Eur. J. Mineral., 32, 27–40, 2020 https://doi.org/10.5194/ejm-32-27-2020 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Determination of the H2O content in minerals, especially zeolites, from their refractive indices based on mean electronic polarizabilities of cations Reinhard X. Fischer1, Manfred Burianek1, and Robert D. Shannon2 1FB 5 Geowissenschaften, Universität Bremen, Klagenfurter Str. 2, 28359 Bremen, Germany 2Geological Sciences/CIRES, University of Colorado, Boulder, Colorado 80309, USA Correspondence: Reinhard X. Fischer (rfi[email protected]) Received: 10 September 2019 – Revised: 14 October 2019 – Accepted: 28 October 2019 – Published: 15 January 2020 Abstract. It is shown here that the H2O content of hydrous minerals can be determined from their mean re- fractive indices with high accuracy. This is especially important when only small single crystals are avail- able. Such small crystals are generally not suitable for thermal analyses or for other reliable methods of measuring the amount of H2O. In order to determine the contribution of the H2O molecules to the opti- cal properties, the total electronic polarizability is calculated from the anhydrous part of the chemical com- position using the additivity rule for individual electronic polarizabilities of cations and anions. This an- hydrous contribution is then compared with the total observed electronic polarizability calculated from the mean refractive index of the hydrous compound using the Anderson–Eggleton relationship. The difference be- tween the two values represents the contribution of H2O. The amount can be derived by solving the equation 0 N 1 − j × C 1:2 1:2 .nj nW / D P C P o × Vm C × αcalc niαicat @αj 10 A nw αW for the number nw of H2O molecules per for- i j o mula unit (pfu), with the electronic polarizabilities αcat for cations, the values N and α describing the anion 3 polarizabilities, the number n of cations and anions, and the molar volume Vm, using a value of αW D 1:62 Å for the electronic polarizability of H2O. The equation is solved numerically, yielding the number nw of H2O molecules per formula unit. The results are compared with the observed H2O content evaluating 157 zeolite-type compounds and 770 non-zeolitic hydrous compounds, showing good agreement. This agreement is expressed by a factor relating the calculated to the observed numbers being close to 1 for the majority of compounds. Zeolites with occluded anionic or neutral species (SO3, SO4, CO2, or CO3) show unusually high deviations between the calculated and observed amount of H2O, indicating that the polarizabilities of these species should be treated differently in zeolites and zeolite-type compounds. 1 Introduction croprobe analyses (EMPA) or analytical transmission elec- tron microscopy (ATEM), on species with a size of a few The water content of hydrous minerals and synthetic com- microns, thermoanalytical methods for the determination of pounds is usually determined by thermogravimetric methods the water content require an amount of a sample in the range recording the weight loss upon dehydration at an increasing of a few milligrams. The same applies to carbon hydrogen temperature. If the chemical composition of the anhydrous and nitrogen (CHN) analyzers which usually need a few mil- part of the compound is known, its formula weight can be ligrams for accurate analyses. Alternatively, the H2O content calculated along with the number of H2O molecules repre- could be derived from the measured density if the specimen senting the weight loss. Whereas the cation content can be is big enough for the experimental determination of the den- derived from microchemical analyses, e.g., by electron mi- sity. The determination of the water content becomes less ac- Published by Copernicus Publications on behalf of the European mineralogical societies DMG, SEM, SIMP & SFMC. 28 R. X. Fischer et al.: Determination of H2O content in minerals curate if lower amounts or even just one single crystal with a ing the Anderson–Eggleton relationship (Anderson, 1975; size of about 100 µm and a mass of a few micrograms or less Eggleton, 1991; see Shannon and Fischer, 2016, for an ex- exists. planation): It is well known that the optical properties vary with the 2 − amount of H2O in a crystalline compound. We mention n 1 Vm αobs D ; (1) two examples: Hey and Bannister (1932a) studied the ef- 4π C 4π − 2:26 n2 − 1 fect of dehydration on the optical properties of natrolite, and 3 Medenbach et al. (1980) investigated the variation in the re- with the molar volume Vm of one formula unit. fractive index of synthetic Mg-cordierite with H2O content, The total electronic polarizability of the anhydrous com- finding a linear relationship between the mean refractive in- pound can be calculated from the sum of the individual ion dex and the weight fraction of H2O. All studies we know so contributions (Shannon and Fischer, 2016) according to far are empirical descriptions of the dependence of the re- fractive indices on the H O content derived by calibration Ncat Nan 2 X X curves for a special system of compounds. Here, we describe αcalc D mi × αicat C ni × αian; (2) D D a theoretical approach for determining the H2O content from i 1 i 1 mean refractive indices of compounds with known chemical with composition of the anhydrous part. We show that the number 1:2 of H O molecules per formula unit (pfu) can be determined o −No=Van 2 αan D α− × 10 ; (3) with high accuracy from the mean refractive indices of hy- o drous crystals. where αcat is taken from Table 4 and α− and No from Table 5 A special focus is on the zeolite group of minerals, repre- in Shannon and Fischer (2016), and the anion volume Van is senting a large and popular group of hydrous minerals. Ze- calculated from the molar volume Vm divided by the number olites represent one of the most important classes of mate- of anions and H2O molecules. rials, used as catalysts in oil refineries for the production of The difference between observed and calculated polariz- gasoline and as ion exchangers as an additive, e.g., in house- abilities 1 D (αobs −αcalc/ is due to the contribution of H2O. hold detergents for the softening of water. Following the def- However, 1 cannot be simply divided by the electronic po- 3 inition of the subcommittee on zeolites of the International larizability 1.62 Å of H2O because it is treated like an anion Mineralogical Association (Coombs et al., 1998), “A zeolite and not like a cation (Shannon and Fischer, 2016). There- mineral is a crystalline substance with a structure character- fore, the number nw of H2O molecules has an influence on ized by a framework of linked tetrahedra, each consisting the calculation of the anion volume Van in Eq. (3), so it is of four O atoms surrounding a cation. This framework con- needed to calculate the contribution of the anions even for tains open cavities in the form of channels and cages. These the anhydrous part of the compound. are usually occupied by H2O molecules and extra-framework If we combine Eqs. (2) and (3) and separate the contribu- cations that are commonly exchangeable”. tion of H2O from the other anions, we get h N i − j × C 1:2 X X o V .nj nW / αcalc D niαicat C αj × 10 2 Theoretical background i j Our approach is based on the fact that the total electronic C nw × αW ; (4) polarizability of a mineral or synthetic compound can be with V D V 1:2, the number n of H O molecules per for- calculated from the sum of the individual contributions of m w 2 mula unit, and the electronic polarizability α D 1:62 Å3 of the electronic polarizabilities α of cations and α of the W cat an H O. anions, following the procedure described by Shannon and 2 Replacing α in Eq. (4) by α from Eq. (1) and solving Fischer (2016). Thus, the total polarizability of the anhydrous calc obs for n yields the number of H O molecules per formula unit. compound can be calculated from the chemical composition w 2 The solution is done numerically using the program PO- which then can be compared with the total polarizability de- LARIO (Fischer et al., 2018). rived from the observed mean refractive indices of the hy- drous compound. The difference represents the contribution of the H2O molecules. To obtain the H2O content, refrac- 3 Dataset tive indices are measured, e.g., by immersion methods with a spindle stage on a petrographic microscope. Anisotropic in- We tested the approach on hydrous minerals with known dices are averaged according to .nx C ny C nz/=3 or .2no C chemical composition, water content, and refractive indices, ne/=3, yielding the mean refractive index <n>. taken from Table S1 in Shannon et al. (2017) and addi- The total observed polarizability of the hydrous compound tional entries compiled here. The group of zeolite minerals is then calculated from the mean refractive index <n> us- is treated separately because it represents one of the most Eur. J. Mineral., 32, 27–40, 2020 www.eur-j-mineral.net/32/27/2020/ www.eur-j-mineral.net/32/27/2020/ Eur. J. Mineral., 32, 27–40, 2020 R. X. Fischer et al.: Determination of H Table 1. Entries of zeolite-type compounds used for the comparison of observed and calculated H2O content. b h No. Zeolite Chem. <n> Vm αobs nw nw nw (obs)/ References a 3 c 3 d e f g name composition (Å / (Å / (obs) (calc) nw (calc) 1 Amicite K3:75Na3:61Ca0:05Al7:86Si8:24O32 · 9:67H2O 1.498 1052.94 87.524 9.67 13.58 0.71 Alberti et al.