Magnesium ion distribution and defect concentrations of MgO-doped lanthanum silicate oxyapatite

Solid State Ionics 258 (2014) 24–29

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Magnesium ion distribution and defect concentrations of MgO-doped lanthanum silicate oxyapatite Kiyoshi Kobayashi ⁎, Tohru S. Suzuki, Tetsuo Uchikoshi, Yoshio Sakka Materials Processing Unit, National Institute for Materials Science, 1-2-1, Sengen, Tsukuba 305-0047, Japan

a r t i c l e

i n f o

Article history: Received 10 September 2013 Received in revised form 7 January 2014 Accepted 9 January 2014 Available online 19 February 2014 Keywords: Lanthanum silicate Oxyapatite Defects Density Conductivity

a b s t r a c t The distribution of magnesium ions at the lanthanum and silicon sites in MgO-doped lanthanum silicate oxyapatite as well as the concentration of neutral lanthanum vacancies were determined using densities and chemical compositions of the doped samples. On the basis of the density data, it was found that magnesium ions are substituted at the silicon site as well as the lanthanum sites in the oxyapatite phase. Owing to the existence of neutral lanthanum vacancies, it was difficult to evaluate the number of the oxygen ions present, which are related to the oxygen ion conductivity of the compound, from the chemical compositions of the samples alone. Further, it was found that the fact that the total conductivity of MgO-doped lanthanum silicate oxyapatite depends on the MgO concentration as well as that of other defects could not be explained on the basis of conventional defect chemistry. © 2014 Elsevier B.V. All rights reserved.

1. Introduction 1.1. General introduction Since the discovery of the high oxygen ion conductivity of lanthanoid silicate oxyapatites by Nakayama et al. [1–3], the lanthanoid silicates have used extensively as a solid electrolyte in solid oxide fuel cells and chemical sensors [4,5]. Yoshioka has attempted to improve its oxygen ion conductivity through chemical doping and has reported that magnesium is effective in increasing the oxygen ion conductivity of lanthanum silicate oxyapatite [6–8]. Other researchers have found that two more sites where magnesium ions can be substituted should exist in lanthanum silicate oxyapatite [6–14]. Finally, although several concepts for describing the molecular formulae of MgO-doped lanthanum silicate oxyapatite have been proposed [6–14], there has been no discussion on which concept is adequate for describing actual oxyapatite solid solution. In previous studies, we had elucidated the chemical compositional region of single-phase MgO-doped lanthanum silicate oxyapatite from the phase diagram of the quasi-ternary LaO1.5–SiO2–MgO system [15,16]. However, the molecular formulae of MgO-doped lanthanum silicate oxyapatite were impossible to determine from only its chemical compositions. The reason is that an extra degree of freedom exists in the compound owing to the existence of neutral lanthanum vacancies (V× La). These abnormal defects are formed owing to the difference between the crystallographic stoichiometry (La10(SiO4)6O2) and the stoichiometry by the charge neutrality (La9.33[V× La]0.67(SiO4)6O2), where ⁎ Corresponding author at: 1-2-1, Sengen, Tsukuba 305-0047, Japan. Tel.: +81 29 860 4562; fax: +81 29 859 2501. E-mail address: [email protected] (K. Kobayashi). 0167-2738/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2014.01.015

V× La is a neutral lanthanum vacancy at the lanthanum sites as the quasi-chemical species. For the lanthanum silicate phase in a quasiternary system, the relationship between the chemical composition and the V× La concentration is not yet known. The molecular formulae of MgO-doped lanthanum silicate oxyapatite can be determined by measuring its material density. In this paper, we discuss the molecular formulae of MgO-doped lanthanum silicate oxyapatite on the basis of its density and chemical compositions. 1.2. Ambiguity regarding molecular formulae of oxyapatite solid solution in the LaO1.5–MgO–SiO2 system The ambiguity regarding the molecular formula of MgO-doped lanthanum silicate oxyapatite arises because the compound can be described as two different standard states. On the basis of the crystal structure of lanthanum silicate oxyapatite, the molecular formula of the perfect state can be said to be La10(SiO4)6O2. When one considers the valence numbers of the lanthanum ion (+3), the silicon ion (+4), and the oxygen ion (−2), the molecular formula La10(SiO4)6O2 does not fulfill the requirement of charge neutrality. Assuming that charge neutrality is determined by the oxygen stoichiometry, the standard molecular formula can be expressed as La9.33[V× La]0.67(SiO4)6O2. On the other hand, if charge neutrality is achieved by completely fulfilling the lanthanum ion, the standard molecular formula should be La10(SiO4)6O3; here one interstitial oxygen ion exists per unit cell. These facts suggest that no perfect state of lanthanum silicate oxyapatite exists in the meaning of conventional defect chemistry. Four different models have been proposed for describing the molecular formulae of MgO-doped lanthanum silicate oxyapatite. The first model (Model 1) is one in which Mg ions are substituted at the La

K. Kobayashi et al. / Solid State Ionics 258 (2014) 24–29

sites, allowing the formation of oxygen ion vacancies and/or interstitial oxygen ions [14]. Using this model, the molecular formula can be expressed as, La9:33þx Mgy ðSiO4 Þ6 O2þð3x=2Þ−ðy=2Þ ; where  0:2 ≤x ≤0:67; 0 ≤y≤2; and  0:2≤x þ y≤0:67: The minimum value of x is still unknown, but seems to be approximately − 0.2 [17–19]. The second model (Model 2) is one in which Mg ions are substituted at the Si site, resulting in the formation of oxygen ion vacancies and/or interstitial oxygen ions [6–10]. Using this model, the molecular formula can be expressed as,   La9:33þx Si1−ðy=6Þ Mgðy=6Þ O4 O2þð3x=2Þ−y ; where  0:13≤ x≤ 0:67; and 0≤ y≤ 1: 6

The third model (Model 3) is one in which Mg ions are substituted at the Si site as well as at the La sites while the oxygen stoichiometry is maintained [11–13]. Using this model, the molecular formula can be expressed as,   La9:33þð−2xþ2yÞ=3 Mgx Si1−ðy=6Þ Mgðy=6Þ O4 O2 ; where 0 ≤x≤0:67; and 0≤y ≤1: 6

The last model (Model 4) is one in which Mg ions are substituted at the Si site as well as at the La sites, allowing the formation of oxygen ion vacancies and/or interstitial oxygen ions [13]. Using this model, the molecular formula can be expressed as,   La9:33þx Mgy Si1−ðz=6Þ Mgðz=6Þ O4 O2þð3x=2Þ−ðy=2Þ−z ; 6

where  0:13≤ x≤0:67; 0≤y≤2; and 0≤ z≤1: If we consider oxygen nonstoichiometry, Model 1 and Model 2 can be represented by Model 4. Hence, the problem is reduced to determining whether Model 3 or Model 4 is appropriate. The difficulty in analyzing these two models is that the compositional regions for the two models almost overlap as shown in Fig. 1 [15,16]. When considering defect control and ionic conductivity, the critical factor is the number of the oxygen ions, which dictates the oxygen ion conductivity. Oxygen ions related to the oxygen ion conduction are

LaO1.5 La2SiO5 Oxyapatite La9.50(SiO4)6O2.25 A1

La10(Si5/6Mg1/6O4)6O26

La9.33(SiO4)6O2

B2 B3 B4

Line B

A2 A3

A4 A5

La2Si2O7

La8Mg2(SiO4)6O2

SiO2 MgO

25

considered to be the oxygen ions at 2a site as well as interstitial sites [20–23]. These are described by the number of oxygen species on the right side in the molecular formulae shown above. This is the number of oxygen species as 2 in the case of Model 3 and 2 + 3x/2 − y/2 − z in the case of Model 4. The number of oxygen species is labeled as No, hereafter. Although Mg ions are distributed at both the La and the Si sites in different ratios and given that the concentrations of oxygen ion vacancies are also different and depend on the model employed, the compositional regions of Models 3 and 4 are almost similar. Hence, it is necessary to determine the defect model appropriate for MgO-doped lanthanum silicate oxyapatite. On comparing the molecular formulae of Models 3 and 4, it was found that the material density should highly depend on the model used if the lattice parameter and the chemical composition can be determined. 2. Materials and methods 2.1. Sample preparation All the samples tested were synthesized by a water-based sol–gel method [15,16,19]. Samples with two series of compositions were used for the density measurements. The first composition series was the solid solution of La9.50(SiO4)6O2 and La8Mg2(SiO4)6O2; this series corresponds to composition line A in Fig. 1. The second series corresponded to composition line B in Fig. 1. This composition line corresponded to the part of SiO2 that was substituted into MgO at a constant LaO1.5 concentration. Powder X-ray diffraction (XRD) patterns of all samples are confirmed as the oxyapatite single phase as shown in Fig. 2(a) and (b) [15,16]. In addition, the single phase formation is consistent from the phase relationships by means of quasi-ternary phase diagram in the LaO1.5–SiO2–MgO system [15,16]. All the sample data related to the density analyses are listed in Tables 1 and 2. For material density measurements, it is preferable to use porous bulk ceramic in order to prevent errors arising from any existing closed pores. Hence, porous MgO-doped lanthanum silicate oxyapatite ceramics were fabricated using the following procedure. First, the precursor powder was prepared by a previously described method [15]. It was then heated at 1273 K for 3 h in air to remove any residual carbon. This preheated powder was then pulverized using an agate mortar and pestle, and the powder was pressed into 6 to 7 pellets having a diameter of 20 mm and a thickness of 3 mm under a pressure of 63 MPa. The powder at this stage shows high sinterability because the primary particle size is less than 100 nm [24]. Next, well-sintered ceramic disks were obtained by heating the pellets at 1773 K for 6 h in air. One sintered pellet was used for electrical conductivity measurements. The remaining sintered pellets were again crashed into a powder using an alumina mortar and pestle and were then pressed into pellets under a pressure of 63 MPa. The resulting pellets had a diameter of 20 mm and a thickness of approximately 6 mm. Next, porous sintered pellets were obtained by sintering these pellets at 1773 K for 6 h in air. Due to rough granulation by hand using alumina mortar and pestle, the sinterability of the powder becomes bad. As a result, porous sintered pellets were obtained by these procedures. The relative densities of these porous pellets were about 60 to 70% of their theoretically expected values. The lattice parameter of the oxyapatite was calculated from the XRD peaks [15,16]. The porous pellets were broken into fragments using an alumina pestle; the smallest edge of these fragments was less than 7 mm. These fragments were subsequently used for the material density measurements.

Line A

Fig. 1. Partial phase diagram of LaO1.5–SiO2–MgO system at 1773 K [15,16]. The closed circles indicate single-phase oxyapatite. The labels indexed in Tables 1 and 2 were shown around the sample composition points. The broken and dotted lines represented the compositional boundary of Model 3 and Model 4, respectively. Inside of the solid line is the oxyapatite single phase region at 1773 K determined by the experiments.

2.2. Material density measurements The material densities of the samples were measured using a glass pycnometer having a volume of 5 ml. 2-Propanol (99.5%, Wako Pure Chemical Industry, Inc., Japan) was used as the saturation solvent. First, the weight of the empty pycnometer was measured. Then, the

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K. Kobayashi et al. / Solid State Ionics 258 (2014) 24–29

a A5

Intensity

A4

A3

A2

A1

10

20

30

40

50

60

b

Table 1 Data for the composition line A. α is the mole fraction value of (1 − α) La9.50(SiO4)6O2.25 − α La8Mg2(SiO4)6O2. The LaO1.5, SiO2, and MgO mole fractions of the samples are presented by x, y, and z, respectively. The unit cell volume (V in unit of 10−22 cm3) of the samples, calculated from their lattice parameters [15], is also listed. The measured material densities and the calculated densities, having the unit g ∙ cm−3, are presented by ρmat and ρcal, respectively. Sample

α

x, y, z

V

ρmat

ρcal

A1 A2 A3 A4 A5

0 0.25 0.5 0.75 1

0.613, 0.387, 0 0.584, 0.384, 0.032 0.556, 0.381, 0.063 0.528, 0.378, 0.094 0.500, 0.375, 0.125

5.870 5.794 5.699 5.635 5.617

5.391 5.343 5.247 5.115 4.936

5.398 5.351 5.323 5.261 5.157

the sample (Wsamp) could be calculated. For all the measurements, the weight of the samples used was approximately 4.8 g. Next, 2-propanol was poured into the pycnometer. Then, the pycnometer was placed in a desiccator and the desiccator was evacuated using an aspirator in order to remove any air bubbles presented in the sample fragments. The samples saturated with 2-propanol were kept under a vacuum state for more than 3 h. Finally, the pycnometer was taken out of the desiccator, more 2-propanol was added to it, a cap was placed on it, and its total weight, (Wtotal samp), was measured. After weight measurements, the samples were removed from the pycnometer. The pycnometer was washed, dried at 373 K, and allowed to cool to room temperature. The weight of the empty pycnometer was then measured. Next, 2-propanol was again poured into the pycnometer, a cap was placed on it, and the total weight of the pycnometer and 2-propanol, (Wtotal pr ), was measured. The density of 2-propanol, ρpr, was calculated (0.792 g ∙ cm−3) from the Wtotal value and the volume pr of the pycnometer (5 ml). Using these data, the material density of the sample in question could be calculated as per the following equation: ρmat ¼

W samp ρpr  : total W samp þ W total pr −W samp

B5

Intensity

B4

Adequacy of the models explained in Section 1.2 was discussed from the relationship between the ρmat, the calculated density by Model 3 and Model 4 and the MgO concentration on compositional line A and line B. In the case of line A, it was impossible to calculate the theoretical density only from the models due to the lack of restriction to the [V× La]. Therefore, the Mg ion distribution was calculated in order to fit the ρmat values and then, the adequacy was discussed by comparing it to the four models. In the case of line B, it was possible to give the restriction of the [V× La] from the result on line A. Hence, the adequacy of the models was discussed by comparing it to the theoretical density values.

B3

2.3. Total conductivity measurements The total conductivities of the MgO-doped lanthanum silicate oxyapatite samples were measured using the two-probe alternating current (ac) method. Sintered disks of the samples approximately B2

20

40

60

2θ [° (Cu Kα)] Fig. 2. XRD patterns of the samples from (a) A1 to A5 and (b) B2 to B5 [15,16]. The cross mark is the measured data. The solid lines overlapping to the mark is the calculated curve by Rietveld analysis. The bar is the peak positions of the oxyapatite phase. Residual curves between the measured values and calculated ones are also plotted.

sample fragments were placed in it and the weight was measured again. From the total weight of the pycnometer and the sample, the weight of

Table 2 Data for composition line B. The LaO1.5, SiO2, and MgO mole fractions of the samples are presented by x, y, and z, respectively. The unit cell volume (V in unit of 10−22 cm3) of the samples, calculated from their lattice parameters [15], is also listed. The measured material densities and theoretical densities, calculated using Models 3 and 4, are represented by ρmat, ρmodel3 and ρmodel4, respectively. Sample

x, y, z

V

ρmat

ρmodel3

ρmodel4

A2 B2 B3 B4 B5

0.584, 0.384, 0.032 0.584, 0.374, 0.042 0.584, 0.364, 0.052 0.584, 0.356, 0.060 0.584, 0.346, 0.070

5.794 5.809 5.810 5.817 5.854

5.343 5.329 5.330 5.303 5.267

5.313 5.321 5.345 5.357 5.347

5.362 5.343 5.332 5.306 5.263

K. Kobayashi et al. / Solid State Ionics 258 (2014) 24–29

5.6

10.0

ρcal

9.8

NLa + N Mg La

5.2

ρmat

La

ρmat, ρcal / g cm

-3

5.4

5.0

9.6

9.4

9.2

0.0

0.2

0.4

α

0.6

0.8

9.0 0.0

1.0

Fig. 3. Relationship between the measured material density (ρmat) values, the calculated density (ρcal), and the values of the parameter α on composition line A. α is the mole fraction of (1 − α) La9.50(SiO4)6O2.25 − α La8Mg2(SiO4)6O2. ρcal was calculated on the basis of the assumption that Mg ions were substituted at La sites. The solid curve is the interpolated one.

16 mm in diameter and 1.5 mm in thickness were polished using #320 to #2000 waterproof abrasive papers. At the centers of both surfaces of the disks, platinum electrodes were painted using a platinum paste (TR-7907, Tanaka Kikinzoku Kogyo, Japan). The diameter of the electrode was 6 mm. The platinum electrodes were attached to the disks by heating the disks at 1273 K for 0.5 h in air. The sample disks were then set in the handmade cell. A platinum mesh and platinum wires were used as the current collector and lead wires, respectively. The impedance of the sample disks was measured using a potentio-galvanostat (1286, SolarTron, UK) and a frequency analyser (1255, SolarTron, UK) in combination. The measurements were made for temperatures ranging from 1273 K to 773 K. The frequency range was 100 k Hz to 0.1 Hz. All the measurements were performed in air. We were unable to differentiate between the bulk resistance and the grain boundary resistance from the impedance spectra. Therefore, the total conductivity was calculated using the sum of the bulk resistance and the grain boundary resistance.

3. Results and discussion 3.1. Density on composition line A In order to confirm the accuracy of the density measurements, the measured and theoretical densities of La9.50(SiO4)6O2.25 were compared because the theoretical density of undoped lanthanum silicate oxyapatite is determined only from its chemical composition and lattice volume. On the basis of this comparison, the validity of the density method could be confirmed because the measured density of La9.50(SiO4)6O2.25 (5.391 g ∙ cm−3) was close to the theoretical density (5.398 g ∙ cm−3) calculated using the chemical composition and unit cell parameters.

Table 3 List of the molecular formulae (MF) for the samples on composition line A. For the samples with α N 0, the ρcal values were calculated by assumption of the molecular formula [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α. Molecular formulae calculated from the ρmat values are listed in the MF (meas.) column. The molecular formulae calculated on the basis of [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α are listed in the MF (cal.) column. Sample

MF (meas.)

MF (cal.)

A1 A2 A3 A4 A5

La9.50(SiO4)6O2.25 La9.11Mg0.49(Si0.998Mg0.002O4)6O2.15 La8.63Mg0.89(Si0.99Mg0.01O4)6O1.75 La8.16Mg1.31(Si0.97Mg0.03O4)6O1.40 La7.68Mg1.55(Si0.96Mg0.04O4)6O0.83

La9.50(SiO4)6O2.25 La9.13Mg0.5(SiO4)6O2.20 La8.75Mg (SiO4)6O2.13 La8.38Mg1.5(SiO4)6O2.07 La8Mg2(SiO4)6O2

0.2

0.4

α

0.6

0.8

1.0

  Fig. 4. Variation in the sum of the number of La ions and Mg ions at La sites N LaLa þ N Mg′ La with α in (1 − α) La9.50(SiO4)6O2.25 − α La8Mg2(SiO4)6O2. The open circles represent values that were calculated using the ρmat. Those represented by the broken line were calculated on the basis of the assumption that Mg ions were substituted at La sites. The solid curve is the interpolated one.

In the case of composition line A, the material density decreased with an increase in α in (1 − α) La9.50(SiO4)6O2.25 − α La8Mg2(SiO4)6O2 (Fig. 3). It can be speculated that Mg ions are substituted at the La sites in the case of composition line A if one takes into account the results of previous studies on Ca-, Sr-, and Ba-doped lanthanum silicate oxyapatites [25–28]. The measured density was compared to the theoretical one, which was calculated on the basis of the assumption that Mg ions are substituted at the La sites, that is, the molecular formulae of the compounds of [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α. The calculated density of [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α was found to be much larger than the measured one for α values greater than 0.25. This result indicated that Mg ions are not only substituted at the La sites but also substituted at the Si site. On the other hand, the molecular formulae could also be determined from the density, lattice volume, chemical composition, and site balance of the oxyapatite structure by assuming that Mg ions are substituted at the La sites as well as the Si sites and that neutral La vacancies and oxygen ion vacancies are formed. A comparison of the molecular formulae of the samples of composition line A is shown in Table 3. The molecular formulae were calculated using the two different methods. The first method uses the [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α model, in which the Mg ions are substituted only at the La sites. The second

2.8 2.4 2.0

NO

4.8

27

1.6 1.2 0.8 0.4 0.0

0.2

0.4

α

0.6

0.8

1.0

Fig. 5. Relationship between the numbers of the oxygen species (No), which is related to the oxygen ion conductivity, and α in (1 − α) La9.50(SiO4)6O2.25 − α La8Mg2(SiO4)6O2. The open circles represent values that were calculated from the ρmat. Those represented by the broken line were calculated on the basis of the assumption that Mg ions were substituted at La sites.

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K. Kobayashi et al. / Solid State Ionics 258 (2014) 24–29

5.40

ρmat, ρmodel3, ρmodel4 /g cm

-3

model 3 5.35

5.30

model 4 5.25

ρmat 5.20 0.03

0.04

0.05

0.06

0.07

z Fig. 6. Variation in the measured density (ρmat) and those calculated using Models 3 (ρmodel3) and 4 (ρmodel4) with the MgO mole fractions of the samples on composition line B. The sample compositions were listed in Table 2.

Fig. 7. Variations in the sum of the number of La ions and Mg ions at La sites   N LaLa þ N Mg′ with MgO mol fraction (z) of the samples on composition line B. The samLa

ple compositions were listed in Table 2. The broken and dotted lines represent values that were calculated using Models 3 and 4, respectively.

method involves calculations to fit the measured density data. In the case of the [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α model, oxygen ions are presented either in excess or in the stoichiometric amount because the No values are greater than 2. On the other hand, the molecular formulae calculated from the material density suggest that oxygen ion vacancies are formed when α increased for α N 0.25, even though the molecular formulae are calculated from the same chemical composition and using the same crystal structure. The reason of this phenomenon is the difference in the V× La concentrations of the samples. The relationship between the number of occupied La sites and α is shown in Fig. 4. The number of occupied La sites is given by the sum of the number of La     ions in La sites N LaLa and the number of Mg ions in La sites NMg′ . La

There is a difference in the number of occupied La sites of the two models that is evident in the following phenomenon. In the case of the model given by [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α, the relationship between NLaLa þ NMg′ and α must be a linear one, with the number La

of occupied La sites being 9.5 at α = 0 and 10 at α = 1. However, the NLaLa þ NMg′ value was the maximum at approximately α = 0.25 La

when estimated from the measured density data. An interesting point to note is that the minimum NLaLa þ NMg′ value at α = 1 is approximate-

agreement with the ρmodel4 values. The molecular formulae used to fit the ρmat values are listed in Table 4. The molecular formulae determined using Models 3 and 4 are also listed for comparison. As was the case for the samples of line A, the oxygen content in the unit cell depended strongly on the MgO dissolution model employed. The fitted molecular formulae were confirmed to be almost similar to the formulae determined using Model 4. In contrast to the relationship between the NLaLa þ NMg′ values and La

the Mg mole fraction for composition line A, the NLaLa þ NMg′ values La

in the case of the samples on composition line B were almost constant (Fig. 7). Moreover, the NLaLa þ NMg′ values estimated from the ρmat La

values were in good agreement with the values calculated using Model 4. On the other hand, in the case of Model 3, the N LaLa þ N Mg′ La

values increased with an increase in the Mg content (Fig. 7). With respect to the NO, the values estimated from the ρmat values were also almost the same as those estimated values using Model 4 (Fig. 8). These experimental results are completely different from those obtained in the case of Model 3, for which the numbers of the conductive oxygen ions did not depend on the Mg contents.

La

ly 9.2, which is very close to the value for neodymium in single-phase neodymium silicate oxyapatite [18,19]. With respect to the NLaLa þ NMg′ dependencies, the number of conductive oxygen ions decreases La

steeply with an increase in α, in contrast to what is noticed in the case of the [La9.50 − 1.50αMg2α](SiO4)6O2.25 − 0.25α model (see Fig. 5). 3.2. Density of composition line B The relationship between the ρmat values and MgO mole fraction (z) of the samples of line B is shown in Fig. 6. Similar to the case for the samples of line A, ρmat decreases with an increase in z. The theoretical densities calculated using Model 3 (ρmodel3) and Model 4 (ρmodel4) are also plotted for comparison. It is clear that the ρmat values were in good

3.3. Total conductivity The total conductivities (σt) of the samples on composition lines A and B are shown in Fig. 9(a) and (b) as functions of the reciprocal temperature. In the case of the samples on composition line A, σt decreased with an increase in the Mg concentration. On the other hand, σt for the samples on composition line B did not show a clear dependency on the Mg concentration. Taking into account all the data together, it can be said that there was no clear correlation between σt and No. Hence, the oxygen ion conductivity of the compounds seemed to be predominantly governed not only by the defects in it but also by another factor. It is necessary to notice again that we cannot separate the grain boundary resistance in this study. In addition, it has been suggested that local cation

Table 4 List of the molecular formulae for the samples on composition line B. The molecular formulae calculated from the ρmat values are listed in the MF (meas.) column. The molecular formulae calculated using Models 3 and 4 are listed in the MF (model3) and MF (model4) columns, respectively. Sample

MF (meas.)

MF (model3)

MF (model4)

A2 B2 B3 B4 B5

La9.11Mg0.49(Si0.998Mg0.002O4)6O2.15 La9.13Mg0.50(Si0.97Mg0.03O4)6O2.03 La9.14Mg0.51(Si0.95Mg0.05O4)6O1.91 La9.12Mg0.49(Si0.93Mg0.07O4)6O1.73 La9.13Mg0.51(Si0.90Mg0.10O4)6O1.61

La9.06Mg0.45(Si0.99Mg0.01O4)6O2 La9.11Mg0.49(Si0.97Mg0.03O4)6O2 La9.17Mg0.53(Si0.95Mg0.05O4)6O2 La9.21Mg0.56(Si0.94Mg0.06O4)6O2 La9.27Mg0.60(Si0.92Mg0.08O4)6O2

La9.13Mg0.5(SiO4)6O2.20 La9.13Mg0.5(Si0.98Mg0.02O4)6O2.03 La9.13Mg0.5(Si0.97Mg0.03O4)6O1.88 La9.13Mg0.5(Si0.93Mg0.07O4)6O1.75 La9.13Mg0.5(Si0.90Mg0.10O4)6O1.59

K. Kobayashi et al. / Solid State Ionics 258 (2014) 24–29

2.4

and La vacancy configurations are strongly influenced by the oxygen ion migration in lanthanum silicate oxyapatite from the first principle calculation [23]. Another possibility is the distribution of the crystalline orientation in the ceramic body because the oxygen ion conductivity of the lanthanum silicate oxyapatite is known to be higher along the c-axis than the other orientations [29–32]. However, it is necessary to fabricate ceramics to control crystalline orientation and grain size for a detailed discussion on the relationship between the MgO concentration and oxygen ion conductivity in MgO-doped lanthanum silicate oxyapatite. Therefore, further careful research is necessary to discuss the relationship between the oxygen ion conductivity and its chemical and defect concentrations.

model 3

2.2

NO

2.0 1.8

model 4

1.6

29

1.4 4. Conclusions

1.2 0.03

0.04

0.05

0.06

0.07

z Fig. 8. Relationship between the numbers of the oxygen species related to oxygen ion conductivity (No) and MgO mol fraction (z) of the samples on composition line B. The sample compositions are listed in Table 2. Broken and dotted lines represent values that were calculated using Models 3 and 4, respectively.

a

T/K 2

1273

1073

873

All possible models for the formation of neutral La and oxygen ion vacancies in lanthanum silicate oxyapatite owing to doping with Mg were discussed. On comparing the measured material densities and the theoretical values obtained using the proposed models, it was found that Mg ions are distributed at the Si site as well as at the La sites in the compounds. Owing to the change in the concentration of the neutral La vacancies, it was impossible to estimate the number of the oxygen ions in a unit cell of MgO-doped lanthanum silicate oxyapatite without also evaluating its material density. Further, no clear correlation between the total conductivity and the defect concentrations was found. Therefore, the predominant factor in determining the total conductivity of Mg-doped lanthanum silicate oxyapatite is a parameter other than the concentration of defects. References

0

[1] [2] [3] [4] [5] [6] [7] [8] [9]

-2

-4

-6 0.7

A1 A2 A3 A5

[10] [11] [12]

0.8

0.9

1.0

1.1

1.2

1.3

1.4

T -1 / 103 K-1

[13] [14]

b

T/K 1

1273

1073

[15] [16] [17]

873

[18] [19]

0 [20] [21] [22]

-1

[23] [24]

-3 0.7

[25] [26] [27] [28] [29]

A2 B2 B3 B5

-2

0.8

0.9

1.0

1.1

1.2

1.3

1.4

T -1 / 103 K-1 Fig. 9. Arrhenius plots of the samples on composition lines (a) A and (b) B. Compositions of the samples are listed in Tables 1 and 2, respectively.

[30] [31] [32]

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