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Synchrotron X-ray absorption spectroscopy and X-ray powder diffraction studies of the structure of johnbaumite [Ca10(AsO4)6(OH,F)2] and synthetic Pb-, Sr- and Ba-arsenate apatites and some comments on the crystal chemistry of the apatite structure type in general

Published online by Cambridge University Press:  05 July 2018

C. M. B. Henderson ,
A. M. T. Bell ,
J. M. Charnock ,
K. S. Knight ,
R. F. Wendlandt ,
D. A. Plant  and
W. J. Harrison
C. M. B. Henderson*
Affiliation:
School ofEarth, Atmospheric and Environmental Sciences (SEAES), University ofManchester, Manchester M13 9PL, UK Photon Science Department, STFC Daresbury Laboratory, Warrington WA4 4AD, UK
A. M. T. Bell
Affiliation:
Photon Science Department, STFC Daresbury Laboratory, Warrington WA4 4AD, UK
J. M. Charnock
Affiliation:
School ofEarth, Atmospheric and Environmental Sciences (SEAES), University ofManchester, Manchester M13 9PL, UK
K. S. Knight
Affiliation:
ISIS, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UK
R. F. Wendlandt
Affiliation:
Colorado School ofMines, Golden, Colorado 80401, USA
D. A. Plant
Affiliation:
School ofEarth, Atmospheric and Environmental Sciences (SEAES), University ofManchester, Manchester M13 9PL, UK
W. J. Harrison
Affiliation:
Colorado School ofMines, Golden, Colorado 80401, USA
*
* E-mail: michael.henderson@manchester.ac.uk
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Abstract

The chemical composition oft he natural arsenate-apatite mineral johnbaumite [nominally Ca10(AsO4)6(OH)2] and its alteration product hedyphane [Ca4Pb6(AsO4)6Cl2] have been determined by electron microprobe analysis and the structures ofjohnbaumite and synthetic Sr-, Ba- and Pbarsenate apatites have been studied by As K-edge X-ray absorption spectroscopy and synchrotron X-ray powder diffraction. All samples belong to the holosymmetric apatite space group P63/m with As5+ substituted for P5+ in the tetrahedral structural site. Johnbaumite contains small amounts ofF and Pb (~0.9 and ~4.4 wt.% respectively) and hedyphane has the ideal composition (formula given above); the compositions of these coexisting phases define the two limbs ofa solvus occurring between Ca- and Pb-arsenate apatite end members. The unit-cell parameters and cation–oxygen bond lengths for the arsenate apatites studied are discussed alongside published data for end-member Ca-, Sr-, Ba- and Pbphosphate apatite analogues with (OH), F, Cl or Br as the anions at the centres of the channels in the apatite structure. This discussion rationalizes the relationships between the two structural sites A(1) and A(2) occupied by divalent cations in terms of the size of the A–O polyhedra and the distortion of the A(1)–O polyhedron as measured by the metaprism twist angle [O(1)–A(1)–O(2) projected onto (001)].

Keywords

Arsenate apatitesjohnbaumiteX-ray structure determinationcrystal chemistry.
Type
Research Article
Information
Mineralogical Magazine , Volume 73 , Issue 3 , June 2009 , pp. 433 - 455
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2009

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References

Alberius-Henning, P., Mattson, C. and Lidin, S. (2000) Crystal structure of two bromapatites, Sr5(PO4)Br and Ba5(PO4)Br. Zeitschrft für Kristallographie - New Crystal Structures, 215, 345—346.Google Scholar
Baikie, T., Ahmad, Z., Srinivasan, M., Maignan, A., Pramana, S.S. and White, T.J. (2007) The crystallographic and magnetic characteristics of Sr2CrO4 (K2NiF4-type) and Sr10(CrO4)6F2 (apatite-type). Journal of Solid State Chemistry, 180, 1538—1546.CrossRefGoogle Scholar
Baikie, T., Ferraris, C., Klooster, W.T., Madhavi, S., Pramana, S.S., Pring, A., Schmidt, G.. and White, T.J. (2008) Crystal chemistry of mimetite, Pb10(AsO4)6Cl1.48O0.26, and finnemanite, Pb10(AsO3)6Cl2. Acta Crystallographica B, 64, 34—41.Google ScholarPubMed
Baker, W.E. (1966) An X-ray diffraction study of synthetic members of pyromorphite series. American Mineralogist, 51, 1712—1721.Google Scholar
Beck, H.P., Douiheche, M., Haberkorn, R. and Kohlman, H. (2006) Synthesis and characterisation of chloro-vanadato-apatites M5(VO4)3Cl (M = Ca, Sr, Ba). Solid State Sciences, 8, 64—70.CrossRefGoogle Scholar
Beevers, C.A. and McIntyre, D.B. (1946) The atomic structure of fluor-apatite and its relation to that of tooth and bone material. Mineralogical Magazine, 27, 254—257, plus 5 plates.Google Scholar
Bell, A.M., Henderson, C.M., Wendlandt, R.F. and Harrison, W.J. (2008) Rietveld refinement of Ba5(AsO4)3Cl from high-resolution synchrotron data. Acta Crystallographica E, 64, i63—i64.CrossRefGoogle Scholar
Bell, A.M., Henderson, C.M., Wendlandt, R.F. and Harrison, W.J. (2009) Rietveld refinement of Sr5(AsO4)3Cl from high-resolution synchrotron data. Acta Crystallographica E, 65, i16—i17.CrossRefGoogle Scholar
Binsted, N. (1998) Daresbury Laboratory EXCURV98 Program.Google Scholar
Binsted, N., Strange, R.W. and Hasnain, S.S. (1992) Constrained and restrained refinement in EXAFS data analysis with curved wave theory. Biochemistry, 31, 12117—12125.CrossRefGoogle ScholarPubMed
Brese, N.E. and O’Keefe, M. (1991) Bond-valence parameters for solids. Acta Crystallographica B, 47, 192—197.Google Scholar
British Geological Survey (2001) Arsenic contamination of groundwater in Bangladesh. Technical Report WC/00/19 (D.G. Kinniburgh and P.L. Smedley, editors). British Geological Survey, Keyworth, UK. (4 volumes).Google Scholar
Brown, I.D. and Altermatt, D. (1985) Bond-valence parameters obtained from a systematic analysis of the inorganic crystal structure database. Acta Crystallographica B, 41, 244—247.Google Scholar
Buschmann, J., Berg, M., Stengel, C. and Sampson, M.L. (2007) Arsenic and manganese contamination of drinking water resources in Cambodia: Coincidence of risk areas with low relief topography. Environmental Science and Topography, 41, 2146—2152.Google ScholarPubMed
Calos, N.J. and Kennard, C.H. (1990) Crystal structure of mimetite, Pb5(AsO4)3Cl. Zeitschrift für Kristallographie, 191, 125 — 129.Google Scholar
Christy, A.G. and Gatedal, K. (2005) Extremely Pb-rich rock-forming silicates including a beryllian scapolite and associate minerals in a skarn from Langban, Varmland, Sweden. Mineralogical Magazine, 69, 995—1018.CrossRefGoogle Scholar
Ciardelli, M.C., Xu, H. and Sahai, N. (2008) Role of Fe(II), phosphate, silicate, sulfide and carbonate in arsenic uptake by coprecipitation in synthetic and natural groundwater. Water Research, 42, 615—624.CrossRefGoogle Scholar
Corker, D.L., Chai, B.H., Nicholls, J. and Loutts, G.B. (1995) Neodymium-doped Sr5(PO4)3F and Sr5(VO4)3F. Acta Crystallographica C, 51, 549—551.Google Scholar
Cotter-Howells, J.D. and Caporn, S. (1996) Remediation of contaminated land by formation of heavy metal phosphates. Applied Geochemistry, 11, 335—342.CrossRefGoogle Scholar
Dai, Y.S. and Harlow, G.E. (1991) Structural relationships of arsenate apatites with their anion-devoid intermetallic phase Ca5As3. Geological Society of America Annual Meeting, Program and Abstracts, 23, A219.Google Scholar
Dai, Y.S. and Hughes, J.M. (1989) Crystal structure refinements of vanadinite and pyromorphite. The Canadian Mineralogist, 27, 189—192.Google Scholar
Dai, Y.S., Hughes, J.M. and Moore, P.B. (1991) The crystal structures of mimetite and clinomimetite, Pb5(AsO4)3Cl. The Canadian Mineralogist, 29, 369—376.Google Scholar
Dordević, T., Šutović, S., Stojanović, J. and Karanović, L. (2008) Sr, Ba, and Cd arsenates with the apatite- type structure. Acta Crystallographica C, 64, i82—i86.Google ScholarPubMed
Duan, C.-J., Wu, X.-Y., Liu, W., Chen, H.-H., Yang, X.- X. and Zhao, J.-T. (2005) X-ray excited luminescent properties of apatitic compounds Ba5(PO4)3X (X: OH-, Cl-, Br-); structure and hydroxyl ion conductivity and barium hydroxylapatite. Journal of Alloys and Compounds, 396, 86—91.CrossRefGoogle Scholar
Dunn, P.J. and Rouse, R.C. (1978) Morelandite, a new barium arsenate chloride member of the apatite group. The Canadian Mineralogist, 16, 601—604.Google Scholar
Dunn, P.J., Peacor, D.R. and Newberry, N. (1980) Johnbaumite, a new member of the apatite group from Franklin, New Jersey. American Mineralogist, 65, 1143 — 1145.Google Scholar
Dunn, P.J., Petersen, E.U. and Peacor, D.R. (1985) Turneaureite, a new member of the apatite group from Franklin, New Jersey, Balmat, New York and Långban, Sweden. The Canadian Mineralogist, 23, 251—254.Google Scholar
Eon, J.G., Bauer-Boechat, C., Malta-Rossi, A. and Terra, J. (2006) A structural analysis of lead hydroxyvana- dinite. Physical Chemistry Chemical Physics, 8, 1845 — 1851.CrossRefGoogle Scholar
Elliott, J.C., Dykes, E. and Mackie, P.E. (1981) Structure of bromapatite and the radius of the bromide ion. Acta Crystallographica B, 37, 435—438.Google Scholar
Essington, M.E. (1988) Solubility of barium arsenate. Soil Science Society America Journal, 52, 1566—1570.CrossRefGoogle Scholar
Ewing, R.C. and Wang, L. (2002) Phosphates as nuclear waste forms. Pp. 673—699 in: Phosphates: Geochemical, Geobiological and Materials Importance, (M.J. Kohn, J. Rakovan and J.M. Hughes, editors). Reviews in Mineralogy and Geochemistry, 48. Mineralogical Society of America, Chantilly, Virginia, USA.CrossRefGoogle Scholar
Fletcher, D.A., McMeeking, R.F. and Parkin, D.J. (1996) The United Kingdom Database Service. Journal Chemistry Information Computing Science, 36, 746-749 .CrossRefGoogle Scholar
Gurman, S.J., Binsted, N. and Ross, I. (1984) A rapid, exact, curved-wave theory for EXAFS calculations. Journal Physique C, 17, 143-151 .CrossRefGoogle Scholar
Harrison, W.J., Wendlandt, R.F. and Wendlandt, A.E. (2002) Low temperature aqueous solubility and stability of apatite-structure arsenates of lead, barium, and strontium and uptake of arsenic by hydroxylapatite. International Mineralogical Association, 18th General Meeting, September 1-6, 2002, Edinburgh, Scotland. Abstract A18-10, Meeting program with abstracts, p.185.Google Scholar
Harrison, W.J., Wendlandt, R.F., Charnock, J.M. and Henderson, C.M. (2005) Spectroscopic investigations of the adsorption of As onto bovine bone. 15th Annual Goldschmidt Conference May 21 -25, Idaho, USA. Geochimica et Cosmochimica Acta, 69, A65.Google Scholar
Hata, M., Marumo, F. and Iwai, S. (1979) Structure of bariumchlorapatite. Acta Crystallographica B, 35, 2382-2384 .CrossRefGoogle Scholar
Hedin, L. and Lundqvist, S. (1969) Effects of electron- electron and electron-phonon interactions on the one-electron states of solids. Solid State Physics, 23, 1-181 .Google Scholar
Hughes, J.M. and Rakovan, J. (2002) The crystal structure of apatite, Ca5(PO4)3(F,OH,Cl). Pp. 1-12 in: Phosphates: Geochemical, Geobiological and Materials Importance (M.J. Kohn, J. Rakovan and J.M. Hughes, editors). Reviews in Mineralogy and Geochemistry, 48. Mineralogical Society of America, Chantilly, Virginia, USA.Google Scholar
Hughes, J.M., Cameron, M. and Crowley, K.D. (1989) Structural variations in natural F, OH, and Cl apatites. American Mineralogist, 74, 870-876 .Google Scholar
Hughes, J.M., Cameron, M. and Crowley, K.D. (1991) Ordering of divalent cations in the apatite structure: Crystal structure refinements of natural Mn- and Sr- bearing apatite. American Mineralogist, 76, 1857-1872 .Google Scholar
Kampf, A.R., Steele, I.M. and Jenkins, R.A. (2006) Phosphohedyphane, Ca2Pb3(PO4)3Cl, the phosphate analog of hedyphane: description and crystal structure. American Mineralogist, 91, 1909-1917 .CrossRefGoogle Scholar
Kim, J.Y., Hunter, B.A., Fenton, R.R. and Kennedy, B.J. (1997) Neutron powder diffraction study of lead hydroxylapatite. Australian Journal of Chemistry, 50, 1061-1065 .CrossRefGoogle Scholar
Kim, J.Y., Fenton, R.R., Hunter, B.A. and Kennedy, B.J. (2000) Powder diffraction studies of synthetic calcium and lead apatites. Australian Journal of Chemistry, 53, 679-686 .CrossRefGoogle Scholar
Kreidler, E.R. and Hummel, F.A. (1970) The crystal chemistry of apatite: Structure fields of fluo- and chlorapatite. American Mineralogist, 55, 170-184 .Google Scholar
Kusachi, I., Henmi, C. and Kobayashi, S. (1996) Johnbaumite from Fuka, Okayama Prefecture, Japan. Mineralogical Journal, 18, 60-66 .CrossRefGoogle Scholar
Larson, A.C. and Von Dreele, R.B. (2004) General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR 86-748.Google Scholar
Le Bail, A., Duroy, H. and Fourquet, J.L. (1988) Ab- initio structure determination of LiSbWO6 by X-ray powder diffraction. Materials Research Bulletin, 23, 447-452 .CrossRefGoogle Scholar
Le Bail, A. (2005) Whole pattern decomposition methods and applications: A retrospection. Powder Diffraction, 20, 316-326 .CrossRefGoogle Scholar
Lee, Y.J., Stephens, P.W., Tang, Y., Li, W., Phillips, B.L., Parise, J.B. and Reeder, R.J. (2009) Arsenate substitution in hydroxylapatite: Structural characterization of the Ca5(PxAs1-xO4)3OH solid solution. American Mineralogist, 94, 666-675 .CrossRefGoogle Scholar
Luo, Y., Hughes, J.M., Rakovan, J. and Pan, Y. (2009) Site preference of U and Th in Cl, F, and Sr apatites. American Mineralogist, 94, 345-351 .CrossRefGoogle Scholar
Mackie, P.E., Elliott, J.C. and Young, R.A. (1972) Monoclinic structure of synthetic Ca5(PO4)3Cl chlorapatite. Acta Crystallographica B, 28, 1840-1848 .CrossRefGoogle Scholar
Madhavi, S., Ferraris, C. and White, T.J. (2005) Synthesis and crystallization of macroporous hydroxyapatite. Journal of Solid State Chemistry, 178, 2838-2845 .CrossRefGoogle Scholar
Mercier, P.H., Y., Le Page, Whitfield, P.S., Mitchell, L.D., Davidson, I.J. and White, T.J. (2005) Geometrical parameterization of the crystal chemistry of P63/m apatites: comparison with experimental data and ab initio results. Acta Crystallographica B, 61, 635-655 .Google Scholar
Mercier, P.H., Dong, Z., Baikie, T., Le Page, Y., White, T.J., Whitfield, P.S. and Mitchel, L.D. (2007) Ab initio constrained crystal-chemical refinement of Ca10(VxP1-xO4)6F2 apatites. Acta Crystallographica B, 63, 37-48 .CrossRefGoogle ScholarPubMed
Naray-Szabo, S.(1930) The structure of apatite. Zeitschrift für Kristallographie, 75, 387-398 .Google Scholar
National Research Council (1999) Arsenic in Drinking Water. National Academies Press, Washington D.C. 330pp. (http://nap.edu/catalog.php?record_id=6444).Google Scholar
Notzold, D., Wulff, H. and Herzog, G. (1994) Differenzthermoanalyse der Bildung des Pentastrontiumchloridphosphats und rontgenogra- phische Untersuchungen seiner Struktur. Journal of Alloys and Compounds. 215, 281-288.CrossRefGoogle Scholar
Pan, Y. and Fleet, M.E. (2002) Compositions of apatite- group minerals: Substitution meachanisms and controlling factors. Pp. 13-49 in: Phosphates: Geochemical, Geobiological and Materials Importance (M.J. Kohn, J. Rakovan and J.M. Hughes, editors). Reviews in Mineralogy and Geochemistry, 48. Mineralogical Society of America, Chantilly, Virginia, USA.Google Scholar
Polya, D.A., Gault, A.G., Diebe, N., Feldman, P., Rosenboom, J.W., Gilligan, E., Fredericks, D., Milton, A.H., Sampson, M., Rowland, H.A., Lythgoe, P.R., Jones, J.C., Middleton, C. and Cooke, D.A. (2005) Arsenic hazard in shallow Cambodian groundwaters. Mineralogical Magazine, 69, 807-823 .CrossRefGoogle Scholar
Pouchou, J.L. and Pichoir, F. (1985) ‘PAP’ j(pZ) procedure for improved quantitative microanalysis. Pp. 104-106 in: Microbeam Analysis (J.T. Armstrong, editor). San Francisco Press, San Francisco, USA.Google Scholar
Reinen, D., Lachwa, H. and Allman, R. (1986) EPR- und ligandfeldspekstoskopische Untersuchungen an Mnv-haltigen Apatiten sowie die Struktur von Ba5(MnO4)3Cl. Zeitschrift Anorgische Allgemeine Chemie, 542, 71-88 .CrossRefGoogle Scholar
Rietveld, H.M. (1969) A profile refinement method for nuclear and magnetic structures. Journal of Applied Crystallography, 2, 65-71 .CrossRefGoogle Scholar
Rouse, R.C., Dunn, P.J. and Peacor, D.R. (1984) Hedyphane from Franklin, New Jersey and Langban, Sweden: cation ordering in an arsenate apatite. American Mineralogist, 69, 920-927 .Google Scholar
Roh, Y.-H. and Hong, S.-T. (2005) Apatite-type Ba4(VO4)3Cl. Acta Crystallographica E, 61, i140-i142.CrossRefGoogle Scholar
Ruby, M.V., Davis, A. and Nicholson, A. (1994) In situ formation of lead phosphates in soils as method to immobilise lead. Environmental Science and Technology, 28, 646-654 .CrossRefGoogle Scholar
Saenger, A.T. and Kuhs, W.F. (1992) Structural disorder in hydroxyapatite. Zeitschrift für Kristallographie, 199, 123-148 .CrossRefGoogle Scholar
Shannon, R.D. (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica A, 32, 751-767 .CrossRefGoogle Scholar
Smith, A.H., Lingas, E.O. and Rahman, M. (2000) Contamination of drinking-water by arsenic in Bangladesh: a public health emergency. Bulletin World Health Organisation, 78, 1093-1103 .Google ScholarPubMed
Smith, G.F. and Prior, G.T. (1910) On fermorite, a new arsenate and phosphate of lime and strontia, and tilasite, from the manganese-ore deposits of India. Mineralogical Magazine, 16, 84-96 .CrossRefGoogle Scholar
Sneddon, I.R., Orueetxebarria, M., Hodson, M.E., Schofield, P.F. and Valsami-Jones, E. (2008) Field trial using bone meal amendments to remediate mine waste derived soil contaminated by zinc, lead and cadmium. Applied Geochemistry, 23, 2414-2424 .CrossRefGoogle Scholar
Sudarsanan, K. and Young, R.A. (1969) Significant precision in crystal structure details: Holly Springs hydoxyapatite. Acta Crystallographica B, 25, 1534-1543 .CrossRefGoogle Scholar
Sudarsanan, K. and Young, R.A. (1972) Structure of strontium hydroxide phosphate, Sr5(PO4)3OH. Acta Crystallographica B, 28, 3668-3670 .CrossRefGoogle Scholar
Sudarsanan, K., Mackie, P.E. and Young, R.A. (1972) Comparison of synthetic and mineral fluorapatite, Ca5(PO4)3F, in crystallographic detail. Materials Research Bulletin, 7, 1331-1338 .CrossRefGoogle Scholar
Swafford, S.H. and Holt, E.M. (2002) New synthetic approaches to monophase fluoride ceramics: synthesis and structural characterization of Na2Mg(PO4)F. Solid State Science, 4, 807-812 .CrossRefGoogle Scholar
Valsami-Jones, E., Ragnarsdottir, K.V., Putnis, A., Bosbach, D., Kemp, A.J. and Cressey, G. (1998) The dissolution of apatite in the presence of aqueous metal cations at pH 2-7. Chemical Geology, 151, 215-233 .CrossRefGoogle Scholar
Valsami-Jones, E., Ragnarsdottir, K.V., Putnis, A., Bosbach, D., Kemp, A.J. and Cressey, G. (1998) The dissolution of apatite in the presence of aqueous metal cations at pH 2-7. Chemical Geology, 151, 215-233 .CrossRefGoogle Scholar
Vegas, A. and Jansen, M. (2002) Structural relationships between cations and alloys; an equivalence between oxygen and pressure. Acta Crystallographica B, 58, 38-51 .CrossRefGoogle Scholar
Wardojo, T.A. and Hwu, S.-J. (1996) Chlorapatite: Ca5(AsO4)3Cl. Acta Crystallographica C, 52, 2959-2960 .CrossRefGoogle Scholar
Welch, A.H., Westjohn, D.B., Helsel, D.R. and Wanty, R.B. (2000) Arsenic in groundwater of the United States - Occurrence and Geochemistry. Ground Water, 38, 589-604 .CrossRefGoogle Scholar
Welin, E. (1968) X-ray powder data for minerals from Langban and the related mineral deposits of Central Sweden. Arkiv for Mineralogi och Geologi, 4, 499-541 .Google Scholar
Wendlandt, A.E., Harrison, W.J. and Wendlandt, R.F. (2002) Investigation of hydroxylapatite as a means of removing dissolved arsenic from potable water. Geological Society of America Annual Meeting, Denver, Colorado, USA, October 27-31, 2002. (Abstract) (http://gsa.conflex.com/gsa/2002AM/ finalprogram/abstract_44300.htm)Google Scholar
White, T.J. and Dong, Z. (2003) Stuctural derivation and crystal chemistry of apatites. Acta Crystallographica B, 59, 1-16 .CrossRefGoogle Scholar
White, T., Ferraris, C., Kim, J. and Madhavi, S. (2005) Apatite - An adaptive framework structure. Pp. 307-401 in: Micro and Mesoporous Mineral Phases (G. Ferraris and S. Merlino, editors). Reviews in Mineralogy and Geochemistry, 57. Mineralogical Society of America, Chantilly, Virginia, USA.Google Scholar
Wilhelmi, K.A. and Jonsson, O. (1965) X-ray studies on some alkali and alkaline-earth chromates. Acta Chimica Scandanavica, 19, 177-184 .CrossRefGoogle Scholar
Wondratschek, H., Merker, L. and Schubert, K. (1964) Relations between apatite structure and the structure of compounds of the Mn5Si3 (D88)-type. Zeitschrift für Kristallographie, 120, 393—395.Google Scholar
World Health Organization (2000) United Nations Synthesis Report on Arsenic in Drinking Water. (http://www.who.int/water_sanitation_health/dwq/arsenic3/en)Google Scholar
Wu, P., Zeng, Y.Z. and Wang, C.M. (2003) Prediction of apatite lattice constants from their constituent elemental radii and artificial intelligence methods. Biomaterials, 25, 1123 — 1130.Google Scholar

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