Phase Separation Boundary Research Articles

The extremum condition for the rate of cellular phase separation

An examination was carried out on the physical basis for the so-called ’’extremum condition’’ which determines the dimension of transformed phases during the steady-state cellular phase-separation reaction. The concept of the ’’balance of forces’’ which employs the balancing of various forces at the moving phase-separation boundary as the condition for the steady-state cellular phase-separation reaction is proposed. The magnitude and the direction of these forces are given by the partial derivatives of the total free-energy reduction due to the phase change at an undercooled condition in terms of the relevant reaction parameters such as the size of the microstructure and the reaction velocity. A simple model of lamellar formation by the eutectic or eutectoid reaction is used to demonstrate the meaning of the extremum condition and also to show the usefulness of the balance-of-forces concept.

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. I. Vapor pressure measurements and their thermodynamic analysis

Sensitive vapor pressure (Psat) measurements of3He-4He mixtures by means of a low-temperature strain gauge are described over the temperature range 0.5–1.5 K and the range 0.4<X<0.85, whereX is the3He mole fraction in the liquid phase. The vapor pressure cell is flat, with a height of only 2 mm, in order to reduce concentration gradients near the tricritical point. The pressure-sensitive device, which resolves changes of about 5×10−8 atm, is described, and its advantages over a conventional manometer system are discussed. Data taken successively on mixtures of small mole fraction difference are used to locate the phase separation boundary in theT-X plane and also the lambda line from a change in (∂Psat/∂T)x at these transitions. The limiting slopes (dT/dX)σ and (dT/dX)λ of the phase separation curve and the lambda line in the vicinity of their junction point, the tricritical point, are presented and compared with previous work. From the vapor pressure data, the concentration susceptibility (∂X/∂Δ)T,P was obtained. Here Δ=μ3−μ4 is the chemical potential difference of the respective isotopic components3He and4He. It is shown that (∂X/∂Δ)t diverges as the tricritical point is approached along various paths in theT-X plane, and the relevant tricritical exponents are presented. The weak divergence of (∂X/∂Δ)T along the lambda line predicted from the postulates of Griffiths and Wheeler could not be detected and it is believed that such divergence has to occur in a temperature interval that is far too small to be resolved with present-day techniques. Furthermore, gravity effects might well prevent observation of the weak divergence. The lambda transition is well evidenced by a distinct “shoulder” in a plot of (∂X/∂Δ)T at constantX as a function ofT. This “shoulder” becomes smaller and gradually gets topped by a peak asX decreases from the tricritical mole fractionXt. From a combination of vapor pressure and calorimetric data the chemical potential difference [Δ(X, T)-Δt] is calculated between 0.78 and 1.22 K. Here Δt is the value at the tricritical point. From this tabulation the critical line and its slope (dΔ/dT)λ are obtained and compared with previous values based on calorimetric experiments only and with calculations based on the excess chemical potentials μ3E and μ4E derived from saturated vapor pressure data.

Analyticity with respect to a parameter of the phase separation boundary in the problem of the crystallization of a melt on immersing a plate in it

Analyticity with respect to a parameter of the phase separation boundary in the problem of the crystallization of a melt on immersing a plate in it