discursive abruptions, recurrent narrative patterns, and underlying continuities. The dissertation demonstrates that the relationship between Darwin s evolutionary narrative and late twentieth-century evolutionary narratives is characterized by reemphasis, omissions, and continuous rewriting. In particular, contemporary evolutionary discourse extends the role assigned to reproduction both sexual and narrative in Darwin s writing, generating a narrative logic that imagines the desire to reproduce as the driving force of evolution and posits the reproductive sex act as the endlessly repeated narrative event that keeps the story going. The study argues that the popular appeal of evolutionary accounts of gender, sexuality, and human nature may arise, to an extent, from this reproductive narrative dynamic. This narrative dynamic, however, is not logically invulnerable. Since the continuation of the evolutionary narrative relies on successful reproduction, the possibility of reproductive failure poses a constant risk to narrative futurity, arousing cultural anxieties that evolutionary narratives need to address. The study argues that evolutionary narratives appease such anxieties by evoking a range of cultural narratives, especially romantic, religious, and national narratives. Furthermore, the study shows that the event-based logic of evolutionary narratives privileges observable acts over emotions, pleasures, identities, and desires, thus engendering a set of conceptual exclusions that limits the imaginative scope of evolution as a cultural narrative.

Describing syntax with star-free regular expressions

Koskenniemen Äärellistilaisen leikkauskieliopin (FSIG) lauseopilliset rajoitteet ovat loogisesti vähemmän kompleksisia kuin mihin niissä käytetty formalismi vittaisi. Osoittautuukin että vaikka Voutilaisen (1994) englannin kielelle laatima FSIG-kuvaus käyttää useita säännöllisten lausekkeiden laajennuksia, kieliopin kuvaus kokonaisuutenaan palautuu äärelliseen yhdistelmään unionia, komplementtia ja peräkkäinasettelua. Tämä on oleellinen parannus ENGFSIG:n descriptiiviseen kompleksisuuteen. Tulos avaa ovia FSIG-kuvauksen loogisten ominaisuuksien syvemmälle analyysille ja FSIG kuvausten mahdolliselle optimoinnillle. Todistus sisältää uuden kaavan, joka kääntää Koskenniemien rajoiteoperaation ilman markkerimerkkejä.

Monte Carlo simulations of molecular clusters in nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Error Checking Digit for Nonconventional Chemical Codes

In handling large volumes of data such as chemical notations, serial numbers for books, etc., it is always advisable to provide checking methods which would indicate the presence of errors. The entire new discipline of coding theory is devoted to the study of the construction of codes which provide such error-detecting and correcting means.l Although these codes are very powerful, they are highly sophisticated from the point of view of practical implementation

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.