Supermarkets supply a variety of liquid floor waxes designed for use on vinyl or linoleum. Commercial cleaning or janitorial supply stores offer options designed specifically for stone or slate surfaces. Your best choice for slate is a vapor-permeable wax that is water- and dirt-resistant but that allows moisture within the slate to escape. Wax finishes will wear down under foot traffic, so yo u must reapply it on a scheduled basis. For the average family, a slate floor in a home's front entry hall may need re-waxing every three months.
Silane/Siloxane sealers permeate and largely fill the internal pores of slate in order to block dirt and fluids from penetrating beneath the surface. This class of sealer is vapor-permeable, which prevents the buildup of internal hydrostatic pressure that might lead to cracks or fissures in the slate. Silane/siloxane sealers are usually applied for outdoor use or in three-season rooms. For indoor use, look for a low-VOC version and ventilate the area thoroughly until the sealant has dried completely.
An all-purpose acrylic or polyurethane finish forms a thin film over the top of the slate. There are plenty of water-based materials available today that will not pollute indoor air during application and are unlikely to emit fumes after drying. It may be helpful to select a nonslip variety or to mix in a slip-resistant additive. An acrylic or polyurethane film can be quite hard, but foot traffic will wear it down over time.
Green coatings for slate can be as traditional as a hand-rubbed wax or as cutting-edge as a bio-based sealant. Natural wax finishes are usually formulated with simple alcohol compounds or citrus-based solvents; they dry to a hard finish with little or no odor. Soy-based penetrating sealers apply and perform much like conventional sealers, and they are naturally vapor-permeable. Natural materials tend to dry more slowly than sealants formulated with petrochemical solvents and after drying may require a few days to achieve maximum performance.