Principal equilibrium-determining component

For the dissolution of a crystal into a melt, if one wants to predict the interface melt composition (that is, the composition of the melt that is saturated with the crystal), the dissolution rate, and the diffusion profiles of all major components, thermodynamic understanding coupled with the diffusion matrix approach is necessary (Liang, 1999). If the effective binary approach is used, it would be necessary to determine which is the principal equilibrium-determining component (such as MgO during forsterite dissolution in basaltic melt), estimate the concentration of the component at the interface melt, and then calculate the dissolution rate and diffusion profile. To estimate the interface concentration of the principal component from thermod5mamic equilibrium, because the concentration depends somewhat on the concentrations of other components, only... 

Diffusive dissolution of MgO-rich olivine and diffusion profiles MgO is the principal equilibrium-determining component and its diffusion behavior is treated as effective binary. Consider the dissolution of an olivine crystal (Fo90, containing 49.5 wt% MgO) in an andesitic melt (containing 3.96 wt% MgO) at 1285°C and 550 MPa (exp 212 of Zhang et al. 1989). The density of olivine is 3198 kg/m, and that of the initial melt is 2632 kg/m. Hence, the density ratio is 1.215. To estimate the dissolution parameter a, it is necessary to know the interface melt... 

Crystai growth distance and behavior of major component This problem is similar to diffusive crystal dissolution. Hence, only a summary is shown here. Consider the principal equilibrium-determining component, which can be treated as effective binary diffusion. The density of the melt is often assumed to be constant. The density difference between the crystal and melt is accounted for. 

Behavior of trace element that can be treated as effective binary diffusion The above discussion is for the behavior of the principal equilibrium-determining component. For minor and trace elements, there are at least two complexities. One is the multicomponent effect, which often results in uphill diffusion. This is because the cross-terms may dominate the diffusion behavior of such components. The second complexity is that the interface-melt concentration is not fixed by thermodynamic equilibrium. For example, for zircon growth, Zr concentration in the interface-melt is roughly the equilibrium concentration (or zircon saturation concentration). However, for Pb, the concentration would not be fixed. 

Calculate Pe = 2aU/D, where D is the diffusivity of the principal equilibrium-determining component. 

Pure rotational spectroscopy in the microwave or far IR regions joins electron diffraction as one of the two principal methods for the accurate determination of structural parameters of molecules in the gas phase. The relative merits of the two techniques should therefore be summarised. Microwave spectroscopy usually requires sample partial pressures some two orders of magnitude greater than those needed for electron diffraction, which limits its applicability where substances of low volatility are under scrutiny. Compared with electron diffraction, microwave spectra yield fewer experimental parameters more parameters can be obtained by resort to isotopic substitution, because the replacement of, say, 160 by lsO will affect the rotational constants (unless the O atom is at the centre of the molecule, where the rotational axes coincide) without significantly changing the structural parameters. The microwave spectrum of a very complex molecule of low symmetry may defy complete analysis. But the microwave lines are much sharper than the peaks in the radial distribution function obtained by electron diffraction, so that for a fairly simple molecule whose structure can be determined completely, microwave spectroscopy yields more accurate parameters. Thus internuclear distances can often be measured with uncertainties of the order of 0.001 pm, compared with (at best) 0.1 pm with electron diffraction. If the sample is a mixture of gaseous species (perhaps two or more isomers in equilibrium), it may be possible to unravel the lines due to the different components in the microwave spectrum, but such resolution is more difficult to accomplish with electron diffraction. 

Mathematical functions play an important role in thermodynamics, classical mechanics, and quantum mechanics. A mathematical function is a rule that delivers a value of a dependent variable when the values of one or more independent variables are specified. We can choose the values of the independent variables, but once we have done that, the function delivers the value of the dependent variable. In both thermodynamics and classical mechanics, mathematical functions are used to represent measurable properties of a system, providing values of such properties when values of independent variables are specified. For example, if our system is a macroscopic sample of a gas at equilibrium, the value of n, the amount of the gas, the value of T, the temperature, and the value of V, the volume of the gas, can be used to specify the state of the system. Once values for these variables are specified, the pressure, P, and other macroscopic variables are dependent variables that are determined by the state of the system. We say that P is a state function. The situation is somewhat similar in classical mechanics. For example, the kinetic energy or the angular momentum of a system is a state function of the coordinates and momentum components of all particles in the system. We will find in quantum mechanics that the principal use of mathematical functions is to represent quantitites that are not physically measurable. 

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