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Synthesis and distribution of cations in substituted lead
phosphate lacunar apatites
Besma Hamdi a,b,c, Hafed El Feki a, Jean-Michel Savariault b,c,*,Abdelhamid Ben Salah a
a Laboratoire de Sciences des Materiaux et d’Environnement, Faculte des Sciences de SFAX,
BP 802, 3018 SFAX, Tunisiab Centre d’Elaboration de Materiaux et d’Etudes Structurales, 29 rue J. Marvig,
BP 4347, 31055 Toulouse Cedex 4, Francec Universite Paul SABATIER, 118 Route de Narbonne, 31400 Toulouse, France
Received 13 September 2005; received in revised form 24 May 2006; accepted 30 May 2006
Available online 11 July 2006
Abstract
Synthesis of apatites, Pb7.4Bi0.3Na2.3(PO4)6 (I), Pb7.36Bi0.32Na2.08Li0.24(PO4)6 (II) and Pb5.78Bi0.81Ca0.60Na2.81(PO4)6 (III), with
anion vacancy were carried out during solid state reactions. The three compounds of apatite-type structure crystallize in the
hexagonal system, space group P63/m. In every compound, a preferential occupation of the (6h) site by Pb and Bi cations is shown
revealing the influence of their lone electronic pair. The introduction of calcium increases the quantity of bismuth in these apatites.
Alkaline metals occupy mainly the (4f) site. Infrared spectroscopy is correlated to the bonding scheme. A connection between the
cations occupying (4f) sites and the c cell parameters is presented.
# 2006 Elsevier Ltd. All rights reserved.
Keywords: A. Inorganic compounds; B. Chemical synthesis; C. X-ray diffraction; C. Infrared spectroscopy; D. Crystal structure; D. Defects
1. Introduction
Apatites form a large family of isomorphous compounds with the general chemical formula M10(YO4)6X2, where
M generally is a divalent cation of alkaline earth group, but also a mono or a trivalent cation, Y represents P, As, Si, S,
V, etc. and X: halogen, O, S or groups like OH, CO3, etc. [1–4]. The apatite structure-type has been known since 1930
when Naray-Szabo determined the structure of Ca10(PO4)6F2 [5]. It generally crystallizes in the hexagonal system with
space group P63/m [6,7]. The apatite structure is described as follows. The YO4 tetrahedrons are arranged around the
63 screw axes forming columns around the crystallographic c axis with X ions on the axis. In 1 cell, the 10 cations are
distributed on 2 sites. Six of them fill the (6h) sites making equilateral triangles. Their coordination number is 7, six O
and one X. The remaining four cations occupy the (4f) sites. They are coordinated to nine O building trigonal tricapped
prisms stacked in columns in the [0 0 1] direction. A diffusion of anionic species (X�) is observed along the column
axis [8].
www.elsevier.com/locate/matresbu
Materials Research Bulletin 42 (2007) 299–311
* Corresponding author. Tel.: +33 5 62 25 78 47; fax: +33 5 62 25 79 99.
E-mail address: [email protected] (J.-M. Savariault).
0025-5408/$ – see front matter # 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.materresbull.2006.05.027
Apatites with lack of X anion, like Pb4M(PO4)3, have already been obtained [9–11]. Studies have shown that, in the
majority of the cases, the M alkaline ions are mainly localized in the column positions (4f) sites, while the triangular
(6h) sites are occupied by lead cations [8].
The aim of the present work is to determine the influence of the kind of ions on their localization in the structure and
consequently on the size of the cell. Two types of substitution of lead were studied, one by sodium and bismuth, and the
other by lithium and bismuth. Several compositions were tried and we present here the results of the study for three
compounds: Pb7.4Bi0.3Na2.3(PO4)6 (I), Pb7.36Bi0.32Na2.08Li0.24(PO4)6 (II) and Pb5.78Bi0.81Ca0.60Na2.81(PO4)6 (III).
2. Experimental
The two parent compounds, Pb8Na2(PO4)6 and Pb6.5Ca1.5Na2(PO4)6, allows the study of cationic substitutions in
apatite using two mechanisms. The first one involves lead substitution, 2Pb2+! 1Bi3+ + 1M+(M = Na or Li), and the
second a mixed substitution, 1Pb2+ + 1Ca2+! 1Bi3+ + 1Na+. The aimed compounds correspond to the formulae:
Pb8�2xNa2BixMx (PO4)6 and Pb6.5�xCa1.5�xNa2BixNax(PO4)6. Among the samples made, only three are single phases
with crystals big enough for structure determination by X-ray diffraction. The first and the second compounds (x = 0.25)
derive from the first formula and involve respectively Na and Li, the third one (x = 0.75) from the second formula.
2.1. Synthesis
The synthesis is carried out starting with the following compounds: PbO, CaCO3, (BiO)2CO3, (NH4)2HPO4 and
M2CO3 (M = Li and Na). These products, commercial grade reagents, were mixed in the amount necessary to the
reactions:
� compound I: x = 0.25, M = Na
7:5 PbO þ 0:125 ðBiOÞ2CO3þ 1:125 Na2CO3þ 6 ðNH4Þ2HPO4
! Pb7:5Bi0:25Na2:25ðPO4Þ6þ 1:25 CO2þ 9 H2O þ 12 NH3
� compound II: x = 0.25, M = Li
7:5 PbO þ 0:125 ðBiOÞ2CO3þ 1:0 Na2CO3þ 6 ðNH4Þ2HPO4þ 0:125 Li2CO3
! Pb7:5Bi0:25Na2Li0:25ðPO4Þ6þ 1:25 CO2þ 9 H2O þ 12 NH3
� compound III: x = 0.75
5:75 PbO þ 0:375 ðBiOÞ2CO3þ 1:375 Na2CO3þ 6 ðNH4Þ2HPO4þ 0:75 CaCO3
! Pb5:75Bi0:75Ca0:75Na2:75ðPO4Þ6þ 2:5 CO2þ 9 H2O þ 12 NH3
The mixtures were ground in an agate mortar during half an hour using ethanol to avoid dust escape. They were put
in a platinum crucible covered with a cap for heating in a muffle furnace. A series of stages of grinding followed by
heating were performed until the reaction ended. The progress of reaction was controlled by X-ray diffraction and IR
spectroscopy. Between each stage, the temperature was increased by 50 K up to a maximum of 1273 K. Crystals
growing was performed by heating the resulting powder one hour at 1328 K followed by a slow cooling down to
1073 K at a 20 K h�1 rate. Then the oven was let to cool with its own speed. It is observed that the size of the crystals
decreases when the quantity of bismuth increases.
2.2. Chemical analyses
Chemical analyses were used to determine the quantity of the following elements: lead, calcium, bismuth, sodium,
lithium and phosphorous. The measurements were done using a Perkin-Elmer 560 atomic absorption
spectrophotometer on powder samples. A verification of the phosphate quantity was performed by colorimetric
method according to Gee and Deitz [12]. EDS analysis of the crystals has shown that they contain the expected atoms
but it was impossible to reach a precision sufficient enough to confirm a composition of the crystal similar to that of the
powder. Table 1 gathers the results of the chemical analysis and the corresponding chemical formulas. The
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311300
experimental formulas show a light variation compared to the expected formulas. This is attributed on the one hand to
the problem of the use of lead oxide, volatile compound at high temperature, and on the other hand to a loss of product
during pounding. It appears that the quantity of Bi substituted for lead depends of the substituting co-cation: with Na,
no more than 0.28 Bi can be introduced, with Li only 0.34 Bi. In the case of Ca containing compound, up to 0.83 Bi can
be incorporated. Mayer and Semadja have prepared similar apatites with bismuth contents up to two [11]. Their
method of synthesis involves nitrates that we did not use. This can explain our difficulties to increase the quantity of
bismuth in our compounds.
2.3. Infrared spectroscopy
Although the samples were made at a temperature where carbonate decomposition is completed, infrared spectra
were recorded in order to verify that no carbonate remains in the compounds. Infrared absorption analysis was
performed with a Perkin-Elmer FT/IR 1725X spectrometer. Each sample used for this measurement was prepared
mixing 3 mg of apatite powder with 500 mg of KBr (dried at 110 8C) and compressed as disk. The spectrum was
recorded in the range 4000–400 cm�1. The spectrum of pure KBr was withdrawn of the spectrum of each sample. Two
measurements were carried out for each compound using different samples taken in the same reaction batch in order to
verify their homogeneity.
The observed IR spectra of compounds (I), (II) and (III) are given in Fig. 1. The main results are that no
characteristics bands of OH or CO3 groups can be observed in the 1400–4000 cm�1 range [3,7,13]. This confirms that
these three apatites contain neither hydroxyl groups, neither water molecules nor carbonate groups. Only four bands
characteristic of the tetrahedral phosphate group are observed instead of the nine active modes expected [14]. This can
be attributed to the low resolution obtained by such transmission measurements. The four bands consist of two strong
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311 301
Table 1
Chemical analysis and experimental composition of compounds (I), (II) and (III)
Element Compound
(I) (II) (III)
Experimental Calculated Experimental Calculated Experimental Calculated
Pb 69.32 69.75 68.94 69.87 58.90 59.24
Bi 2.64 2.34 3.20 2.34 8.56 7.79
Na 2.35 2.32 2.14 2.06 3.16 3.14
Ca – – – – 1.25 1.49
Li – – 0.07 0.08 – –
P 8.37 8.34 8.36 8.35 9.17 9.24
Phosphate 25.69 25.57 25.65 25.62 28.12 28.33
Expected formula Pb7.5Na2Bi0.25Na0.25(PO4)6 Pb7.5Na2Bi0.25Li0.25(PO4)6 Pb5.75Ca0.75Na2.0Bi0.75-
Na0.75(PO4)6
Experimental formula Pb7.42Bi0.28Na2.27(PO4)6 Pb7.39Bi0.34Na2.06Li0.22(PO4)6 Pb5.76Bi0.83Ca0.63Na2.79(PO4)6
Values are given in percent of mass with an absolute error of 0.02. Calculated values come from expected formulas.
Fig. 1. Infrared transmission spectrum of (I), (II) and (III) samples at room temperature.
ones corresponding to the n3 symmetric and n1 antisymmetric stretching modes and two medium ones, n2 symmetric
and n4 antisymmetric bending modes (Table 2).
2.4. Structure
Patterns of powder X-ray diffraction (XRD) are collected on a Seifert XRD 3000TT diffractometer, equipped with a
graphite monochromator situated on the diffracted beam and ruled to offer a Cu Ka copper radiation. Every peaks of
the pattern are indexed using an apatite cell indicating a crystallized monophasic compound. The cell dimensions are
given in Table 3.The structures of these apatites are determined by X-ray diffraction on single-crystal, using a Nonius
Mach 3 kappa CCD diffractometer with graphite monochromatized Mo Ka radiation. The crystals data, the
parameters used for the X-ray diffraction collection and the results of structures determinations are listed in Table 3.
Absorption corrections were performed using the numerical method included in PLATON [15]. Atomic scattering
factors were taken from the International Tables for X-ray Crystallography [16]. Position of Bi and Pb cations were
located using SHELXS-97 program [17], whereas P and O atomic positions were deduced from Fourier synthesis
during the refinements with the SHELXL-97 program [18]. The principal difficulty, which arises in the determination
of the structure, is the quantity of atoms of different kind to be put in one site. In both (6h) and (4f) sites, at least three
kinds of atoms must be included. In order to solve this problem, some chemical properties must be taken into account.
A same composition of the crystal and the powder is expected according to the similarity of the cell parameters
determined in both cases. Elements present in the compound are supposed to be in ionic form (M3+, M2+ and M+), then
electroneutrality is imposed. The cation sites were assumed fully occupied. All these supplementary conditions were
inserted in the refinement as restraints. Because they only applied to the occupation factors, they break the correlation
generally observed between thermal displacement parameters and occupation factors. More, the atoms pertaining to a
same site were considered with same coordinates and same thermal displacement parameters. The final fractional
atomic coordinates and the final anisotropic thermal displacement parameters for compounds (I), (II) and (III) are
gathered in Tables 4 and 5. A view of the structure along [0 0 1] is given in Fig. 2.
3. Results
3.1. Allotment in Pb7.4Bi0.3Na2.3(PO4)6 (I)
Once all the sites are found, a Fourier summation reveals that the electron density in (6h) and (4f) sites does not
correspond to that of one of the atoms contained in the compound. So we must assume that these sites are occupied by
several elements. The electron density of the (6h) site being stronger than the one of (4f) site, the heavy atoms, Pb or
Bi, must occupy preferentially the (6h) site. In the beginning, we have assumed that Bi is only localized in this site.
Then refinements, with the constraints already described, allow finding the Na quantity in each site. In the final
refinement, only the restraint on electroneutrality was kept. We may remark that all other distributions of Bi, only in
(6h) sites or in (4f) site or in both (4f) and (6h) sites, give the same final agreement. Although it is impossible to
differentiate Bi3+ from Pb2+, the constraint on electroneutrality allows determining the Bi quantity. Two limit formulas
can be proposed for compound (I):
½Pb1:87Na2:13�4f ½Pb5:53Bi0:30Na0:17�6hðPO4Þ6 or ½Pb1:57Bi0:30Na2:13�4f ½Pb5:83Na0:17�6hðPO4Þ6
Arbitrarily the first formula will be used in the following. As already found in relative lead compounds, the heavy
atoms, which carry a lone electron pair, are preferentially localized in (6h) site. This allows the formation of metal
triangle, which stabilized the structure by the overlap of the lone electron pairs [8,19] (Fig. 3). We may remark than
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311302
Table 2
IR band spectra assignments (cm�1) for PO4 group of compounds (I), (II) and (III)
Samples n1 (cm�1) (s) n2 (cm�1) (m) n3 (cm�1) (s) n4 (cm�1) (m)
(I) 1000 540 1056 581
(II) 1004 535 1048 555
(III) 927 541 1019 588
Note: s, strong; m, medium.
0.17 sodium in (6h) site appears meaningless. But, it indicates that this site is not fully occupied by lead and/or
bismuth. Effectively, a refinement without sodium in this site leads to a quantity of 5.83 heavy atoms showing an
effective defect. This lack of atoms was filled up by sodium in order to solve the electroneutrality problem. The added
sodium allows to reach a formula of the compound similar to the one found by chemical analysis.
3.2. Allotment in Pb7.36Bi0.32Na2.08Li0.24(PO4)6 (II)
In this compound, four kinds of atoms fill the cationic (6h) and (4f) sites. Electron density obtained by Fourier
synthesis shows that heavy atoms are till localized in (6h) site. We have assumed the Bi fully localized in this site as in
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311 303
Table 3
Crystal data and structure refinement information for compounds (I), (II) and (III)
Chemical formula
(I) Pb7.4Bi0.3Na2.3(PO4)6 (II) Pb7.36Bi0.32Na2.08Li0.24(PO4)6 (III) Pb5.78Bi0.81Ca0.60Na2.81(PO4)6
Powder data
a (A) 9.7065(7) 9.6916(8) 9.6529(7)
c (A) 7.1705(6) 7.1751(7) 7.1153(7)
Crystal data
Chemical formula weight (g/mol) 2218.60 2211.10 2025.30
Cell setting Hexagonal Hexagonal Hexagonal
Space group (N8: 176) P63/m P63/m P63/m
a (A) 9.7070(10) 9.691(3) 9.6530(6)
c (A) 7.170(3) 7.1753(9) 7.1150(2)
V (A3) 585.1(3) 583.6(3) 574.16(5)
Z 1 1 1
rcal (g cm�3) 6.297 6.292 5.857
F(0 0 0) 939 936 866
m (mm�1) 55.840 55.844 49.116
Morphology Prismatic Prismatic Prismatic
Crystal color Transparent and colorless Transparent and colorless Transparent and colorless
Source of material Synthesis Synthesis Synthesis
Crystal volume (10�5 mm3) 53.1 31.9 9.1
Intensity measurements
Temperature (K) 293(2) 293(2) 293(2)
Wavelength Mo Ka (A) 0.71073 0.71073 0.71073
u range (8) 37.99 37.99 41.93
Range of h, k, l �16 � h � 7 �15 � h � 12 �18 � h � 13
�6 � k � 16 �16 � k � 4 �6� k � 18
�5 � l � 12 �5 � l � 12 �13 � l � 6
Total unique reflections 1121 1123 1416
Rint 0.089 0.097 0.098
Structure determination
Absorption correction
Tmin 0.0601 0.0488 0.1369
Tmax 0.1669 0.1933 0.3660
Unique reflections with I > 2s(I) 807 728 804
Refined parameters 43 46 44
Agreement factors
R 0.036 0.042 0.047
wR2 0.080 0.070 0.074
Goodness of fit: s 1.062 1.005 0.988
Note: wR2 ¼P½WðF2
o � F2c Þ
2=½WðF2
oÞ2�
1=2;R1 ¼
PFoj j � Fcj jj j=
PFoj j, where W ¼ 1=½s2ðF2
oÞ þ ð0:045PÞ2 þ 1:18P� and P ¼ ðF2o þ 2F2
c Þ=3.
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311304
Table 4
Final atomic parameters with estimated standard deviation of compounds (I), (II) and (III)
Atom Site occupancy x y z Ueq (A2)
Pb7.4Bi0.3Na2.3(PO4)6 (I)
Pb, Bi, Na(6h) 0.923(12), 0.050(7), 0.027(5) 0.74486(4) 0.00156(4) 1/4 0.01781(13)
Pb, Na(4f) 0.467(3), 0.533(3) 2/3 1/3 0.48875(10) 0.0163(2)
P 1 0.6000(3) 0.6211(3) 1/4 0.0107(4)
O3 1 0.6531(9) 0.7305(7) 0.4203(7) 0.0301(12)
O2 1 0.4158(8) 0.5204(9) 1/4 0.0314(19)
O1 1 0.6734(9) 0.5145(9) 1/4 0.0214(13)
Pb7.36Bi0.32Na2.08Li0.24(PO4)6 (II)
Pb, Bi, Li(6h) 0.906(5), 0.054(4), 0.041(2) 0.74536(5) �0.00126(5) 1/4 0.01728(13)
Pb, Na(4f) 0.480(3), 0.520(3) 2/3 1/3 0.51079(11) 0.0147(2)
P 1 0.6214(3) 0.5999(3) 1/4 0.0107(4)
O3 1 0.7304(7) 0.6517(8) 0.4207(7) 0.0270(14)
O2 1 0.5213(12) 0.4180(10) 1/4 0.042(3)
O1 1 0.5168(10) 0.6752(14) 1/4 0.0244(18)
Pb5.78Ca0.60Bi0.81Na2.81(PO4)6 (III)
Pb, Bi, Na(6h) 0.7787(8), 0.1359(4), 0.0855(18) 0.74345(3) �0.00083(3) 1/4 0.01703(6)
Pb, Na, Ca(4f) 0.2738(2), 0.5760(6), 0.1502(5) 2/3 1/3 0.51055(11) 0.01514(16)
P 1 0.62010(18) 0.59617(19) 1/4 0.0113(3)
O3 1 0.7296(4) 0.6516(6) 0.4214(4) 0.0308(9)
O2 1 0.5258(6) 0.4105(6) 1/4 0.0324(14)
O1 1 0.5105(6) 0.6667(6) 1/4 0.0226(9)
Notes: Ueq ¼ 1=3P
i
PjUði; jÞa�i a�jaia j.
Table 5
Final anisotropic displacement thermal parameters (A2) with estimated standard deviations for compounds (I), (II) and (III)
Atom U(1,1) U(2,2) U(3,3) U(1,2) U(1,3) U(2,3)
Pb7.4Bi0.3Na2.3(PO4)6 (I)
Pb, Bi, Na(6h) 0.01532(17) 0.01541(17) 0.02191(19) 0.00773(12) 0 0
Pb, Na(4f) 0.0155(2) 0.0155(2) 0.0179(4) 0.00709(13) 0 0
P 0.0123(9) 0.0099(8) 0.0109(8) 0.0064(7) 0 0
O3 0.051(4) 0.030(3) 0.018(2) 0.026(3) �0.013(2) �0.009(2)
O2 0.004(2) 0.022(4) 0.064(6) 0.003(2) 0 0
O1 0.027(3) 0.026(4) 0.019(3) 0.019(3) 0 0
Pb7.36Bi0.32Na2.08Li0.24(PO4)6 (II)
Pb, Bi, Li(6h) 0.0172(2) 0.0140(2) 0.02105(19) 0.00810(17) 0 0
Pb, Na(4f) 0.0141(3) 0.0141(3) 0.0160(4) 0.00703(15) 0 0
P 0.0087(11) 0.0106(14) 0.0131(9) 0.0049(10) 0 0
O3 0.025(3) 0.055(4) 0.015(2) 0.030(3) �0.012(3) �0.003(2)
O2 0.024(5) 0.007(4) 0.095(8) 0.008(4) 0 0
O1 0.031(5) 0.030(5) 0.027(3) 0.027(4) 0 0
Pb5.78Ca0.60Bi0.81Na2.81(PO4)6 (III)
Pb, Bi, Na(6h) 0.01433(10) 0.01700(11) 0.02018(10) 0.00816(9) 0 0
Pb, Na, Ca(4f) 0.0155(2) 0.0155(2) 0.0145(3) 0.00774(11) 0 0
P 0.0105(6) 0.0132(6) 0.0112(6) 0.0066(5) 0 0
O3 0.0263(16) 0.055(2) 0.027(2) 0.0254(16) 0.0163(15) 0.0127(14)
O2 0.019(2) 0.013(2) 0.064(4) 0.0057(19) 0 0
O1 0.019(2) 0.030(2) 0.027(2) 0.0184(18) 0 0
Note: The form of the anisotropic displacement parameter is: exp[�2p2{h2a*2U(1,1) + k2b*2U(2,2) + l2c*2U(3,3) + 2hka*b*U(1,2) + 2hla*-
2b*2U(2,2) + l2c*2U(3,3) + 2hka*b*U(1,2) + 2hla*c*U(1,3) + 2klb*c*U(2,3)}], where a*, b* and c* are reciprocal lattice constants.
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311 305
Fig. 2. View of the lacunars apatite structure along [0 0 1].
Fig. 3. Metal and oxygen arrangement around (6h) sites. Arrows indicate an expected orientation of the lone electron pairs.
previous structure. But, here, there are two kinds of co-cations: Na and Li. The trigonal prisms around the (4f) sites
building columns parallel to the c parameter (Fig. 4), we can assume that this parameter varies with the size of the
cation localized in the prism. The ionic radius of lithium being smaller than the sodium one, Li substituted for Na
would decrease this parameter. The experimental c parameter being very similar, including errors, to the one of
compound (I), we can assume that the same atoms, Pb and Na, occupy this site. Using the same constraints as
previously, the resulting formula is written:
½Pb1:92Na2:08�4f ½Pb5:44Bi0:32Li0:24�6hðPO4Þ6
An attempt of refinement with the (6h) site fully occupied by Bi or Pb leads to an R factor of 0.066 that implies
rejecting this assumption. As remarked in structure of compound (I), Bi can be distributed in (4f) and/or (6h) sites
without any changes of the refinement criteria.
3.3. Allotment in Pb5.78Bi0.81Ca0.60Na2.81(PO4)6 (III)
In this compound, both (4f) and (6h) sites can be occupied by Pb, Bi, Ca and Na atoms. Fourier summation reveals
that the (6h) site receives the heavy atoms preferentially. Like previously, Bi is arbitrarily assigned to this site. Using
the same argument as before, a substitution of calcium for lead may result in a decrease of the c parameter, the ionic
radius of Ca2+ being smaller than the one of Pb2+ (0.99 and 1.20 A, respectively). The c parameter having decreased
effectively, a Ca fully localized in the (4f) site appears as a good assumption. The same constraints as used previously
are applied. The final refinement gives the following distribution of atoms in the sites.
½Pb1:10Ca0:60Na2:30�4f ½Pb4:68Bi0:81Na0:51�6hðPO4Þ6:
Once again, Bi can be distributed in both (4f) and/or (6h) sites.
4. Discussion
The structures of compounds (I), (II) and (III) are derived from the one of Pb8Na2(PO4)6 compound. Their chemical
formulas:
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311306
Fig. 4. View of the M(4f) prisms building columns along [0 0 1] with linking PO4 tetrahedrons.
I: [Pb1.87Na2.13]4f[Pb5.53Bi0.30Na0.17]6h(PO4)6 or Pb7.40Bi0.30Na2.30(PO4)6;
II: [Pb1.92Na2.08]4f[Pb5.44Bi0.32Li0.24]6h(PO4)6 or Pb7.36Bi0.32Na2.08Li0.24(PO4)6;
III: [Pb1.10Ca0.60Na2.30]4f[Pb4.68Bi0.81Na0.51]6h(PO4)6 or Pb5.78Bi0.81Ca0.60Na2.81(PO4)6.
are very close to that obtained by elemental analyses on powders and differs slightly from the expected ones (Table 1).
It should be noted that the quantity of bismuth, which is introduced is weak. Mayer and Semadja prepared similar
apatites but the quantity of bismuth they could introduced was limited to two [11]. The introduction of Bi3+, cation
with high electric charge, can explain the observed limitation.
The ionic allotment found in the three compounds revealed that the (6h) site contains respectively 5.83, 5.76 and
5.49 atoms with lone electron pair, which is very near the saturation of the site. Moreover, the increase of bismuth
quantity corresponds to a decrease of the quantity of heavy atoms. Surprisingly, the charge brought by the cations of
this site appears constant (12.1, 12.1, 12.3, respectively) and near the 12.0 observed in Pb8Na2(PO4)6 compound. This
may point out that this charge value is the upper limit that allows the stabilization of apatite with anionic vacancies.
The geometrical information about the PO4 tetrahedrons the cations found in the three compounds are gathered in
Tables 6 and 7, respectively. Although the P–O distances are equal within 3s, a general tendency is observed: the P–O1
distances are the shortest and the P–O2 the longest. The short P–O1 bond is associated to the long O1–M(4f) distances
and reciprocally, the long P–O2 to the short O2–M(4f) distances. Such phenomenon is well known and has already
been explained [3,7]. The distortions of the PO4 tetrahedron are obtained using the standard deviation (s) of the O–P–
O average angles ((I) 109.43 (s = 2.28); (II) 109.43 (s = 1.68); (III) 109.41 (s = 2.58)). Compound (II), which contains
Li, exhibits the lowest s. Moreover, the average P–O distances in compound (II) appears the shortest of the three
compounds ((I) P–O = 1.532(7) A; (II) P–O = 1.525(7) A; (III) P–O = 1.530(4) A). In compound (II), the PO4
geometry approaching the one of the regular PO4 tetrahedron, the interaction with surrounding cations is weak. The
size of the lithium ion, which is the smallest, can explain that. In compound III, it is important to remark that Ca
substitution for Pb preserves the PO4 distortion observed in compound (I).
The P–O distances are nevertheless shorter than the one generally observed for phosphates group. Moreover, the
thermal displacement parameters of the oxygen atoms are greater than those of the other atoms. Although light atoms
exhibit higher agitation, a global motion of the PO4 group is expected. A TLS analysis (Table 8) of these parameters
reveals that the PO4 group presents oscillations, which can be separated in librations (L) and translation (T) motions
[20]. The amplitudes of these motions, given as the root mean square (RMS) of the eingen values of the corresponding
tensors, are presented in Table 8. In any compound, the translation oscillations appear homogenous and weak. In
compound (II), the librations motions appear the greatest and principally its component nearly parallel to [0 0 1]
direction. Similarly, the infrared study (Table 2) reveals a different behavior of the bending mode. A shift to low wave
number of the n2 and n4 bending modes confirms the specificity of its PO4 behavior. These observations confirm that in
this compound, PO4 makes weak interaction with its environment.The rigid body corrections of the P–O bonds are
given in Table 8. Except P–O1 bond, the corrected bond lengths become equal to those found in phosphate groups
(1.54 A).The infrared study reveals that the n1 and n3 stretching modes of compound (III) are shifted to low wave
numbers. The P–O distances do not explain such behavior, even after rigid body correction. The cavity where PO4 lies
being smaller in compound (III) than in the two other compounds ((I) 37 A3; (II) 37 A3; (III) 35 A3), the PO4
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311 307
Table 6
Interatomic distances (A) and angles (8) of PO4 in the (I), (II) and compounds (III)
(I) (II) (III)
P–O1 1.522(7) 1.516(8) 1.518(6)
P–O2 1.550(7) 1.529(9) 1.552(5)
P–O3 1.528(5) 1.529(5) 1.525(3)
P–O3s1 1.528(5) 1.529(5) 1.525(3)
O1–P–O2 110.8(5) 111.3(5) 112.3(3)
O3s1–P–O2 108.7(3) 108.3(3) 108.0(2)
O3–P–O2 108.7(3) 108.3(3) 108.0(2)
O1–P–O3s1 111.2(3) 111.1(3) 111.0(2)
O3s1–P–O3 106.0(5) 106.5(5) 106.2(3)
O1–P–O3 111.2(3) 111.1(3) 111.0(2)
Note: Symmetry code, s1: x, y, 0.5 � z.
interactions to its surrounding cations should be the greatest. This can explain the weakest motion observed in this
compound by the TLS analysis.
The oxygen surrounding of (4f) site has the shape of a trigonal tricapped prism (Fig. 4). These prisms are stacked in
the [0 0 1] direction. The lone electron pair influence of the Pb2+ ions is revealed by the shift of the cation to the center
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311308
Table 7
Interatomic distances (A) around cations sites of the compounds (I), (II) and (III)
(I) (II) (III)
(6h) site
M(6h)–O2s2 2.245(8) 2.2267(6) 2.265(5)
M(6h)–O3s10 2.501(5) 2.5124(3) 2.479(3)
M(6h)–O3s9 2.501(5) 2.5124(3) 2.479(3)
M(6h)–O3s11 2.620(6) 2.6132(6) 2.608(4)
M(6h)–O3s12 2.620(6) 2.6132(6) 2.608(4)
M(6h)–O1s3 2.807(8) 2.7851(8) 2.853(5)
M(6h)–M(6h)s13 4.304(2) 4.263(1) 4.282(3)
(4f) site
M(4f)–O1s2 2.431(5) 2.443(6) 2.414(4)
M(4f)–O1 2.431(5) 2.443(6) 2.414(4)
M(4f)–O1s3 2.431(5) 2.443 (6) 2.414(4)
M(4f)–O2s4 2.703(6) 2.704(7) 2.618(4)
M(4f)–O2s5 2.703(6) 2.704(7) 2.618(4)
M(4f)–O2s6 2.703(6) 2.704(7) 2.618(4)
M(4f)–O3s7 2.919(6) 2.900(1) 2.888(5)
M(4f)–O3s8 2.919(6) 2.900(1) 2.888(5)
M(4f)–O3s9 2.919(6) 2.900(1) 2.888(5)
M(4f)–M(4f)s1 3.424(2) 3.433(2) 3.4074(15)
M(4f)–M(4f)s9 3.746(2) 3.742(2) 3.7076(15)
Note: M(6h): Pb, Bi or Na. M(4f): Pb, Ca, Li or Na. Symmetry codes, s1: x, y, 0.5 � z; s2: 1 � y, x � y, z; s3: 1 � x + y, 1 � x, z; s4: 1 + x � y, x,
0.5 + z; s5: 1 � x, 1 � y, 0.5 + z; s6: y, � x + y, 0.5 + z; s7: 1 + x � y, x, 1 � z; s8: 1 � x, 1 � y, 1 � z; s9: y, � x + y, 1 � z; s10: y, � x + y,
� 0.5 + z; s11: x, � 1 + y, 0.5 � z; s12: x, � 1 + y, z; s13: 2 � x + y, 1 � x, z; s14: 1 � y, � 1 + x � y, z; s15: x, y, 1.5 � z.
Table 8
TLS analysis with rigid body correction for PO4 group
(I) (II) (III)
TLS analysis
Libration tensor RMS (8)1 8.41 8.90 7.99
2 5.50 1.97 0.84
3 2.93 1.84 4.23
Translation tensor RMS (A)
1 0.11 0.13 0.13
2 0.10 0.11 0.12
3 0.09 0.12 0.21
Rigid body correction
d (P–O1) (A)
Observed 1.522 1.516 1.518
Corrected 1.526 1.523 1.522
d (P–O2) (A)
Observed 1.550 1.526 1.552
Corrected 1.556 1.535 1.556
d (P–O3) (A)
Observed 1.528 1.529 1.525
Corrected 1.545 1.546 1.535
of the cavity ((I) d = 0.271 A; (II) d = 0.267 A; (III) d = 0.262 A). This makes two different M–M distances in the
[0 0 1] direction (Table 7). More, the short O1–O1 distances correspond to the short M–M distance and the long
O2–O2 distances to the long M–M distance. This infers that the size of the M–(O1)3–M cavity is smaller than the one
of the M–(O2)3–M cavity. This observation allows assuming that the lone electron pairs of Pb2+ cations are in the
second cavity, the first one being free of lone electron pair.
In a cell, the c parameter is equal to the pile up of two prisms (Fig. 4). We can assume that the height of a prism is
related to the size of the cation it contains. Fig. 5 presents the evolution of the c parameters of phosphate apatites
containing only one kind of cation versus the radius of the cation. The values of these parameters are taken from
references [21–31] and reported in Table 9. It shows that the main factor of the c variation is the size of the cation
present in the (4f) site. However, it shall notice that the nature of the anions influences these variations, which depend
not only of their ionic radius, but also of their position in the cell. F� is inserted in the middle of the cations triangle,
except in Pb compound, Cl� and Br� between the triangles. Using the values of the c parameter found in these
compounds and assuming a linear variation with the ionic radius of the cation, it is possible to calculate the height of a
prism characteristic of a cation. But, in this study, the anion located on the ternary axis is missing and thus its influence
on the structure must be omitted. To take into account this lack, the c parameter of Pb8Na2(PO4)6 is used as an
anchoring point. The following empirical formula is proposed:
Hprism ¼ 2:866þ 0:676rcation
When several types of cations occupy the (4f) site, the length of c can be approximated by a weighted sum of the
height of single prisms corresponding to one kind of cation.
The c parameter is calculated according to c ¼P
xi=2Hi, with xi the number of cations of i type in (4f) site and Hi,
the height of the prism containing cation i.
The corresponding c parameters can be calculated:
Pb8Na2(PO4)6: the (4f) site contains 2 Pb and 2 Na, then c = 2/2 HNa + 2/2 HPb; ccalc = 7.185 A [8]; cobs = 7.185 A.
Pb8K2(PO4)6: ccalc = 7.404 A [31]; cobs = 7.435 A;
B. Hamdi et al. / Materials Research Bulletin 42 (2007) 299–311 309
Fig. 5. Variation of c parameters vs. the radius of the cation in apatite compounds with monotype cation.
Table 9
Cell parameters for apatites with monotype cation
Cations Radius (A) M10(PO4)6F2 M10(PO4)6Cl2 M10(PO4)6Br2
a (A) c (A) Ref. a (A) c (A) Ref. a (A) c (A) Ref.
Ca2+ 0.99 9.363 6.878 [21] 9.590 6.766 [22,23] 9.761 6.739 [22,24]
Sr2+ 1.13 9.712 7.285 [25] 9.877 7.189 [26] 9.964 7.207 [27]
Pb2+ 1.20 9.760 7.300 [22,28] 9.998 7.344 [22,29] 10.062 7.359 [22]
Ba2+ 1.35 10.153 7.733 [30] 10.284 7.651 [31] – –
(I) ccalc = 7.174 A; cobs = 7.170 A;
(II) ccalc = 7.177 A; cobs = 7.175 A;
(III) ccalc = 7.114 A; cobs = 7.115 A.
The fine agreement observed confirms a c parameter directly correlated to the allotment of ions in (4f) site. But this
correlation must be limited to the case of lead apatite with Na substitution. In the case of Pb8K2(PO4)6, the discrepancy
observed shows the limits of such empirical formula.
Cations localized in the (6h) sites form triangles (Fig. 3). The values of the M–M distances of these triangles appear
constant for all compounds (4.28(2) A, Table 7). These triangles allow the stabilization of the lacunars structure by
accumulation of electron density in their center, this last one being brought by the overlap of the Pb2+ or Bi3+ lone
electron pairs [8,19,32,33]. Here, the M–M distance is a little longer than the corresponding one observed in calcium
fluorapatite (4.079 A) where fluorine occupies the center of the cation triangle. This enlargement shows the respective
influence of the lone electron pairs overlap attraction and of the repulsive effect due to the charge of the (6h) cations on
the structure. However this M–M distance is shorter than the one existing in the compound Pb8Na2(PO4)6 (dPb2–
Pb2 = 4.333 A). This fact can be attributed to the presence of less bulky and less charged cations in this site (Na+ or
Li+). Indeed, the shortest distance corresponds to a filling of 0.51 sodium ion in this site for compound (III).
The apatite structure, presented in Fig. 2, shows that the a parameter is directly related to the distance between two
columns of (4f) prisms. But this distance is not connected with specific dimensions of the prisms or of the tetrahedrons
because, first, prisms and tetrahedrons exhibit rotations, second, the prisms are twisted and have non-equal ends, third,
the sizes of the anions and cations in the tunnel distend the tunnel wall. Table 9 and Fig. 6 reveals such behavior in the
case of apatites with monotype cation. A strong influence of the anions located in the center of the tunnel is observed
with a variation of length of about 3%.
These structure determinations confirm that the cations with lone electron pair are mainly localized in the (6h) site.
Moreover, they reveal that the main factor influencing the c parameter is the ionic radius of the cations inserted in the
(4f) sites. Besides, the a parameter cannot be approximated by simple relations, too many factors being involved. It
results that the tetrahedrons XO4 and the prisms containing the cations of the (4f) sites mainly manage the apatite
structure. The other ions, located in the (6h) tunnel, only deform the skeleton thus made, assuring the electroneutrality
and the stability of these compounds.
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