I. INTRODUCTION
A family of compounds with general formula Ca9 R(EO4)7 (R = REE or Bi3+; E = P, V) are isostructural with mineral whitlockite (Calvo and Glopal, Reference Calvo and Glopal1975). The vanadate Ca3(VO4)2 with β-Ca3(PO4)2-type structure consists of isolated VO4 tetrahedra, which are linked with MO n polyhedral via common vertices forming heteropolyhedral three-dimensional quasi-framework (Gopal and Calvo, Reference Gopal and Calvo1973). The crystal structures of whitlockite-type vanadates characterized by the presence of five cation sites (M1, M2, M3, M4, and M5) (Yashima et al., Reference Yashima, Sakai, Kamiyama and Hoshikawa2003) different in size and coordination environment. The M1 and M2 sites are characterized by eightfold oxygen coordination, whereas M3 site has ninefold polyhedron. The smallest M5 site is characterized by octahedral coordination. The environment of M4 and M6 sites are M 4O15 and M 6O13-polyhedra, respectively. Occupation factor of the M4 site varies from zero (fully vacant) to half, which allows for different heterovalent substitutions. Cations distribution in the host lattice has a direct impact on many properties of whitlockite-type compounds.
Ca9Bi(VO4)7 is an advanced material with ferroelectric, ionic conductivity, and non-linear optical properties (Evans et al., Reference Evans, Huang and Sleight2001; Lazoryak et al., Reference Lazoryak, Baryshnikova, Stefanovich, Malakho, Morozov, Belik, Leonidov, Leonidova and VanTendeloo2003). Bi3+ cations with a stereoactive lone electron pair form highly polarisable asymmetric metal–oxygen bonds, which usually leads to increasing of non-linear optical activity of compounds. A similar behavior was established for substances containing Pb2+ cations with similar lone electron pairs (Deineko et al., Reference Deineko, Stefanovich, Mosunov, Baryshnikova and Lazoryak2013). Non-linear optical activity enhancement can be achieved by bivalent metals incorporation forming Ca9−x M x Bi(VO4)7 (M 2+ = Cd2+, Zn2+) solid solution (Malakho et al., Reference Malakho, Vorontsova, Morozov, Stefanovich and Lazoryak2004; Vorontsova et al., Reference Vorontsova, Malakho, Morozov, Stefanovich and Lazoryak2004). Because of the short bond lengths of <Zn–O> in M5 site, more space is available for the highly polarizable Bi3+ atom.
Mean distance <M5–О> in Ca8ZnBi(VO4)7 is 2.15 Å (Malakho et al., Reference Malakho, Vorontsova, Morozov, Stefanovich and Lazoryak2004); however, the same distance in Ca9Bi(VO4)7 is 2.298 Å. Incorporation of larger Pb2+ cations [r VIII(Pb2+) = 1.29 Å (Shannon, Reference Shannon1976)] than Bi3+ [r VIII(Bi3+) = 1.17 Å] extends existing spare space in the whitlockite structure. It provides a retention rotating mobility of VO4 tetrahedra at low temperatures (Deyneko et al., Reference Deyneko, Stefanovich, Mosunov, Baryshnikova and Lazoryak2013) and, as a result, decreasing the Curie points.
In this work, the structure of Ca6.5Pb1.5ZnBi(VO4)7 is refined from powder X-ray diffraction (PXRD) data. Structural details, an effect of crystal structure on the second harmonic generation (SHG) efficiency, and dielectric properties of Ca8−x Pb x ZnBi(VO4)7 solid solution are investigated.
II. EXPERIMENTAL
A. Synthesis of powders
Powders and ceramics of compounds with whitlockite-type structure belong to solid solution Ca8−x Pb x ZnBi(VO4)7 (0 ≤ × ≤ 1.5) were prepared by solid-state method from stoichiometric mixtures of CaCO3 (99.99%), PbO (99.8%), V2O5 (99.8%), ZnO (99.8%), and Bi2O3 (99.8%). The raw materials were homogenized and reacted in Al2O3 crucibles in air at 1193 K during 150 h, and then cooled to room temperature with intermediate grindings every 20 h.
B. Powder diffraction data collection and structure refinement
The XRD peaks of synthesized Ca8−x Pb x ZnBi(VO4)7 (0 ≤ x ≤ 1.5) system were compared with the ICDD-PDF (file 04-005-5986) standard of Ca9Bi(VO4)7. The XRD data for the system indicated the single-phase whitlockite-type structure. The XRD powder pattern is characterized by the absence of impurity reflections. Lattice parameters were determined by the Le Bail decomposition (Le Bail et al., Reference Le Bail, Duroy and Fourquet1988). In the whole range of X, the unit-cell parameters and the volume of compounds gradually change in accordance with Pb2+ amount (Table I).
Unit-cell parameters, SHG signal values [I 2ω /I 2ω (SiO2)] for powders with grain size 40–60 µm, and phase-transition points (T c) in Ca8−x Pb x ZnBi(VO4)7 solid solution.
XRD pattern of powdered sample Ca6.5Pb1.5ZnBi(VO4)7 was collected at room temperature using BRUKER D8 advance powder diffractometer (CuKα 1,2-radiation reflection geometry). The whitlockite-type structure is well known (Calvo and Glopal, Reference Calvo and Glopal1975). There are no significant reflections above 65°. The wide 2θ angular range is usually used to provide more careful refinement (Chen et al., Reference Chen, Liang and Wang1995); therefore, the data were collected up to 2θ ≈ 90°. The main details of the data collection, crystal data, and structure refinement procedure are summarized in Table II. Figure 1 displays observed, calculated, and difference PXRD pattern for Ca6.5Pb1.5ZnBi(VO4)7, which are in a good agreement with whitlockite-type compounds (Beskorovaynaya et al., Reference Beskorovaynaya, Deyneko, Baryshnikova, Stefanovich and Lazoryak2016). Crystal structure was refined by Rietveld method using the JANA2006 software (Dusek et al., Reference Dusek, Petrícek, Wunschel, Dinnebier and Van Smaalen2001; Petricek et al., Reference Petricek, Dusek and Palatinus2014). The choice of a non-centrosymmetric space group was confirmed by the high second harmonic signal.
The final Rietveld refinement plot for Ca6.5Pb1.5ZnBi(VO4)7. The small crosses (×) correspond to experimental values and the continuous line to the calculated pattern. Vertical bars indicate the positions of the Bragg peaks. The lower trace depicts the difference between the experimental and calculated intensity values.
Crystallographic data, details of data collection, and refinement parameters for Ca6.5Pb1.5ZnBi(VO4)7.
The fractional atomic coordinates of Ca6.5Pb1.5MgBi(VO4)7 (Beskorovaynaya et al., Reference Beskorovaynaya, Deyneko, Baryshnikova, Stefanovich and Lazoryak2016) were used for initial structural model. Atomic coordinates and distances were refined using the pseudo-Voigt profile function. Because of small ionic radii of Zn2+ cations [r VI(Zn2+) = 0.74 Å] and based on previous crystal structure refinement of similar compound Ca6.5Pb1.5CdBi(VO4)7 (Petrova et al., Reference Petrova, Deyneko, Stefanovich and Lazoryak2017) at first step, the M5 site [6a: 0 0 0, a i(Zn2+) = 1] was refined. The further refinement of large cation arrangement shows that the M1–M3 sites are predominantly occupied by calcium. Admixture of Pb2+ was localized in the M3 site, while Bi3+ - in the M1–M2 sites. Such cation distribution is in good agreement with similar whitlockite-type compounds (Lazoryak et al., Reference Lazoryak, Baryshnikova, Stefanovich, Malakho, Morozov, Belik, Leonidov, Leonidova and VanTendeloo2003). The M4 site is vacant in accordance with substitution scheme: 3Са2+ → 2Ln3+ + □.
After the last refinement cycle, a good agreement between the observed and calculated patterns was observed. The fractional atomic coordinates, atomic displacement parameters, cation occupancies, and main relevant interatomic distances for Ca6.5Pb1.5ZnBi(VO4)7 are listed in Tables III and IV. A polyhedral representation of the Ca6.5Pb1.5ZnBi(VO4)7 structure along the [001] direction is shown in Figure 2. It shows M 5O6, M 3O9 polyhedra, V2O4 tetrahedra, and position of M4 and M6 vacancies.
(Colour online) Fragment of the Ca6.5Pb1.5ZnBi(VO4)7 structure depicted using coordination polyhedral along the [001] direction.
Structural parameters for Ca6.5Pb1.5ZnBi(VO4)7.
The main interatomic distances (Å) for Ca6.5Pb1.5ZnBi(VO4)7.
Bond-valence sum (BVS) calculations were performed using the bond-length parameters from Krivovichev and Brown (Reference Krivovichev and Brown2001) for Pb2+–O, Krivovichev (Reference Krivovichev2012) for Bi3+–O, and Brown and Altermatt (Reference Brown and Altermatt1985) for Ca2+–O; and V5+–O (Table III). BVSs were obtained by multiplying the calculated sums with the refined site-occupancy factors.
C. Properties investigations
Optical SHG investigations were performed on graduated powders within electric furnace in one channel of optical installation, and 3 µm α-SiO2 powder was used as a standard in the other channel. The two channels were identical and operated in the reflection geometry, as described in (Kurtz and Perry, Reference Kurtz and Perry1968). In each channel, the SHG signal was excited by 1.064 µm radiation of Q-switched pulsed Nd:YAG laser (Minilite-I, f = 15 Hz). Generated in the samples, green light of SH at λ = 0.532 µm was registered. Measured signal from the sample under investigation was calibrated in relation to quartz standard signal from the second channel, so value Q = I 2ω /I 2ω (SiO2) always presented quantitatively SHG activity of the powder in between 293 and 1100 K.
The dielectric parameters were measured in the temperature range from 293 to 1073 K by a two-probe method in frequency range from 0.3 Hz to 1 MHz using Novocontrol Beta-N Impedance analyzer equipped with Probostar A cell. Full reproducibility of σ(T)-curves in heating–cooling cycles indicated retention of quasi-equilibrium conditions in samples in all experiments.
III. RESULTS AND DISCUSSION
SHG analysis indicated higher non-linear optical activity of Pb2+-containing compounds in comparison with Ca9Bi(VO4)7 (Evans et al., Reference Evans, Huang and Sleight2001; Lazoryak et al., Reference Lazoryak, Baryshnikova, Stefanovich, Malakho, Morozov, Belik, Leonidov, Leonidova and VanTendeloo2003). The highest SHG signal corresponds to Ca6.5Pb1.5ZnBi(VO4)7. Incorporation of Zn2+ cations (with smaller ionic radius than Ca2+) into octahedral M5 site results in decreasing of <M5–О> distance in comparison with (Gopal and Calvo, Reference Gopal and Calvo1973) and increasing of coordination polyhedral volume of M1, M2, and M3 sites. Providing more space for stereoactivity of lone electron pairs of Pb2+ and Bi3+ cations leads to an enhancement of the non-linear optical properties.
In accordance with differences of ionic radii of Mg2+ [r VI(Mg2+) = 0.72 Å] and Zn2+ as well as increasing of <M5–О> distance because of replacement of magnesium, the SHG signal decreases by 100 units in comparison with Ca8−x Pb x MgBi(VO4)7 (0 ≤ x ≤ 1.5) (Beskorovaynaya et al., Reference Beskorovaynaya, Deyneko, Baryshnikova, Stefanovich and Lazoryak2016).
In the case of ferroelectric–paraelectric phase transition at high temperatures, structural extension is critically necessary for transformation of polar crystal structure into centrosymmetric ones. Curie temperatures for Ca8−x Pb x ZnBi(VO4)7 solid solution are observed in the temperature range 800–1065 K (Table I), which is significantly lower than T c = 1062 K for previously studied Сa8ZnBi(VO4)7 (Malakho et al., Reference Malakho, Vorontsova, Morozov, Stefanovich and Lazoryak2004), but slightly higher than for Ca8−x Pb x MgBi(VO4)7 (Beskorovaynaya et al., Reference Beskorovaynaya, Deyneko, Baryshnikova, Stefanovich and Lazoryak2016).Transition from paraelectric phase to centrosymmetric group is attributed to structural transformation R3c ↔ R3̄c. Ferroelectric phase transitions are confirmed by SHG and dielectric measurements. Dielectric data of constant ε for Ca8−x Pb x ZnBi(VO4)7 are given in Figure 3. Dielectric spectroscopy and SHG data demonstrate relatively equal of T c and show linear decreasing of their Curie temperature with Pb2+ content.
(Colour online) Temperature dependencies of dielectric constant ε for Ca8−x Pb x ZnBi(VO4)7, 300 kHz.
SUPPLEMENTARY MATERIAL
To view supplementary material for this article, please visit https://doi.org/10.1017/S0885715617000744.
ACKNOWLEDGEMENTS
This work was supported by the RFBR (grant no. 16-33-00197), Foundation of the President of the Russian Federation (grant no. MK-7926.2016.5).
