Natrolite, part I: Refinement of high-order data, separation of internal and external vibrational amplitudes from displacement parameters

A single crystal of natrolite, Na2Al2Si3O10·2H2O, was studied by X-ray diffraction methods at room temperature. The intensities were measured with MoKα radiation (λ = 0.7107 Å) in a complete sphere of reflection up to sin θ/λ = 0.903 Å−1. The structure was refined in the orthorhombic space group Fdd2 with a = 18.2929 (7) Å, b = 18.6407(9) Å, c = 6.5871(6) Å, V = 2246 Å3, Z = 8. A refinement of high-order diffraction data yielded reliability factors of R(F) = 0.9%, R w(F) = 0.8%, GoF = 1.40 for 1856 high-angle reflections (0.7 šin θ/λ <0.903 Å−1) and R(F) = 1.0%, R W(F) = 1.2%, GoF = 3.07 for all 3471 independent reflections in the complete sphere of reflection. The T-O distances as well as the T-O-T angles were found to be strongly influenced by the different bond strengths received by the individual oxygen atoms. The T O distances calculated using Baur's extended valence rule agree on average within 0.003 Å with the observed values. An analysis of the mean square displacement amplitudes allowed a separation of the external and internal vibrational amplitudes along the T-O bonds as well as along the Na O and H2O-O bond directions and the calculation of force constants. The internal vibrational amplitudes (ΔU) of the T-O vibrations are in the range of 5 to 11 × 10-4 Å2, that is about one order of magnitude smaller than the mean square displacement amplitudes of the external vibrations. The corresponding force constants are F = 354 to 824 Nm−1. The values of the force constants of the motion of the Na-ion and the water molecule against the framework oxygen atoms lie in the range between F = 57 and 293 Nm−1. This is the first instance where displacement amplitudes from a zeolite structure refinement could be apportioned between contributions from internal and external vibrations for individual bonds.