My mug broke

My water heater (don’t tell campo) is right next to my window in my room and I was making some tea. When I poured the water into the mug and then placed the mug on the window sill which is typically pretty cold because there is a small draft of air from my window. The bottom of my cup instantly cracked, and the boiling hot water began to leak out.

I figured this must have something to do with the expansion of the inside of the mug, where the boiling hot water (~100℃) was touching, and the shrinking of the outside of the mug, where the cold air (~10℃) was touching. The rate at which one was shrinking and the other expanded is what caused the crack.

(expansion constant of various ceramics and metals)

ΔV=βV0ΔT

I am not sure what type of ceramic my mug was made of, and potentially it is not shown in the diagram shown above, but if the expansion constant (β) were on the higher side (10.5 x 10^-6) then ΔV would have been larger. If it would have been on the smaller side (2.6 x 10^-6) then ΔV would have been less.

Additionally, the change in temperature of both the water and the cold air would cause the temperature of mug to either rise or fall in temperature rapidly. The cold air would cause the mug to have a negative change in volume, and the hot water would have a positive change in the volume.  The ΔT is important because if it is large on both the inside and outside of the cup then there must be a point where the mug can do neither, without breaking.