Triclinic apatites

Apatites commonly adopt P6₃/m hexagonal symmetry. More rarely, monoclinic chemical analogues have been recognized, including the biologically significant hydroxyapatite, Ca₁₀(PO₄)₆(OH)₂, but the driving force towards lower symmetry has not been systematically examined. A combination of diffraction observations and ab initio calculations for Ca₁₀(AsO₄)₆F₂ and Ca₁₀(VO₄)₆F₂ show these materials are triclinic apatites in which the AsO₄ and VO₄ tetrahedra tilt to relieve stress at the metal and metalloid sites to yield reasonable bond-valence sums. An analysis of the triclinic non-stoichiometric apatites La_10 - x(GeO₄)₆O_3 - 1.5x and Ca₁₀(PO₄)₆(OH)_2 - xO_x/2 confirms this scheme of tetrahedral rotations, while Cd₁₀(PO₄)₆F₂ and Ca₁₀(CrO₄)₆F₂ are predicted to be isostructural. These distortions are in contrast to the better known P112₁/b monoclinic dimorphs of chloroapatite and hydroxyapatite, where the impetus for symmetry reduction is ordered anion (OH^- and Cl^-) displacements which are necessary to obtain acceptable bond lengths. These results are important for designing apatites with specific structural and crystal-chemical characteristics.

Computing details

Figures

(Ca10VO46F2)

Crystal data

?	β = 89.172 (3)°
Mr = ?	γ = 120.136 (2)°
?, P1	V = 570.46 (4) Å^3
a = 9.6987 (3) Å	Z = ?
b = 9.6933 (3) Å	? radiation, λ = ? Å
c = 7.0170 (2) Å	× × mm
α = 90.637 (3)°

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
Ca1	0.244 (2)	0.004 (2)	0.250 (2)	0.7 (2)
Ca2	0.001 (2)	0.245 (2)	0.261 (2)	0.7 (2)
Ca3	0.762 (2)	0.769 (1)	0.244 (2)	0.4 (2)
Ca4	0.339 (2)	0.654 (2)	0.000 (2)	1.0 (3)
Ca5	0.336 (2)	0.677 (2)	0.497 (2)	1.5 (3)
V1	0.396 (2)	0.373 (2)	0.257 (2)	0.6 (2)
V2	0.633 (2)	0.026 (2)	0.248 (2)	0.9 (2)
V3	0.970 (2)	0.602 (2)	0.240 (2)	0.7 (2)
O1	0.310 (1)	0.486 (1)	0.267 (2)	0.9 (2)
O2	0.510 (1)	0.827 (1)	0.249 (2)	1.2 (2)
O3	0.176 (2)	0.689 (2)	0.230 (2)	2.0 (3)
O4	0.604 (2)	0.474 (1)	0.270 (2)	1.4 (2)
O5	0.527 (1)	0.129 (1)	0.224 (1)	0.7 (2)
O6	0.870 (2)	0.404 (2)	0.271 (2)	2.0 (3)
O7	0.342 (1)	0.256 (2)	0.064 (2)	1.2 (2)
O8	0.765 (2)	0.074 (1)	0.071 (2)	1.5 (2)
O9	0.901 (2)	0.647 (1)	0.049 (2)	1.7 (2)
O10	0.662 (2)	0.758 (2)	0.555 (2)	1.3 (2)
O11	0.266 (2)	0.903 (2)	0.550 (2)	1.4 (2)
O12	0.069 (1)	0.308 (1)	0.575 (2)	0.7 (2)
F	0.006 (2)	0.005 (2)	0.252 (2)	2.1 (2)

(Ca10AsO46F2)

Crystal data

?	β = 88.869 (3)°
Mr = ?	γ = 120.371 (3)°
?, P1	V = 565.15 (5) Å^3
a = 9.6841 (5) Å	Z = ?
b = 9.6906 (5) Å	? radiation, λ = ? Å
c = 6.9815 (3) Å	× × mm
α = 90.623 (3)°

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
Ca1	0.234 (2)	0.990 (2)	0.249 (3)	0.8 (3)
Ca2	0.005 (2)	0.251 (2)	0.262 (3)	0.7 (2)
Ca3	0.770 (2)	0.767 (2)	0.245 (2)	0.7 (3)
Ca4	0.345 (2)	0.653 (2)	0.003 (2)	0.9 (4)
Ca5	0.343 (2)	0.681 (2)	0.499 (2)	1.0 (3)
As1	0.398 (1)	0.374 (1)	0.261 (2)	0.4 (2)
As2	0.628 (1)	0.024 (1)	0.239 (2)	0.5 (2)
As3	0.975 (2)	0.606 (1)	0.243 (2)	0.7 (2)
O1	0.311 (2)	0.480 (2)	0.275 (2)	0.6 (2)
O2	0.510 (2)	0.827 (2)	0.243 (2)	0.8 (2)
O3	0.173 (2)	0.681 (2)	0.226 (2)	1.0 (3)
O4	0.604 (2)	0.475 (2)	0.277 (2)	0.8 (2)
O5	0.530 (2)	0.124 (2)	0.220 (2)	1.1 (2)
O6	0.878 (2)	0.407 (2)	0.274 (2)	1.2 (2)
O7	0.351 (2)	0.263 (2)	0.063 (2)	1.4 (3)
O8	0.774 (2)	0.079 (2)	0.072 (2)	1.4 (3)
O9	0.905 (2)	0.639 (2)	0.040 (2)	1.1 (2)
O10	0.669 (2)	0.766 (2)	0.552 (2)	0.9 (2)
O11	0.274 (2)	0.907 (2)	0.555 (2)	1.1 (2)
O12	0.068 (2)	0.301 (2)	0.584 (2)	1.3 (2)
F1	0.007 (2)	0.007 (2)	0.245 (2)	0.8 (2)