A dilithium cracking station was an automated facility that was designed to "crack" dilithium into a crystalline structure so that it could be used aboard starships.

Akladi was the site of a major Federation dilithium cracking station in the mid-23rd century. (TOS novel: Mudd's Angels)

A dilithium cracking station on the planet Tarba in the mid-24th century produced dilithium for Starfleet use. (TNG novel: Survivors)

A dilithium cracking station on Kinooine was one of the businesses owned by Rod Portlyn under the pseudonym Benzev Kaz. (CoE eBook: The Art of the Comeback)

It is debatable whether the "lithium cracking station" seen on Delta Vega I in the TOS episode: "Where No Man Has Gone Before" was in fact a dilithium cracking station, or a similar or wholly different type of facility.
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