Final answer:
The metamorphic facies associated with diamonds in the mantle is eclogite facies, a high-pressure metamorphic rock composed of garnet and pyroxene.
Step-by-step explanation:
The metamorphic facies associated with diamonds in the mantle is eclogite facies. Eclogite is a high-pressure, high-temperature metamorphic rock consisting primarily of garnet and pyroxene. This facies is well known for conditions suitable for the formation of diamonds, as it exists in the deeper parts of the Earth's mantle where the necessary high-pressure environment is found for diamond formation.
Diamonds often originate in the Earth's mantle at depths greater than 150 kilometers where pressures are sufficiently high enough to crystallize carbon into diamond rather than graphite. They are then brought close to the surface by deep-source volcanic eruptions through a type of igneous rock known as kimberlite or sometimes lamproite, which acts as a carrier for these rare gemstones.