Expansivity against temperature graph

[Outrageous]

β = 1/T
from the equation, T increase ,β should decrease.
But refer to graph,
http://www.sciencedirect.com/science/article/pii/S0025540809001081
Why β increase as temperature increase?
thank you.

 

[mfb]

$\beta=\frac{1}{T}$ is a relation for ideal gases. MgO is not an ideal gas.