State of reference

It must be emphasized that the choice of a particular standard state of reference has no influence on the result of equilibrium calculations and is only a matter of convenience. It is generally convenient to adopt as standard state for solid components the condition of pure component in the pure phase at the P and T of interest or, alternatively, the condition of pure component in the pure phase at P = 1 bar and T = 298.15 K. ... 

It is evident from equation 5.204 that the intrinsic significance of equation 5.206 is closely connected with the choice of standard state of reference. If the adopted standard state is that of the pure component at the P and T of interest, then AG%i is the Gibbs free energy of reaction between pure components at the P and T of interest. Deriving in P the equilibrium constant, we obtain... 

Nevertheless, if the standard state of reference is that of the pure component at P = bar and T of interest, then... 

When speaking of solutions, we implicitly state that the H2O solvent has a different standard state of reference with respect to solutes (note that the term mixture is used when all components are treated in the same way see section 2.1). The standard state generally used for the solvent in aqueous solutions is that of pure solvent at P and T of interest (or P = 1 bar and T = 298.15 K). For solutes, the hypothetical one-molal solution referred to infinite dilution, at P and T of interest (or P = bar and T = 298.15 K) is generally used. This choice is dictated by practical considerations. 

Table 9,9 Interpolation parameters giving solubility of Ar in silicate melts as a function of R Standard state of reference for gaseous phase is pure gas Ar at P = 15 kbar and T = 1600 °C. Concentration is adopted standard state for Ar in melt. is molar volume of Ar in melt,...

The concept of hole here implies that T itself is the state of reference, not the Fermi sea or other state models. 

A,, j, , The state of reference used to define the homo and lumo orbitals... 

Taking as a state of reference the extended mesogenic units shown in Fig. 28, we consider rotation of benzenes in respect to the symmetry axis as indicated in... 

Equation (9) differs from previous renditionsaccording to which w y through choice of the randomly disoriented rods (y = x) as the state of reference, instead of adopting the state of perfect aligment (y = 1) for this purpose. The difference is of no signiflcance in applications of the theory here discussed. 

The simplest way to reach this result is to replace directly the Kronecker 8 appearing in Eq.(19) by JD +1 D. Note that the possibility of replacing a Kronecker 8 by its expression in terms of the 1 -RDM and the l-HRDM, irrespective of whether the state of reference is an FCI or an HF one, implies that... 

Extension ratio relative to isotropic state of reference Wavelength of the incident hght Poisson s ratio... 

Comp. A Comp. B T. T g3 T c,pure A T m,pure A Physical state of References... 

A standard state corresponding to ai= 1 shouid be defined for each species. Except in the case of soiutions (see beiow), most of the time the standard state of species i at temperature Tcorresponds to the pure compound in its physicai state (gas, soiid, iiquid) at the same temperature and under the standard pressure of P°= 1 bar. A standard state of reference is aiso defined for each pure compound, and this corresponds to the standard state of the pure compound in its most stabie physicai state at the temperature in question. 

The quantities X, are the principal extension ratios, which specify the strain relative to an isotropic state of Reference Chapt, 5. The cycle rank 4 was first introduced by Flory and is the number of independent circuits in the network or the number of chains which have to be cut to reduce the network to an acyclic structure or tree. Subsidiary quantities called the number of effective chains and junctions noted, respectively, and Pe can be defined by the relationship... 

By characterizing the equilibrium state of reference analogously the condition of saturation turns out to be given by... 

In classical conceptions weakly distorted systems travel via relaxation towards an equilibrium state [5, 6, 8, 9]. To get the same logistics we have to postulate that in dissipative open systems optimised stationary states operate as temporary states of reference. If sufficiently fast processes are available there is no objection against the hypothesis that relaxation towards such stationary states should exhibit analogous features as in classical models [9]. If the external conditions vary steadily it should also be possible that relaxation is running off while the state of reference passes slowly through a logical sequence of temporary stationary patterns. 

The real part n cOc) characterises the energy that can be stored in a growing cell ensemble at defined distances from a stationary state of reference. "(cOc) should describe dissipation during relaxation. Relaxation of the cell ensemble is then consequently considered as a superposition of many Debye processes, the fractions of which are given by the normalised universal mass fraction of the cells of different sizes (see Eq. 11). 

In this equation, 4 s the activity of the element i (i=V, C, N) at equilibrium. In the case of infinite dilution, the activity is proportional to the atomic fraction at equilibrium X-(Henry state of reference). This assessment is true for V and N but remains a simplification for C. is the Gibbs energy of formation of the carbonitride and... 

Further, it should be emphasized that the standard state (p ,c ) is a computational state of reference, which is not necessarily physically possible for all... 

The state of reference is a hypothetic state in which any component / is pure (Xi = 1) at temperature T under pressure P and in the same physical state as the phase (even if this physical state is hypothetical for this pure component under these conditions). Then ... 

The state of reference is now the infinitely diluted solution in one (or several) of the components called solvent(s). The other conqxments are called the solutes ... 

The values of partial molar properties involved in operator [3.5] can be considered under aity conditions thus, we can define a standard Gibbs energy associated with R for which the reactants and the products are selected in their state of reference ... 

The calculation of the Gibbs energy of formation of the nuclei starting from the precursor or Gibbs energy of condensation encounters a difficulty related to the definition of the state of reference ... 

The solid forms a phase in which it is insulated, which thus constitutes the state of reference. The chemical potential of the solid is constant and equal to its molar Gibbs energy of formation. 

On the other hand, the A species (the precursor) is present in a phase with several components (molecules or ions in a fluid or point defects in a sohd) its state of reference depends on the choice of convention (I, II, in section 3.2.1), and its chemical potential depends on its abundance, expressed in molar fraction, for example. 

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