Apatites commonly adopt P6(3)/m hexagonal symmetry. More rarely, monoclinic chemical analogues have been recognized, including the biologically significant hydroxyapatite, Ca(10)(PO(4))(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 Ca(10)(AsO(4))(6)F(2) and Ca(10)(VO(4))(6)F(2) show these materials are triclinic P\bar 1 apatites in which the AsO(4) and VO(4) 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)(GeO(4))(6)O(3 - 1.5x) and Ca(10)(PO(4))(6)(OH)(2 - x)O(x/2) confirms this scheme of tetrahedral rotations, while Cd(10)(PO(4))(6)F(2) and Ca(10)(CrO(4))(6)F(2) are predicted to be isostructural. These distortions are in contrast to the better known P112(1)/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.
/npsi/ctrl?lang=en http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?lang=fr Access and use of this website and the material on it are subject to the Terms and Conditions set forth at http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=en NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. For the publisher's version, please access the DOI link below./ Pour consulter la version de l'éditeur, utilisez le lien DOI ci-dessous.http://dx.doi.org/10.1016/j.cemconres. 2004.05.012 Cement and Concrete Research, 34, 9, pp. 1717Research, 34, 9, pp. -1724Research, 34, 9, pp. , 2004 LDH, and CaAl2NS LDH produced a tilted orientation of NBA and 26NS anions in the interlayer space, while 2NS anions induced a perpendicular bilayer arrangement.Materials characterization was carried out using X-ray diffraction, IR-spectroscopy, thermal analysis and Scanning Electron Microscopy. These preliminary results open up a new direction towards the synthesis of nanocomposites using polymeric entities and layered materials for future applications in cement and concrete science, e.g. control of the effect of admixtures on the kinetics of cement hydration by programming their temporal release.
Experimental structure refinements and ab initio simulation results for 18 published, fully ordered P6(3)/m (A;{\rm I}_4)(A;{\rm II}_6)(BO4)6X2 apatite end-member compositions have been analyzed in terms of a geometric crystal-chemical model that allows the prediction of unit-cell parameters (a and c) and all atom coordinates. To an accuracy of +/- 0.025 A, the magnitude of c was reproduced from crystal-chemical parameters characterizing chains of ...-A(II)-O3-B-O3-A(II)-... atoms, whereas that of a was determined from those describing (A(I)O6)-(BO4) polyhedral arrangements. The c/a ratio could be predicted to +/-0.2% using multi-variable functions based on geometric crystal-chemical model predictions, but could not be ascribed to the adjustment of a single crystal-chemical parameter. The correlations observed between algebraically independent crystal-chemical parameters representing the main observed polyhedral distortions reveal them as the minimum-energy solution to accommodate misfit components within this flexible structure type. For materials with given composition, good agreement (within +/- 0.5-2.0%) of ab initio crystal-chemical parameters was observed with only those from single-crystal refinements with R = 4.0%. Agreement with single-crystal work with R > 4.0% was not as good, while the scatter with those from Rietveld refinements was considerable. Accordingly, ab initio cell data, atomic coordinates and crystal-chemical parameters were reported here for the following compositions awaiting experimental work: (Zn,Hg)10(PO4)6(Cl,F)2, (Ca,Cd)10(VO4)6Cl2 and (Ca,Pb,Cd)10(CrO4)6Cl2.
Singular value decomposition (SVD) of the matrix of normal equations is used here both passively to assess numerical stability, and actively to troubleshoot problem refinements, singular or not. Such systems can then either be cured by rank reduction or solved with arbitrary-precision arithmetic carrying a number of digits known to be sufficient. SVD analysis provides objective information about such required rank reduction or number of digits. Pre-conditioning of the normal matrix is seen to decrease its condition number by many orders of magnitude in actual cases, illustrating its great practical usefulness. The methods and tools developed here have general applicability to diagnose problems with least squares, in particular ill-conditioned Rietveld refinements. Crystal-chemical and standard refinements described in the work by Mercieret al.[J. Appl. Cryst.(2006),39, 369–375] are shown to have similar numerical stability. The programSVDdiagnosticis freely available at http://www.tothcanada.com.
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