NATROLITE .1. 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 measure d with MoKalpha radiation (lambda = 0.7107 angstrom) in a complete sph ere of reflection up to sin theta/lambda = 0.903 angstrom-1. The struc ture was refined in the orthorhombic space group Fdd2 with a = 18.2929 (7) angstrom, b = 18.6407(9) angstrom, c = 6.5871(6) angstrom, V = 224 6 angstrom3, Z = 8. A refinement of high-order diffraction data yielde d reliability factors of R(F) = 0.9%, R(W)(F) = 0.8%, GoF = 1.40 for 1 856 high-angle reflections (0.7 less-than-or-equal-to sin theta/lambda less-than-or-equal-to 0.903 angstrom-1) and R(F) = 1.0%, R(W)(F) = 1. 2 %, GoF = 3.07 for all 3471 independent reflections in the complete s phere of reflection. The T - O distances as well as the T - O - T angl es were found to be strongly influenced by the different bond strength s received by the individual oxygen atoms. The T - O distances calcula ted using Baur's extended valence rule agree on average within 0.003 a ngstrom with the observed values. An analysis of the mean square displ acement amplitudes allowed a separation of the external and internal v ibrational 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 (DELTAU) of the T - O vibrations a re in the range of 5 to 11 x 10(-4) angstrom2, 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 N a-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 whe re displacement amplitudes from a zeolite structure refinement could b e apportioned between contributions from internal and external vibrati ons for individual bonds.