Observation of Andreev-Pushkarov vacancy clusters in phase-separated solid solutions of $^4$He in $^3$He

New features are observed for the pressure in a phase-separated dilute solid solution of $^4$He in $^3$He subjected to multiple temperature cycling within the phase-separation region. The results are explained within the framework of the hypothesis of A. F. Andreev and D. I. Pushkarov that the vacancies in a crystal without ideal periodicity are surrounded by clusters with a periodic structure. The equation for determining the radius of a cluster of pure $^4$He in a solution of $^4$He in $^3$He is refined. This hypothesis is shown to provide quantitative agreement between the calculated and experimental data under the assumption that the homogenization of the phase-separated solution is accompanied by the formation of metastable vacancies with a concentration of $\sim(4-5)\times 10^{-5}$.