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On the Relation Between lambda Lines and Phase Separations.

¹Department of Chemistry, University of North Carolina, Chapel Hill, N.C. 27514.

Proceedings of the National Academy of Sciences of the United States of America

|April 1, 1973

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This study challenges the assumption that specific heat is maximal on lambda lines in (3)He-(4)He solutions. It reveals that chemical potentials likely do not vanish, and specific heat may not reach its maximum, except at tricritical points.

Area of Science:

Thermodynamics
Statistical Mechanics
Condensed Matter Physics

Background:

Traditional assumption: slope of isotherm vanishes on lambda line, leading to maximal specific heat (e.g., C(V)) and adherence to Buckingham-Fairbank relation.
This assumption is prevalent in understanding phase transitions and thermodynamic properties.

Purpose of the Study:

To investigate the behavior of chemical potentials and specific heat in (3)He-(4)He solutions along the lambda line.
To re-evaluate the conditions under which specific heat reaches its maximum value.
To provide a statistical thermodynamic description of tricritical points and compare with experimental data.

Main Methods:

Heuristic theoretical arguments applied to (3)He-(4)He solutions.
Analysis of chemical potentials (μ(4), μ(3)) and mole fraction (x(3)).

Related Experiment Videos

Statistical thermodynamic modeling of tricritical points.

Examination of experimental data for solid NH(4)Cl and (3)He-(4)He solutions.

Main Results:

In (3)He-(4)He solutions, chemical potentials ([unk]μ(4)/[unk]x(3) and [unk]μ(3)/[unk]x(3)) likely do not vanish along the lambda line.
Specific heat C(x3) may not attain its maximum possible value, though it can approach infinity as x(3) approaches 0.
Only at the tricritical point does [unk]μ(4)/[unk]x(3) vanish, and C(x3) reaches a maximum before instability.
Experimental data for solid NH(4)Cl suggests [unk]P/[unk]V(T) does not vanish along the transition line at higher temperatures.
Singular behavior observed at the tricritical point in (3)He-(4)He solutions appears to be present along the lambda line as well.
Analysis of binary liquid solutions indicates that a tendency for C(V) to exceed its maximum can lead to a flattened coexistence curve.

Conclusions:

The assumption of vanishing isotherm slopes and maximal specific heat on lambda lines is challenged for (3)He-(4)He solutions.
Tricritical points represent unique states where specific thermodynamic conditions are met, unlike general lambda lines.
The findings offer a more nuanced understanding of phase transitions and critical phenomena in multi-component systems.