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Pure larnite (β-Ca 2 SiO 4 ; Lrn) was synthesized at 6 GPa and 1473 K for 6 h by using a cubic press, its thermal expansivity was investigated up to 923 K by using an X-ray powder diffraction technique (ambient  P ), and its compressibility was investigated up to ∼16 GPa by using a diamond-anvil cell coupled with synchrotron X-ray radiation (ambient  T ). Its volumetric thermal expansion coefficient (α  V  ) and isothermal bulk modulus ( K  T ) were constrained as  α V   = 4.24(4) × 10 −5  K −1  and  K  T  = 103(2) GPa [the first pressure derivativeK  T  ′$K_{\rm{T}}^\prime $    obtained as 5.4(4)], respectively. Its compressibility was further studied with the CASTEP code using density functional theory and planewave pseudopotential technique. We obtained the  K  T  values as 123(3) GPa (LDA; high boundary) and 92(2) GPa (GGA; low boundary), with the values of theK  T  ′$K_{\rm{T}}^\prime $    as 4.4(9) and 4.9(5), respectively. The phonon dispersions and vibrational density of states (VDoS) of Lrn were simulated using density functional perturbation theory, and the VDoS was combined with a quasi-harmonic approximation to compute the isobaric heat capacity ( C P  ) and standard vibrational entropy(    S   298   0    )$\left( {S_{298}^0} \right)$   , yielding  C P   = 212.1(1) − 9.69(5) × 10 2  T  −0.5  − 4.1(3) × 10 6  T  −2  + 5.20(7) × 10 8  T  −3  J/(mol.K) for the  T  range of ∼298–1000 K and(    S   298   0    )      =     129.8   (   13   )$\left( {S_{298}^0} \right)\, = \,129.8\left( {13} \right)$    J/(mol.K). The microscopic and macroscopic thermal Grüneisen parameters of Lrn at 298 K were calculated to be 0.75(6) and 1.80(4), respectively.

Some thermodynamic properties of larnite (β-Ca 2 SiO 4 ) constrained by high T/P experiment and/or theoretical simulation