Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 1, pp 199–205 | Cite as

Thermal expansion of phosphate–sulfates of eulytite structure

  • V. I. Pet’kov
  • A. S. Dmitrienko
  • A. I. Bokov


New phosphate–sulfates of the next chemical formulae ASr2Eu(PO4)2SO4 (A = K, Rb, Cs), NaBa6Zr(PO4)5SO4, Pb2Mg2(PO4)2SO4, and BaxSr4−x(PO4)2SO4 (0 ≤ x ≤ 4) have been designed and synthesized with the aim of investigating their thermal expansion properties in the low-temperature region. Obtained samples have been characterized with X-ray, IR, DTA, and microprobe electron analyses. Crystal structure and unit cell parameters were derived from the least-squares refinement of powder X-ray diffraction data (eulytite-type, sp. gr. \(I 4 {\bar{\text{3}}}d\)). The magnitudes of average linear thermal expansion coefficients vary from 1.1 × 10−5 to 1.7 × 10−5 K−1, which is conducive for application in optics and electronics.

Graphical Abstract


Phosphate–sulfates Aqueous solutions chemistry X-ray diffraction Eulytite crystal structure Thermal expansion 


A large number of compounds isostructural with eulytite (Fig. 1) have been reported over the past three decades [1, 2, 3, 4, 5]. Eulytite itself has received a resurged interest by the ceramic industries due to its multifunctionality possessing and interesting dielectric, thermoluminescent, and photocatalytic characteristics [6]. The crystal structure features of Bi4(SiO4)3 were elucidated by Liu and Kuo in 1997 [7]. Eulytite-like compounds are defined with a general formula M 4 I–IV (TO4)3, where M is metals in oxidation states from +1 to +4 and T is elements which are capable of forming tetrahedral anions (Si, P, S, Se, As, Cr, V, Ge). Investigations into phosphates of eulytite structure form the basis for the following manufacturing of hi-tech devices, being active laser medium, optical isolators [8], hybrid integrated circuits, LTCC tapes [9], and others. Being exploited under harsh temperature conditions, it is vital to make such materials thermally stable and resistant to cracking. That can be attained by controlling the extent of thermal expansion. By investigating thermal expansion, it is possible to draw certain conclusions concerning the character of interaction between atoms in the crystal, as the thermal expansion coefficient is associated with the strength of chemical bonds in the structure: The weaker the bonds between the atoms are, the greater the expansion is. If it comes to the reduction of the thermal expansion, there are certain techniques that could be especially useful. Those include usage of relatively small cations occupying framework positions with the aim of decreasing the volume of the framework, and filling framework hollows, if possible, with bulky cations. Given that there are no such hollows in eulytite-like compounds which might conceivably be accommodated, the former variant seems only viable. There is a plethora of data related to implementing of various isomorphous substitutions in pursuit of enhancing optical or dielectric properties of eulytite-like compounds, while there is no research conducted in order to shed the light on the ways of controlling thermal expansion of compounds involved. The goal of our research is to examine the thermal expansion of mixed phosphate–sulfates consisting of alkali, alkaline, and rare earth elements.
Fig. 1

Crystal structure of eulytite Bi4(SiO4)3. The framework is comprised of BiO6 octahedra and SiO4 tetrahedra (For interpretation of the references to the color in this figure legend, the reader should refer to the web version of this article)



All chemicals of NaCl, KCl, CsCl, Pb(NO3)2, Ba(NO3)2, SrCl2, MgO, FeCl3·6H2O, ZrOCl2·8H2O, H3PO4, H2SO4 were provided by “Reachem” and used without further purification. Their purity was not less than 99.5%.

Preparation of phosphate–sulfates

All samples were produced via sol–gel process. Stoichiometric amounts of 1 M aqueous solutions of the salts were poured together under constant stirring at 293 K. Shortly afterward, the solutions of sulfuric and orthophosphoric acids were added. The precursor mixture (gel) was heated up to 363 K until full water evaporation. Once the desiccated mixtures were obtained, they were subjected to stepwise isothermal heating at 973–1423 K for 24 h. Stepwise heating alternated with grinding in an agate mortar for 30 min. The phosphate–sulfates of ASr2Eu(PO4)2SO4 (A = K, Rb, Cs) composition were obtained at 1323 K, NaBa6Zr(PO4)5SO4 at 1123 K, and Pb2Mg2(PO4)2SO4 at 973 K and those of BaxSr4−x(PO4)2SO4 at 1423 K.


The chemical composition and homogeneity of the samples were checked with X-ray microanalysis on a JEOL JSM 7600F field emission (Schottky cathode) scanning electron microscope (SEM). The microscope was equipped with an Oxford Instruments X-Max 80 (Premium) energy-dispersive spectrometer system for X-ray microanalysis equipped with a semiconductor silicon drift detector. The elemental composition of the samples was determined with the accuracy of 2.0 mol%.

X-ray diffraction patterns were obtained on Shimadzu XRD-6000 diffractometer (Ni-filtered CuK α radiation, λ = 1.54178 Å, angular range 2θ = 10°–110°). Unit cell parameters were determined through indexing X-ray diffraction patterns. Rietveld method was employed for diffraction pattern processing and structure refinement [10, 11]. The peak profiles were approximated by means of modified pseudo-Voight function [12]. The crystal structures were refined by gradual adding of the parameters to be refined under regular visualization of peak profiles, so that the R-factors are stabilized.

Low-temperature X-ray diffraction measurements of samples concerned were made with the same diffractometer in the temperature range 173–473 K at 50 K intervals using Anton Paar TTK 450 thermal accessory. Cooling effect was attained with the controlled flow of liquid nitrogen. The temperature was monitored with a resistance thermometer Pt100 RTD. The range of diffraction angles remained the same (2Θ = 10°–60°), regardless of the temperature selected. Si was selected as an external standard.

DTA analyses of the precursors, calcined at 473 K beforehand, have been performed in argon atmosphere with Labsys TG–DTA/DSC in the temperature range 298–1273 K with the heating and cooling speed being 10 K min−1. Analyses were performed in alundum crucible. Sample mass was 0.085 g.

Functional composition of the samples was confirmed by IR-spectroscopy on a Shimadzu FTIR 8400S spectrometer within the range 450–1300 cm−1.

Results and discussion

DTA analysis in conjunction with X-ray diffractometry

DTA and X-ray analyses (Fig. 2) of an intermediate mixture of ASr2Eu(PO4)2SO4 (A = K, Rb, Cs) system stoichiometry exhibited an exothermic effect at 1310–1323 K (depends on the alkali cation) attributed to the crystallization of the phosphate–sulfates. The exothermic effect related to the crystallization of NaBa6Zr(PO4)5SO4 was observed at 1120 K and for BaxSr4−x(PO4)2SO4 at approximately 1420 K. As for Pb2Mg2(PO4)2SO4, more complicated DTA curve was acquired as a result of DTA implementation. The exothermic effect related to crystallization of this phosphate–sulfate was spotted at 923 K. The ensuing endothermic effect at 1173 K was proved to be reversible and was attributed to the congruent melting of the substance (Fig. 3).
Fig. 2

XRD patterns of ASr2Eu(PO4)2SO4 phosphate–sulfates

Fig. 3

DTA curve of Pb2Mg2(PO4)2SO4 precursor

Electron microprobe analysis

The electron probe X-ray microanalysis results indicated that the sample grains were about 8 μm (Fig. 4) and uniform in composition, which coincides with the theoretical one within experimental uncertainty (Table 1).
Fig. 4

SEM image of NaBa6Zr(PO4)5SO4 phosphate–sulfate

Table 1

Chemical composition of the phosphate–sulfates

Theoretical formula

Virtual formula (X-ray microanalysis data)














Ba2.98(3)Sr1.01(2)P2.00(3)S1.01(2)O 12







Crystal structure

The Rietveld refinement of the step-scan data was performed with the least square method using RIETAN software [10, 11]. Table 2 summarizes the measurement conditions, unit cell parameters, and main data of the structure refinement for Ba2Sr2(PO4)2SO4. The data related to the measurement conditions of other compounds were omitted, as being the same. Figure 5 presents fragments of the experimental, calculated, and different X-ray diffraction patterns, as well as the line diagram of the diffraction pattern of the Ba2Sr2(PO4)2SO4 phosphate–sulfate. Assuming that it belongs to the eulytite family, Ba and Sr, P and S and O atoms occupy 16c, 12a, and 48e Wyckoff positions, respectively, of \(I 4 {\bar{\text{3}}}d\) space group. The refinement leads to a rather good agreement between the experimental and calculated diffraction pattern and yields acceptable reliability factors (R p ≤ 4, R wp ≤ 5.5). The phosphate–sulfate of Ba2Sr2(PO4)2SO4 consists of a framework formed by grossly distorted BaO6 and SrO6 octahedra, which form the inner framework by means of edge linking, and independent SO4 and PO4 tetrahedra connected by vertices via Ba–O–P, Sr–O–P, Ba–O–S, and Sr–O–S structural bridges (Fig. 6). The structures of other eulytite-like compounds examined with Rietveld technique were analogous.
Table 2

Summary of crystallographic data for Ba2Sr2(PO4)2SO4 compound



Structural analogue


Crystal system


Space group

\(I 4 {\bar{\text{3}}}d\) (No. 220)



Unit cell parameters



10.4459 (3)


1139.82 (5)

d calc /g cm−3

4.288 (5)

2θ angular range/°


Total number of reflections


Number of refined parameters


R wp /%


R p /%


Fig. 5

Fragments of the (blue) experimental, (red dots) calculated, and (green) different X-ray diffraction patterns, and (black) line diagram of Ba2Sr2(PO4)2SO4 phosphate–sulfate diffraction pattern. (Color figure online)

Fig. 6

Crystal structure of Ba2Sr2(PO4)2SO4: a inner octahedral framework (tetrahedral fragments omitted); b general structure [dodger blue (Ba,Sr)O6 octahedra, bright green (P,S)O4 tetrahedra] (For interpretation of the references to the color in this figure legend, the reader should refer to the web version of this article). (Color figure online)


IR spectra of NaBa6Zr(PO4)5SO4 and Pb2Mg2(PO4)2SO4 crystallizing in eulytite structural type are shown in Fig. 7. In the space group \(I 4 {\bar{\text{3}}}d\) (factor group T d), ions \({\text{PO}}_{ 4}^{{ 3 { - }}}\) and \({\text{SO}}_{ 4}^{{ 2 { - }}}\) occupy the positions with S4 symmetry. Selection rules enable six asymmetric stretching ν 3, four asymmetric bending ν 4, and two symmetric bending bands ν 2 for each tetrahedral ion. Absorption bands in range 1250–1000 cm−1 are related to the asymmetric stretching vibrations ν3 of (P,S)O4 ion. Bands in range 650–470 cm−1 were related to the bending ν4 vibrations of (P,S)O4 ion, whereas ν2 were not spotted as being located below 450 cm−1. The values of vibration wave numbers of S–O and P–O bonds are identical, due to the negligible difference between oxidation degrees of sulfur and phosphorus and resemblance between values of interatomic distances (for S–O and P–O bonds). The spectra of compounds studied within the scope of this research were analogous. Overall, IR spectra have shown the absence of amorphous impurities (i.e., pyrophosphates).
Fig. 7

FTIR transmittance spectra of NaBa6Zr(PO4)5SO4 and Pb2Mg2(PO4)2SO4 (For interpretation of the references to the color in this figure legend, the reader should refer to the web version of this article)

Thermal expansion

The dependencies between lattice parameter a of examined compounds and temperature are depicted in the Figs. 810. In accordance with the obtained data, it can be inferred that lattice parameters of compounds grow with the increase in temperature, which in turn is caused by correlated rotation of MO6 octahedra and (P,S)O4 tetrahedra. It is a well-known fact that thermal expansion has a direct effect on the average kinetic energy of the vibrating particles of a body and the average distances between the crystal lattice points [13]. It also contributes to the asymmetry (anharmonicity) of the thermal vibrations of atoms; as a result, under variable temperature conditions, the interatomic distances change.
Fig. 8

Temperature dependence of ASr2Eu(PO4)2SO4 unit cell parameters a (red K, bright green Rb, blue Cs) (For interpretation of the references to the color in this figure legend, the reader should refer to the web version of this article). (Color figure online)

Fig. 9

Temperature dependence of NaBa6Zr(PO4)5SO4 and Pb2Mg2(PO4)2SO4 unit cell parameters a

Fig. 10

Temperature dependence of BaxSr4−x(PO4)2SO4 unit cell parameters a

As far as linear thermal expansion coefficients (LTECs) of the ASr2Eu(PO4)2SO4 are concerned, one can notice the descending trend of LTECs going from K as an A cation to Cs (Fig. 11). Such tendency can be explained via the A–O bond energy, which conspicuously grows from K to Cs [14, 15, 16]. Such strengthening of A–O bonds makes a substantial contribution to the inflexibility of the main framework. Furthermore, given that alkali atoms and Eu are relatively bulky, the decline in the magnitudes of LTECs can well be caused by straining the main framework, where polyhedra are interconnected with one another via edges and vertices, precluding the following elongation of the bonds.
Fig. 11

Dependence between LTECs α a and cation radii for ASr2Eu(PO4)2SO4 (A = K, Rb, Cs)

As for the BaxSr4−x(PO4)2SO4 solid solution, the negative deviation (Fig. 12) from the Vegard’s law is observed. Such behavior can well be attributed to the extreme structure disorder taking place, while Ba and Sr cations, which are different in size, occupy the framework positions simultaneously.
Fig. 12

Concentration dependence LTECs α a for BaxSr4−x(PO4)2SO4 (0 ≤ x ≤ 4)

The values of the linear coefficients of thermal expansion are presented in Table 3. Evidently, all compounds relate to highly expanding isotropic materials.
Table 3

Average thermal expansion coefficients α a in the region of 173–473 K


α a × 106/K−1






















We were the first to acquire ASr2Eu(PO4)2SO4 (A = K, Rb, Cs), NaBa6Zr(PO4)5SO4, Pb2Mg2(PO4)2SO4, and BaxSr4−x(PO4)2SO4 (0 ≤ x ≤ 4) phosphate–sulfates of eulytite structure and examine their thermal expansion parameters. As it turned out, compounds in question exhibit traits of highly expanding isotropic materials. The controlling of thermal expansion of eulytite-like compounds with the aim of its reduction has yet to be fulfilled.



The present work was performed at the Lobachevsky State University of Nizhni Novgorod with the financial support of the Russian Foundation for Basic Research (Project No. 18-03-00043).


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  • V. I. Pet’kov
    • 1
  • A. S. Dmitrienko
    • 1
  • A. I. Bokov
    • 1
  1. 1.Lobachevsky State University of Nizhni NovgorodNizhni NovgorodRussia

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