Causes of anomalous mineralogical diversity in the periodic table

Prévia do material em texto

Causes of anomalous mineralogical diversity in the
Periodic Table
ANDREW G. CHRISTY
Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University,
Canberra, ACT 0200, Australia
[Received 9 December 2014; Accepted 24 February 2015; Associate Editor: S. Krivovichev]
ABSTRACT
When crustal abundance (A, measured in atomic parts per million) of a chemical element is plotted vs.
number of mineral species in which that element is an essential constituent (S), a significantly positive
correlation is obtained, but with considerable scatter. Repeated exclusion of outliers at the 90%
confidence level and re-fitting leads, after the sixth iteration, to a steady state in which 40 of the 70
elements initially considered define a trend with log S = 1.828 + 0.255 log A (r = 0.96), significantly
steeper than the original. Three other methods for reducing the effect of outliers independently
reproduce this steeper trend. The ‘diversity index’ D of an element is defined as the ratio of observed
mineral species to those predicted from this trend. D separates elements into three groups. More than
half of the elements (40 of 70) have D = 0.5�2.0. Apart from these ‘typical’ elements, a group of 15
elements (Sc, Cr, Ga, Br, Rb, In, Cs, La, Nd, Sm, Gd, Yb, Hf, Re and Th) form few species of their own
due to being dispersed as minor solid solution constituents, and a hitherto unrecognized group of 15
elements are essential components in unusually large numbers of minerals. The anomalously diverse
group consists of H, S, Cu, As, Se, Pd, Ag, Sb, Te, Pt, Au, Hg, Pb, Bi and U, with Te and Bi by far the
most mineralogically diverse elements (D = 22 and 19, respectively). Possible causes and inhibitors of
diversity are discussed, with reference to atomic size, electronegativity and Pearson softness, and
particularly outer electronic configurations that result in distinctive stereochemistry. The principal
factors encouraging mineral diversity are: (1) Particular outer electronic configurations that lead to a
preference for unique coordination geometries, enhancing an element’s ability to form distinctive
chemical compounds and decreasing its ability to participate in solid solutions. This is particularly
noteworthy for elements possessing geometrically flexible ‘lone-pair cations’ with an s2 outer
electronic configuration. (2) Siderophilic or chalcophilic geochemical behaviour and intermediate
electronegativity, allowing elements to form minerals that are not oxycompounds or halides.
(3) Access to a wide range of oxidation states. The most diverse elements can occur as anions, native
elements and in more than one cationic valence state.
KEYWORDS: mineral diversity, geochemical abundance, stereochemistry, Periodic Table.
Introduction
SOME of the biggest questions in mineralogy are:
(1) Why do some chemical compounds occur in
nature as minerals, and others not? (2) Why do
some elements form many minerals, while others
do not? (3) What range of structures and
compositions can occur as minerals?
‘Minerals’ here can be taken to mean ‘distinct
mineral species’, as discussed in more detail
below. The answers to the questions above are
not trivial, in that several distinct considerations
appear to contribute, with different relative weights
in different circumstances. In order to identify the
factors that are most important, one strategy is to
* E-mail: Andrew.Christy@anu.edu.au
DOI: 10.1180/minmag.2015.079.1.04
Mineralogical Magazine, February 2015, Vol. 79(1), pp. 33–49
# 2015 The Mineralogical Society
examine the elements that show extremes of
diversity in their mineralogical occurrences.
If mineral species are enumerated for each
chemical element, and the abundances of the
elements in the Earth’s crust are compared, a
rough positive correlation is obtained. Common
elements occur in Nature in a large number of
mineral species, while rare elements are essential
constituents of relatively few minerals. The
overall correlation is seen in plots of ‘‘number
of minerals containing a chemical element’’
against ‘‘abundance in the upper part of the
Earth’s crust’’ by Yaroshevsky and Bulakh (1994)
and Wenk and Bulakh (2004). Higgins and Smith
(2010) plotted ‘‘number of minerals with element
in formula’’ against ‘‘crustal abundance’’, and
obtained a similar pattern. In all cases, most
elements lie on a trend in a log�log diagram that
is broadly linear, suggesting a power-law relation-
ship between abundance and number of species.
However, as discussed by Higgins and Smith
(2010), several elements deviate markedly from
the overall trend in that they occur in far fewer
species than would be expected for their
abundance. In almost all cases, this is evidently
due to their dispersal as minor solid-solution
components, substituting for much more abundant
elements of similar size and charge. Thus, most of
the time, lanthanides other than Ce do not form
their own minerals, but are minor components of
Ce-dominant or Y-dominant species (cf.
Miyawaki and Nakai, 1996). Similarly, Sc and
Ga are hidden in substitution for Al and Fe3+,
while the same is true for Rb for K and Br for Cl.
The treatment in the current study differs from
those cited above as follows:
(1) From the point of view of availability of
atoms to make compounds, it is the atomic
abundance of elements, not the mass abundance,
which is important. All the studies cited above use
mass abundance, and thus treat heavy elements as
if they were more abundant than they are, but
light elements, particularly H, as less abundant.
Here, the atomic abundance is used.
(2) Higgins and Smith (2010) use ‘‘number of
minerals with element in formula’’, which
includes mineral species where a given element
may be a minor, non-essential substituent. Thus,
they obtain a disproportionately large number of
species for elements which enter solid solutions
readily, whether common (such as Mg and Fe) or
very rare (they plot ~20 minerals for Gd, which is
actually the dominant rare earth in only one
species, lepersonnite-(Gd): Deliens and Piret,
1982). It is not clear what criteria were used by
Yaroshevsky and Bulakh (1994) and Wenk and
Bulakh (2004) to decide whether a given mineral
contained a given element. Here, whether a
species is deemed to contain an element is
defined restrictively, as discussed below.
(3) In the present study a more rigorous
definition has been sought for the trend repre-
senting the typical correlation between abundance
and number of species.
It will be seen that there also exists a population
of elements which form many more distinct
mineral species than would be expected on the
basis of abundance, and that there are good
reasons why this is so.
Data acquisition and filtering
The crustal (not upper-crustal) abundances by
mass of the elements were taken from the CRC
Handbook of Chemistry and Physics (Haynes et
al., 2013). These data have not been updated since
the earlier edition of the CRC Handbook used by
Higgins and Smith (2010). Other similar compila-
tions include those of Ahrens (1995), Greenwood
and Earnshaw (1997), Emsley (2002) and ‘‘Kaye
and Laby’’ (National Physical Laboratory, 2005).
Note that these are all secondary or even tertiary
sources. In all cases, data are compiled from older
sources that are less complete. Important primary
references include Wa¨nke et al. (1984), Weaver
and Tarney (1984), Taylor and McLennan (1985).
Yet more sources are cited in the historical
reviews of Wedepohl (1995) and Yaroshevsky
(2006), the first of which also presents some new
concentration estimates. Comparison of datasets
shows that most values for a given element are in
goodagreement, although some of the very rare
elements show significant spread: there is a factor
of two variation for Te and Au data, 10 for Ir and
25 for Os. However, recalculation using the other
datasets does not substantially affect the results of
this study. Abundances by mass were divided by
the relative atomic masses for each element and
renormalized to total number of atoms = 100%, in
order to obtain abundances by atom.
‘Distinct mineral species’ are here defined using
the rigorous criteria for defining the compositional
and structural limits of species, as evolved by
Nickel (1995), Nickel and Grice (1998), Hatert
and Burke (2008) and Mills et al. (2009).
Essentially, a given mineral species has a
particular crystal structural topology, combined
with a particular element in a specified valence
34
ANDREW G. CHRISTY
state predominating on each site of the crystal
structure or group of crystallochemically similar
sites. Only sometimes are species distinguished by
the identity of subordinate elements in such a site
or site group. Species boundaries for particularly
complex mineral groups such as the amphiboles
are defined in the reports of various subcommit-
tees of the Commission on New Minerals,
Nomenclature and Classification (CNMNC) of
the International Mineralogical Association
(IMA). The names and formulae of valid minerals
are contained in the regularly updated mineral list
of the IMA, available at the CNMNC website
(http://ima-cnmnc.nrm.se/imalist.htm).
The numbers of mineral species were obtained
by performing chemical searches in the online
mineral database Mindat (www.mindat.org) in
October 2014, revised on 5th February, 2015. The
lists returned for each element were then screened
visually so as to include only mineral names that
were valid according to the September 2014
edition of the IMA list of minerals at the
CNMNC website. Additionally, it was necessary
to filter only those species where the searched
element was an essential, species-defining consti-
tuent, as discussed above. In some cases, decisions
were not completely unambiguous, as the corre-
spondence between ‘mineral species’ and
‘chemical endmember’ is not always straightfor-
ward. When charge balance required two elements
of difference valence to be equally present on a
site, as for some endmembers discussed by
Hawthorne (2002), both were regarded as essential.
However, some species can undergo multiple
charge-coupled heterovalent substitutions, and
thus embrace several ‘Hawthornian’ endmembers
containing a variety of minority charge-balancing
species which were not considered to be essential.
Examples may be seen in Atencio et al. (2010).
The additional criteria applied for this study are
quite restrictive, as evidenced by the generally
smaller numbers of species that result, compared
with other recent compilations such as that of
Krivovichev and Charykova (2014). The species
that are currently known only from meteorites were
not excluded because (1) they are very few in
number; and (2) many species previously thought
to be of exclusively meteoritic or lunar origin have
since been found in terrestrial parageneses (e.g.
cohenite and schreibersite, Pauly, 1969; tranquilli-
tyite: Rasmussen et al., 2012).
Using the criteria above, 70 elements were
found to be essential constituents of known
mineral species. No minerals are known for the
noble gases He, Ne, Ar, Kr or Xe, the radioactive
elements Tc, Pm, Po�Ac, Pa or Np onwards, or
lanthanides Pr, Eu, Tb�Tm and Lu. These
elements have been excluded from the current
study. Out of ~5000 known species, oxygen was
found to be essential in ~80% and hydrogen in
55%, in accord with the importance of water and
oxygen near the surface of the Earth. Silicon was
essential in ~30% of species.
Abundance and species data for the remaining
elements are summarized in Table 1.
Definition of trend
The abundance and species number data plotted
on a log�log chart, as per Wenk and Bulakh
(2004) and Higgins and Smith (2010) are shown
in Fig. 1. An overall positive correlation is
evident, although there is increasing scatter for
the rarer elements. Linear regression of logS
against logA for the full dataset gives the relation
logS = 1.809 + 0.218 logA (Fig. 1a). The Pearson
correlation coefficient r = 0.64 for this regression
is rather low, but the correlation is nevertheless
highly significant. Calculation of the Student t
statistic t = r/H(1 � r2)6H(n � 2), where n =
degrees of freedom = 70 � 2 = 68, gives t = 6.92.
This large value of t corresponds to a tiny
probability a = 2610�9 for n = 68, and implies
that the null hypothesis of no dependence of S on
A can be rejected with better than (1 � a)
confidence.
While the data points for A > 100 ppm do
appear to lie along a linear trend in Fig. 1a, those
for rarer elements splay into a broader, almost
triangular distribution, which is the main cause of
the low overall correlation coefficient. Thus, it is
by no means clear that a simple linear regression
identifies the most appropriate trend line. Figure
1a also shows 90% and 95% confidence interval
contours for the regression. Because of the broad
scatter, only eight data points lie outside the 90%
contours: those for Te and Bi above the line, and
Ga, Rb, Sm, Gd, Yb and Hf below it. If these
extreme outliers are excluded, a new regression
line can be fitted through the remaining points and
new, narrower confidence intervals calculated,
which identify more outliers. After six such
iterations, a self-consistent state is obtained
where no new outliers are rejected at the 90%
level. The excluded outliers are distributed
symmetrically above and below the new regres-
sion line, with 15 data points above the line and
15 below it. As outliers are progressively
ANOMALOUS MINERALOGICAL DIVERSITY IN THE PERIODIC TABLE
35
TABLE 1. Crustal abundance and number of species data for the 70 chemical elements that are essential
constituents of mineral species.
Atomic
number
Element symbol Awt Aat S R(Aat) R(S) D
1 H 1400 28,900 2768 4 2 2.98
3 Li 20 60 103 19 37 0.54
4 Be 2.8 6.5 116 33 33 1.07
5 B 10 19 263 28 20 1.83
6 C 200 346 386 14 16 1.29
7 N 19 28 93 24 38 0.59
8 O 461,000 599,000 3961 1 1 1.97
9 F 585 640 336 12 18 0.96
11 Na 23,600 21,300 872 6 8 1.01
12 Mg 23,300 19,900 586 8 10 0.69
13 Al 82,300 63,400 1007 3 6 0.89
14 Si 282,000 209,000 1412 2 3 0.92
15 P 1050 705 566 11 12 1.57
16 S 350 227 1007 15 7 3.74
17 Cl 145 85 339 17 17 1.62
19 K 20,900 11,100 410 9 15 0.56
20 Ca 41,500 21,500 1161 5 4 1.35
21 Sc 22 10.2 15 29 57 0.12
22 Ti 5650 2450 327 10 19 0.66
23 V 120 49 209 20 24 1.15
24 Cr 102 41 82 21 41 0.47
25 Mn 950 359 539 13 13 1.78
26 Fe 56,300 21,000 1022 7 5 1.19
27 Co 25 8.8 61 31 43 0.52
28 Ni 84 30 140 23 29 0.87
29 Cu 60 20 648 27 9 4.49
30 Zn 70 22 242 25 21 1.63
31 Ga 19 5.7 6 36 62 0.057
32 Ge 1.5 0.43 28 45 =49 0.52
33 As 1.8 0.50 584 43 11 10.3
34 Se 0.05 0.013 117 59 32 5.24
35 Br 2.4 0.62 8 42 61 0.13
37 Rb 90 22 3 26 66 0.020
38 Sr 370 88 108 16 34 0.51
39 Y 33 7.7 107 32 35 0.94
40 Zr 165 38 120 22 30 0.70
41 Nb 20 4.5 104 37 36 1.05
42 Mo 1.2 0.26 54 49 45 1.12
44 Ru 0.001 0.0002 5 65 63 0.65
45 Rh 0.001 0.0002 14 66 58 1.82
46 Pd 0.015 0.0029 63 61 42 4.14
47 Ag 0.075 0.014 161 58 27 7.05
48 Cd 0.15 0.028 26 57 52 0.96
49 In 0.25 0.045 12 55 60 0.39
50 Sn 2.3 0.40 90 46 39 1.68
51 Sb 0.2 0.034 233 56 23 8.19
52 Te 0.001 0.00016 158 68 28 21.7
53 I 0.45 0.074 24 54 53 0.69
55 Cs 3 0.47 18 44 56 0.32
56 Ba 425 64 205 18 26 1.05
57 La 39 5.8 35 35 48 0.33
58 Ce 66.5 9.9 119 30 31 0.98
36
ANDREW G. CHRISTY
excluded, the slope of the regression line becomessteeper, the intercept decreases, and the correla-
tion coefficient increases markedly. The equation
for the new regression line through data for the
remaining 41 elements is logS = 1.828 + 0.255
logA with r = 0.96. This line is shown in Fig. 1b,
along with the outlying elements that were
excluded from the regression.
Other choices of trendline can be fitted through
the data in order to define ‘typical’ behaviour.
Higgins and Smith (2010) outline a band of
‘typical’ elements between approximately logS =
2.5 � 0.5 + 0.11 logA (bearing in mind that their
definition of A and their rules for counting S are
different from here). This appears to have been
identified subjectively, and is clearly influenced
by the data points that define the high-S end of the
distribution. In effect, they correspond to an S-
weighted fit. The overall slope of these lines is
very shallow, and the plot of Higgins and Smith
gives the misleading impression that there are
many elements with unusually small S, but none
with unusually large S. More satisfactory alter-
native fits would exclude comparable numbers of
outliers above and below the trend line. Three
possibilities are as follows:
(1) Linear regression in which more abundant
elements are given more weight, reflecting the
greater accuracy with which A is known, the
better relative stability of S and the lower
sensitivity of the A-S signal to random and non-
random perturbation. As abundance varies over
ten orders of magnitude, a weight that is a small
positive power of A should be used. The
weighting increases the slope of the regression
line and the correlation coefficient relative to the
unweighted fit, and decreases the y-intercept. For
instance, if A0.1 weighting is used, we have logS =
1.752 + 0.268 logA with rw = 0.75.
(2) ‘Robust regression’ using non-parametric
fits that are not sensitive to outliers. The Theil-
Sen regression estimates the slope as the median
of the slopes of the lines between all pairs of data
points (�n(n�1) = 2415 pairs in this case), and
the y-intercept as the median of the intercepts
obtained if lines of that slope are drawn through
the data points (Theil, 1950; Sen, 1968). The line
thus obtained is 1.866 + 0.236 logA.
(3) Non-parametric selection of a most-mono-
tonic subset of the data, based on closeness of rank
in abundance R(A) and rank in species number R(S),
which are given in Table 1. For the 38 elements
60 Nd 41.5 6.0 23 34 54 0.22
62 Sm 7.05 0.97 2 39 =67 0.030
64 Gd 6.2 0.82 1 41 =69 0.016
70 Yb 3.2 0.38 4 47 =64 0.076
72 Hf 3 0.35 1 48 =69 0.019
73 Ta 2 0.23 50 51 46 1.08
74 W 1.25 0.14 39 52 47 0.95
75 Re 0.0007 0.000078 2 70 =67 0.33
76 Os 0.0015 0.00016 4 67 =64 0.55
77 Ir 0.001 0.00011 13 69 59 1.99
78 Pt 0.005 0.00053 28 63 =50 2.85
79 Au 0.004 0.00042 29 64 49 3.13
80 Hg 0.085 0.0088 90 60 40 4.47
81 Tl 0.85 0.086 57 53 44 1.58
82 Pb 14 1.4 486 38 14 6.61
83 Bi 0.0085 0.00085 209 62 25 18.9
90 Th 9.6 0.86 22 40 55 0.34
92 U 2.7 0.24 262 50 22 5.06
Awt = elemental abundance by mass in parts per million, Aat = elemental abundance by number of atoms in p.p.m.,
S = number of mineral species in which element is an essential component, R(Aat) = rank in atomic abundance,
R(S) = rank in number of species, D = diversity index (see text).
TABLE 1 (contd.)
Atomic
number
Element symbol Awt Aat S R(Aat) R(S) D
ANOMALOUS MINERALOGICAL DIVERSITY IN THE PERIODIC TABLE
37
38
ANDREW G. CHRISTY
with |R(S) � R(A)| 4 10, a line is obtained with
logS = 1.844 + 0.275 logA with r = 0.92.
These trend lines are plotted in Fig. 1c, where it
is seen that they are all very close to each other
and to the line of Fig. 1b, lying well within its
95% confidence limits. Thus, these four indepen-
dent means of rejecting outliers return very
similar ‘typical’ relationships between A and S.
For this study, the equation of the line in
Fig. 1b above was used to predict a number of
mineral species Sˆ for each element. This number
was then compared with the number S of species
observed, and the ratio D = (S/Sˆ) calculated. This
‘diversity index’ is given in the final column of
Table 1. D > 1 for elements that occur in more
species than would be expected from the trendline
of Fig. 1b, and 0 < D < 1 for elements that have
fewer species than predicted by the trendline. A
Periodic Table in which elements are coloured
according to their D values is shown in Fig. 2.
The linear relationship between log A and
log S (and hence power-law relationship
between A and S) is likely to be driven by two
main factors: (1) greater abundance means that it
is more likely that a given element can occur in
concentrations in mineralizing fluids that are
sufficient to saturate the fluid in one of its
minerals, or at least to ensure its predominance
over competing solid solution substituents; and
(2) the greater a mineral’s overall abundance, the
wider the range of geochemical environments in
which it is likely to reach such mineralizing
concentrations, and the greater the number of
other elements that it is likely to meet with which
to form minerals. Hazen et al. (2014) noted that
the minerals which we observe for very rare
elements are determined by the chance compo-
nent in such encounters, and probably represent a
small subset of the minerals which could
plausibly occur.
FIG. 1 (Above and facing page). (a) Logarithm (base 10) of number of species for which an element is essential (logS)
vs. logarithm of atomic crystal abundance (logA). Unweighted regression line is blue; slightly curved lines indicate
95% confidence interval (red) and 90% confidence interval (pink). (b) logA � logS plot after six iterations of
excluding outliers from the regression. New regression line is steeply and more tightly constrained. Excluded data
points are in red. (c) Three alternative trendlines: abundance-weighted line (solid green), Theil-Sen line (purple dash-
dotted) and line through rank-based subset of data (orange dashes). Lines of (b) are shown in grey for comparison.
ANOMALOUS MINERALOGICAL DIVERSITY IN THE PERIODIC TABLE
39
The diversity index D ranges over a factor of
~1400 for the elements of this present study. Its
smallest values are for the elements which rarely
form their own minerals, reaching a minimum of
0.016 for Gd, a moderately abundant lanthanide
for which the relationship of Fig. 1b predicts 64
minerals with essential Gd, while lepersonnite-
(Gd) is the only one known to date. Conversely, D
is at a maximum of 21.7 for Te, an extremely rare
element for which only seven species are
predicted, while 158 are known. The significance
of this measure, and of these extreme values, is
emphasized by the fact that diversity is between
2.0 and 0.5 for 40 out of 70 of the elements of this
study. The remaining elements are divided into 15
‘dispersed elements’ (Sc, Cr, Ga, Br, Rb, In, Cs,
La, Nd, Gd, Sm, Yb, Hf, Re and Th) which tend to
occur as subordinate solid solution components
rather than to form their own species, and 15
‘anomalously diverse’ elements (H, S, Cu, As, Se,
Pd, Ag, Sb, Te, Pt, Au, Hg, Pb, Bi and U). While
the majority of these elements are extremely rare,
greater abundance combines with intrinsic diver-
sity to yield impressive numbers of species for Cu
(648), As (584) and Pb (486).
Causes of mineral diversity
The diversity index D derived above represents
the residual speciosity of the elements after the
effect of crustal abundance has been removed. It
is evident that additional factors have a major
effect on the number of species in which a mineral
occurs. However, it will be seen below that while
such influences can be identified, they are in
general difficultto quantify, and thus the strengths
of their influences are not amenable to evaluation
through procedures such as principal factor
analysis. Possible contributors to the variation in
D will now be considered.
Solid solution
As mentioned above, dispersal of some elements
through solid solution is well known, and has
often been asserted in the literature. In general,
substitution of one element for another at a site in
a crystal structure occurs most readily if: (1) the
sizes of the two species are very similar
(typically, within 15%), as measured by ionic or
atomic radius; (2) the electronegativities are very
FIG. 2. Periodic Table showing elements colour-coded according to the diversity index of Table 1, with key below.
Anomalously abundant elements (D5 2) are in violet and blue hues, the 40 typical elements used for the regression
of Fig. 1b are in green/yellow, and dispersed elements are in orange/red/brown.
40
ANDREW G. CHRISTY
similar; and (3) the valences are the same (or
within one valence unit). These principles were
first expressed for metal alloys by Hume-Rothery
and Powell (1935) and for minerals by
Goldschmidt (1937). Easy solid solution for
these reasons is observed for all of the dispersed
elements of this study, all of which have at least
one host element that is very similar in size,
electronegativity and valence but more abundant.
The question remains whether it is possible to
form a quantitative combination of closeness in
crystal-chemical and geochemical parameters that
reliably predicts the resulting reduction in number
of species. The rare earth elements provide the
examples of La and Nd, which are dispersed in
solution with Ce as trivalent cations. Both are
~1.7 times rarer than Ce (Table 1). Both have
extremely similar ionic radii (DrLa�Ce = +0.022 A˚
and DrNd�Ce = �0.033 A˚ for 9-fold coordination
using the data of Shannon, 1976) and electro-
negativities (DwLa�Ce = +0.02 and DwNd�Ce =
�0.02 using the data of Pauling, 1960). While Ce
is a typical element with D = 0.98, the numbers of
species are reduced from those expected by a
factor of 3.0 for La and 4.5 for Nd. Thus, D is
reduced for such similar elements by a factor
larger than the abundance ratios. Among non-
lanthanide trivalent cations, Ga is similar to both
Al (DrGa–Al = +0.085 A˚ for 6-fold coordination
and DwGa�Al = +0.20) and particularly to Fe
(DrGa�Fe = �0.02 A˚ and DwGa�Fe = �0.02), while
being 14,000 times rarer than Al and 3700 times
rarer than Fe. However, D for Ga is only 21 times
less than that of Al and 16 times less than that of
Fe, suggesting that in this case, it varies as a
relatively low power (approximately the cube
root) of A. It is clearly non-trivial to quantify just
the effect of abundance, let alone the degree of
similarity or difference in the other parameters, in
reducing D for the dispersed elements.
Unusual phase stability
Note that multicomponent solid solution is likely
to increase the stability of minerals containing the
host element. If some phases are disproportio-
nately stabilized, this might lead to the host
element forming a disproportionately small
number of highly stable phases, which would
result in reducing D for the host element as well
as its substituents. In fact, occurrence of particular
overwhelmingly stable phases as minerals might
be a mechanism by which an element acquires a
low D index without being dispersed as a solid
solution component. However, there appears to be
only one probable example of low speciosity due
to the existence of such an extraordinarily stable
phase, namely Sn (see ‘‘Group 14’’ below).
More on size and electronegativity
Numerical parameters relating to the size of atoms
and the strength of attraction between atom and
bonding electrons have proven of great utility in
modelling chemical differences and similarities
between elements and also in delineating stability
fields for different structure types of binary and
ternary compounds, and thus predicting what
compounds can occur. Examples include the
earliest attempts at predicting coordination using
ionic radius ratios (cf. Pauling’s First Rule),
structure maps based on electronegativity differ-
ence vs. principal quantum number (Mooser and
Pearson, 1959) or ionic and covalent contributions
to bonding energy (Phillips, 1970), and various
applications of angular-momentum dependent
pseudopotential core radii (Bloch and
Schatteman, 1981; Zunger, 1981; Burdett et al.,
1981; Godovikov and Hariya, 1997). For the
elements of this present study, Fig. 3 shows the
Pauling electronegativity (Pauling, 1960) plotted
against a measure of atomic size that does not
vary with valence or coordination number, as does
ionic radius (Shannon, 1976). In Fig. 3, a recently
published set of unit-valence covalent radii is
used (Cordero et al., 2008), although a similar
pattern is obtained with other analogous
measures, such as the size parameter r of
O’Keeffe and Brese (1991). Note that the
dispersed elements cover a very wide range of
electronegativities from Cs to Br. An apparent
clustering at the large-electropositive corner of
the plot is due to six out of 15 of these elements
being lanthanides or actinides. The anomalously
diverse elements span a wide range of sizes, from
small H and S to large U. However, they do show
a clustering towards intermediate electronega-
tivity values. All of these elements except U have
electronegativities in the range 1.85�2.6,
although note that they are still not well separated
from other elements with similar atomic proper-
ties but less diversity, particularly Mo, Sn, W and
the rarer platinum-group elements Ru, Rh, Os and
Ir. The null hypothesis, that this clustering of the
diverse elements is due to chance, can be rejected
at the p = 1 � 2610�6 confidence level (w2 =
22.8, n = 70 and 1 degree of freedom). The
preference of diverse elements to have inter-
ANOMALOUS MINERALOGICAL DIVERSITY IN THE PERIODIC TABLE
41
mediate electronegativity values implies that large
numbers of mineral species are most easily
formed if bonding is not strongly polar, being
dominantly covalent or metallic rather than ionic.
In turn, this suggests that having a wide range of
bonding partners is important: highly electro-
positive cationic elements form stable ionic bonds
in minerals with only a small number of anions
(O2�, F� and Cl�, almost exclusively), while a
much wider range of ligands are available to less
electropositive cations in intermetallic or polar-
covalently bonded compounds. The strong direc-
tionality of covalent bonding also suggests that
distinctive stereochemistry may play a role in
enhancing speciosity, through restriction of solid
solution.
Phase complexity
Krivovichev and Charykova (2014) have
recently published a study of both the numbers
of mineral species for the chemical elements and
also the number of different essential compo-
nents for mineral species, which varies over the
range 1�10 with a mode at 4�5. However, they
did not present any data on linkage between
these two distributions, and hence did not discuss
whether some elements might tend to occur in
more chemically complex minerals than others.
A somewhat related type of structural
complexity was defined and explored by
Krivovichev (2013): this quantitative parameter
expresses the amount of digital information
required to describe the distinct crystallographic
sites in a primitive unit cell of the mineral’s
crystal structure. However, his list of the 20 most
complex minerals shows little correlation with
the presence or absence of diverse elements. The
list has a greaterproportion of silicates than is
typical (the typically speciose element Si is in
85% of the list, compared with 30% of mineral
species in general), and contains only one Cu
mineral, one U mineral and three S minerals. The
only diverse element that is over-represented is
H (18 out of 20 minerals). It appears that while
composition may indeed relate to structural
complexity, this is not in turn related to an
increase in number of species.
FIG. 3. Covalent radius vs. Pauling electronegativity for the 70 elements of this study. Symbols are colour-coded for
diversity index, as in Fig. 2.
42
ANDREW G. CHRISTY
Outer electronic configuration
The visualization of D in Fig. 2 shows clearly that
the dispersed elements, apart from their concen-
tration among the lanthanides, are rather
randomly distributed. However, this is not true
of the anomalously diverse elements. The 15
elements with D > 2 are confined to two
distinctive regions in the lower right of the
Periodic Table, except for two outliers. One of
the two regions contains the late transition
elements Pd, Pt, Cu, Ag, Au and Hg, while the
other contains the p-block elements S, As, Se, Sb,
Te, Pb and Bi. The outlying diverse elements are
H and U, which are well separated from all the
others and from each other, given that H is the
lightest element to form its own minerals (Z = 1),
while U is the heaviest element to do so (Z = 92).
The separation of the two clusters by a region of
more normal diversity (Zn, Ga, Ge, Cd, In, Sn and
Tl) is noteworthy.
The clustering of the anomalously diverse
elements in the Periodic Table implies that
mineralogical diversity may arise from causes
that are related to their outer electronic
configuration.
The majority of anomalously diverse elements
(all except H and U) classify as ‘‘siderophile’’ or
‘‘chalcophile’’ in the classification of Goldschmidt
(1937). This implies that they have cations that
are ‘‘soft’’ in the sense of Pearson (1963), and
prefer ligands other than oxygen in their
compounds, consistent with their intermediate
electronegativity, as noted above. The side-
rophiles Pd, Pt and Au form native metals and
intermetallic compounds in the crust, while
chalcophiles such as the p-block elements tend
to crystallize initially as compounds with the
heavier chalcogenides or pnictides (e.g. as
sulfides, arsenides and tellurides), forming
oxycompounds on subsequent oxidation. Unlike
lithophiles, these elements have a mineralogy that
is not dominated by oxycompounds, and the
increased chemical diversity of their minerals is a
major factor in increasing the total number of
species.
However, note that siderophile elements such
as Ru, Rh, Re, Os and Ir are not abnormally
diverse, and that the chalcophile elements include
several elements that are not abnormally diverse
(e.g. Co, Ni, Zn, Cd and In) and one that is
extremely under-diverse (Ga). The diversity of H
and U also implies that geochemical preference is
not the sole driver of mineral diversity. Both of
these elements are lithophilic, and form strong
bonds only to oxygen in minerals of the Earth’s
crust.
What is noteworthy about the majority of the
diverse elements including H and U is that they
have extremely distinctive stereochemistries.
These can almost always be related to outer
electron configuration. However, the details vary
in different regions of the Periodic Table, which
are discussed below on a column-wise basis.
Group 1
The hydrogen cation is uniquely small: the H+
cation is formally a naked proton with no core
electrons. H is the only species that forms only
one strong bond to oxygen in minerals. Its ability
to simultaneously form one or more ‘hydrogen
bonds’ to other species, that are necessarily much
longer and weaker than the primary H�O bond,
gives the hydrogen-bearing complexes OH� and
H2O a very special role in mineral structures as
‘transformers’ between cations and anions of
different Lewis acid base strengths, thus facil-
itating the formation of minerals with complex
formulae, containing combinations of several very
different species (Hawthorne, 1992; Schindler and
Hawthorne, 2001).
Actinides
Uranium also shows behaviour that is unique
amongst mineral-forming elements. The majority
of its minerals are U6+ species, and with only a
couple of exceptions, they contain the very stable
cationic uranyl complex [O=U=O]2+, which forms
4�6 additional much longer and weaker bonds
that lie in a plane perpendicular to the uranyl
group (Burns et al., 1996). Distortion of the
coordination polyhedron relative to one with more
equal bond lengths can be regarded as due to a
second-order Jahn-Teller effect in which devel-
opment of a unique uranyl axis permits stronger
interaction between the oxygen 2p valence
orbitals and the ostensibly lowest-unoccupied
uranium 5f and 6d orbitals (cf. Craw et al.,
1995; Denning, 2007), with the resulting p-
bonding electron density concentrating into a
single pair of U�O bonds. The combination of
relatively large-size, high-valence and unusual
coordination geometry means that U6+ is rarely a
significant solid solution component with other
cations; markcooperite, Pb(U,Te)TeO8, is a rare
example (Kampf et al., 2010). Similarly, most
uranium minerals have no isostructural non-
uranium species in Nature. Instead, U6+
ANOMALOUS MINERALOGICAL DIVERSITY IN THE PERIODIC TABLE
43
coordination polyhedra link together with each
other and with other species to form a great
variety of distinctive uranyl species (Burns,
1999).
The only other actinide element with an isotope
that is long-enough lived relative to the Earth to
form its own minerals is Th. However, the nuclear
charge and formal valence of Th4+ are lower than
those of U6+, resulting in less interaction of the
lowest-unoccupied Th orbitals with valence
orbitals, and no destabilization of relatively
isotropic coordination geometry, as seen in the
ThO8�9 polyhedra of minerals such as the thorite
and huttonite polymorphs of ThSiO4, which
resemble those of Zr4+ and the larger, lighter
lanthanides such as Ce3+ in zircon and monazite,
respectively (Taylor and Ewing, 1978). Heavier
actinides such as Np and Pu might well behave
similarly to U as they form similarMO2
n+ cationic
complexes (Krivovichev et al., 2007; May et al.,
2007), but occur in the crust at concentrations too
small to form their own species.
The lanthanides themselves do not form
complexes like uranyl, because of the more core-
like behaviour of 4f electrons compared with 5f,
which limits interaction with oxygen orbitals and
access to higher valence states for the cation.
Note that similar interactions between an empty
cation-based LUMO and oxygen-dominated
valence band results in centrosymmetry-breaking
distortions for polyhedra surrounding high-
valence (5 5) cations that have the d0 outer
electronic configuration with either no f subshell
(early transition elements of the 3d and 4d rows)
or a closed, core-like f14 subshell (5d row).
Examples include Nb5+ Mo6+ and W6+
(O’Keeffe, 1989). For the d1 cation V4+, the
same mechanism produces extremely distorted
polyhedra featuring the [V=O]2+ vanadyl
complex. Vanadyl occasionally shows some
crystallochemical similarity to uranyl, as mani-
fested in the near-isotypic structural relationship
between sincosite, Ca[VO]2[PO4]2·5H2O and
‘u r a n -m i c a s ’ s u ch a s me t a - au t un i t e ,
Ca[UO2]2[PO4]2·6�8H2O (Zolensky, 1985).
However, the irregular coordination does not
result in anomalous diversity for any of these
early d-block elements, which all lie very close to
the trend lines of Fig.1b,c.
Group 10
Pd2+ and Pt2+ compounds often show the
otherwise unusual square-planar coordination
characteristic of a low-spin d8 electronic config-
uration, due to a second-order Jahn-Teller effect.
This is seen, for example, in vysotskite (Genkin
and Zvyagintsev, 1962) and the polymorphs of
PtS (Bannister and Hey, 1932), braggite (P42/m,
isomorphous with vysotskite) and cooperite
(P42/mmc). However, the main factor that makes
the species number for these elements larger than
it would otherwise be seems to be the production
of intermetallic compounds and alloys that do not
oxidize readily. These have high coordination
numbers and frequently feature short, bonded
distances between PGE (Platinum Group
Element) atoms, as well as between PGE and
non-PGE. For example, even the metalloid-rich
mineral froodite, PdBi2 (Cabri et al., 1973), has
Pd surrounded by not just seven Bi neighbours at
2.773�3.323 A˚ but also by two other Pd at
2.916 A˚. A very wide range of stoichiometries are
possible for such metallic and near-metallic
materials, unrestricted by normal charge-balance
considerations. For instance, binary palladium
arsenides range from vincentite (Pd3As), stillwa-
terite and arsenopalladinite (both ideally Pd8As3)
and palladoarsenide and palladodymite (both
Pd2As), while Pt forms sperrylite (PtAs2). The
siderophilic behaviour of these elements is
probably due to relativistic perturbations to their
orbital energies (see below). Similar chemical
behaviour is exhibited by the Group 8�9
elements Ru, Rh, Os and Ir. It may be the case
that they potentially have great diversity, but that
their diversity is suppressed due to their scarcity
and incorporation as solid solution components in
minerals of Pd and Pt.
Groups 11�12
Apart from a few exceptions such as cuprite
(Cu2O), copper is divalent in its oxycompounds
but univalent in its sulfides. The d9 configuration
of Cu2+ results in a preference for strong
distortion of octahedral coordination through the
Jahn-Teller effect (Eby and Hawthorne, 1993;
Burns and Hawthorne, 1996), which doubtless
boosts the number of Cu minerals by preventing
Cu from entering solid solution with other
divalent cations, and encouraging adoption of
unique structures with square-planar, pyramidal
or elongated octahedral coordination. Note,
however, that such proliferation is not obvious
for the only other cation experiencing a similar
Jahn-Teller effect that is significant in crustal
environments, namely d4 Mn3+.
The coinage metals, Cu, Ag and Au, in their +1
valence states and Hg2+ with d10 configuration are
44
ANDREW G. CHRISTY
soft, chalcophilic cations. They form a distinctive
group that frequently occurs in linear 2-fold
coordination by ligands. As a result, they show
little tendency to undergo solid solution with
other species in many of their compounds, which
are therefore unique to these elements.
This distortion occurs only around the transi-
tion from d-block to p-block in the Periodic
Table, particularly for the heavier species. It has
been explained as due to a second-order Jahn-
Teller effect triggered by s�d mixing (Orgel,
1958), inaccessibly high energies of the cation
p-orbitals (Nyholm, 1961), and a combination of
these effects, amplified by relativistic shifts in
orbital energies for these elements (Kaupp von
Schnering, 1994a) which reach a maximum for
Au (Pyykko¨, 2012 and references cited therein).
For HgO, the ‘s�d mixing’ has been shown to be
mediated through oxygen 2p orbitals (Glans et al.,
2004).
One effect of the relativistic adjustments to
orbital energies, noted by Pyykko¨ (2012), is an
increased tendency to metal�metal interactions.
This is manifest in the increased number of
intermetallic compounds for the PGE (discussed
above) and in this group also. This is particularly
the case for Au minerals, which are dominated by
intermetallic phases such as maldonite (Au2Bi)
and its isotype hunchunite (Au2Pb), which have
the cubic Laves structure of Cu2Mg (Jurriaanse,
1935), with Au coordinated by 6 Au + 6 (Pb/Bi).
The square-planar primary coordination seen in
some minerals is consistent with low-spin d8 Au3+
(cf . buckhorn i te , [Pb2BiS3]
+ [AuTe2]
�,
Effenberger et al., 2000). However, whereas
‘aurophilicity’ involving presumed Au�Au
bonding interactions is well documented in
synthetic phases, there is currently no evidence
of it in minerals. Tellurides such as calaverite,
AuTe2 (Bindi et al., 2009) or krennerite,
Au3AgTe8 (Dye and Smyth, 2012) show no
unusually short Au_Au distances.
Most Hg2+ minerals have unique structures and
chemistries. The relativistic favouring of
metal�metal interactions also stabilizes the
[Hg2]
2+ dimer (cf. Kaupp von Schnering,
1994b), which effectively doubles the number of
Hg minerals through access to an extra oxidation
state. A tendency to form small metal clusters is
seen also in the occurrence of the triangular
[Hg3]
4+ group in terlinguaite, [Hg3]
4+Hg2+O2Cl2
(Brodersen et al., 1989) and tetrahedral
[Ag3Hg]
3+ in tillmannsite, [Ag3Hg][VO4] (Sarp
et al., 2003).
The lighter cogeners of Hg, Zn2+ and Cd2+,
show no evidence of this unusual behaviour, as
the relativistic effects are much smaller for them.
Thus, these elements show normal mineral
diversity.
Group 13
This column of the Periodic Table deserves
mention as the hub of the ‘valley of low diversity’
between the two diversity clusters in Fig. 2.
Gallium, In and Tl are chalcophilic elements, of
which rare primary minerals are sulfides, although
much Ga also occurs in silicates and oxides as a
trace replacement of Al and Fe3+. Such dispersal
appears to be the main reason for their low
diversity, as Ga and In also substitute for elements
such as Fe, Cu, Zn and Sn in sulfides: note the
proximity of these elements in Fig. 3. Unlike the
lighter elements which form trivalent d10 cations,
Tl occurs primarily as the 1+ cation with the s2
outer electronic configuration and a stereoactive
lone pair, which should increase its diversity (see
below under ‘‘Group 15�16’’). It has also been
noted that Tl+ cations show anomalously short
distances in a growing number of sulfosalt
minerals such as arsiccioite, AgHg2TlAs2S6
(Biagioni et al., 2014). This may represent a last
vestige of the relativity-induced tendency to metal
clustering discussed for Groups 9�12 above, and
may stabilize Tl+ in environments that are not
suited to other cations, thus enhancing its number
of species. However, it frequently substitutes for
Ag or Pb rather than forming its own minerals, so
enhancing and suppressing effects cancel, and the
overall diversity of Tl is in fact rather average.
Group 14
While Ge and Sn have electronegativities which
suggest the potential for diversity (Fig. 3), they
have quite typical S values. In the case of Ge, this
may be explained by dispersal in solid solution
with Si in silicates and Sn in sulfides. The low
diversity of Sn cannot be explained in this way. It
is noteworthy, however, that Sn mineralization is
dominated by a single mineral species, the oxide
cassiterite, SnO2. This may be an example where
the existence of a single extremely stable phase
leads to a reduction in the number of other species
containing the element. The heavier cogener Pb
behaves quite differently. While Ge occurs
exclusively as a 4+ cation and Sn mainly so, Pb
in the crust is most stable in its lower valence state
2+, where it has a stereoactive lone pair of
electrons like the Group 15�16 elements discussed
ANOMALOUS MINERALOGICAL DIVERSITY IN THE PERIODIC TABLE
45
below, which appears to be another mechanism for
generatinga large number of species.
Groups 15�16
The diversity of the Group 15�16 elements
does not exclusively involve unusual coordination
polyhedra. Instead, it seems to be a function of
them occurring in a wide range of valence states
and electron configurations, which may be anionic
(p6 configuration, e.g. As3�) as well as cationic
(d10 As5+ or s2 As3+, in the case of arsenic).
Phosphorus, which forms only a few phosphide
minerals under extremely reducing conditions, is
not anomalously diverse.
The lower-valence cations of p-block elements
have ‘lone pairs’ of non-bonding electrons which
are stereochemically active in almost all their
oxycompounds and a large proportion of sulfides.
Traditionally, this has been assumed to result
through s�p hybridization in the formation of a
directed non-bonding orbital, which repels
ligands. Recent modelling implies that, like the
‘s�d mixing’ above, the effect is actually
mediated through interaction with ligand p
orbitals (Walsh et al., 2011). In any case, the
result is a highly asymmetric coordination
environment, which restricts the possibilities for
the element to be dispersed in solid solution.
The low symmetry of coordination polyhedra for
s2 cations gives them considerable freedom to vary
in geometry, which allows the shape and also the
volume of the polyhedron to be tuned to match a
wide range of possible host structures. Furthermore,
dipolar cations with stereoactive lone-pair electrons
can form weak bonding interactions, not just with
anions, but also with other lone pairs and with
cations. These additional types of structural
flexibility are discussed in the case of Te4+ by
Christy and Mills (2013). The combination of such
effects should contribute disproportionately to
mineral diversity, beyond the level expected for
an additional valence state alone.
In minerals, the s2 species Bi3+ is the only
cationic Bi species to occur, while Tl+, Pb2+ and
Se4+ are much commoner than their oxidized d10
analogues Tl3+, Pb4+ and Se6+. Conversely, Sn2+
and As3+ are less important than Sn4+ and As5+,
while the comparable stability of the s2 and d10
options for Sb and Te double the numbers of
oxyminerals found for these elements. Other
effects prevent extraordinary diversity occurring
for Sn and Tl, as discussed above. However, for the
other elements, the accessibility of closed-shell and
lone-pair cationic states, additional anionic states
and the ability to form diverse sulfide and
intermetallic minerals strongly increases the total
species count.
Conclusions
Two different methods for excluding outliers to
define a quantitative abundance-speciosity trend
both indicate an ~0.3 power law dependence of
species number on crustal abundance for ‘typical’
elements. A ‘diversity index’ D is defined as the
ratio of observed mineral species to those
predicted from the typical trend. The diversity
index allows elements to be separated into a large
group with D = 0.5�2.0, 15 elements that occur in
abnormally few mineral species of their own due
to being dispersed as minor solid solution
constituents, and 15 elements that are essential
components in unusually large numbers of
minerals. The anomalously diverse group is the
focus of this study and consists of H, S, Cu, As,
Se, Pd, Ag, Sb, Te, Pt, Au, Hg, Pb, Bi and U, with
Te and Bi by far the most mineralogically diverse
elements (D = 22 and 19 respectively).
The principal factors that encourage elements
to show great mineralogical diversity are:
(1) Specific outer electronic configurations that
lead to distinctive stereochemistry, which
enhances an element’s ability to form distinctive
chemical compounds and decreases its ability to
participate in solid solutions. Mineral species
proliferate particularly for elements which can
form ‘lone-pair cations’ with s2 outer electronic
configuration, which show great flexibility in their
coordination geometry.
(2) Siderophilic or chalcophilic geochemical
behaviour and intermediate electronegativity,
allowing elements to bond to a wide range of
ligands and form minerals that are not oxycom-
pounds or halides.
(3) Access to a wide range of oxidation states.
This has already been noted by Moore (1970) for
Mn, which, although not anomalously diverse
overall, nevertheless contributes significantly to
the large number of species found in the
exceptionally diverse ore deposit at La˚ngban,
Sweden. The most mineralogically diverse
elements occur as anions, as native elements and
as cations in more than one valence state.
Acknowledgements
Dr Stuart Mills, Professors Roger Mitchell and
Sergey Krivovichev and an anonymous reviewer
46
ANDREW G. CHRISTY
are thanked for their comments, which have much
improved this manuscript.
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