Crystal structure solution and high-temperature thermal expansion in NaZr₂(PO₄)₃-type materials

The NaZr₂P₃O₁₂ family of materials have shown low and tailorable thermal expansion properties. In this study, SrZr₄P₆O₂₄ (SrO·4ZrO₂·3P₂O₅), CaZr₄P₆O₂₄ (CaO·4ZrO₂·3P₂O₅), MgZr₄P₆O₂₄ (MgO·4ZrO₂·3P₂O₅), NaTi₂P₃O₁₂ [½(Na₂O·4TiO₂·3P₂O₅)], NaZr₂P₃O₁₂ [½(Na₂O·4ZrO₂·3P₂O₅)], and related solid solutions were synthesized using the organic–inorganic steric entrapment method. The samples were characterized by in-situ high-temperature X-ray diffraction from 25 to 1500°C at the Advanced Photon Source and National Synchrotron Light Source II. The average linear thermal expansion of SrZr₄P₆O₂₄ and CaZr₄P₆O₂₄ was between −1 × 10⁻⁶ per °C and 6 × 10⁻⁶ per °C from 25 to 1500°C. The crystal structures of the high-temperature polymorphs of CaZr₄P₆O₂₄ and SrZr₄P₆O₂₄ with R3c symmetry were solved by Fourier difference mapping and Rietveld refinement. This polymorph is present above ∼1250°C. This work measured thermal expansion coefficients to 1500°C for all samples and investigated the differences in thermal expansion mechanisms between polymorphs and between compositions.

1. Introduction

NaZr₂P₃O₁₂ [`NZP' or ½(Na₂O·4ZrO₂·3P₂O₅)] and structurally related materials have been studied primarily for their thermal expansion (Lind, 2012; Shi et al., 2021; Evans, 1999; Barrera et al., 2005; Takenaka, 2018; Romao et al., 2013; Dove & Fang, 2016; Breval & Agrawal, 1995; Roy et al., 1989) and ionic conductivity properties (Goodenough et al., 1976; Rao et al., 2021). The NZP structure was first solved by Hagman & Kierkegaard (1968). A study by Boilot et al. (1979) of the related solid solution Na_l+xZr₂Si_xP_3–xO₁₂ (where 0 < x < 3) showed low thermal expansion near x = 0, and high ionic conductivity near x = 2. Since the 1980s, many cation substitutions in this NZP structure have been found and studied, leading to a class of materials called NZP-type materials (Breval & Agrawal, 1995; Limaye et al., 1987, 1991; Agrawal, 1996; Agrawal & Stubican, 1985; Pet'kov & Asabina, 2004; Govindan Kutty et al., 1998, 1994; Miyazaki et al., 2008).

NZP-type material properties have been explored for their low and tailorable thermal expansion, including thermal shock resistance, substrates for optical applications, and thermal barrier coatings (Trice et al., 1999). Additionally, there has been research into their use in energy storage/solid state electrolyte applications due to the high ionic conductivity of certain compositions (Goodenough et al., 1976; Rao et al., 2021). For this reason, they have been called NaSiCON (Na super-ionic conductors) materials (Zhang et al., 2023; Li et al., 2022; Aono & Suginoto, 1996). The ability to incorporate a range of cations into the NZP framework structure and its high-temperature stability has led to its investigation for use as an actinide host material for the containment of spent fuel from nuclear reactors (Gregg et al., 2013; Krishnaiah et al., 2003). NZP-type materials have also been studied for their electrical and thermal conductivity applications (Trice et al., 1999; Gregg et al., 2013; Krishnaiah et al., 2003; Liu et al., 1994) as well as for use in gas sensors (Dang & Guo, 2011; Kida et al., 2011).

The NZP crystal structure can have many substitutions for each cation in its unit cell (Pet'kov & Orlova, 2003; Alamo, 1993; Breval et al., 2000; Breval & Agrawal, 1995). In NZP, the Na⁺ cation that resides on the M1 and M2 sites can have substitutions by most Group I or II elements, as well as many transition metals and rare earth elements. The Zr⁴⁺ cation on the R site can have substitutions by Ge⁴⁺, Sn⁴⁺, Ti⁴⁺, Hf⁴⁺ and Nb⁵⁺ cations as well as partial occupancy of several other elements. The P⁵⁺ cation that resides on the P-site can have substitutions with Si⁴⁺ and S⁶⁺. Having a wide range of substitutions while maintaining a similar crystal structure allows for the opportunity to tailor the material property of interest. In the Na₄Zr₂(SiO₄)₃ structure there are four times as many Na⁺ sites as in NaZr₂(PO₄)₃. In Na₄Zr₂(SiO₄)₃, instead of residing only between two ZrO₆ octahedra, there are additional M sites between ZrO₆ octahedra and SiO₄ tetrahedra. A description of all the M sites can be found elsewhere (Qui et al., 1981) and some of these sites are shown in Fig. S1 (supporting information). This wide variation in number of cations and their valence charges in the NZP-type structure has resulted in numerous studies (Breval & Agrawal, 1995; Limaye et al., 1987, 1991; Agrawal, 1996; Agrawal & Stubican, 1985). These studies probed the changes in physical properties due to variations in the NZP lattice structure and its accommodation of different cations on each of the M, R and P sites.

NZP-type materials form several different variations of the standard NZP crystal structure based on composition and synthesis methods, leading to crystallization in the following space groups: , , R32, Pbcn, and P2₁/3 (Pet'kov & Orlova, 2003). There are many ways in which the symmetry elements are broken or added between these different space groups. Generally, these structural changes depend on whether there is an atom:

(i) on the M1 site,

(ii) on M1, M2 or one of the other six common interstitial sites,

(iii) on none of the M sites,

(iv) partially occupying M and R sites with another element,

(v) if the R-site octahedron begins to rotate off the c unit-cell axis (for the monoclinic space groups), or

(vi) if there is a change in valence charge for the M, R and/or P sites (often changing the occupancy to satisfy charge balance).

In the past, there has been disagreement over the correct crystal structure for some NZP-type materials (Senbhagaram et al., 1989), which are sometimes differentiated by several relatively small XRD peaks.

Past thermal expansion studies on NZP-type materials covered the temperature range of 25 to 500°C for most compositions. Few samples have been studied over 1000°C (Breval & Agrawal, 1995). The melting point of these materials was shown to be between 1600 to 1900°C (Agrawal, 1996; Pet'kov & Asabina, 2004), suggesting the possibility that they may be used over a wide range of temperatures. However, use of NZP-type materials between 1000°C and their melting point would require substantial extrapolation of phase stability and thermal expansion from lower-temperature crystallographic data reported in the literature.

One of the variations on the NZP-type structure that was studied here is CaZr₄P₆O₂₄ (CaO·4ZrO₂·3P₂O₅ or `CaZP'), the crystal structure of which at 25°C is depicted in Fig. 1. It consists of a network structure of corner-sharing PO₄ tetrahedra and ZrO₆ octahedra. Ca²⁺ occupies the site between two ZrO₆ octahedra along the c axis and is six-coordinated. The P—O and Zr—O bonds are more rigid and have relatively minor increases in length with temperature, whereas the Ca—O bond is weaker and has more expansion with temperature (Khosrovani & Sleight, 1999; Hazen & Prewitt, 1977). For this reason, NZP-type materials have sometimes been studied by treating the PO₄ tetrahedra and ZrO₆ octahedra each as rigid units (Tao & Sleight, 2003; Khosrovani & Sleight, 1999). Coordinated vibrational movements of rigid polyhedra can be described in terms of the rigid-unit-modes (RUM) characteristic of their thermal expansion behavior (Tao & Sleight, 2003; Liang et al., 2008). In structures with corner-sharing polyhedra, the static structural distortions of metal–oxygen–metal (M–O–M) angles, or bridging-oxygen angles, are measured to describe the way in which sets of connected polyhedra rotate. The rotation of polyhedra relative to the unit-cell axes have also been measured to describe thermal expansion mechanisms in related systems (Alamo, 1993; Lenain et al., 1987). Unit-cell diagrams for NaZr₂(PO₄)₃ and Na₄Zr₂(SiO₄)₃ illustrating the differences in interstitial site vacancy and polyhedron connectivity related to the P site can be found in Fig. S1.

Figure 1 Crystal structure for CaZr4P6O24 (CaZP) at 25°C in (space group No. 148): (a) showing the corner-sharing nature of ZrO6 octahedra and PO4 tetrahedra seen in NZP-type materials, with alternate views (b) along the c axis and (c) along the b axis. SrZr4P6O24 (SrZP) is isostructural, having the same space group, similar unit-cell lengths and atom positions.

The effect of M1-, M2- and R-site substitutions on unit-cell parameters is shown in Fig. 2 for the 25°C structures in the hexagonal setting for many NZP-type materials. Larger cations on the M1/M2 site cause the a and b unit-cell axes (which are equal in the hexagonal setting) to contract and the c unit-cell axis to expand. Larger cations on the R site cause both the a and c axes to expand. Examining the effect of cation substitutions at 25°C can begin to explain directions and modes by which the NZP-type network structure can accommodate changes. The data in Fig. 2 are from PDF card entries in the ICDD-PDF 4+ database (ICDD v. 2022, International Center for Diffraction data, Newton Square, PA, USA) (Kabekkodu et al., 2002) which are tabulated in Table S4.

Figure 2 The c versus a unit-cell parameters for several NZP-type materials with substitutions on the M and R sites. The filled black circles show the effect of substitution of the M (M1 and/or M2) site cation in (M)2Zr4P6O24, where M = Li, Na, K, Rb and Cs. The red triangles show the effect of substitution of the R site cation in Na2(R)4P6O24, where R = Ge, Ti, Sn, Zr and Hf. The black and red arrows indicate the directions of increasing size of atomic radii for the M and R sites, respectively. Tabulated unit-cell parameter values from the ICDD database (Kabekkodu et al., 2002) are given in Table S4.

In contrast to the unit-cell parameters at 25°C, thermal expansion values do not always follow similar trends with cation substitutions. Alamo (1993) described a trend in the NZP-type materials in which there is differing thermal expansion in the a unit-cell axis depending on crystal symmetry. It was shown that NZP-type materials which crystallize in space group exhibit negative thermal expansion of the a unit-cell axis on heating, whereas those which crystallize in space group show positive expansion. Both space groups exhibit expansion along the c axis on heating. However, CaZP does not follow this trend and crystallizes in space group and shows contraction along the a axis. Past studies of this material have not determined what causes this anomaly (Pet'kov et al., 2002; Woodcock et al., 1999a).

Near room-temperature SrZr₄P₆O₂₄ (SrZP) and CaZP exhibit low positive and low negative thermal expansion, respectively (Limaye et al., 1987; Breval & Agrawal, 1995). This difference in thermal expansion is due to thermal expansion along the a axis having opposite signs. Several studies (Woodcock et al., 1999a; Rashmi & Shrivastava, 2011; Govindan Kutty et al., 1998; Wang et al., 2018; Pet'kov et al., 2002; Agrawal & Stubican, 1985; Limaye et al., 1987; Fischer et al., 2004; Chakraborty et al., 2005) have investigated the Ca_1–xSr_xZr₄P₆O₂₄ solid solution to determine the solid solution range with approximately zero thermal expansion. However, the x-value and temperature range is not agreed upon. The reason for this unexpected difference in thermal expansion along the a-axis has still not been determined, which is surprising given that these materials, each having two cations, Sr²⁺ and Ca²⁺, possess similar ionic radii and valence charges. A study (Woodcock et al., 1999a) investigated Ca_0.5Sr_0.5Zr₄P₆O₂₄ by neutron powder diffraction from 25 to 800°C, including the unusual behavior of the a-axis expansion. It is unclear if there are compositions in the Ca_1–xSr_xZr₄P₆O₂₄ solid solution that have near-zero thermal expansion at temperatures above 800°C. Past research has been unable to determine a difference in the thermal expansion mechanism explaining how crystal structures accommodate these different thermal expansions along the a axis.

NaTi₂P₃O₁₂ (NaTP) has been studied for its promising properties and application as an anode material in Na-ion batteries (Wu et al., 2019). NaTP exhibits the usual thermal expansion for NZP-type materials that crystallize in space group . It has a negative value along the a axis and positive value along the c axis. However, a recent study (Ribero et al., 2016) shows that the a axis contraction appears to change direction near 1000°C. If this is indeed the case, NaTP could be a good candidate to understand the thermal expansion mechanism for the differing a-axis expansions in NZP-type materials.

The goal in this study was to measure the thermal expansion values of several NZP-type materials from 25 to 1500°C, determine phase stability in this temperature range, solve the high-temperature crystal structures of SrZP and CaZP, probe the differences in mechanisms of thermal expansion between the opposite a-axis thermal expansions in SrZP and CaZP, and examine how the thermal expansion changes in high-temperature NaTP. The NZP-type material compositions studied here are SrZr₄P₆O₂₄, CaZr₄P₆O₂₄, NaTi₂P₃O₁₂, NaZr₂P₃O₁₂ and MgZr₄P₆O₂₄ (MgZP).

2. Experimental

2.1. Powder synthesis

Ca_1–xSr_xZr₄P₆O₂₄ (where x = 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1), Na₂Zr₄P₆O₂₄, Na₂Ti₄P₆O₂₄ and MgZr₄P₆O₂₄ powder samples were synthesized via the organic–inorganic steric entrapment method (Nguyen et al., 1999), as depicted in Fig. 3 for CaZP. Stoichiometric ratios of calcium nitrate, Ca(NO₃)₂·xH₂O, and zirconium oxynitrate hydrate, ZrO(NO₃)₂·xH₂O, were mixed in an aqueous solution. For NTP, titanium isopropoxide, Ti[OCH(CH₃)₂]₄, in iso­propanol was the R-site cation precursor source. For SrZP, CaZP, MgZP and NTP, strontium nitrate [Sr(NO₃)₂·xH₂O] calcium nitrate [Ca(NO₃)₂·xH₂O] magnesium nitrate [Mg(NO₃)₂·xH₂O] and sodium nitrate (NaNO₃), respectively, were the precursor chemicals for the M-site cation. Then ammonium phosphate dibasic [(NH₄)₂HPO₄] in aqueous solution was added to the solution, dropwise using a pipette. Polyvinyl alcohol (PVA), diluted to 5 wt% in deionized water, was added to achieve a PVA monomer to total cation valence charge ratio of four to one, with the total charge being +48 from the precursors in CaZP for the Ca²⁺, Zr⁴⁺ and P⁵⁺ cations. The concentrations of the resulting aqueous solution were not measured after being combined. The amounts of solvent used varied; an unmeasured amount was employed to cleanse the beakers while transferring. The amount of solvent was not measured due to its removal during the first heat treatment step. Additional details describing the steric entrapment method can be found in the following references: Nguyen et al. (1999), Gülgün et al. (1999, 2002), Ribero & Kriven (2015).

Figure 3 Flow chart for the synthesis of CaZP by the organic–inorganic steric entrapment method. The molar ratios of the precursors are determined by the stoichiometry of the sample.

The solution was stirred for 4 h at 25°C, then heated to evaporate some of the iso­propanol and water, leaving a viscous gel. This was followed by drying for 3 h at 200°C following a 5°C min⁻¹ ramp rate of in a Carbolite box furnace to remove any remaining iso­propanol and water. This porous mass was then ground with a mortar and pestle and calcined at 700°C for 16 h after a 5°C min⁻¹ ramp rate. After the calcination step the powder was again ground using a mortar and pestle and formed into ∼0.5-inch diameter pellets at a load of ∼60 MPa in a Carver press. These pellets were then set on platinum foil and covered with some sacrificial powder in an alumina crucible and crystallized at 1200°C for 24 h after a 5°C min⁻¹ ramp rate.

2.2. Preliminary characterization

Successful synthesis of each sample was determined prior to in-situ synchrotron experiments by X-ray diffraction (XRD) and X-ray fluorescence (XRF). The crystal structure of the samples was determined by XRD with a Bruker D8 Advance diffractometer, using Cu Kα radiation (1.5418 A, 40 kV, 30 mA). The crystalline phase was identified with reference to the International Centre for Diffraction Data PDF-4+ database (Kabekkodu et al., 2002) accessed through Jade 9.4.1 software (Materials Data Inc., Livermore, CA, USA). X-ray fluorescence (XRF) determined the elemental composition of each sample on a Shimadzu EDX-7000 (Shimadzu America, Chicago, IL, USA) spectrometer by collecting a qualitative scan and a quantitative scan of the elements present.

2.3. High-temperature synchrotron powder XRD

In-situ XRD experiments were used to study these samples in an optical furnace in capillaries from 25°C to 1600°C. Experiments were conducted with optical furnaces: a Quadrupole Lamp Furnace (QLF) (Sarin et al., 2006) at beamline 17 BM-B, Advanced Photon Source (APS), Argonne National Laboratory or a Hexapole Lamp Furnace (HLF) at beamline 28-ID-2 (Shi et al., 2013), National Synchrotron Light Source II, Brookhaven National Laboratory. The QLF is composed of four halogen bulbs, whereas the HLF uses six bulbs, which were focused on to the point coincident with the X-ray and sample. Both the QLF and HLF were capable of temperatures up to 2000°C, though the maximum temperature achieved in these experiments was ∼1600°C. Two optical furnaces and beamlines were used due to beamtime availability. In preparation for optical furnace XRD experiments, each powder sample was mixed with ∼5 wt% Pt which served as an internal reference material and as a heat conductor, ensuring even heating. Pt peaks in the XRD patterns were used to calculate the temperature of each scan (Touloukian, 1975). Sample and Pt powder samples were mounted in sapphire (Crytur Co., Czech Republic) or fused-silica capillaries (Charles Supper Company) at the end of an alumina tube. Each sample was held in the goniometer head of the diffractometer.

Debye–Scherrer (transmission) geometry powder XRD experiments were conducted with a flat panel area detector. The X-ray wavelength at 17 BM-B at APS, was 0.24117 Å (65.554 keV), with a sample-detector distance of ∼1002 mm which was refined with an external CeO₂ (SRM 647b NIST standard). Data were collected between 1.5 and 12.5° 2θ (d⁻¹ 0.217–1.795 Å⁻¹) with a step size of 0.001°. The X-ray wavelength at 28 ID-2 at BNL was 0.1847 Å (67.12 keV), with a sample-detector distance of ∼1423 mm at BNL, which was refined with an internal Pt reference material.

2.4. Data processing and analysis

Synchrotron area detector image data were azimuthally integrated with the program GSAS-II (Toby & Von Dreele, 2013). Changes in the crystal structures were determined using Rietveld refinement (Rietveld, 1969; Loopstra & Rietveld, 1969) applied to XRD data. This analysis was performed with Bruker TOPAS v.5 (Bruker, 2007; Coelho, 2018). Rietveld refinement parameters included phase scale, background, atom positions, atomic displacement factors, and occupancy for certain atoms. A more detailed Rietveld procedure is given in supporting information. The high-temperature crystal structure was solved using Fourier difference maps in TOPAS and changes in space group symmetry checked with PLATON (Spek, 2020, 2009). Structures and Fourier difference map iso-surfaces were plotted using VESTA (Momma & Izumi, 2008).

2.5. Thermal expansion calculation

The thermal expansion tensor, α, is a description of the three-dimensional crystallographic change as a function of temperature (Jones et al., 2013; Paufler & Weber, 1999). It is a second rank tensor, the components of which, denoted as α_x, are called the coefficients of thermal expansion. The linear and volumetric coefficients of thermal expansion are calculated from the temperature-dependent length or volume (at 25°C) as shown in equations (1) and (2) below.

The unit-cell parameters as a function of temperature were fit to second-order polynomials with the least-squares method. These quadratic polynomials [a(T) and c(T)] were then used to calculate the axial, linear thermal expansion value [α_a(T) and α_c(T)] via equation (1). A discussion of the functional forms used to fit the unit-cell parameters for a thermal expansion calculation is included in the supporting information Section S2.3. The linear α value can be converted to volumetric β value through the following equation for the hexagonal symmetry: β = 2α_a+ α_c (Taylor, 1998), where α_a and α_c describe the thermal expansion in the a and c unit-cell axis directions, respectively. The average linear thermal expansion value used here is β/3. Additional details describing α and its calculation can be found elsewhere (Taylor, 1998; Schlenker et al., 1975; Paufler & Weber, 1999; Touloukian, 1975; Jessen & Küppers, 1991).

3. Results and discussion

This section presents the thermal evolution of the crystal structures and thermal expansion values for the CaZP, SrZP, NTP and NZP compositions. The CaZP and SrZP compositions also include a high-temperature structure solution and investigation into the thermal expansion mechanism. The thermal expansion of MgZP is also included in the supporting information. For each dataset, (i) tabulated unit-cell parameter values, (ii) a corresponding diffraction pattern file (.xye), (iii) TOPAS output file ( .out), and (iv) a crystallographic information format file (.cif) can be reached by the online repository at the hyperlink in the supporting information.

3.1. CaZr₄P₆O₂₄ and SrZr₄P₆O₂₄

CaZP and SrZP were studied, including the crystal structure solution of a high-temperature polymorph, phase transformation, thermal expansion values, and thermal expansion mechanism. The in-situ XRD data were collected at beamline 17 BM-B at the APS.

3.1.1. Crystal structure solution

In-situ synchrotron data were collected from 25 to 1500°C. The diffraction patterns showed the disappearance of several peaks on heating to 1262 (±4)°C for SrZP and 1268 (±2)°C for CaZP, indicating a phase transformation from the low-temperature (space group No. 148) space group to a higher symmetry one. These peaks reappeared on cooling. Fourier difference mapping in TOPAS (Bruker, 2007; Coelho, 2018) was used to determine the locations of missing and excess electron density in the unit cell. Trial-and-error was involved in determining the correct choice of atoms to move to best describe the phase transition. Adding a 0.5 occupancy Sr (or Ca for CaZP) atom to the (0,0,0) site worked best to account for the electron density movement in the high-temperature structure. Additional information can be found in the supporting information Section S2.2.

The ADDSYM function in PLATON (Spek, 2020, 2009) was used to determine changes in symmetry that could be present within a given crystal structure. It suggested that the new polymorph has (space group No. 167) symmetry. Powder XRD patterns and Rietveld refined structure of the high-temperature polymorphs, refined with this new structure for CaZP and SrZP, are displayed in Fig. 4. Crystallographic and Rietveld data are provided in Table 1. The same high-temperature polymorphs were found in both CaZP and SrZP. Impurities are present in both specimens, including ZrP₂O₇ due to off-stoichiometry synthesis, and Pt which was added as a reference material as described in Section 2.3.

Table 1
Crystallographic and Rietveld data for the high-temperature polymorph of CaZP and SrZP with estimated standard uncertainties show in parenthesis

	CaZr4P6O24					SrZr4P6O24
Crystal data
Crystal family	Hexagonal					Hexagonal
Space group (number)	(167)					(167)
Z	3					3
T (°C)	1420 (2)					1409 (4)
a, b (Å)	8.72614 (7)					8.76035 (8)
c (Å)	23.4444 (4)					23.0338 (4)
α, β (°)	90					90
γ (°)	120					120
Unit-cell volume (Å^3)	1546.02 (3)					1530.87 (4)
Rietveld refinement
Computer program	TOPAS (v. 5)					TOPAS (v. 5)
Weight % - Rietveld†	92.0					92.8
Rwp (%)‡	5.20					6.26
Rexp (%)‡	1.22					1.13
Rp (%)‡	4.22					4.72
GoF (%)‡	4.25					5.53
RBragg‡	2.45					2.61
	Fractional coordinate					Fractional coordinate
Atom site label	x	y	z	Occupancy	Beq (Å^2)	x	y	z	Occupancy	Beq (Å^2)
Ca1 or Sr1	0	0	0.5	0.5	11.01 (17)	0	0	0.5	0.5	11.6 (4)
Zr1	0	0	0.14803 (5)	1	2.14 (5)	0	0	0.14685 (6)	1	1.97 (6)
P1	0.2873 (4)	0	0.25	1	2.99 (11)	0.2884 (4)	0	0.25	1	2.99 (12)
O1	0.0376 (7)	0.8282 (6)	0.6985 (2)	1	4.64 (12)	0.0297 (7)	0.8257 (6)	0.6960 (2)	1	5.36 (14)
O2	0.2000 (5)	0.1733 (6)	0.0939 (2)	1	4.64 (12)	0.1923 (6)	0.1680 (6)	0.0909 (2)	1	5.36 (14)

†Remaining wt% from Pt or minor phases.
‡Values are as defined in Bruker TOPAS software.

Figure 4 Synchrotron diffraction pattern and calculated diffraction patterns from the Rietveld refined structure for the new high-temperature polymorph of (a) CaZP at 1420 (±2)°C and (b) SrZP at 1409 (±4)°C. Pt is the internal reference material for temperature measurement and ZrP2O7 is a minor phase.

The crystal structures of SrZP, including the low- and high-temperature polymorphs, are shown in Fig. 5 with parameters for the structure given in Table 1. Fig. 5 also shows how the Fourier difference map and misplaced electron density from the low-temperature structure was used to determine the location of missing Sr atoms within the unit cell at the (0, 0, 0) site (and the symmetry related locations) for the high-temperature polymorph. This shows that the Sr²⁺ cation goes from being ordered (only on the M1 sites) to being disordered (randomly distributed on the M1 and M2 sites). The solution method and resulting structure for the high-temperature CaZP polymorph are analogous to SrZP.

Figure 5 (a) Low-temperature, low-symmetry phase in (space group No. 148), (b) high-temperature, high-symmetry phase in (space group No. 167), (c) iso-surface plot from the Fourier difference map showing differences in electron density from the low-temperature phase with missing electron density shown in yellow and excess electron density shown in light blue, and (d) cross section of the iso-surface plot to provide more detail in the variation in intensity.

The change in XRD patterns with temperature is shown in Fig. 6 as SrZP undergoes the phase transformation. This transition is reversible and was measured on heating and cooling (though it is only shown on heating here). The systematic absence of peaks in this pattern can also be used to determine the new space group. The phase transformation is associated with the loss of several peaks in the XRD pattern of the high-temperature phase, as shown in Fig. 6, including the peaks shown in Table 2. The systematic absence of certain peaks matched the reflection condition shown in Table 3 and corresponded to a c glide. This added symmetry came from the added Sr site at (0,0,0) with 0.5 occupancy found by Fourier difference mapping and the PLATON (Spek, 2020, 2009) search for symmetry. Using both the reflection conditions for the absent peaks and the Fourier difference maps were good self-consistency checks for this high-temperature crystal structure. A comparison with other CaZP studies is given in the supporting information section.

Table 2
Tracking the loss of XRD peaks in Fig. 6 through their Miller–Bravais indices

Hexagonal Miller index	Hexagonal Miller–Bravais index	Peak appearance in high-temperature phase
003	0003	Absent
101		Absent
012		Present
104		Present
110		Present
015		Absent
006	0006	Present
		Present
021		Present
202		Present
024		Present
107		Absent
205		Absent
106		Present

Table 3
Systematic absence conditions† for hexagonal crystallographic coordinate systems

Type of reflections (Miller–Bravais indices)	Reflection condition	Glide vector	Symbol	Orientation of the plane
	l ≠ 2	c/2	c

†From Table 2.1.3.4 in the Teaching Edition of International Tables for Crystallography (2021).

Figure 6 Temperature series on heating of SrZP XRD patterns showing the phase transformation to a higher symmetry space group. Peaks that are absent in the high-temperature polymorph are labeled with black arrows and their Miller plane indices.

3.1.2. Unit-cell data and coefficients of thermal expansion

It was shown previously (Woodcock et al., 1999a; Alamo, 1993) that the thermal expansions between related NZP-type materials in each of these space groups tend to show positive thermal expansion in the a and c axis directions, whereas show negative thermal expansion in the a axis and positive expansion in the c axis. The phase transformation from to in the Ca_1–xSr_xZr₄P₆O₂₄ solid solution presented an opportunity to understand the differences in a unit-cell axis expansion.

Additionally, CaZP and SrZP have markedly different thermal expansions within the phase. The a unit-cell axis contracts on heating for CaZP, whereas it expands for SrZP. The c unit-cell axis expands for both. Negative thermal expansion in the a and b unit-cell axes in CaZP is perhaps unique among the NZP-type materials that crystallize in the space group (Alamo, 1993). Most NZP-type materials in the space group show negative thermal expansion in the a axis. The a axis changes from positive to negative thermal expansion at a composition of x = 0.45 in Ca_1–xSr_xZr₄P₆O₂₄, as shown in supporting information.

This creates the opportunity to learn more about both the mechanism leading to the difference in anisotropy in the expansion of the a axis between Ca and Sr, as well as the changes in expansion through the phase transformation from to , while keeping cations on the other sites constant. Previous studies probing these differences in thermal expansion did so by examining different compositions of NZP-type materials with substitutions on the M1/M2 and R sites, which led to more possible differences between the materials (bond strength, cation size, electron orbitals) that could influence the thermal expansion.

All Ca_1–xSr_xZr₄P₆O₂₄ samples were shown to be stable from 25 to 1500°C. The unit-cell parameters and volume for three representative samples are shown below in Fig. 7. The change in slope of the unit-cell parameters versus temperature shows the phase transformation temperature. Additional compositions in the Ca_1–xSr_xZr₄P₆O₂₄ solid solution can be found in the supporting information.

Figure 7 Temperature-dependent, unit-cell parameters (a) a and (b) c, (c) unit-cell volume, and (d) relative integrated peak intensity of (101)/(110) in Ca1–xSrxZr4P6O24, for compositions x = 0.0, 0.5, and 1.0. The transformation can be seen here in (a) by the changes in slopes of the a unit-cell parameters and in (d) by the decreases in the (101) peak intensities. Data were collected on both heating and cooling, leading to variability in values for each composition. Most error bars are smaller than the data markers.

The a and c axes, and average thermal expansion values are summarized in Fig. 8 for both low- and high-temperature phases. In the low-temperature phase, the a unit-cell parameter underwent negative thermal expansion for Ca-rich samples in the Ca_1–xSr_xZr₄P₆O₂₄ system up to x = 0.45, after which the a axis had a positive thermal expansion. The volumetric thermal expansion was also lowest for these samples from 25 up to ∼500°C, at which point the coefficient of thermal expansion continued to increase and at the upper range of temperatures it had the higher coefficient of thermal expansion. The thermal expansion was almost isotropic for SrZP, with nearly overlapping a axis and c axis values. The Ca-rich end of the solid solution experienced greater anisotropy in thermal expansion with a larger positive c-axis thermal expansion and a negative a-axis thermal expansion. This anisotropy between the c and a axes led to an overall very similar average thermal expansion throughout the CaZP–SrZP solid solution, with average values between −1 and 4 × 10⁻⁶ per °C.

Figure 8 The temperature-dependent thermal expansion (α) for (a) CaZP, (b) Ca0.5Sr0.5Zr4P6O24 and (c) SrZP plotting the thermal expansion coefficients along the a axis, c axis, and average linear thermal expansions.

In the high-temperature phase, unit-cell parameters behaved similarly for both CaZP and SrZP. The a unit-cell parameter experienced negative thermal expansion, whereas the c parameter underwent positive thermal expansion. The average linear thermal expansion had values from 0.7 × 10⁻⁶ per °C to 2.5 × 10⁻⁶ per °C with the lower values measured at higher temperatures. This type of a and c axis thermal expansion is typical of NZP-type materials in the space group (Lenain et al., 1987; Alamo, 1993).

Ca_0.5Sr_0.5Zr₄P₆O₂₄ was previously found to have an average linear thermal expansion of 0°C⁻¹ (Limaye et al., 1991; Breval et al., 2000), however that was not observed here. Only CaZP underwent a negative average linear thermal expansion, and only from 25 to 200°C (as seen in the supporting information for a specimen in which more data points were collected in the low-temperature range). At temperatures above 500°C it began to expand faster than the Sr-rich end of the solid solution Ca_1–xSr_xZr₄P₆O₂₄.

All compositions in this solid solution had low average thermal expansion values of less than 4.5 × 10⁻⁶ per °C. The high-temperature phase also had low thermal expansion values, in fact the average thermal expansion value decreased for all compositions of Ca_1–xSr_xZr₄P₆O₂₄ above the phase transformation temperature. SrZP had the lowest anisotropy in coefficients of thermal expansion between the a and c axis directions. While CaZP had a smaller thermal expansion value in the a axis than any other in this solid solution, it also had the largest thermal expansion along the c axis. This large anisotropy in CaZP would likely lead to increased strain in polycrystalline solids. Studies of dilatometry-derived thermal expansion values of bulk NZP-type materials have sometimes differed from XRD-derived crystallographic values, which has been attributed to densification when sintering as well as strain between grains due to anisotropic thermal expansion values along the a- and c-axis directions (Evans, 2002).

3.1.3. Thermal expansion mechanism

Investigation of the underlying atomistic mechanism leading to the observed thermal expansion involves examining the changes in groupings of atoms such as interatomic distances and polyhedral angles. It is important to have the language to describe the different unique atomic sites within the unit cell. A subset of the CaZP unit cell with atom labels is shown in Fig. 9 for the and space groups; these atoms must be labeled separately because each space group generates different atomic positions/labels.

Figure 9 A selected subset of the CaZP unit cell illustrated with atom labels to depict the corner-sharing nature of the PO4 tetrahedra and ZrO6 octahedra for the (a) low temperature, (space group No. 148), and (b) high temperature, (space group No. 167). The Ca, Zr and vacancy in this subset lie along the c-unit cell axis. The same labeling scheme is used for SrZP.

Previously, several methods have been used to investigate the thermal expansion behavior in low and negative thermal expansion materials, including interatomic distances, angles involving bridging oxygen atoms (M—O—M angles) (Tao & Sleight, 2003; Evans et al., 1996) and the rotation of a polyhedron relative to the rest of the unit cell (Alamo, 1993). These methods are complementary and the benefits of using both have been demonstrated in related systems of materials (Woodcock et al., 1999a). Both methods were employed here to describe the underlying crystallographic changes that took place during the thermal expansion and phase transformation. There are several interatomic angles and distances that are related or describing part of the same interaction of atoms, so some covariance was expected.

Interatomic distances, cation-bridging oxygen angles and atomic displacement parameters. Fig. 10 tracks the atomic displacement parameters (ADPs), selected interatomic distances, and angles for both SrZP and CaZP. The ADPs in Figs. 10(b) and 10(c) increase with higher temperatures, as expected due to increased thermal motion. There is a discontinuity in the ADP at the transformation temperature, which is likely due to the way atoms are represented in each space group. While they have the same number of atoms per unit cell, the low-temperature crystal structure in has twice as many atoms explicitly represented as does the structure in . The space group has more symmetry-generated atoms in the unit cell.

Figure 10 Occupancy (a) of the Ca and Sr cations shows significant disordering of the M1 and M2 sites before the phase transition temperature. The dependence of temperature on ADP for (b) SrZP and (c) CaZP. Data are shown for both heating and cooling of specimens.

The M1 and M2 sites demonstrate some differences, relative to the atoms surrounding them, between SrZP and CaZP. The distance between Zr2–Sr1 of 3.52 Å is larger than the 3.34 Å between Zr2–Ca1. This also corresponds to a larger Zr–vacancy distance for SrZP than for CaZP. Zr–M1 cation and Zr–vacancy distances each converge just before the transformation in which there is disordering of Sr or Ca to M1 and M2 sites. There is a larger difference between the M1 site size (Zr2–Sr1) and the M2 vacancy size (Zr1–Vac) for SrZP than for CaZP.

Cation-bridging oxygen angles (M—O—M angles) are illustrated in Fig. 11 for both SrZP and CaZP, including the P1—O—Zr in the and phases. In , the P—Ox—Zrx angles in Figs. 11(a) and 11(b) indicate that the P1—O1—Zr1 angle appears to converge to the same value as P1—O4—Zr2, and P1—O2—Zr2 with P1—O3—Zr1 for SrZP just before the phase transformation temperature. This convergence to similar values of P1—Ox—Zrx angles is not seen in CaZP. For CaZP, there are large fluctuations in these P1—Ox—Zrx angles. It would be expected that an increase in P1—O1—Zr1 and P1—O2—Zr2 angles would correspond to an increase in the c axis, and an increase in P1—O3—Zr1 and P1—O4—Zr2 angles would correspond to an increase in the a axis. In , P1—O1—Zr1 and P1—O2—Zr1 have similar values near 150° and each increase in value for SrZP. For CaZP in the phase, the P1—O1—Zr1 and P1—O2—Zr1 are ∼152° and 148°, respectively, and stay approximately constant with temperature. While there are several differences in the behavior of these angles between CaZP and SrZP, it is hard to determine if these angles are useful in determining the differences in thermal expansion mechanism of between these materials.

Figure 11 The distance from Zr1/Zr2 to the M2/M1 site is shown for (a) SrZP and (b) CaZP, illustrating the merging of the M1 and M2 sites. Cation-bridging oxygen (M—O—M) bond angles between both and phases for P—O—Zr are presented for (c) SrZP and (d) CaZP, as well as the Zr—O—M1/M2 angles for (e) SrZP and (f) CaZP. Data are shown for both heating and cooling of specimens.

The Zr—O—M angles in Fig. 11(e) experience a wide separation of 87 to 95°, then converging values near the phase transformation for SrZP. However, for CaZP these values are scattered near 91(±2)°C and do not show as clear a trend. This is consistent with the changes in the related bond distances given in Figs. 11(a), (b), S4(c) and S4(d), in which there are more clearly defined convergences of the Zr—M and M—O distances for SrZP than for CaZP. The difference seen between SrZP and CaZP appear to be due to the greater compression of the M2 site (vacancy) and expansion of the M1 site (Sr1) in SrZP, whereas the vacancy and Ca1 sites are more similar in size between the and phases for CaZP.

Polyhedral rotations. Two types of polyhedral rotations were examined, one in the ZrO₆ octahedra and another in the PO₄ tetrahedra. This type of examination of NZP-type materials is like those of Alamo (Alamo, 1993; Alamo & Rodrigo, 1992) and Woodcock (Woodcock et al., 1999a, 1998). The rotation and distortion of each polyhedron was measured using their projections on to the ab plane, which helped to probe the atomistic mechanism leading to differences in expansion in the a and b axes between SrZP and CaZP. The mechanism of positive thermal expansion in the c axis has already been explained in terms of interatomic distances and angles.

The angle φ measures how O₁, O₂, O₃ and O₄ in a ZrO₆ octahedron rotate about the c axis as illustrated and summarized in Fig. 12, where a ZrO₆ octahedron is drawn with atom labels in both the and space groups. Fig S3 also depicts the definition of φ. The difference between φ values in the space group has also been used to measure the distortion between the top and bottom layer of atoms within an octahedron(Alamo, 1993; Woodcock et al., 1999a). There is a larger range of φ values for the SrZP phase from about 0 to 33°, compared to −2 to 20° for CaZP. For both phases, there is a larger difference between φ angles for SrZP than for CaZP, which corresponds to a greater distortion (differing rotations of the top and bottom oxygen layers) of the ZrO₆ octahedron in SrZP. The largest rotations for both CaZP and SrZP occur in the φ₁ (φ for the O1 atom) in both phases, which corresponds to the oxygen atom that is bonded between Zr1 and P1, which is farther from the occupied M1 site.

Figure 12 The φ angle is the angle between the Zr—O bonds and the a unit-cell axis (and the a + b direction) when the bond is projected onto the ab plane. Definition of the φ angle is depicted in (a) the space group. Variation in the angle is systematically plotted for (b) SrZP and (c) CaZP. Datasets are shown for both heating and cooling.

The angle τ projects a PO₄ tetrahedron on to the ab plane, then measures the angle of the P1—Ox vector relative to the a axis, as summarized in Fig. 13. Unlike the φ-angle, which gives a measurement relative to Zr1/Zr2, which lie on the c axis, P1 does not reside on any unit-cell axis, so differing P1—Ox values of τ cannot be compared directly. For both SrZP and CaZP, the τ angles have a discontinuity in their values at the transformation temperature from the (low temperature) to (high-temperature) phases. At the phase change, τ1, τ2, and τ4 all increase and τ3 decreases, describing a sudden rotation of PO₄ tetrahedra relative to the a and b axes. The τ₁ and τ₂ values only for CaZP each increase by 20 to 30° between 300 and 700°C, but do not in SrZP, suggesting that a more distorted or rotated PO₆ tetrahedron exists in this temperature range in CaZP. This temperature range also corresponds to the increase in distance of P1 from the c axis shown in Fig. 13(b). However, the uncertain and large error bars for both the φ and τ angles make comparison of the relatively minor changes in these angles difficult to determine differences that could cause significant changes in the thermal expansion between SrZP and CaZP.

Figure 13 The (a) τ angle is the angle that the P1—Ox bond direction makes with the a axis when projected on the ab plane is plotted for (b) SrZP and (c) CaZP. Definition of the τ angle is shown in (a) the space group in black text and the space group in red text. Thermal evolution of τ is described with the nomenclature. Datasets are shown for both heating and cooling.

There was a clear rotation of both ZrO₆ and PO₄ polyhedra during the to transformation, seen in both the CaZP and SrZP. In the structures, the thermal expansion for both CaZP and SrZP was similar to other NZP-type materials when the R site is filled with Zr⁴⁺. While the a axis contracts in both the and phases of CaZP, it is likely that they do so through different mechanisms because their a unit-cell parameters have different slopes (and different thermal expansion values). Both SrZP and CaZP show expansion along the c axis in and and contraction along the a axis in . The mechanism behind the opposite signs for these a-axis thermal expansions in the phase is still unclear. Previous studies have suggested that the reason could be due to opposite rotations of the polyhedra; however, that was not definitively seen here. There were several small differences between the rotations of ZrO₆ octahedra and PO₄ tetrahedra and small changes in M—O—M bonds, but there were no major differences in the direction of rotation for these polyhedra. What can be concluded, however, is that the M1/M2 site in SrZP went through larger variations in size than did the M1/M2 sites in CaZP, as measured by the M1/M2 to Zr distance. The vacancy on M2 in SrZP was larger than on the M2 site than CaZP and it went through larger changes in size than CaZP.

In the structures, no significant differences in value or rotation direction of the ZrO₆ octahedra and PO₄ tetrahedra between SrZP and CaZP were observed to explain the opposing thermal expansions along the a axis, in contrast to previous predictions. However, there is larger uncertainty in the angles and distance measurements that involve oxygen atoms than those only involving other atoms, which likely comes from the lower atomic scattering factor of oxygen than the other higher atomic number atoms in these materials (Henke et al., 1993). It is still possible that PO₄–ZrO₆ rotations are the thermal expansion mechanism leading to the differences in anisotropy along the a axes in CaZP and SrZP; however, that cannot be conclusively shown from this powder XRD data. The M1 cation size affects the size and compressibility of the M2 site vacancy, which is likely important for the differences in thermal expansion. Future directions to investigate the positive and negative thermal expansions in the a axis of SrZP and CaZP include measurements that are sensitive to local changes in bonding, in addition to total scattering experiments to probe local order in addition to the average structure measured in diffraction experiments.

3.2. NaTi₂(PO₄)₃ thermal expansion coefficients

NaTi₂(PO₄)₃ (NTP) crystallizes in the space group and maintains this crystal structure for the entire range studied from 25 to 1425°C. Above this temperature the specimen melted and/or reacted with the sapphire capillary. This extended the previous temperature range in a powder diffraction study by a few hundred degrees (Ribero et al., 2016). This higher temperature range is of interest due to the change in a-axis thermal expansion and the opportunity to examine the difference.

Unit-cell parameters and thermal expansion values are shown in Fig. 14. While there was no phase change in the measured temperature range and the M1 and M2 sites were each fully occupied by the Na⁺ cations, there was still a change from negative to positive thermal expansion of the a axis of the unit cell above 1100°C. This is uncommon in the NZP-type materials in space group , as most show a contraction along the a axis for all temperatures (Alamo, 1993).

Figure 14 NaTi2(PO4)3 temperature dependent (a) a axis and (b) c axis unit-cell parameters, (c) unit-cell volume, (d) thermal expansion coefficients along the a and c axes, and average linear thermal expansion, (e) atomic displacement parameters, (f) Na^+ to Ti^4+ distance which describes the Na^+ site size, (g) P—O—Ti inter-polyhedral angles, and (h) φ angles describing TiO6 octahedral rotation. Datasets are shown for both heating and cooling.

3.3. NaZr₂(PO₄)₃ thermal expansion coefficients

NaZr₂(PO₄)₃ (NZP) crystallizes in space group and maintains this crystal structure for the entire range studied here from 25 to 1378 (±10)°C. The average linear thermal expansion values varied from 4.2 × 10⁻⁶ per °C at 25°C to 2.3 × 10⁻⁶ per °C at 1380°C. It exhibited a highly anisotropic behavior between the negative thermal expansion in the a axis and positive one in the c axis as displayed in Fig. 15. Because there were no phase changes or significant variations in thermal expansion coefficients, the thermal expansion mechanism was not explored further here.

Figure 15 NaZr2(PO4)3 temperature dependent (a) a axis and (b) c axis unit-cell parameters, (c) unit-cell volume, and (d) thermal expansion coefficients along the a and c axes, and average linear thermal expansion. Datasets are shown for both heating and cooling measurements.

4. Conclusion

CaZP, SrZP, NaTP, and NZP powders were synthesized and their thermal expansion values, phase stability, and thermal expansion mechanisms measured from 25 to 1500°C via in-situ, synchrotron diffraction. A high-temperature polymorph of CaZP and SrZP was solved with Fourier difference mapping and Rietveld refinement, its crystal structure is in the space group. This phase is present above 1268 (±2)°C and 1262 (±4)°C for CaZP and SrZrP, respectively. The new phase shows disorder on the M1 and M2 sites where it has 0.5 occupancy of the cation Ca²⁺ or Sr²⁺ on each site. The low-temperature structure shows an ordering of the Ca²⁺ or Sr²⁺ on the M1 and M2 sites with an occupancy of 1 on the M1 site and 0 on the M2 site.

The linear thermal expansion of the Ca_1–xSr_xZr₄P₆O₂₄ solid solution was measured as between −1 and 6 × 10⁻⁶ per °C in the phase and between 0 and 3 × 10⁻⁶ per °C in the high-temperature phase. The phase for both Ca and Sr showed negative thermal expansion of the a axis and positive thermal expansion of the c axis. CaZP showed the lowest thermal expansion from 25 to 200°C where it had a negative average thermal expansion value (between −1 and 0 × 10⁻⁶ per °C).

Negative and positive thermal expansions along the a axis of the phase of CaZP and SrZP, respectively, was investigated. The M1 (Ca) and M2 (vacancy) sites in CaZP were more similar in size than in SrZP in which the vacancy was more compressed at low temperatures. This suggests that the compressibility of each cation site is important to the difference in thermal expansion. However, there was not a clear relation between the differences in a-axis thermal expansion and the inter-polyhedral angles or relative rotation of PO₄ tetrahedra or ZrO₆ octahedra, as was suggested previously (Woodcock et al., 1998, 1999b; Lenain et al., 1987; Alamo, 1993; Alamo & Rodrigo, 1992). This implies the need for additional measurements. Neutron total scattering (Dove et al., 2002) can combine long-range order, using Bragg peaks, with short-range order, derived from diffuse scattering. Total scattering experiments have been useful in examining rigid body rotations caused by low-frequency vibrational modes in other network structures (Tucker et al., 2005; Baise et al., 2018) and would be a good characterization technique to study the thermal expansion mechanism in SrZP and CaZP. Total scattering enabled the measurement of disordered structural materials in which local structural changes are different from the structural average described from diffraction experiments using Bragg peaks.

A combination of both X-ray pair distribution function (XPDF) and X-ray absorption fine structure (XAFS) led to a study of the changes in a network structure (Cao et al., 2003; Bridges et al., 2014) that were caused by low-energy vibrational modes. A recent study that combined temperature-dependent solid-state NMR, neutron diffraction, and computation DFT (Morgan et al., 2022) examined Na_l+xZr₂Si_xP_3–xO₁₂. It could be useful to apply these techniques to understanding the differences in a-axis positive and negative expansions in the CaZP-SrZP system.

NaTP was shown to undergo a change in the thermal expansion of its a axis from negative to positive at 1100°C. Previously, only a negative thermal expansion in the a axis was reported. An investigation of the differences in the thermal expansion mechanism in the positive and negative expansion regions did not support changes in the rotation direction of the interconnected PO₄ tetrahedra and TiO₆ octahedra described previously. NaTP is another example illustrating that the trend that NZP-type materials in the space group undergo negative thermal expansion in the a axis and positive thermal expansion in the c axis is not valid for all temperatures ranges or compositions.

5. Related literature

The following references are cited in the supporting information: Chakraborty et al. (2005), Fischer et al. (2004), Gregg et al. (2013), Liu et al. (2018), Alamo & Rodrigo (1992), Momma & Izumi (2008), Hill (1992), Hill & Cranswick (1994), Bruker (2007), Coelho (2018), McCusker et al. (1999), Dinnebier et al. (2018), Toby & Von Dreele (2013), Hulbert & Kriven (2023), Hulbert et al. (2021), Allen (1974), Quan (1988), Montgomery et al. (2012), Deshpande & Mudholker (1961), Jones et al. (2013, 2012), Jones (2012), Langreiter & Kahlenberg (2015), Kempter & Elliott (1959), Weber et al. (1998), McCormack et al. (2018), Seymour et al. (2016, 2015), Knight et al. (1999, 1996), Ballirano & Melis (2009), Saxena & Shen (1992), Küppers (2013), Cline (2020), Brown (1988), Dean-Mo & Brown (1992, 1993), Kabekkodu et al. (2002).

Supporting information

Link http://doi.org/10.5281/zenodo.8121948
Raw X-ray diffraction data (.XYE), TOPAS input (.INP) and output (.OUT) files for NZP materials, including SrZr4P6O24, CaZr4P6O24, NaTi2P3O12, and NaZr2P3O12

Computing details

(phase_1_R-3c_SrZr4PO46)

Crystal data

O12P3Sr0.50Zr2	V = 1546.02 (3) Å^3
Mr = 511.17	Z = 6
Hexagonal, R3c	Dx = 3.294 Mg m^−3
Hall symbol: -R 3 2"c	Synchrotron radiation
a = 8.72615 (7) Å	T = 1682 K
c = 23.4444 (4) Å

Data collection

Synchrotron: APS 17 BM-B diffractometer	Scan method: step
Radiation source: synchrotron, APS beamline 17 BM-B

Refinement

Rp = 4.218	RBragg = 2.448
Rwp = 5.200	(Δ/σ)max = 0.004
Rexp = 1.224

Special details

Experimental. mounted in a sapphire capillary in air

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Sr1	0	0	0.5	11.01 (17)*	0.5
Zr2	0	0	0.14803 (5)	2.14 (5)*
P4	0.2873 (4)	0	0.25	2.99 (11)*
O6	0.0376 (7)	0.8282 (6)	0.6985 (2)	4.64 (12)*
O7	0.2000 (5)	0.1733 (6)	0.0939 (2)	4.64 (12)*

Geometric parameters (Å, º)

Sr1—O7^i	2.746 (4)	O6—O7^xvii	2.429 (7)
Sr1—O7^ii	2.746 (4)	O6—O7^xviii	2.465 (6)
Sr1—O7^iii	2.746 (4)	O6—O6^xix	2.480 (10)
Sr1—O7^iv	2.746 (4)	O6—O6^xx	2.922 (11)
Sr1—O7^v	2.746 (4)	O6—O6^xxi	2.922 (11)
Sr1—O7^vi	2.746 (4)	O6—O7^xxii	2.927 (7)
Zr2—O6^vii	2.061 (6)	O6—O7^xv	3.001 (7)
Zr2—O6^viii	2.061 (6)	O7—P4^xiv	1.509 (4)
Zr2—O6^ix	2.061 (6)	O7—Zr2	2.075 (4)
Zr2—O7	2.075 (4)	O7—O6^xxiii	2.429 (7)
Zr2—O7^x	2.075 (4)	O7—O6^xviii	2.465 (6)
Zr2—O7^xi	2.075 (4)	O7—O7^xxiv	2.470 (9)
P4—O6^xii	1.500 (5)	O7—Sr1^xxv	2.746 (4)
P4—O6^viii	1.500 (5)	O7—O7^x	2.843 (6)
P4—O7^xiii	1.509 (4)	O7—O7^xi	2.843 (6)
P4—O7^xiv	1.509 (4)	O7—O6^ix	2.927 (7)
O6—P4^xv	1.500 (5)	O7—O6^viii	3.001 (7)
O6—Zr2^xvi	2.061 (6)
O7^ii—Sr1—O7^i	180.000	O7^xxii—O6—O6^xix	155.72 (17)
O7^iii—Sr1—O7^ii	117.66 (13)	O7^xxii—O6—O7^xviii	145.4 (3)
O7^iii—Sr1—O7^i	62.34 (13)	O7^xxii—O6—O7^xvii	126.0 (2)
O7^iv—Sr1—O7^iii	180.0000 (1)	O7^xxii—O6—Zr2^xvi	45.13 (12)
O7^iv—Sr1—O7^ii	62.34 (13)	O7^xxii—O6—P4^xv	161.8 (4)
O7^iv—Sr1—O7^i	117.66 (13)	O7^xv—O6—O7^xxii	57.29 (17)
O7^v—Sr1—O7^iv	62.34 (13)	O7^xv—O6—O6^xxi	88.50 (15)
O7^v—Sr1—O7^iii	117.66 (13)	O7^xv—O6—O6^xx	59.23 (18)
O7^v—Sr1—O7^ii	62.34 (13)	O7^xv—O6—O6^xix	132.4 (3)
O7^v—Sr1—O7^i	117.66 (13)	O7^xv—O6—O7^xviii	98.7 (2)
O7^vi—Sr1—O7^v	180.0000 (1)	O7^xv—O6—O7^xvii	148.2 (2)
O7^vi—Sr1—O7^iv	117.66 (13)	O7^xv—O6—Zr2^xvi	43.65 (13)
O7^vi—Sr1—O7^iii	62.34 (13)	O7^xv—O6—P4^xv	133.1 (2)
O7^vi—Sr1—O7^ii	117.66 (13)	Zr2—O7—P4^xiv	151.7 (3)
O7^vi—Sr1—O7^i	62.34 (13)	O6^xxiii—O7—Zr2	160.5 (3)
O6^viii—Zr2—O6^vii	90.3 (2)	O6^xxiii—O7—P4^xiv	36.04 (18)
O6^ix—Zr2—O6^viii	90.3 (2)	O6^xviii—O7—O6^xxiii	60.9 (3)
O6^ix—Zr2—O6^vii	90.3 (2)	O6^xviii—O7—Zr2	118.4 (2)
O7—Zr2—O6^ix	90.1 (2)	O6^xviii—O7—P4^xiv	34.86 (16)
O7—Zr2—O6^viii	93.06 (19)	O7^xxiv—O7—O6^xviii	59.0 (2)
O7—Zr2—O6^vii	176.6 (2)	O7^xxiv—O7—O6^xxiii	60.42 (18)
O7^x—Zr2—O7	86.49 (18)	O7^xxiv—O7—Zr2	137.8 (2)
O7^x—Zr2—O6^ix	176.6 (2)	O7^xxiv—O7—P4^xiv	35.1 (3)
O7^x—Zr2—O6^viii	90.1 (2)	Sr1^xxv—O7—O7^xxiv	107.8 (2)
O7^x—Zr2—O6^vii	93.06 (19)	Sr1^xxv—O7—O6^xviii	148.3 (2)
O7^xi—Zr2—O7^x	86.49 (18)	Sr1^xxv—O7—O6^xxiii	87.4 (2)
O7^xi—Zr2—O7	86.49 (18)	Sr1^xxv—O7—Zr2	91.01 (13)
O7^xi—Zr2—O6^ix	93.06 (19)	Sr1^xxv—O7—P4^xiv	117.2 (2)
O7^xi—Zr2—O6^viii	176.6 (2)	O7^x—O7—Sr1^xxv	58.83 (7)
O7^xi—Zr2—O6^vii	90.1 (2)	O7^x—O7—O7^xxiv	166.5 (2)
O6^viii—P4—O6^xii	111.5 (5)	O7^x—O7—O6^xviii	133.4 (3)
O7^xiii—P4—O6^viii	107.7 (3)	O7^x—O7—O6^xxiii	117.7 (3)
O7^xiii—P4—O6^xii	110.0 (2)	O7^x—O7—Zr2	46.76 (9)
O7^xiv—P4—O7^xiii	109.9 (5)	O7^x—O7—P4^xiv	150.1 (4)
O7^xiv—P4—O6^viii	110.0 (2)	O7^xi—O7—O7^x	60.000
O7^xiv—P4—O6^xii	107.7 (3)	O7^xi—O7—Sr1^xxv	58.83 (7)
Zr2^xvi—O6—P4^xv	152.9 (4)	O7^xi—O7—O7^xxiv	112.43 (19)
O7^xvii—O6—Zr2^xvi	164.8 (2)	O7^xi—O7—O6^xviii	151.1 (3)
O7^xvii—O6—P4^xv	36.27 (19)	O7^xi—O7—O6^xxiii	142.86 (18)
O7^xviii—O6—O7^xvii	60.6 (3)	O7^xi—O7—Zr2	46.76 (9)
O7^xviii—O6—Zr2^xvi	134.4 (3)	O7^xi—O7—P4^xiv	147.3 (4)
O7^xviii—O6—P4^xv	35.09 (15)	O6^ix—O7—O7^xi	62.66 (16)
O6^xix—O6—O7^xviii	58.8 (2)	O6^ix—O7—O7^x	91.50 (15)
O6^xix—O6—O7^xvii	60.28 (18)	O6^ix—O7—Sr1^xxv	121.48 (18)
O6^xix—O6—Zr2^xvi	121.8 (2)	O6^ix—O7—O7^xxiv	94.4 (2)
O6^xix—O6—P4^xv	34.3 (2)	O6^ix—O7—O6^xviii	89.5 (2)
O6^xx—O6—O6^xix	81.59 (17)	O6^ix—O7—O6^xxiii	147.69 (18)
O6^xx—O6—O7^xviii	98.5 (3)	O6^ix—O7—Zr2	44.74 (16)
O6^xx—O6—O7^xvii	141.76 (19)	O6^ix—O7—P4^xiv	111.8 (3)
O6^xx—O6—Zr2^xvi	44.85 (11)	O6^viii—O7—O6^ix	59.0 (2)
O6^xx—O6—P4^xv	108.2 (3)	O6^viii—O7—O7^xi	89.99 (12)
O6^xxi—O6—O6^xx	60.000	O6^viii—O7—O7^x	60.05 (14)
O6^xxi—O6—O6^xix	94.56 (4)	O6^viii—O7—Sr1^xxv	118.88 (16)
O6^xxi—O6—O7^xviii	149.4 (2)	O6^viii—O7—O7^xxiv	133.2 (3)
O6^xxi—O6—O7^xvii	121.9 (2)	O6^viii—O7—O6^xviii	81.3 (2)
O6^xxi—O6—Zr2^xvi	44.85 (11)	O6^viii—O7—O6^xxiii	122.3 (2)
O6^xxi—O6—P4^xv	126.4 (2)	O6^viii—O7—Zr2	43.29 (13)
O7^xxii—O6—O6^xxi	61.74 (15)	O6^viii—O7—P4^xiv	115.5 (3)
O7^xxii—O6—O6^xx	89.93 (12)

Symmetry codes: (i) −y, −x, z+1/2; (ii) y, x, −z+1/2; (iii) −x+y, y, z+1/2; (iv) x−y, −y, −z+1/2; (v) −x, −x+y, −z+1/2; (vi) x, x−y, z+1/2; (vii) −x+y−1, y−1, z−1/2; (viii) −y+1, −x, z−1/2; (ix) x, x−y+1, z−1/2; (x) −x+y, −x, z; (xi) −y, x−y, z; (xii) x−y+1, x, −z+1; (xiii) −x+y+1/3, y−1/3, z+1/6; (xiv) −x+2/3, −y+1/3, −z+1/3; (xv) −y, −x+1, z+1/2; (xvi) −x+y, y+1, z+1/2; (xvii) −y+1/3, x−y+2/3, z+2/3; (xviii) y−1/3, x+1/3, −z+5/6; (xix) −x, −x+y, −z+3/2; (xx) −x+y−1, −x+1, z; (xxi) −y+1, x−y+2, z; (xxii) x, x−y+1, z+1/2; (xxiii) −x+y−1/3, −x+1/3, z−2/3; (xxiv) x−y+1/3, −y+2/3, −z+1/6; (xxv) −x+y, y, z−1/2.

(phase_1_R-3c_CaZr4PO46)

Crystal data

Ca0.50O12P3Zr2	V = 1530.87 (4) Å^3
Mr = 487.40	Z = 6
Hexagonal, R3c	Dx = 3.172 Mg m^−3
Hall symbol: -R 3 2"c	Synchrotron radiation
a = 8.76036 (8) Å	T = 1693 K
c = 23.0337 (4) Å

Data collection

Synchrotron: APS 17 BM-B diffractometer	Scan method: step
Radiation source: synchrotron, APS beamline 17 BM-B

Refinement

Rp = 4.218	RBragg = 2.606
Rwp = 5.200	(Δ/σ)max = 0.020
Rexp = 1.224

Special details

Experimental. mounted in a sapphire capillary in air

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Sr1	0	0	0.5	11.6 (4)*	0.5
Zr2	0	0	0.14685 (6)	1.97 (6)*
P4	0.2884 (4)	0	0.25	2.99 (12)*
O6	0.0297 (7)	0.8257 (6)	0.6960 (2)	5.36 (14)*
O7	0.1923 (6)	0.1680 (6)	0.0909 (2)	5.36 (14)*

Geometric parameters (Å, º)

Sr1—O7^i	2.628 (5)	O6—O7^xvii	2.493 (8)
Sr1—O7^ii	2.628 (5)	O6—O6^xviii	2.527 (11)
Sr1—O7^iii	2.628 (5)	O6—O7^xix	2.546 (6)
Sr1—O7^iv	2.628 (5)	O6—O6^xx	2.897 (12)
Sr1—O7^v	2.628 (5)	O6—O6^xxi	2.897 (12)
Sr1—O7^vi	2.628 (5)	O6—O7^xxii	2.906 (7)
Zr2—O6^vii	2.020 (6)	O6—O7^xv	2.936 (8)
Zr2—O6^viii	2.020 (6)	O7—P4^xiv	1.556 (4)
Zr2—O6^ix	2.020 (6)	O7—Zr2	2.046 (4)
Zr2—O7	2.046 (4)	O7—O6^xxiii	2.493 (8)
Zr2—O7^x	2.046 (4)	O7—O7^xxiv	2.532 (10)
Zr2—O7^xi	2.046 (4)	O7—O6^xix	2.546 (6)
P4—O6^xii	1.533 (6)	O7—Sr1^xxv	2.628 (5)
P4—O6^viii	1.533 (6)	O7—O7^x	2.752 (7)
P4—O7^xiii	1.556 (4)	O7—O7^xi	2.752 (7)
P4—O7^xiv	1.556 (4)	O7—O6^ix	2.906 (7)
O6—P4^xv	1.533 (6)	O7—O6^viii	2.936 (8)
O6—Zr2^xvi	2.020 (6)
O7^ii—Sr1—O7^i	180.000	O7^xxii—O6—O7^xix	147.5 (3)
O7^iii—Sr1—O7^ii	63.16 (15)	O7^xxii—O6—O6^xviii	153.6 (2)
O7^iii—Sr1—O7^i	116.84 (15)	O7^xxii—O6—O7^xvii	123.4 (3)
O7^iv—Sr1—O7^iii	180.0000 (1)	O7^xxii—O6—Zr2^xvi	44.75 (14)
O7^iv—Sr1—O7^ii	116.84 (15)	O7^xxii—O6—P4^xv	159.8 (4)
O7^iv—Sr1—O7^i	63.16 (15)	O7^xv—O6—O7^xxii	56.21 (18)
O7^v—Sr1—O7^iv	116.84 (15)	O7^xv—O6—O6^xxi	88.29 (17)
O7^v—Sr1—O7^iii	63.16 (15)	O7^xv—O6—O6^xx	59.8 (2)
O7^v—Sr1—O7^ii	63.16 (15)	O7^xv—O6—O7^xix	102.6 (2)
O7^v—Sr1—O7^i	116.84 (15)	O7^xv—O6—O6^xviii	136.1 (3)
O7^vi—Sr1—O7^v	180.000	O7^xv—O6—O7^xvii	148.4 (3)
O7^vi—Sr1—O7^iv	63.16 (15)	O7^xv—O6—Zr2^xvi	44.14 (15)
O7^vi—Sr1—O7^iii	116.84 (15)	O7^xv—O6—P4^xv	136.9 (3)
O7^vi—Sr1—O7^ii	116.84 (15)	Zr2—O7—P4^xiv	147.3 (3)
O7^vi—Sr1—O7^i	63.16 (15)	O6^xxiii—O7—Zr2	160.9 (3)
O6^viii—Zr2—O6^vii	91.6 (2)	O6^xxiii—O7—P4^xiv	35.91 (19)
O6^ix—Zr2—O6^viii	91.6 (2)	O7^xxiv—O7—O6^xxiii	60.88 (19)
O6^ix—Zr2—O6^vii	91.6 (2)	O7^xxiv—O7—Zr2	134.7 (3)
O7—Zr2—O6^ix	91.2 (2)	O7^xxiv—O7—P4^xiv	35.6 (3)
O7—Zr2—O6^viii	92.4 (2)	O6^xix—O7—O7^xxiv	58.8 (2)
O7—Zr2—O6^vii	175.0 (2)	O6^xix—O7—O6^xxiii	60.2 (3)
O7^x—Zr2—O7	84.5 (2)	O6^xix—O7—Zr2	114.9 (3)
O7^x—Zr2—O6^ix	175.0 (2)	O6^xix—O7—P4^xiv	34.23 (17)
O7^x—Zr2—O6^viii	91.2 (2)	Sr1^xxv—O7—O6^xix	150.2 (3)
O7^x—Zr2—O6^vii	92.4 (2)	Sr1^xxv—O7—O7^xxiv	111.8 (3)
O7^xi—Zr2—O7^x	84.5 (2)	Sr1^xxv—O7—O6^xxiii	90.3 (2)
O7^xi—Zr2—O7	84.5 (2)	Sr1^xxv—O7—Zr2	91.85 (14)
O7^xi—Zr2—O6^ix	92.4 (2)	Sr1^xxv—O7—P4^xiv	120.8 (3)
O7^xi—Zr2—O6^viii	175.0 (2)	O7^x—O7—Sr1^xxv	58.42 (7)
O7^xi—Zr2—O6^vii	91.2 (2)	O7^x—O7—O6^xix	131.1 (3)
O6^viii—P4—O6^xii	110.9 (5)	O7^x—O7—O7^xxiv	169.7 (2)
O7^xiii—P4—O6^viii	107.6 (3)	O7^x—O7—O6^xxiii	119.5 (3)
O7^xiii—P4—O6^xii	111.0 (3)	O7^x—O7—Zr2	47.74 (10)
O7^xiv—P4—O7^xiii	108.9 (5)	O7^x—O7—P4^xiv	150.2 (5)
O7^xiv—P4—O6^viii	111.0 (3)	O7^xi—O7—O7^x	60.000
O7^xiv—P4—O6^xii	107.6 (3)	O7^xi—O7—Sr1^xxv	58.42 (7)
Zr2^xvi—O6—P4^xv	154.6 (4)	O7^xi—O7—O6^xix	150.5 (3)
O7^xvii—O6—Zr2^xvi	161.6 (3)	O7^xi—O7—O7^xxiv	113.1 (2)
O7^xvii—O6—P4^xv	36.5 (2)	O7^xi—O7—O6^xxiii	144.8 (2)
O6^xviii—O6—O7^xvii	60.95 (19)	O7^xi—O7—Zr2	47.74 (10)
O6^xviii—O6—Zr2^xvi	122.1 (2)	O7^xi—O7—P4^xiv	148.6 (5)
O6^xviii—O6—P4^xv	34.5 (3)	O6^ix—O7—O7^xi	62.45 (18)
O7^xix—O6—O6^xviii	58.9 (2)	O6^ix—O7—O7^x	91.73 (17)
O7^xix—O6—O7^xvii	60.3 (3)	O6^ix—O7—Sr1^xxv	120.9 (2)
O7^xix—O6—Zr2^xvi	138.0 (3)	O6^ix—O7—O6^xix	88.5 (2)
O7^xix—O6—P4^xv	34.81 (15)	O6^ix—O7—O7^xxiv	91.2 (3)
O6^xx—O6—O7^xix	101.3 (3)	O6^ix—O7—O6^xxiii	145.3 (2)
O6^xx—O6—O6^xviii	83.73 (18)	O6^ix—O7—Zr2	44.02 (18)
O6^xx—O6—O7^xvii	144.6 (2)	O6^ix—O7—P4^xiv	109.5 (3)
O6^xx—O6—Zr2^xvi	44.19 (12)	O6^viii—O7—O6^ix	59.4 (3)
O6^xx—O6—P4^xv	111.0 (3)	O6^viii—O7—O7^xi	91.09 (14)
O6^xxi—O6—O6^xx	60.000	O6^viii—O7—O7^x	61.34 (16)
O6^xxi—O6—O7^xix	149.9 (2)	O6^viii—O7—Sr1^xxv	119.76 (18)
O6^xxi—O6—O6^xviii	93.87 (6)	O6^viii—O7—O6^xix	77.4 (2)
O6^xxi—O6—O7^xvii	120.2 (2)	O6^viii—O7—O7^xxiv	128.3 (3)
O6^xxi—O6—Zr2^xvi	44.19 (12)	O6^viii—O7—O6^xxiii	120.5 (2)
O6^xxi—O6—P4^xv	125.5 (2)	O6^viii—O7—Zr2	43.42 (15)
O7^xxii—O6—O6^xxi	60.79 (17)	O6^viii—O7—P4^xiv	111.3 (3)
O7^xxii—O6—O6^xx	88.87 (13)

Symmetry codes: (i) −y, −x, z+1/2; (ii) y, x, −z+1/2; (iii) x−y, −y, −z+1/2; (iv) −x+y, y, z+1/2; (v) −x, −x+y, −z+1/2; (vi) x, x−y, z+1/2; (vii) −x+y−1, y−1, z−1/2; (viii) −y+1, −x, z−1/2; (ix) x, x−y+1, z−1/2; (x) −x+y, −x, z; (xi) −y, x−y, z; (xii) x−y+1, x, −z+1; (xiii) −x+y+1/3, y−1/3, z+1/6; (xiv) −x+2/3, −y+1/3, −z+1/3; (xv) −y, −x+1, z+1/2; (xvi) −x+y, y+1, z+1/2; (xvii) −y+1/3, x−y+2/3, z+2/3; (xviii) −x, −x+y, −z+3/2; (xix) y−1/3, x+1/3, −z+5/6; (xx) −x+y−1, −x+1, z; (xxi) −y+1, x−y+2, z; (xxii) x, x−y+1, z+1/2; (xxiii) −x+y−1/3, −x+1/3, z−2/3; (xxiv) x−y+1/3, −y+2/3, −z+1/6; (xxv) −x+y, y, z−1/2.