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 N − j × + 1.2 1.2 (nj nW ) = P + P o × Vm + × αcalc niαicat αj 10 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 = 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 = , (1) two examples: Hey and Bannister (1932a) studied the ef- 4π + 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 = mi × αicat + ni × αian, (2) = = 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 = 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 = (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 × + 1.2 X X o V (nj nW ) αcalc = niαicat + αj × 10 2 Theoretical background i j
Our approach is based on the fact that the total electronic + nw × αW , (4) polarizability of a mineral or synthetic compound can be with V = 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 = 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 + ny + nz)/3 or (2no + chemical composition, water content, and refractive indices, ne)/3, yielding the mean refractive index
Eur. J. Mineral., 32, 27–40, 2020 www.eur-j-mineral.net/32/27/2020/ R. X. Fischer et al.: Determination of H2O content in minerals 29 h ˇ ˇ (1934) (2008) Cerný (1974) Pongiluppi (1974) Cerný (1974) from Alberti andzalini Vez- (1979) (1993) (1966) g (obs)/ References (calc) w w n n f w n (calc) e w n (obs) d ) obs 3 α (Å c m ) 3 V (Å b 1.486 160.71 13.034 1.1 1.09 1.01
Eur. J. Mineral., 32, 27–40, 2020 www.eur-j-mineral.net/32/27/2020/ R. X. Fischer et al.: Determination of H2O content in minerals 31 h ˇ ˇ ˇ ˇ ˇ ˇ ˇ Cerný (1972) Passaglia (1969) Cerný (1974) Cerný (1974) Cerný (1974) Cerný (1974) Cerný (1974) Cerný (1974) g (obs)/ References (calc) w w n n f w n (calc) e w n (obs) d ) obs 3 α (Å c m ) 3 V (Å b
0 important classes of hydrous minerals and because we used . 08
K mean electronic polarizability for the calculation of their to- 0 aecomposition name alnieCa Paulingite . 42
Continued tal polarizabilities in contrast to the non-zeolitic minerals, Ca
0 where the total polarizabilities are calculated from electronic . 84
Mg polarizabilities of cations with specific coordination num- 0 .
29 bers (CNs). Whereas the cation coordination is known for Sr most of the non-zeolitic minerals, it is not clearly determined 0 . 03 0 Ba 0 0 0 0 1 1 1 2 0 0 4 3 5
. for most of the zeolite species where the chemical compo- 90 0 0 0 ...... 589 629 630 188 620 840 005 000 97 99 20 92 60 . . . 005 01 007 0 Ca . Na Be Ba Ba Sr 09 sition and the refractive indices have been determined but Ca Na Na Na Na Na Na Na Na Ca Ca 1 1 Al 3 0 0 . 0 . 01 0 . . . 0 0 0 04 7 1 0 2 1 . 02 35 33 0 . 0
05 not the crystal structure. Therefore, Table 1 lists the results 3 . . . e . . . . . 88 173 156 114 g . . 144 475 745 710 035 Al a . K 658 889 17 P K K bevdnme of number Observed Mg atrrltn h acltdt h observed the to calculated the relating Factor Na 0 1 2 7 6
Fe on 149 zeolites obtained with mean electronic polarizabil- Li Li Li Al Al Al Al Al . . . Na Sr . . 70 97 93 00 54 0 0 0 0 0 0 . . 7 4 4 4 5 0 Ba 08 02 O . . . Si . Na Na 0 . . . . . 051 079 053 08 . ities, and Table S1 in the Supplement lists the results on 684 520 585 615 030 012 . 7 594 Al Al 3 0 . Si . 1 1 88 . 08 Rb Rb Rb 30 . . Si Si Si Si Si Na 2 1 8 40 31 770 non-zeolitic minerals and synthetic compounds based K ( . . . O 00 94 12 5 5 5 4 Cu 81 OH 0 0 0 0 Al Al . . . . 0 12 . . . 430 455 355 970 . 022 022 020 Fe Si . . O 014 316 013 on electronic polarizabilities taken from Table 4 in Shan- 2 5 5 ) . 24 · 6 . . 90 0 2 60 23 O O O O 5 . K K K Al . . 09 O K 02 11 . · 20 20 20 20 Fe non and Fischer (2016) for specific coordination numbers of Si Si 43H 0 0 0 10 39 0 O 1 . . . Si H 010 009 006 . · 36 36 . 0 · · · · 007 800 16 . . 4H . 2 916 6 6 5 5 5 84H
09 cations. For the zeolites, the mean electronic polarizabilities . . 2 . O . . . . 40 99 Ca Al Ca 95 34H 10H 48H 95H · .1 0. 44754 .809 ecre l (1984) al. et Peacor 0.91 5.98 5.43 34.447 403.8 1.511 O Al Fe 2 Al 4 oeue e oml nta ie ntersetv literature. respective the in given as unit formula per molecules O O · .2 7. 41143710 atr(1992) Walter 1.08 3.7 4 24.161 276.7 1.523 O O 0 2 0 0 .
2 of a cation in a certain oxidation state is calculated as the 9 0 20H . 11 84 84 . . O 884 16 . 002 003 . . 2 2 2 2 004 025 00H . .1 6. 84363 .111 e n anse (1932b) Bannister and Hey 1.17 5.41 6.34 48.483 565.0 1.514 O .2 6. 91761 .710 e n anse (1932b) Bannister and Hey 1.04 5.87 6.10 49.187 563.3 1.523 O .2 6. 98954 .608 e n anse (1932b) Bannister and Hey 0.84 6.56 5.48 49.809 565.0 1.528 O .3 6. 05859 .309 e n anse (1932b) Bannister and Hey 0.93 6.43 5.95 50.528 566.7 1.534 O a mte eas of because omitted was 85 · · · average of all cations of the same kind with different coor- Si 50 46 Al Mg 2 7 Fe Si Si .9 4.53.8 .040 .3Pniup (1977) Pongiluppi 1.03 4.06 4.20 36.686 441.35 1.498 O . 2 2 96H . . 0 4 . 0 12 .8 160 09790 .010 hnadCa (1980) Chao and Chen 1.00 9.00 9.00 90.947 1126.02 1.484 O 1H 7H 112 0 . dination numbers weighted by the number of entries used . . 836 166 . 004 . 003 06 2 2 2 O .7 72723255. 7418 abadOe(1960) Oke and Kamb 1.83 27.4 50.1 213.285 2702.7 1.473 O .7 72723254. 881.62 28.8 46.7 213.285 2702.7 1.473 O Si .8 1. 18879 .111 og ta.(1993) al. et Boggs 1.14 7.01 7.96 41.818 518.8 1.483 O O Si O to determine the polarizability (see Table 4 in Shannon and Al 6 12 2 48 5 · . 0 . 161 0 993 . ( . Fischer, 2016). The mean values are listed in Table 2. They 037 . 856 OH 27H H O O 2 Si · O 6 are internally stored in POLARIO (Fischer et al., 2018) used ) 15 2 8 2 · 2 . . content. .2 5.21.6 .705 0.51 0.53 0.27 13.866 159.72 1.520 O . 27H 0 . 44 917 151
. to calculate the water content of zeolites in Table 1. Zeolite 33H · Fe 14 O · 2 b 2 3
.9 1. 63822 .811 eiadOi(1969) Oki and Seki 1.15 1.98 2.27 26.378 316.7 1.499 O entries are selected if they belong to one of the 237 types 6 enrfatv index refractive Mean 2 . O . 01H 93H · .1 5.01.9 .305 0.58 0.57 0.33 13.793 159.80 1.517 O h 3 0 .
pi atc aaees n Ii ercieindex. refractive is RI and parameters, lattice is lp listed in the Database of Zeolite Structures of the Interna- muiis(asgi,1970). (Passaglia, impurities 21H 2 2 .0 95916251.12. .1Efnegre l (1998) al. et Effenberger 0.51 27.4 14.01 166.235 1975.9 1.504 O .9 4. 65239 .109 brene l (1971) al. et Eberlein 0.98 4.01 3.93 36.562 440.8 1.497 O tional Zeolite Association (Baerlocher and McCusker, 2019). 2 .2 5.21.4 .106 0.34 0.61 0.21 13.947 159.72 1.523 O Thus, it also contains minerals like cancrinite which are not
b zeolite-type framework. Only those entries are included in
c and the unit-cell parameters are available for the same spec- V 3 oa volume Molar ) m f c
ubrof Number imen. There are a few exceptions where it was clear that the data from different publications can be assigned to the same (Å α 3 obs crystal. We were aiming for a dataset large enough to have ) d H V
2 a representative selection and not necessarily for complete- m O (obs) e oml unit. formula per
oeue e oml acltda xlie ntetx,uigthe using text, the in explained as calculated formula per molecules ness. n w e i All entries in Table 1 conform to the criteria listed above. hbzt ihcomposition with Chabazite
(calc) However, the entries at the end of Table 1 (no. 145 to 149) n
w show unusual deviations between observed and calculated f
d H O content which are assumed to be due to uncertain- n 2 bevdttleetoi oaiaiiycalculated polarizability electronic total Observed n w w
(calc) ties in the chemical composition. Zeolites and zeolite-type os/References (obs)/ compounds having occluded anionic or neutral species also g show high deviations and are listed separately in Table 3. en n ipo (1978) Simpson and Cerný en n ipo (1978) Simpson and Cerný en n ipo (1978) Simpson and Cerný ˇ ˇ ˇ Details are discussed below. Not considered in this com- pilation of hydrous minerals are compounds containing el- ements where the electronic polarizabilities have not been h determined in Shannon and Fischer (2016). These are, for example, cations with lone-pair electrons (Tl+, Sn2+, Pb2+, As3+, Sb3+, Bi3+,S4+, Se4+, Te4+, Cl5+, Br5+, and I5+) which do not fit the simple scheme of additivity. Also ex- cluded from the compilation are compounds with sterically strained structures (Gagné et al., 2018) and some compounds with corner-shared or edge-shared octahedral networks (see Shannon and Fischer, 2016; Shannon et al., 2017) showing
Eur. J. Mineral., 32, 27–40, 2020 www.eur-j-mineral.net/32/27/2020/ R. X. Fischer et al.: Determination of H2O content in minerals 33 systematic deviations between observed and calculated po- Alternatively, the H2O content could be calculated using larizabilities. the Gladstone–Dale approach after Mandarino (1976), where the refractive index n is calculated from n = · + = P ki pi Kc D 1 with Kc 100 and where ki values are 4 Example i Gladstone–Dale constants, pi values are weight per- centages, and D is the density (see also Shannon and The approach used here is demonstrated in the example of Fischer, 2016). For the example of analcime, the re- synthetic analcime (entry 2 in Table 1) having the chemi- sulting number of H O molecules would be 0.89 H O cal composition Na Al Si O ·1.1H O, with data from 2 2 0.9 0.9 2.1 6 2 per formula unit using Gladstone–Dale constants from sample 1 in Table 1 of Cernýˇ (1974). The following steps Mandarino (1981) and Eggleton (1991). A detailed are taken to determine the water content from the refractive comparison between our polarizability approach and the indices. Gladstone–Dale concept will be published in a follow- up paper. 1. The observed total electronic polarizability αobs is cal- 3 culated using Eq. (1) with Vm = 160.71 Å (unit-cell volume from Table 1 in Cerný,ˇ 1974, V = 2571.35 Å3, 5 Comparison between observed and calculated H2O divided by the number of formula units, Z = 16) and content in hydrous minerals 3 isotropic n = 1.486, yielding αobs = 13.034 Å . As mentioned above, the group of zeolite minerals was 2. The calculated total electronic polarizability αcalc of studied separately using mean electronic polarizabilities for the anhydrous part of the chemical composition is cal- the calculations. Figure 1 shows the water content calcu- culated using the additivity rule with the individual lated with Eq. (4) compared with the water content derived electronic polarizabilities of ions from Shannon and from analytical determinations as published in the respec- Fischer (2016). Because the coordination number (CN) tive references listed in Table 1. The factors relating the of Na is not determined in analcime (Cerný,ˇ 1974), a calculated to the observed values are shown in Fig. 2. It mean value for Na with different CNs is used calcu- clearly demonstrates that the calculated values show a rea- lated according to α(Na) = (17 · 0.760 + 27 · 0.650 + sonable fit with the observed amount of H2O, with factors 207 · 0.560 + 97 · 0.490 + 197 · 0.430 + 49 · 0.380 + 25 · f = nw(obs)/nw(calc) being close to 1. Outliers in Figs. 1 0.340 + 5 · 0.300 + 9 · 0.270)/633 = 0.489 Å3, with val- and 2 are mainly explained by uncertainties in the determi- ues taken from Table 4 in Shannon and Fischer (2016). nation of chemical compositions and/or refractive indices. For the framework atoms Al and Si, the respective val- In paulingite (145), something must be wrong in the chem- ues for CN = 4 are used. Electronic polarizabilities ical composition. The authors state the following: “The Al/Si and the mean values are internally stored in the pro- ratio of 0.15 given by the analysis conflicts with the cation gram POLARIO (Fischer et al., 2018), which is used composition . . . which requires an Al/Si ratio of 0.47. Either for all calculations. Thus, αcalc(anhydrous) = 0.9·α(Na) the analysis is internally inconsistent, or else anions must +0.9 · α(Al) +2.1 · α(Si) +6 · α(O) = 0.9 · 0.489 + 0.9 · be present outside the tectosilicate framework” (Kamb and 0.533+2.1·0.284+6·1.688 = 11.439 Å3, where α(O) Oke, 1960). The composition given in Table 1 is scaled to 42 o 3 is calculated using Eq. (3), with α− = 1.79 Å and N = framework cations and fixed to 84 O atoms corresponding 1.776 Å3 taken from Table 5 in Shannon and Fischer to a factor of 3.5 relative to the original composition given 3 (2016) and Van = Vm/6 = 26.79 Å . in Kamb and Oke (1960), whereas 89.95 O atoms would be needed for charge compensation, which, however, does 3 3. The difference αobs − αcalc = 1.595 Å represents the not represent a TO2 framework. Alternatively, in the second contribution of H2O to the total electronic polarizability. line 145 in Table 1 the non-oxygen content is scaled down The individual electronic polarizability of H2O taken to achieve charge balance. Then the factor relating calcu- from Table 5 in Shannon and Fischer (2016) is α(H2O) lated and observed H2O content changes from 1.83 to 1.62, = 1.62 Å3. However, the simple determination of the which is lower but still rather high. In later work, Lengauer et number of H2O molecules nw pfu according to nw = al. (1997) investigated paulingite (94) with a different com- 1.595/1.62 = 0.98 is not correct because nw adds to the position with 27 H2O molecules derived from thermogravi- anion volume (Van = V (O) +V (H2O) = Vm/(nO +nw) metric analysis (TGA) and 33.5 H2O calculated from the and thus contributes to the polarizability of the anhy- refractive index, yielding a factor of 0.81. The misfits for drous part as well as that expressed in Eq. (4). Only pollucite (146–148) might be due to errors in the chemical the solution of Eq. (4) solved for nw yields the correct composition and/or the determination of the H2O content. value. This is done numerically in POLARIO, yielding According to Beger (1969) the sum of Cs + H2O should 1.09 H2O molecules pfu, which compares well with the be equal to 1, whereas it is 0.34, for example, in pollucite observed 1.100 molecules determined in Cernýˇ (1974). (148). In tschörtnerite (149), “A quantitative determination www.eur-j-mineral.net/32/27/2020/ Eur. J. Mineral., 32, 27–40, 2020 34 R. X. Fischer et al.: Determination of H2O content in minerals
Figure 1. Histogram of observed (blue) and calculated (red) water content. Entries 145 to 149 are omitted (see text for explanation). The two entries with H2O content > 50 (8 – boggsite; 69 – gottardiite) are not shown.
of H2O/OH was not possible because of the small amount of der to achieve charge balance” (Effenberger et al., 1998). In material available” (Effenberger et al., 1998). A number of total, this yields high uncertainties concerning the real H2O 14 molecules pfu was calculated by difference from electron content in tschörtnerite. The authors assume an H2O content microprobe analyses (EMPAs), and 20 H2O were determined ≥ 20, which is much closer to the amount of 27.4 molecules from the crystal-structure analysis. A loss of H2O is assumed calculated by us. due to the high-vacuum measuring conditions in the EMPA: There are nine compounds listed in Table 3 containing an- “A part of the total amount of H2O is given as OH in or- ionic and/or neutral species (SO3, SO4, CO2, or CO3) oc-
Eur. J. Mineral., 32, 27–40, 2020 www.eur-j-mineral.net/32/27/2020/ R. X. Fischer et al.: Determination of H2O content in minerals 35
Figure 2. Plot of factors relating calculated to observed amount of H2O in zeolite-type minerals. The sequence from left to right follows the sequence of entries in Table 1. Entries 145 to 149 are omitted (see text for explanation).
Table 2. Electronic polarizabilities α of cations from Table 4 in Shannon and Fischer (2016) averaged over different coordination numbers, including NH4 and five HxOy species.
Cation α (Å3) Cation α (Å3) Cation α (Å3) Cation α (Å3) Ag+ 3.100 Fe2+ 2.036 Mg2+ 0.665 Si4+ 0.283 Al3+ 0.487 Fe3+ 3.854 Mn2+ 2.062 Sm3+ 3.579 As5+ 1.629 Ga3+ 1.641 Mn3+ 3.840 Sn4+ 2.910 B3+ 0.085 Gd3+ 3.516 Mo6+ 4.512 Sr2+ 2.073 Ba2+ 3.285 Ge4+ 1.625 N5+ 0.001 Ta5+ 5.200 2+ + + 3+ Be 0.165 H3O 1.450 Na 0.489 Tb 3.269 4+ − 5+ 6+ C 0.001 H3O2 2.670 Nb 5.780 Te 4.430 2+ 4− 3+ 4+ Ca 1.616 H4O4 6.400 Nd 3.796 Th 4.395 2+ + 4+ 3+ Cd 2.692 H5O2 3.100 NH 3.180 Ti 3.600 3+ − 2+ 4+ Ce 3.916 H7O4 9.500 Ni 1.710 Ti 4.954 Ce4+ 7.157 Hf4+ 3.310 P5+ 0.036 Tm3+ 2.847 Cl7+ 0.007 Hg+ 7.000 Pr3+ 3.825 U4+ 5.000 Co2+ 1.725 Hg2+ 6.000 Pu4+ 4.300 V3+ 2.960 Cr3+ 3.020 Ho3+ 3.045 Rb+ 1.857 V4+ 2.627 Cr6+ 5.400 I7+ 3.075 Re7+ 3.200 V5+ 4.229 Cs+ 3.102 In3+ 2.520 Rh3+ 4.020 W6+ 3.879 Cu2+ 4.420 K+ 1.340 S6+ 0.011 Y3+ 2.757 Dy3+ 3.180 La3+ 4.057 Sb5+ 3.100 Yb3+ 2.799 Er3+ 3.027 Li+ 0.307 Sc3+ 2.308 Zn2+ 1.709 Eu2+ 3.875 Lu3+ 2.767 Se6+ 1.510 Zr4+ 4.103 Eu3+ 3.117
cluded in the zeolite cavities. All these compounds show un- contain H2O, which might confirm our findings in addition usually high deviations between the observed and calculated to the problem with the anionic species. amount of H2O. It is apparent that these species in zeolites The mean value of the factor relating the calculated must be treated separately in our concept, with individual amount of H2O to the observed one is more or less mean- electronic polarizabilities deviating from other sulfates, sul- ingless because high and low factors, each representing large fites, and carbonates. For liottite (156 in Table 3; Merlino errors, level each other out. More significant is the distri- and Orlandi, 1977b) the number of H2O molecules was even bution of factors as shown in Fig. 3, where the bars in the calculated to be negative because the total polarizability of histogram represent the frequency of occurrence of factors the anhydrous part of the compound was already higher than within a range of factors indicated on the horizontal axis. the corresponding observed value. However, it was shown in The mode is between 0.9 and 1.0, with 64 % of the factors subsequent work by Ballirano et al. (1996) that it does not between 0.9 and 1.1 and 86 % between 0.8 and 1.2. www.eur-j-mineral.net/32/27/2020/ Eur. J. Mineral., 32, 27–40, 2020 36 R. X. Fischer et al.: Determination of H2O content in minerals al 3. Table 5 aciieNa Chem. Cancrinite 150 Zeolite No. 5 aciiieNa Cancrisilite 151 5 abbsrt Na Carbobystrite 152 5 emirt Na Depmeierite 153 5 ansieNa Farneseite 154 5 rniieNa Franzinite 155 5 itieCa Liottite 156 5 aielt Na Marinellite 157 aecomposition name nre fzoietp opud ihocue noi pce.Nmeigcniust h eunei al 1. Table in sequence the to continues Numbering species. anionic occluded with compounds zeolite-type of Entries 10 6 6 7 7 36 21 31 . . . . 89 70 40 58 . . . . 76 43 53 86 Ca K K K Na K K K 0 0 0 0 . . . 9 5 11 08 38 12 . 9 . . 12 18 22 . . 29 13 Ca Al Si Mg Ca Ca K 6 Ca 6 0 . . 19 . 8 12 3 04 09 0 . 6 . 75 82 . . . Al 03 Si 50 06 Fe Si Al K 6 5 Mg Al 0 . . 42 02 81 0 . 17 05 . 36 02 . 0 . O O
50 Figure 3. Frequency of occurrence of the factors for the zeolite en- 66 Mg . . 20 02 Si 24 24 Al Fe 7 Fe Si tries 1–144 listed in Table 1 and shown in Fig. 2. (a) Factors cal- ( ( 0 . 41 CO PO . 0 20 03 35 0 . 16 . . 50 Al culated from polarizability analysis using different electronic po- 08 Al . 4 3 98 Si ) ) O 4 Si 0 4 O · . 18 . . 168 larizabilities for cations with different coordination numbers (from 90 47 3 79 31 144 . . 34 O 5H ( . Si 32 ( CO Table 4 in Shannon and Fischer, 2016). (b) Factors calculated from 24 . SO O 6 7 2 Al . ( . 72 21 .9 1. 9423540 .6Koykve l (2010) al. et Khomyakov 0.86 4.09 3.5 59.482 718.5 1.496 O 02 SO 3
4 polarizability analysis using mean electronic polarizabilities from 28 ) ) ( O 0 ( 11 SO CO 4 . . 24 22 68
) Table 2. . 43 8 . 4 ( O 26 . 3 12 OH ) F ) 120 3 ( 1 0 . Cl CO 91 . . 10 ) 16 ( 0 1 ( SO . ( . CO Cl 3 02 62 SO ) 0 0 4 ( · . 3 . SO ) 4 91 48 3 The situation is similar for the non-zeolitic minerals listed 7 ) ) . 1 . 0 41H 72 · . · 4 . 72 04 3 3 )
( in Table S1, with 770 entries. The factors relating the cal- 0 . . CO Cl 20H 03H . · 2 01 2 .9 531377234 .804 oacriadOlni(2003) Orlandi and Bonaccorsi 0.43 7.98 3.41 377.762 4563.1 1.496 O 2 culated number of H O molecules to the observed ones . . 3 2 · 79H 61 2 2 ) 3 2 .0 9. 86932 .007 hmao ta.(1991b) al. et Khomyakov 0.76 4.20 3.20 58.699 699.1 1.503 O .0 355 4.3 .39503 áaae l (2005) al. et Cámara 0.32 9.5 3.03 443.631 5315.54 1.500 O . ( . 35H OH 03 are plotted in Fig. 4, which shows a few outliers caused 2 .0 9.05.9 .937 .5Koykve l 19a cited (1991a) al. et Khomyakov 0.75 3.73 2.79 58.699 699.10 1.503 O ( OH ) 2 by inaccuracies in the chemical compositions, difficulties in 3 .9 2. 03533 .806 eo ta.(2011) al. et Pekov 0.65 5.18 3.35 60.385 729.4 1.496 O . 58 )
3 the measurement of the refractive indices, or the observed . · 46 1 . Cl 83H H2O content just estimated or calculated and not determined 0 . 59 2 by thermal analyses. Lotharmeyerite (entry 675) shows the .2 282229418 .0MrioadOlni(1977b) Orlandi and Merlino 0.00 0 1.83 202.984 2298.2 1.529 O · 4
. largest deviation from 1 in Fig. 4a and b because of uncer- 31H tainties in the observed OH (partially disordered) and H2O 2 .1 811359643 .578 eln n rad (1977a) Orlandi and Merlino 7.84 0.55 4.31 325.966 3821.1 1.511 O content (Yang et al., 2012). Because the majority of the en-
n V
(Å cision of the number of molecules listed in the original publi- 3 m (Å ) cations. The number of H2O molecules for the first 30 entries in Table S1, for example, is given in integral numbers by the α obs
3 authors but calculated with all decimal places. If the calcu- os (calc) (obs) ) lated values are rounded to integers, they correspond exactly
n to the observed numbers except chukhrovite (27), where 12 w H2O molecules are measured and 11.28 are calculated.
n Thus, there are various sources of possible deviations. This w might include rounded numbers, especially for low H2O con- n n w w tent, where a number of 1 H2O molecule could be anything os/References (obs)/ (calc) between 0.5 and 1.5 and therefore might already represent an error of 50 %. Other sources of errors are uncertainties in the
nJmo n rw(1993) Grew and Jambor in chemical compositions, especially when they are based on energy-dispersive X-ray spectroscopy (EDX) analyses, esti- mated and not experimentally determined H2O content, in- sufficient quality of crystals for accurate measurements of the refractive indices, and also errors in our empirically deter- mined electronic polarizabilities of cations and anions (Shan- non and Fischer, 2016), which are derived in least-squares procedures. The cumulation of such errors will be reflected by factors significantly deviating from 1. Despite these in-
Eur. J. Mineral., 32, 27–40, 2020 www.eur-j-mineral.net/32/27/2020/ R. X. Fischer et al.: Determination of H2O content in minerals 37
Figure 4. Plot of factors relating calculated to observed amount of H2O in non-zeolitic minerals. The sequence from left to right follows the sequence of entries in Table S1.
fluences, the data shown in Figs. 1 to 5 clearly show that there is on average a very good fit between the observed and calculated amount of H2O. In general the best results are achieved using the individual electronic polarizabilities of cations with specific coordination numbers (Table 4 in Shannon and Fischer, 2016). However, mean polarizabili- ties (Table 2) yield results that are sufficiently accurate if the CN of cations has not been determined. This is shown in Fig. 4, comparing the two approaches yielding essentially similar results with a few outliers. Entries 55 (priceite), 110 (calcioancylite-Nd), and 432 (bassanite), for example, have factors much higher for mean polarizabilities, but entries 152 (milarite), 366 (Li SO · H O), and 630 (martyite), for ex- 2 4 2 Figure 5. Frequency of occurrence of the factors for the non-zeolite ample, have factors closer to 1 as compared with the cor- entries listed in Table S1 and shown in Fig. 4. The three outliers responding values from the individual polarizabilities. Gen- with factors > 2 are omitted. erally we recommend verifying questionable results derived from mean polarizability with corresponding calculations us- ing the CN-dependent polarizabilities. dimensions < 100 µm, usually used in X-ray diffraction anal- yses, can be used to determine the number of H2O molecules 6 Conclusions per formula unit if higher amounts of the sample are not available for thermal analyses. Based on the excellent over- The evaluation of 927 hydrous minerals and inorganic com- all agreement between the observed and calculated H2O con- pounds showed that their H2O content can be calculated from tents of 157 zeolites and 770 other hydrates and the unusual their mean refractive indices if the anhydrous part of the deviations of paulingite, pollucite, tschörtnerite, liottite, and chemical composition is known. Thus, single crystals with lotharmeyerite, we suggest that when strong disagreements www.eur-j-mineral.net/32/27/2020/ Eur. J. Mineral., 32, 27–40, 2020 38 R. X. Fischer et al.: Determination of H2O content in minerals occur, the refractive index, composition, and/or crystal struc- Beger, R. M.: The crystal structure and chemical composition of ture should be more carefully investigated. pollucite, Z. Kristallogr., 129, 280–302, 1969. Boggs, R. C., Howard, D. G., Smith, J. V., and Klein G. L.: Tsch- ernichite, a new zeolite from Goble, Columbia County, Oregon, Code availability. The program POLARIO (Fischer et al., 2018) Am. Mineral., 78, 822–826, 1993. calculates the mean refractive index from the chemical composi- Bonaccorsi, E. and Orlandi, P.: Marinellite, a new feldspathoid of the cancrinite-sodalite group, Eur. J. Mineral., 15, 1019–1027, tion and the molar volume. 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