How Old is That Hunk of Clay?

While researching my WIP, I wondered how archaeologists determine the age of pottery fragments. ¹⁴C dating is useful for organic substances (bones, teeth, parchment, fabric, pollen, or other remnants of carbon-based life forms). The clays used in ceramics are made from inorganic silica compounds that don’t contain much carbon. Pottery fragments can be dated by: 

¹⁴C dating of burned food residues (link) 
In the days before dishwashers, steel wool and foaming detergents, food stuck to the crockery. 

¹⁴C dating of lipids that were absorbed by unglazed pottery (link)
It’s always been hard to scrub grease off dirty dishes. This method was used to demonstrate that dairy farming has existed in Britain for 6000 years. 

Determining the water of re-hydroxylation (link, link)
After bricks or pottery are removed from a kiln and exposed to the atmosphere, the clay begins to chemically combine with water at a time-dependent rate. This water can be removed with heat. The change in mass (before and after heating) is used to determine when the ceramic was first fired. This method appears to be accurate except for bricks from buildings bombed during WWWII where high temperatures reset the hydroxylation clock. 

The age of ¹⁴C-dated objects is expressed in years BP (Before Present) (link) with January 1, 1950 as the origin because radiocarbon dating expanded in use in the 1950s. BP is sometimes interpreted as Before Physics since nuclear testing during the 1950s spiked the atmosphere with radioisotopes of carbon and increased the amount of ¹⁴C in samples.