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The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure, thermodynamics, and physical properties

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Abstract

Results of ab initio molecular orbital (MO) calculations provide a basis for the interpretation of structural and thermodynamic properties of crystals, glasses, and melts containing tetrahedrally coordinated Si, Al, and B. Calculated and experimental tetrahedral atom-oxygen (TO) bond lengths are in good agreement and the observed average SiO and AlO bond lengths remain relatively constant in crystalline, glassy, and molten materials. The TOT framework geometry, which determines the major structural features, is governed largely by the local constraints of the strong TO bonds and its major features are modeled well by ab initio calculations on small clusters. Observed bond lengths for non-framework cations are not always in agreement with calculated values, and reasons for this are discussed in the text. The flexibility of SiOSi, SiOAl, and AlOAl angles is in accord with easy glass formation in silicates and aluminosilicates. The stronger constraints on tetrahedral BOB and BOSi angles, as evidenced by much deeper and steeper calculated potential energy versus angle curves, suggest much greater difficulty in substituting tetrahedral B than Al for Si. This is supported by the pattern of immiscibility in borosilicate glasses, although the occurrence of boron in trigonal coordination is an added complication. The limitations on glass formation in oxysulfide and oxynitride systems may be related to the angular requirements of SiSSi and Si(NH)Si groups.

Although the SiO and AlO bonds are the strongest ones in silicates and aluminosilicates, they are perturbed by other cations. Increasing perturbation and weakening of the framework occurs with increasing ability of the other atom to compete with Si or Al for bonding to oxygen, that is, with increasing cation field strength. The perturbation of TOT groups, as evidenced by TO bond lengthening predicted by MO calculations and observed in ordered crystalline aluminosilicates, increases in the series Ca, Mg and K, Na, Li. This perturbation correlates strongly with thermochemical mixing properties of glasses in the systems SiO2-M n/n+1 AlO2 and SiO2-M n+O n/2 (M=Li, Na, K, Rb, Cs, and Mg, Ca, Sr, Ba, Pb), with tendencies toward immiscibility in these systems, and with systematics in vibrational spectra. Trends in physical properties, including viscosity at atmospheric and high pressure, can also be correlated.

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References

  • Baur WH (1970) Bond length variation and distorted coordination polyhedra in inorganic crystals. Trans Am Crystallogr Assoc 6:125–155

    Google Scholar 

  • Baur WH (1981) Interatomic distance predictions for computer simulation of crystal structures. In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals II. Academic Press, New York, pp 31–52

    Google Scholar 

  • Boettcher AL, Burnham CW, Windom KE, Bohlen SR (1982) Liquids, glasses, and the melting of silicates at high pressure. J Geol 90:127–138

    Google Scholar 

  • Brawer SA, White WB (1975) Raman spectroscopic investigation of silicate glasses. I. The binary alkali silicates. J Chem Phys 63:2421–2432

    Google Scholar 

  • Bray PJ (1967) Magnetic resonance studies of bonding, structure, and diffusion in crystalline and vitreous solids. In: Bishay O (ed) Interaction of radiation with solids. Plenum Press, New York, pp 25–54

    Google Scholar 

  • Bray PJ (1978) NMR studies of borates. In: Pye LD, Frechette VD, Kreidl NF (eds) Borate glasses: Structure, properties, applications. Plenum Press, New York, pp 321–352

    Google Scholar 

  • Brown GE Jr, Dikmen FD, Waychunas GA (1983) Total electron yield K-XANES and EXAFS investigation of aluminum in amorphous and crystalline aluminosilicates. Stanford Synchrotron Radiation Lab Rept 83101:146–147

    Google Scholar 

  • Brown BE, Bailey SW (1964) The structure of maximum microcline. Acta Crystallogr 17:1391–1400

    Google Scholar 

  • Byker HJ, Craig RER, Eliezer I, Eliezer N, Howald RA, Viswanadham P (1981) Thermodynamic treatments of the CaO-SiO2 system. CALPHAD 5:217–224

    Google Scholar 

  • Calas G, Petiau J (1983) Structure of oxide glasses: spectroscopic studies of local order and crystallochemistry. Geochemical implications. Bull Mineral 106:33–55

    Google Scholar 

  • Carsky P, Urban M (1980) Ab initio calculations. Methods and applications in chemistry. Lecture notes in chemistry 16. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Chakoumakos B, Gibbs GV (1983) A study of molecular models for germanate crystals (abstr). Joint Annual Meeting, Geol Assoc Can and Mineral Assoc Can, Program and Abstracts, Victoria, BC, p A 10

  • Charles RJ, Wagstaff FE (1968) Metastable immiscibility in the B2O3-SiO2 system. J Am Ceram Soc 51:16–20

    Google Scholar 

  • Cohen JP, Ross FK, Gibbs GV (1977) An X-ray and neutron diffraction study of hydrous low cordierite. Am Mineral 62:67–78

    Google Scholar 

  • DeJong BHWS, Brown GE Jr (1980) Polymerization of silicate and aluminate tetrahedra in glasses, melts, and aqueous solutions — I. Electronic structure of H6Si2O7, H6AlSi2O 1−7 , and H6Al2O 1−7 . Geochim Cosmochim Acta 44:491–511

    Google Scholar 

  • Domenici M, Pozza F (1970) Neutron diffraction study of the structure of Li2O-SiO2 binary glasses. J Mater Sci 5:746–751

    Google Scholar 

  • Downs JW, Gibbs GV (1981) The role of BeOSi bond in the structures of beryllosilicate minerals. Am Mineral 66:819–826

    Google Scholar 

  • Drew RAL, Hampshire S, Jack KH (1981) Nitrogen glasses. In: Taylor D, Popper P (eds) Special ceramics 7. British Ceramic Society, Shelton, Stoke-on-Trent, pp 119–132

    Google Scholar 

  • Effenberger H (1980) Petalit, LiAlSi4O10: Verfeinerung der Kristallstruktur, Diskussion der Raumgruppe und Infrarot-Messung. Tschermaks Mineral Petrogr Mitt 27:129–142

    Google Scholar 

  • Eliezer N, Howald RA, Marinkovic M, Eliezer I (1978) Vapor pressure measurements, thermodynamic parameters, and phase diagram in the system potassium oxide-silicon oxide at high temperatures. J Phys Chem 82:1021–1028

    Google Scholar 

  • Eliezer I, Eliezer N, Howald RA, Verwolf MC, Viswanadham P (1979) The enthalpy of sodium silicate glasses and liquids. CALPHAD 3:1–8

    Google Scholar 

  • Fegley MB (1981) The thermodynamic properties of silicon oxynitride. Comm Am Ceram Soc C124–C126

  • Furukawa T, Fox KE, White WB (1981) Raman spectroscopic investigation of the structure of silicate glasses. III. Raman intensities and structural units in sodium silicate glasses. J Chem Phys 75:3226–3237

    Google Scholar 

  • Gauckler LJ, Weiss J, Tien TY, Petzow G (1978) Insolubility of Mg in β-Si3N4 in the system Al-Mg-Si-O-N. J Am Ceram Soc 61:397–398

    Google Scholar 

  • Galeener FL, Leadbetter AL, Stringfellow MW (1983) Comparison of the neutron, Raman, and infrared vibrational spectra of vitreous SiO2, GeO2, and BeF2. Phys Rev B27:1052–1078

    Google Scholar 

  • Gaskell DR (1973) The thermodynamic properties of the Masson polymerization model of liquid silicates. Metall Trans 4:185–193

    Google Scholar 

  • Geissberger AE, Bray PJ (1983) Determinations of structure and bonding in amorphous SiO2 using 17O NMR. J Non-Cryst Solids 54:121–137

    Google Scholar 

  • Geisinger KL (1983) A theoretical and experimental study of bonding in silicates and related materials. PhD dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA

    Google Scholar 

  • Geisinger KL, Gibbs GV (1981) SiSSi and SiOSi bonds in molecules and solids: a comparison. Phys Chem Minerals 7:204–210

    Google Scholar 

  • Geisinger KL, Gibbs GV, Navrotsky A (1985) A molecular orbital study of bond length and angle variations in framework structures. Phys Chem Minerals 11:266–283

    Google Scholar 

  • Gibbs GV (1982) Molecules as models for bonding in solids. Am Mineral 67:421–450

    Google Scholar 

  • Gibbs GV, Meagher EP, Newton MD, Swanson DK (1981) A comparison of experimental and theoretical bond length and angle variations for minerals, inorganic solids and molecules. In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals I. Academic Press, New York, pp 195–225

    Google Scholar 

  • Greaves GN, Fontaine A, Lagarde P, Raoux D, Gurman SJ (1981) Local structure of silicate glasses. Nature 293:611–616

    Google Scholar 

  • Griscom DJ (1978) Borate glass structure. In: Pye LD, Frechette VD, Kreidl NJ (eds) Borate glasses: Structure, properties, applications. Plenum Press, New York, pp 11–138

    Google Scholar 

  • Gupta A, Tossell JA (1983) Quantum chemical studies of distortions and polymerization of borate polyhedra. Am Mineral 68:989–995

    Google Scholar 

  • Gurr GE, Montgomery PW, Kuntson CD, Gorres BT (1970) The crystal structure of trigonal diboron trioxide. Acta Crystallogr B26:906–915

    Google Scholar 

  • Haller W, Blackburn DH, Wagstaff FE, Charles RJ (1970) Metastable immiscibility surface in the system, Na2O-B2O3-SiO2. J Am Ceram Soc 53:34–39

    Google Scholar 

  • Harlow GE, Brown GE Jr (1980) Low albite: An X-ray and neutron diffraction study. Am Mineral 65:986–995

    Google Scholar 

  • Henry DJ, Navrotsky A, Zimmermann HD (1982) Thermodynamics of plagioclase-melt equilibria in the system albite-anorthitediopside. Geochim Cosmochim Acta 46:381–391

    Google Scholar 

  • Hervig RL, Navrotsky A (1984) Thermochemical study of glasses in the system NaAlSi3O8-KAlSi3O8-Si4O8 and the join Na1.6Al1.6Si2.4O8-K1.6Al1.6Si2.4O8. Geochim Cosmochim Acta 48:513–522

    Google Scholar 

  • Hervig RL, Navrotsky A (1985) Thermochemistry of sodium borosilicate glasses. J Am Ceram Soc (submitted)

  • Hess PC (1971) Polymer model of silicate melts. Geochim Cosmochim Acta 35:289–306

    Google Scholar 

  • Hess PC, Wood MI (1982) Aluminum coordination in metaaluminous and peralkaline silicate melts. Contrib Mineral Petrol 81:103–112

    Google Scholar 

  • Hill RJ, Louisnathan SJ, Gibbs GV (1977) Tetrahedral bond length and angle variations in germanates. Aust J Chem 30:1673–1684

    Google Scholar 

  • Hon R, Henry DJ, Navrotsky A, Weill DF (1981) A thermochemical calculation of the pyroxene saturation surface in the system albite-anorthite-diopside. Geochim Cosmochim Acta 45:157–161

    Google Scholar 

  • Jack KH (1976) Sialons and related nitrogen ceramics. J Mater Sci 11:1135–1158

    Google Scholar 

  • Kieffer SW (1979) Thermodynamics and lattice vibrations of minerals: 3. Lattice dynamics and an approxiation for minerals with applications to simple substances and framework silicates. Rev Geophys Space Phys 17:35–58

    Google Scholar 

  • Kingery WD, Bowen HK, Uhlmann DR (1976) Introduction to ceramics. Wiley, New York

    Google Scholar 

  • Konijnendijk WH, Stevels JM (1975) The structure of borate glasses studied by Raman scattering. J Non-Cryst Solids 18:307–331

    Google Scholar 

  • Konijnendijk WL, Stevels JM (1976) The structure of borosilicate glasses studied by Raman scattering. J Non-Cryst Solids 20:193–224

    Google Scholar 

  • Konnert JH, Appleman DE (1978) The crystal structure of low tridymite. Acta Crystallogr B34:391–403

    Google Scholar 

  • Konnert JH, Karle JH, Ferguson GA (1973) Crystalline ordering in silica and germania glasses. Science 179:177–178

    Google Scholar 

  • Krogh-Moe J (1962) Structure interpretation of freezing point depression in the sodium borate system. Phys Chem Glasses 3:101–110

    Google Scholar 

  • Kushiro I (1978) Viscosity and structural changes of albite (NaAlSi3O8) melt at high pressure. Earth Planet Sci Lett 41:87–96

    Google Scholar 

  • Levien L, Prewitt CT (1981) High-pressure crystal structure and compressibility of coesite. Am Mineral 66:324–333

    Google Scholar 

  • Levin EM, Robbins CR, McMurdie HF (1964) Phase diagrams for ceramists. American Ceramic Society, Columbus, OH

    Google Scholar 

  • Loehman RE (1980) Oxynitride glasses. J Non-Cryst Solids 42:433–446

    Google Scholar 

  • Matson DW, Sharma SK, Philpotts JA (1983) The structure of high-silica alkali-silicate glasses. A Raman spectroscopic investigation. J Non-Cryst Solids 58:323–352

    Google Scholar 

  • McMillan P (1981) A structural study of aluminosilicate glasses by Raman spectroscopy. PhD Dissertation, Arizona State University

  • McMillan P (1984a) Structural studies of silicate glasses and melts — applications and limitations of Raman spectroscopy. Am Mineral 69:622–644

    Google Scholar 

  • McMillan P (1984b) A Raman spectroscopic study of glasses in the system CaO-MgO-SiO2. Am Mineral 69:645–659

    Google Scholar 

  • McMillan P, Piriou B (1983a) Raman spectroscopy of calcium aluminate glasses and crystals. J Non-Cryst Solids 55:221–242

    Google Scholar 

  • McMillan P, Piriou B (1983b) Raman spectroscopic studies of silicate and related glass structure — a review. Bull Mineral 106:57–75

    Google Scholar 

  • McMillan PF, Piriou B, Navrotsky A (1982) A Raman spectroscopic study of glasses along the joins silica-calcium aluminate, silica-sodium aluminate, and silica-potassium aluminate. Geochim Cosmochim Acta 46:2021–2037

    Google Scholar 

  • Misawa M, Price DL, Suzuki K (1980) The short-range structure of alkali disilicate glasses by pulsed neutron total scattering. J Non-Cryst Solids 37:85–97

    Google Scholar 

  • Morey GW (1961) The ternary system Na2O-B2O3-SiO2. J Soc Glass Technol 35:270–283

    Google Scholar 

  • Morikawa H, Marumo F, Koyam T, Yamane M, Oyobe A (1983) Structural analysis of 12CaO.7Al2O3 glass. J Non-Cryst Solids 56:355–360

    Google Scholar 

  • Mozzi RL, Warren BE (1969) The structure of vitreous silica. J Appl Crystallogr 2:164–172

    Google Scholar 

  • Mozzi RL, Warren BE (1970) The structure of vitreous boron oxide. J Appl Crystallogr 3:251–257

    Google Scholar 

  • Mysen BO, Virgo D, Scarfe CM (1980) Relations between the anionic structure and viscosity of silicate melts — a Raman spectroscopic study. Am Mineral 65:690–710

    Google Scholar 

  • Mysen BO, Virgo D, Kushiro I (1981) The structural role of aluminum in silicate melts — a Raman spectroscopic study at 1 atmosphere. Am Mineral 66:678–701

    Google Scholar 

  • Mysen BO, Virgo D, Seifert FA (1982) The structure of silicate melts: Implications for chemical and physical properties of natural magna. Rev Geophys Space Phys 20:353–383

    Google Scholar 

  • Nakajima Y, Swanson DK, Gibbs GV (1980) Calculation of tetrahedral Si-N bond lengths and angles (abstract). EOS, Trans Am Geophys Union 61:408

    Google Scholar 

  • Navrotsky A (1971) Thermodynamics of formation of the silicates and germanates of some divalent transition metals and of magnesium. J Inorg Nucl Chem 33:4035–4050

    Google Scholar 

  • Navrotsky A, Hon R, Weill DF, Henry DJ (1980) Thermochemistry of glasses and liquids in the systems CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8, SiO2-CaAlSi2O8-NaAlSi3O8 and SiO2-Al2O3-Na2O. Geochim Cosmochim Acta 44:1409–1423

    Google Scholar 

  • Navrotsky A, Peraudeau G, McMillan P, Coutures JP (1982a) A thermochemical study of glasses and crystals along the joins silica-calcium aluminate and silica-sodium aluminate. Geochim Cosmochim Acta 46:2039–2047

    Google Scholar 

  • Navrotsky A, Capobianco C, Stebbins J (1982b) Some thermodynamic and experimental constraints on the melting of albite at atmospheric and high pressure. J Geol 90:679–698

    Google Scholar 

  • Newton MD, Gibbs GV (1980) Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes. Phys Chem Minerals 6:221–246

    Google Scholar 

  • O'Keeffe M, Hyde BG (1981) The role of nonbonded forces in crystals. In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals I. Academic Press, New York, pp 227–254

    Google Scholar 

  • Ostvold T, Kleppa OJ (1969) Thermochemistry of the liquid system lead oxide-silica at 900°. Inorg Chem 8:78–82

    Google Scholar 

  • Ostvold T, Kleppa OJ (1970) Thermochemistry of liquid borates. II. Partial enthalpies of solution of boric oxide in its liquid mixtures with lithium, sodium, and potassium oxides. Inorg Chem 9:1395–1400

    Google Scholar 

  • Peacor DR (1973) High-temperature single crystal study of the cristobalite inversion. Z Kristallogr 138:274–298

    Google Scholar 

  • Piriou B, Arashi H (1980) Raman and infrared investigations of lead silicate glasses. High Temp Sci 13:299–313

    Google Scholar 

  • Porai-Koshits IA, Golubkov VV, Titov AP, Vasilevskaya TN (1982) The microstructure of some glasses and melts. J Non-Cryst Solids 49:143–156

    Google Scholar 

  • Rein RH, Chipman J (1965) Activities in the liquid solution SiO2-CaO-MgO at 1,600° C. Trans Metall Soc AIME 233:415–425

    Google Scholar 

  • Ribes M, Ravaine D, Souquet JL, Mavrin M (1979) Synthese, structure et conduction ionique de nouveaux verres a base de sulfures. Rev Chim Mineral 16:339–348

    Google Scholar 

  • Riebling EF (1965) Structure of sodium aluminogermanate melts with Na2Al2O4 ratio equal to unity. J Chem Phys 43:499–502

    Google Scholar 

  • Robie RA, Hemingway BS, Fisher JR (1978) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 pascals) pressure and at higher temperatures. US Geol Survey Bull 1452

  • Ross NL, Meagher EP (1984) A molecular orbital study of H6Si2O7 under simulated compression. Am Mineral 69:1145–1149

    Google Scholar 

  • Roy BN, Navrotsky A (1984) Thermochemistry of charge-coupled substitutions in silicate glasses: The systems M n+1/n AlO2-SiO2 (M=Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Pb). J Amer Ceram Soc 67:606–610

    Google Scholar 

  • Sakka S, Kamiya K (1982) Structure of alkali germanate glasses studied by spectroscopic techniques. J Non-Cryst Solids 49:103–116

    Google Scholar 

  • Sato S, Kleppa OJ (1978) Enthalpies of mixing in liquid mixtures of alkali tungstates with tunsten oxide. High Temp Sci 10:85–94

    Google Scholar 

  • Sauer J, Engelhardt G (1982) Relative stability of AlOAl linkages in zeolites. A nonempirical molecular orbital study. Z Naturforsch 37A:277–279

    Google Scholar 

  • Seifert FA, Mysen BO, Virgo D (1982) Three-dimensional network structure of quenched melts (glass) in the systems SiO2-NaAlO2, SiO2-CaAl2O4 and SiO2-MgAl2O4. Am Mineral 67:696–717

    Google Scholar 

  • Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Crystallogr B25:925–946

    Google Scholar 

  • Sharma SK, Simons B (1981) Raman study of crystalline polymorphs and glasses of spodumene composition quenched from various pressures. Am Mineral 66:118–126

    Google Scholar 

  • Sharma SK, Virgo D, Mysen BO (1979) Raman study of the coordination of aluminum in jadeite melts as a function of pressure. Am Mineral 64:779–787

    Google Scholar 

  • Smith CF (1978) The vibrational analysis of boron in vitreous silica. In: Pye LD, Frechette VD, Kreidl NJ (eds) Borate glasses: Structure, properties, applications. Plenum Press, New York, pp 307–319

    Google Scholar 

  • Taylor M, Brown GE Jr (1979a) Structure of mineral glasses I. The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8. Geochim Cosmochim Acta 43:61–74

    Google Scholar 

  • Taylor M, Brown GE Jr (1979b) Structure of mineral glasses II: The SiO2-NaAlSiO4 join. Geochim Cosmochim Acta 43:1467–1473

    Google Scholar 

  • Tscherry V, Schulz H, Laves F (1972) Average and superstructure of β-eucryptite (LiAlSiO4). Part II, superstructure. Z Kristallogr 135:175–198

    Google Scholar 

  • Urbain G (1974) Viscosité et structure de silicoalumineux liquides. I. — méthode de mesure et résultats expérimentaux. Rev Int Hautes Temp Refract 11:133–145

    Google Scholar 

  • Urbain G, Bottinga Y, Richet P (1982) Viscosity of liquid silica, silicates and alumino-silicates. Geochim Cosmochim Acta 46:1061–1072

    Google Scholar 

  • Wainwright JE, Starkey J (1971) A refinement of the structure of anorthite. Z Kristallogr 133:75–84

    Google Scholar 

  • Waseda Y (1981) Current structural information on molten slags by means of a high temperature X-ray diffraction. Cab Metall Q 20:57–67

    Google Scholar 

  • Waseda Y, Suito H (1977) The structure of molten alkali metal silicates. Trans Iron Steel Inst Jpn 17:82–91

    Google Scholar 

  • Waseda Y, Toguri JM (1977) The structure of molten binary silicate systems CaO-SiO2 and MgO-SiO2. Metall Trans 8B:563–568

    Google Scholar 

  • Waseda Y, Toguri JM (1978) The structure of the molten FeO-SiO system. Metall Trans 9B:595–601

    Google Scholar 

  • Wong J (1978) Infrared spectra and structure of CVD B2O3-SiO2 glasses. In: Pye LD, Frechette VD, Kreidl NJ (eds) Borate glasses: Structure, properties, applications. Plenum Press, New York, pp 297–305

    Google Scholar 

  • Wright AF, Lehmann MS (1981) The structure of quartz at 25 and 590° C determined by neutron diffraction. J Solid State Chem 36:371–380

    Google Scholar 

  • Yin CD, Okuno M, Morikawa H, Marumo F (1983) Structure analysis of MgSiO3 glass. J Non-Cryst Solids 55:131–141

    Google Scholar 

  • Zhang ZG, Gibbs GV (1983) Molecular modeling of borate minerals (abstr). GSA Abstracts with Programs 15:727

    Google Scholar 

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  1. Department of Chemistry, Arizona State University, 85287, Tempe, Arizona, USA

    A. Navrotsky, K. L. Geisinger & P. McMillan

  2. Department of Geological Sciences, Virginia Polytechnic Institute and State University, 24061, Blacksburg, Virginia, USA

    G. V. Gibbs

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  1. A. Navrotsky
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Navrotsky, A., Geisinger, K.L., McMillan, P. et al. The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure, thermodynamics, and physical properties. Phys Chem Minerals 11, 284–298 (1985). https://doi.org/10.1007/BF00307406

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