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Mass action law

About: Mass action law is a(n) research topic. Over the lifetime, 168 publication(s) have been published within this topic receiving 2684 citation(s).

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Abstract: Doping limits in semiconductors are discussed in terms of the amphoteric defect model (ADM). It is shown that the maximum free electron or hole concentration that can be achieved by doping is an intrinsic property of a given semiconductor and is fully determined by the location of the semiconductor band edges with respect to a common energy reference, the Fermi level stabilization energy. The ADM provides a simple phenomenological rule that explains experimentally observed trends in free carrier saturation in a variety of semiconductor materials and their alloys. The predictions of a large enhancement of the maximum electron concentration in III–N–V alloys have been recently confirmed by experiment.

309 citations

Journal ArticleDOI
TL;DR: The present approach highlights both the crucial role of the intrinsic entropy of each state and the physically questionable role of chemiostats for deriving the first law for molecular motors subject to an external force under realistic conditions.
Abstract: For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept of internal energy, intrinsic entropy and free energy for states follows from a microscopic description using one assumption on time scale separation. A first-law energy balance then allows the unique identification of the heat dissipated in one transition. Consistency with the second law on the ensemble level enforces both stochastic entropy as third contribution to the entropy change involved in one transition and the local detailed balance condition for the ratio between forward and backward rates for any transition. These results follow without assuming weak coupling between the enzyme and the solutes, ideal solution behavior or mass action law kinetics. The present approach highlights both the crucial role of the intrinsic entropy of each state and the physically questionable role of chemiostats for deriving the first law for molecular motors subject to an external force under realistic conditions.

106 citations

Journal ArticleDOI
Abstract: The electron concentration and mobility in polycrystalline In 2 O 3 have been measured as a function of temperature and partial oxygen pressure, in the temperature range from 25 to 700°C. These experimental data are critically compared with literature data. A conduction model is proposed. Theoretical values of the electron concentration as a function of the partial oxygen pressure are reported for temperatures from 700 to 1400°C. An estimate is given for the minimum room temperature “intrinsic” electron concentration in In 2 O 3 after a high temperature annealing experiment. It is also shown that interpretations of conductivity values for porous material in terms of carrier concentration only, can be very misguiding.

97 citations

Journal ArticleDOI
Abstract: The point defect chemistry in sapphire ({alpha}-Al{sub 2}O{sub 3}) has been investigated using traditional mass action calculations. These required a consistent set of defect formation and cluster binding energies, which were provided by atomistic simulation calculations. The defect reactions studied include those associated with intrinsic defects and the aliovalent impurities Mg{sup 2+} and Ti{sup 4+}. Both perfect co-doping and doping that assumes an excess of Mg{sup 2+} or Ti{sup 4+} ions were considered. In all cases the intrinsic defect concentrations are dramatically affected by dopant ions, even at the p.p.m. level. This is a consequence of the high intrinsic defect formation energies. Thus, even in unintentionally doped sapphire, it is suggested that the point defect chemistry will be controlled by background trace impurity ions.

88 citations

Journal ArticleDOI
Abstract: A quantitative investigation has been made of ion-exchange diffusion and equilibria in the felspathoids, basic cancrinite (M$\_{2}$O.Al$\_{2}$O$\_{2}$.2$\cdot $4SiO$\_{2}$.0$\cdot $6 M OH.xH$\_{2}$O), basic sodalite (M$\_{2}$O.Al$\_{2}$O$\_{3}$.2$\cdot $5SiO$\_{2}$.0$\cdot $34 MOH.xH$\_{2}$O) and K and Rb analcite (M$\_{2}$O.Al$\_{2}$O$\_{3}$.4SiO$\_{2}$). The isotherm contours were of three kinds: an 'ideal' form obeying the mass action law K = (B$\_{c}$A$\_{s}$/A$\_{c}$B$\_{s}$) (Na-Li, Na-K, Li-K and Na-Ag in basic sodalite); a sigmoid form obeying the equation log$\_{10}$ K = log$\_{10}$ (B$\_{c}$A$\_{s}$/A$\_{c}$B$\_{s}$) + C(1-2B$\_{c}$) where the constant C takes a negative value (Na-Li in basic cancrinite); and a form exhibiting hysteresis (Na-Ag and Li-Ag in basic cancrinite and K-Rb in analcite). The hysteresis was shown to be due to limited mutual solid solubility of the end-members of the exchange and to an associated difficulty in nucleating crystallites of one growing phase on or in a matrix of the other. This effect is most strikingly found in the Rb-K exchange in analcite, for which various scanning loops were traversed. A quantitative approach to the theory of the above types of exchange isotherm has been given, and applied to the present and to earlier results obtained with crystalline exchangers. This gives a possible theoretical basis of the equation log$\_{10}$ K = log$\_{10}$ (B$\_{c}$A$\_{s}$/A$\_{c}$B$\_{s}$) + C(1-2B$\_{c}$) and for Kielland's equation log$\_{10}$ f$\_{Ac}$ = CB$_{c}^{2}$. Examination of selectivity coefficients shows that the crystalline exchangers may possess very high selectivities towards one alkali metal ion as against another or for heavy metal ions such as Ag or T1. These selectivities may change radically as one crystal is substituted for another. Ion sieve effects, partial or complete, were observed and can bring about a Donnan membrane hydrolysis of salts even of strong acids or bases, such as CsCl. Comparison has been made of the exchange diffusion coefficients evaluated in these laboratories for several kinds of crystal. A feature of exchanges where the temperature variable has been studied is the normally small temperature coefficient of the exchange equilibria and so a small value of the heat of exchange. A model has been proposed which regards the reactions as an interchange of ions between two inert dielectrics. This interpretation provides a simple explanation of the observed behaviour.

73 citations

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