Structural Derivation and Crystal Chemistry of Apatites

Abstract

The crystal structures of the [A(1)2][A(2)3](BO4)3X apatites and the related compounds [A(1)2][A(2)3](BO5)3X and [A(1)2][A(2)3](BO3)3X are collated and reviewed. The structural aristotype for this family is Mn5Si3 (D88 type, P63/mcm symmetry), whose cation array approximates that of all derivatives and from which related structures arise through the systematic insertion of anions into tetrahedral, triangular or linear interstices. The construction of a hierarchy of space-groups leads to three apatite families whose high-symmetry members are P63/m, Cmcm and P63cm. Alternatively, systematic crystallographic changes in apatite solid-solution series may be practically described as deviations from regular anion nets, with particular focus on the O(1)-A(1)-O(2) twist angle projected on (001) of the A(1)O6 metaprism. For apatites that contain the same A cation, it is shown that decreases linearly as a function of increasing average ionic radius of the formula unit. Large deviations from this simple relationship may indicate departures from P63/m symmetry or cation ordering. The inclusion of A(1)O6 metaprisms in structure drawings is useful for comparing apatites and condensed-apatites such as Sr5(BO3)3Br. The most common symmetry for the 74 chemically distinct [A(1)2][A(2)3](BO4)3X apatites that were surveyed was P63/m (57%), with progressively more complex chemistries adopting P63 (21%), P (9%), P (4.3%), P21/m (4.3%) and P21 (4.3%). In chemically complex apatites, charge balance is usually maintained through charge-coupled cation substitutions, or through appropriate mixing of monovalent and divalent X anions or X-site vacancies. More rarely, charge compensation is achieved through insertion/removal of oxygen to produce BO5 square pyramidal units (as in ReO5) or BO3 triangular coordination (as in AsO3). Polysomatism arises through the ordered filling of [001] BO4 tetrahedral strings to generate the apatite-nasonite family of structures.

Full text

Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 1
research papers
Acta Crystallographica Section B
Structural
Science
ISSN 0108-7681
Structural derivation and crystal chemistry of
apatites
T. J. White* and Dong ZhiLi
Centre for Advanced Research of Ecomaterials,
Institute for Environmental Science and Engi-
neering, Innovation Centre, Nanyang Techno-
logical University, Block 2, Unit 237, 18
Nanyang Drive, Singapore 637723
Correspondence e-mail: tjwhite@ntu.edu.sg
#2003 International Union of Crystallography
Printed in Great Britain ± all rights reserved
The crystal structures of the [A(1)
2
][A(2)
3
](BO
4
)
3
Xapatites
and the related compounds [A(1)
2
][A(2)
3
](BO
5
)
3
Xand
[A(1)
2
][A(2)
3
](BO
3
)
3
Xare collated and reviewed. The
structural aristotype for this family is Mn
5
Si
3
(D8
8
type,
P6
3
/mcm symmetry), whose cation array approximates that of
all derivatives and from which related structures arise through
the systematic insertion of anions into tetrahedral, triangular
or linear interstices. The construction of a hierarchy of space-
groups leads to three apatite families whose high-symmetry
members are P6
3
/m,Cmcm and P6
3
cm. Alternatively,
systematic crystallographic changes in apatite solid-solution
series may be practically described as deviations from regular
anion nets, with particular focus on the O(1)ÐA(1)ÐO(2)
twist angle 'projected on (001) of the A(1)O
6
metaprism. For
apatites that contain the same Acation, it is shown that '
decreases linearly as a function of increasing average ionic
radius of the formula unit. Large deviations from this simple
relationship may indicate departures from P6
3
/msymmetry or
cation ordering. The inclusion of A(1)O
6
metaprisms in
structure drawings is useful for comparing apatites and
condensed-apatites such as Sr
5
(BO
3
)
3
Br. The most common
symmetry for the 74 chemically distinct [A(1)
2
][A(2)
3
]-
(BO
4
)
3
Xapatites that were surveyed was P6
3
/m(57%), with
progressively more complex chemistries adopting P6
3
(21%),
P
3 (9%), P
6 (4.3%), P2
1
/m(4.3%) and P2
1
(4.3%). In
chemically complex apatites, charge balance is usually
maintained through charge-coupled cation substitutions, or
through appropriate mixing of monovalent and divalent X
anions or X-site vacancies. More rarely, charge compensation
is achieved through insertion/removal of oxygen to produce
BO
5
square pyramidal units (as in ReO
5
)orBO
3
triangular
coordination (as in AsO
3
). Polysomatism arises through the
ordered ®lling of [001] BO
4
tetrahedral strings to generate the
apatite±nasonite family of structures.
Received 27 August 2002
Accepted 31 October 2002
1. Introduction
Although the `apatites' are an industrially important group of
materials with applications in catalysis, environmental reme-
diation, bone replacement and ceramic membranes amongst
others, to our knowledge there has been no recently published
collation of crystallographic data that systematizes the entire
range of chemistries and compositions that have been studied
to date. In general, the apatite varieties have not been placed
in the context of the entire family, with a view to under-
standing their crystallographic derivation from simpler
structures.
The apatite prototype Ca
5
(PO
4
)
3
F structure was ®rst
determined by Naray-Szabo (1930) and was con®rmed to
adopt P6
3
/msymmetry. An extensive apatite compilation was

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2White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
prepared by Wyckoff (1965), who
noted that the lack of thorough
structure determinations left many
unanswered questions about the
distribution of metals and oxy-
anions. Subsequently, numerous
studies of biological, mineralogical
and synthetic apatites and apatite-
related substances greatly expanded
the range of known chemistries.
McConnell (1973) summarized the
work up to the 1970s and high-
lighted the limitations associated
with failing to consider the under-
lying chemical principles that
govern apatite crystallography and
the need for precise chemical
analyses to properly account for
apatite properties. Elliot (1994)
updated and expanded the work of
McConnell by covering a wider
range of apatites, reviewing iso- and
altervalent substitutions, and
detailing the identi®cation of
compounds of lower symmetry.
Since then there has been a
substantial increase in the number
of apatites for which excellent
crystallographic data exist.
However, the extent of these
chemistries, which are convention-
ally regarded as conforming to
A
5
(BO
4
)
3
X, and the relative complexity of the structures have
at times obscured either the underlying crystallochemical
principles that govern the formation of apatite or the impor-
tant systematic changes in crystallography that appear as a
function of compositional variation.
In general, structure drawings highlight only the relatively
regular BO
4
tetrahedra, while other features are usually
grouped as `irregular' polyhedra. In this paper, we have
collated the data of more than 85 chemically distinct apatites
for which crystallographic determinations have been
completed. These structures are described as anion-stuffed
cation arrays of the D8
8
alloy type (Wondratschek et al., 1964;
O'Keeffe & Hyde, 1985; Vegas & Jansen, 2002) and as deri-
vatives of hexagonal anion networks (Povarennykh, 1972).
The former approach formalizes the structural hierarchy of
apatites with the Mn
5
Si
3
structure type at the apex, while the
latter proves useful for systematizing topological distortions as
a function of average ionic radius. These descriptions also
readily accommodate A
5
(BO
3
)
3
Xand A
5
(BO
5
)
3
Xderivatives
and apatite polysomatism. This paper summarizes the current
knowledge of apatite structures, particularly with respect to
the literature that has appeared since the publication of
Elliot's work, and complements the work of Nriagu & Moore
(1984) and Brown & Constantz (1994), who deal with phos-
phate compounds.
2. Structural derivation
2.1. The conventional description
The two most common representations of P6
3
/mapatite ± in
this case Ca
5
(PO
4
)
3
F (Sudarsanan et al., 1972)
1
± are shown in
Fig. 1. In general, drawings are projected along [001] and give
prominence to the BO
4
tetrahedra, either in ball-and-stick or
tetrahedral display. This projection highlights aspects of the
symmetry and the regular polyhedra, but usually the coordi-
nation of the Acations is not emphasized. Rather, the A(1)
ions at the 4fposition are described as having coordination to
nine O atoms (six near and three more distant), while the A(2)
ions on the 6hposition are eight coordinated (to seven O
atoms and one F atom). For ¯uorapatite, the F ion lies at
position 2awith z=1
4, while for larger ions, such as Cl, the 2b
position with z= 0 is occupied. In the latter case, the symmetry
can be reduced to monoclinic P2
1
/bwith the caxis unique and
the Xion offset along [001] to statistically occupy the 4e
Figure 1
The [001] projection of ¯uorapatite Ca
5
(PO
4
)
3
F represented in the conventional way with PO
4
units
highlighted, as ball and stick or tetrahedral representations, and with the oxygen coordination to the A
cations de-emphasized.
1
The re®ned stoichiometry is Ca
4.938
(PO
4
)
3
F
0.906
. It seems likely that many, or
perhaps most, of the apatites that are reported as having integral
stoichiometry are in fact somewhat non-stoichiometric, particularly with
respect to Xanions. It is, however, often dif®cult to determine such
compositional variations directly. For this paper, which is concerned primarily
with topological arrangements, small deviations from stoichiometry are not
directly relevant.

position to yield an A(2)O
7
Cl polyhedron [e.g. Bauer & Klee
(1993), but see also Kim et al. (2000)]. These descriptions,
while certainly correct, may not be entirely satisfactory when
we seek to relate systematic crystallographic changes as a
function of composition or to study structural relationships
between apatites. These limitations have been discussed
previously by O'Keeffe & Hyde (1985).
2.2. An anion-stuffed D8
8
alloy
Alternatively, apatite can be regarded as an anion-stuffed
derivative of the Mn
5
Si
3
(D8
8
) alloy type (Wondratschek et al.,
1964; O'Keeffe & Hyde, 1985; Nyman & Andersson, 1979;
Vegas et al., 1991). Here the A
5
B
3
arrangement is emphasized,
as in Fig. 2, where the Ca
5
P
3
topology of Ca
5
(PO
4
)
3
F is shown.
This description highlights the regular arrangement of cations
and uses a Ca(2)
6
octahedron with all edges capped by Ca(1)
and P as the fundamental unit. These units are corner-
connected in (001) and face sharing along [001]. Anions are
then introduced into cavities in the alloy. In ¯uorapatite,
oxygen ions ®ll tetrahedral [O(1) and O(3)] or trigonal
bipyramids [O(2)] while ¯uorine occupies the triangular
interstices between the metals. In chlorapatite the halide
moves from triangular to octahedral coordination. A
comparison of the bond lengths in these anion-centred poly-
hedra is summarized in Table 1. Predictably, the oxygen
polyhedra are highly distorted since they include A(1), A(2)
and Bcations, whereas the X-centred triangles and octahedra
are regular as they involve XÐA(2) bonding only. A similar
description has been presented by Schriewer & Jeitschko
(1993), who considered the arrangement of the A
5
B
3
Xportion
of apatite to be similar to that of the carbide Mo
5
Si
3
C. The
underlying physical basis for the
stuffed-alloy model for apatites has
recently been considered by Vegas &
Jansen (2002), who list the alloy
equivalents of 14 varieties.
If the D8
8
alloy structure with
space group P6
3
/mcm is taken as the
aristotype ± where this terminology is
analogous to that adopted to describe
perovskites (Lefkowitz et al., 1966;
Megaw, 1973) ± it follows that anion-
stuffed derivatives can adopt maximal
non-isomorphic subgroups as shown
by the three branches of the hier-
archical tree in Fig. 3. Prototypical
A
5
(BO
4
)
3
Xapatite with P6
3
/m
symmetry is at the head of the middle
branch, and, as discussed below,
apatites of lower symmetry (P6
3
,P
3,
P
6, P2
1
/m,P2
1
) are numerous.
Indeed, it has been suggested by
several workers (e.g. Huang &
Sleight, 1993) that some apatites that
are reported to conform to P6
3
/mmay
have lower symmetry, a proposition
Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 3
research papers
Figure 2
The structure of ¯uorapatite projected down [001]. We show only the D8
8
cation array represented as
corner-connected Ca(2) octahedra that are capped on all 12 edges by Ca(1) and P. On the right a single
structural Ca
12
P
6
unit is shown projected on [001] in the upper portion and [110] in the lower.
Table 1
Bond lengths (A
Ê) of anion-centred coordination polyhedra.
Ideal hexagonal net Chlorapatite Fluorapatite
O(1)ÐA(1) 2.300 2 O(1)ÐCa(1) 2.335 2 O(1)ÐCa(1) 2.391 2
O(1)ÐB1.675 O(1)ÐP 1.855 O(1)ÐP 1.534
O(1)ÐCa(2) 2.860 O(1)ÐCa(2) 2.818
O(2)ÐA(1) 2.300 2 O(2)ÐCa(1) 2.400 2 O(2)ÐCa(1) 2.451 2
O(2)ÐB2.901 O(2)ÐP 2.886 O(2)ÐP 3.147
O(2)ÐB1.592 O(2)ÐP 1.515 O(2)ÐP 1.540
O(2)ÐA(2) 3.138 O(2)Ð Ca(2) 2.335 O(2)ÐCa(2) 2.384
O(3)ÐA(1) 3.042 O(3)ÐCa(1) 2.894 O(3)ÐCa(1) 2.800
O(3)ÐB2.170 O(3)ÐP 1.592 O(3)ÐP 1.533
O(3)ÐA(2) 2.303 O(3)ÐCa(2) 2.292 O(3)ÐCa(2) 2.384
O(3)ÐA(2) 2.365 O(3)ÐCa(2) 2.455 O(3)ÐCa(2) 2.395
XÐA(2) 2.239 6 ClÐCa(2) 2.932 6 FÐCa(2) 2.229 3
Figure 3
Symmetry relationships for apatite hettotypes that are derived from the
Mn
5
Si
3
aristotype. [Adapted from Schriewer & Jeitschko (1993).]

research papers
4White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
that appears to be gaining acceptance as increasing numbers
of detailed structure solutions are presented. With respect to
the other branches, Aneas et al. (1983) and Plaisier et al. (1995)
have synthesized osmium and rhenium apatites (in which the
oxygen coordination of Bcations is raised to 5) that have
Pcmn and P6
3
cm symmetries.
2.3. Hexagonal anion nets
While many crystal structures are regarded as derivatives of
near-regular anion packing, this description has not generally
been applied to the apatites, although when taken in isolation
the anion layers subscribe recognizable, though partially
occupied, hexagonal networks. The similarity of the regular
anion layers ...b(ab)a... for idealized apatite and
...b(ab0a0b)a... for (hexagonal) chlorapatite is clear (Fig. 4).
The band b0layers are differentiated through the twisting of
alternate O
3
triangles about [001].
2.3.1. Model I ± idealized chlorapatite type. Idealized
chlorapatite is constructed by ®lling trigonal prismatic and
tetrahedral interstices in an ordered fashion, such that the
A(1) cations are located in the blayers and the A(2) and B
cations occupy the alayers. The atomic coordinates of this
derived apatite are given in Table 2, and its structure is illu-
strated in Fig. 5(a). The dominant feature is formed by the 6h
A(2) cations that occupy A(2)O
4
X
2
trigonal prism trimers that
share common edges along [001]. Filled and empty trigonal
prisms alternate along c.TheA(1) cations form continuous
isolated A(1)O
6
trigonal prism columns parallel to c(Fig. 4a)±
for clarity the three more distant O atoms that cap each of the
square faces are not indicated. These columns are linked
through the BO
4
tetrahedra, which share edges with the A(2)
trigonal prisms and corners with the A(1) trigonal prisms.
Apatite is not generally represented in this way; however, a
notable exception is the short description and associated
®gure given in Povarennykh (1972), where the Acoordination
polyhedra are emphasized and described as distorted trigonal
prisms.
The similarity of the atomic coordinates and topology of the
idealized structure and chlorapatite (P6
3
/msymmetry) is
obvious, as is the deviation from the perfect hexagonal net
(Fig. 5b). In chlorapatite, the largest departure from the ideal
position is for the A(2) cation, which is displaced from the
centre of the trigonal prism such that it moves closer to
O(1)/O(2) and increases its anion coordination from six to
eight. This modi®cation allows for the incorporation of larger
cations into the structure.
The regular trigonal prisms of the A(1) cations are
converted into metaprisms through the twisting of oxygen
triangles, as described above, to generate a polyhedron that is
intermediate between a trigonal prism and an octahedron
(O'Keeffe & Hyde, 1996). This twist angle ', which is the (001)
projection of O(1)ÐA(1)ÐO(2), is equal to 19.1(Fig. 6). The
reduced volume of the metaprism permits the accommodation
of relatively smaller cations.
2.3.2. Model II ± idealized fluorapatite type. The ideal
¯uorapatite model retains A(1)O
6
and BO
4
polyhedra iden-
tical to those of the chlorapatite model; however, because the
Xanions are displaced by z/4, the coordination sphere of A(2)
changes to octahedral A(2)O
5
X(Fig. 7a, Table 2). These
octahedra, which are corner-connected to each other and to
the A(1)O
6
trigonal prisms, are cation-centred on the banion
nets, and form groupings of three, which are joined at a
common Xatom at one of their apices. The A(2) octahedra
parallel to (001) edge-share with the BO
4
tetrahedra. This
description of apatite was put forward by Alberius-Henning,
Landa-Canovas et al. (1999), who regarded the A(2)O
5
X
octahedral arrangement as NaCl-like. For the real ¯uorapatite
structure the A(1) metaprismatic twist angle '=23.3
(Figs. 6
and 7b).
2.3.3. Model III ± idealized glaserite type. In models I and
II the A(1)O
6
trigonal prismatic coordination was retained,
Table 2
Crystal data for idealized apatite compared with crystal data for
chlorapatite and ¯uorapatite.
Idealized hexagonal net, model I
with A(2) trigonal prisms,
a9.5 A
Ê,c6.9 A
ÊChlorapatite (Hendricks et al., 1932),
a= 9.532 A
Ê,c= 6.850 A
Ê
A(1) 4f1/3 2/3 0 Ca(1) 4f1/3 2/3 0.000
A(2) 6h0.1667 0.042 1/4 Ca(2) 6h1/4 0 1/4
(1/6) (1/24)
B6h0.4231 0.3846 1/4 P 6h0.417 0.361 1/4
(11/26) (5/13)
O1 6h0.3847 0.5385 1/4 O1 6h1/3 1/2 1/4
(5/13) (7/13)
O2 6h0.6153 0.4615 1/4 O2 6h0.600 0.467 1/4
(8/13) (6/13)
O3 12i0.3077 0.2308 0 O3 12i1/3 1/4 0.064
(4/13) (3/13)
X2b000Cl2b000
Idealized hexagonal net, model II
with A(2) octahedra, a9.5 A
Ê,
c6.9 A
ÊFluorapatite (Sudarsanan et al., 1972)
a= 9.363 (2) A
Ê,c= 6.878 (2) A
Ê
A(1) 4f1/3 2/3 0 Ca(1) 4f1/3 2/3 0.0012
A(2) 6h0.1923 0.0769 1/4 Ca(2) 6h0.2413 0.0071 1/4
(5/26) (1/13)
B6h0.4231 0.3846 1/4 P 6h0.3982 0.3689 1/4
(11/26) (5/13)
O1 6h0.3847 0.5385 1/4 O1 6h0.3268 0.4850 1/4
(5/13) (7/13)
O2 6h0.6153 0.4615 1/4 O2 6h0.5881 0.4668 1/4
(8/13) (6/13)
O3 12i0.3077 0.2308 0 O3 12i0.3415 0.2569 0.0704
(4/13) (3/13)
X2b0 0 1/4 F 2a0 0 1/4
Idealized hexagonal net, model
III with A(1) octahedra,
a9.5 A
Ê,c5.4 A
Ê
A(1) 4f1/3 2/3 0
A(2) 6h0.1667 0.3333 1/4
(1/6) (1/3)
B6h0.3333 0.3333 1/4
(1/3) (1/3)
O1 6h0.3333 0.5000 1/4
(1/3) (1/2)
O2 6h0.6667 0.5000 1/4
(2/3) (1/2)
O3 12i0.1667 0.1667 0
(1/6) (1/6)
X2b000

albeit somewhat elongated along [001]. However, in real chlor-
and ¯uorapatite, the twisting converted these polyhedra to
metaprisms. The maximum possible twist angle 'is 60,in
which case A(1)O
6
coordination is octahedral (Fig. 6), if
collapse is invoked along [001] to maintain edges of equal
length, or elongated octahedral otherwise. The fractional
coordinates of the atoms in this arrangement, which can be
described as a double h.c.p. structure, are given in Table 2.
While no real structure that adopts this arrangement could be
identi®ed, layers of this type are found in the glaserite-type
Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 5
research papers
Figure 4
The anion arrangement in (a) idealized chlorapatite and (b) the real chlorapatite structure. The upper portion shows the [110] projection and emphasizes
the stacking sequence using the conventional ...b(ab)a... notation. In real chlorapatite, anion displacements lead to a doubling of the [001]
crystallographic repeat and hence to the sequence ...b(ab0a0b)a.... In the lower portion three (001) anion slices are drawn. The anion layers are
evidently not fully occupied although their derivation from a triangular network is clear.

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6White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
structure. Indeed the formal relationship between glaserite
[typi®ed by P
3K
3
Sc(PO
4
)
2
] and apatite has been discussed by
Wondratschek (1963).
3. Apatites with BO
4
tetrahedra
A compilation of 77 distinct A
5
(BO
4
)
3
Xcompounds for which
complete crystallographic data exist is presented in Table 3. It
is recognized that the occurrence of chemical analogues is
more widespread (e.g. Cockbain, 1968). However, for this
analysis single-crystal determinations or powder re®nements
are essential. Similarly, intermediate members of solid-solu-
tion series were not included, except where information for
the chemical endmembers was unavailable or complex
chemistries led to lower symmetries.
While P6
3
/mis dominant (57% of the total), apatites lower
in the hierarchical tree are not uncommon, especially P6
3
(21%) and P
3 (9%). Lower symmetries result from an
increase in chemical complexity, as a greater number of
acceptor sites (seven in P6
3
/mand 18 in P2
1
/m) are required to
accommodate the different bonding requirements of the A
and Bcations (Table 4). Note that apatites that adopt P2
1
/bdo
so because statistical occupation of the 4esite by the Xanion
(Cl
ÿ
or OH
ÿ
) is required ± the rest of the structure
maintains P6
3
/m. Therefore, monoclinic apatites such as
Ca
4.95
(PO
4
)
2.99
Cl
0.92
(Ikoma et al., 1999) are not strictly
accommodated through direct derivation from the D8
8
aris-
totype. Rather they can be considered as interpenetrating
lattices of commensurate structure (that based on D8
8
) and
(in)commensurate structure of resulting X-anion±X-vacancy
ordering.
Figure 5
Arrangement of cation-centred polyhedra in (a) model I, which
approximates the arrangement in chlorapatite, and (b) the re®ned
structure of chlorapatite. In the upper part the projection along [001] is
shown, while A(1)O
6
,A(2)O
4
X
2
and BO
4
connectivity is emphasized in
the lower clinographic projections. Note that the statistical occupancy of
chlorine is not considered in this representation.
Figure 6
Twist angles of A(1)O
6
polyhedra in (a) models I and II, (b) chlorapatite,
(c) ¯uorapatite, and (d) model III (as found in glaserite).
Figure 7
Arrangement of cation-centred polyhedra in (a) model II, which
approximates the arrangement in ¯uorapatite, and (b) the re®ned
structure of ¯uorapatite. In the upper part the projection along [001] is
shown, while A(1)O
6
,A(2)O
5
Xand BO
4
connectivity is emphasized in
the lower clinographic projections.

Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 7
research papers
Table 3
[A(1)
2
][A(2)
3
](BO
4
)
3
Xapatites.
Space group/
mineral name Composition Unit-cell parameters (A
Ê) Reference
P6
3
/m(176)
Na
6.35
Ca
3.65
(SO
4
)
6
F
1.65
a= 9.4364 (21), c= 6.9186 (16) Piotrowski, Kahlenberg &
Fischer (2002)
Na
6.39
Ca
3.61
(SO
4
)
6
Cl
1.61
a= 9.5423 (1), c= 6.8429 (1) Piotrowski, Kahlenberg &
Fischer (2002)
Carocolite (high) Na
3
Pb
2
(SO
4
)
3
Cl a= 9.810 (20), c= 7.140 (20) Schneider (1967)
Na
3
Pb
2
(BeF
4
)
3
Fa= 9.531 (3), c= 7.028 (2) Engel & Fischer (1990)
Na
2
Ca
6
Sm
2
(PO
4
)
6
F
2
a= 9.3895 (3), c= 6.8950 (4) Toumi et al. (2000)
Fluroapatite Ca
5
(PO
4
)
3
Fa= 9.363 (2), c= 6.878 (2) Sudarsanan et al. (1972)
Chlorapatite Ca
5
(PO
4
)
3
Cl a= 9.5902 (6), c= 6.7666 (2) Kim et al. (2000); Hendricks et
al. (1932)
Ca
5
(PO
4
)
3
Br a= 9.761 (1), c= 6.739 (1) Elliot et al. (1981); Kim et al.
(2000)
Ca
5
(PO
4
)
3
OH a= 9.4302 (5), c= 6.8911 (2) Kim et al. (2000; Hughes et al.
(1989)
Ca
15
(PO
4
)
9
IO² a= 9.567, c= 20.758 Alberius-Henning, Lidin &
Petrõ
Âcek (1999)
Ca
5
(CrO
4
)
3
OH a= 9.683, c= 7.010 Wilhelmi & Jonsson (1965)
Tourneaurite Ca
5
(AsO
4
)
3
Cl a= 10.076 (1), c= 6.807 (1) Wardojo & Hwu (1996)
Hedyphane Ca
2
Pb
3
(AsO
4
)
3
Cl a= 10.140 (3), c= 7.185 (4) Rouse et al. (1984)
Sr
5
(PO
4
)
3
Cl a= 9.877 (0), c= 7.189 (0) No
Ètzold et al. (1994)
Sr
5
(PO
4
)
3
Br a= 9.964 (0), c= 7.207 (0) No
Ètzold & Wulff (1998)
Sr
5
(PO
4
)
3
OH a= 9.745 (1), c= 7.265 (1) Sudarsanan & Young (1972)
(Sr
4.909
Nd
0.061
)(V
0.972
O
4
)
3
F
0.98
a= 10.0081 (1), c= 7.434 (1) Corker et al. (1995)
Sr
5
(VO
4
)
3
(Cu
0.896
O
0.95
)a= 10.126 (1), c= 7.415 (1) Carrillo-Cabrera & von
Schnering (1999)
Cd
4.92
(PO
4
)
3
Cl
0.907
a= 9.633 (4), c= 6.484 (4) Sudarsanan et al. (1977);
Wilson et al. (1977)
Cd
5
(PO
4
)
3
Cl a= 9.625 (4), c= 6.504 (2) Ivanov et al. (1976); Sudara-
sanan et al. (1973)
Cd
4.82
(PO
4
)
3
Br
1.52
a= 9.733 (1), c= 6.468 (1) Sudarsanan et al. (1977);
Wilson et al. (1977)
Cd
5
(PO
4
)
3
OH a= 9.335 (2), c= 6.664 (3) Hata et al. (1978)
Cd
4.92
(AsO
4
)
3
Br
1.52
a= 10.100 (1), c= 6.519 (1) Sudarsanan et al. (1977);
Wilson et al. (1977)
Cd
4.64
(VO
4
)
3
I
1.39
a= 10.307 (1), c= 6.496 (1) Sudarsanan et al. (1977);
Wilson et al. (1977)
Cd
4.86
(VO
4
)
3
Br
1.41
a= 10.173 (2), c= 6.532 (1) Sudarsanan et al. (1977);
Wilson et al. (1977)
Ba
5
(PO
4
)
3
Fa= 10.153 (2), c= 7.733 (1) Mathew et al. (1979)
Ba
5
(PO
4
)
3
Cl a= 10.284 (2), c= 7.651 (3) Hata et al. (1979)
Ba
5
(AsO
4
)
2
SO
4
Sa= 10.526 (5), c= 7.737 (1) Schiff-Francois et al. (1979)
Ba
5
(MnO
4
)
3
Fa= 10.3437, c= 7.8639 Dardenne et al. (1999)
Ba
5
(MnO
4
)
3
Cl a= 10.469 (1), c= 7.760 (1) Reinen et al. (1986)
Pb
5
(PO
4
)
3
Fa= 9.760 (8), c= 7.300 (8) Belokoneva et al. (1982); Kim
et al. (2000)
Pyromorphite Pb
5
(PO
4
)
3
Cl a= 9.998 (1), c= 7.344 (1), Dai & Hughes (1989); Kim et
al. (2000)
Pb
5
(PO
4
)
3
Br a= 10.0618 (3), c= 7.3592 (1) Kim et al. (2000)
Pb
5
(PO
4
)
3
OH a= 9.866 (3), c= 7.426 (2) Bruecker et al. (1995); Kim et
al. (1997, 2000); Barinova et
al. (1998)
Vanadinite Pb
5
(VO
4
)
3
Cl a= 10.317 (3), c= 7.338 (3) Dai & Hughes (1989)
Pb
9.85
(VO
4
)
6
I
1.7
a= 10.442 (5), c= 7.467 (3) Audubert et al. (1999)
Mimetite Pb
5
(AsO
4
)
3
Cl a= 10.211 (1), c= 7.418 (4) Calos & Kennard (1990)
Pb
5
(GeO
4
)(VO
4
)
2
a= 10.097 (3), c= 7.396 (2) Ivanov & Zavodnik (1989);
Ivanov (1990)
Pb
5
(SO
4
)(GeO
4
)
2
a= 10.058 (4), c= 7.416 (1) Engel & Deppisch (1988)
Pb
5
(CrO
4
)(GeO
4
)
2
a= 10.105 (3), c= 7.428 (2) Engel & Deppisch (1988)
Pb
3
(PO
4
)
2
a= 9.826 (4), c= 7.357 (3) Hata et al. (1980)
Pb
4
Na(VO
4
)
3
a= 10.059 (1), c= 7.330 (1) Sirotinkin et al. (1989)
Pb
8
K
2
(PO
4
)
6
a= 9.827 (1), c= 7.304 (1) Mathew et al. (1980)
Mn
5
(PO
4
)
3
Cl
0.9
(OH)
0.1
a= 9.532 (1), c= 6.199 (1) Engel et al. (1975)
Nd
4
Mn(SiO
4
)
3
Oa= 9.499 (1), c= 6.944 (2) Kluever & Mueller-Busch-
baum (1995)
NaY
9
(SiO
4
)
6
O
2
a= 9.332 (2), c= 6.759 (1) Gunawardane et al. (1982)
La
9
Na(GeO
4
)
6
O
2
a= 9.883 (2), c= 7.267 (3) Takahashi et al. (1998)
La
10
(Si
3.96
B
1.98
O
4
)
6
O
2
a= 9.5587 (2), c= 7.2171 (2) Mazza et al. (2000)
La
3
Nd
11
(SiO
4
)
9
O
3
²a= 9.638 (2), c= 21.350 (8) Malinovskii et al. (1990)
Britholite (Ce
0.4
Ca
0.35
Sr
0.25
)
2
(Ce
0.86
Ca
0.14
)
3
(SiO
4
)
3
(O
0.5
F
0.38
)a= 9.638 (1), c= 7.081 (1) Genkina et al. (1991)

research papers
8White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
3.1. A(1) metaprism twist angle
The metaprism twist angle 'is, not surprisingly, sensitive to
apatite composition ± the smallest ('= 5.2) is found for
Ca
2
Pb
3
(AsO
4
)
3
Cl, while the largest ('= 26.7) has been
observed for Pb
5
(PO
4
)
3
OH (Fig. 8). For P6
3
/mapatites 'can
be calculated for any individual metaprism from the fractional
coordinates of A(1), O(1) and O(2) via the general expression
Table 3 (continued)
Space group/
mineral name Composition Unit-cell parameters (A
Ê) Reference
P6
3
(173)
K
3
Sn
2
(SO
4
)
3
Cl a= 10.230 (20), c= 7.560 (20) Howie et al. (1973); Donaldson
& Grimes (1984)
K
3
Sn
2
(SO
4
)
3
Br a= 10.280 (20), c= 7.570 (20) Howie et al. (1973); Donaldson
& Grimes (1984)
KNd
9
(SiO
4
)
6
O
2
a= 9.576 (2), c= 7.009 (2) Pushcharovskii et al. (1978)
Ca
10
(PO
4
)
6
Sa= 9.455 (0), c= 8.840 (0) Sutich et al. (1986)
Ca
4
Bi(VO
4
)
3
Oa= 9.819 (2), c= 7.033 (2) Huang & Sleight (1993)
Sr
7.3
Ca
2.7
(PO
4
)
6
F
2
a= 9.865 (8), c= 7.115 (3) Pushcharovskii et al. (1987);
Klevtsova (1964)
Sr
5
(CrO
4
)
3
Cl a= 10.125, c= 7.328 Mueller-Buschbaum & Sander
(1978)
Cd
5
(PO
4
)
3
OH² a= 16.199 (0), c= 6.648 (0) Hata & Marumo (1983)
Ba
5
(PO
4
)
3
OH a= 10.190 (1), c= 7.721 (2) Bondareva & Malinovskii
(1986)
Ba
5
(CrO
4
)
3
OH a= 10.428, c= 7.890 Mattausch & Mueller-Busch-
baum (1973)
Ba
5
[(Ge,C)(O,OH)
4
)]
3
[(CO
3
(OH)]
1.5
(OH) a= 10.207 (3), c= 7.734 (2) Malinovskii et al. (1975)
La
6
Ca
3.5
(SiO
4
)
6
(H
2
O)F a= 9.664 (3), c= 7.090 (1) Kalsbeek et al. (1990)
Na
0.97
Ca
1.40
La
2.20
Ce
3.69
Pr
0.32
Nd
0.80
[(Si
5.69
P
0.31
)
4
]
6
(OH,F) a= 9.664 (3), c= 7.090 (1) Kalsbeek et al. (1990)
Sm
10
(SiO
4
)
6
N
2
a= 9.517 (6), c= 6.981 (4) Gaude et al. (1975)
(Sm
8
Cr
2
)(SiO
4
)
6
N
2
a= 9.469 (5), c= 6.890 (4) Maunaye et al. (1976)
P
3 (147)
Ca
9.93
(P
5.84
B
0.16
O
4
)
6
(B
0.67
O
1.79
)a= 9.456 (1), c= 6.905 (1) Ito et al. (1988)
Sr
9.402
Na
0.209
(PO
4
)
6
B
0.996
a= 9.734 (4), c= 7.279 (2) Calvo et al. (1982)
Ba
4
Nd
3
Na
3
(PO
4
)
6
F
2
a= 9.786 (2), c= 7.281 (1) Mathew et al. (1979)
Belovite Na
0.5
Ca
0.3
Ce
1.00
Sr
2.95
(PO
4
)
3
OH a= 9.692 (3), c= 7.201 (1) Nadezhina et al. (1987)
Na
0.981
La
0.999
Sr
2.754
Ba
0.12
Ca
0.06
(PO
4
)
3
OH a= 9.664 (0), c= 7.182 (0) Kabalov et al. (1997)
Na
2
Ca
2
Sr
6
(PO
4
)
6
(OH)
2
a= 9.620, c= 7.120 Klevtsova & Borisov (1964)
P
6 (174)
Cesanite Na
6.9
Ca
3.1
(SO
4
)
6
OH
1.1
a= 9.4434 (13), c= 6.8855 (14) Piotrowski et al. (2002)
Ca
10
(PO
4
)
6
Oa= 9.432, c= 6.881 Alberius-Henning, Landa-
Canovas et al. (1999)
Ba
3
LaNa(PO
4
)
3
Fa= 9.939 (0), c= 7.442 (1) Mathew et al. (1979)
P2
1
/m(11)
Hydroxyellestad-
tite
Ca
10
(SiO
4
)
3
(SO
4
)
3
[F
0.16
Cl
0.48
(OH)
1.36
]a= 9.476 (2), b= 9.508 (2),
c= 6.919 (1), = 119.5
o
Sudarsanan (1980); Hughes &
Drexler (1991)
Fermorite (Ca
8.40
Sr
1.61
)(AsO
4
)
2.58
(PO
4
)
3.42
F
0.69
(OH)
1.31
a= 9.594 (2), b= 9.597 (2),
c= 6.975 (2), = 120.0 (0)
Hughes & Drexler (1991)
Carocolite (low) Na
3
Pb
2
(SO
4
)
3
Cl² a= 19.620, b= 9.810, c= 7.140,
= 120
Schneider (1969)
P2
1
/b(14)
Ca
5
(PO
4
)
3
OH a= 9.421 (1), b= 18.843 (2),
c= 6.881 (1), = 120.0 (1)
Elliot et al. (1973)
Ca
4.95
(PO
4
)
2.99
Cl
0.92
a= 9.426 (3), b= 18.856 (5),
c= 6.887 (1), = 119.97 (1)
Ikoma et al. (1999)
Ca
9.97
(PO
4
)
3
Cl
1.94
²a= 9.632 (7), b= 19.226 (20),
c= 6.776 (5), = 119.9 (1)
Bauer & Klee (1993); Mackie
et al. (1972)
Clinomimetite Pb
5
(AsO
4
)
3
Cl² a= 10.189 (3), b= 20.372 (6),
c= 7.456 (6), = 119.0 (0)
Dai et al. (1991)
P2
1
(4)
Ellestadite (low) Ca
10
(Si
3.14
S
2.94
C
0.08
P
0.02
)O
24
[(O H)
1.12
Cl
0.316
F
0.05
]a= 9.526 (2), b= 9.506 (4),
c= 6.922 (1), = 120.0 (0)
Organova et al. (1994)
Britholite (Na
1.46
La
8.55
)(SiO
4
)
6
(F
0.9
O
0.11
)a= 9.678 (1), b= 9.682 (3),
c= 7.1363 (1), = 120.0 (0)
Hughes et al. (1992)
Britholite (Ce) (Ca
2.15
Ce
2.85
)(SiO
4
)
3
[F
0.5
(OH)
0.5
]a= 9.580 (5), b= 9.590 (4),
c= 6.980 (3), = 120.1 (0)
Noe et al. (1993)
² Superstructure.

cos 'G3ÿG12H3ÿH12G1ÿG22

H1ÿH22ÿG2ÿG32ÿH2ÿH32
=2G3ÿG12H3ÿH12

G1ÿG22H1ÿH22

1=2;
where
G10:866xA1;H1yA1ÿ0:5xA1;
G20:866xO1;H2yO1 ÿ0:5xO1 ;
G30:866xO2;H3yO2 ÿ0:5xO2 :
When 'is calculated for a range of apatites, it is observed to
vary inversely with average crystal radii and unit-cell volume
(Table 5). In fact, for those P6
3
/mapatites with the same A
cation (e.g. calcium or cadmium), the relationship is very
nearly linear (Fig. 9), regardless of whether substitution is
made on the Bor Xsites. In other words, for apatites with
smaller average crystal radii, the structure must collapse
further to satisfy shorter bond-length requirements, and this
fact is re¯ected in larger 'values, which lead to shorter A(1)Ð
O distances. If A(1)O
6
twisting is considered to be the pivotal
structural feature, then the collapse towards octahedral
bonding will also accommodate the shortening of the cell
edges and a general reduction of A(2)ÐOÐXbond lengths.
[A detailed consideration of the geometry of metaprism
twisting is given in Dong & White (2003).] In contrast the BO
4
tetrahedra will essentially remain invariant. Therefore, the
metaprism twist angle 'is a useful qualitative ± and in some
cases quantitative ± predictor of apatite distortion from ideal
h.c.p. packing. Indeed, for all the apatites in Table 5 only two
compositions were exceptional. Ba
5
(MnO
4
)
3
Cl (Reinen et al.,
1986) and Pb
5
(PO
4
)
3
OH (Bruecker et al., 1995) have 'values
of 22.3and 26.7, respectively. These appear anomalously
high compared with the average crystal radii and bond angle
(Table 5). Possible explanations may be the adoption of lower
symmetry, the distortion of the MnO
4
tetrahedra or A-site
non-stoichiometry for the Pb compound.
3.2. X-site non-stoichiometry
It has long been understood that larger Xanions (Cl, Br, I)
may be displaced away from their 2aand 2bspecial positions,
especially if the A(2) sites are occupied by smaller cations, and
that a portion of the sites may be vacant. Substantial quanti-
tative treatments of the phenomena have been undertaken by
several workers (e.g. Kim et al., 2000; Hashimoto & Matsu-
moto, 1998; Hata et al., 1979; Mackie et al., 1972). While the
location of the anions over available sites is generally assumed
to be statistical, it has now been demonstrated that cadmium
phosphate bromate and cadmium vanadate iodate exhibit
incommensurate ordering of Xanions and vacancies (Christy
et al., 2001). For lead-rich apatites the Xsite may be
completely vacant, as in Pb
3
(PO
4
)
2
,Pb
4
Na(VO
4
)
3
and
Pb
8
K
2
(PO
4
)
6
. It is reasonable to assume that the stereo-
chemically active lone pair of Pb
2+
, which occupies a volume
close to that of oxygen, allows such compounds to be stable
(Mathew et al., 1980). Stoichiometrically similar non-lead-
bearing compounds [e.g. Cd
5
(PO
4
)
2
GeO
4
], which do not have
the bene®t of lone-pair stabilization, adopt the carnotite
Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 9
research papers
Table 4
Atom acceptor sites in apatites that adopt different space groups.
Space group
P6
3
/m(176) P6
3
(173) P
3 (147) P
6 (174) P2
1
/m(11)
Site types
Wyckoff
number
Number of
site types
Wyckoff
number
Number of
site types
Wyckoff
number
Number of
site types
Wyckoff
number
Number of
site types
Wyckoff
number
Number of
site types
Large Acations 6h16c16g13k,3j22a,2e23
Small Acation 4f12b22 2d22 2i,2h24f1
Bcations 6h16c16g13k,3j22e33
Total number
of cation
acceptor sites
34 4 6 7
Oxygen anions 6h2, 12i36c44 6g44 3k2,
3j2,
6l2
62e6,
4f3
9
Xanions 2aor 2b
or 4e
12a11a,1b21a,1bor 2g1/2 2aor 2e2
Total number
of anion
acceptor sites
4 5 6 7/8 11
Examples of
cation
occupancy
[Ca
6
][Ca
4
][P
6
][K
6
][K
2
Sn
2
][S
6
] [Ba
4
Nd
1
Na
1
][Nd
2
Na
2
][P
6
] [Ba
5
La
1
][La
1
Na
1.3
Ba
1.7
][P
6
] [Ca
6
][Ca
4
][Si
3
S
3
]
[A
6
][A
4
][B
6
]-
[O
24
][X
2
]
Ca
10
(PO
4
)
6
F
2
K
6
Sn
4
(SO
4
)
6
Cl
2
Ba
4
Nd
3
Na
3
(PO
4
)
6
F
2
Ba
6.7
La
2
Na
1.3
(PO
4
)
6
F
2
Ca
10
(SiO
4
)
3
(SO
4
)
3
[F
0.16
Cl
0.48
(OH)
1.36
]

research papers
10 White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
structure type (Engel & Fischer, 1985). It is possible that
trivalent bismuth-rich apatites may also exploit the space-
®lling properties of the lone pairs (Huang & Sleight, 1993;
Buvaneswari & Varadaraju, 2000); however, this is yet to be
demonstrated. The calculations of Le Bellac et al. (1995) have
proved useful in locating electron lone pairs in complex
oxides, such as Pb
3
P
2
O
8
and Bi
2
Sr
2
CaCu
2
O
8
, and, if applied to
plumbous apatites, would underpin a quantitative discussion
on this point.
It has been demonstrated that metals may also be incor-
porated into the 2a/2bsites. Carillo-Cabrera & von Schnering
(1999) successfully synthesized Sr
5
(VO
4
)
3
(Cu
0.896
O
0.95
), in
which (CuÐO) strings ®lled the Xpositions. While presently
the only example of this type, it is not inconceivable that other
linearly bonded cation±oxygen strings (e.g. Pd
1+
ÐO, Ag
1+
ÐO,
Hg
2+
ÐO) might also be prepared, provided larger A
(e.g. Ba
2+
) and B(e.g. Mn
5+
) ions are available to suf®ciently
dilate the unit cell.
3.3. Polysomatism
All [A(1)
2
][A(2)
3
](BO
4
)
3
Xapatites of whatever symmetry
regularly ®ll every other BO
4
tetrahedral interstice in corner-
connected strings along [001] (Fig. 10). Alternative ®lling
schemes are of course possible, such that the same overall
occupancy is maintained while producing crystallographically
distinct polysomates. Alternate ®lling has been observed in
two minerals ± nasonite and ganomalite (Engel, 1972).
Nasonite, which has the ideal formula Pb
6
Ca
4
(Si
2
O
7
)
3
Cl
2
, was
determined by Giuseppetti et al. (1971) to have P6
3
/m
symmetry with consecutive sites ®lled as Si
2
O
7
units. Bre
Áset al.
(1987) used high-resolution electron microscopy to demon-
strate that the situation is more complex, as on the unit-cell
scale P6
3
/msymmetry is broken. For the intermediate mineral
ganomalite (Carlson et al., 1997) Si
2
O
7
units alternate with
SiO
4
tetrahedra to give an ideal formula Pb
6
Ca
3.33
Mn
0.67
-
(SiO
4
)
2
(Si
2
O
7
)
2
and a structure that conforms to P
6 symmetry.
In this compound Pb cations (IR 1.29 A
Ê) are distributed into
the larger 6l,3ksites as expected; the Ca (1.12 A
Ê) occupy the
2i,2h,1cmetaprisms in an ordered way with a height along
(001) of 3.5 A
Ê, while Ca/Mn (average IR 1.04 A
Ê)on1e®ll an
untwisted prism of height 3.07 A
Ê(Fig. 11). Intergrowth
between apatite layers that have different heights and twist
angles is yet another mechanism for accommodating cations of
substantially different ionic radii. A more rigorous determi-
nation of natural nasonite will probably reveal similar detail.
In addition, the synthetic analogue of ganomalite
Pb
5
(GeO
4
)(Ge
2
O
7
) has been studied extensively because of
its ferroelectric properties (Newnham et al., 1973; Iwata,
1977). Stemmermann (1992) synthesized the longer-period
Pb
40
(Si
2
O
7
)
6
(Si
4
O
13
)
3
with c= 28.7 A
Ê. All the members so far
reported for the apatite±nasonite family are lead-rich with the
role of lone-pair stabilization yet to be fully investigated. Note
Table 5
Twist angle ('), average crystal radius per unit-cell content and unit-cell
volume.
Composition
Metaprism angle
()
Average crystal
radius (A
Ê)² Volume (A
Ê
3
)
Ca
10
(PO
4
)
6
F
2
23.3 1.143 522.6
Ca
10
(PO
4
)
6
OH
2
23.2 1.146 530.3
Ca
10
(PO
4
)
6
Cl
2
19.1 1.166 537.6
Ca
10
(CrO
4
)
6
OH
2
17.8 1.171 569.2
Ca
10
(PO
4
)
6
Br
2
16.3 1.173 556.1
Ca
10
(AsO
4
)
6
Cl
2
13.0 1.189 598.5
Ca
4
Pb
6
(AsO
4
)
6
Cl
2
5.2 1.214 639.8
Cd
10
(PO
4
)
6
OH
2
25.8 1.139 502.9
Cd
10
(PO
4
)
6
Cl
2
19.5 1.158 521.1
Cd
10
(PO
4
)
6
Br
2
16.0 1.165 530.6
Cd
10
(AsO
4
)
6
Br
2
11.6 1.189 575.9
Cd
10
(VO
4
)
6
Br
2
8.8 1.192 585.4
Cd
10
(VO
4
)
6
I
2
8.4 1.203 597.6
Sr
10
(PO
4
)
6
OH
2
23.0 1.183 597.5
Sr
10
(PO
4
)
6
Cl
2
21.1 1.203 606.6
Sr
10
(PO
4
)
6
Br
2
19.6 1.210 619.7
Pb
10
(PO
4
)
6
F
2
23.5 1.185 602.2
Pb
10
(PO
4
)
6
OH
2
26.7 1.189 603.2
Pb
10
(PO
4
)
6
Cl
2
17.6 1.208 635.8
Pb
10
(VO
4
)
6
Cl
2
17.5 1.235 676.5
Pb
10
(VO
4
)
6
I
2
16.7 1.253 702.4
Ba
10
(PO
4
)
6
F
2
22.5 1.219 690.3
Ba
10
(PO
4
)
6
Cl
2
21.0 1.242 700.8
Ba
10
(MnO
4
)
6
Cl
2
22.3 1.254 736.6
Ba
10
(AsO
4
)
4
(SO
4
)
2
S 16.2 1.259 742.4
² Calculated using effective ionic radii of Shannon (1976).
Figure 8
The preferred topological representation of four apatites; both the A(1)O
6
trigonal prisms/metaprisms and the BO
4
tetrahedra are emphasized. The
idealized structural endmembers are emphasized in (a) model I with '=0
and (d) model III with '=60
. The intermediate structures shown are for (b)
hedyphane Ca
4
Pb
6
(AsO
4
)
6
Cl
2
with '= 5.2and (c)Pb
10
(PO
4
)
6
(OH)
2
with '= 26.7.

that stoichiometric adjustments are required in order to
generate these tetrahedrally ordered apatite superstructures,
and therefore these compounds are described as part of a
polysomatic, rather than polytypic, series (Table 6).
4. Apatites with BO
5
and BO
3
polyhedra
The description of apatite as an anion-stuffed alloy proves
especially compelling when the scope of the apatite family is
broadened to include the less common [A(1)
2
][A(2)
3
](BO
5
)
3
X
and [A(1)
2
][A(2)
3
](BO
3
)
3
Xcompounds (Table 7). In these
cases a greater or lesser number of M
4
,M
3
and M
2
metal
interstices are ®lled with oxygen while the distinctive metal
arrangement of the D8
8
aristotype is maintained.
Finnemanite Pb
5
(AsO
3
)
4
Cl (Effenberger & Pertlik, 1977) is
a reduced form of mimetite Pb
5
(AsO
4
)
4
Cl (Dai et al., 1991).
Both compounds adopt P6
3
/msymmetry with the former
missing one 6hoxygen to compensate for the substitution of
As
5+
$As
3+
. In ®nnemanite the BO
4
tetrahedron is
completely replaced by BO
3
with the arsenic lying above
the triangular oxygen plane (Fig. 12a). To date, this is the
only reported example of a completely ordered
[A(1)
2
][A(2)
3
](BO
3
)
3
Xapatite. However, partial substitutions
of BO
3
for BO
4
are known. In biologically important carbo-
nated hydroxyapatite, recent studies con®rm that partial
replacement of PO
43ÿ
$CO
33ÿ
, which is similar to
AsO
43ÿ
$AsO
33ÿ
, occur. However, ordering is incomplete,
as either of the two possible O
3
triangular faces that lie
parallel to [001] of the BO
4
tetrahedron can be used to
accommodate the carbonate unit (Ivanova et al., 2001). It
must also be feasible to introduce boron in a similar way.
Ito et al. (1988) have reported the existence of
[Ca
9.93
(P
5.84
B
0.16
)
4
]
6
(B
0.067
O
1.79
); however, whether a prefer-
ence is shown by BO
3
to occupy particular face(s) of the O
4
tetrahedron has not been resolved.
A number of ruthenates and osmates have been described
(Schriewer & Jeitschko, 1993) whose structures are also
derived from the D8
8
alloy (O'Keeffe & Hyde, 1985). In this
case, four of the ®ve O atoms of the BO
5
square pyramid are in
OM
4
tetrahedra, while the last is in linear OM
2
coordination
(Fig. 12c). In [A(1)
2
][A(2)
3
](BO
5
)
3
Xcompounds the BO
5
pyramids have a `sense of direction' in that their apical O
atoms can lie up or down along [001], and indeed examples of
both types have been discovered (Schriewer & Jeitschko, 1993;
Plaisier et al., 1995). In Ba
5
(ReO
5
)
4
Cl, with P6
3
cm symmetry,
all of the ReO
5
pyramids' apices are unidirectional, whereas in
Pnma Sr
5
(ReO
5
)
4
Cl one-third of the ReO
5
strings adopt
antiparallel orientations (Fig. 13).
Finally, an interesting example of an apatite-related struc-
ture is Sr
5
(BO
3
)
3
Br (Alekel & Keszler, 1992). It can be
regarded as a condensed apatite phase, even though the
stoichiometry is outwardly similar to that of ®nnemanite.
2
In
all other structures that we discuss, the AO
6
metaprisms are
connected exclusively through BO
3
/BO
4
/BO
5
polyhedra,
whereas in Sr
5
(BO
3
)
3
Br some SrO
6
prism columns share an
edge with their neighbour ± a comparison of Figs. 7(a) and 14
makes the relationship clear. Following the proposition of
Moore & Araki (1977) it is possible to isolate Sr
4
(BO
3
)
12
as
the stable unit of this structure. This unit is analogous to
Ca
4
(PO
4
)
12
columns, which through rotational operations can
generate signi®cant segments of the structures of hydro-
xyapatite, octacalcium phosphate and samuelsonite. However,
Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 11
research papers
Figure 10
Tetrahedral strings and c-axis repetition in (a) apatite, c
ap
,(b) ganomalite,
1.33c
ap
, and (c) nasonite, 2c
ap
.
Figure 9
Relationship between twist angle (') and average crystal radius for
several [A(1)
2
][A(2)
3
](BO
4
)
3
X,P6
3
/m, apatites in which the Acation is
®xed and only Band Xvary. For the Ca- and Cd-apatites there is very
nearly a linear relationship. This also holds true for Sr-apatites although
only three examples were included. While the general trend is also true
for the Pb-apatites, the relationship is not so direct.
2
Compositionally similar Mg
5
(BO
3
)
3
F is unrelated to ®nnemanite and is a
leucophoenicite-type mineral (White & Hyde, 1983).

research papers
12 White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
as yet the range of available compounds is insuf®cient to test
this hypothesis.
5. Discussion and conclusions
In summarizing the crystallographic data for the
materials [A(1)
2
][A(2)
3
](BO
4
)
3
X,[A(1)
2
][A(2)
3
](BO
5
)
3
Xand
[A(1)
2
][A(2)
3
](BO
3
)
3
X, their description as `apatite' or
`apatite-related' can be replaced by a formal description as
anion-stuffed hettotypes of the D8
8
aristotype. From this
perspective, all are members of the apatite structural family, in
the same way that even rather complex perovskites (such as
giant magnetoresistance CaCu
3
Mn
4
O
12
and superconducting
YBa
2
Cu
3
O
7-
) possess similar genealogy. This proposition has
been most fully articulated by O'Keeffe & Hyde (1985) but
has also been recognized by Wondratschek et al. (1964) and
more recently Schriewer & Jeitschko (1993) and Vegas &
Jansen (2002). When formalized, this approach leads to a
hierarchical tree of possible symmetries, which is increasingly
pertinent as the structures of more apatites become available.
While P6
3
/mis the most common symmetry of
[A(1)
2
][A(2)
3
](BO
4
)
3
Xapatites, it is by no means dominant.
With increasing chemical complexity, the lower symmetries
P6
3
,P
3, P
6, P2
1
/mand P2
1
are required in order to accom-
modate cation ordering, and it may be expected that addi-
tional lower-symmetry varieties will be recognized. Huang &
Sleight (1993) have noted that many P6
3
/mapatites may
actually have lower symmetry, and this prescience is borne out
by high-precision redeterminations. The most recent of these
is the reinvestigation of cesanite Na
6.9
Ca
3.1
(SO
4
)
6
(OH)
1.1
by
Piotrowski, Kahlenberg, Fischer et al. (2002), who through the
careful analysis of systematic absences were able to allocate
P
6 as the correct symmetry.
The middle branch of the structural tree, the branch that
leads from P6
3
/m, is evidentially the most heavily populated,
with only a few representatives reported for the Cmcm and
Table 6
Polysomatic apatites.
Mineral name Space group Composition Unit-cell parameters (A
Ê) Reference
P
6Pb
5
(GeO
4
)(Ge
2
O
7
)a= 10.260, c= 10.696 Iwata (1977)
Ganomalite P
6Pb
9
Ca
5
Mn(Si
2
O
7
)
3
(SiO
4
)
3
a= 9.850 (50), c= 10.130 (50) Carlson et al. (1997)
P
6Pb
9
Ca
6
(Si
2
O
7
)
3
(SiO
4
)
3
a= 9.875, c= 10.176 Stemmermann (1992)
P
6Pb
12
Ca
3
(Si
2
O
7
)
3
(SiO
4
)
3
a= 9.880, c= 10.210 Stemmermann (1992)
P
6 (?) Pb
3
Ca
2
(Si
2
O
7
)(SiO
4
)a= 9.879 (1), c= 10.178 (1) Engel (1972)
P
6 (?) Pb
3
BiNa(Si
2
O
7
)(SiO
4
)a= 9.876 (1), c= 10.175 (1) Engel (1972)
P
6 (?) Pb
3
Cd
2
(Si
2
O
7
)(SiO
4
)a= 9.810 (4), c= 10.124 (4) Engel (1972)
P-6 (?) Pb
3
Ca
2
(Ge
2
O
7
)(GeO
4
)a= 10.104 (1), c= 10.379 (1) Engel (1972)
P
6 (?) Pb
3
BiNa(Ge
2
O
7
)(GeO
4
)a= 10.084 (1), c= 10.398 (1) Engel (1972)
P
6Pb
6
Ca
4
(Si
2
O
7
)
3
Cl
2
a= 10.074, c= 13.234 Stemmermann (1992)
Nasonite P
6 (?) Pb
9
Ca
4
(Si
2
O
7
)
3
a= 10.080, c= 13.270 Giuseppetti et al. (1971)
Monoclinic (?) Pb
40
(Si
2
O
7
)
6
(Si
4
O
13
)
3
a= 17.075, b= 9.844, c= 26.678, = 90.09Stemmermann (1992)
Figure 11
The three apatite layers in ganomalite Pb
6
Ca
3.33
Mn
0.67
(SiO
4
)
2
(Si
2
O
7
)
2
. The ®gure demonstrates the intergrowth of layers with different twist angles (').
Layers 1 and 3 contain trigonal prisms whose triangular faces are of different size and '= 17.2. Layer 2, which contains the Mn atom, has '=0
. In the
upper portion of the drawing the connectivity of the SiO
4
tetrahedra are emphasized; the Si
2
O
7
unit occurs in the middle layer.

P6
3
cm branches. However, for the latter, the chemistries
studied remain sparse, and it is possible that new repre-
sentatives with stoichiometry [A(1)
2
][A(2)
3
](BO
5
)
3
Xwill be
discovered.
The derivation of apatites from a regular oxygen sublattice
also proves valuable, as it includes the BO
4
tetrahedra that are
the common recognizable units shown in most structure
drawings. These ideas, ®rst used by Povarennykh (1972) and
developed by Alberius-Henning, Landa-Canovas et al. (1999),
have been extended in this paper to include the A(1)O
6
trigonal metaprisms as a key structural unit, along with the
BO
4
tetrahedra, in order to portray apatite chemical series.
This depiction provides a highly visual and quantitative
measure of apatite distortion from a perfect hexagonal anion
net. For apatites that contain one species of Acation, the
metaprismatic twist angle 'varies linearly over a wide range
of compositions and changes inversely with atomic radius. The
analysis of 'can be used to rapidly detect structures that fall
outside expected bounds or deviate from compositional
trends. Naturally, 'is not in itself suf®cient to dismiss a
structure solution as de®cient; however, 'can indicate
possible misinterpretation, particularly with respect to
symmetry. For apatites that contain mixed and ordered A(1)
cations, the interpretation becomes more complex, as the
height of the metaprism (along [001]) is also in¯uenced by the
requirement to satisfy AÐO bond lengths. In work to be
published for (Ca
10ÿx
Pb
x
)(VO
4
)
6
(O,F)
2ÿ
,0<x< 9, apatites
(Dong & White, 2003), 'has been used as a sensitive probe to
detect disequilibrium. Furthermore, microdomains observed
directly by HRTEM were only removed after 'stabilized.
Acta Cryst. (2003). B59, 1±16 White and ZhiLi Apatites 13
research papers
Figure 12
The structures of (a) ®nnemanite Pb
5
(AsO
3
)
4
Cl, (b) mimetite Pb
5
(AsO
4
)
4
Cl and (c)Ba
5
(ReO
5
)
4
Cl. The ®gures show the progressive insertion of oxygen,
the conversion of AsO
3
to AsO
4
and the ReO
5
coordination. In ®nnemanite the Pb(1) ions are drawn as they occupy half-trigonal prisms (with three
capping O atoms at a greater distance). Stereochemically active lone-pairs probably play a key role in stabilizing this structure.
Table 7
[A(1)
2
][A(2)
3
](BO
5
)
3
Xand [A(1)
2
][A(2)
3
](BO
3
)
3
Xapatites.
Mineral name Space group Composition Unit-cell parameters (A
Ê) Reference
Finnemanite P6
3
/mPb
5
(AsO
3
)
3
Cl a= 10.322 (7), c= 7.054 (6) Effenberger & Pertlik (1977)
C222
1
Sr
5
(BO
3
)
3
Br a= 10.002 (2), b= 14.197 (2), c= 7.458 (1) Alekel & Keszler (1992)
P6
3
cm Ba
5
(ReO
5
)
3
NO
4
a= 11.054 (5), c= 7.718 (4) Aneas et al. (1983)
P6
3
cm Ba
5
(ReO
5
)
3
Cl a= 10.926 (1), c= 7.782 (1) Schriewer & Jeitschko (1993); Besse et al. (1979)
P6
3
cm Ba
5
(OsO
5
)
3
Cl a= 10.928 (2), c= 7.824 (5) Plaisier et al. (1995)
Pnma Sr
5
(ReO
5
)
3
Cl a= 7.438 (1), b= 18.434 (2), c= 10.563 (2) Schriewer & Jeitschko (1993)
Figure 13
The arrangement of ReO
5
square pyramids in (a)Sr
5
(ReO
5
)
4
Cl, where
the directionality is antiparallel between some SrO
6
metaprisms, and (b)
Ba
5
(ReO
5
)
4
Cl, where the arrangement is always parallel, i.e. with the
apical oxygen always pointing the same way.

research papers
14 White and ZhiLi Apatites Acta Cryst. (2003). B59, 1±16
The structural relationship between apatite and nasonite is
well established (Engel, 1972), and members of this polyso-
matic series are possibly more prevalent than is currently
recognized. Ganomalite Pb
6
Ca
3.33
Mn
0.67
(SiO
4
)
2
(Si
2
O
7
)
2
(Carlson et al., 1997) and Pb
40
(Si
2
O
7
)
6
(Si
4
O
13
)
3
(Stemmer-
mann, 1992) have been identi®ed as intermediate members of
this homologous series. However, the structural principle of
ordered ®lling of tetrahedral sites can give rise to an inde®nite
number of structures. It is less clear whether lead is a critical
component of these structures but all current examples are
substantially plumbous. At the atomic level, these structures
may be quite complex. In the one instance where single-crystal
X-ray diffraction and HRTEM have been undertaken, Bre
Áset
al. (1987) observed on the same sample a clear discrepancy in
crystallographic features, the diffraction results being consis-
tent with well ordered P6
3
/m, while direct imaging showed
microdomains of lower symmetry.
The rich chemistry and structural diversity of apatites
provides fertile ground for the synthesis of technology-rele-
vant compounds. Novel materials will continue to be discov-
ered and possibly exploited in such diverse applications
as zinc-rich bioactive apatites that accelerate tissue
regrowth, mercury-bearing compounds analogous to
Sr
5
(VO
4
)
3
(Cu
0.896
O
0.95
) for polishing industrial wastewaters
and catalytic apatites for photovoltaic devices.
This work was supported through A*STAR Grant 012 105
0123. The manuscript bene®ted through the constructive
comments of the referees.
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Figure 14
Sr
5
(BO
3
)
3
Br projected on (001). The apatite-like elements are obvious but are condensed such
that some SrO
6
trigonal prisms share edges rather than being connected through BO
3
triangles.

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