Mass Action Constants Research Articles

Amphoteric behaviour of group V dopants in (Hg, Cd)Te

The electrical behaviour of phosphorus in bulk Hg0.8Cd0.2Te crystals is compared with that in Hg0.7Cd0.3Te epitaxial films grown from Te-rich solutions. The mass action constants associated with the process of site transfer of phosphorus atoms from Hg to Te or interstitial lattice sites have been deduced for the bulk crystals and the epitaxial films. Additionally, the mass action constants for the lattice site transfer of As and Sb have also been deduced. The values of these constants indicate that the lack of site transfer from Hg to Te or interstitial lattice sites in the case of Sb and Bi, inferred experimentally in epitaxial films, is ascribed to a lower diffusivity of the Sb and Bi atoms in (Hg, Cd)Te. The implications of the amphoteric behaviour of the group V dopants on device fabrication are also discussed.

Solid state chemistry of highTcsuperconductors

Abstract The oxidation of YBa2Cu3O6+y for 0.2 < y< 1 is described by an equilibrium reaction that involves the filling of vacancies in the reference structure YBa2Cu3O7, and the creation of two hole species per added oxygen. The oxygen content as a function of temperature and oxygen partial pressure is accurately fit by a simple mass-action treatment of the oxidation reaction. The mass-action constants are independent of composition and are thermally activated with a single enthalpy of oxidation of −0.99 eV. The constancy of the thermodynamic parameters across this broad compositional range suggests that there is a considerable amount of order in what has been generally considered to be a disordered tetragonal structure.

Thermodynamic Properties of Nonstoichiometric Yttria‐Stabilized Zirconia at Low Oxygen Pressures

Thermodynamic properties of 8‐mol%‐yttria‐stabilized zirconia have been determined in the 810° to 1040°C temperature range at low Po2. A high‐temperature solid‐state coulometric titration method was used. The mass action constant, Kma, can be represented at low Po2 as Kma=0.677 exp [(–3.98 ±0.03 eV)/kT].

Oxygen Association Pressure Measurements on Nonstoichiometric Cerium Dioxide

The data that were obtained by using a capacitance manometer system to measure the deviation from stoichiometry in nonstoichiometric cerium dioxide as a function of oxygen partial pressure at 800°C were analyzed along with existing data obtained at other temperatures. It was determined that, for values of log less than −2.4, the observed −1/5 dependence of the deviation from stoichiometry upon the oxygen partial pressure is due to the existence of doubly ionized nonstoichiometric vacancies along with the presence of charge compensating doubly ionized vacancies that are caused by Ca impurities. The mass action constants that were calculated for the defect reaction at various temperatures were then used to analyze the conductivity data that exists at corresponding temperatures. It was determined that the −1/5 dependence of the conductivity upon the oxygen partial pressure is also due to the presence of doubly ionized nonstoichiometric vacancies along with the existence of charge compensating doubly ionized vacancies caused by Ca impurities. Finally, it was also shown that, for values of log less than −2.4, not only is the mobility a function of temperature only, but also that the oxygen partial molal enthalpy change is independent of both temperature and composition.

Auger transitions in semiconductors and their computation

To obtain an accurate theoretical determination of Auger transition rates from first principles it is essential that the multidimensional integral of the transition probabilities should not be approximated, particularly with regard to the overlap functions, as has been done previously. In considering general interband Auger transitions (with direct or indirect bands) the difficulty of complicated limits imposed by energy and momentum conservation is removed by a transformation of the variables, resulting in an integration over a complete six-dimensional solid angle. This makes accurate computation possible without approximating the integrand-within the limitation of the best available overlap functions and band structure. The initial application is to InSb where small- and large-signal Auger lifetimes, mass-action constants and impact ionisation rates are determined using Fermi-Dirac statistics, non-parabolic energy bands for all states and overlap functions derived from the four-band k.p model.

Thermodynamics and Statistical Mechanics

Peter T Landsberg 1979 Oxford: Oxford University Press xii + 461 pp price £9.75 This new book by Professor Landsberg deserves as much success as his earlier book and contains new topics and fresh approaches to better known material. As well as covering the traditional topics of classical thermodynamics, additional topics such as phase transitions including critical exponents, the law of mass action and equilibrium constants are explained, the latter being normally reserved for books in chemistry and chemical engineering.

Absorption and ionic conductivity of oxygen‐containing SrF2 crystals

AbstractAn absorption band at 3644 cm−1 is caused by isolated OH− ions. O− ions cause an absorption band at 213 nm the oscillator strength of which is 0.020. Charge‐compensation of O− ions is effected by F− ion vacancies (F). As for CaF2 crystals there occur monomers and dimers of [O− – F] complexes. The mass action constants of association of F with oxygen centres are KAD = ⅓ exp (4.28 – 0.82 eV/kT) for [O− – F], KAT = 4 exp (17.4 – 1.25 eV/kT) for [2 O− – F] and KAQ = exp (4.2 – 0.89 eV/kT) for [2 O− – 2 F].

Borate Exchanges of Lemna minor L. as Studied with the Help of the Enriched Stable Isotopes and of a (n,α) Nuclear Reaction

Despite the lack of a convenient radioisotope of boron, it is possible to measure unidirectional fluxes of borate between cellular systems and their external medium. It was accomplished by using the two purified stable isotopes ((10)B and (11)B), with (10)B specifically detected by a (n,alpha) nuclear reaction. The method was applied to compartmental analysis of borate with intact plants of Lemna minor L. Four compartments were suggested. Three of them apparently correspond to the three classical ones: free space (including easily dissociable borate monoesters), cytoplasm, and vacuole. The fourth one was interpreted as corresponding to very stable borate diesters in the cell walls. The method allows the determination of the borate capacities of the various compartments and of the borate unidirectional fluxes between the different compartments, at borate flux equilibrium. Other physicochemical data (mono and diester mass action constants, turn over numbers) were evaluated. The results are consistent with what is known of pure substances.

Revised calculation of point defect equilibria and non-stoichiometry in gallium arsenide

From an analysis of relevant published literature, it is deduced that the dominant disorder in GaAs is Frenkel defect formation on the arsenic sub-lattice with the arsenic vacancy exhibiting donor-like behaviour at high temperatures. Standard methods of chemical thermodynamics are used to derive expressions for the concentrations of the neutral and charged point defects. Mass action constants are obtained from a combination of a priori estimates and fitting to experimental data. The phase extent of GaAs is mapped and the model shown to account adequately for the density, lattice parameter and internal friction variations in as-grown and heat treated material as well as for the high temperature Hall coefficient behaviour.

Solubility and point defect-dopant interactions in gallium arsenide—III: Germanium-doping

The form of the solubility curves for VPE and LPE grown material are rationalised using a thermodynamic model which predicts that compensation of donors in VPE material is due to the donor-gallium vacancy complex Ge Ga V − ga whereas, in LPE material, the dominant acceptor making the material p type is the arsenic substituted state Ge − As. Mass action constants for the incorporation reactions for these entities and for the donor Ge + Ga are obtained. The compensation ratio in crystals grown from a congruent melt is predicted to be N D / N A ~ 5.9, and the transition to p type conductivity as one grows from Ga-rich solutions at progressively lower temperature is shown to occur at less than 100°C below the congruent melting point so that all LPE material should be p type. The superlinear behaviour of the total-germanium solubility curve at very high doping levels is postulated to be due to the formation of neutral Ge GaGe As pairs.

The geochemistry of an invariant point in the metamorphosed basic volcanics at Sofala, New South Wales

A system, consisting of a modified Fisher and Zen representation of an end-member reaction model (CaO-MgO-SiO2-H2O-CO2quartz, talc, tremolite, magnesite, calcite, dolomite, fluid), is first calibrated using a fit of Greenwood's equation to experimental data. Secondly, the same system is calibrated using tabulated thermodynamic data. The two calibrations are used to study the relationships amongst solid-solution activity models, natural assemblages, bulk compositions and fluid geochemistry over a small area at Sofala, N.S.W., where previous work has mapped a series of reactions/invariant points∗∗The Sofala assemblages used here are inferred to have formed at 415°C, 2 kbar and so the words invariant point/reaction apply to assemblages which are in fact divariant/trivariant. in greenschist facies metamorphosed basic volcanics. Between the two calibrations, the calculations indicate that there are significant differences in a(H2O), as well as in a(CO2), which are primarily related to significant differences in ΔSf(solids). A data table, necessary for the calculations, is given for the apparent free energy of formation of CO2 at P and T based on Perchuk and Karpov's work.The chemistry of the natural phases is considered in the modified Fisher and Zen equation through the use of various solid solution activity models and the mass action constant (K̄) for the solid phases in a reaction. For the Sofala rocks, this process suggests a mild preference for the first calibration and for the full Temkin activity model for solid solutions. In the first calibration, the magnesite-absent invariant point occurs twice in the interval 300–600°C, but the two occurrences approach each other, coincide, and then disappear below 0.5 kbar. The field of stability of the assemblage talc + calcite is shown to be sensitive to ø (the mole fraction of constituents other than molecules of H2O and CO2 in the fluid phase) that any implied pressure control can be reversed by 0 ≦ ø ≦ 0.05. A ln K̄ diagram reveals that the natural occurrences of the magnesite-absent invariant point imply 0 ≦ ø ≦ 0.1 at Sofala. The ln K̄ diagram also indicates that extensive dilution of the components in the end-member model (by extra components in the Sofala rocks) causes complete instability of the magnesite-absent invariant point and partial to complete instability of the reactions that define the invariant point. The ln K̄ diagram thus indicates the bulk compositions that are favourable for the existence of reaction/invariant points in the field.

Theory of the lonization Equilibrium in Dense Plasmas

AbstractThe SAHA equation for the ionization equilibrium in plasmas is analyzed. Especially the balance between the effect of bound states (mass action constant) and the effect of free states (lowering of the ionization energy) is investigated.The lowering of the ionization energy is represented as an expansion with respect to the density. It is shown that the coefficients of this expansion and the mass action constant are connected with the known quantum statistical virial coefficients. The question of introducing the energy levels of a screened COULOMB potential is investigated. Several possibilities for the choice of the weight factor in the mass action constant are discussed. In the case of higher densities PADÉ approximations for the ionization energy are constructed. The existence of instabilities of the NORMAN‐STAROSTIN‐type is discussed.

Auger effect involving recombination centres

The concentration dependence of the lifetime of minority carriers in copper-diffused germanium is explained quantitatively. The fit yields an Auger effect mass-action constant which is shown to be in order-of-magnitude agreement with theory.

Recombination statistics for auger effects with applications to p-n junctions

A generalization is presented of the usual Shockley-Read recombination statistics to include the effect of Auger transitions. This yields a new expression for the steady-state recombination rate of electrons and holes. The current density through a p-n junction is then exhibited as essentially a sum of recombination currents. With these ideas it is shown how junction characteristics can be discussed, and a rough classification is given of these characteristics for various conditions. Only the case of moderate bias is considered, subject to the assumption of mass-action laws, with the mass-action constants independent of applied potential. A simple variation of quasi-Fermi and electrostatic potential through the junction is also assumed, and the limitations of the model are discussed. Suggestions are made concerning the identification of mass-action constants from experimental characteristics.

The dielectric capacity of electrolytes in mixed solvents: ion association in solutions of magnesium sulphate

The remarkable achievements of Debye and Hückel, Onsager, and their colleagues in explaining and rationalizing the experimental data upon the behaviour of strong electrolytes in dilute solution have naturally led to much intensive research directed towards the extension of their theories to ranges of greater ionic concentration. From this work the theory of ion association, sponsored by Niels Bjerrum, has emerged with marked success. Assuming that the forces between oppositely charged ions obey the simple Coulomb law, Bjerrum has calculated the probability of such ions being within a distance, q 0 , at which the thermal energy per degree of freedom is but one-quarter of the electrostatic energy holding the ions together. Oppositely charged ions at less than this distance from one another are termed short-range pairs. The true degree of association (1— α *) of an electrolyte, as distinguished from the classical conception of undissociated molecules, is a measure of the number of short-range pairs, and Bjerrum has shown that the law of mass action may be applied to this association to develop a relation which reproduces the activities of electrolytes in more concentrated solution with remarkable fidelity. Onsager (1927) has calculated some approximate values of the true degree of association by consideration of the discrepancies between experimental conductivity data for aqueous solutions and the figures derived from his equation. Similar, and more extensive and more accurate measurements have been made by Davies (1927). In solvents of lower dielectric constant, the increased inter-ionic forces lead to still wider discrepancies, and many workers have shown that electrolytes which are almost completely non-associated in water are appreciably associated in solvents of reduced dielectric capacity. Martin (1928) has shown that the alkali metal halides are incompletely dissociated in benzonitrile and that the association obeys a generalized law of mass action. Fuoss and Kraus (1933 a ) have observed the same effects with the alkali metal nitrates dissolved in ammonia and other solvents of low dielectric constant. The mass-action constants derived from their results are in complete agreement with those predicted by the Bjerrum ion-association theory and, using measurements of the conductivity of tetra iso - amylammonium nitrate in dioxan-water mixtures, the same workers (1933 b ) have succeeded in extending the theory to include higher forms of association. Swift (1938) has confirmed the views of Fuoss and Kraus for ions of small radii by an investigation of the conductivities of solutions of the alkali metal halides in dimethylamine.

The kinetics of hœmoglobin IV- General methods and theoretical basis for the reactions with carbon monoxide

Some years ago, Hartridge and Roughton published four papers (1923-1927) upon the kinetics of the rapid reactions between oxygen and hæmoglobin. Following on this work an investigation has been made of the corresponding reactions between carbon monoxide and hæmoglobin, and also of the reactions in which carbon monoxide and oxygen both compete for union with hæmoglobin. According to the classical paper of Douglas, Haldane and Haldane (1912) the hæmoglobin-carbon monoxide reactions should only differ from the hæmoglobin-oxygen reactions in the numerical value of the mass action constants. It was therefore expected that the kinetic study of these sister reactions would contribute towards a fuller understanding of these sister reactions would contribute towards a fuller understanding of the reactions between oxygen and hæmoglobin. Furthermore, a knowledge of rates of the carbon monoxide reactions is of service, not only in working out the factors involved in the passage of O 2 into the red blood corpuscle (Roughton, 1932), but also in interpreting the measurements of the carbon monoxide as a "physiological reagent," e. g. , determination of blood volume and distribution, indirect measurement of O 2 pressure in arterial blood, cool gas poisoning, etc. Lastly, the similarity between the kinetics of the reactions of O 2 and CO with hæmoglobin and the kinetics of numerous enzyme processes, as set forth especially by J. B. S. Haldane in his recent book (1930), makes this problem well worth working out from the viewpoint of enzyme chemistry.