β-Ca₃(PO₄)₂-related structure and dielectric properties of Ca₈CdLa(PO₄)₇

Abstract

A Ca₈CdLa(PO₄)₇ phase was prepared by a high-temperature solid-state reaction in air. The bulk and local cation composition was determined by inductively coupled plasma atomic emission spectroscopy and by energy-dispersive X-ray spectrometry. Second-harmonic generation, differential scanning calorimetry and dielectric measurements revealed the presence of a reversible ferroelectric first-order phase transition from a ferroelectric β-phase (space group (SG) R3c) to a paraelectric β′-phase (SG R3̄c). The phase transition temperature, T_c, is 865 ± 10 K. The β-Ca₃(PO₄)₂ (β-TCP) related structure was refined by the Rietveld method in the SG R3c using powder synchrotron X-ray diffraction data. The distribution of Ca²⁺, Cd²⁺ and La³⁺ cations among the sites of the β-TCP-type structure was found. According to crystal structure refinement, M5O₆ octahedra are occupied by Ca²⁺ and Cd²⁺ (M5 = 0.307(6)Ca²⁺ + 0.693(6)Cd²⁺) while Ca²⁺ and La³⁺ cations occupy M1 and M3 sites of the β-TCP-type structure. Analysis of the difference electron density map [ρ_dif: (x; y; z)] revealed the presence of small residual electron density at the M4 site. The M4 position is partially occupied by Ca²⁺ cations (M4 = 0.131(6)Ca²⁺). The elemental composition after the Rietveld refinement is determined as Ca_8.61Cd_0.70La_0.82(PO₄)₇. Conductivity measurements revealed that the calculated σ_bulk (σ_bulk = 4.01 × 10⁻⁶ S cm⁻¹ at 900 K and σ_bulk = 1.49 × 10⁻⁴ S cm⁻¹ at 1270 K) for Ca_8.61Cd_0.70La_0.82(PO₄)₇ was lower than one for other β-TCP-type compounds.

---

1. Introduction

Ca₈MLn(AO₄)₇ (M = Mg, Zn, Ca; Ln = rare-earth elements (REE); A = P, V) compounds with the β-Ca₃(PO₄)₂-type (β-TCP) structure¹ attract attention due to their applications as phosphors² and lasers,³ nonlinear optical,⁴ bioactive,⁵ ferroelectric⁶ and antiferroelectric⁷ materials. Substitution of Ca²⁺ by various cations in the β-TCP-type structure allows obtaining materials with multifunctional properties and fine-tuning several of them. The introduction of some cations (Mg²⁺,⁸ Zn²⁺,⁹ Sr²⁺¹⁰) into the β-TCP-type structure reduces the ferroelectric transformation temperature or even suppresses the ferroelectric ordering. In particular, in the case of Ca₉Ln(PO₄)₇ phosphates, the substitution of Ca²⁺ with Mg²⁺,¹¹ Zn²⁺,¹² or Cd²⁺ (ref. 13) leads to a change in the structure at room temperature (T_R) from non-centrosymmetric (space group (SG) R3c) for Ca₉Ln(PO₄)₇ phosphates to centrosymmetric (SG R3̄c) for Ca₈MLn(AO₄)₇ (M = Mg, Zn, Cd; Ln = REE; A = P, V), and transformation of ferroelectrics¹⁴ to antiferroelectrics.¹⁵

A similar change of ferroelectric to antiferroelectric phase was found in Ca_9.5–1.5xMgEu_x(PO₄)₇ during step-by-step substitution of Ca²⁺ by Eu³⁺, which formed cation vacancies in the structure.¹⁶ The polar structure with SG R3c corresponds to compositions where 0 ≤ x < 1, while Ca₈MgEu(PO₄)₇ exhibits an antiferroelectric phase. In Ca_3−xSr_x(PO₄)₂ solid solutions, increasing the Sr²⁺ content from x = 0 to x = 12/7 ¹⁰ reduces the ferroelectric-to-paraelectric phase transition temperature from 920 K to 520 K. This change also decreases the second-harmonic generation response at T_R from 3.2 to 0.04, with a maximum at x = 5/7. Further increasing the Sr²⁺ content from x = 12/7 to x = 13/7 changes the structure symmetry from R3c to R3̄m at the ferroelectric–paraelectric phase transition point (T_c).

A ferroelectric transition proceeds from a ferroelectric β-phase (SG R3c) to a paraelectric β′-phase (SG R3̄c) while an antiferroelectric transition happens from an antiferroelectric β-phase (SG R3̄c) to a paraelectric β′-phase (SG R3̄m).^8,9

In this work, we describe the structure and thermal, dielectric, nonlinear optical and ion-conducting properties of the β-TCP-related Ca_8.61Cd_0.70La_0.82(PO₄)₇ phosphate.

2. Experimental

2.1. Materials and sample preparation

A Ca₈CdLa(PO₄)₇ (CCLP) phase was prepared by a high-temperature solid-state reaction in air from stoichiometric amounts of CaCO₃ (99.9%), CdO (99%), La₂O₃ (99.99%) and CaHPO₄·2H₂O (99.9%). All chemicals are commercial products from Sigma-Aldrich. The synthesis was performed in alumina crucibles at 1373 ± 10 K for 100 h. During the synthesis, the samples were ground every 24 hours of firing. After the final annealing, the samples were slowly cooled in a furnace from 1373 K to T_R. An annealing temperature of 1373 K was used by analogy with previous studies.¹⁷

2.2. Characterization

The bulk cation composition of CCLP was determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES) on an Agilent ICP-AES 5100 with an SPS4 autosampler device. Substances were previously dissolved in hydrochloric acid (37%, ISO grade). Calibration functions for elements were found using solutions of Ca, Cd and Eu. The collection of the emission was carried out at several wavelengths, and the obtained values were averaged. The local cation composition of CCLP was determined by energy-dispersive X-ray spectrometry (TEM-EDX) using a probe aberration corrected ThermoFisher Titan Themis Z transmission electron microscope at 200 kV equipped with a Super-X system for EDX analysis and an EDAX attachment. A sample for TEM was prepared by crushing powders in an agate mortar and dispersing them in methanol. A few drops of the dispersion were placed on copper grids with a holey carbon film. The EDX measurements of the Ca/Cd/La ratio were provided for probe diameters of 100–200 nm.

A second-harmonic generation (SHG) powder technique similar to the one suggested by Kurtz and Perry¹⁸ was used for the center of symmetry test in CCLP. The SHG at the wavelength λ_ω = 0.532 μm was excited by a Minilite-I YAG: Nd-laser operating in a Q-switched mode at λ_ω = 1.064 μm and recorded in reflection geometry. Polycrystalline α-SiO₂ with 3–5 μm size particles was used as a standard in order to calibrate the intensity of the SHG response I_2ω according to the q = I_2ω/I_2ω(SiO₂) relation. The sample was previously crushed into 3–5 μm powder for the sake of comparability with the α-SiO₂ sample.

We used a NETZSCH STA Jupiter 449F1 simultaneous thermal analyzer to perform differential scanning calorimetric (DSC) measurement. DSC data were collected at 670–965 K with a heating/cooling rate of 10 K min⁻¹ in Pt crucibles with pierced lids in air.

Dielectric properties at heating/cooling mode were measured on a Novocontrol Alpha-ANT impedance-analyzer in a ProboStat measuring cell using the four-wire two contact method in a frequency range of 10⁻¹–1.4 × 10⁷ Hz at 473–1273 K. The frequency dependence of the complex impedance Z*(ω) = Z′(ω) + iZ″(ω) was measured during step heating under temperature stabilization conditions (the average heating rate was 0.8 K min⁻¹). Ceramic pellets were 40–50 mm² in area and 1–2 mm in height. A Pt paste was placed on flat surfaces of pellets and heated at 1023 ± 10 K for 1 h to obtain Pt electrodes. The density of the ceramic samples was above 80% of the theoretical one. The bulk and grain boundary conductivities, σ_b and σ_gb, were calculated from the impedance spectra by means of equivalent electric circuits.

Powder X-ray diffraction (PXRD) data for phase analysis were obtained on a Thermo ARL X'TRA powder diffractometer (CuK_α radiation, λ = 1.5418 Å, Bragg–Brentano geometry, scintillation detector) over the 5–65° 2θ range with a step of 0.02°. The phase analysis was performed using the JCPDS PDF-2 database. Lattice parameters were determined by Le Bail decomposition¹⁹ using JANA2006 software.²⁰ To determine the structure of CCLP, we used experimental synchrotron XRD (SXRD) data obtained on the BL15XU beamline of SPring-8 (λ = 0.65298 Å)^21,22 between 2.0° and 60.2° with a step of 0.003° in 2θ. Lindemann glass capillaries with an inner diameter of 0.1 mm were used as sample holders.

3. Results

3.1. Elemental analysis, SHG, DSC and dielectric measurements

Using ICP-AES, the Ca : Cd : La ratio in CCLP was found to be 8.3 ± 0.2 : 0.90 ± 0.02 : 0.90 ± 0.02, which differs from the expected bulk composition Ca₈CdLa(PO₄)₇. Elemental contents were measured using TEM-EDX analysis at 10 points for each sample. The La_L, Cd_L and Ca_K lines in the EDX spectra were used. The oxygen and phosphorus contents were not quantified by EDX. TEM-EDX determined the composition to be Ca_8.5Cd_0.80La_0.82(PO₄)₇ (83.9 ± 4 at% (Ca), 7.9 ± 0.3 at% (Cd), 8.1 ± 0.3 at% (La)).

Fig. 1a shows the temperature dependence of the SHG signal (I_2ω/I_2ω(SiO₂)) during the heating/cooling of CCLP. The presence of SHG response (I_2ω/I_2ω(SiO₂) > 1.5) at T_R indicates the absence of a symmetry center in this structure, confirming a non-centrosymmetric structure with the SG R3c. Heating causes a sharp decline of the SHG signal to zero at 850 ± 10 K, while subsequent cooling results in signal recovery with a temperature hysteresis of several degrees. The disappearance/appearance of the SHG response upon heating/cooling indicates a reversible phase transition (PT) in CCLP. Substitution of Ca²⁺ by Cd²⁺ cations slightly increases the SHG signal magnitude from I_2ω/I_2ω(SiO₂) = 0.87 in Ca₉La(PO₄)₇ (ref. 23) to I_2ω/I_2ω(SiO₂) = 1.8 in CCLP.

Fig. 1 Temperature dependence for CCLP: (a) SHG signal (I_2ω/I_2ω(SiO₂)) at heating/cooling mode; (b) heating/cooling DSC curves (heating/cooling rate is 10 K min⁻¹); dielectric constant (ε (c)) and dielectric loss tangent (tan δ (d)) at different frequencies.

The reversible first-order PT in CCLP was studied using DSC analysis. Fragments of heating/cooling DSC curves for CCLP are shown in Fig. 1b. Reproducible endothermic/exothermic effects were observed. The DSC curves for CCLP reveal a single peak at 857 ± 5 K (at heating mode) and another at 839 ± 5 K (at cooling mode). This temperature hysteresis ΔT confirms the first-order PT found by SHG study. Although the endothermic effect is quite small (Fig. 1b), both the first-order PT and its temperature range are further confirmed by dielectric and conductivity measurements.

The reversible PT was detected by dielectric ε(T) anomalies appearing as slightly diffused maxima (Fig. 1c) in CCLP. The position of this maximum remains constant regardless of the applied field frequency. The transition temperature was found to be 863 ± 5 K during the heating. Temperature dependencies and dielectric loss tangent (tan δ) at different frequencies in CCLP are shown in Fig. 1d. The anomaly on the ε(T) curve can be associated with both ferroelectric (FE) and antiferroelectric (AFE) phase transitions. In FE compounds, the dielectric loss tangent tan δ(T) usually exhibits a maximum below the PT temperature – known as the Curie temperature T_c. This maximum is attributed to a change in the domain structure just below T_c. Antiferroelectrics, however, do not exhibit such a maximum on the tan δ(T) curve. The presence of a maximum in tan δ(T) at a temperature below T_c confirms the FE phase transition in CCLP.

3.2. Powder X-ray diffraction (PXRD) study

The PXRD pattern of CCLP is similar to previously studied Ca₈MR(PO₄)₇ (M = Mg, Zn; R = REE)^8,9 compounds and is related to the β-TCP-type structure¹ with the unit cell parameters: a = 10.4590(4) Å, c = 37.422(2) Å and V = 3545.2(3) ų. The absence of any impurity reflections on the PXRD patterns (Fig. 2) shows that La³⁺ and Cd²⁺ cations were completely incorporated into the β-TCP-type host.

Fig. 2 Parts of the PXRD patterns for CCLP in the 2θ range of 8–46°. Tick marks denote the peak positions of possible Bragg reflections.

The SXPD data were used to refine the crystal structure. The structure was refined by the Rietveld method²⁴ using the JANA2006 programme package.²⁰ The main data under the SXPD data conditions and the results of the Rietveld refinement are presented in Table 1. The difference electron density maps in the (010) plane for the CCLP structure is shown in Fig. 3.

Table 1 Crystallographic data for Ca_8.61Cd_0.70La_0.82(PO₄)₇ (Z = 6, T = 293 K)

Refined composition	0.989(4)Ca8.61Cd0.70La0.82(PO4)7 + 0.011(4)Ca3La(PO4)3
Composition after TEM-EDX	Ca8.5Cd0.8La0.82(PO4)7
Composition after ICP-AES	Ca8.3Cd0.9La0.9(PO4)7
Space group	R3c
Lattice parameters: a, Å	10.46310(1)
c, Å	37.42078(6)
Unit cell volume V, Å^3	3547.842(7)
Calculated density, g cm^−3	3.38(2)
Data collection
Diffractometer	BL15XU beamline of SPring-8
Radiation/wavelength (λ, Å)	Synchrotron/0.65298
2θ range (°)	2.042–60.235
Step scan (2θ)	0.003
Number of points	19 394
I max	339 601
Refinement
Refinement	Rietveld
Background function	Legendre polynomials, 15 terms
No. of reflections (all/observed)	2147/2123
No. of refined parameters/refined atomic parameters	89/65
R and Rw (%) for Bragg reflections (Rall/Robs)	3.58/3.51 and 4.35/4.34
R P, RwP; Rexp (%)	2.22, 3.63, 1.08
Goodness of fit (ChiQ)	3.37
Max./min. residual density	1.36/−2.50
Selected crystal structure data
n f-CaM1	1.115(7)
n f-CaM2	∼1.00(5)
n f-CaM3	1.521(6)
n f-CaM4	0.153(6)
n f-CaM5	2.170(9)
n f-CdM4	0.058(2)
n f-CdM5	0.817(3)
CCDC	2473599

---

Fig. 3 [ρ_dif: (x; y; z)] difference electron density maps in the (010) plane for the CCLP structure after the refinement in the models with free (a) and occupied M4 positions (b). Solid lines correspond to positive values of the electron density with 0.2e × Å³ steps, respectively. A color scale of the electron density is shown. M4, M5, P1 and O1 positions are shown.

In contrast to laboratory PXRD patterns, the SXRD study of CCLP (Fig. 4) revealed the presence of a Ca₃La(PO₄)₃ impurity (JCPDS, PDF-2, No. 29-0338) with the eulytite-type (Bi₄(SiO₄)₃ (ref. 25) structure (SG I4̄3d, a = 9.9508 Å). According to the SHG data, the CCLP structure is noncentrosymmetric (Fig. 1a). The structural data for β-TCP (SG R3c (ref. 1)) were used as a starting model for the CCLP structure refinement. There are six cationic (M1–M6) sites in the β-TCP-related structures. The M1–M3 (18-fold) and M5 (6-fold) positions are always occupied, while the occupation of the M4 (6-fold) position can change from 0 to 1, and the M6 (6-fold) position is usually vacant. An overview of cation distributions among the M1–M5 sites of the β-TCP-type structure is given in ref. 26.

Fig. 4 Observed, calculated and difference (at the bottom) SXRD patterns for the Ca₈CdLa(PO₄)₇ sample. Tick marks denote the peak positions of possible Bragg reflections for Ca_8.61Cd_0.70La_0.82(PO₄)₇ (1) and Ca₃La(PO₄)₃ (2). The strongest reflection of the Ca₃La(PO₄)₃ phase is indicated with a red arrow.

At the second stage, the f curves for Cd²⁺ (M5 sites) were used, and all parameters of the chosen model were refined. The occupancy of the M5 position by Cd²⁺ is smaller than 1 (Table 1, n_f-CdM5) indicating that a small amount of Ca²⁺ is located at the M5 site (M5 = nCd²⁺ + (1–n)Ca²⁺) as in the case of the previously studied Ca_8.223Cd_0.777Eu(PO₄)₇.¹⁷

In the final stage, the distribution of La³⁺ cations over the M1–M3 positions and Cd²⁺ across the M5 position was refined considering their multiplicities: (M1–M3) = nCa²⁺ + (1–n)Eu³⁺) and (M5) = nCa²⁺ + (1–n)Cd²⁺, without stoichiometric constraints on the global Eu/Ca and Cd/Ca ratios. The positional parameters (x; y; z) of La³⁺ and Ca²⁺ cations over the M3 position were refined without constraints. Analysis of the difference electron density map [ρ_dif: (x; y; z)] revealed a small residual electron density at the M4 site (Fig. 3a), indicating that this position is not empty but occupied by Ca²⁺ cations (Fig. 3b). The occupation of the M4 site by Ca²⁺ cations was chosen so that the composition from the structure refinement was close to the composition from TEM-EDX.

Atomic parameters of the Ca₃Bi(PO₄)₃ structure²⁷ were used as initial parameters for phase content refinement. The atomic parameters, site occupancies, and atomic displacement parameters for all atoms of the Ca₃La(PO₄)₃ structure were not refined. Using the Ca₃La(PO₄)₃ structural data enabled the determination of the sample's phase composition: 0.989(4)Ca_8.61Cd_0.70La_0.82(PO₄)₇ + 0.011(4)Ca₃La(PO₄)₃. The final results of the refinement are presented in Table 1. The fractional atomic coordinates, isotropic atomic displacement parameters, cation occupancies, the results of bond valence sum (BVS) calculations and main relevant interatomic distances for Ca_8.61Cd_0.70La_0.82(PO₄)₇ are listed in Tables S1 and S2 of the SI. The CCDC deposition number is 2473599.

The differences in the determination of the elemental composition by the Rietveld refinement and ICP-AES method is due to the following reasons: firstly, the presence of a secondary Ca₃La(PO₄)₃ phase revealed by SXRD study may explain the difference between ICP-AES and Rietveld refinement results. Secondly, perhaps Cd²⁺ cations are also located in the M1 and M3 positions of the Ca_8.61Cd_0.70La_0.82(PO₄)₇ structure as the ionic radius of Cd²⁺ (r_VIII(Cd²⁺) = 1.10 Å) is very close to that of Ca²⁺ (r_VIII(Cd²⁺) = 1.12 Å); however, it is impossible to find the remaining 1.2 Cd²⁺ cations (the difference between the TEM-EDX and Rietveld refinement results is 0.2 × 6 for Z = 6) at 36 site positions (M1 (18-fold) and M3 (18-fold)), also containing much heavier La³⁺ cations.

3.3. Conductivity measurements

Fig. 5a shows complex electrical impedance diagrams for CCLP at 473–1273 K. Impedance spectra for CCLP are composed by parts of two semicircles at high and low frequencies (ω). The high-ω part of the complex impedance is known to characterize bulk transport properties of ionic conductors, whereas charge migration through the boundary interfaces is a lower-ω process.²⁸

Fig. 5 (a) The impedance spectra for CCLP recorded at 980–1034 K, and the equivalent electrical circuit served for approximation in the inset (R_bulk – bulk resistance of ceramic grains, R_bg – resistance of grain boundaries, CPE1 and CPE2 – constant phase elements (CPE = 1/(A(iω)ⁿ)). (b) Arrhenius plots of conductivity σ for CCLP at 473–1273 K in the heating (red)/cooling (blue) cycle.

Fig. 5b presents the temperature dependence at the heating/cooling mode of conductivity (σT) for bulk and grain boundary transport for CCLP at 473–1273 K. Different dependencies of ln(σT) vs. 1000/T as an Arrhenius plot are observed in a temperature range from 473 to 1273 K. In this temperature range, the dependence for bulk and grain boundary conductivity at heating/cooling can be divided into two approximately linear portions with different slopes. For example, at the heating mode, the activation energies (E_a) for these linear portions for the grain boundary are E_a ∼ 1.8 eV in a range from 473 to 800 K, and E_a ∼ 1.89 eV for a high-temperature region from 865 to 1273 K. The activation energy for the linear portion for bulk conductivity at 473–800 K is close to E_a for the grain boundary while approximated E_a ∼ 1.06 eV at 865–1273 K is lower than that for the grain boundary. A sharp increase of the conductivity above 800 K results in phase transition.

4. Discussion

The refinement of the Ca_8.61Cd_0.70La_0.82(PO₄)₇ structure revealed that incorporating Cd²⁺ and La³⁺ ions into the β-TCP-type structure does not create an inversion center at T_R or change the SG from R3c to R3̄c. This differs from previously studied phosphates containing Zn²⁺,^9,23 Mg²⁺ (ref. 8) (Table 2) and Cd²⁺/Eu³⁺ ions.¹⁷ The changing of lattice cell parameters of Ca₈MLa(PO₄)₇ (M = Mg, Zn, Cd, Ca) from the M²⁺ radius (CN = 6) is shown in Fig. S1 of the SI. Substituting Ca²⁺ (r_VI = 1.00 Å (ref. 29)) with Mg²⁺ (r_VI = 0.72 Å (ref. 29)) increases the lattice cell parameters while the maximum of the “a” parameter is observed for M = Cd.

Table 2 Lattice parameters, SHG response, phase transition temperatures, cation position occupancies, selected distances (Å), polyhedra distortion index (DI) and tetrahedral distortion parameters Δd and Δα for Ca₈MLa(PO₄)₇ (M = Mg, Zn, Ca) and Ca_8.61Cd_0.70La_0.82(PO₄)₇ structures

		Mg	Zn	Cd	Ca
a Ref. 29. b Dielectric data.
Space group		R3̄c	R3̄c	R3c	R3c
(rVI(M^2+), Å^a		0.72	0.74	0.95	1.00
Lattice parameters: a, Å		10.3859(1)	10.387(8)	10.46310(1)	10.456(4)^11
c, Å		37.256(1)	37.260(1)	37.42078(6)	37.476(4)
Unit cell volume, Å^3		3480.3(2)	3481.7(4)	3547.842(7)	3648.6(2)
I 2ω/I2ω(SiO2)		<0.1,^8 0.03 (ref. 15)	0.0,^23 0.1,^9 0.05 (ref. 15)	1.8	0.87 (ref. 23)
T c, K^b		735 (ref. 8)	782.2 (ref. 9)	865	892 (ref. 14)
P1O4	<P1–O>	1.536	1.540	1.57	1.46
	Δd	0.0277	0.0270	0.0212	0.0432
	Δα	0.0001	0.0006	0.0006
P2O4	<P2–O>	1.526	1.549	1.56	1.52
	Δd	0.0293	0.0254	0.0233	0.0336
	Δα	0.0015	0.0012	0.0017
P3O4	<P3–O>			1.54	1.55
	Δd			0.0277	0.0267
	Δα			0.0028
Occupancy M1		0.96Ca^2+ + 0.04La^3+	0.95Ca^2+ + 0.05La^3+	0.97Ca^2+ + 0.03La^3+	0.97Ca^2+ + 0.03La^3+
<M1–O>		2.471	2.458	2.501	2.499
DI(M1–O)		0.029	0.030	0.054	0.045
Occupancy M2				1Ca^2+	0.97Ca^2+ + 0.03La^3+
<M2–O>				2.454	2.442
DI(M2–O)				0.041	0.022
Occupancy M3		0.372Ca^2+ + 0.128La^3+	0.38Ca^2+ + 0.12La^3+	0.754Ca^2+ 0.246La^3+	0.74Ca^2+ + 0.26La^3+
<M3–O>		2.541	2.586	2.629, 2.602	2.548
DI(M3–O)		0.055	0.060	0.070, 0.054	0.089
Occupancy M4		0	0	0.128Ca^2+	0
Occupancy M5		1Mg^2+	1Zn^2+	0.692Cd^2+ 0.308Ca^2+	1Ca^2+
<M5–O>		2.089	2.082	2.250, 2.252	2.305
DI(M5–O)		0	0	0.029, 0.057	0.033
M3′–M3″		1.082(2)	1.248(16)	0.279(5)	0
			0.213(17)
			1.091(16)
M5′–M5″		0	0	0.093(6)	0

---

The β-TCP-related structure of Ca_8.61Cd_0.70La_0.82(PO₄)₇ consists of isolated PO₄ tetrahedra that connect the MO_n polyhedra into a 3D framework via common vertices. According to crystal structure refinement, M5O₆ octahedra in Ca₈CdLa(PO₄)₇ are occupied by Ca²⁺ and Cd²⁺ (M5 = 0.307(6)Ca²⁺ + 0.693(6)Cd²⁺), while Ca²⁺ and La³⁺ cations occupy the M1 and M3 sites of the β-TCP-type structure. Previously, similar occupation of the M5 position by Ca²⁺ and Cd²⁺ was observed in the Ca_8.223Cd_0.777Eu(PO₄)₇ structure (M5 = 0.223(4)Ca²⁺+0.777(4)Cd²⁺ (ref. 17)).

The symmetry of the averaged crystal field of the ligands created near the M1–M3 and M5 sites of the R3c structure is higher for the R3̄c structure. The average distances M1–O, M2–O, M3–O and M5–O are reducing with decreasing M²⁺ radius. Also, this was confirmed by the polyhedral distortion index (DI) for different coordination numbers calculated as:

where n is the coordination number of the central cation, l_i is the distance from the central cation to the O atom, and l_av is the average bond length. The data on the DI are given in Table 2. The DI for the cation sites of the structure decreases with decreasing M²⁺ radius. Usually, the structure adopts changing size and charge of the cations at the cation position through the deformation of the PO₄ tetrahedra, which occurs as an antiphase alternation of two distortion modes with either stretching P–O bonds or bending O–P–O bond angles. The tetrahedral distortion parameters Δd and Δα, characterizing the deviations of P–O interatomic distances from the average value and the deviations of O–P–O bond angles from the perfect tetrahedral angle, were used for the analysis of the distortion of PO₄ in Ca₈MLa(PO₄)₇ (M = Mg, Zn, Ca) and Ca_8.61Cd_0.70La_0.82(PO₄)₇ (Table 2). The parameters are defined as:

where d_n is the individual P–O bond length, d is the average P–O bond length, α_n is the individual O–P–O bond angle and α is the perfect tetrahedral angle.

The absence of a center of symmetry at T_R was confirmed by the presence of SHG response (Fig. 1a). The disappearance/appearance of the SHG response during heating/cooling indicates a reversible PT in Ca_8.61Cd_0.70La_0.82(PO₄)₇ from a non-centrosymmetric to centrosymmetric structure at 850 ± 10 K. DSC measurements show that this PT is first-order, with an endothermic effect at 857 ± 5 K when heated and an exothermic effect at 839 ± 5 K during cooling (Fig. 1b). The presence of an anomaly on the ε(T) curve (Fig. 1c) at T_c and a maximum in tan δ(T) at temperature below T_c (Fig. 1d) indicates the FE phase transition in Ca_8.61Cd_0.70La_0.82(PO₄)₇ similar to that in Ca₉La(PO₄)₇ (ref. 23) from a ferroelectric β-phase (SG R3c) to a paraelectric β′-phase (SG R3̄c).

In contrast to Ca_8.61Cd_0.70La_0.82(PO₄)₇ and Ca₉La(PO₄)₇, the PT for Ca_8.223Cd_0.777Eu(PO₄)₇ is AFE from a antiferroelectric β-phase (SG R3̄c) to a paraelectric β′-phase (SG R3̄m).¹⁷ The R3̄c structure of the AFE phase is close to the R3c structure of the FE phase (Fig. 6a). The cation locations in M1–M3 positions in the R3c phase deviate only slightly from the centrosymmetric one. The anionic R3̄c subcell becomes centrosymmetric as a result of half of the P1O₄ tetrahedra turning over. Three disordered fragments exist in the R3̄c structure in comparison to the R3c structure (Fig. 6b): I) disordering of P1O₄ tetrahedra; II) two M1O₈ polyhedra due to disordering of P1O₄ tetrahedra and III) cation disordering at the M3 sites due to a displacement of the M3 positions from the center of symmetry (1/2, 0, 0).

Fig. 6 (a) The atomic columns in the R3c and R3̄c β-TCP-related structures; (b) three disordering fragments in the R3̄c structure: (I) the P1O₄ tetrahedra disordering; (II) two M1O₈ polyhedra and (III) two M3O₇ polyhedra due to the M3 site cation disordering.

La³⁺ and Ca²⁺ occupy the M1–M3 positions of FE Ca_8.61Cd_0.70La_0.82(PO₄)₇ and AFE Ca_8.223Cd_0.777Eu(PO₄)₇ β-TCP-related structures, while Cd³⁺ and Ca²⁺ occupy M5 sites. The occupancy of the M4 position by Ca²⁺ is close to 0, and M4 positions are free in Ca_8.223Cd_0.777Eu(PO₄)₇. In contrast to structures with the R3̄c space group, the M4 site occupancy differs from 0 in Ca_8.61Cd_0.70La_0.82(PO₄)₇, and this position is partially occupied by Ca²⁺ cations (M4 = 0.131(6)Ca²⁺ (Table S1 of the SI)).

A transition from the FE to AFE phase was found for Ca_9.5–1.5xMgEu_x(PO₄)₇ during progressive substitution Ca²⁺ → Eu^3+.16 Dielectric loss tangent (tan δ) maxima were detected for all samples except when x = 1, while characteristic maxima in the temperature dependence of dielectric constant ε(T) were observed across all compositions. The R3c structure corresponds to compositions where 0 ≤ x < 1 in Ca_9.5–1.5xMgEu_x(PO₄)₇, while Ca₈MgEu(PO₄)₇ (x = 1) is AFE R3̄c phase. Substitution of Ca²⁺ with Eu³⁺ leads to the cation vacancy formation in the M4 position in the structure up to x = 1. The occupancy of the M4 position by Ca²⁺ for x = 1 is 0 and M4 positions are fully free for Ca₈MgEu(PO₄)₇. This allows rotations of P1O₄ tetrahedra and a transformation from the FE to AFE phase. Thus, based on the dielectric loss tangent (tan δ) curve, we can give a conclusion about the relation between the occupancy of the M4 position and the FE or AFE nature of the phase transition.

The calculated σ_bulk for Ca_8.61Cd_0.70La_0.82(PO₄)₇ (σ_bulk = 4.01 × 10⁻⁶ S cm⁻¹ at 900 K and σ_bulk = 1.49 × 10⁻⁴ S cm⁻¹ at 1270 K) is lower than that for other β-TCP-type compounds: σ_bulk = 0.8 × 10⁻² S cm⁻¹ at 1270 K for Ca_7.5M_1.5Gd(PO₄)₇ (M = Zn, Cd),¹⁵σ_bulk = 0.6 × 10⁻² S cm⁻¹ at 1270 K for β-TCP;¹⁰σ_bulk = 0.86 × 10⁻³ S cm⁻¹ at 1200 K for Ca₉Bi(VO₄)₇.³⁰E_a for σ_bulk is approximated as ∼1.06 eV at 865–1273 K for Ca_8.61Cd_0.70La_0.82(PO₄)₇ (Fig. 5) and is different than that for other β-TCP-type compounds: E_a ∼ 1.24 eV at 713–873 K for Ca₉ZnLi(PO₄)₇;³¹E_a ∼ 1.00 eV at 865–1273 K for Ca₉Bi(VO₄)₇.³⁰

According to the bond valence energy landscape (BVEL) analysis,³² the β-TCP-type single crystals enclose a 3D migration network for cations and are characterized by the 3D character of ionic conductivity. In addition to I (… → M3 → M4 → M3′ → M6 → M3″ → …) and II (… → M4 → M2 → M4′→ …) pathways,³³ the III pathway has been proposed (… → M2 → M4 → M2′ → M1 → M6 → M1′ → M2″ → …).³⁴ Ca²⁺ cations can migrate along all pathways through the common faces of polyhedra or between faces of neighboring polyhedra. The M4 positions are involved in all pathways.

We compared the calculated σ_bulk for Ca_8.61Cd_0.70La_0.82(PO₄)₇ with σ_bulk for other β-TCP-type compounds: Ca_7.5M_1.5Gd(PO₄)₇ (M = Zn, Cd), β-TCP and Ca₉Bi(VO₄)₇. The M4 sites are free in Ca_7.5M_1.5Gd(PO₄)₇ (M = Zn, Cd) and Ca₉Bi(VO₄)₇, while they are partially occupied by Ca²⁺ cations in the β-TCP and Ca_8.61Cd_0.70La_0.82(PO₄)₇ structures. The filling of M3 positions with La³⁺ cations in Ca_8.61Cd_0.70La_0.82(PO₄)₇ leads to the blocking of the I pathway for the Ca²⁺ ion migration. Probably the filling of M3 positions with La³⁺ cations and M4 site occupation by Ca²⁺ cations in the Ca_8.61Cd_0.70La_0.82(PO₄)₇ structure are reasons for reducing σ_bulk.

Conclusions

The Ca_8.61Cd_0.70La_0.82(PO₄)₇ phase with a β-TCP-related structure was prepared by a high-temperature solid-state reaction in air. Bulk and local cation compositions were determined by ICP-AES and TEM-EDX, respectively. The structure was refined by the Rietveld method in the space group R3c using powder synchrotron X-ray diffraction data. The distribution of Ca²⁺, Cd²⁺ and La³⁺ cations among the sites of the β-TCP-type structure was found. The phase transition temperature, T_c, is 865 ± 10 K. Dielectric measurements confirmed the ferroelectric nature of the phase transition. This reversible, first-order phase transition occurs between a polar ferroelectric β-phase (SG R3c) and a centrosymmetric paraelectric β′-phase (SG R3̄c).

Author contributions

The manuscript was prepared with contributions from all authors. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the SI. Fractional atomic coordinates, site symmetry, isotropic displacement atomic parameters (U_iso) and site occupation for Ca_8.61Cd_0.70La_0.82(PO₄)₇ samples from synchrotron SXRD data (Table S1). Selected distances (Å) in Ca_8.61Cd_0.70La_0.82(PO₄)₇ samples from synchrotron SXRD data (Table S2). The lattice cell parameters of Ca₈MLa(PO₄)₇ (M = Mg, Zn, Ca) and Ca_8.61Cd_0.70La_0.82(PO₄)₇ (Fig. S1).

Supplementary information: fractional atomic coordinates, site symmetry, isotropic displacement atomic parameters (U_iso), site occupation, and BVS values for Ca_8.61Cd_0.70La_0.82(PO₄)₇ samples from synchrotron SXRD data (Table S1). Selected distances (Å), distortion indices (DIs), and, the tetrahedral distortion parameters Δd and Δα in Ca_8.61Cd_0.70La_0.82(PO₄)₇ samples from synchrotron SXRD data (Table S2). The lattice cell parameters of Ca₈MLa(PO₄)₇ (M = Mg, Zn, Ca) and Ca_8.61Cd_0.70La_0.82(PO₄)₇ (Fig. S1). See DOI: https://doi.org/10.1039/d5ce00787a.

CCDC 2473599 contains the supplementary crystallographic data for this paper.³⁵

Acknowledgements

This research was funded by the Russian Science Foundation (RSF Project 24-13-00148), https://rscf.ru/en/project/24-13-00148/. The synchrotron radiation experiments were conducted at the former NIMS beamline (BL15XU) of SPring-8 with the approval of the former NIMS Synchrotron X-ray Station (proposal numbers 2019A4501). We thank Dr. Y. Katsuya and Dr. M. Tanaka for their help at SPring-8.

References

1. B. Dickens, L. W. Schroeder and W. E. Brown, J. Solid State Chem., 1974, 10, 232–248.
2. Y. Huang, C. Jiang, Y. Cao, L. Shi and H. J. Seo, Mater. Res. Bull., 2009, 44, 793–798.
3. M. B. Kosmyna, P. V. Mateychenko, B. P. Nazarenko, A. N. Shekhovtsov, S. M. Aksenov, D. A. Spassky, A. V. Mosunov and S. Y. Stefanovich, J. Alloys Compd., 2017, 708, 285–293.
4. V. A. Morozov, A. A. Belik, S. Y. Stefanovich, V. V. Grebenev, O. I. Lebedev, G. Van Tendeloo and B. I. Lazoryak, J. Solid State Chem., 2002, 165, 278–288.
5. Q. Z. Liu, J. H. Kim, M. J. Cho, S. H. Kim, B. Xu, S. Amirthalingam, N. S. Hwang and J. H. Lee, Mater. Des., 2023, 229, 111914.
6. V. V. Titkov, S. Y. Stefanovich, D. V. Deyneko, Y. Y. Dikhtyar, S. M. Aksenov, O. V. Baryshnikova, A. A. Belik and B. I. Lazoryak, J. Solid State Chem., 2019, 279, 120966.
7. B. I. Lazoryak, E. S. Zhukovskaya, O. V. Baryshnikova, A. A. Belik, O. N. Leonidova, D. V. Deyneko, A. E. Savon, N. G. Dorbakov and V. A. Morozov, Mater. Res. Bull., 2018, 104, 20–26.
8. A. A. Belik, V. A. Morozov, D. V. Deyneko, A. E. Savon, O. V. Baryshnikova, E. S. Zhukovskaya, N. G. Dorbakov, Y. Katsuya, M. Tanaka, S. Y. Stefanovich, J. Hadermann and B. I. Lazoryak, J. Alloys Compd., 2017, 699, 928–937.
9. Y. Y. Dikhtyar, D. A. Spassky, V. A. Morozov, D. V. Deyneko, A. A. Belik, O. V. Baryshnikova, I. V. Nikiforov and B. I. Lazoryak, J. Alloys Compd., 2022, 908, 164521.
10. A. A. Belik, F. Izumi, S. Y. Stefanovich, A. P. Malakho, B. I. Lazoryak, I. A. Leonidov, O. N. Leonidova and S. A. Davydov, Chem. Mater., 2002, 14, 3197–3205.
11. A. El Khouri, M. Elaatmani, G. Della Ventura, A. Sodo, R. Rizzi, M. Rossi and F. Capitelli, Ceram. Int., 2017, 43, 15645–15653.
12. R. Rizzi, F. Capitelli, B. I. Lazoryak, V. A. Morozov, F. Piccinelli and A. Altomare, Cryst. Growth Des., 2021, 21, 2263–2276.
13. E. S. Zhukovskaya, D. V. Deyneko, O. V. Baryshnikova, A. A. Belik, I. I. Leonidov, A. V. Ishchenko, S. Y. Stefanovich, V. A. Morozov and B. I. Lazoryak, J. Alloys Compd., 2019, 787, 1301–1309.
14. A. V. Teterskii, V. A. Morozov, S. Y. Stefanovich and B. I. Lazoryak, Russ. J. Inorg. Chem., 2005, 50, 986–989.
15. A. V. Teterskii, S. Y. Stefanovich, B. I. Lazoryak and D. A. Rusakov, Russ. J. Inorg. Chem., 2007, 52, 308–314.
16. D. V. Deyneko, D. A. Spassky, V. A. Morozov, S. M. Aksenov, S. P. Kubrin, M. S. Molokeev and B. I. Lazoryak, Inorg. Chem., 2021, 60, 3961–3971.
17. D. V. Deyneko, V. A. Morozov, E. S. Zhukovskaya, I. V. Nikiforov, D. A. Spassky, A. A. Belik and B. I. Lazoryak, J. Alloys Compd., 2020, 815, 152352.
18. S. K. Kurtz and T. T. Perry, J. Appl. Phys., 1968, 39, 3798–3813.
19. A. Le Bail, H. Duroy and J. L. Fourquet, Mater. Res. Bull., 1988, 23, 447–452.
20. V. Petricek, M. Dusek, L. Palatinus, V. Petrícek, M. Dušek and L. Palatinus, Z. Kristallogr. - Cryst. Mater., 2014, 229, 345–352.
21. M. Tanaka, Y. Katsuya and A. Yamamoto, Rev. Sci. Instrum., 2008, 79, 075106.
22. M. Tanaka, Y. Katsuya, Y. Matsushita and O. Sakata, J. Ceram. Soc. Jpn., 2013, 121, 287–290.
23. Y. Y. Dikhtyar, D. V. Deyneko, K. N. Boldyrev, O. V. Baryshnikova, A. A. Belik, V. A. Morozov and B. I. Lazoryak, J. Lumin., 2021, 236, 118083.
24. H. M. Rietveld, J. Appl. Crystallogr., 1969, 2, 65–71.
25. D. J. Segal, B. P. Santoro and R. E. Newnham, Z. Kristallogr. - Cryst. Mater., 2014, 123, 73–76.
26. D. V. Deyneko, V. A. Morozov, J. Hadermann, A. E. Savon, D. A. Spassky, S. Y. Stefanovich, A. A. Belik and B. I. Lazoryak, J. Alloys Compd., 2015, 647, 965–972.
27. P. P. Sahoo and T. N. Guru Row, Inorg. Chem., 2010, 49, 10013–10021.
28. B. Evgenij and M. J. Ross, Impedance Spectroscopy Theory, Experiment, and Applications, John Wiley & Sons, Inc, 2005.
29. R. D. Shannon, Acta Crystallogr., Sect. A, 1976, 32, 751–767.
30. B. I. Lazoryak, O. V. Baryshnikova, S. Y. Stefanovich, A. P. Malakho, V. A. Morozov, A. A. Belik, I. A. Leonidov, O. N. Leonidova and G. Van Tendeloo, Chem. Mater., 2003, 15, 3003–3010.
31. D. Wei, Y. Huang, J. S. Kim, L. Shi and H. J. Seo, J. Electron. Mater., 2010, 39, 441–446.
32. D. V. Deyneko, D. A. Petrova, S. M. Aksenov, S. Y. Stefanovich, O. V. Baryshnikova, S. S. Fedotov, P. C. Burns, M. B. Kosmyna, A. N. Shekhovtsov and B. I. Lazoryak, CrystEngComm, 2019, 21, 1309–1319.
33. I. A. Leonidov, A. A. Belik, O. N. Leonidova and B. I. Lazoryak, Russ. J. Inorg. Chem., 2002, 47, 305–312.
34. S. Y. Stefanovich, D. A. Petrova, V. A. Morozov, E. A. Fortalnova, D. A. Belov, D. V. Deyneko, O. V. Barishnikova, A. A. Belik, B. I. Lazoryak, B. I. Lazoryak, O. V. Barishnikova, A. A. Belik and B. I. Lazoryak, J. Alloys Compd., 2018, 735, 1826–1837.
35. CCDC 2473599: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2p0zj7.

---