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Mean grain diameters from thin sections: matching the average to the problem

Published online by Cambridge University Press:  02 January 2018

Robert S. Farr ,
Victoria C. Honour  and
Marian B. Holness
Robert S. Farr*
Affiliation:
Unilever RD Colworth Science Park, Sharnbrook, Bedford MK44 1LQ, UK
Victoria C. Honour
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
Marian B. Holness
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
*
*E-mail: robert.s.farr@gmail.com
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Abstract

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It is common practice to estimate a mean diameter for spherical or sub-spherical particles or vesicles in a rock by multiplying the average diameter of the approximately circular cross-sections visible in thin section by a factor of 1.273. This number-weighted average may be dominatedby the hard-to-measure fine tail of the size distribution, and is unlikely to be representative of the average particle diameter of greatest interest for a wide range of geological problems or processes. Average particle size can be quantified in a variety of ways, based on the mass or surfacearea of the particles, and here we provide exact relations of these different average measures to straightforward measurements possible in thin section, including an analysis of how many particles to measure to achieve a desired level of uncertainty. The use of average particle diameter isillustrated firstly with a consideration of the accumulation of olivine phenocrysts on the floor of the 135 m thick picrodolerite/crinanite unit of the Shiant Isles Main Sill. We show that the 45 m thick crystal pile on the sill floor could have formed by crystal settling within about a year.The second geological example is provided by an analysis of the sizes of exsolved Fe-rich droplets during unmixing of a basaltic melt in a suite of experimental charges. We show that the size distribution cannot be explained by sudden nucleation, followed by either Ostwald ripening or Browniancoalescence. We deduce that a continuous process of droplet nucleation during cooling is likely to have occurred.

Keywords

petrologymicrostructuregrain sizecrystal settlingliquid immiscibility
Type
Research Article
Information
Mineralogical Magazine , Volume 81 , Issue 3 , June 2017 , pp. 515 - 530
Creative Commons
Creative Common License - CCCreative Common License - BY
© [2017] The Mineralogical Society of Great Britain and Ireland. This is an open access article distributed under the terms of the Creative Commons Attribution (CC BY) licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2017

References

Alderliesten, M. (1990) Mean particle diameters, Part I, Evaluation of definition systems. Particle Particle Systems Characterization, 7, 233–241.CrossRefGoogle Scholar
Alderliesten, M. (2008) Mean particle diameters: from statistical definition to physical understanding. Unpublished PhD thesis, TU Delft, The Netherlands.Google Scholar
Bottinga, Y and Weill, D.F. (1970) Densities of liquid silicate systems calculated from partial molar volumes of oxide components. American Journal of Science, 269, 169–182.CrossRefGoogle Scholar
Cabane, H., Laporte, D. and Provost, A. (2001) Experimental investigation of the kinetics of Ostwald ripening of quartz in silicic melts. Contributions to Mineralogy and Petrology, 142, 361–373.CrossRefGoogle Scholar
Cabane, H., Laporte, D. and Provost, A. (2005) An experimental study of Ostwald ripening of olivine and plagioclase in silicate melts: implications for the growth and size of crystals in magmas. Contributions to Mineralogy and Petrology, 150, 37–53.CrossRefGoogle Scholar
Campbell, I.H., Roeder, P.L. and Dixon, J.M. (1978) Plagioclase buoyancy in basaltic liquids as determined with a centrifuge furnace. Contributions to Mineralogy and Petrology, 67, 369–377.CrossRefGoogle Scholar
Carlson, W.D. and Denison, C. (1992) Mechanisms of porphyroblast crystallisation: results from high-resolution computed X-ray tomography. Science, 257, 1236–1239.CrossRefGoogle Scholar
Carman, P.C. (1937) Fluid flow through granular beds. Transactions, Institution of Chemical Engineers, London, 15, 150–166.Google Scholar
Cashman, K.V. (1992) Groundmass crystallisation of Mount St. Helens dacite, 1980-1986: a tool for interpreting shallow magmatic processes. Contributions to Mineralogy and Petrology, 109, 431–149.CrossRefGoogle Scholar
Cashman, K.V. (1993) Relationship between plagioclase crystallisation and cooling rate in basaltic melts. Contributions to Mineralogy and Petrology, 113, 126–142.CrossRefGoogle Scholar
Cashman, K.V. and Marsh, B.D. (1988) Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization II: Makaopuhi lava lake. Contributions to Mineralogy and Petrology, 99, 292–305.CrossRefGoogle Scholar
Charlier, B. and Grove, T.L. (2012) Experiments on liquid immiscibility along tholeiitic liquid lines of descent. Contributions to Mineralogy and Petrology, 164, 27–4.CrossRefGoogle Scholar
Charlier, B., Namur, O., Toplis, M.J., Schiano, P., Cluzel, N., Higgins, M.D. and Vander Auwera, J. (2011) Large-scale silicate liquid immiscibility during differentiation of tholeiitic basalt to granite and the origin of the Daly gap. Geology, 39, 907–910.CrossRefGoogle Scholar
Chung, H.-Y. and Mungall, J.E. (2009) Physical con-straints on the migration of immiscible fluids through partially molten silicate, with special reference to magmatic sulphide ores. Earth and Planetary Science Letters, 286, 14–22.CrossRefGoogle Scholar
Ciamarra, M.P and Coniglio, A. (2008) Random very loose packings. Physical Review Letters, 101, 128–201.CrossRefGoogle ScholarPubMed
Crist, B. and Nesarikar, A.R. (1995) Coarsening in polyethylene-copolymer blends. Macromolecules, 28, 890–896.CrossRefGoogle Scholar
Denison, C. and Carlson, W.D. (1997) Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography: Part II. Application to natural samples. Journal of Metamorphic Geology, 15, 45–57.CrossRefGoogle Scholar
Dong, K.J., Yang, R.Y., Zou, R.P and Yu, A.B. (2006) Role of interparticle forces in the formation of random loose packing. Physical Review Letters, 96, 145–505.Google ScholarPubMed
Drever, H.I. and Johnston, R. (1959) The lower margin of the Shiant Isles sill. Quarterly Journal of the Geological Society of London, 94, 343–365.Google Scholar
Duchêne, S., Pupier, E., Le Carlier De Veslud, C. and Toplis, M. J. (2008) A 3D reconstruction of plagioclase crystals in a synthetic basalt. American Mineralogist, 93, 893–901.CrossRefGoogle Scholar
Epstein, N. and Young, M. J. (1962) Random loose packing of binary mixtures of spheres. Nature, 196, 885–886.CrossRefGoogle Scholar
Farr, R.S. (2013) Random close packing fractions of lognormal distributions of hard spheres. Powder Technology, 245, 28–34.CrossRefGoogle Scholar
Farrell, G.R., Martiniti, K.M. and Menon, N. (2010) Loose packings of frictional spheres. Soft Matter, 6, 2925–2930.CrossRefGoogle Scholar
Gibb, F.G.F. and Henderson, C.M.B. (1984) The structure of the Shiant Isles sill complex, Outer Hebrides. Scottish Journal of Geology, 20, 21–29.CrossRefGoogle Scholar
Gibb, F.G.F. and Henderson, C.M.B. (1989) Discontinuities between picritic and crinanitic units in the Shiant Isles sill: evidence of multiple intrusion. Geological Magazine, 126, 127–137.CrossRefGoogle Scholar
Gibb, F.G.F. and Henderson, C.M.B. (1996) The Shiant Isles main sill: structure and mineral fractionation trends. Mineralogical Magazine, 60, 67–97.CrossRefGoogle Scholar
Gibb, F.G.F. and Henderson, C.M.B. (2006) Chemistry of the Shiant Isles main sill, NW Scotland, and wider implications for the petrogenesis of mafic sills. Journal of Petrology, 47, 191–230.CrossRefGoogle Scholar
Giordano, D., Russell, J.K. and Dingwall, D.B. (2008) Viscosity of magmatic liquids: a model. Earth and Planetary Science Letters, 271, 123–134.CrossRefGoogle Scholar
Hammer, J.E., Cashman, K.V., Hoblitt, R.P. and Newman, S. (1999) Degassing and microlite crystallisation during pre-climatic events of the 1991 eruption of Mt. Pinatubo, Philippines. Bulletin ofVolcanology, 60, 355–380.CrossRefGoogle Scholar
Henderson, C.M.B., Gibb, F.G.F. andFoland, K.A. (2000) Mineral fractionation and pre-and post-emplacement processes in the uppermost part of the Shiant Isles main sill. Mineralogical Magazine, 64, 779–790.CrossRefGoogle Scholar
Herd, R.A. and Pinkerton, H. (1997) Bubble coalescence in basaltic lava: Its impact on the evolution of bubble populations. Journal of Volcanology and Geothermal Research, 75, 137–157.CrossRefGoogle Scholar
Higgins, M.D. (1994) Numerical modelling of crystal shapes in thin sections: estimation of crystal habit and true size. American Mineralogist, 79, 113–119.Google Scholar
Higgins, M.D. (1996) Magma dynamics beneath Kameni volcano, Thera, Greece, as revealed by crystal size and shape measurements. Journal of Volcanology and Geothermal Research, 70, 37–48.CrossRefGoogle Scholar
Higgins, M.D. (2000) Measurement of crystal size distributions. American Mineralogist, 85, 1105–1116.CrossRefGoogle Scholar
Holness, M.B. (1997) Geochemical self-organisation of olivine-grade contact metamorphosed chert nodules in dolomite marble, Kilchrist, Skye. Journal of Metamorphic Geology, 15, 765–775.CrossRefGoogle Scholar
Holness, M.B., Stripp, G., Humphrys, M.C.S., Veksler, I.V., Nielsen, T.F.D. and Tegner, C. (2011) Silicate liquid immiscibility within the crystal mush: late-stage mag-matic microstructures in the Skaergaard Intrusion, East Greenland. Journal of Petrology, 52, 175–222.CrossRefGoogle Scholar
Holness, M.B., Richardson, C. and Helz, R.T. (2012) Disequilibrium dihedral angles in dolerite sills: A new proxy for cooling rate. Geology, 40, 795–798.CrossRefGoogle Scholar
Hughes, D.W. (1978) A disaggregation and thin section analysis of the size and mass distribution of the chondrules in the Bjurbole and Chainpur meteorites. Earth and Planetary Science Letters, 38, 391–400.CrossRefGoogle Scholar
Jerram, D.A., Cheadle, M.J. and Philpotts, A.R. (2003) Quantifying the building blocks of igneous rocks: are clustered crystal frameworks the foundation. Journal of Petrology, 44, 2033–2051.CrossRefGoogle Scholar
Johnson, M.R. (1994) Thin section grain size analysis revisited. Sedimentology 41, 985–999.CrossRefGoogle Scholar
Kong, M., Bhattacharya, R.N., Jama, C. and Basu, A. (1995) A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions. Geological Society of America Bulletin, 117, 244–249.CrossRefGoogle Scholar
Kress, V.C. and Carmichael, I.S.E. (1991) The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contributions to Mineralogy and Petrology, 108, 82–92.CrossRefGoogle Scholar
Lange, R.A. and Carmichael, I.S.E. (1987) Densities of Na2O-K2O-MgO-FeO-Fe2O3-Al2O3-TiO2-SiO2 liquids: New measurements and derived partial molar properties. Geochimica et Cosmochimica Acta, 51, 2931–2946.CrossRefGoogle Scholar
Lifshitz, I.M. and Slyozov, YY (1961) The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids, 19, 35–50.CrossRefGoogle Scholar
Marsh, B.D. (1988) Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallisation I. Theory. Contributions to Mineralogy and Petrology, 99, 277–291.CrossRefGoogle Scholar
Martin, B. and Kushiro, Y (1991) Immiscibility synthesis as an indicator of cooling rates in basalts. Journal of Volcanology and Geothermal Research, 45, 289–310.CrossRefGoogle Scholar
McClements, D.J. (2016) Food emulsions, principles, practices and techniques. CRC Press, Taylor Francis Group.Google Scholar
Meinders, M.B.J., Kloek, W. and van Vliet, T (2001) Effect of surface elasticity on Ostwald ripening in emulsions. Langmuir, 17, 3923–3929.CrossRefGoogle Scholar
Mock, A. and Jerram, D.A. (2005) Crystal size distributions (CSD) in three dimensions: insights from the 3D reconstruction of a highly porphyritic rhyolite. Journal of Petrology, 46, 1525–1541.CrossRefGoogle Scholar
Morgan, D.J. and Jerram, D.A. (2006) On estimating crystal shape for crystal size distribution analysis. Journal of Volcanology and Geothermal Research, 154, 1–7.CrossRefGoogle Scholar
Onoda, G.Y and Liniger, E.G. (1990) Random loose packings of uniform spheres and the dilatancy onset. Physical Review Letters, 64, 2727–2780.CrossRefGoogle ScholarPubMed
Philpotts, A.R. (1979) Sillicate liquid immiscibility in tholeiitic basalts. Journal of Petrology, 20, 99–118.CrossRefGoogle Scholar
Philpotts, A.R. (1982) Compositions of immiscible liquids in volcanic rocks. Contributions to Mineralogy and Petrology, 80, 201–218.CrossRefGoogle Scholar
Robertson, J. and Barnes, S. (2015) Dynamics of magmatic sulphide droplets during transport in silicate melts and implications for magmatic sulphide ore formation. Journal of Petrology, 56, 2445–2472.CrossRefGoogle Scholar
Roedder, E. and Weiblen, P.W. (1971) Petrology of silicate melt inclusions, Apollo 11 and Apollo 12 and terrestrial equivalents. Proceedings of the Second Lunar Science Conference, 1, 507–528.Google Scholar
Russ, J.C. (1986) Practical Stereology. Plenum Press, New York.CrossRefGoogle Scholar
Sahagian, D.L. and Proussevitch, A.A. (1998) 3D particle size distributions from 2D observations: stereology for natural applications. Journal of Volcanology and Geothermal Research, 84, 173–196.CrossRefGoogle Scholar
Simakin, A.G., Trubitsyn, V.P. and Kharybin, E.V. (1998) The size and depth distribution of crystal settling in solidifying magma chamber. Izvestiya, Physics of the Solid Earth, 34(8), 30-37.Google Scholar
Swift, D.L. and Friedlander, S.K. (1964) The coagulation of hydrosols by Brownian motion and laminar shear flow. Journal of Colloid Science, 19, 621–647.CrossRefGoogle Scholar
VanTongeren, J.A. and Mathez, E.A. (2012) Large-scale liquid immiscibility at the top of the Bushveld Complex, South Africa. Geology, 40, 491–494.CrossRefGoogle Scholar
Veksler, I.V., Dorfman, A.M., Borisov, A.A., Wirth, R. and Dingwell, D.B. (2007) Liquid immiscibility and the evolution of basaltic magma. Journal of Petrology, 48, 2187–2210.CrossRefGoogle Scholar
Veksler, I.V, Kahn, J., Franz, G. and Dingwell, D.B. (2010) Interfacial tension between immiscible liquids in the system K2O-FeO-Fe2O3-Al2O3-SiO2 and implications for the kinetics of silicate melt unmixing. American Mineralogist, 95, 1679–1685.CrossRefGoogle Scholar
Wagner, C. (1961) Theorie der Alterung von Niederschlägen durch Umlosen (Ostwald-Reifung). Zeitschrift fur Elektrochemie, 65, 581–591.Google Scholar
Wicksell, S.D. (1925) The corpuscle problem, a mathematical study of a biometric problem. Biometrika, 17, 84–99.Google Scholar
Yang, R.Y., Zou, R.P., Dong, K.J., An, X.Z. and Yu, A. (2007) Simulation of the packing of cohesive particles. Computer Physics Communications, 177, 206–209.CrossRefGoogle Scholar
Zamponi, F. (2008) Mathematical physics: packings close and loose. Nature, 453, 606–607.CrossRefGoogle ScholarPubMed