Brachiopods are marine, shelled organisms that appeared about 550 million years ago when living systems first exerted control on biomineral formation. Brachiopod shells are composed of calcium carbonate (calcite) or calcium phosphate (apatite). This is an extraordinary mix of shell material in a single phylum, since most invertebrate shells are composed solely of calcium carbonate while calcium phosphate is almost exclusively utilised by vertebrates in the formation of bone and teeth.
The far-reaching implications of Williams' discovery that there is a major change in secretory regime from silica to calcium phosphate production were published in Science in 1998.
Williams was the editor and first author of the first brachiopod Treatise on Invertebrate Palaeontology (two volumes) in 1965, he fulfilled the same roles in the second edition: four volumes of which were published (1997-2003), and he left another two in press at the time of his death.