**5.1 Apatite-type lanthanium silicates**

During recent decades, oxyapatite2 -type structure with the general formula: REE9.33+xSi6O26+3x/2 (where REE is rare-earth element) [3],[4], REE9.33□0.67(SiO4)6O2 [5] or REE10−x(SiO4)6O2+y [6] has attracted considerable attention as oxide ion conductors. Apatite-type oxides have attracted much attention as the material for electrolytes in solid oxide fuel cell and sensors (**Chapter 10**).

In low atomic number rare-earth silicate systems, an apatite phase occurs with a range of stability extending from Ln4.67(SiO4)3O to Ln4(SiO4)3. The stability decreases as the rare-earth atomic number increases, with a mixture of Ln2SiO5 and Ln2Si2O7 replacing apatite as the preferred phase assemblage [7],[8],[9],[10],[11].

Apatite-type rare-earth element (REE) silicates of the composition of REE10−x(SiO4)6O2+y, where REE = La, Nd, Gd and Dy, were prepared by MARTÍNEZ-GONZÁLEZ et al [6] via the mechano‐ chemical synthesis (stabilized zirconia planetary ball mill: ball-to-powder ratio ~10:1, 350 rpm for maximum time of 9 h) starting from the stoichiometric mixtures of constituent oxides, REE2O3 and SiO2 (molar ratio = 4:5), followed by post-milling thermal treatment (1500°C for 3 h). The ionic conductivity increases with the increasing size of REE cations.3 The mechano‐

Apatite-type silicates described in this chapter can be also named as oxy-britholites (oxybritholites) [84].

<sup>2</sup> Since the prefix "oxy-" can be explained as containing oxygen or additional oxygen, and the prefix "oxo-" is used for the functional group or substituent oxygen atom connected to another atom by a double bond (=O), the names oxyapatite, oxy-apatite, oxoapatite and oxo-apatite can be considered as synonyms. In the published literature, the name oxyapatite is the most frequently used (~90%), and the term oxy-apatite is the second (~8%). The names oxoapatite and oxo-apatite are used much rarely (only about ~2%).

<sup>3</sup> This conclusion is in discrepancy with the findings of HIGUCHI et al [12] described below.

chemical synthesis of apatite-type lanthanum silicates from the mixture of La2O3 and amor‐ phous silica without post-milling thermal treatment was described by FUENTES et al [4].

Rare-earth element-doped apatite-type lanthanum silicates of the composition of La9MSi6O27, where M = Nd, Sm, Gd and Yb, were synthesized by the high-temperature solid-state reaction process by XIANG et al [3]. All rare-earth oxide powders (La2O3, Nd2O3, Sm2O3, Gd2O3 and Yb2O3) were firstly pre-calcined at 900°C for 2 h in order to achieve complete decarbonation and dehydroxylation before weighing. The stoichiometric mixtures were mechanically mixed in absolute ethanol for 24 h using zirconia milling media at the speed of 400 rpm and dried at 100°C in air. The powder mixture was calcined at 1350°C for 10 h and then ground by hand with an agate mortar and pestle to reduce the particle size. After that, the powders were uniaxially pressed at 20 MPa and then statically cold pressed at 200 MPa for 5 min. The compacts were pressureless sintered at 1650 K for 10 h in air.


**Table 1.** The properties of apatite-type lanthanium silicates [3],[8].

**Fig. 1.** Illustration of "microporous" M(1)(XO4)6 framework of the apatite (M10(XO4)6O2) structure (a): tetrahedra MO4, M(1) cation at the center of trigonal meta-prism. Remaining M(2)6O2 units occupy the cavities within this framework

(where REE is rare-earth element) [3],[4], REE9.33□0.67(SiO4)6O2 [5] or REE10−x(SiO4)6O2+y [6] has attracted considerable attention as oxide ion conductors. Apatite-type oxides have attracted much attention as the material for electrolytes in solid oxide fuel cell and sensors (**Chapter 10**).

In low atomic number rare-earth silicate systems, an apatite phase occurs with a range of stability extending from Ln4.67(SiO4)3O to Ln4(SiO4)3. The stability decreases as the rare-earth atomic number increases, with a mixture of Ln2SiO5 and Ln2Si2O7 replacing apatite as the

Apatite-type rare-earth element (REE) silicates of the composition of REE10−x(SiO4)6O2+y, where REE = La, Nd, Gd and Dy, were prepared by MARTÍNEZ-GONZÁLEZ et al [6] via the mechano‐ chemical synthesis (stabilized zirconia planetary ball mill: ball-to-powder ratio ~10:1, 350 rpm for maximum time of 9 h) starting from the stoichiometric mixtures of constituent oxides, REE2O3 and SiO2 (molar ratio = 4:5), followed by post-milling thermal treatment (1500°C for 3

<sup>2</sup> Since the prefix "oxy-" can be explained as containing oxygen or additional oxygen, and the prefix "oxo-" is used for the functional group or substituent oxygen atom connected to another atom by a double bond (=O), the names oxyapatite, oxy-apatite, oxoapatite and oxo-apatite can be considered as synonyms. In the published literature, the name oxyapatite is the most frequently used (~90%), and the term oxy-apatite is the second (~8%). The names oxoapatite and oxo-apatite

h). The ionic conductivity increases with the increasing size of REE cations.3

Apatite-type silicates described in this chapter can be also named as oxy-britholites (oxybritholites) [84].

This conclusion is in discrepancy with the findings of HIGUCHI et al [12] described below.


The mechano‐

(b): large spheres are M(2) cations and small spheres are O anions [2].

246 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

**5.1 Apatite-type lanthanium silicates**

preferred phase assemblage [7],[8],[9],[10],[11].

During recent decades, oxyapatite2

are used much rarely (only about ~2%).

3

The lattice parameters and the properties of prepared apatite-type lanthanium silicates are listed in **Table 1**. All prepared compounds possess hexagonal apatite structure with the space group P63/M. The temperature dependence of total electrical conductivity for different compositions is determined using the Arrhenius equation4 [13],[14],[15] in the following form [3],[5],[16],[17]:

$$
\sigma \sigma \ T = \sigma\_0 \cdot \exp\left(-\frac{E}{k\_B T}\right) = \sigma\_0 \cdot \exp\left(-\frac{\Delta H\_{\rm m} + \Delta H\_{\rm d}}{k\_B T}\right) \tag{1}
$$

where *σ* is the total electrical conductivity, *σ*0 is the pre-exponential factor related to the effective number of mobile oxide ions, *E* is the activation energy for the electrical conduction process, *k*B is the Boltzmann constant and *T* is absolute temperature. Δ*H*m and Δ*H*a denote the

<sup>4</sup> The equation of SVANTE AUGUST ARRHENIUS [13],[14], which predicts that the rate constant *k* depends on the tempera‐ ture: *k* = *A exp* (-*E*a/*RT*), where *A* is the frequency (pre-exponential factor), *E*a is the activation energy, *R* is universal gas constant (8.314 J·K−1·mol−1) and *T* is the thermodynamic temperature [13].

migration enthalpy of oxygen ion and the association enthalpy of defects, respectively. The determined activation energy and pre-exponential factor are listed in **Table 1**. It can be seen that the activation energy gradually increases from La10Si6O27 to La9GdSi6O27. Total electrical conductivity can be calculated from the following equation:

$$
\sigma = \frac{\text{h}}{\text{RS}} \tag{2}
$$

where *h* is the thickness of the specimen, *S* is the electrode area of the specimen surface and *R* is the total resistance including grain and grain boundary resistance. Lanthanum silicates doped with Nd or Yb cations exhibit higher total electrical conductivity than undoped lanthanum silicates. The highest total conductivity value obtained at 500°C is 4.31·10−4 S·cm−1 for La9NdSi6O27. The total electrical conductivity is also a function of partial pressure of oxygen [3].

**Fig. 2.** Crystal structure of apatite-type rare-earth element silicate viewed along the c-axis [12].

The measurements using single crystals revealed definite anisotropy of the electrical conduc‐ tivity of Ln9.33(SiO4)6O2, that is, the conductivity parallel to the c-axis is larger by one order of magnitude than that perpendicular to the c-axis. This fact clearly indicates that the channel oxide ions not bonded to silicon are the principal charge carriers in apatite-type lanthanum silicates. The structure of apatite-type rare-earth silicate is shown in **Fig. 2**. SiO4 tetrahedra are isolated mutually, and Ln ions (REE ions, in general) at 6*h* sites (sevenfold coordinated site (x,y,¼)) [18]5 form channels, in which oxide ions at 2*a* sites are located (possess the threefold coordination with rare-earth ions at the 6*h* sites in the same plane), along the c-axis.

These mobile ions at these sites have much larger anisotropic displacement parameters in the direction of the c-axis than those in the direction of the a-axis, even at room temperature, which reflects high oxide ion conduction along the c-axis. The ninefold coordinate position (4*f* site (1/3,2/3,*z*)) is the second site for the accommodation of REE cations in the structure of apatitetype REE silicate [6],[12],[19],[20].

migration enthalpy of oxygen ion and the association enthalpy of defects, respectively. The determined activation energy and pre-exponential factor are listed in **Table 1**. It can be seen that the activation energy gradually increases from La10Si6O27 to La9GdSi6O27. Total electrical

> h σ

where *h* is the thickness of the specimen, *S* is the electrode area of the specimen surface and *R* is the total resistance including grain and grain boundary resistance. Lanthanum silicates doped with Nd or Yb cations exhibit higher total electrical conductivity than undoped lanthanum silicates. The highest total conductivity value obtained at 500°C is 4.31·10−4 S·cm−1 for La9NdSi6O27. The total electrical conductivity is also a function of partial pressure of

RS <sup>=</sup> (2)

conductivity can be calculated from the following equation:

248 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

6*h* site (Ln)

4*f* site (Ln)

*c*

**Fig. 2.** Crystal structure of apatite-type rare-earth element silicate viewed along the c-axis [12].

*a* 2*a* site (O) SiO4

The measurements using single crystals revealed definite anisotropy of the electrical conduc‐ tivity of Ln9.33(SiO4)6O2, that is, the conductivity parallel to the c-axis is larger by one order of magnitude than that perpendicular to the c-axis. This fact clearly indicates that the channel oxide ions not bonded to silicon are the principal charge carriers in apatite-type lanthanum silicates. The structure of apatite-type rare-earth silicate is shown in **Fig. 2**. SiO4 tetrahedra are isolated mutually, and Ln ions (REE ions, in general) at 6*h* sites (sevenfold coordinated site

coordination with rare-earth ions at the 6*h* sites in the same plane), along the c-axis.

form channels, in which oxide ions at 2*a* sites are located (possess the threefold

*a*

oxygen [3].

(x,y,¼)) [18]5

Since the interstitial space provided by these rare-earth ions is the smallest throughout the channel along the c-axis of the apatite structure, the migration of oxide ions through the channel will not be affected significantly even if the sizes of rare-earth ions are varied. It is therefore reasonable that the electrical conductivities of apatite-type rare-earth silicates are independent on the kind of rare-earth elements [12].

Conventional oxide ion conductors are designed on the basis of the oxygen vacancy model by the introduction of aliovalent6 [21] cations. In Ln9.33(SiO4)6O2, however, cation vacancies are present rather than oxygen vacancies. Therefore, the introduction of cation vacancies into the structure of an oxide material may induce high oxide ion conductivity if the structure has a channel or a plane that can be a path for the migration of oxide ions [12].

Apparent exchange of O(1), O(2) and O(3) oxide ions bonded to Si was observed by 17O NMR measurement on La9.33Si6O26 by KIYINO et al [22], while it was not observed for oxide ion on the isolated site O(4). The results indicate that oxide ions bonded to Si at the position O(1), O(2) and O(3) are the main diffusion species in the oxide ion conductivity.

Trivalent and divalent dopants7 [23] have been introduced into the La9.33(SiO4)6O2 structure according to the following nominal mechanisms [24]:

$$\text{Si}^{4\*} \rightarrow \text{M}^{3\*} + \frac{1}{3} \text{La}^{3\*} \tag{3}$$

$$\frac{2}{3}\text{La}^{3\*} \rightarrow \text{AEE}^{2\*} \tag{4}$$

$$\frac{1}{3}\text{La}^{3+} \rightarrow \text{AEE}^{2+} + \frac{1}{2}\text{O}^{2-} \tag{5}$$

<sup>5</sup> According to the WYCKOFF notation: the specification of actual coordinates of atoms within the unit or primitive cell, which can be generated by the point-group operations or may be found by reference in the International Tables for Crystallography [18].

<sup>6</sup> Cation with different valence. Apatite structure shows large flexibility upon the substitution of other aliovalent cations at the 'Ca' sites, pentavalent and tetravalent ions such as V5+, As5+ and Si4+ at the 'P' site and halide, oxide ions at the 'OH' site [21], as was described.

<sup>7</sup> Dopants are also termed as doping agents. It can be defined as an impurity element added to the material structure in low concentration (usually <1 wt.% [23]) in order to alter its properties.

where M = Al, Ga, B, Co, Fe, Mn, … and AEE denotes the alkaline-earth elements (Ca, Sr and Ba). Doping with Al, Ga and B according to the formula: La9.33+x/3(SiO4)6−x(MO4)xO2, via the mechanism in **Eq. 3**, causes that bulk conductivity increases in up to two orders of magni‐ tude in the case of Al for *x* = 1 – 1.5. If, however, the sample is stoichiometric on both cation and anion sites, as for La8Sr2(SiO4)6O2, the AEE doping reduces the conductivity and increas‐ es the activation energy for the conduction compared to La9.33(SiO4)6O2.

The effect of Fe doping on the electrical properties of lanthanum silicates of the composition of La10Si6−xFexO27−x/2 (where *x* = 0.2, 0.4, 0.6, 0.8 and 1.0) was performed by SHI and ZHANG [16] via the sol-gel process. Tetraethyl orthosilicate (TEOS), La(NO3)3·6H2O and Fe(NO3)3·9H2O were used as starting materials. Stoichiometric amounts of Fe(NO3)3·9H2O and La(NO3)3·6H2O were dissolved in the mixture of ethanol, acetic acid and distilled water. The appropriate amount of TEOS was added to the solution while continuous stirring. The solution became gradually a purple clear sol. After refluxing at 80°C for 1 – 2 h, the sol transferred to a clear gel. Then, the wet gel was dried at 100°C for 20 h. The gel was heated at 600°C for 4 h to remove water and organic components and to decompose nitrates. In order to get the desired phase, obtained precursor was then calcined at 1000°C for 4 h.


**Table 2.** Lattice parameters of Fe-doped apatite-type lanthanium silicates [16].

All synthesized samples have hexagonal lattice structure with the space group of P63/M. The lattice parameters of prepared Fe-doped apatite-type lanthanium silicates and the activation energy of conductivities (**Eq. 1**) for different Fe contents are listed in **Table 2**. When *x* = 0.6, La10Si5.4Fe0.6O26.7 exhibits the lowest activation energy. The lattice parameters of La10Si6O27 (**Table 1**) and doped specimen (**Table 2**) show that the values of *a*, *c* and *V* increase with the content of iron. The conductivity of La10Si6−xFexO27−x/2 is independent of oxygen partial pressure in the range from 0 to 100 kPa, which indicates that the conductivity of all samples is mainly ionic [16].

The oxygen ionic and electronic transport in apatite ceramics with the composition of La10Si6−xFexO27−x/2 (*x* = 1 – 2) [25] and La10−xSi6−yAlyO27−3x/2−y/2 (*x* = 0 – 33; *y* = 0.5 – 1.5) [26],[27] was investigated by SHAULA et al In both cases, the essential role of oxygen content on the ionic conductivity of apatite phase was recognized. The ion transference number8 [28] increases with decreasing partial pressure of oxygen. Such behavior indicates that the conduction under oxidizing condition is predominantly of p-type9 (with respect to n-type of conductivity). Similar to the foundation of SHI and ZHANG [16], the conductivity of these phases is predominantly ionic and almost independent on partial pressure of oxygen. The ion transference numbers are higher than 0.99, while the p-type electronic contribution to total conductivity is about 3% (700 – 950°C, La10Si4Fe2O26). The oxygen ionic conductivity should increase with decreasing iron content due to higher concentration of oxygen interstitials.

Another important factor influencing the oxygen diffusion is M-site deficiency, which affects the unit cell volume and may cause the O(5) ion displacement into interstitial sites, thus creating the vacancies in the O(5) sites at fixed total oxygen content. In particular, an en‐ hanced ionic conduction was found in the system La9.33+x/3Si6−xAlxO26, where Al doping is compensated by the A-site vacancy concentration without oxygen content variations [29],[30].

The incorporation of praseodymium in the apatite-type lattice of La9.83−xPrxSi4.5Fe1.5O26+δ (*x* = 0 – 6) decreases the unit cell volume, suppresses the Fe4+ formation according to Mössbauer spectroscopy10 [31],[32],[33],[34] and increases p- and n-type electronic contributions to total conductivity under oxidizing conditions, while the level of oxygen ionic transport at tem‐ peratures above 1000 K remains unaffected [35].

Since the size of the conduction channel increases with the Mg doping, the enhancement of the ionic conductivity of lanthanum silicate-based apatites can be reached by optimizing the La content and the Mg doping level at the same time. The ionic conductivities of La10Si5.8Mg0.2O26.8 and La9.8Si5.7Mg0.3O26.4 at 800°C are 88 and 74 mS·cm−1 with the activation energy of 0.43 and 0.42 eV, respectively [36].

The ionic conduction in cation-deficient apatite La9.33−2x/3MxSi6O26, where M = Mg, Ca and Sr was investigated by YUAN et al [37]. The nature of dopant and the extent of substitution have a significant effect on the conductivity. The greatest decrease in conductivity is observed for Mg doping followed by Ca- and Sr-doped apatites. The effect is ultimately attributed to the amount of oxygen interstitials, which is affected by the crystal lattice distortion arising from the cation vacancies.

The incorporation of additional La2O3 into La9.33(SiO4)6O2 to form La10(SiO4)6O3 or intermedi‐ ate compositions can most obviously be achieved by filling empty interstitial sites with oxygen. The only alternative scenario would involve the creation of cation vacancies on the Si sublattice, which is unlikely as Si is present as a complex anion. The incorporation of excess of La2O3 into La9.33(SiO4)6O2 can therefore be expressed as [10]:

where M = Al, Ga, B, Co, Fe, Mn, … and AEE denotes the alkaline-earth elements (Ca, Sr and Ba). Doping with Al, Ga and B according to the formula: La9.33+x/3(SiO4)6−x(MO4)xO2, via the mechanism in **Eq. 3**, causes that bulk conductivity increases in up to two orders of magni‐ tude in the case of Al for *x* = 1 – 1.5. If, however, the sample is stoichiometric on both cation and anion sites, as for La8Sr2(SiO4)6O2, the AEE doping reduces the conductivity and increas‐

The effect of Fe doping on the electrical properties of lanthanum silicates of the composition of La10Si6−xFexO27−x/2 (where *x* = 0.2, 0.4, 0.6, 0.8 and 1.0) was performed by SHI and ZHANG [16] via the sol-gel process. Tetraethyl orthosilicate (TEOS), La(NO3)3·6H2O and Fe(NO3)3·9H2O were used as starting materials. Stoichiometric amounts of Fe(NO3)3·9H2O and La(NO3)3·6H2O were dissolved in the mixture of ethanol, acetic acid and distilled water. The appropriate amount of TEOS was added to the solution while continuous stirring. The solution became gradually a purple clear sol. After refluxing at 80°C for 1 – 2 h, the sol transferred to a clear gel. Then, the wet gel was dried at 100°C for 20 h. The gel was heated at 600°C for 4 h to remove water and organic components and to decompose nitrates. In order to get the desired phase,

**Apatite-type lanthanium silicate Lattice parameters [Å]** *V E* **(600 – 800°C)** *E* **(400 – 550°C)** *a c* **[Å3**

All synthesized samples have hexagonal lattice structure with the space group of P63/M. The lattice parameters of prepared Fe-doped apatite-type lanthanium silicates and the activation energy of conductivities (**Eq. 1**) for different Fe contents are listed in **Table 2**. When *x* = 0.6, La10Si5.4Fe0.6O26.7 exhibits the lowest activation energy. The lattice parameters of La10Si6O27 (**Table 1**) and doped specimen (**Table 2**) show that the values of *a*, *c* and *V* increase with the content of iron. The conductivity of La10Si6−xFexO27−x/2 is independent of oxygen partial pressure in the range from 0 to 100 kPa, which indicates that the conductivity of all samples is mainly

The oxygen ionic and electronic transport in apatite ceramics with the composition of La10Si6−xFexO27−x/2 (*x* = 1 – 2) [25] and La10−xSi6−yAlyO27−3x/2−y/2 (*x* = 0 – 33; *y* = 0.5 – 1.5) [26],[27] was investigated by SHAULA et al In both cases, the essential role of oxygen content on the ionic

decreasing partial pressure of oxygen. Such behavior indicates that the conduction under

conductivity of apatite phase was recognized. The ion transference number8

La10Si5.8Fe0.2O26.9 9.725 7.192 589.1 0.78 0.96 La10Si5.6Fe0.4O26.8 9.729 7.208 590.8 0.74 0.95 La10Si5.4Fe0.6O26.7 9.732 7.220 592.2 0.72 0.89 La10Si5.2Fe0.8O26.6 9.735 2.217 592.3 0.74 1.01 La10Si5FeO26.5 9.743 7.229 593.5 0.75 1.02

**] [eV]**

[28] increases with

es the activation energy for the conduction compared to La9.33(SiO4)6O2.

250 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

obtained precursor was then calcined at 1000°C for 4 h.

**Table 2.** Lattice parameters of Fe-doped apatite-type lanthanium silicates [16].

ionic [16].

<sup>8</sup> The fraction of total current that is transferred by a given ion is affected by its mobility. The sum of transport numbers for all ions in electrolyte is equal to one [28].

<sup>9</sup> The p-type carriers possess typically higher mobility [25].

<sup>10</sup> The technique is based on the Mössbauer effect of recoil-free nuclear resonance fluorescence [31], i.e. the phenom‐ enon of emission or absorption of X-ray photon without the loss of energy. The Mössbauer effect has been detected in a total of 88 X-ray transitions in 72 isotopes of 42 different elements [32]. The 57Fe Mössbauer isotope is the most frequently used [33]. The Mössbauer spectroscopy can be used to determine the oxidation states of iron in minerals and to identify the presence of some mineral species in samples of unknown composition [31].

$$\mathrm{La}\_{9.33} \left[ \begin{array}{c} \text{I}\_{0.67} \text{(SiO}\_4\text{)}\_6 \text{O}\_2 + \text{I} / 3 \text{ La}\_2 \text{O}\_3 \rightarrow \text{La}\_{10} \text{(SiO}\_4\text{)}\_6 \text{O}\_2 \text{O}\_i \text{(La}\_{10} \text{(SiO}\_4\text{)}\_3 \text{O}\_3 \end{array} \right] \tag{6}$$

Thus, in the ideal pure La10(SiO4)6O3, the 4*f* and 6*h* sites are fully occupied by La3+ ions, while an extra oxygen interstitial is introduced into the lattice to maintain the electroneutrality. The oxygen interstitial may benefit the oxide ion transportation if it is located nearby the [001] direction c-axis of the conventional unit cell. From the space-filling consideration, the most appropriate sites for the oxygen occupation are in this position; however, some distortion of the O 2*a* sites would be required to accommodate extra oxygen atoms. This could be ach‐ ieved by decreasing the symmetry from P63/M to P63 allowing oxygen to move from 0,0,1/4 to 0,0,x. Recent studies suggest that a range of partially occupied (0,0,x) sites may accommo‐ date this extra interstitial oxygen. From this point of view, La10(SiO4)6O3 should exhibit higher conductivity than La9.33(SiO4)6O2 [10],[38].

Introducing Sr2+ cations to the La3+ atomic positions, as in the La10(SiO4)6O3 phase, leads to complete elimination of vacancies according to the substitution [39]:

$$\mathrm{La}\_{10}\left(\mathrm{SiO}\_{4}\right)\_{6}\mathrm{O}\_{3} \xrightarrow{\ast \mathrm{Sr}^{2\*}} \mathrm{La}\_{8}\mathrm{Sr}\_{1}\left(\mathrm{SiO}\_{4}\right)\_{6}\mathrm{O}\_{2\cdot 3} \xrightarrow{\ast \mathrm{Sr}^{2\*}} \mathrm{La}\_{8}\mathrm{Sr}\_{2}\left(\mathrm{SiO}\_{4}\right)\_{6}\mathrm{O}\_{2}\tag{7}$$

The substitution of La2O3 by SrO, taking into account the charge balance and the oxygen content, can be represented as follows (KRÖGER-VINK notation11 [40],[41]):

$$\text{SrO} + 1/2\text{ O}\_{\text{o}}^{\text{x}} + \text{La}\_{\text{La}}^{\text{x}} \rightarrow \text{Sr}\_{\text{La}}^{\text{'}} + 1/2\text{ V}\_{\text{o}}^{\text{'''}} + 1/2\text{ La}\_{2}\text{O}\_{3} \tag{8}$$

Lanthanum oxyapatite phases are substantially stable with respect to their binary oxides. The general trend in the formation enthalpies as a function of (La + Sr)/(La + Sr + Si) shows that the apatite phase becomes more energetically stable as the cation vacancy and oxygen excess concentrations decrease. The stoichiometric sample achieved by Sr2+ doping, with no cation vacancies or interstitial oxygen atoms, is the most stable composition. The energetics of lanthanum silicate apatite materials (La9.33+x(SiO4)6O2+3x/2 and La10−xSrx(SiO4)6O3−0.5x) depends on lanthanum deficiency and oxygen interstitial12 [42],[43] concentrations, and the cation vacan‐ cy concentrations appear to be the dominant factor in energetics [39].

<sup>11</sup> The KRÖGER-VINK notation indicates the lattice position for the point defect species in the crystal and its effective electric charge relative to the perfect lattice: **M**<sup>Y</sup> Z is the atomic species **M** (or vacancy **V**) that occupies the lattice site **Y** and possesses the effective charge **Z**, where the symbols ●, ' and × are used for the effective charge +1, -1 and neutral particle, respectively) [40]. For example, **Ali ●●●** is Al3+ ion at interstitial site (*i*), **VAlʹʹʹ** is Al3+ vacancy, VO ●● is O2− vacancy, SrLa' (**Eq. 8**) means Sr2+ ion replacing La3+ at lattice site, TiAl ● means Ti4+ replacing Al3+ at lattice site, *e*' is electron and *h*● is the hole. The equation must fulfill the following three rules: mass balance (1), electroneutrality or charge balance (2) and site ratio conservation balance (3) [41].

<sup>12</sup> Interstitial sites are sites between normal (equilibrium) atomic positions of ideal lattice atoms [42]. Interstitial atoms and vacancies (lattice site where atom is absent) are the simplest types of point defects in a crystal. A vacancy and interstitial atoms positioned close together are referred to as the Frenkel pair. Apart from the point defects, the line crystal defects (dislocation and disclination) are recognized [43].

**Fig. 3.** Schematic diagram of preparation of lanthanum silicate by a sol-gel process [44].

9.33 [ ] ( ) 4 2 2 3 10 4 2 i 10 4 3 () () ( ) 0.67 6 6 La SiO O 1/ 3 La O La SiO O O La SiO O + ® (6)

Thus, in the ideal pure La10(SiO4)6O3, the 4*f* and 6*h* sites are fully occupied by La3+ ions, while an extra oxygen interstitial is introduced into the lattice to maintain the electroneutrality. The oxygen interstitial may benefit the oxide ion transportation if it is located nearby the [001] direction c-axis of the conventional unit cell. From the space-filling consideration, the most appropriate sites for the oxygen occupation are in this position; however, some distortion of the O 2*a* sites would be required to accommodate extra oxygen atoms. This could be ach‐ ieved by decreasing the symmetry from P63/M to P63 allowing oxygen to move from 0,0,1/4 to 0,0,x. Recent studies suggest that a range of partially occupied (0,0,x) sites may accommo‐ date this extra interstitial oxygen. From this point of view, La10(SiO4)6O3 should exhibit higher

Introducing Sr2+ cations to the La3+ atomic positions, as in the La10(SiO4)6O3 phase, leads to

The substitution of La2O3 by SrO, taking into account the charge balance and the oxygen

Lanthanum oxyapatite phases are substantially stable with respect to their binary oxides. The general trend in the formation enthalpies as a function of (La + Sr)/(La + Sr + Si) shows that the apatite phase becomes more energetically stable as the cation vacancy and oxygen excess concentrations decrease. The stoichiometric sample achieved by Sr2+ doping, with no cation vacancies or interstitial oxygen atoms, is the most stable composition. The energetics of lanthanum silicate apatite materials (La9.33+x(SiO4)6O2+3x/2 and La10−xSrx(SiO4)6O3−0.5x) depends on

11 The KRÖGER-VINK notation indicates the lattice position for the point defect species in the crystal and its effective electric charge relative to the perfect lattice: **M**<sup>Y</sup> Z is the atomic species **M** (or vacancy **V**) that occupies the lattice site **Y** and possesses the effective charge **Z**, where the symbols ●, ' and × are used for the effective charge +1, -1 and neutral particle,

(**Eq. 8**) means Sr2+ ion replacing La3+ at lattice site, TiAl ● means Ti4+ replacing Al3+ at lattice site, *e*' is electron and *h*● is the hole. The equation must fulfill the following three rules: mass balance (1), electroneutrality or charge balance (2) and site

12 Interstitial sites are sites between normal (equilibrium) atomic positions of ideal lattice atoms [42]. Interstitial atoms and vacancies (lattice site where atom is absent) are the simplest types of point defects in a crystal. A vacancy and interstitial atoms positioned close together are referred to as the Frenkel pair. Apart from the point defects, the line crystal

® ® (7)

xx / •• SrO 1/ 2 O La Sr 1/ 2 V 1/ 2 La O + + ®+ + o La La <sup>o</sup> 2 3 (8)

[40],[41]):

[42],[43] concentrations, and the cation vacan‐

**●●●** is Al3+ ion at interstitial site (*i*), **VAlʹʹʹ** is Al3+ vacancy, VO ●● is O2− vacancy, SrLa'

( ) ( ) ( ) 2 2 Sr Sr 10 4 3 9 1 4 2.5 8 2 4 2 66 6 La SiO O La Sr SiO O La Sr SiO O + + + +

complete elimination of vacancies according to the substitution [39]:

252 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

content, can be represented as follows (KRÖGER-VINK notation11

cy concentrations appear to be the dominant factor in energetics [39].

lanthanum deficiency and oxygen interstitial12

defects (dislocation and disclination) are recognized [43].

respectively) [40]. For example, **Ali**

ratio conservation balance (3) [41].

conductivity than La9.33(SiO4)6O2 [10],[38].

The schematic diagram of the sol-gel process used by TAO and IRVINE [44] for the preparation of apatite-type lanthanium silicates is shown in **Fig. 3**. The room-temperature structure is hexagonal, the space group is P63 or P63/M, with *a* = 9.722 and *c* = 7.182 Å for La10(SiO4)6O3 and *a* = 9.717 and *c* = 7.177 Å for La9.33(SiO4)6O2, i.e. the cell volume of La10(SiO4)6O3 is a little greater than that of La9.33(SiO4)6O2. Both compositions exhibit high ionic conductivity, although the grain boundary resistance is the dominant feature in the impedance spectrum of both. In general, the conductivity of La10(SiO4)6O3 is higher than that of La9.33(SiO4)6O2 and this indicates that oxygen interstitials may be introduced into the apatite lattice of La10(SiO4)6O3, which may benefit the oxygen ion transportation [44].

The La10Si6O27 nanopowders with apatite structure were synthesized by the LI et al [45] coprecipitation method. After the calcination at 900°C and then removing of La2O3 by acid washing, the pure stoichiometric La10Si6O27 nanopowders are obtained. The oxyapatite ceramics with the density higher than 95% can be obtained at rather low sintering tempera‐ ture of 1300°C, and it has comparable total conductivity with the samples sintered at 1650°C from the powders prepared by solid-state reaction.

La2O3 and TEOS in stoichiometric amount were used by MASUBUCHI et al [46] as the starting materials for the preparation of both powder and film of apatite-type La9.33(SiO4)6O2 via the alkoxide hydrolysis. Lanthanum oxide was dissolved in HNO3 (6 mol·dm−3) and mixed with ethanol. Then, stoichiometric amount of TEOS in ethanol was added (La:Si = 9.33:6) to this solution. The precursor solution was obtained by refluxing for one night. This solution was heated to gelating on the hot plate followed by calcination and annealing in powder prepara‐ tion. Either quartz glass or Pt foil substrate was dipped to the gelatinous solution and dried for the film preparation. It was calcined at 500°C for 1 h to remove the organic contents and then fired at 1000°C for 10 h. This preparation steps were repeated to increase the film thickness. The film showed preferred orientation of the apatite crystal in thinner film. The conductivity of sintered body was lower in about one order of magnitude than the value of single crystal perpendicular to c-axis [46].

The synthesis and the conductivities of Ti-doped apatite-type phases of the composition of (La/Ba)10−x(Si/Ge)6O26+z, where Ti substituted at the Si/Ge site, were reported by SANSOM et al [47]. The conductivities were shown to be the highest for the samples containing either cation vacancies or oxygen excess, which is consistent with previous studies of apatite-type oxide ion conductors. However, the Ti doping was shown to generally decrease the conductivity in comparison with equivalent samples containing only Si/Ge at the tetrahedral sites, with the greatest decrease for Si-containing samples.

Vanadium-doped oxyapatite phases of the composition of La10−xVx(SiO4)6O3+x were prepared by YUAN et al [48] via the sol-gel method. The apatite phase begins to form at 800°C, which is much lower than in the case of conventional solid-state synthesis method. The best conduc‐ tivity of La9V(SiO4)6O4 is 1.67·10−2 S·cm−1, which is significantly higher than that for lantha‐ num silicate oxides (1.19·10−2 S·cm−1). The valence ion V5+ doped for La3+ does lead to the formation of hexagonal apatites even with high oxygen contents.

The phase La5Si2BO13 [49],[50],[51] crystallizes with apatite-related structure (**Fig. 4**) with the space group P63/M and the cell parameters *a* = 9.5587 Å, *c* =7.2173 Å and *Z* = 2. The composi‐ tion of these apatite-like compounds can be also expressed via the general formula: La9.33+xSi6−2yB3yO6, where 0 ≤ *x* ≤ 0.67. At limiting compositions *x* = 0.67, La(2) site is fully occupied, and the formula referred to the unit cell is La10Si4B2O26 or, more simply, La5Si2BO13.

**Fig. 4.** The crystal structure of La5Si2BO13 (a) [51] and the upper section of the ternary phase diagram La2O3-SiO2-B2O3 at 1100°C (b) [49].

The comparison with other apatite-like structures shows lower distortion in the M(1) polyhe‐ dron and unusually short bond length from La in the M(2) site and O(4) oxygen in the column site (2.303 Å). These results can be explained in view of the presence of trivalent La and divalent O, respectively, in the M(1) and M(2) sites and in the column anion site, whereas, in apatites, these sites are occupied by divalent and monovalent ions, respectively [49].

The preparation of La-Si-O apatite-type thin films was described by VIEIRA et al [52] with Si/(La + Si) atomic ratios ranging from 0.36 to 0.43 being produced via the magnetron sputter‐ ing in reactive Ar/O discharge gas. The apatite-type lanthanum silicate phase was formed in all as-deposited films upon the annealing at 900°C for 1 h. The lanthanum silicate films obtained by annealing the as-deposited films with lower Si/(La + Si) atomic ratios have a preferential orientation with the c-axis perpendicular to the substrate, while low-intensity diffraction peaks ascribed to La2Si2O7 phase were detected in the films deposited with higher Si content. Preferentially oriented films have higher activation energy and lower ionic conductivity, as the ionic conductivity measurements were performed in the direction perpendicular to the c-axis. The highest ionic conductivity was obtained for the film deposit‐ ed with a Si/(La + Si) atomic ratio of 0.42, with a value of 1.2 × 10−2 S·cm−1 at 750°C. By the incorporation of oxygen in the as-deposited films, the silicon segregation upon annealing was avoided.

**Fig. 5.** Primary phase diagram of ternary system La2O3-Ga2O3-SiO2 around LGS [53].

The synthesis and the conductivities of Ti-doped apatite-type phases of the composition of (La/Ba)10−x(Si/Ge)6O26+z, where Ti substituted at the Si/Ge site, were reported by SANSOM et al [47]. The conductivities were shown to be the highest for the samples containing either cation vacancies or oxygen excess, which is consistent with previous studies of apatite-type oxide ion conductors. However, the Ti doping was shown to generally decrease the conductivity in comparison with equivalent samples containing only Si/Ge at the tetrahedral sites, with the

Vanadium-doped oxyapatite phases of the composition of La10−xVx(SiO4)6O3+x were prepared by YUAN et al [48] via the sol-gel method. The apatite phase begins to form at 800°C, which is much lower than in the case of conventional solid-state synthesis method. The best conduc‐ tivity of La9V(SiO4)6O4 is 1.67·10−2 S·cm−1, which is significantly higher than that for lantha‐ num silicate oxides (1.19·10−2 S·cm−1). The valence ion V5+ doped for La3+ does lead to the

The phase La5Si2BO13 [49],[50],[51] crystallizes with apatite-related structure (**Fig. 4**) with the space group P63/M and the cell parameters *a* = 9.5587 Å, *c* =7.2173 Å and *Z* = 2. The composi‐ tion of these apatite-like compounds can be also expressed via the general formula: La9.33+xSi6−2yB3yO6, where 0 ≤ *x* ≤ 0.67. At limiting compositions *x* = 0.67, La(2) site is fully occupied, and the formula referred to the unit cell is La10Si4B2O26 or, more simply, La5Si2BO13.

La2SiO5

La4.67Si3O13 SiO2

**Fig. 4.** The crystal structure of La5Si2BO13 (a) [51] and the upper section of the ternary phase diagram La2O3-SiO2-B2O3 at

The comparison with other apatite-like structures shows lower distortion in the M(1) polyhe‐ dron and unusually short bond length from La in the M(2) site and O(4) oxygen in the column site (2.303 Å). These results can be explained in view of the presence of trivalent La and divalent O, respectively, in the M(1) and M(2) sites and in the column anion site, whereas, in apatites,

The preparation of La-Si-O apatite-type thin films was described by VIEIRA et al [52] with Si/(La + Si) atomic ratios ranging from 0.36 to 0.43 being produced via the magnetron sputter‐ ing in reactive Ar/O discharge gas. The apatite-type lanthanum silicate phase was formed in all as-deposited films upon the annealing at 900°C for 1 h. The lanthanum silicate films obtained by annealing the as-deposited films with lower Si/(La + Si) atomic ratios have a preferential orientation with the c-axis perpendicular to the substrate, while low-intensity diffraction peaks ascribed to La2Si2O7 phase were detected in the films deposited with higher

La2O3

La3BO6

La5Si2BO13 B2O3

greatest decrease for Si-containing samples.

formation of hexagonal apatites even with high oxygen contents.

254 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

La(1)O3

La(2)O7–C3 La(2)O y <sup>7</sup>

z x

1100°C (b) [49].

La(1)O3–C3

these sites are occupied by divalent and monovalent ions, respectively [49].

mirror plane

The formation of ternary compound with apatite structure in the system La2O3-Ga2O3-SiO2 (**Fig. 5**) was first reported by WANG and UDA [53]. The apatite phase, which precipitates from the melt of the composition around that of stoichiometric La3Ga5SiO14 (LGS), can be descri‐ bed by the formula: La14GaxSi9−xO39−x/2, where 0 ≤ *x* ≤ 3.5. Since there is a large field for the formation of solid solutions with the range extending from La14Si9O39 to Ga2O3, some Si4+ sites are probably substituted by Ga3+.

The liquidus surface of LS(G) was determined to be the field on the Ga2O3-poor side of boundary curve ABCD. The liquidus surface of LS(G) covers the stoichiometric composition of LGS. In this field, the crystallization of LS(G) aciculae was observed in all samples that were heated to temperatures above 1500°C. The liquidus volume of LGS is denoted by the field BCEF. It seems to be a narrow field in the composition between the liquidus surfaces of LS(G) and Ga2O3. E and F are eutectic points, where LGS + LaGaO3 + Ga2O3 + liquid and LGS + Ga2O3 + La2Si2O7 + liquid were found, respectively [53].

The CaO-La2O3-SiO2-P2O5 phase diagram was investigated by EL OUENZERFI et al [54] in order to determine a domain inside which all points correspond to pure apatitic oxyphosphosili‐ cates with the general formula: CaxLay(SiO4)6−u(PO4)uOt . The defined domain (**Fig. 6**) is only a part of the whole existence domain of the apatitic structure, but it allows to prepare pure apatitic samples with well-controlled composition.

**Fig. 6.** Britholite stability domain in the CaO-SiO2-La2O3-P2O5 quaternary system [54].

For these samples, the continuous change of the stoichiometry of each element proves that it exists as a solid solution including the oxygen content. This observation completes the literature data where britholites are presented as limited to three series corresponding to the stoichiometry [54],[55]:


Inside this domain, the solid solution continuously varies between pure phosphate apatites CaxLay(PO4)6Ot and pure silicate apatites CaxLay(SiO4)6Ot and also between oxyapatites CaxLay(SiO4)6−u(PO4)uOt and nonoxyapatites CaxLay(SiO4)6−u(PO4)u.

During the investigation of the kinetics of solid-state sintering14 of strontium-doped apatitetype lanthanum silicates (SrxLa10−xSi6O27−x/2) under isothermal conditions (1250 – 1550°C), BONHOMME et al [56] recognized that the densification mechanism of the apatite ceramics was

<sup>13</sup>WANMAKER et al [55] reported the synthesis of apatite-type compounds of the composition:

<sup>(</sup>a) M2+(II)M(III)8−x(SiO4)6−x(PO4)xO2, where 0 ≤ *x* ≤ 6;

<sup>(</sup>b) M(II)3+xM(III)6−x(SiO4)6−x(PO4)x, where 0 ≤ *x* ≤ 1.4;

<sup>(</sup>c) M(II)4+xM(III)6−x(SiO4)6−x(PO4)xO, where 0 ≤ *x* ≤ 6.

where M(II) = Ca, Sr, Ba, Mg, Zn or Cd and M(III) Y or La. The paper also contains structural data for several other newly prepared oxy-britholites, including Zn2La8(SiO4)6O2, BaMgY8(SiO4)6O2, Zn2Y8(SiO4)6O2, Cd2Y8(SiO4)6O2, Ca4La5(SiO4)5(PO4) and Ba4La5(SiO4)5(PO4).

controlled by the diffusion of rare-earth element (La) at the grain boundaries. This process showed the activation energy of 470 kJ·mol−1.

The ternary phase diagram Al2O3-SiO2-La2O3 at 1300°C (**Fig. 7**) was investigated by MAZZA and RONCHETTI [57]. La14Si9O39 was described by KUZ'MIN and BELOV [58] as an apatite-like struc‐ ture of hexagonal symmetry (space group P63/M). Isomorphous compounds were also reported for Nd [59], Ce [60] and Sm [58]. The La14Si9O39 compound extends its stability range in the interior of the phase diagram, forming the solid solution of the type La14+1x/3Si9−xAlxO39, which is stable from *x* = 0 to *x* = 1.5. This substitution stoichiometry (Al + 1/3La ↔ Si) can be described as a tetrahedral Al for Si substitution on the 6*h* position and contemporary occupation of vacant La sites [57].

**Fig. 7.** Ternary phase diagram at 1300°C in air [57].

$$\mathbf{(a)} \,\, \frac{d\,\,\rho}{dt} = \frac{AD}{T\,D\_m^{\,\,\nu}}$$

LaO1.5

<sup>k</sup> <sup>r</sup> <sup>l</sup>

For these samples, the continuous change of the stoichiometry of each element proves that it exists as a solid solution including the oxygen content. This observation completes the literature data where britholites are presented as limited to three series corresponding to the

;

Inside this domain, the solid solution continuously varies between pure phosphate apatites

type lanthanum silicates (SrxLa10−xSi6O27−x/2) under isothermal conditions (1250 – 1550°C), BONHOMME et al [56] recognized that the densification mechanism of the apatite ceramics was

where M(II) = Ca, Sr, Ba, Mg, Zn or Cd and M(III) Y or La. The paper also contains structural data for several other newly prepared oxy-britholites, including Zn2La8(SiO4)6O2, BaMgY8(SiO4)6O2, Zn2Y8(SiO4)6O2, Cd2Y8(SiO4)6O2,

and nonoxyapatites CaxLay(SiO4)6−u(PO4)u.

and pure silicate apatites CaxLay(SiO4)6Ot

During the investigation of the kinetics of solid-state sintering14

13WANMAKER et al [55] reported the synthesis of apatite-type compounds of the composition:

f <sup>g</sup> <sup>h</sup>

m n

CaO

qo

La3PO7

LaPO4

At the domain limits In the domain

PO2.5

and also between oxyapatites

of strontium-doped apatite-

t s

β-Ca3(PO4)2

i

La2Si2O7

SiO2

stoichiometry [54],[55]:

CaxLay(PO4)6Ot

CaxLay(SiO4)6−u(PO4)uOt

**1.** Sr2+xLa8−x(SiO4)6−x(PO4)xO2 with 0 ≤ *x* ≤ 6 <sup>13</sup>

**2.** Sr3+xLa6−x(SiO4)6−x(PO4)x with 0 ≤ *x* ≤ 1.5;

**3.** Sr4+xLa6−x(SiO4)6−x(PO4)xO with 0 ≤ *x* ≤ 6.

(a) M2+(II)M(III)8−x(SiO4)6−x(PO4)xO2, where 0 ≤ *x* ≤ 6; (b) M(II)3+xM(III)6−x(SiO4)6−x(PO4)x, where 0 ≤ *x* ≤ 1.4; (c) M(II)4+xM(III)6−x(SiO4)6−x(PO4)xO, where 0 ≤ *x* ≤ 6.

Ca4La5(SiO4)5(PO4) and Ba4La5(SiO4)5(PO4).

a b <sup>c</sup> <sup>p</sup>

256 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

d p <sup>e</sup> <sup>j</sup>

**Fig. 6.** Britholite stability domain in the CaO-SiO2-La2O3-P2O5 quaternary system [54].

The coefficient of diffusion *D* is thermally activated:

$$\text{(b)}\ D = D\_0 \quad \exp\left(-\frac{E\_x}{RT}\right)$$

where *D*0 is the pre-exponential coefficient of diffusion, *R* is the universal gas constant and *E*a is the apparent activation energy of diffusion of the rate limiting process. Exponent *n* in **Eq. (a)** depends on the mechanism of transport of the limiting species governing the kinetics of densification.

<sup>14</sup> The densification rate is considered as the function of temperature (*T*) and mean grain size (*D*m). Constant *A* depends on the surface energy (*γ*sg) of grains, on the apatite molar volume (Ω) and on average coefficient of diffusion of limiting species *D*. This relationship can be written as follows [56]:
