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.

Aspects of tautomerism. Part II. Reactions of the pseudo-acid chloride of o-benzoylbenzoic acid with nucleophiles

Reactions of fourteen nucleophiles with the pseudo-acid chloride of o-benzoylbenzoic acid in two solvents have been studied. The nucleophiles that react primarily at the tetrahedral carbon atom to give pseudo derivatives, are weaker than those that react at the carbonyl carbon atom causing opening of the lactone ring. An explanation for this phenomenon is advanced.

Aspects of tautomerism. Part III. A new dimerisation reaction of pseudo-acid chlorides

Pseudo-acid chlorides of five 4′-substituted o-benzoylbenzoic acids are converted into a mixture of dilactones with sodium iodide in acetone. The meso-isomer is always formed to a larger extent than the (±)-mixture. These results imply that the radicals involved are not planar.

Raman spectra of crystalline double sulphates Part II. Ammonium double sulphates

Raman spectra of single crystals of (NH4)2M(SO4)2·6 H2O where M=Mg, Zn Ni or Co have been recorded using λ 2537 excitation. Interesting results concerning the substitution of the divalent atoms in the double sulphate lattice on the sulphate and ammonium frequencies are observed. The spectra of these double sulphates are discussed in the light of the known crystal structure details and in relation, to the spectra of the corresponding potassium double sulphates, reported recently by the author. The Raman spectrum of NaNH4SO4·2 H2O has also been recorded for the first time and the results obtained are also included.

Polarisation studies on the Raman spectra of cubic crystals - Part II: Calcium fluoride and potassium aluminium sulphate

Polarisation characters of the Raman lines of calcium fluoride (fluorspar) and potassium aluminium sulphate (alum) were investigated under the following conditions. Unpolarised light was incident normally on a face of the crystal making an angle 22.5° with a cubic face and the light scattered transversely along a cubic axis was analysed by a double image prism kept with its principal axes inclined at 45° to the vertical. Under these conditions the depolarisation factors of the Raman lines belonging to the totally symmetric (A), the doubly degenerate (E) and the triply degenerate (F) modes should be respectively =1, >1 and <1. The characteristic Raman line of CaF2 at 322 cm-1 exhibited a depolarisation value less than 1, showing thereby that the corresponding mode is a triply degenerate one (F). The Raman lines observed in the spectrum of K-alum were also classified and the results were compared with those given by previous investigators using standard crystal orientations.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part I. Copper(I and II)-ammonia and methylamine complexes

The equilibrium between cuprous ion, cupric ion and metallic copper has been studied using polarographic and redox potential measurements, by reducing cupric ion with copper gauze until equilibrium. Using the well-defined anodic diffusion current plateau, an amperometric method for estimating cuprous copper based on the titration of cuprous ion with dichromate or permanganate has been developed. The diffusion current constant and the disproportionation constant of cuprous ion and the standard potential for the reduction reaction of Cu2+ → Cu+ have been determined. Polarograms have been taken after reducing cupric complexes of ammonia and methylamine with copper until equilibrium. In the case of the copper-ammonia system, reduction to the cuprous state is practically complete while in the case of the cupric-methylamine system, the first cathodic wave occurs to some extent. A new method, called the polarographic-redox potential method, for determining the stability constants of cuprous and cupric complexes has been developed. The method depends upon the determination of the concentration of complexes by polarographic wave heights, and free cupric anc cuprous ions by redox potentials. The stability constants of the following complexes have been obtained: Cu(NH3)2+4, Cu(NH3)+2, Cu(CH3NH2)2(OH)2, Cu(CH3NH2)+2. The stability constants determined by the new method and the half-wave potential shift method agree and the value for the cupric-ammonia complex is in good agreement with Bjerrum method, indicating the reliability of this method.

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.

The Raman spectra of organic compounds -Part I. Methyl, ethyl, n-propyl and n-butyl alcohols

The Raman spectra of methyl alcohol, ethyl alcohol, n-propyl alcohol and n-butyl alcohol have been recorded using λ 2537 excitation. 35, 49, 45 and 51 Raman lines respectively have been identified in the spectra of these alcohols, in addition to the rotational 'wings'. In each case, a large number of additional lines have been recorded. The existence of Raman lines with frequency shifts greater than 3800 cm.-1, first reported by Bolla in the spectrum of ethyl alcohol, has been confirmed. Similar high-frequency shift Raman lines have also been recorded in the spectrum of methyl alcohol. They have been assigned as combinations. Proper assignments have been given for the prominent Raman lines appearing in the spectra of these alcohols.

Isomerisations of substituted β-keto-esters - Part II. Isomerisation of ethyl 1-ethoxycarbonyl 2oxocyclopentyl acetate into 2, 3-diethoxycarbonylcyclohexanone

A mechanism for the isomerisation of ethyl 1-ethoxycarbonyl-2-oxocyclopentylacetate (I) into a cyclohexane β-keto-ester as proceeding through an intermediate bicyclic /gb-diketone (VII) has been considered as an alternative mechanism to one earlier suggested.1 The determination of the structure of the isomerised β-keto-ester as 2, 3-diethoxycarbonylcyclohexanone (V) has provided support for the earlier mechanism.

Raman spectra of single crystals of dicarboxylic acids - Part I. β-malonic acid and β-succinic acid

Raman spectra of single crystals of β-malonic acid and β-succinic acid have been photographed using λ 2536·5 radiation. 32 Raman lines have been recorded in the case of β-malonic acid. Of these 21 lines have been recorded for the first time. The three intense lattice lines at 52, 90 and 144 cm.-1 have been attributed to rotational lattice oscillations. 29 Raman lines in the case of β-succinic acid have been recorded. The entire lattice spectrum and many internal frequencies have been recorded for the first time. The three intense lattice lines at 80, 135 and 160 cm.-1 have been assigned to the rotational oscillations of the two molecules of the succinic acid in the unit cell.

Studies on the hydrolysis of metal ions - Part II-Nickel

A detailed investigation of the hydrolysis of nickel in the lower concentration range has been made. The results have been analysed on the basis of 'Core + links' theory and on the assumption of the formation of one predominant complex. Evidence is obtained for the formation of Ni2 (OH)62- and its stability constant is calculated to be 1038.78

Possible use of self-calibration to reduce systematic uncertainties in determining distance-redshift relation via gravitational radiation from merging binaries

By observing mergers of compact objects, future gravity wave experiments would measure the luminosity distance to a large number of sources to a high precision but not their redshifts. Given the directional sensitivity of an experiment, a fraction of such sources (gold plated) can be identified optically as single objects in the direction of the source. We show that if an approximate distance-redshift relation is known then it is possible to statistically resolve those sources that have multiple galaxies in the beam. We study the feasibility of using gold plated sources to iteratively resolve the unresolved sources, obtain the self-calibrated best possible distance-redshift relation and provide an analytical expression for the accuracy achievable. We derive the lower limit on the total number of sources that is needed to achieve this accuracy through self-calibration. We show that this limit depends exponentially on the beam width and give estimates for various experimental parameters representative of future gravitational wave experiments DECIGO and BBO.