Author: admin
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Free energy
The free energy of mixing is defined as: ΔGmix = ΔHmix – TΔSmix The variation in free energy as a function of composition and temperature can be considered for three different situations: an ideal solution, a non-ideal solution with a positive enthalpy of mixing, and a non-ideal solution with a negative enthalpy of mixing. 1. Ideal solid solution, ΔHmix = 0…
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Thermodynamics of solid solutions
Entropy The entropy of the two endmembers, A and B, of a solid solution are SA and SB, and are mainly vibrational in origin (i.e. related to the structural disorder caused by thermal vibrations of the atoms at finite temperature). The entropy of the solid solution will always be greater than the entropy of the mechanical mixture. The…
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Olivine
Olivine is a name for a series of minerals with the formula M2SiO4, where M is most commonly Fe or Mg. Fayalite (Fe2SiO4) and forsterite (Mg2SiO4) form a substitutional solid solution where the iron and magnesium atoms can be substituted for each other without significantly changing the crystal structure. As mentioned previously, there is a size mismatch of only about 7%…
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Solid solutions
A solid solution is a single phase which exists over a range of chemical compositions. Some minerals are able to tolerate a wide and varied chemistry, whereas others permit only limited chemical deviation from their ideal chemical formulae. In many cases, the extent of solid solution is a strong function of temperature, with solid solution…
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Introduction
The extent to which the components of an alloy are miscible depends on the interaction between the atoms: In these solid solutions, different types of atoms or molecules exist in the same crystal lattice. A good example of a solid solution is the Cu-Ni system, for which the phase diagram is shown below Phase diagram…
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Resistances
We can use concepts of mass transfer resistance to make the analysis of mass transfer with combined mechanisms much easier. Definition of resistance A resistance is the driving potential (or driving force) divided by the transfer rate: resistance=driving potentialtransfer rate We are probably familiar with Ohm’s law, in which the driving potential is the voltage and the…
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Combined diffusion and convection
What do we do in cases like this hypothetical mass transfer device? Given the concentrations of species A at points 1 and 2 (��1, ��2), how do we compute the rate of mass transfer between them? We need to consider convective and diffusive mass transfer in multiple media. Concentration profiles The concentration profile owing purely to…
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Mass Convection
As we saw earlier, mass transfer refers to mass in transit due to a species concentration gradient in a mixture, and mass convection is one of the mechanisms for this transit. Mass transfer by convection involves the transport of material between a boundary surface (such as solid or liquid surface) and a moving fluid or…
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The diffusion coefficient
One of the big unknowns in Fick’s equation above is the diffusion coefficient, ���. The diffusion coefficient (or diffusivity) is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). On a theoretical basis, the diffusion coefficient is proportional to…
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Diffusion
Describing diffusion quantitatively Exercise: Diffusion Suppose we have molecule � diffusing in a domain between boundary 1 and boundary 2, where ��,1 and ��,2 are held fixed. What happens to �� between boundary 1 and boundary 2 and what is the rate of diffusional mass transfer (moles/time) across some area �? Note that � represents an area � by � into the figure. Here is a particle simulation. Fick’s law of diffusion…