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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 Mate ´riaux et d’Environnement, Faculte ´ des Sciences de SFAX, BP 802, 3018 SFAX, Tunisia b Centre d’Elaboration de Mate ´riaux et d’Etudes Structurales, 29 rue J. Marvig, BP 4347, 31055 Toulouse Cedex 4, France c 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, Pb 7.4 Bi 0.3 Na 2.3 (PO 4 ) 6 (I), Pb 7.36 Bi 0.32 Na 2.08 Li 0.24 (PO 4 ) 6 (II) and Pb 5.78 Bi 0.81 Ca 0.60 Na 2.81 (PO 4 ) 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 P6 3 /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 M 10 (YO 4 ) 6 X 2 , 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, CO 3 , etc. [1–4]. The apatite structure-type has been known since 1930 when Na ´ray-Sza ´bo determined the structure of Ca 10 (PO 4 ) 6 F 2 [5]. It generally crystallizes in the hexagonal system with space group P6 3 /m [6,7]. The apatite structure is described as follows. The YO 4 tetrahedrons are arranged around the 6 3 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

Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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Page 1: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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

Page 2: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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

Page 3: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 4: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 5: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 6: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 7: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 8: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 9: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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.

Page 10: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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

Page 11: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

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] – –

Page 12: Synthesis and distribution of cations in substituted lead phosphate lacunar apatites

(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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