Phase separation in dilute solutions of ${}^3\mathrm{He}$ in solid ${}^4\mathrm{He}$

We report the results of studies of the phase separation of solid solutions of dilute concentrations of ${}^3\mathrm{He}$ in ${}^4\mathrm{He}$. The temperatures and the kinetics of the phase separation were determined from NMR experiments for ${}^3\mathrm{He}$ concentrations $1.6\times {10}^{-5}<x_3<2.0\times {10}^{-3}$. The experimentally observed phase separation temperatures are found to be in excellent agreement with regular solution theory as augmented by Edwards and Balibar [Phys. Rev. B 39, 4083 (1989)]. The growth of ${}^3\mathrm{He}$ droplets shows a $t^{1/3}$ time dependence at long times consistent with Ostwald ripening.

Figure 1

The phase diagram for regular binary mixtures such as solid ${}^3\mathrm{He}–{}^4\mathrm{He}$ mixtures. The green line is the binodal line; it designates the phase separation temperature, $T_{ps}$, and the red line is the spinodal line. The blue arrow shows a large amount of supercooling.

Figure 2

Variation of the phase separation temperatures for dilute solutions of ${}^3\mathrm{He}$ in solid ${}^4\mathrm{He}$. Solid red line, ${\mathrm{\Delta }}_3=0.255$ K [Eq. (8)], ${}^3\mathrm{He}$ precipitate liquid droplets; dashed blue line, ${\mathrm{\Delta }}_3=0.0135$  K [Eq. (4)], precipitates all solid; dotted green line, ${\mathrm{\Delta }}_3=0$; blue crosses, Ganshin et al.—cooling [12]; rotated blue crosses, Ganshin et al.—warming [12]; red diamonds, Huan et al.—NMR amplitude [15]; red circles, Huan et al.—NMR relaxation [15]; red square, Kingsley et al. [16]. (After Fig. 17 of Ref. [17].)

Figure 3

Change in NMR amplitudes of ${}^3\mathrm{He}$ NMR signal occurring at the phase separation in low density solid ${}^3\mathrm{He}–{}^4\mathrm{He}$ mixtures. (Reproduced, with permission, from Fig. 2 of Candela et al. [20]).

Figure 4

Observed decay of the NMR amplitude following the formation of droplets after a 100 mK temperature change at the phase separation temperature. Diamonds: Huan et al. [15]; solid line: exponential decay with time constant 2.20 h; and the broken line represents an added $t^{1/3}$ dependence to fit the data at long times.

Figure 5

Comparison of the excess amplitude at late times for droplet growth of ${}^3\mathrm{He}$ during phase separation (shown in Fig. 4) relative to a pure exponential decay. The solid line is the fit for a $t^{1/3}$ dependence.