OOCs, Partial Relative Difference Families and a Conjecture of Golomb

The cyclic difference sets constructed by Singer are also examples of perfect distinct difference sets (DDS). The Bose construction of distinct difference sets, leads to a relative difference set. In this paper we introduce the concept of partial relative DDS and prove that an optical orthogonal code (OOC) construction due to Moreno et. al., is a partial relative DDS. We generalize the concept of ideal matrices previously introduced by Kumar and relate it to the concepts of this paper. Another variation of ideal matrices is introduced in this paper: Welch ideal matrices of dimension n by (n - 1). We prove that Welch ideal matrices exist only for n prime. Finally, we recast an old conjecture of Golomb on the Welch construction of Costas arrays using the concepts of this paper. This connection suggests that our construction of partial relative difference sets is in a sense, unique

Thermodynamic study of oxygen in liquid lead tin alloys

The activity coefficients of oxygen in liquid lead-tin alloys have been measured between 550 and 1100°C by use of solid oxide galvanic cells Pt, Ni-NiO I Zr02 Solid electrolyte I 0 (Pb + Sn), Cermet, Pt Pt, Fe-FeO I Zr02 Solid electrolyte I O(Pb + Sn), Cermet, Pt Alcock and Richardson's quasi-chemical equation, with the coordination number of atoms set to 2, is found to predict successfully the activity coefficients of oxygen in these alloys.The relative partial molar enthalpy and entropy of oxygen ?t 1 atom per cent in the alloys have been calculated from ttva variation of the activity coefficient with temperature. The addition of tin to an unsaturated solution of oxygen in lead is shown to decrease significantly both the partial molar enthalpy and entropy of oxygen. As the measurements were restricted to a narrow range between 750-1100'C in lead-rich alloys, however, the pronounced variation of the partial molar enthalpy of oxygen with temperature at constant alloy composition predicted by the quasi-chemical model could not be verified.

Evidence of residual entropy in the cubic spinel Zn2TiO4

The standard free energies of formation of Zn2Ti04 and ZnTi03 have been determined in the temperature range 930° to i ioo'x from electromotive force measurements on reversible solid oxide galvanic cells;Ag-5at%znll I Pt, + CaO-Zr02 ZnO I II Ag-5at%Zn Y20r Th02 CaO-Zr02 + ,Pt Zn2Ti04+ ZnTi03 and II Ag-5at%Zn CaO-Zr02 + ,Pt ZnTi03+ Ti02 The values may be expressed by the equations,2ZnO (wurtz) + Ti02(rut) -> Zn2Ti04(sp), f:!:.Go = -750-2-46T (±75)cal;ZnO(wurtz) +Ti02(rut) -> ZnTi03(ilmen) ,f:!:.Co = -]600-0·]99T(±50)cal.Combination of the free energy values with the calorimetric heat of formation, and low-temperature and high-temperature heat capacity of Zn2Ti04 reported in literature, suggests a residual entropy of ],9 (±0·6) cal K-1 mol ? for the cubic spinel. Ideal mixing of Zn2+ and Ti4+ ions on the octahedral sites would result in a configurational contribution to the entropy of 2· 75 cal K-1 rnol ".The difference is indicative of short-range ordering of cations on octahedral sites.

An entropy meter based on the thermoelectric potential of a nonisothermal solid electrolyte cell

The theory, design, and performance of a solid electrolyte twin thermocell for the direct determination of the partial molar entropy of oxygen in a single-phase or multiphase mixture are described. The difference between the Seebeck coefficients of the concentric thermocells is directly related to the difference in the partial molar entropy of oxygen in the electrodes of each thermocell. The measured potentials are sensitive to small deviations from equilibrium at the electrodes. Small electric disturbances caused by simultaneous potential measurements or oxygen fluxes caused by large oxygen potential gradients between the electrodes also disturb the thermoelectric potential. An accuracy of ±0.5 calth K−1 mol−1 has been obtained by this method for the entropies of formation of NiO and NiAl2O4. This “entropy meter” may be used for the measurement of the entropies of formation of simple or complex oxides with significant residual contributions which cannot be detected by heat-capacity measurements.

Correlations between structure and thermodynamic properties of spinels and their applications in technology

Measurements a/the Gibbs' energy enthalpy and entrupy vffarmation oj chromites, vanadites and alumlnat.:s 0/ F", Ni. Co'. Mn, Zn Mg and Cd, using solid oxide galvanic cells over a ternperature range extending approximately lOOO°C, have shown that the '~'Ilir"!,,, J'JrIl/iJ~ tion 0/ cubic 2-3 oxide spinel phases (MX!O,), from component oxide (MO) with rock-salt and X.Os whir c(1f'l/!ldwn st!'llt'lw,·. call b,' represented by a semi-empirical correlalion, ~S~ = --LiS + L'i,SM +~S~:"d(±O.3) cal.deg-1 mol-1 where /',.SM Is the entropy 0/calian mixing oillhe tetrahedral alld octahedral sites o/the spinel and Sr:~ is tlie enfropy associaf,'d Wifh Ih,' randomization a/the lahn-Telier distortions. A review a/the methods/or evaluating the cation distriblltion lfl spille!s suggeJ{j' l/r,l! Ihe most promising scheme is based Oil octahedral site preference energies from the crystal field theory for the Iral1silioll IIIl'f"! IlIIL';. For I/""-Irallsifioll melal cal ions site preference energies are derived relative /0 thol'lt fLI, [ransilion metal ions from measured high tClllP('ftJi ure Cal iUlI disll iiJuriol1 in spine! phases thar contail! one IransilioJl metal and another non-transition metal carion. For 2-3 srinds compulatiorrs b,IS"J Oil i.!c[J;' Temkin mixing on each catioll subialtice predici JistributionJ that are In fair agreement with X-ray and 1I1'IIIrOll ditTraction, /IIdg""!ic dll.! electrical propcrries, and spectroscopic measurements. In 2-4 spineis mixing vI ions do not foliow strictly ideal slllIistli:al Jaws, Th,' OIl/up) associated with the randomizalion 0/the Jllhn-Teller dislOriioll" appear to be significant, only ill spinels witll 3d'. 3d', 3d' (ifld~UI' iOtls in tetrahedral and 3d' and 3d9 ions in octahedral positions. Application 0/this structural model for predicting the thermodynamic proputies ofspinel solid .,olutiofl5 or,' illustrated. F,lr complex systems additional contributions arising from strain fields, redox equilibria and off-center ions have to be qllalllififti. The entropy correlation for spinels provides a method for evaluating structure tran:.jormafiofl entropies in silllple o.\id.-s, ["founlllion on the relative stabilities ofoxides in different crystallCtructures is USe/III for computer ea/culaliof! a/phase dfugrullls ofIlIrer,',,1 III (N.lll1ie5 by method, similar to thost: used by Kaufman and Bernstein for refractory alloy systems. Examples oftechnoiogical appliCation tnclude the predictioll ofdeoxidation equilibria in Fe-Mn-AI-O s),slelll at 1600°C duj ,'Ulllpltfalion 0/phase relutions in Fe-Ni-Cr-S system,

The standard enthalpy and entropy of formation of Rh2O3 - A third-law optimization

The standard Gibbs energy of formation of Rh203 at high temperature has been determined recently with high precision. The new data are significantly different from those given in thermodynamic compilations.Accurate values for enthalpy and entropy of formation at 298.15 K could not be evaluated from the new data,because reliable values for heat capacity of Rh2O3 were not available. In this article, a new measurement of the high temperature heat capacity of Rh2O3 using differential scanning calorimetry (DSC) is presented.The new values for heat capacity also differ significantly from those given in compilations. The information on heat capacity is coupled with standard Gibbs energy of formation to evaluate values for standard enthalpy and entropy of formation at 289.15 K using a multivariate analysis. The results suggest a major revision in thermodynamic data for Rh2O3. For example, it is recommended that the standard entropy of Rh203 at 298.15 K be changed from 106.27 J mol-' K-'given in the compilations of Barin and Knacke et al. to 75.69 J mol-' K". The recommended revision in the standard enthalpy of formation is from -355.64 kJ mol-'to -405.53 kJ mol".

Thermodynamic properties of calcium titanates: CaTiO3, Ca4Ti3O10, and Ca3Ti2O7

The chemical potentials of CaO in two-phase fields (TiO2 + CaTiO3), (CaTiO3 + Ca4Ti3O10), and (Ca4Ti3O10 + Ca3Ti2O7) of the pseudo-binary system (CaO + TiO2) have been measured in the temperature range (900 to 1250) K, relative to pure CaO as the reference state, using solid-state galvanic cells incorporating single crystal CaF2 as the solid electrolyte. The cells were operated under pure oxygen at ambient pressure. The standard Gibbs free energies of formation of calcium titanates, CaTiO3, Ca4Ti3O10, and Ca3Ti2O7, from their component binary oxides were derived from the reversible e.m.f.s. The results can be summarised by the following equations: CaO(solid) + TiO2(solid) → CaTiO3(solid), ΔG° ± 85/(J · mol−1) = −80,140 − 6.302(T/K); 4CaO(solid) + 3TiO2(solid) → Ca4Ti3O10(solid), ΔG° ± 275/(J · mol−1) = −243,473 − 25.758(T/K); 3CaO(solid) + 2TiO2(solid) → Ca3Ti2O7(solid), ΔG° ± 185/(J · mol−1) = −164,217 − 16.838(T/K). The reference state for solid TiO2 is the rutile form. The results of this study are in good agreement with thermodynamic data for CaTiO3 reported in the literature. For Ca4Ti3O10 Gibbs free energy of formation obtained in this study differs significantly from that reported by Taylor and Schmalzried at T = 873 K. For Ca3Ti2O7 experimental measurements are not available in the literature for direct comparison with the results obtained in this study. Nevertheless, the standard entropy for Ca3Ti2O7 at T = 298.15 K estimated from the results of this study using the Neumann–Koop rule is in fair agreement with the value obtained from low-temperature heat capacity measurements.

Magnetic Field Dependence of Entropy And Specific Heat of YBa2Cu3O7-delta Superconductors

The change in thermodynamic quantities (e. g., entropy, specific heat etc.) by the application of magnetic field in the case of the high-T-c superconductor YBCO system is examined phenomenological by the Ginzburg-Landau theory of anisotropic type-II superconductors. An expression for the change in the entropy (Delta S) and change in specific heat (Delta C) in a magnetic field for any general orientation of an applied magnetic field B-a with respect to the crystallographic c-axis is obtained. The observed large reduction of specific heat anomaly just below the superconducting transition and the observed variation of entropy with magnetic field are explained quantitatively.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Optimal placement of Distributed Generation for a projected load increase using Relative Electrical Distance approach

There is a lot of pressure on all the developed and second world countries to produce low emission power and distributed generation (DG) is found to be one of the most viable ways to achieve this. DG generally makes use of renewable energy sources like wind, micro turbines, photovoltaic, etc., which produce power with minimum green house gas emissions. While installing a DG it is important to define its size and optimal location enabling minimum network expansion and line losses. In this paper, a methodology to locate the optimal site for a DG installation, with the objective to minimize the net transmission losses, is presented. The methodology is based on the concept of relative electrical distance (RED) between the DG and the load points. This approach will help to identify the new DG location(s), without the necessity to conduct repeated power flows. To validate this methodology case studies are carried out on a 20 node, 66kV system, a part of Karnataka Transco and results are presented.