When scientists are measuring the uranium and lead in a rock—specifically in the mineral zircon, found in many igneous rocks—to determine its age (U/Pb geochronology), they need to dissolve the zircon. Zircon is a very stable mineral, so to dissolve zircon, the mineral grains are subjected to acids at high temperatures (~200 °C) and pressures. Thick steel pressure vessels are needed to contain an inner teflon vessel when it heats up and the liquid inside boils.
In the picture above, there are two pressure vessels. On the right of the red marker, a smaller vessel is used when the zircons from one rock sample are being partially dissolved to remove the exterior surface (chemical abrasion). To the left of the red marker, the large vessel is used for the final dissolution, when zircon grains are on teflon racks with individual teflon capsules.
When purifying a mineral from whole rock, one of the most useful separations is by density. Water, being less dense than most rock, is not especially useful for this. However, lithium metatungstate (LMT, mixed with water) and sodium polytungstate (SPT, also mixed with water) can create denser—albeit more viscous—liquids, with densities approaching 2.9–3.1 g/cm3. These denser liquids are enough to separate feldspar and quartz (<2.7 g/cm3) from zircon, titanite (sphene), and barite (densities >3.5 g/cm3).
Separations are fairly straightforward. A crushed, sieved rock sample is poured into a separatory funnel filled 1/2–2/3 full with the heavy liquid. The slurry is stirred vigorously with a stirring rod, and allowed to settle (it may take a couple hours if the grain size is fine and the liquid viscous). After it settles, the dense minerals should have sunk to the bottom, while the light minerals will float. A filter funnel is then placed under the separatory funnel. When the stopcock is opened, the dense minerals and some of the heavy liquid will pour out the bottom. The stopcock is then closed when the heavy separate has passed through. A second filter funnel is then used to capture the light fraction. With good filtering, the heavy liquid can be reused. The separates can be washed with distilled water and dried.
Heavy liquid separation is often used in combination with magnetic separation to purify minerals for analysis. Depending on the difference in densities being separated, a liquid may need to be fairly precisely calibrated with larger samples of the desired minerals. Sanidine (~2.55 g/cm3) and quartz (~2.65 g/cm3) need a well-calibrated liquid to achieve good separation, while either (or both) of them from zircon can be done with any LMT solution >2.7 g/cm3.