A. Synthesis of powders

Powders and ceramics of compounds with whitlockite-type structure belong to solid solution Ca_8−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 Ca_8−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).

XRD pattern of powdered sample Ca_6.5Pb_1.5ZnBi(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 Ca_6.5Pb_1.5ZnBi(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.

Figure 1. The final Rietveld refinement plot for Ca_6.5Pb_1.5ZnBi(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.

The fractional atomic coordinates of Ca_6.5Pb_1.5MgBi(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 Ca_6.5Pb_1.5CdBi(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 Ca_6.5Pb_1.5ZnBi(VO₄)₇ are listed in Tables III and IV. A polyhedral representation of the Ca_6.5Pb_1.5ZnBi(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.

Figure 2. (Colour online) Fragment of the Ca_6.5Pb_1.5ZnBi(VO₄)₇ structure depicted using coordination polyhedral along the [001] direction.

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.