Isomorphous Substitution of Rare-Earth Elements in Lacunary Apatite

Feb 12, 2016 - Department of Chemistry and Geology, Minnesota State University at Mankato, 241 ...... Fleet , M. E.; Liu , X.; Pan , Y. J. Solid State...
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Isomorphous Substitution of Rare-Earth Elements in Lacunary Apatite Pb8Na2(PO4)6 Evgeni I. Get’man,†,‡ Stanislav N. Loboda,† Alexey V. Ignatov,† Vadim V. Prisedsky,*,§ Mohammed A. B. Abdul Jabar,⊥ and Lyudmyla I. Ardanova∥ †

Department of Inorganic Chemistry, Donetsk National University, 24 Universitetskaya, Donetsk 83001, Ukraine Department of Analytical Chemistry, Donetsk National University, 21 600-richya, Vinnytsia, 21021, Ukraine § Department of General Chemistry, Donetsk National Technical University, 58 Artema, Donetsk 83001, Ukraine ⊥ Department Medical Lab Technologies, Bilad Al-Rafidain University College, Baaqubah 32001 Iraq ∥ Department of Chemistry and Geology, Minnesota State University at Mankato, 241 Ford Hall, Mankato, Minnesota 56001, United States ‡

ABSTRACT: The substitution of rare-earth elements (REEs) for Pb in the lacunary apatite Pb8Na2(PO4)6 with void structural channels was studied by means of powder X-ray diffraction (including the Rietveld refinement), scanning electron microscopy, energy-dispersive X-ray microanalysis, and IR spectroscopy and also measurements of the electrical conductivity. The substitution limits (xmax in Pb8−xLnxNa2(PO4)6Ox/2) at 800 °C were found to decrease with the atomic number of the REE from 1.40 for La to 0.12 for Yb with a rapid drop from light to heavy lanthanides (between Gd and Tb). The REE atoms substitute for Pb predominantly at Pb2 sites of the apatite structure according to the scheme 2Pb2+ + □ → 2Ln3+ + O2−, where □ is a vacancy in the structural channel. The substitution in lacunary apatite produces quite different changes in the structural parameters compared with broadly studied alkaline-earth hydroxyapatites. In spite of the much lower ionic radii of REE than that of Pb2+, the mean distances ⟨Pb1−O⟩ somewhat increase, whereas the distances ⟨Pb2−Pb2⟩ and ⟨Pb2−O4⟩ do not change considerably with the degree of substitution. This implies control of the substitution by not only spatial and charge accommodation of REE ions but also the availability of a stereochemically active 6s2 electron pair on Pb2+. The high-temperature electrical conductivity shows dependence on the degree of substitution with a minimum at x = 0.2 indicative of a possible change of the type of conductivity.

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INTRODUCTION The majority of modern solid-state materials are based on far more complex systems than individual chemical compounds. The isomorphism is important because the properties of singlephase materials or separate phases in composites may be effectively modified by the introduction of isomorphous additives into their structure. Using various dopants and changing their amounts, one can change not only the structural parameters such as the size of the unit cell, interatomic distances, crystallographic site occupancies, and character of the chemical bond but also the functional properties of the material. An important piece of information is the solubility limit (xmax) for a substitute in the host lattice. As is typically the case, the chemical and physical properties change in a regular fashion with the degree of substitution within the solid solution (homogeneity) region, 0 ≤ x ≤ xmax. Thus, information about the compositional limit of a particular dopant in the structure is crucial for formulating a synthetic material having the desired properties. The optimum properties may be found at both quite © 2016 American Chemical Society

low (e.g., at 1 atom % and less for luminescent and laser materials1) and quite high (as for the catalysts2) contents of dopant. Compounds with the apatite structure have the general composition M10(ZO4)6X2, where M = Na+, K+, Ca2+, Sr2+, Ba2+, Pb2+, Cd2+, Y3+, La3+, lanthanides Ln3+, etc., Z = Si4+, Ge4+, P5+, V5+, As5+, S6+, Cr6+, etc., and X = OH−, F−, Cl−, Br−, I−, O2−, □ (anion vacancy). This structure type accommodates a variety of isovalent and heterovalent substitutions facilitating the origin of many interesting and useful properties. Because of these advantages, the compounds and solid solutions with the apatite structural type are widely studied and used as biomaterials in medicine, luminescent and laser materials, sensors, solid electrolytes, sorbents, catalysts, etc.1−4 In the apatite crystal structure, two crystallographically different positions for M cations are distinguished, and the general formula may be presented as (M1)4(M2)6(ZO4)6X2. Received: November 6, 2015 Published: February 12, 2016 2165

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

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Inorganic Chemistry

favorable because it lowers the electrostatic energy of intercationic repulsion. Judging from the comparison of the measured interatomic distances and the ionic radii, the character of chemical bonding in the M1 9-fold coordination polyhedra is close to ionic because the mean cation−oxygen distance ⟨M1−O⟩ (2.687 Å) is almost identical with the sum of the ionic radius of O2− (1.40 Å) and the arithmetic mean radius of Pb2+ (1.35 Å) and Na+ (1.24).9 With the same approach, Pb−O bonds in the M2 6fold coordination polyhedra are more covalent in character because the mean distance ⟨M2−O⟩ (2.533 Å) is smaller than the sum of the ionic radii of O2− (1.40 Å) and Pb2+ (1.19 Å).9 So, Pb cations in the apatite Pb8Na2(PO4)6 behave in two different ways: (a) Pb1 cations with stereochemically inactive lone pairs 6s2 are engaged in an almost totally ionic bond Pb1/ Na−O in the mixed M1 site; (b) Pb2 cations are engaged in a Pb2−O bond with more covalent character, where its lone pair 6s2 becomes stereochemically active and constitutes the seventh ligand of Pb cations.9,15 It is important to note that the conclusion on the covalent character of the Pb−O bond is based mainly on a single specific fact: a very short M2−O2 distance (2.225 Å), which may be explained by the location of O2− in the axial plane of the coordination bipyramid opposite stereochemically active electron pair 6s2 of the Pb atom inside this bipyramid.18 If one does not take into account the shortening of the M2−O2 bond, the mean M2−O distance is calculated as 2.595 Å and is practically equal to the sum of the ionic radii of O2− and Pb2+. This example indicates that the prediction of particular interatomic distances in substituted apatites, and hence the properties of their solid solutions, requires further study. Isomorphous substitution of REEs (from Ce to Er) for Pb in Pb 8 Na 2 (PO 4 ) 6 with the formation of solid solutions Pb8−xLnxNa2(PO4)6Ox/2 as well as their luminescent properties was reported19 for a small degree of substitution (x = 0.25). There is a possibility of much larger degrees of substitution under the scheme 2Pb2+ + □ → 2Ln3+ + O2− in Pb8Na2(PO4)6, keeping in mind that in this apatite the hexagonal channels are free from OH− groups, which prevent O2− ions from entering into the channels because of electrostatic repulsion. In this work, we conducted an investigation of the isomorphous substitution of REEs for Pb in Pb8Na2(PO4)6 under the scheme 2Pb 2+ + □ → 2Ln3+ + O2−, with Ln = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Tm, Yb, and Y in a wide compositional region, and their effect on the solubility limits, structural parameters, and electrical conductivity of solid solutions Pb8−xLnxNa2(PO4)6Ox/2.

The 9-fold coordination M1 sites (4f position) are surrounded by nine O atoms belonging to ZO4 tetrahedra. The M2 sites (6h position) are surrounded by six O atoms and also one X anion (2a position). The cations in the M2 sites form a series of triangles in the planes perpendicular to the c axis of the unit cell. The succession of these triangles along the c axis constitutes the walls of the tunnels of hexagonal symmetry accessible for location of X anions and easy one-dimensional diffusion of charge carriers, which can be both anions and cations.5 Because of these features, the apatite structure easily accommodates isomorphous replacements of all of the structural units M, Z, and X. Isomorphous substitution of rare-earth elements (REEs) for alkaline-earth elements in hydroxyapatites M10(ZO4)6(OH)2 has been studied intensively and shown to take place under the scheme M2+ + OH− → Ln3+ + O2−, with Ln3+ ions occupying mainly M2 sites and O atoms filling the hexagonal channels.6−8 Pb-containing hydroxyapatites Pb10(ZO4)6(OH)2 have the advantage of much lower temperature required for their solidstate synthesis and sintering (800 °C10,11 compared to 1200− 1450 °C for alkaline-earth apatites6). Except technological advantages, this facilitates the fabrication of ceramic samples with lower grain sizes. The ionic radius of Pb2+ is close to those of alkaline-earth elements. This implies a mechanism similar to that of isomorphous substitution in Pb-containing apatites. Nevertheless, there is no information in the literature on the substitution of REE in lead hydroxyapatite Pb10(ZO4)6(OH)2 under the same substitution scheme. This may be related to the influence of stereochemically active lone 6s2 electron pairs held by Pb2+ cations and oriented toward the tunnel axis.9 Such pairs behave like entire ligands and prevent O2− from entering into the channels filled with OH− groups. Lead alkali apatites without X anions in their composition, Pb8A2(ZO4)6, where A = Na, K, Rb, Cs, Tl, and Ag and Z = P, V, and As, were first reported in ref 11. Such lacunary apatites may be considered as derivatives of lead hydroxyapatite Pb10(ZO4)6(OH)2 produced by substitution under the scheme 2Pb2+ + 2OH− → 2A+ + 2□. Then they were studied by X-ray diffraction (XRD)12−14 and IR, Raman, and NMR spectroscopies.15 The availability of hexagonal structural channels free from hydroxide anions OH− creates necessary preconditions for the sodium cationic conductivity in Pb8Na2(ZO4)6.16 The ionic character of the electrical conductivity at 196−600 °C and its anisotropy was confirmed also for monocrystalline Pb8.5Na1.5(PO4)6O0.25.19 Refinement of the crystal structure of Pb 8 A 2 (ZO 4 ) 6 compounds showed that they crystallize in the apatite structure type (space group P63/m), with the M2 sites occupied totally by Pb2+ cations and the M1 sites statistically filled by an equal number of Pb2+ and A+ cations, while hexagonal channels are completely devoid. Stabilization of this structure was shown to depend critically on the presence of a minimum electronic density within the hexagonal channels, as assured by the lone pairs 6s2 of Pb2+.9 Mean interatomic distances M1−O are larger than M2−O by approximately 0.15 Å.15−18 One might expect that smaller Na+ ions would occupy smaller M2 sites. In spite of such geometrical considerations, Na+ locates predominantly at M1 sites. Intercationic distances M1−M1 (3.44 Å) are shorter than M2−M2 (4.32 Å). The location of less-charged Na+ cations at the M1 sites, leaving the M2 sites with longer cation−cation distances for more highly charged Pb2+, is more energetically

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EXPERIMENTAL SECTION

To study isomorphous substitution in a broad range of compositions, the series of samples Pb8−xLnxNa2(PO4)6Ox/2 with x = 0, 0.05, 0.10, 0.15, 0.20, 0.25, 0.40, 0.60, 0.80, 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0 were prepared by high-temperature solid-state synthesis. In some special cases, samples with intermediate composition were also prepared. As starting reagents for the apatite synthesis, we used PbO, Na2CO3, (NH4)2HPO4, and rare-earth oxides La2O3, Pr6O11, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb4O7, Dy2O3, Ho2O3, Tm2O3, Yb2O3, and Y2O3 provided by Sinbias (Ukraine). Because many of these substances can absorb uncontrolled quantities of water and carbon dioxide at their storage, they were heat-treated before use to remove volatile absorbants. Lead oxide PbO was annealed at 400 °C for 4 h, Na2CO3 at 500 °C for 3 h, and REE oxides at 1050 °C for 4 h. Annealed reagents were cooled to room temperature in a drying 2166

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

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Inorganic Chemistry chamber with freshly calcined silica gel and kept in a desiccator until weighing. Appropriate mixtures of preweighed (±0.2 mg) initial components with a total weight of 1.5 g were thoroughly ground in an agate mortar for 30 min, followed by annealing in an alumina crucible at 300 °C for 3 h to remove volatile substances. In synthesizing apatite solid solutions, we focused on attaining equilibrium in the studied systems at minimum temperatures to reduce possible volatility of lead oxide at high temperatures. To determine the optimum conditions of the synthesis, successive annealings were conducted in the range 400−800 °C in steps of 100 °C and with intermittent grindings after each step.20 The duration of annealing for the last temperature step was determined by attaining a stable phase composition of synthesized samples, as verified by XRD analysis. The following optimum durations (in hours) of annealing at 800 °C were found for the synthesis of single-phase apatites Pb8−xLn xNa2(PO4)6Ox/2 for different Ln atoms in the studied systems: La, 116; Pr, 105; Nd, 50; Sm, 102; Eu, 72; Gd, 72; Tb, 247; Dy, 204; Ho, 208; Tm, 247; Yb, 250; Y, 208. Powder XRD data were collected using modernized electronically controlled DRON-2 and DRON-3 diffractometers, using Ni-filtered Cu Kα radiation at a scanning rate of 2° (2θ)/min. For phase identification, the Match program and PDF-2 (ICCD) database were used. The unit cell parameters were calculated by the least-squares procedure based on 16 unambiguously indexed independent reflections rescanned at 1° (2θ)/min in the range 16 ≤ 2θ ≤ 54°. Si was used as an external standard. To obtain data for crystal structure refinement by the Rietveld procedure, the samples were scanned in steps of 0.05° (2θ) in the range 15° ≤ 2θ ≤ 140° with a counting time of 3 s/step. The data were analyzed with the program FullProf.2k (version 3.40)21 and the WinPLOTR graphical interface.22 As starting data in the refinement, atomic coordinates in calcium hydroxoapatite, as presented in ref 23, were taken. IR spectra were recorded in the wavenumber range from 400 to 4000 cm−1 with a PerkinElmer Spectrum BX spectrophotometer with Fourier transformation. The samples for investigation were first calcined at 600 °C to remove adsorbed water and then pressed into pellets with KBr (1:600) under a pressure of 900 MPa. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopic microanalysis (EDXMA) were applied for determination of the grain shapes and sizes, elemental analysis, and element distribution across the grain surfaces. A JSM-6490LV (JEOL, Japan) scanning electron microscope and INCA Penta FETx3 (Oxford Instruments, England) energy-dispersive spectrometer were used for these purposes. The data for elemental analysis were collected at 25− 30 points in 5−6 fragments of the sample. The electrical conductivity was studied on disk pellets of 0.8 cm diameter and 0.1 cm thickness pressed from synthesized apatite powders under 120 MPa pressure and then sintered at 800 °C for 50 h. The relative densities of the sintered samples were in the range of 86−96% of their theoretical value. Electrodes were deposited as silver paste and fired at 800 °C. Conductivity measurements were conducted in the cycles of heating the samples at 2 °C/min from 300 to 700 °C using a LCR meter DE-5000 (Taiwan) in the range of frequencies from 100 Hz to 100 kHz.

The elemental compositions determined as average values of 25−30 local EDXMA analyses at various points across the sample are presented in Table 1. There is no evidence of Pb Table 1. Results of Elemental Microanalysis of Grains of Synthesized Apatites: 1, Pb8Na2(PO4)6; 2, Pb7.4Gd0.6Na2(PO4)6O0.3; 3, Pb7.6Ho0.4Na2(PO4)6O0.2 element content (found/calcd, mass %) sample

Pb

Na

1 2 3

74.8/72.9 67.6/68.2 69.4/69.7

1.5/2.0 3.6/2.1 3.3/2.0

Ln

P

O

3.6/4.2 2.2/2.9

8.9/8.2 7.8/8.3 7.4/8.2

14.8/16.9 17.4/17.3 17.7/17.1

loss due to PbO volatility during high-temperature synthesis in these data. The difference in the values of experimentally found and calculated element contents does not exceed 2%, which is usually acceptable for such a method of determination.24 Intervals of Isomorphous Substitution. As was established in elaboration of the synthetic procedure, attaining an equilibrium and stable phase composition in Pb8−xLnxNa2(PO4)6Ox/2 systems at 800 °C requires a long annealing time: up to 100 h for light REE elements of the cerium group and 250 h for heavy REE elements of the yttrium group. In particular, Pb8−xHoxNa2(PO4)6Ox/2 samples were annealed for 208 h to reach a stable phase composition. A further increase in the time of heat treatment does not change the correlation between the reflection intensities in the diffraction patterns. In all of the studied compositional range, the peaks of the apatite structure dominate in the X-ray patterns, whereas reflections from HoPO4 and PbO phases appear at x > 0.4 (Figure 1). The intensities of these latter reflections increase

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Figure 1. XRD patterns from the samples in the system Pb8−xHoxNa2(PO4)6Ox/2.

RESULTS AND DISCUSSION The experimental results presented and discussed in this section are illustrated primarily with the data on Pb8−xGdxNa2(PO4)6Ox/2 and Pb(8−x)HoxNa2(PO4)6Ox/2 systems, which have not been published previously. SEM and X-ray Spectroscopy. SEM studies show that synthesized apatite powders consist of equiaxial grains of usually less than 5−10 μm diameter. The microphotographs in characteristic X-ray radiation (Pb Mα1, Na Kα1, Ln Lα1, P Kα1, and O Kα1) reveal a uniform distribution of all of the constituting elements in the samples.

with the REE content. At x = 0.35−040, a very weak peak from a phase with HoPO4 structure may be noticed just above the background. The fact of apatite phase homogeneity and hence isomorphic substitution in the range 0 ≤ x ≤ 0.4 is demonstrated also in the system Pb8−xHoxNa2(PO4)6Ox/2 by the observed tendency toward a decrease in the unit cell parameters a and c (Figure 2), although the total changes of the parameters do not exceed much the measurement error. The decrease of a and c with x is consistent with the difference in the ionic radii of Ho3+ (1.041 Å) and Pb2+ (1.33 2167

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

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Inorganic Chemistry

Å], a substantial increase in the unit cell size is not observed. It follows that the introduction of alkali metals into Pb10(PO4)6(OH)2 additionally compacts the apatite structure most probably because of removal of the OH− anions from the structural tunnels: Pb2+ + OH− → Na+ + □. This minimizes the energy of the anion mutual electrostatic repulsion as well as their repulsion from the stereochemically active electron pairs of Pb2+. In this situation, substitution of REE elements for Pb in Pb8Na2(PO4)6 under the scheme 2Pb2+ + □ → 2Ln3+3+ + O2− produces two opposite effects on the lattice parameters: a decrease due to spatial accommodation of smaller REE ions (the ionic radii change from 1.172 to 1.008 Å in the series La− Yb) in Pb2+ (1.33 Å) sites and an increase due to empty channels filling with O2− anions and increasing electrostatic repulsion between anions and lone electron pairs on Pb2+. This explains why the changes of the unit cell parameters in the homogeneity region of Pb8−xLnxNa2(PO4)6Ox/2 are not large. It makes the exact determination of the substitution limits from such dependences (as in Figure 2, for example) more difficult. To overcome that, the solubility limits of REE elements (xmax) were determined by two methods: the “bend” (inflection) on a plot of the unit cell parameters versus degree of substitution (Figures 2 and 3) and the “disappearing phase” method.33 In the latter case, the intensity of a strong reflection of a nonapatitic phase in the annealed sample is plotted against the REE content in the system’s heterogeneous region. Extrapolation of this linear relationship to the intersection with the abscissa axis (intensity = 0) gives an estimation for the homogeneity region boundary. In Figure 4, such an extrapolation shows xmax at 0.95 in the system Pb8−xGdxNa2(PO4)6Ox/2 in good agreement with the value obtained by the “inflection” method, as shown in Figure 3.

Figure 2. Dependence of the lattice parameters a and c on the degree of substitution in Pb8−xHoxNa2(PO4)6Ox/2.

Å) (here and in the following the ionic radii are given according to Shannon25 for the coordination number 6), although the value of a decreases only by 0.008 Å and c by 0.015 Å. Such a small decrease needs an explanation because the difference in the ionic radii is considerable, r(Pb2+) − r(Ho3+) = 0.289 Å. In the system Pb8−xGdxNa2(PO4)6Ox/2, a decrease in the apatite lattice parameters with x is more distinct (Figure 3), but again it is smaller than may be expected from the difference in the ionic radii.

Figure 3. Compositional dependences of the lattice parameters a and c in the system Pb8−xGdxNa2(PO4)6Ox/2.

To find an explanation for such small changes in the lattice parameters, let us first compare the published values of the unit cell parameters for unsubstituted and substituted alkali metals with lead apatites. As seen from the data presented in Table 2, a substantial decrease in the unit cell parameters, as a result of the partial substitution of alkali metals for Pb in Pb10(PO4)6(OH)2, takes place not only for Na but also and unexpectedly for K, although r(K+) = 1.52 Å > r(Pb2+) = 1.33 Å. Even after substitution by Rb with a still larger ionic radius [r(Rb) = 1.66 Table 2. Unit Cell Parameters and Volumes in Selected Lead Apatites apatite

a (Å)

c (Å)

V (Å3)

ref

Pb10(PO4)6(OH)2 Pb10(PO4)6(OH)2 Pb10(PO4)6(OH)2 Pb8Na2(PO4)6 Pb8Na2(PO4)6 Pb8Na2(PO4)6 Pb8Na2(PO4)6 Pb8Na2(PO4)6 Pb8Na2(PO4)6 Pb8K2(PO4)6 Pb8K2(PO4)6 Pb4Rb(PO4)3 Pb4Rb(PO4)3

9.8612(4) 9.866(3) 9.905 (3) 9.722 9.7249(8) 9.731(3) 9.726(1) 9.734 9.7260(2) 9.827(1) 9.827 9.86 9.888

7.4242(2) 7.426(2) 7.201(3) 7.193 7.190(1) 7.200(2) 7.203(1) 7.200 7.1927(2) 7.304(1) 7.303 7.37 7.412

625.21 625.97 611.8 588.76 588.87 590.42 590.06 590.78 589.22 610.83 610.74 620.49 627.58

26 27 28 29 9 31 32 13 this work 18 13 11 14

Figure 4. Plot of the intensity of the GdPO4 (120) reflection versus degree of substitution (x) in the Pb8−xGdxNa2(PO4)6Ox/2 system.

The determined REE substitution limits in apatites Pb8−xLnxNa2(PO4)6Ox/2 are shown as a function of the ionic radius (r) and atomic number of REE in Figure 5 (our data for Ln = La, Pr, Nd, and Eu have been reported previously20,34−36). There are two linear parts in the plot (La−Gd and Tb−Yb) with a smooth decrease of xmax and a sudden quick fall between Gd and Tb. 2168

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Inorganic Chemistry

Figure 5. Plot of the substitution limit versus ionic radius of REE in Pb8−xLnxNa2(PO4)6Ox/2.

On the whole, the decrease in the REE solubility correlates with the difference in the ionic radii, r(Pb2+) − r(Ln3+), increasing with the Ln atomic number as a result of the Ln contraction. The discontinuous change between Gd and Tb and a steeper change from Tb to Yb correlate exactly with the transition from light (La−Gd) to heavy (Tb−Lu) Ln atoms. Starting from Tb, 4f orbitals are being filled with electrons pairing with ones already present to form 4f lone pairs. It is this exact correlation that let us assume that 4f lone pairs on Ln3+ maintain some level of stereochemical activity (similar to that of lone pairs 6s2 on Pb2+) in spite of the well-known fact of their screening with outer 5s and 5p electrons. Then the drop in the heavy Ln solubility in the lacunary apatite may be related to an increased energy of electrostatic repulsion of Ln 4f lone pairs from anions O2− in the channels and lone pairs on Pb2+ at M2 sites. This correlates also with the much longer periods of time required to reach equilibrium during high-temperature synthesis of apatites doped with heavy Ln atoms. IR Absorption Spectroscopy. The substitutions in the cation sublattices of compounds with tetrahedral oxyanions reveal themselves in IR spectra only indirectly, affecting the atomic vibrations in anion groups.37 Taking that into account, the IR spectra of studied samples were recorded in the region of the internal vibrations of phosphate groups and on the samples with composition inside the homogeneity region. As an example, the IR spectra of samples Pb8−xGdxNa2(PO4)6Ox/2 are shown in Figure 6. The spectra display absorption bands which, according to refs 13, 15, and 31, can be assigned to internal vibrations of (PO4)3− ions: symmetric bending ν2 mode at 445 cm−1, asymmetric bending ν4 at 539 and 580 cm−1, and asymmetric stretching ν3 mode at 987 and 1051 cm−1. The distribution of bands in IR spectra of both substituted and unsubstituted lead−sodium phosphate apatites is presented in Table 3. All main bands reported in the spectrum of Pb8Na2(PO4)613 are present in the spectra recorded for the studied samples except the weak band at 422 cm−1 seen only as a trace in Figure 6 and a broad band at 539−545 cm−1 in the place of resolved bands at 538 (539) and 550 (554) cm−1 according to refs 13 and 31. In the spectra of substituted samples, the frequencies of (PO4)3− vibrations are somewhat higher but do not change noticeably with the atomic number of REE (Table 3). At the same time, these frequencies increase by 2−10 cm−1 with increasing degree of substitution (Figure 6). This is indicative of both the solubility of REE in the Pb8Na2(PO4)6 lattice and an effect of cation substitution on atomic vibrations in anions.

Figure 6. IR spectra of samples in the system Pb8−xGdxNa2(PO4)6Ox/2.

The wave numbers of absorption bands in the spectra of the samples with REE of the yttrium subgroup change in a similar way, but the bands shift less due to lower REE solubility. The behavior of the absorption band at 630−642 cm−1 is different from that of all other bands. It is not found, in the spectrum of Pb8Na2(PO4)6, that its intensity increases with the degree of substitution and its frequency increases with the atomic number of REE (Table 3). This band is not observed in the IR spectra of solid solutions with light REE of the yttrium subgroup and is seen only as a trace in the spectrum of the sample with Nd. This band cannot be related to any admixture and probably is due to the RE−O bond. Peculiarities of the Pb8−xLnxNa2(PO4)6Ox/2 Crystal Structure. As shown previously,9,15 practically all Na+ ions occupy the M1 (4f) sites in the structure of Pb8Na2(PO4)6 apatite. So, in the Rietveld structural refinement of studied apatites Pb8−xLnxNa2(PO4)6Ox/2, sodium was supposed to occupy totally the M1 sites. These refinements have shown that REE ions substitute preferentially in the M2 (6h) sites (Table 4). Cations in the M1 positions are at shorter cation−cation lengths in the apatite structure than those in the triangular M2 sites delimiting the structural tunnels.15 The electrostatic repulsion energy is thus lowered by setting more highly charged Ln3+ ions instead of Pb2+ into the M2 sites with longer intercationic distances. Besides, the M2 sites are surrounded by five (PO4)3− groups, and the M1 sites by six. So, the Ln3+−P5+ repulsion energy is also minimized by placing fewer Ln3+ ions in the M1 sites. 1 5 The only found exception is Pb8−xEuxNa2(PO4)6Ox/2, in which the occupancy of the M1 site by a REE ion is greater than that of M2. Probably, the occupancy of a lattice site depends not only on the substituent ion size and charge but also on the element electronegativity which is for Eu greater than for other RE elements.38,39 Some selected interatomic distances in substituted and unsubstituted lead−sodium apatites are compared in Table 5. The preferential location of REE in the M2 sites results in a decrease in the mean Pb2−O distances due to stronger electrostatic attraction in the M2 coordination polyhedra occupied by REE ions with higher charges and smaller sizes. The former causes also some elongation of the Pb1−O mean distances. However, the distances Pb2−Pb2 in the triangles as 2169

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

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Inorganic Chemistry Table 3. Distribution of Absorption Bands (cm−1) in IR Spectra of Pb8Na2(PO4)6 and Pb8−xLnxNa2(PO4)6Ox/2 Pb8Na2(PO4)6

ν2 ν4

ref31

La, x = 0.8

Pr, x = 0.6

Nd, x = 0.6

Sm, x = 0.6

Gd, x = 0.6

446 538 550 581

451

448

450

449

449

539 580

422 447 539 554 581

544 584 630

545 583 631

545 584 tr

543 584 635

544 585 642

987 1051

921 986 1050

990 1056

1001 1061

1004 1055

991 1056

989 1054

993 1059

445

ν3

Pb8−xLnxNa2(PO4)6Ox/2

ref13

this work

Ca (1.14 Å). Such behavior is determined by an increased electrostatic interaction between cations in the triangle corners and O2− anions in the channels opposite the triangle centers as a result of the replacement under the scheme Ca2+ + OH− → La3+ + O2−. The practical constancy of the Pb,Ln2−Pb,Ln2 and Pb,Ln2− O4 distances is a distinguishing feature of the substitution in Pb-containing Pb8‑xLnxNa2(PO4)6Ox/2 apatites. This indicates that O2− anions in the structural tunnels are unable to come nearer to Pb2 cations as the concentration of anions increases with the degree of substitution due to their repulsion from stereochemically active lone 6s2 electron pairs of Pb2+ ions. As shown by Koumiri et al.,9 five O atoms around Pb2 are set out in the form of an irregular pentagon, and the coordination polyhedron is completed on one side of this pentagon by O2 (forming the shortest bond Pb2−O related in its turn to the longest bond P−O), and on the other side, pointed toward the tunnel axis, by the 6s2 lone pair of the Pb2 cation acting like an entire ligand. Consequently, the values of some interatomic distances in the apatite structure and their changes in the course of isomorphous substitution depend not so much on the sizes of the replacing structural units as on the availability of stereochemically active lone electron pairs in such atoms as Pb2+, Bi3+, or Tl+. It is important to take this factor into account in designing new materials. For instance, the efficiency of luminescent materials depends, in particular, on the distance between the activators. Too short distances Ln2−Ln2 may result in poisoning and quenching of the luminescence. Electrical Conductivity. Temperature dependences of the electrical conductivity (σ) of Pb8−xGdxNa2(PO4)6Ox/2 samples at 1 kHz in the range 300−700 °C are shown in Figure 7 as

Table 4. RE Occupancies of M1 (4f) and M2 (6h) Sites in Pb8−xLnxNa2(PO4)6Ox/2 site occupancy Ln in Pb8−xLnxNa2(PO4)6Ox/2

x

La

0.1 0.2 0.3 0.4 0.5 0.4 0.3 1.0 0.8 0.4

Pr Nd Sm Eu Gd

M1 (4f) 0.049(41)

0.033(42) 0.158(42) 0.351(53) 0.509(50) 0.069(39)

M2 (6h) 0.147(43) 0.151(41) 0.384(41) 0.477(42) 0.467(42) 0.242(42) 0.344(46) 0.649(53) 0.291(50) 0.331(39)

Table 5. Selected Mean Interatomic Distances in the Structure of Pb8−xLnxNa2(PO4)6Ox/2 Compared to Pb8Na2(PO4)6 interatomic distances (Å) cations in phosphate apatite

Pb1−O

Pb2−O

Pb2−Pb2

Pb2−O4

Pb8Na2... Pb7.9La0.1Na2 Pb7.8La0.2Na2 Pb7.7La0.3Na2 Pb7.6La0.4Na2 Pb7.5La0.5Na2 Pb7.6Pr0.4Na2 Pb7.7Nd0.3Na2 Pb7SmNa2... Pb8.2Eu0.8Na2 Pb7.6Gd0.4Na2 Pb7.8Ho0.2Na2

2.603(10) 2.617(9) 2.630(10) 2.653(9) 2.680(9) 2.690(9) 2.663(8) 2.740(7) 2.676(14) 2.583(12) 2.659(8) 2.627(9)

2.553(13) 2.527(13) 2.523(13) 2.523(13) 2.504(13) 2.501 (13) 2.515(11) 2.480(6) 2.423(18) 2.478(18) 2.515(12) 2.559(10)

4.349(6) 4.350(8) 4.339 (5) 4.352(9) 4.337(4) 4.339(4) 4.339(7) 4.340(10) 4.327(9) 4.322(12) 4.355(7) 4.342(4)

2.511(5) 2.505(5) 2.513(5) 2.504(5) 2.505(5) 2.504(4) 2.506(5) 2.497(6) 2.496(7) 2.514(5) 2.514(5)

well as the Pb2−O4 distances do not change noticeably. They depend on neither the ionic radius of REE nor the degree of substitution. In this respect, substitution of RE elements in Pb-containing apatites behaves quite differently from that in calcium or strontium apatites. In the latter case, as in the systems Ca10−xLnx(PO4)6(OH)2−xOx or Sr10−xLnx(PO4)6(OH)2−xOx, the distances M2−M2 and M2−O4 decrease with the degree of substitution.6,40−42 For instance, in Ca 10−xLa x (PO4 ) 6 (OH) 2−x Ox , the Ca,La2−Ca,La2 length changes from 4.052(5) to 3.860(6) Å and Ca,La2−O4 from 2.380(3) to 2.240(4) Å, with x increasing from 0 to 0.80,6 in spite of the ionic radius of La (1.17 Å) being larger than that of

Figure 7. Temperature dependence of the electrical conductivity of Pb8−xGdxNa2(PO4)6Ox/2 samples. Horizontal lines indicate temperature intervals studied in refs 30 and 42. 2170

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

Article

Inorganic Chemistry Arrhenius plots of log(σT) against the inverse temperature (1/ T). Two linear parts with different slopes (distinguished with two black straight lines shown for the sample with x = 0) are seen in these plots corresponding to the regions of intrinsic (at higher temperatures and with a steeper slope) and extrinsic (at lower temperatures) conductivity. The values of the activation energy (calculated from the slopes, tan α, of the straight-line portions of the Arrhenius plots as EA = |tan α| × 2.3R) for intrinsic (EA1) and extrinsic (EA2) regions are given in Table 6 together with the transition Table 6. Volume Densities (ρ, % of the Theoretical Value), Activation Energies in the Intrinsic (EA1) and Extrinsic (EA2) Regions, and Transition Temperatures (Ttr) to the Intrinsic Type of Conductivity for Pb8−xNa2Gdx(PO4)6Ox/2 Samples x ρ (%) EA1 (eV) EA (eV)30 EA2 (eV) EA (eV)19 EA (eV)43 Ttr (°C)

0 92.4 1.26 1.44 0.39 0.35 0.77 535

0.1 94.9 1.36

0.2 90.6 1.70

0.3 91.9 1.59

0.4 86.1 1.33

0.5 88.9 1.31

0.37

0.25

0.25

0.23

0.21

563

549

515

471

458

Figure 8. Compositional dependence of the electrical conductivity of Pb8−xGdxNa2(PO4)6Ox/2 at 650 and 700 °C. Experimental data (black and green) are compared with calculated curves (red).

from the cationic to anionic conductivity. The total ionic conductivity (σi) is related to the ion concentrations and mobilities with the equation σi = σMe + σO = qMec MeμMe + |qO|cOμO

where q is the electric charge, c is the concentration, μ is the mobility of the ion, and subscripts Me and O label the cation and anion properties, respectively. With an increase in the degree of REE substitution (x), the structural channels are filled with O atoms, blocking the movement of cations and creating mobile O2− anions. Assuming a decrease in the cation mobility and the mobile anion concentration directly proportional to x, we get

temperatures (Ttr) to the intrinsic conductivity (determined as the intersections of extrapolated straight-line portions of the plots). In the intrinsic region, the activation energy increases with x at small degrees of RE substitution (0 ≤ x ≤ 0.2) and then decreases with x over 0.2. The activation energy in the extrinsic region decreases with increasing x in the entire studied interval. The results on the activation energy obtained in the studies30,43 of the ionic conduction in Pb8Na2(PO4)6 by complex impedance spectroscopy are also presented in Table 6. The temperature intervals of these measurements are shown with horizontal lines in Figure 7. Comparison with our results shows that the data of Laghzizil et al.30 lie in the region of the intrinsic conductivity and the value of EA is in approximate agreement with our result for EA1. The activation energy found in the alternating-current (ac) conductivity measurements below 600 °C by Brixner and Bierstadt19 is in agreement with our result for EA2 (Table 6), whereas the impedance measurements by Mehnaoui et al.43 relate to the transitional region between the impurity-controlled and intrinsic conductivity, and this explains why their value of EA is almost twice as much as our result for EA2. The conductivity does not change monotonously with the degree of substitution (Figure 8). First, at low values of x, it decreases and reaches a minimum at x = 0.2 and then gradually increases with x. The initial drop in the conductivity is especially pronounced in the sample with Ho: at x = 0.1, the drop is an order of magnitude larger than that for Gd. The temperatures of the transition to intrinsic conductivity behave in a similar way: Ttr increases from x = 0 to 0.1 and then decreases by more than 100 °C to x = 0.5. The values of the activation energy EA1 of the intrinsic conductivity go through a maximum at x = 0.2 (Table 6). Lead−sodium phosphate apatite Pb8Na2(PO4)6 exhibits a predominant cationic conductivity due to a high mobility of Na+ ions along empty hexagonal structural channels.16,30 The observed dependence of σ against x may be described by a simple mathematical model considering a possible transition

O μMe = μMe (1 − ax)

and

cO = bx

where μOMe is the mobility at x = 0. Then, at constant T, the dependence of σi on x is given by σi = A(1 − ax) + Bx

where A = qMecMeμOMe and B = |qO|μOb. Because there is no available data on the ionic diffusivities and mobilities in these apatites, parameters A, B, and b at a given temperature were determined from the experimental values of conduction σi at x = 0 and x = xmax assuming dominant cationic conduction at x = 0. The calculated curves (red) are compared with experimental points in Figure 8 and show a reasonable correspondence. The dependence of the electrical conductivity on the frequency of the electric field (Figure 9) shows an increasing slope of the log σ vs log f plot. This corresponds to the jump relaxation model of hopping movement of a mobile ion.28,44 The conductivity increases with increasing frequency, indicating the existence of an ion jump relaxation during the conduction process. The relaxation is due to the coulomb interaction of the hopping ion and the disorder within the structure in its immediate neighborhood. Such disorder arises along the diffusion paths in the tunnels as a result of Ln3+ substitution for Pb2+. The resulting fluctuating coulomb potential tends to hinder and draw the hopping ion back. These hampered hops may still contribute to the ac conductivity at high frequencies but not at lower frequencies. The slopes of log σ versus log f plots decrease with rising temperature, suggesting a slowing down of the jump relaxation at higher temperatures.28,44 2171

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

Inorganic Chemistry

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Figure 9. Isothermic frequency dependence of the conductivity in Pb7.75Na2Ho0.25(PO4)6O0.125.

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CONCLUSIONS Rear-earth-substituted sodium−lead apatites Pb8−xLnxNa2(PO4)6Ox/2 were synthesized at 800 °C. Attaining an equilibrium and stable phase composition required a long annealing time: up to 116 h for the samples with REE of the Ce subgroup and 250 h for the Y subgroup. The limits of REE solubility (xmax) decrease smoothly with the atomic number within light (La−Gd) and heavy (Tb−Lu) Ln families but with an abrupt drop between Gd (xmax = 0.95) and Tb (xmax = 0.55). This abrupt change correlates with the appearance of 4f lone pairs in the electronic structure of Ln atoms. REE ions substitute for Pb2+ predominantly at Pb2 sites with accretion of anions O2− in void hexagonal structural tunnels according to the scheme 2Pb 2+ + □ → 2Ln3+ + O2−. The substitution produces two opposite effects on the unit cell parameters and interatomic distances: a decrease due to the spatial accommodation of smaller RE ions in Pb2+ sites and an increase due to filling of the empty channels with O2− ions and hence increasing electrostatic repulsion between these anions and active lone 6s2 electron pairs of Pb2+. The interplay of these competitive factors results in a much smaller (than might be expected from the values of the ionic radii) change of the unit cell parameters a and c and practical constancy of such interatomic distances as ⟨Pb2−Pb2⟩ and ⟨Pb2−O4⟩ with increasing degree of substitution. In this respect, REE substitution in the lacunary apatite behaves quite differently from what is observed in broadly studied alkaline-earth hydroxyapatites and fluorapatites with filled hexagonal tunnels. Therefore, REE substitution in lacunary apatite Pb8Na2(PO4)6 is controlled not only by spatial and charge accommodation of REE ions but also by the availability of the stereochemically active electron pair 6s2 on Pb2+. The electrical conductivity at high temperatures depends at a minimum on the degree of substitution, indicating the possibility of a transition from cationic to anionic conductivity. The obtained results may be useful for the development of new functional materials with apatite structure.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +38 095 1363370. Notes

The authors declare no competing financial interest. 2172

DOI: 10.1021/acs.inorgchem.5b02571 Inorg. Chem. 2016, 55, 2165−2173

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