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If the membrane becomes free to move, it would move to the left, compressing the left chamber and expanding the right to equilibrate the pressure difference. However, if the membrane is constrained, the fluid may cavitate in the left chamber to relieve the low pressure. This is analogous to the formation of voids in the Kirkendall effect.
3.1.4 Diffusion of Interstitial Particles in a Chemical Concentration Gradient
Another system obeying Fick's law is one involving the diffusion of small interstitial solut atoms (componen 1) among the interstitces of a host crystal in the presence of an interstitial-atom concentration gradient. The large solvent atoms (component 2) essentially remain in their substitutional sites and diffuse much more slowly than do the highly mobile solute atoms, which diffuse by the interstitial diffusion mechanism. The solvent atoms may therefore by considered to be immobile.
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The Nernst-Einstein equation expresses a link between the mobility and the diffusivity
3.1.5 On the Algebraic Signs of Diffusivities
The rate of entropy production is nonnegative. M1 is also nonnegative and L11 must be nonnegative.
A negative diffusivity leads to an ill-posed diffusion equation; so formulations based on fluxes and their conjugate driving forces are preferred to Fick's law and are more physical
3.1.6 Summary of Diffusivities
Four different types of diffusivities include the self-diffusivity in a pure material, the self-diffusivity of solute i in a binary system, the intrinsic diffusivity of component i in a chemically inhomogeneous system, and the interdiffusivity in a chemically inhomogeneous system
3.2 Mass Diffusion in an Electrical Potential Gradient
A gradient in electrostatic potential can produce a driving force for the mass diffusion of a species. Two examples of this are the potential-gradient-induced diffusional transport of charged ions in ionic conductors and the electron.
3.2.1 Charged Ions in Ionic Conductors
Consider an ionic material that contains a dilute concentration of positively charged ions that diffuse interstitially.
The conductivity is direcly proportional to the diffusivity
3.2.2 Electromigration in Metals
An applied electrical potential gradient can induce diffusion (electromigration) in metals due to a cross effect between the diffusing species and the flux of conduction electrons that will be present. When an electric field is applied to a dilute solution of interstitial atoms in a metal, there are two fluxes in the system: a flux of conduction electrons, Jq, and a flux of interstitials, J1.
Evaluating the quantity L1q requires understanding the physical mechanism that couples the mass flux of the interstitials to the electron current.
The force arises from the change in the self-consisten electronic charge distribution surrounding the interstitial defect. The defect scatters the current-carrying electrons and creates a dipole, which in turn creates a resistance and a voltage drop across the defect. This dipole, known as Landauer resistivity dipole, exerts an electrostatic force on the nucleus of the interstitial. This current-induced force is usually described phenomenoligically by ascribing an effective charge to the defect, which couples to the applied electric field to create an effective force.
The force, in turn, induces a diffusional drift flux of interstitials.
Consider the interstitial flux in a material subjected to both an electrostatic driving force and a concentration gradient.
Beta can be measured by passing a fixed current through an isothermal system until a quasi-steady state is achieved where J1 approaches zero. Uphill diffusion (flux in the direction of the concentration gradient) takes place until the concentration gradient term cancels the electromigration term.
Electromigration can be used to purify a variety of metals by sweeping interstitials to one end of a specimen
3.3 Mass Diffusion in a Thermal Gradient
Both thermal gradients and electrical-potential gradients can induce mass diffusion.
THe interstitial chemical potential is a function of both concentration and temperature.
The parameter Q1trans, which is seen to have dimensions of energy, is termed the heat of transport
Mass diffusion can be induced by gradients in either the composition, or the temperature, or both. The origin of Q1trans is the asymmettry between the energy states before, during, and after a diffusing species jumps to a neighboring site.
Methods of measuring Q1trans are similar to those for measuring Beta in an electromigratino experiment