Introduction

Calcium phosphates have aroused much interest as bioactive compounds. They are used as components of different kinds of materials applied in dental and orthopedic surgery [1, 2].

Among other bioactive calcium compounds, tricalcium bis(phosphate), Ca3(PO4)2, is one of the most interesting materials. It melts congruently at a high temperature (T m = 1,810 °C) [3], and it has three polymorphic modifications: β, α, and α′. The α′ form exits at temperatures above 1430 °C [4] and it has a trigonal structure (S.G P\( \bar{3} \)m) with parameters: a = b = 5.3507(8), c = 7.684(1) Å [5]. It is not possible to overcool the polymorph, even in the course of quenching.

The α-Ca3(PO4)2 form is stable in a temperature range of 1,125–1,430 °C [6–8] and has a monoclinic structure with a P21/a space group [5, 9]. The biodegradation and bioreabsorption processes of α-Ca3(PO4)2 occur in physiological environment faster than that of hydroxyapatite and β-Ca3(PO4)2. This makes the α-phase suitable for application as osteoconductive material and/or biodegradable drug carrier [10, 11].

At temperatures below 1,125 °C exists the low-temperature β-Ca3(PO4)2 form, which is characterized by a trigonal structure with unit cell parameters: a = b = 10.4352(2) Å, c = 37.4029(5) Å [12]. The structure of the phase is complicated: there are five cationic sites with coordination number relative to oxygen from 3 to 8. In pure β-Ca3(PO4)2 or doped with divalent cations one of the Ca sites is half occupied [13, 14]. The same Ca position is empty for RE 3+ doping, which is associated with charge balance mechanism [15, 16]. This feature of the structure makes the β-Ca3(PO4)2 phase a perfect host lattice for doping with mono-, di-, and/or trivalent cations. The wide range of dopants and doping concentrations enables modification of physicochemical properties of Ca3(PO4)2. The β-Ca3(PO4)2-derived phases show optical activity [17–20], are considered as bioceramics or biocements [21–26] and show interesting electric properties [27–29].

The β→α structural change has a reconstructive character. This implies that a long-term heating at a temperature above the phase transition point is necessary to complete the β→α transformation. The process is reversible, however due to the high activation energy of the α→β transformation the monoclinic form of Ca3(PO4)2 does not revert to the low-temperature form, when cooled with moderate cooling rate (5 °C min−1) [8, 30].

The thermodynamically stable form of YPO4 is of xenotime type with structural parameters of tetragonal elementary cell (S.G. I41/amd): a = 6.8840(3), c = 6.0202(3) Å [31]. It is refractory material with a melting point at 1,995 ± 20 °C [32] or 2,150 °C [33].

Phase diagrams of phosphate systems with rare earth elements have been studied by our group in last decades [34–39]. In the Ca3(PO4)2-REPO4 systems (RE = Y, La, Ce) form compounds with the formula Ca3 RE(PO4)3 [34–36]. They exist only at high temperatures and have a regular structure of eulytite (S.G. I\( \bar{4} \)3d) [40, 41]. It has been also reported that the Ca3Y(PO4)3 phase has a complicated thermal behavior. According to Ref. [34] the phosphate melts congruently at 1,790 °C and at temperatures below 1,215 °C it decomposes to YPO4 and Ca3(PO4)2. In addition, the compound has a reversible β→α polymorphic transition at 1,255 °C. The Ca3Y(PO4)3 phase forms with Ca3(PO4)2 and YPO4 two eutectic systems with melting temperature at 1,684 and 1,674 °C, respectively. The Ca3Y(PO4)3 phase can be quenched to room temperature, however, during heating/cooling with rate of 40–400 °C min−1 occurs a martensitic transformation [41].

In the Ca3(PO4)2-REPO4 systems (RE = La, Ce, and Eu) fields of limited solid solution with the structure of β–Ca3(PO4)2 were found [16, 35, 36]. In contrast to the results, the study of the phase relationships in the Ca3(PO4)2–YPO4 system did not consider existence of any type of solid solution [34]. The comparison of the most recent phase equilibria studies of systems with Ca3(PO4)2 implies that the phase relationships in the Ca3(PO4)2–YPO4 system are more complicated as presented in the Ref. [34]. Because of an growing interest on materials derived from Ca3(PO4)2 and doped with rare earth elements, a revision of the Ca3(PO4)2–YPO4 system has been undertaken. The aim of the present research was to clarify the divergences between reported studies with the attention focused on thermal and concentration range of solid-solution phase fields, as well as on the polymorphism of the Ca3Y(PO4)3 eulytite phase.

Experimental

Synthesis

The following analytical reagents were used to obtain the Ca3(PO4)2 compound: CaCO3, CaHPO4 (analytical grade, POCh Gliwice). The phosphate was prepared in a solid state by the ceramic method according to method proposed in [42]. In this synthesis route, a stoichiometric mixture of CaCO3 and Ca2P2O7 was annealed at 900 °C for 5 h, which was followed by grinding in an agate mortar and heating for 5 h at 1,400 °C. The Ca2P2O7 compound was prepared from CaHPO4 by calcination at 900 °C (2 h).

The YPO4 was obtained by precipitation from a suspension of Y2O3 (99.99 %, POCh, Poland) in diluted H3PO4 (85 %, POCh Gliwice). The molar ratio of [PO4 3−]:[Y3+]:H2O was 1:0.023:25. The suspension was boiled under reflux for at least 6 h. The obtained precipitate was filtered and washed with hot distilled water. Finally, the powder was calcined at 1,400 °C for 2 h to expel moisture and adsorbed pyrophosphates.

The binary samples of the {(100–x)Ca3(PO4)2 + xYPO4} composition, where x ≤ 50 (x—the mass% of YPO4), were synthesized by carefully grinding of a mixture of Ca3(PO4)2 and YPO4. The chemical composition of samples under study is shown in the Tab. S1 (supplementary material). The powders were pelletized, preliminary heated at 900 °C for 10 h, and finally at 1,100 °C for 40 h in several heating steps. Between the stages samples were quenched, ground, and homogenized in an vibratory mill (Fritsch, Pulverisette 23) in isopropanol. The phase composition of samples was examined by X-ray diffraction (XRD) method. The same results of XRD measurements after two annealing steps were a prove that equilibrium state had been reached.

The Ca3Y(PO4)3 eulytite was obtained from Ca2P2O7 and Y2O3. The ground and pelletized mixture of the reagents was quenched after sintering stage at 1,400 °C for 10 h.

The samples were quenched from high temperatures (above 1,400 °C) as follows: the pelletized powders were closed in welded ampoules made of Pt30Rh and after appropriate heating steps dropped into a mixture of water and ice from a vertical tubular furnace.

Characterization methods

The DTA/TG experiments were carried out using Derivatograph 3427 (MOM, Hungary). The samples were heated in a temperature range of 20–1,450 °C (heating rate: 7.5 °C min−1, Pt crucible, sample mass 450–600 mg, air atmosphere). The temperature calibration factor for the thermal experiments was obtained at the phase transition temperature of K2SO4 (583 °C), its melting point (1,070 °C) and the melting point of Ca2P2O7 (1,353 °C).

Phase analysis of the samples was made using XRD technique and a Siemens D5000 diffractometer equipped with a Cu X-ray tube. The measurements were performed in 2θ range of 5–80° with a 0.02° step and at least 4 s per step. Silicon (99.995 % ABCR GmbH) was used as an external standard for refinement of structural parameters. Lattice constants of the β-Ca3(PO4)2 unit cell were refined using Checkcell software [43].

Results and discussionwec

Phase equilibria study

The phase composition of samples sintered at selected temperatures was obtained by the XRD measurements. In the diffraction patterns of samples sintered at 1,100 °C the main phase was β-Ca3(PO4)2 (Fig. 1). The YPO4 phase was found in samples with x(YPO4) ≥ 20 mass%. It should be also mentioned that several of the most intensive YPO4 reflections overlapped with these of β-Ca3(PO4)2. This made the qualitative analysis of the patterns complicated. The SEM study of the samples confirmed that the samples with x > 25 mass% are biphasic. In the Fig. 2 are shown the BSE images of samples with x(YPO4) = 15–30 mass%. The sample with the lowest content of YPO4 has a single-phase character (Fig. 2a). In the images of samples with x = 25 and 30 mass% secondary grains of light color are visible (Fig. 2b, c). The light color of grains is connected with high concentration of yttrium (element with high mass number). Unfortunately, the yttrium L line (1.922 keV) is very close to the P(K) absorption edge (2.013 keV). Since the lines overlap, the accurate determination of Y concentration in samples containing both elements (yttrium and phosphorus) can be not determined.

Fig. 1
figure 1

The XRD patterns of samples with different YPO4 concentration. Samples were obtained by quenching from 1,100 °C

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Fig. 2
figure 2

The SEM images (the BSE mode) of samples quenched from 1,100 °C. Sample with x(YPO4) = 15 (a), 25 (b), and 30 mass% (c)

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The lattice constants of the β-Ca3(PO4)2 unit cell for samples with the x ≤ 25 mass% were refined using the Checkcell software on basis of the β-Ca3(PO4)2 phase parameters reported in [13]. The change of the obtained lattice constants versus molar fraction of YPO4 is shown in Fig. 3 and the values are shown in Table 1. There is an evident decrease of c parameter value in the concentration range of 0–15 mass% (0–23 mol%) and according to the Vegard’s rule in the range exits the limited solid solution of YPO4 in β-Ca3(PO4)2. The ionic radius of yttrium (1.02 Å) is smaller than that of calcium 1.12 Å [44] and hence the exchange of yttrium for calcium ions in the structure of β-Ca3(PO4)2 results in a decrease of the solid solution unit cell volume (Table 1).

Fig. 3
figure 3

The unit cell parameters of the solid solution of YPO4 in β-Ca3(PO4)2 versus molar fraction of YPO4

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Table 1 The lattice parameters of Ca3−3z Y z (PO4)2−z solid solution in samples heated at 1,100 °C for 40 h and quenched in ice
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The chemical composition of the obtained solid solution can be expressed by the formula: Ca3−3z Y z (PO4)2−z , where z is the molar fraction of YPO4. Yttrium is introduced into the structure of β-Ca3(PO4)2 with simultaneous formation of vacancy according to the scheme: 3Ca2+→ 2Y3+ + \( \square \) [15, 16]. It has been stated in Refs. 15–17 that the maximal REPO4 concentration in the β-Ca3(PO4)2 solid solution should not exceed 25 mol%. The maximal RE concentration is connected with the fact that at that point, the smallest and irregular Ca site is completely vacant [16, 17].

The phase composition of samples quenched from 1,400 °C was depended on mass content of YPO4. The Fig. 4 presents the XRD patterns of samples with x ≤ 12 mass% of YPO4 heated at the temperature.

Fig. 4
figure 4

The XRD patterns of samples with different YPO4 concentration quenched from 1,400 °C

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In the sample with 2.4 mass% of YPO4 reflections of only α-Ca3(PO4)2 have been found. The same phase composition has been found by XRD for the sample quenched from 1,600 °C. The pellets quenched from high temperatures were cracked, which was a sign of transitions occurring in the material. In order to obtain the sample with x(YPO4) = 2.4 mass% in the α structure, quenching from high temperatures was necessary. The same powders cooled in an electric furnace with moderate cooling rate were characterized by the presence of only β phase. This finding is in contradiction with the metastable character of the overcooled α form in the Ca3(PO4)2–Mg3(PO4)2 system [8]. The authors of the manuscript stated that quenching is not required to retain the α phase on cooling.

The preparation with x = 5 mass% of YPO4 was diphase; both α and β-Ca3(PO4)2 phase reflections were identified in the XRD pattern (Fig. 4). The diffractogram of the sample quenched from 1,600 °C did not show considerable changes. On the DTA curve of the powder, three endothermic effects were registered at 1305, 1375, and 1420 °C.

The powders with 10 < x<50 sintered at 1,400 °C were biphasic and contained β-Ca3(PO4)2 solid solution and Ca3Y(PO4)3 phosphate.

The presence of the β phase in the samples quenched from high temperatures was surprising, since the α/α′-Ca3(PO4)2 solid solutions formation has been evidenced in the sample with the lowest YPO4 content. As mentioned above, on the DTA curves of the powders with the low YPO4 content, thermal effects connected to phase transitions have been observed. The presence of the β form instead of the α (or α′) solid solution could be explained by the probable lower energy barrier of the α→β transition occurring on cooling in the Ca3(PO4)2 solid solutions in comparison to the undoped Ca3(PO4)2. Since the high-energy barrier stabilizes the metastable α phase at room temperature, its lowering should result in rapid transition and presence of the low-temperature solid solution in samples quenched from high temperatures. At the same time, the α′ modification of Ca3(PO4)2 could be not obtained by quenching [4].

Thermal behavior of Ca3Y(PO4)3

The Ca3Y(PO4)3 phosphate belongs to phases existing at high temperatures. Presence of the compound was identified only in samples quenched from temperatures above 1,255 °C. In the present study, the phase pure compound has been obtained by reacting of Ca2P2O7 and Y2O3 at 1,400 °C. In the previously published studies [35, 36, 45] it has been shown that the most effective route to obtain phase pure Me 3 RE(PO4)3 phases is the application of more reactive substrates, for instance Me 2P2O7 and RE oxides. This eliminates the problem with the relative slow eulytite formation, which is dependent on diffusion processes occurring upon β-Ca3(PO4)2 solid solution decomposition. In addition, quenching from high temperatures (above of ~1,250 °C) is necessary to obtain single-phase powders. When quenched, the Me 3 RE(PO4)3 phases show metastable character, since slow diffusion in bulk at room temperature stops the decomposition of the compound.

The thermal behavior of phase pure Ca3Y(PO4)3 was studied by DTA (Fig. 5a) and XRD (Fig. 6) techniques. On the heating curve of the compound quenched from 1,400 °C two thermal effects were identified: exothermic and endothermic one at, respectively, 840 and 1,275 °C (Fig. 5a).

Fig. 5
figure 5

The DTA curves of heating of Ca3Y(PO4)3 compound obtained by quenching from 1,400 °C (a) and the same sample subjected to heating 20 h at 1,100 °C (b)

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Fig. 6
figure 6

The XRD patterns of Ca3Y(PO4)3 compound obtained at 1,400 °C (a) and the same sample after heating at 400 °C (b), 1,240 °C (c), and 1,285 °C(d)

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The single-phase powder (consisting of eulytite phase only) subjected to 20 h heating at 1,100 °C was biphasic (Fig. 6c). It composed of a mixture of β-Ca3(PO4)2 solid solution and YPO4 and showed a slightly different thermal behavior (Fig. 5b). No exothermic effects were observed on the DTA curve, however, two endothermic effects were recognized: one broad and weak peak at ~1,255 °C and one strong effect at 1,315 °C.

The XRD patterns of the Ca3Y(PO4)3 sample heat treated at different temperatures (Fig. 6) helped to explain the observed thermal effects. The Ca3Y(PO4)3 compound has been found in powders quenched from 1,400 and 1,285 °C (Fig. 6a, d). Heating of the phase pure phosphate at a temperature below 840 °C, i.e., below the temperature of the exothermic effect, did not change the phase composition of the powder, it remained single phase (Fig. 5b). The same powder quenched from 1,100 and 1,240 °C was biphasic and composed of a mixture of YPO4 and β-Ca3(PO4)2 solid solution (Fig. 6c). From the results of the XRD study, it can be concluded that the formation point of Ca3Y(PO4)3 lies between 1,240 and 1,285 °C and the metastable phase decomposes at temperature range 840–1,255 °C.

Summarizing, the thermal effects visible on the DTA heating curves of Ca3Y(PO4)3 (Fig. 5) can be attributed to following processes:

  • decomposition of the overcooled (metastable) Ca3Y(PO4)3 phase into the β-Ca3(PO4)2 solid solution and YPO4 at ~840 °C (the exothermic effect in Fig. 5a);

  • crystallization of the Ca3Y(PO4)3 phase from parent phosphates taking place in a temperature range (the endothermic effects on both DSC curves in the temperature range 1,255–1,315 °C).

The onset temperature of the first endothermic effect (1,255° C) was chosen as the starting point of the compound synthesis from YPO4 and β-Ca3(PO4)2 solid solution. The formation of Ca3Y(PO4)3 occurs with difficulties at this temperature because it is accompanied by a significant change in the chemical composition of the solid solution being in equilibrium. Above 1,255 °C the Ca3Y(PO4)3 compound should be regarded as a thermodynamically stable phase.

The observed thermal behavior of the Ca3Y(PO4)3 compound is similar to that of the Ca3Ce(PO4)3 and Sr3Ce(PO4)3 phases [36, 45]. The phases can be quenched from temperatures exceeding their formation point and they are metastable present at room temperature. Upon heating of the metastable phases at a moderate temperature (upto ~800 °C) the decomposition of the phosphates is stopped, by kinetic hindrances. First at ~800 °C starts the decomposition, which manifests on DTA curves in form of exothermal effects. Above the temperature, the powders can attain the equilibrium state. Under further heating YPO4 and β-Ca3(PO4)2 solid solution react at a temperature above of 1,255 °C, which results in formation of the eulytite-type phase. The synthesis of the high-temperature phosphate is accompanied by a registration one or two endothermic effects on the DTA heating curves. The same thermal behavior has been registered for the Ca3Ce(PO4)3 phase [36].

It has been shown in [34] that the Ca3Y(PO4)3 phosphate forms at 1,215 °C and has a polymorphic transition at 1,255 °C. In contrast to the statement, it has been above revealed that the compound is not a stable phase at 1,240 °C. In addition, in Refs. [38, 45] it has been shown that the thermal effects connected to the formation/decomposition of Me3RE(PO4)3 are characterized by a large thermal hysteresis. The difference between the onset temperatures of effects on heating and cooling DTA curves is connected to kinetic hindrances occurring by the decomposition/formation of new phases and is a sign of reconstructive-type transformations [45, 46]. Because the experiments presented in [34] were carried out in cooling runs, the most probably the effects at 1,215 and 1,255 °C were both connected to the decomposition of Ca3Y(PO4)3.

The phase diagram of the Ca3(PO4)2–YPO4 system

On basis of results of the XRD and DTA study, it was possible to propose a revised version of the Ca3(PO4)2–YPO4 phase diagram (Fig. 7). The figure summarizes all onset temperatures of the endothermic effects registered during the DTA heating runs of samples sintered at 1,100 °C. The temperature and composition of eutectic points, as well as the melting point of Ca3Y(PO4)3 have been adopted from [34]. The melting point of Ca3(PO4)2 has been taken from [3].

Fig. 7
figure 7

The phase diagram of the Ca3(PO4)2–YPO4 system. The abbreviations α′ss, αss, and βss denote, respectively, α′, α, and β-Ca3(PO4)2 solid solutions. [∇–onset temperatures of endothermic effects registered on DTA heating curves]

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There are three solid-solution phase fields. The composition range of the limited solid solution of YPO4 in β-Ca3(PO4)2 has been found by the XRD study. At 1,100 °C the maximal content of YPO4 in the solid solution is ~15 mass% (~23 mol%).

The existence of the limited solid solutions at high temperatures has been evidenced by the observed temperature change of β→α and α→α′ transitions. The limited solid solutions with the α and α′-Ca3(PO4)2 structure exist in narrowed phase fields in comparison to the β phase. The maximal doping of the α solid solution with RE amounts to ~3 mass%. This may not be sufficient active ion content in the α phase necessary to achieve a long-lasting phosphorescence or to apply the material in thermoluminescence dosimetry [47].

There are several similarities between the Ca3(PO4)2–YPO4 and Ca3(PO4)2–CePO4 systems [36]. Despite the difference between the CePO4 (monazite) and YPO4 structures (xenotime), concentration and temperature ranges of all phases in the systems are close to each other.

Conclusions

The phase diagram of the Ca3(PO4)2–YPO4 system has been proposed in the revised form. The presented results confirm existence of three fields of limited solid solution with β, α-, and α′-Ca3(PO4)2 structure. At 1,100 °C the single-phase field of the YPO4 solid solution in β-Ca3(PO4)2 extends to ~15 mass% (~23 mol%). The high-temperature solid solutions form in narrowed concentration range in comparison to the β phase.

The doping by YPO4 results in easier α→β transformation than in pure Ca3(PO4)2. The metastable α solid solution can be obtained only by quenching of samples with the low YPO4 content. Since the doped material crack on cooling, obtaining of dense ceramic with the α structure is not possible.

The Ca3Y(PO4)3 phosphate is a thermodynamically stable phase at temperature exceeding 1,255 °C, and it has one structural form.