The role of hydrogen bonding in the thermal expansion and dehydration of brushite, di-calcium phosphate dihydrate

Abstract

The unit-cell and atomic parameters of perdeuterated brushite have been extracted from Rietveld analysis of neutron powder diffraction data within the temperature range 4.2 to 470 K. The thermal expansion of brushite is anisotropic, with the largest expansion along the b axis due principally to the effect of the O(1)···D(4) and O(3)···D(2) hydrogen bonds. Expansion along the c axis, influenced by the Ow1···D(5) interwater hydrogen bond, is also large. The high temperature limits for the expansion coefficients for the unit-cell edges a, b and c are 9.7(5) × 10⁻⁶, 3.82(9) × 10⁻⁵ and 5.54(5) × 10⁻⁵ K⁻¹, respectively, and for the cell volume it is 9.7(1) × 10⁻⁵ K⁻¹. The β angle displays oscillatory variation, and empirical data analysis results in α _β = 1.28(3) × 10⁻⁶sin(0.0105 T) K⁻¹, within this temperature range. The evolution of the thermal expansion tensor of brushite has been calculated between 50 ≤T≤ 400 K. At 300 K the magnitudes of the principal axes are α₁₁ = 50(6) × 10^{−6 K−1}, α₂₂ = 26.7(7) × 10⁻⁶ K⁻¹ and α₃₃ = 7.0(5) × 10⁻⁶ K⁻¹. The intermediate axis, α₂₂, is parallel to b, and using IRE convention for the tensor orthonormal basis, the axes α₁₁ and α₃₃ have directions equal to (−0.228, 0, −0.974) and (−0.974, 0, 0.228) respectively. Under the conditions of these experiments, the onset of dehydration occurred at temperatures above 400 K. Bond valence analysis combined with assessments of the thermal evolution of the bonding within brushite suggests that dehydration is precipitated through instabilities in the chemical environment of the second water molecule.