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Joseph R. Smyth <HR>
University of Colorado David L. Bish <HR>
Los Alamos National Laboratory
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Crystal Structures and Cation Sites of the Principal Rock-Forming
Minerals
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<"Title">
<|,"17">Crystal Structures and Cation Sites of the Principal <SR>
Rock-Forming Minerals
<"Authors">
Joseph R. Smyth <HR>
University of Colorado <HR>
David L. Bish <HR>
Los Alamos National Laboratory
<"Para01">
CONTENTS
<"Para01">
Acknowledgement iii <HR>
Introduction 1
<"Head01">
Unit Cell Tables 2 <HR>
Site Data Tables 3 <HR>
Systematics of Site Parameter Variation
Trace and Minor Element Substitutions 7
5 <HR>
<"Head02">
Chapter 1. Single Oxides 10
<"Head01",
Bottom Margin =
Section
11<HR>
Section
14<HR>
Section
17<HR>
Section
Section
Section
27<HR>
Section
Section
34<HR>
Section
Section
Section
Section
0 Inches>
1.1<Tab>Cuprite Group
1.2<Tab>Periclase Group
1.3<Tab>Zincite Group
1.4<Tab>Tenorite and Montroydite
1.5<Tab>Corundum Group
1.6<Tab>Bixbyite Group
1.7<Tab>Arsenic and Antimony Sesquioxides
1.8<Tab>Rutile Group
1.9 <Tab> TiO2 Polymorphs
1.10 <Tab>MnO2 Polymorphs 41 <HR>
1.11 <Tab>Uraninite Group 44 <HR>
1.12 <Tab>TeO2 Polymorphs 47
20<HR>
24<HR>
30<HR>
37 <HR>
<"Head02">
Chapter 2. Double Oxides 51
<"Head01">
Section
52<HR>
Section
Section
Section
Section
2.1<Tab>Ilmenite Group
2.2<Tab>Perovskite
2.3<Tab>Oxide Spinel Group
2.4<Tab>Pseudobrookite Group
2.5<Tab>Tungstate Group
56<HR>
59<HR>
63<HR>
67
<"Head07">
Chapter 3. Hydroxides 72
<"Head03">
Chapter 4.<Tab>Orthosilicates 79
<"Head01">
Section 4.1<Tab>Garnet Group
80<HR>
Section 4.2<Tab>Olivine Group
85<HR>
<|,"18">Section 4.3<Tab>Silicate Spinel Group
90<HR>
Section 4.4<Tab>Silicate Zircon Group
94<HR>
Section 4.5<Tab>Willemite Group
Section 4.6<Tab>Aluminosilicate Group
Section 4.7<Tab>Humite Group
108<HR>
Section 4.8<Tab>Titanite Group
117<HR>
Section 4.9<Tab>Staurolite
120
98<HR>
102<HR>
<"Head02">
Chapter 5. Soro- and Cyclo-silicates 124
<"Head04",
Bottom Margin =
Section 5.1
Section 5.2
0 Inches>
Epidote Group<Tab>125<HR>
Melilite Group<Tab>130
<"Head01">
Section 5.3<Tab>Beta Spinel Group
135<HR>
Section 5.4<Tab>Lawsonite
139<HR>
Section 5.5<Tab>Tourmaline
Section 5.6<Tab>Vesuvianite
146
142<HR>
<"Head02">
Chapter 6. Chain Silicates 152
<"Head01">
Section
153<HR>
Section
Section
164<HR>
Section
Section
Section
6.1<Tab>Orthopyroxenes and Primitive Clinopyroxenes
6.2<Tab>C-centered Clinopyroxenes
6.3<Tab>Pyroxenoids
159<HR>
6.4<Tab>Orthoamphiboles
6.5<Tab>Clinoamphiboles
6.6<Tab>Aenigmatite
175<HR>
178<HR>
<"Head03">
Chapter 7.<Tab>Layer Silicates 183
<"Head06">
Section 7.1 Talc and Pyrophyllite 184 Section 7.2 Trioctahedral Micas
189 Section 7.3 Dioctahedral <SR>
Micas 194 Section 7.4 Clays 199
<"Head03">
Chapter 8.<Tab>Tectosilicates 204
<"Head01">
Section
205<HR>
Section
Section
Section
Section
225<HR>
Section
Section
234
8.1<Tab>Silica Minerals
8.2<Tab>Alkali Feldspar Group
8.3<Tab>Alkaline Earth Feldspars
8.4<Tab>Feldspathoid Group
8.5<Tab>Beryl and Cordierite
212<HR>
216<HR>
220<HR>
8.6<Tab>Scapolite Group
8.7<Tab>Zeolites
230<HR>
<"Para03",
Bottom Margin =
0.14 Inches>
Chapter 9. Carbonates, Nitrates, Sulfates, and Phosphates 262 <HR>
Section 9.1 Calcite group 263 <HR>
Section 9.2 Dolomite Group 267 <HR>
Section
Section
Section
Section
Section
9.3
9.4
9.5
9.6
9.7
Aragonite Group 270 <HR>
Barite Group 274 <HR>
Gypsum and Anhydrite 278 <HR>
Apatite 283 <HR>
Monazite 287
<"Head05">
<|,"19">Chapter 10. Halides 290
<"Head04">
Section 10.1. Halite Group<Tab>291<HR>
Section 10.2. Fluorite Group<Tab>293
<"Para03">
Chapter
Section
Section
Section
Section
Section
Section
11. Cation Sites Listed by Mean Distance. 295 <HR>
11.1 Two- and Three-fold Sites
296 <HR>
11.2 Four-fold Sites 297 <HR>
11.4 Five-fold Sites 303 <HR>
11.5 Six-fold Sites 304 <HR>
11.6 Eight-fold Sites 309 <HR>
11.7 Site of C.N. > 8 310
<"Para03">
References 311
<"Para03">
Mineral Index 319
<"Title",
Begin New Page =
yes>
<|,"20">Crystal Structures and Cation Sites of the Principal <SR>
Rock-Forming Minerals
<"Authors">
Joseph R. Smyth <HR>
University of Colorado <HR>
David L. Bish <HR>
Los Alamos National Laboratory <HR>
<"Head01">
Introduction
<"Para01">
Over the past two decades, with the advent of automated x-ray and
neutron single-crystal <SR>
diffractometers, there has been a major improvement in the precision
with which atom positions in <SR>
minerals are known. Shannon and Prewitt (1969, 1970), Whittaker and
Muntus (1970), and <SR>
Shannon (1976) have compiled crystal structure data for synthetic
compounds and minerals in <SR>
order to estimate effective ionic radii. These compilations and estimates
have proven immensely <SR>
useful to geochemists, mineralogists, and petrologists in understanding
the substitution behavior <SR>
and distribution of elements in natural systems, eg. Onuma et al.
(1968), Jensen (1973), Philpotts <SR>
(1978). Whereas Bragg et al. (1965) and Zoltai and Stout (1984) have
compiled descriptions of <SR>
mineral structures, and Wyckoff (1963) has compiled atom location
data for most inorganic <SR>
structures, there has never been a compilation of data on the nature
of cation sites in minerals.
<"Para01">
Robie et al. (1978) compiled thermodynamic data for many of the rockforming
minerals and <SR>
oxides. For some of these compounds there have been more recent and
accurate cell <SR>
determinations, so that improved data on molar volume and density
are available. Further, <SR>
thermodynamic data compilations do not include information on atomic
environments in these <SR>
compounds. .PP We have undertaken a compilation of recent data on
crystal structures for a large <SR>
group of the common minerals. From atom positional and cell data,
we have calculated <SR>
nearest-neighbor distances, coordination numbers, volumes of coordination
polyhedra, distortion <SR>
indices, and electrostatic energies in a consistent fashion. The
objective
in this work is to make the <SR>
recent improvements in crystal structure data available to a larger
group of petrologists and <SR>
geochemists seeking to understand the chemical behavior of these minerals
in natural systems.
<"Para01">
In order to reduce this to a manageable task we have had to make
some rather arbitrary <SR>
decisions in selecting and grouping the data. First, we have limited
the the group to the oxygen and <SR>
halide minerals with the understanding that ionic radii have at least
some relevance to these <SR>
structures. This has led to the exclusion of the sulfides from the
current compilation. In selecting <SR>
structures, we have endeavored to choose ordered end-members whenever
possible so that <SR>
cation site data will be more easily interpretable. In order to document
atomic environments in <SR>
standard thermodynamic states we have included a large number of simple
oxide minerals. This <SR>
<|,"21">has led to the inclusion of some less-than-common minerals
in this group, but otherwise we have <SR>
included only the more common minerals of igneous, metamorphic, and
sedimentary rocks. Finally, <SR>
in order to facilitate comparisons, we have grouped together data
from isomorphous structures, and <SR>
in a few cases, polymorphous structures. This has led to a few instances
of duplication which we feel <SR>
are justified in order to allow comparisons.
<"Head01">
Unit Cell Tables
<"Para01">
We have organized the structure data into those pertaining to unit
cells and those pertaining to <SR>
specific sites. In addition, we have summarized the site data, grouped
them according to <SR>
coordination number, and listed them by mean distance in Chapter 11.
Within the mineral groups, <SR>
unit cell tables consist of formula, formula weight, calculated density,
molar volume, Z, crystal <SR>
system, class, and space group, cell parameters, and reference. In
general, the formula is that given <SR>
in the reference, except that we have omitted elements constituting
less than 1.0 weight percent of <SR>
the mineral. In a few instances we have recalculated formulas to the
same number of oxygens for <SR>
comparison across an isomorphous series. The formula weight, density,
and molar volume are our <SR>
calculation from the stated formula and cell. Z is the number of formula
units per cell. The reference <SR>
is not repeated in the site tables, but site data are presented
sequentially
in the same order <SR>
permitting unambiguous citation.
<"Head01">
Site Data Tables
<"Para01">
Similar sites in isomorphous series are grouped together to facilitate
comparisons and show <SR>
variability of analogous features across the series. The tabulated
data consist of a site name, <SR>
coordination number (C.N.), occupants, point symmetry, Wyckoff notation,
fractional coordinates, <SR>
nearest neighbor distances, mean and standard deviation of distances,
polyhedral volume, <SR>
quadratic elongation, variance of central angle, electrostatic site
energy, and a model charge. The <SR>
coordination number is the number of nearest anion neighbors. The
occupant is that inferred from <SR>
the formula or stated in the reference. In a few instances, for partially
occupied sites, a total site <SR>
occupancy is given. Tetrahedral Al-Si occupancies for some of the
zeolites were calculated from <SR>
the mean T-O distance when site occupancies were not reported. The
point symmetry and Wyckoff <SR>
notation are those for the site (Hahn, 1983). Fractional coordinates
for the site are included to avoid <SR>
any ambiguities in site nomenclature that may arise and to show
variability
across the series. <SR>
Individual nearest neighbor distances are given throughout with a
major exception being those for <SR>
the framework silicate structures (Chapter 8). With the low symmetries
of many of these structures, <SR>
it was found very difficult to present these in a way that would be
both concise and meaningful. Also, <SR>
we have omitted the cavity geometries for the zeolites as these are
documented elsewhere (Mortier, <SR>
1982).
<"Para01">
<|,"22">The mean distance is our calculated average of the given
distances.
The<F7@Z7@Lam> s<F0> is the standard <SR>
deviation of the distances. It is thus an estimate of the distortion
of the site, not an estimate of the <SR>
error in the determination. Errors are regrettably not given because
this would have more than <SR>
doubled the size of the data base, greatly complicating the handling
of the data. The polyhedral <SR>
volume (Poly. Vol.), quadratic elongation (Q.E.), and angle variance
(Ang.Var.) were calculated with <SR>
a slightly modified version of the program VOLCAL (L.W. Finger, personal
communication). The <SR>
units of polyhedral volume are cubic Angstroms. Quadratic elongation
as defined by Robinson et al. <SR>
(1971) is unitless, and the units of the variance of the central
polyhedral
angle are degrees squared. <SR>
These two quantities are defined only for octahedra and tetrahedra.
The electrostatic site energy <SR>
was calculated with the program ELEN (Y. Ohashi, personal communication).
Calculations were <SR>
performed on a VAX 11/750 computer using double-precision arithmetic.
High symmetry <SR>
structures were reduced to triclinic symmetry. The units are kcal/mole
and are the amount of <SR>
electrostatic energy derived by placing 1 mole of cations of the stated
charge into the site, assuming <SR>
a purely point charge model. This energy is recalculated as electron
volts (eV) in Chapter 11. The <SR>
model charge is that used for the electrostatic calculation, however
this may be omitted in instances <SR>
where it is an integer unambiguously inferred from site occupants.
These energies are included for <SR>
qualitative comparisons among sites and should not be used for
quantitative
calculations because <SR>
they exclude repulsive forces entirely. In addition, partial charges
do not accurately model the <SR>
effects of disorder.
<"Head01">
Systematic Variation of Site Parameters
<"Para01">
With a data base of this size, it is relatively straightforward to
examine correlations between <SR>
various site parameters. Such correlations help explain the nature
of variations seen from structure <SR>
to structure. Two particularly useful correlations are between angle
variance and quadratic <SR>
elongation and between electrostatic potential and mean cation-anion
distance for individual sites.
<"Para01">
<F8@Z7@Lam>Distortions.<F0>There are several parameters that can be
used as indicators of distortions or <SR>
regularity of coordination polyhedra. For regular tetrahedra and
octahedra,
the angular distortions <SR>
are conveniently indicated by the variance of the central angle
(Ang.Var.).
In addition to angular <SR>
distortion is distance distortion, a convenient measure of which is
the standard deviation of the <SR>
distances ($sigma$) which can be used to indicate distortion of cations
of any coordination number. <SR>
A factor called quadratic elongation (Q.E.) (Robinson et al., 1971)
is also calculated for each <SR>
octahedron and tetrahedron and is a convenient measure of both angular
and distance distortions. <SR>
Figure 0.1 is a plot of angle variance versus quadratic elongation
for a large number of tetrahedra <SR>
and shows that the two parameters are, of course, strongly correlated.
There are a few instances in <SR>
which the angle variance plots well below the trend, but no instances
in which it plots above. This is <SR>
<|,"23">likely due to the fact that in a few instances, such as for
a tetrahedron on three-fold axis, the angles <SR>
may be more strongly constrained by symmetry than the distances.
<"Para01">
<F8@Z7@Lam>Electrostatic Energies.<F0> It is also of interest to examine
the variation of electrostatic energy with <SR>
distance. The electrostatic energy reported in the site tables is
in kcal/mole of sites. In Chapter 11, <SR>
these energies are converted to electron-volts and divided by the
charge to give a potential in volts. <SR>
The total electrostatic energy of the crystal would then be half the
sum for all sites in the formula unit. <SR>
The total electrostatic energies calculated for each of these mineral
structures is adequate to allow <SR>
full ionization of all species to their normal valences, if reasonable
allowances for repulsion energies <SR>
are included in Born-Haber calculations.
<"Para01">
The electrostatic energy is by no means the total energy of the crystal.
It specifically excludes <SR>
nearest-neighbor repulsion energies which may be ten percent or more
of total energy. In addition, <SR>
it excludes any estimate of distortion energies of electron distributions
(e.g. crystal field stabilization <SR>
energies) and energies of thermal vibrations. The energies cannot
be used to compute heats of <SR>
formation or predict relative thermodynamic stability of various
polymorphs
because the energy <SR>
differences between polymorphs is typically much smaller than the
excluded terms. The energies <SR>
are, however, useful and instructive for qualitative comparisons between
sites. Further, much <SR>
progress has been made in recent years on prediction of mineral
structures
based on electrostatic <SR>
energies combined with simple to complex expressions for nearest-neighbor
repulsion energies <SR>
(e.g., Catlow et al., 1982, Price and Parker, 1984).
<"Para01">
We have plotted electrostatic potential (eV/chg) versus mean cation-anion
distance for some <SR>
700 sites (Figure 0.2) and observe a very strong correlation. This
figure shows clearly that there is a <SR>
systematic electrostatic contribution to the energy of the crystals.
Further, we have preliminary <SR>
indication that deviations from the observed trend are significant
and potentially useful indicators of <SR>
minor element substitutions.
<"Head01">
Trace and Minor Element Substitutions
<"Para01">
One of the major reasons for undertaking this compilation was to provide
geochemists with a <SR>
convenient and comprehensive source of information on mineral sites.
We hope that it will be of use <SR>
in understanding trace element and minor element distributions in
geochemical systems. We have <SR>
noted a few interesting correlations and general observations that
are worth mentioning here. We <SR>
hope that users of this volume will find many more.
<"Para01">
The electrostatic energy and its variation with mean cation-anion
distances may be a potentially <SR>
useful indicator of minor element substitution sites. For example,
of the two large cation sites in the <SR>
epidote group (5.1), the A2 site has the much deeper electrostatic
potential well despite its larger <SR>
<|,"24">volume. It has, in fact the largest electrostatic energy per
charge (potential) of any site surveyed with <SR>
coordination number greater than 8 (Table 11.7). This accounts for
the preference of trivalent rare <SR>
earth elements for the A2 site over the A1 site in allanite and may
explain why allanite has been <SR>
observed to have distribution coefficients for rare earths relative
to whole rocks of 1000 or more. It is <SR>
relatively straightforward, then to identify potential sites for
lanthanides
and actinides from Tables <SR>
11.6 and 11.7.
<"Para01">
We have also noted that sites tend to favor minor element substitutions
that minimize distortions <SR>
of the site or of the mineral as a whole, that is, of the other sites
in the mineral as well. Recent <SR>
geochemical studies have noted that the rhombohedral carbonates siderite
and calcite both show <SR>
large distribution coefficients for Mn relative to aqueous fluids
(Ishikuni, 1984). In plotting distortion <SR>
coefficients of the octahedral site versus mean distance in pure
carbonates,
we see a minimum in <SR>
the distortion, particularly in angle variance, near Mn. This is in
marked contrast to most silicate <SR>
octahedral sites which show a preference for smaller cations and may
reflect a smaller effective <SR>
radius for oxygen in the silicate octahedra relative to the carbonate
octahedra. This may also be true <SR>
for a broad range of octahedral sites in silicates and may account
for the observation of Goldschmidt <SR>
(1958) that in general mineral sites prefer smaller, rather than larger,
cations. We note that for many <SR>
silicates (e.g. olivine and orthopyroxene) the distortions of the
octahedral sites decrease with radius <SR>
at least down to the radius of Ni and that these structures have a
strong preference for smaller <SR>
cations in these sites.
<"Para01">
The preference for smaller cations by silicate sites is certainly
not applicable to sites other than <SR>
regular octahedra. The X site in garnet is a fine example. It may
contain Ca, Mn, Fe, or Mg and is <SR>
highly symmetric with point symmetry 222. Its only measure of distortion,
<F7@Z7@Lam>s<F0>, does not vary strongly <SR>
with cation radius, but the distortion of the Si site decreases strongly
with increasing X-site radius. <SR>
We would predict from these considerations then that if garnet
crystallized
as a liquidus phase, as it <SR>
apparently does in the eclogite system, it would preferentially accept
Ca, then Fe, then Mg, and thus <SR>
possibly enrich residual liquids in Mg.
<"Para01">
We have included these discussions on major and trace element
distributions
to encourage <SR>
users of these tables to look for correlations between crystal structure
parameters and element <SR>
distributions in natural systems. It is our sincere hope in compiling
these data that they will lead to <SR>
greater understanding of geochemistry as well as mineralogy.
<"Title",
Begin New Page =
<|,"25">ACKNOWLEDGEMENT
<"Para01">
yes>
This work was supported in part by the U.S. Department of Energy,
Office of Basic Energy <SR>
Sciences, through several grants to Los Alamos National Laboratory
which is operated by The <SR>
University of California under contract number W-7405-ENG-6 The authors
particularly thank Dr. <SR>
George Kolstadt (OBES - Chemistry, Earth, and Life Sciences) and Dr.
Ryszard Gajewski (OBES - <SR>
Advanced Energy Projects) for generous support of the project. The
authors thank Drs. Y. Ohashi <SR>
(ARCO, Plano, TX), R. X. Fischer (Johannes Gutenberg Universitaet,
Mainz), and L. W. Finger <SR>
(Carnegie Institution, Washington, DC) for providing computer codes
and discussions and Drs. <SR>
George Zweig, Klaus Lackner, and Wes Myers (Los Alamos National
Laboratory)
for discussions, <SR>
support, and encouragement throughout the project. Theoretical Division
Office of Los Alamos <SR>
National Laboratory is also thanked for its support, and Tamsin C.
McCormick is gratefully <SR>
acknowledged for tireless proofreading, technical assistance and moral
support.