Crystal structure, physical properties and bond valence analysis of NaLuP 2 O 7 Anis Béjaoui a, * , Karima Horchani-Naifer a , Mounir Hajji b , Mokhtar Férid a a Laboratoire de Physicochimie des matériaux Minéraux et leurs Applications, Centre National des Recherches en Sciences des Matériaux, BP No. 73, 8027 Soliman, Tunisia b Laboratoire de Valorisation des Matériaux Utiles, Centre National des Recherches en Sciences des Matériaux, BP No. 73, 8027 Soliman, Tunisia article info Article history: Received 28 February 2013 Received in revised form 4 February 2014 Accepted 17 February 2014 Available online 27 February 2014 Keywords: Sodium lutetium diphosphate Crystal structure Ionic conductivity Dielectric relaxation Bond valence analysis abstract Single crystals of a diphosphate NaLuP 2 O 7 have been synthesized by the flux method and characterized by single-crystal X-Ray diffraction. NaLuP 2 O 7 crystallizes in the monoclinic system with P2 1 /n space group with cell parameters: a ¼ 8.9985(8) A, b ¼ 5.3473(5) A, c ¼ 12.756(1) A, b ¼ 103.174 (1), V ¼ 597.67 (9) A 3 , Z ¼ 4. Its structure consists of a three-dimensional framework of P 2 O 7 units that are corner-shared by LuO 6 octahedra, forming tunnels running parallel to [010] which are occupied by Na atoms. NaLuP 2 O 7 powder was characterized by XRD, SEM, FTIR and Raman spectroscopy. The activation energy of (1.49 eV) obtained by electrical measurements suggests the charge carriers to be the sodium cations. The activation energies obtained from impedance and loss spectra were analyzed in order to explain the mechanism of conduction. The correlation between ionic conductivity of NaLuP 2 O 7 and its crystallographic structure was investigated and the most probable transport pathway model was determined. Ó 2014 Elsevier Masson SAS. All rights reserved. 1. Introduction Many studies of phosphates have attracted much attention in recent years, due to their interesting structural and electrical properties to specify some mechanisms of transport [1e6] also physical properties such as pyroelectricity, ferroelectricity, ferro- magnetism and magnetoelectric in LiFeP 2 O 7 [7,8]. The studies of alkali metal lanthanide diphosphates compounds with the formula M 1 LnP 2 O 7 (where M 1 is a monovalent cation and Ln rare earth element or yttrium) have been limited to investigate their interesting conductivity coming from the mobile M 1 ions located in the diphosphates group. The essential structural feature of alkali rare earth diphosphates is a three-dimensional, cation- anion network having an interconnected interstitial space occu- pied by mobile M 1 ions. The relationship between diffusion and structure has been discussed also by Horchani-Naifer and co- workers [9]. By tracking the trajectories of the M 1 ions, most agree that the M 1 ions diffuse through channels, although there is no consensus as to the origin of these channels. Therefore, the ionic conductivity occurs through ion hopping mechanism between adjacent sites having equivalent coordination symmetries. The structural and spectroscopic properties [10e15] of M 1 LnP 2 O 7 have been subject to great interest for a long time. So far, the diphosphates are known to adopt various types of structure depending on the ionic radii of the alkali metal and the rare earth element. They present different crystallographic forms, of which the single crystal structure resolution was firstly reported for CsYbP 2 O 7 (P2 1 /c) [16], KYP 2 O 7 (Cmcm) [17] and NaYP 2 O 7 (P2 1 ) [18]. After literature survey, Férid and coworkers have conducted studies on the structure of the sodium and Ln diphosphates, and have synthesized a new form of NaLnP 2 O 7 . They recognized that the series of the Ln diphosphates are also defined by two different structure types. They described NaPrP 2 O 7 (P2 1 /n) [19], NaEu- P 2 O 7 (P2 1 /n) [20], NaHoP 2 O 7 [6], NaYbP 2 O 7 (P2 1 /n) [21] in the monoclinic system and NaLaP 2 O 7 (Pnma) [22], NaCeP 2 O 7 (Pnma) [9] in the orthorhombic system. It has been shown that di- phosphates compounds change structure with decreasing Ln ionic radius: the NaLnP 2 O 7 diphosphates (La and Ce) crystallize in orthorhombic system (Pnma), while the NaLnP 2 O 7 diphosphates from Pr to Lu crystallize in the monoclinic system (P2 1 /n). In a previous work on sodium lutetium diphosphate, the crystal struc- ture of NaLuP 2 O 7 was obtained via powder XRD Rietveld refine- ment and reported by Yuan & al [23]. In a previous work, we presented a spectroscopic study of NaLuP 2 O 7 doped with ytterbium. This compound has interesting optical properties due to the fact that LueLu distances are relatively * Corresponding author. Tel.: þ216 79 32 54 70; fax: þ216 79 32 53 14. E-mail address: [email protected](A. Béjaoui). Contents lists available at ScienceDirect Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie http://dx.doi.org/10.1016/j.solidstatesciences.2014.02.014 1293-2558/Ó 2014 Elsevier Masson SAS. All rights reserved. Solid State Sciences 31 (2014) 46e53
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Solid State Sciences 31 (2014) 46e53
Contents lists avai
Solid State Sciences
journal homepage: www.elsevier .com/locate/ssscie
Crystal structure, physical properties and bond valence analysis ofNaLuP2O7
Anis Béjaoui a,*, Karima Horchani-Naifer a, Mounir Hajji b, Mokhtar Férid a
a Laboratoire de Physicochimie des matériaux Minéraux et leurs Applications, Centre National des Recherches en Sciences des Matériaux, BP No. 73,8027 Soliman, Tunisiab Laboratoire de Valorisation des Matériaux Utiles, Centre National des Recherches en Sciences des Matériaux, BP No. 73, 8027 Soliman, Tunisia
a r t i c l e i n f o
Article history:Received 28 February 2013Received in revised form4 February 2014Accepted 17 February 2014Available online 27 February 2014
http://dx.doi.org/10.1016/j.solidstatesciences.2014.02.01293-2558/� 2014 Elsevier Masson SAS. All rights re
a b s t r a c t
Single crystals of a diphosphate NaLuP2O7 have been synthesized by the flux method and characterizedby single-crystal X-Ray diffraction. NaLuP2O7 crystallizes in the monoclinic system with P21/n spacegroup with cell parameters: a ¼ 8.9985(8) �A, b ¼ 5.3473(5) �A, c ¼ 12.756(1) �A, b ¼ 103.174� (1),V ¼ 597.67 (9) �A3, Z ¼ 4. Its structure consists of a three-dimensional framework of P2O7 units that arecorner-shared by LuO6 octahedra, forming tunnels running parallel to [010] which are occupied by Naatoms. NaLuP2O7 powder was characterized by XRD, SEM, FTIR and Raman spectroscopy. The activationenergy of (1.49 eV) obtained by electrical measurements suggests the charge carriers to be the sodiumcations. The activation energies obtained from impedance and loss spectra were analyzed in order toexplain the mechanism of conduction. The correlation between ionic conductivity of NaLuP2O7 and itscrystallographic structure was investigated and the most probable transport pathway model wasdetermined.
� 2014 Elsevier Masson SAS. All rights reserved.
1. Introduction
Many studies of phosphates have attracted much attention inrecent years, due to their interesting structural and electricalproperties to specify some mechanisms of transport [1e6] alsophysical properties such as pyroelectricity, ferroelectricity, ferro-magnetism and magnetoelectric in LiFeP2O7 [7,8].
The studies of alkali metal lanthanide diphosphates compoundswith the formula M1LnP2O7 (where M1 is a monovalent cation andLn rare earth element or yttrium) have been limited to investigatetheir interesting conductivity coming from the mobile M1 ionslocated in the diphosphates group. The essential structural featureof alkali rare earth diphosphates is a three-dimensional, cation-anion network having an interconnected interstitial space occu-pied by mobile M1 ions. The relationship between diffusion andstructure has been discussed also by Horchani-Naifer and co-workers [9]. By tracking the trajectories of the M1 ions, most agreethat the M1 ions diffuse through channels, although there is noconsensus as to the origin of these channels. Therefore, the ionicconductivity occurs through ion hopping mechanism betweenadjacent sites having equivalent coordination symmetries.
x: þ216 79 32 53 14.i).
14served.
The structural and spectroscopic properties [10e15] ofM1LnP2O7 have been subject to great interest for a long time. So far,the diphosphates are known to adopt various types of structuredepending on the ionic radii of the alkali metal and the rare earthelement. They present different crystallographic forms, of which thesingle crystal structure resolutionwas firstly reported for CsYbP2O7(P21/c) [16], KYP2O7 (Cmcm) [17] and NaYP2O7 (P21) [18].
After literature survey, Férid and coworkers have conductedstudies on the structure of the sodium and Ln diphosphates, andhave synthesized a new form of NaLnP2O7. They recognized that theseries of the Ln diphosphates are also defined by two differentstructure types. They described NaPrP2O7(P21/n) [19], NaEu-P2O7(P21/n) [20], NaHoP2O7 [6], NaYbP2O7(P21/n) [21] in themonoclinic system and NaLaP2O7 (Pnma) [22], NaCeP2O7 (Pnma)[9] in the orthorhombic system. It has been shown that di-phosphates compounds change structure with decreasing Ln ionicradius: the NaLnP2O7 diphosphates (La and Ce) crystallize inorthorhombic system (Pnma), while the NaLnP2O7 diphosphatesfrom Pr to Lu crystallize in the monoclinic system (P21/n). In aprevious work on sodium lutetium diphosphate, the crystal struc-ture of NaLuP2O7 was obtained via powder XRD Rietveld refine-ment and reported by Yuan & al [23].
In a previous work, we presented a spectroscopic study ofNaLuP2O7 doped with ytterbium. This compound has interestingoptical properties due to the fact that LueLu distances are relatively
Table 1Crystallographic data, recording conditions and refinement results for NaLuP2O7.
Diffractometer Nonius Kappa CCDFormula NaLuP2O7
Formula weight 371.90Temperature 293(2) KWavelength 0.71073 �A (Mo)Crystal system MonoclinicSpace group P21/n (no.14)Unit cell dimension a ¼ 8.9985(8) �A, b ¼ 5.3473(5) �A
c ¼ 12.756(1) �A, b ¼ 103.174� (1)Volume, Z 597.67 (9) �A3, 4Density (calculated) 4.133 g cm�3
Absorption coefficient 17.109 mm�1
F(000) 672Theta range for data collection 3.14�e31.87�
Limiting indices �13 � h � 13, �7 � k � 7, �18 � l � 18Reflections collected 8098Independent reflections 1992Absorption correction IntegrationRefinement method Full-matrix least-square on F2
Goodness-of-fit on F2 1.088Final R indices [I > 2s(I)] R1 ¼ 0.0358, wR2 ¼ 0.0907R indices (all data) R1 ¼ 0.0373, wR2 ¼ 0.0925Extinction coefficient 0.031(2)
Table 2Atomic coordinates and equivalent isotropic displacement parameters for NaLuP2O7.
Atom Wyck. x/a y/b z/c Uéq
Lu 4e 0.73087(2) 0.23641(3) 0.97599(1) 0.0172(1)Na 4e 0.8609(3) �0.2259(3) 0.8063(2) 0.0228(4)P(1) 4e 0.5285(2) �0.2506(2) 0.8468(1) 0.0182(3)P(2) 4e 0.9306(1) 0.7182(2) 1.1179(1) 0.0177(2)O(1) 4e 0.4397(6) �0.2597(5) 0.9331(4) 0.0222(8)O(2) 4e 0.6412(3) �0.4671(6) 0.8538(2) 0.0192(5)O(3) 4e 0.6092(3) �0.0036(6) 0.8397(2) 0.0195(5)O(4) 4e 0.4039(4) �0.2800(5) 0.7355(3) 0.0189(6)O(5) 4e 1.0943(4) 0.7943(6) 1.1229(3) 0.0210(6)O(6) 4e 0.9072(3) 0.4396(5) 1.0970(2) 0.0194(5)O(7) 4e 0.8156(3) 0.8750(6) 1.0418(2) 0.0214(5)
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e53 47
large, leading to a very weak concentration fluorescence quenching[24]. The structural study of NaLuP2O7 is characterized by a three-dimensional structure and showed that it has tunnels along the[010] which do not communicate with each other. In these tunnelsare located the Naþ ions who is the charge carrier, indeed, thestructural study requires that the process of ion transport can beassumed as due to displacements of Naþ ions in the direction of thetunnels ([010]). Although the ionic conductivity of NaLuP2O7 showsthat this compound is a weak ionic conductor, the study of thecorrelation between the structure and the ionic conductivity re-mains interesting to indicate the most likely paths of ionic con-duction and to clarify transport mechanisms.
In this paper, we will describe, for the first time the synthesismethod of NaLuP2O7, with its crystal structure solved by usingsingle crystal X-ray diffraction data. The ionic conductivity mea-surements of NaLuP2O7 powder were performed as function oftemperature. The transport mechanism for ionic conductivity wasinvestigated. The most probable sodium conduction pathway aresimulated and discussed as function of NaLuP2O7 structure.
2. Experimental
2.1. Synthesis
NaLuP2O7 crystals were grown by the flux method. Three gramsof sodium carbonate NaPO3 and 0.5 g of Lu2O3 (Fluka, 99.99%) asstartingmaterials weremixed. The solutionwas gradually heated inplatinum crucible to 1000 �C for 20 h, then cooled and maintainedat 600 �C for 10 h, then cooled to room temperature. A colorless,transparent and parallelepiped crystals are obtained by this pro-cedure. The crystals were separated by washing the product inboiling water.
After structure determination, a polycrystalline sample wassynthesized by a conventional solid-state reaction starting fromstoichiometric proportions of the rawmaterial constituents. Na2CO3(ALDRICH, 99%), (NH4)2HPO4 (MERK, 99%), Lu2O3 (Fluka, 99.99%)were used. Themixturewas ground in an agatemortar to ensure thebest homogeneity and reactivity, then placed in a porcelain crucibleand heated from room temperature to 500 �C, 600 �C and 710 �Cduring 48 h for each temperature. At the end of each heating period,the mixture was well ground and samples were taken from thismixture for X-ray diffraction and infrared spectroscopy analysis. Themorphology was investigated using scanning electron microscopy(SEM) analysis for the sample treated at 710 �C.
2.2. Measurements
Powder XRD measurements were carried out at room temper-ature on a PANAnalytical X’PERT Pro diffractometer with Cu Karadiation of wavelength 1.5418�A and 2q values between 5� and 70�.
The structure was determined from single crystal X-raydiffraction data, collected at room temperature by Nonius KappaCCD diffractometer using monochromated Mo-Ka radiation(l ¼ 0.7107 �A); 8098 reflections were measured for 1992 inde-pendent reflections. The systematic absences k ¼ 2n þ 1 for 0 k0 and h þ l ¼ 2n þ 1 for h 0 l indicated the monoclinic space groupP21/n. The datawere solved and refined using SHELX-97 [25,26]. Allcalculation were performed using the WinGX crystallographicsoftware package [27]. The position of the lutetium atom was ob-tained using the Patterson heavy atom method [26] and successiveFourier analysis allowed the other atoms to be located. A finalrefinement cycle using all atomic positions and including aniso-tropic displacement parameters led to the reliability factorsR ¼ 0.0358 and WR ¼ 0.0907. The recording conditions and crys-tallographic data are reported in Table 1. The atomic isotropic
displacement coordinates parameters were refined using a full-matrix least-square method and they appear in Table 2. Bond dis-tances and angles calculated from the final atomic coordinates aregiven in Table 3.
The IR spectra of anionic group of the NaLuP2O7 are recorded ona Perkin Elmer (FTIR 2000) spectrometer in the range of 400e4000 cm�1. Sample in powder form was pressed into disk usingpellet of KBr. The Raman spectrum was recorded at room temper-ature using a Renishaw RM 1000 spectrometer equipped with CCDcamera and Argon source (514.5 nm) at 20 mW. The morphologywas investigated with scanning electron microscopy (SEM) (FEIQUANTA 200).
The conductivity measurements were carried out by the com-plex impedance method. The powder sample of NaLuP2O7 werecrushed and pressed into disks at 6t/cm2 with 13.18 mm in diam-eter and 1 mm in thickness. A layer of silver paint was deposited onthe edges to ensure good electrical contact between the sample andthe Pt electrical junctions. The ac impedance measurements weremade using HP 4192A impedance analyzer in the range from 1 to13000 Hz between 703 and 863 K.
3. Results and discussion
3.1. Powder phase analysis
The powder diffraction pattern of NaLuP2O7 was consistent withthat calculated from the structure determined by single crystal
Table 3Bond distances (�A) and angles (�) in NaLuP2O7.
Symmetry codes: (i) 1 � x, �y, 2 � z; (ii) x, �1 þ y, z; (iii) 2 � x, 1 � y, 2 � z; (iv) x,1þ y, z; (v) 1.5� x, 0.5þ y, 1.5� z; (vi) 2� x,�y, 2� z; (vii) 1.5� x,�0.5þ y, 1.5� z;(viii) �0.5 þ x, 0.5 � y, �0.5 þ z; (ix) 0.5 þ x, 0.5 � y, 0.5 þ z.
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e5348
X-ray diffraction. However, the calculated and experimental pow-der XRD patterns are totally similar from that reported previously(ICDD card No. 41-0418) [28]. It shows that the product wasessentially a single phase. All of the peaks observed in the experi-mental powder XRD pattern were indexed to a pure monoclinicphase with space group P21/n (no.14) (Fig. 1). The refined unit cellparameters correspond to NaLuP2O7: a ¼ 12.762 (5) �A, b ¼ 5.371(2) �A, c ¼ 9.028 (4) �A, b ¼ 103.369 (6)�, Z ¼ 4. Fig. 2 shows themorphology of NaLuP2O7 powder particles sintered at 710 �C. Thesample consists of prisms shaped with a wide distribution by sizebut also submicron particles slightly rounded and the powderparticles have a size of approximately 1e5 mm.
The infrared and Raman spectra of polycrystalline powderregistered at room temperature are presented in Fig. 3. The fre-quencies of the P2O7 groups are assigned on the basis of the
characteristic vibrations of the PeOeP bridge and PO3 groups [29].The strong and broad absorption bands observed in the 1257e1100 cm�1 region are attributed to the asymmetric stretching vi-bration (yas) of PeO in the PO3 group. The bands due to the sym-metric stretching vibration (ys) of PO3 are generally observed in the1100e1022 cm�1 region [29]. We note that the vibration fre-quencies of PO3 are expected to be higher than those of PeOePbecause the PeO bond in the PO3 groups is stronger than that in thePeOeP bridge. The IR bands recorded at 758 and 966 cm�1 areattributed respectively to the symmetric and asymmetric (ys andyas) of PeOeP bridge [30,31]. The bands due to d(PO3) and d(POP)deformations are observed in the regions 585e419 cm�1 (Table 4).
In the Raman spectrum of NaLuP2O7, the symmetric vibrationmodes of ys(PO3) and ysPeOeP are located, respectively, between1080e1000 cm�1 and 800e750 cm�1 as medium infrared bandsand strong Raman line. The lines observed located around 1200e1090 and 1000e900 cm�1 can be attributed respectively to theasymmetric stretching vibrations (yas) of PO3 species and of PeOePbridges. In the region below 600 cm�1, it is very difficult todistinguish between the asymmetric (das) and symmetric (ds) modeof PO3 species and dPeOeP bridge. Moreover, these modes overlaywith external modes [31]. A comparison between the Raman andinfrared bands positions shows that the majority of them arecoincident.
3.2. Description of the structure
NaLuP2O7 crystallizes in the monoclinic system with the spacegroup P21/n. The asymmetric unit contains 11 atomic positionsincluding one for the Na atoms, one for the Lu atoms, two for theP atoms and seven for the O ones. All these positions are occu-pying general positions of space group P21/n. The atomicarrangement of this structure is characterized by a three-dimensional framework of PO4 tetrahedra (forming P2O7 groupsvia corner-sharing) and LuO6 octahedra leading to narrow tunnelsparallel to [010] which are occupied by Na atoms. This frameworkis composed by four crystallographically building blocks: fourNaO7 polyhedra, four LuO6 octahedra, and four P2O7 diphosphatein the unit cell where the cohesion of the structure is provided bybridges Lu-O-P and NaeOeP. The projection of the structure isshown in Fig. 4.
In this structure, the P2O7 formed by P(1) and P(2) atomsbound by bridging oxygen O(4) atoms. These groups adopt theeclipsed configuration with P(1)eO(4)eP(2) angle equal to 125.6(2)�. The distances PeO are typical of a diphosphate unity inwhich the longer distances 1.604(4) and 1.607(4) (�A) characterizethe PeOeP bridge, whereas the shorter PeO distances corre-spond to the external bond. The values of angles OePeO vary inthe interval 104.8 (2)e114.4 (2) �. Fig. 5 shows that the P2O7groups adopt a staggered orientation with P(1)eO(4)eP(2) angleequal to 125.6 (2)�, this result confirms what was found in pre-vious work. In the orthorhombic system [22,9], the P2O7diphosphate groups adopt an eclipsed orientation of the two PO3groups through PeOeP bridge, but with the monoclinic system[19e21], the P2O7 diphosphate groups adopt a staggeredorientation.
The Lu atom is coordinated by six oxygen atoms forming a dis-torted octahedron that belong to six P2O7 anions. The corre-sponding LueO distances range from 2.128(6) to 2.241(3) (�A). Theminimal distance between two atoms of lutetium is 5.019 (�A). TheLuO6 polyhedra are isolated from each other in the sense that theydo not share any oxygen atom. In our and other previous works, indiphosphates compounds with the formula NaLnP2O7, theLanthanum [22], Cerium [9] and europium [20] cations are coor-dinated by nine and eight oxygen atoms, whereas in NaYbP2O7 and
Fig. 1. Experimental and calculated XRD pattern of NaLuP2O7.
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e53 49
NaLuP2O7 the coordination number is six. The difference of the rareearth coordination can be explained by the size effect of the cations,but electronic configuration of the rare earth element may also playan important role.
The sodium ion is coordinated with seven oxygen atoms withNaeO distances falling in the 2.445(4)e2.967(4) (�A). The NaO7polyhedra form infinite zigzag chains by sharing (O2, O3 and O5)and running parallel to the crystallographic b-direction. Maininteratomic distances and angles are listed in Table 4. As com-parison with the structure of NaHoP2O7 [6], the both structurescrystallize in the monoclinic system with space group P21/n, butwe can see that there are some differences. We can deduce thatthe orientation of the P2O7 group and the coordination poly-hedron of the sodium atom is not the same in both structures. Itcan be noted that the coordination numbers of Na atom is sevenin NaLuP2O7 and the polyhedron of the sodium atom shares aface (O5, O3 and O2) with a neighboring polyhedral but it isdifferent of that of Na in NaHoP2O7 where it is surrounded by sixatom of oxygen and shares an edge (O3, 02) with neighboringpolyhedral.
Fig. 2. SEM morphology of NaLuP2O7 powder.
3.3. Impedance spectroscopy analysis
3.3.1. ConductivityThe complex impedance spectroscopy is an important tool to
clarify the electrical conductivity and to distinguish the ion trans-port mechanism by means of the correlation between the sampleelectrical behavior and its structure. The electrical conductivitygenerally consists of the both ionic and electronic conduction. Theelectronic conductivity in oxides is due to overlapping of non-completely filled d or f orbitals of cations or to electron hoppingfrom aliovalent ions. In the title compound the conductivity shouldbe totally ionic, as lutetium shows only one valence state (Lu3þ).The complex impedance diagrams as a function of the temperatureshowing �Z00 versus Z0 are shown in Fig. 6. They show that theinvestigated compound follows the ColeeCole law. The values ofthe conductivity as a function of the temperature range froms ¼ 4.87 � 10�7 U�1 cm�1 at 703 K to s ¼ 3.81 � 10�5 U�1 cm�1 at863 K.
The response in Z0 plane has the form of semi-circular arcpassing through the origin. The electric response was further fittedby a parallel RC equivalent circuit in the frequency range analysis,where R represents the bulk resistance and C the bulk or geometriccapacitance of the samples [32e34]. The electric conductivity of thebulk, s, was derived from bulk resistance values (Table 5). Thoseresults are used elsewhere to show the evolution of the conduc-tivity versus reciprocal temperature Log10(sT) ¼ f (103/T) for thetitled compound (Fig. 7).
In the temperature range 703 Ke863 K, the experimental pointsare located on one side of a line corresponding to low and hightemperature behaviors. An Arrhenius-type law (sT¼ s0 exp (�DEs/KT)) characterizes this temperature domain. The plot form oflog(sT) versus 1000/T is linear, the conductivity value iss ¼ 3.81 � 10�5 U�1 cm�1 at 863 K and the ionic jump activationenergy is 1.49 eV. This material shows similar conductivity per-formances, as compared to the compound NaCeP2O7 (Ea ¼ 1.39 eV)[9].
3.3.2. Frequency responseThe formalism of complex modulus M* ¼ juC0Z* ¼ M0 þ jM00 is
used to determine the parameters of charge carriers such as fre-quency hopping and relaxation time. This formalism, with respect
Fig. 3. IR (a) and Raman (b) spectra of NaLuP2O7 powder.
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e5350
to the complex impedance, allows to cross problems related tograin boundary effects, polarization of electrodes and other inter-face effects in solid electrolytes [35]. To verify the contribution ofthese phenomena in the process of conduction, we examined thevariation of the real part M0 of the complex modulus at differenttemperatures depending on the frequency shown schematically inFig. 8. This graphic representation shows thatM0 tends to a constantlimit value M0
N ¼ 1/ 3’N in the areas of temperature and frequencyswept. It is also worth noting that, for low frequencies, M0 tends tolow values; indicating that the phenomena mentioned above canbe neglected when the electrical data are analyzed by the complexmodulus formalism [36,37].
On the other hand, the variation of the normalized M00/M00max
imaginary part versus log (f) for the diphosphate NaLuP2O7 hasbeen evaluated at various temperatures and is presented in Fig. 9.At a given temperature, these spectra show asymmetric relaxationpeaks centered in the dispersion region of M00 whose maximumfrequency fp is displaced to higher values as the temperature in-creases. The significant asymmetric broadening of the peaks withincrease in temperature suggests the existence of a temperaturedependent electrical relaxation phenomenon in the material with aspread of relaxation time. The region to the left of the peak is where
Table 4Mode frequencies cm�1 in NaLuP2O7.
IR Raman Assignment
1226 m 1177 m yas(PO3)1172 vs 1149 s1146 vs 1139 s1110 s 1098 s1084 m 1077 vs ys(PO3)1063 m 1063 s1023 vw 1056 m959 vs 934 vw yas(POP)759 s 775 vs ys(POP)652 w 587 vw d(PO3)þ585 m 553 m d(POP)564 s 525 m527 vs 488 w480 m 429 vw420 w
376 s External mode280 m166 vw111 vw
Note: vs: very strong; s: strong; m: medium; w: weak; vw: very weak.
the Naþ ion is mobile over long distances; the region to the right iswhere the ions are spatially confined to their potential wells.
Fig. 10 shows the curves M00/M00max ¼ f (log f � log fp) in the
temperature range between 703 K and 853 K. We see that thevalues of the full width at half maximum (FWHM) is almostconstant as a function of temperature and are of the order of 39 Hz(log f z 1.59). These curves show the existence of a single relaxa-tion mechanism therefore one mechanism of ion transport.
The mechanism of ion conduction is determined from the var-iations of the frequency fp ¼ 1/2pss relaxation and conductivity as afunction of temperature. Fig. 7 shows the variation of the peakfrequency (fp) as function of temperature and it obeys Arrheniusrelation.
fp ¼ fpo exp�� Ef =kT
�
The plot form of Ln (fp) versus 1000/T is linear with activationenergy (Efp) for the relaxation process of 1.45 eV. It is almost thesame as that of the activation energy for conduction(Ea ¼ 1.49 eV). The close value of activation energies obtainedfrom the analyses of M00 and conductivity data confirms that the
Fig. 4. Perspective view of the NaLuP2O7 showing cavities where the Naþ ions arelocated.
Fig. 5. Projection of the NaLuP2O7 diphosphate with anisotropic displacement pa-rameters draw at 50% probability level showing different interatomic distances and thesymmetry code: (viii) �1/2 þ x, 1/2 � y, �1/2 þ z.
Table 5Ionic conductivity (s) of NaLuP2O7.
T (K) R (U) s (U�1 cm�1)
703 150260 4.87784 � 10�7
713 120070 6.10408 � 10�7
723 94644 7.7437 � 10�7
733 72932 1.00496 � 10�6
743 58212 1.25908 � 10�6
753 43238 1.69511 � 10�6
763 32745 2.23838 � 10�6
773 25114 2.91849 � 10�6
783 19604 3.73875 � 10�6
793 14679 4.99321 � 10�6
803 11552 6.34485 � 10�6
813 8167.8 8.97368 � 10�6
823 5984.9 1.22468 � 10�5
833 4860.3 1.50805 � 10�5
843 3407 2.15133 � 10�5
853 2771.4 2.64472 � 10�5
863 1919.0124 3.81945 � 10�5
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e53 51
transport is through ion hopping mechanism in NaLuP2O7. Thistransport mechanism is thermally activated to overcome the po-tential barrier [38].
4. Conduction paths simulated by the model BVS
The BVS model found one of its applications in a correlationbetween the structure and the ionic conductivity. It identifies themobile species and helps to determine the mechanisms of con-duction, as show by several authors including: Adams hasextended this approach to anionic conductors [39,40], Leblancet al. in the borates [41] and Ouerfelli et al. in the diarsenates[42,43]. Mazza [44] shows that the bond valence sum V (x,y,z) iscalculated for any point (x,y,z) of the interstice of anionicnetwork. By moving the arbitrary point (x,y,z) over a gridcovering the whole unit cell volume, one can find the probabletrajectory for cationic charge possessor. The direction is not fixedduring the path and the ion is left free to direct itself followingthe lowest V (x,y,z) way inside a solid angle with an iterativeprocess.
Fig. 6. Complex impedance diagrams of NaLuP2O7 at different temperatures (703 Ke813 K).
The application of this model to the compound NaLuP2O7 showsthe most probable paths according to the directions [010] and [111](Fig. 11). In the direction [010], the sodium traveled a distance of 4�Awhen he moves from its site to another neighbor. Fig. 12 shows thatif the Na cation moves in the [010] direction, it must overcome thebottlenecks limited by O2, O3 and O5, while the position of Naþ hasan average distance <NaeO> ¼ 1.89 �A. Along this direction, themaximum value of the sum of valence bonds is V (d) ¼ 1.92 whilstthe minimum is V (d) ¼ 1.1. Points in the ionic pathways with thelowest V values correspond to stable positions, the highest valuesare associated with bottlenecks. The large difference between theminimum and maximum V values (0.8) implies that motion seemsdifficult.
The Naþ motion appears to be more easily along the [111] di-rection connecting two Na ion in the same position. Fig. 13 showsthat if the cation Na þ moves in the [111] direction, it must gothrough the [010] direction, then the sodiummoves in the structure(zigzag direction) and passes through an interstitial site when ittravels between two LuO6 polyhedra and two P2O7 diphosphates.Before reaching its equivalent site, the Naþ must first pass througha potential barrier (bottlenecks) when the value of the sum ofvalence bonds V (d) ¼ 1.7. By comparing the values of the sum ofvalence bonds found for each position, we can say that the path[111] is more favorable to the movement of sodium and the NaeNacommunication may be possible at high temperatures, requiringmuch of energy.
5. Conclusion
In this work, the chemical preparation and crystal structure ofNaLuP2O7 are described for the first time. This diphosphate
Fig. 7. (a) The log sT vs 1000/T plot. (b) The log fp vs 1000/T plot, where fp is theM00max
peak frequency.
1 2 3 4 5 6 7 8-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0 703 713 723 733 743 753 763 773 783
793 803 813 823 833 843 853 863
log
M'
log f (Hz)
(Ω)
Fig. 8. Graphical representation of the real part M0 as function of frequency.
1 2 3 4 5 6 7
0.0
0.4
0.8
823 833 843 853 863
703 713 723 733 743 753 763 773 783 793 803 813
M"/
Mm
ax
log f (Hz)
Fig. 9. Graphical representation of M00 normalized as function of frequency.
Fig. 11. Bond valence sum for sodium ions vs. the covered distance.
Fig. 12. Representation of the conduction path of sodium along [010].
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e5352
crystallizes in the monoclinic system (P21/n). The powder ofNaLuP2O7 has been synthesized by solidestate reaction andcharacterized by SEM, XRD, FTIR and RAMAN. X-ray diffractiondata shows that NaLuP2O7 was a single phase and the conduc-tivity has subsequently been investigated as a function of tem-perature. It shows an ionic conductivity and activation energy(Ea ¼ 1.49 eV) corresponding to the mobility of the Naþ cationsalong one dimensional tunnel. The relaxation is examined usingcomplex electric modulus formalism in view of the medium ionicconductivity. The activation energies obtained from the imped-ance and modulus spectra are close, suggesting that ionic trans-port in the material investigated can be described by hoppingmechanism. The coupling of the structural analysis with the BVS
-4 -3 -2 -1 0 1
0,0
0,2
0,4
0,6
0,8
1,0
M''/
M'' m
ax
logf-logfp (Hz)
logf/(logf0=logfp)
793 803 813 823 833 843 853 863
703 713 723 733 743 753 763 773 783
FWHM
Fig. 10. Plots of M00/M00max against log f � log f0 at different temperatures.
model for NaLuP2O7 has better measurements interpretation ofthe ionic conductivity and presents the modeling conductionpaths of monovalent cations. The most probable conductionpathways are determined. It appears that Naþ ions move alongtunnels created by P2O7 diphosphates and LuO6 polyhedra in the[111] direction.
Fig. 13. Schematic representation of the structural arrangement of NaLuP2O7 showsthe sodium conduction pathway along the [111] direction.
A. Béjaoui et al. / Solid State Sciences 31 (2014) 46e53 53
Acknowledgment
This work is supported by the Ministry of Higher Education andScientific Research in Tunisia.
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