The thermal expansivity, α, decreases by compression. The Anderson-Grüneisen parameter, δT, describes the degree of decrease in α by compression. Namely,
Chopelas and Bohler  suggested δT = 5.5 ± 0.5 for mantle minerals. This means that, if V decreases by 10% by compression, α decreases by 40~50%.
Anderson  showed the following relation:
In the case of MgSiO3 bridgmanite at ambient conditions, α = 2.0×10-5 K-1 [Tange et al., 2012], KT = 260×109 Pa [Tange et al., 2012], (∂KT/∂T)P = -0.029×109 Pa K-1 [Aizawa et al., 2004]. These values give δT = 5.6. Katsura et al.  suggested α of MgSiO3 bridgmanite at HP-HT to be δT = 5.8(2). Thus, Eq (3) agrees with the experimental data.
Here, we here prove Eq. (3). We start from the following equation,
The left side of Eq (4) is:
The right hand of Eq. (4) is:
By using Eq. (4), Eq. (1) becomes: