Rudimental research progress of rare-earth silicate oxyapatites:their identification as a new compound until discoveryof their oxygen ion conductivity

Kiyoshi KOBAYASHI³ and Yoshio SAKKA

Materials Processing Unit, National Institute for Materials Science, 1–2–1 Sengen, Tsukuba, Ibaraki 305–0047, Japan

Rudimental research progress of oxyapatite-type rare-earth silicates is reviewed based on the published papers mainly from 1959to 1993 that have not yet been discussed in detail. The knowledge of oxyapatite-type rare-earth silicates significantly increasedduring this period. Chemical compounds of rare-earth oxides and silica were discovered around 1960. Because of the complexchemical composition of the oxyapatite phase, the composition was initially considered as 2RE2O3·3SiO2, which was calledorthosilicate. “RE” is the rare-earth elements. Different compositions of 2RE2O3·3SiO2 have been proposed by crystal structureanalysis based on the crystal chemistry and the leaping model. With respect to crystal structure analysis, knowledge has graduallyimproved step-by-step, including the implicit distinction between oxygen-stoichiometric apatite and oxygen-deficient apatite.Based on the published work, the rare-earth silicate oxyapatites are considered to have an apatite-like structure. Initially,application research focused on the optical properties of oxyapatite because rare-earth metals were constituent elements of thecrystals, and on the use of oxyapatite as a stabilizer of unwanted radioactive waste produced in nuclear power reactors becauseoxyapatites can dissolve the actinide elements.©2014 The Ceramic Society of Japan. All rights reserved.

Key-words : Rare-earth silicate, Oxyapatite, Synthetic apatite, Phase diagram, Crystal structure

[Received April 23, 2014; Accepted June 6, 2014]

1. Introduction

Since Nakayama et al. reported high oxygen ion conductivityin lanthanoid silicate oxyapatites,1)­3) many researchers havebeen interested in these materials because of their fundamentallydifferent properties from typical oxygen ion conductors suchas stabilized zirconia.4) One peculiar property is the presenceof interstitial oxygen ions, which were first proposed in theliterature at 2000.5) Some specialists in solid-state oxygen ionicconductors did not believe the initial reports. Lanthanoid silicateand rare-earth silicate compounds were first identified in 1959.6)

However, the compounds corresponding to oxyapatites wereidentified as orthosilicate. On the other hand, lanthanoid silicateoxyapatites seemed to be recognized after 1995 in recent papers.In this review, we focused on the research of the rare-earthsilicate oxyapatites before 1995. Furthermore, a part of thestocked knowledge until 1993 seemed not to be taken over after1995.In the early 1960s, there was research competition for clari-

fication of the phase diagram of rare-earth oxides and silicabetween the USA and Soviet Union. Some rare-earth silicatecompounds were discovered by Warshaw et al.7) and Toropovet al.6) The chemical composition of the apatite phase, however,was not correctly identified because of an anomalous propertyof the oxyapatite phase and the low resolution of the analytical

instruments at that time. Therefore, the new compound waspresented as orthosilicate.Almost at the same time, the existence of rare-earth silicate

oxyapatites was also recognized by mineralogists because ofthe similarity between rare-earth and silicon-containing minerals.However, the oxygen ion conductive function at high temperaturewas not identified until about 30 years later. Before the discoveryof their good oxygen ion conductive properties, the main researchfocus was crystallographic analysis, their possible application aslaser hosts, their fluorescent properties, and stabilizer host ofunwanted radioactive waste. On the other hand, the accumulationand precision of the crystallographic data for rare-earth silicateoxyapatites and the similarities between the phase diagrams ofrare-earth oxides and silica played an important role in thediscovery of the oxygen ion conductivity. In this review, wesummarize the research history of rare-earth silicate oxyapatitesfrom the identification of the new compound (1959) up until thediscovery of the oxygen ion conductivity (1993).

2. Identification of new compounds andthe phase diagrams of rare-earth oxide and

silica quasi-binary system

In the early 1960s, clarification of the chemical and physicalproperties of rare-earth element compounds was a very importantscientific topic.8) Tropov and Bondar reported that the “U. S.Bureau of Mines planned a large program of fundamental researchon the refractory properties of rare-earth oxides individually andin combination with other oxides” (See Appendix A), and “Inthe Institute of Silicate Chemistry, a large program of work hasbeen planned for the study of phase diagrams of systems contain-ing silica and oxides of rare and disperse elements, and theinvestigation of the physical and physicochemical properties of

³ Corresponding author: K. Kobayashi; E-mail: KOBAYASHI.kiyoshi@nims.go.jp

‡ This article was selected from the presentations at "STAC-7" (The7th International Conference on the Science and Technology forAdvanced Ceramics) held in Yokohama, Japan (2013), through theregular reviewing procedure.

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crystalline and vitreous phases of these systems” in the SovietUnion.8) According to the large program in the Soviet Union,systematic research on the clarification of the phase diagrams ofrare-earth oxide and silica quasi-binary systems was performedby Toropov’s group at the Institute of Silicate Chemistry and atthe Leningrad Lensoviet Technological Institute.9)

From 1958 to 1959, three groups reported new rare-earthsilicates with different compositions. Toropov’s group reported anew compound with composition 2La2O3·3SiO2.6) Roy’s groupreported two new compounds with compositions of RE2O3·SiO2

and RE2O3·2SiO27) by studying the phase diagrams of silica and

rare-earth (RE) oxide binary systems. In addition, Wanmaker’sgroup reported one lanthanum silicate compound, La2Si2O7,10) inthe same year. These studies were the initial research related tosynthetic silicate­oxyapatites (See Appendix B).In 1961, Keler et al.11)­13) published three papers related to the

phase diagrams of quasi-binary systems of praseodymium oxide,lanthanum oxide (La2O3), neodymium oxide (Nd2O3), gadoli-nium oxide (Gd2O3), and reduced cerium oxide (Ce2O3) withsilica. In these papers, they discovered the three compoundsRE2O3·SiO2 (RE2SiO5), 2RE2O3·3SiO2 (RE4Si3O12), and RE2O3·2SiO2 (RE2Si2O7), (RE = La, Nd, Pr, Gd, and Ce). Based on thereported phase relationships, most of the samples might not bereached to the equilibrium state. Because the phase relationshipin the La2O3­SiO2 system presented in reference11) (Fig. 1) doesnot satisfy the Gibbs’ phase rule,14) except for the La2O3·2SiO2 (La2Si2O7) composition at 1923K for 1.5 h. Based on theX-ray diffraction (XRD) patterns in,11)­13) it is almost impossibleto distinguish between single-phase samples and the two phasescoexisting because of low diffraction angle accuracy and lowintensity of XRD for the analysis of quasi-binary system in rare-earth oxide and silica systems.From 1960 to 1962, a series of eight papers related to the phase

diagrams of rare-earth oxides and silica quasi-binary systemswere published by Toropov et al.8),15)­21) In the first paper,8)

Toropov et al. confirmed only one complex oxide in La2O3­SiO2

quasi-binary system. The complex oxide was determined to havethe composition La4Si3O12 (2La2O3·3SiO2). From comparisonof the microhardness, the hardness of this new compound wasbetween apatite and albite. From the XRD pattern analysis andthe compound density, they concluded that the molecular formulain the unit cell was La8Si6O24 and this new compound belongedto the olivine group with isolated [SiO4]4­ anions. From thisexplanation, the new compound was not identified as theoxyapatite phase. In addition, the phase diagram of the La2O3­

SiO2 quasi-binary system was completely different from thephase diagrams in the following papers in the series (Fig. 2). Thereason for the different identification of the complex oxides ofrare-earth oxides and silica by Toropov’s group was the lowresolution of the XRD patterns. Based on the XRD pattern givenin the reference,8) it is almost impossible to determine whetherthe sample is the single phase or multiple phases because ofthe low angle resolution and peak intensity. The main methodused to identify the new phases was to use an optical micrographwith polished sample surfaces obtained by slow cooling from atemperature higher than the melting point to room temperature.The symmetry of the segregated crystal was determined from theshape of the precipitates. Although this method is too simple fortoday’s analysis, they surprisingly reached the conclusion thatthe unit cell of the La4Si3O12 crystal had hexagonal symmetry.However, the Miller indices of the XRD peaks and the calculatedlattice constants (a = 1.123 nm, c = 0.467 nm) of their resultswere incorrect compared with the present data, for example, com-pared with the lattice constant of La9.33(SiO4)6O2 (a = 0.9714 nmand c = 0.7183 nm).22)

In the second to eighth papers,15)­19) Toropov’s group alsoconfirmed two compounds, RE2O3·SiO2 and RE2O3·2SiO2 (RE =Y, Nd, Gd, Dy, Er, Sm, and Yb), discovered by Roy’s group.According to this confirmation, the phase diagrams of theRE2O3­SiO2 quasi-binary system were revised to the same asthe data in the Phase Equilibria database23) (Fig. 3). A furtherrevision was made that RE4Si3O12 (2RE2O3·3SiO2) was unstablebelow about 1873K because the sample with composition2RE2O3·3SiO2 was in the two phases RE2O3·SiO2 and RE2O3·2SiO2. However, the proof for the decomposition from 2RE2O3·3SiO2 to 2RE2O3·SiO2 and RE2O3·SiO2 was only from one imageobserved by optical microscope (Fig. 4). In addition, the unitcell parameters of 2RE2O3·3SiO2 presented in these papers weredifferent from today’s data. Although the phase boundary curvesrelated to the liquid phases were investigated by thermodynamicmodeling,24),25) the phase decomposition of 2RE2O3·3SiO2 below1600°C has not been confirmed.In 1964, Miller and Rase26) claimed that the phase diagram

of the Nd2O3­SiO2 quasi-binary system proposed by Toropov20)

[Fig. 5(a)] was incorrect [Fig. 5(b)]. The main differences weretwo eutectic reaction temperatures and the stability temperatureregion of Nd2O3·2SiO2 (Nd2Si2O7). The eutectic reaction temper-ature differences at 55 and 74mol% SiO2 in the (100-x) mol%Nd2O3-x mol% SiO2 system were 130 and 35K, respectively.

Fig. 1. Phase relationship of the La2O3­SiO2 quasi-binary system byKeler et al. in 1961.11) The diagram was re-drawn from Fig. 4 inreference.11) The labels in this figure are as follows: L: La2O3, LS:La2O3·SiO2, L2S3: 2La2O3·3SiO2, LS2: La2O3·2SiO2, and S: SiO2.

Fig. 2. Phase diagram of the La2O3­SiO2 quasi-binary system in thefirst paper by Toropov et al. in 1960.8) The diagram was re-drawn fromFig. 1(b) in reference.8) The labels in the figure are as follows: L: La2O3,L2S3: 2La2O3·3SiO2, S: SiO2, liq: liquid phase, and liq1 and liq2 are theliquid phase with different composition in the miscibility gap.

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In addition, they reported that the melting temperature of theNd2O3·2SiO2 (Nd2Si2O7) system was 1953K, which was 70Klower than Toropov’s data.20) Comparing to these phase dia-grams, temperature region where Nd2O3·2SiO2 (Nd2Si2O7) phasewas stable, was different from each other. Miller and Raseconcluded that Nd2O3·2SiO2 (Nd2Si2O7) phase was stable onlyabove 1843K because two phase formation was confirmedconstructed by 2Nd2O3·3SiO2 phase and SiO2 phase wasobserved by the heating below 1843K.26) On the other hand,Toropov reported that Nd2O3·2SiO2 (Nd2Si2O7) phase was stablebetween 2023K and 1773K.20) Existence of immiscibility ofthe liquid phase in the composition region higher than 80mol%SiO2 was reported by Glasser et al.,27) Toropov,20) and Millerand Rase.26) With respect to the miscibility gap, themodynamicmodeling was performed based on the analytical expression ofthe Gibbs energy in the liquid phase.28)

In 1967, Roy’s group published a paper on the preparation ofSm4(SiO4)3 (2Sm2O3·3SiO2) and Nd4(SiO4)6 (2Nd2O3·3SiO2).29)

In this paper, they pointed out that this compound was stablebelow 1903K, which corresponds to the decomposition temper-ature for Sm4(SiO4)6 (2Sm2O3·3SiO2) reported by Toropov’sgroup.19) With respect to Nd4(SiO4)6 (2Nd2O3·3SiO2), Toropovdid not report whether it was stable or not below 1903K, because

the Nd4(SiO4)6 (2Nd2O3·3SiO2) line was drawn as a broken linein the phase diagram.20) However, the results that Sm4(SiO4)3(2Sm2O3·3SiO2) and Nd4(SiO4)6 (2Nd2O3·3SiO2) compoundswere stable below 1903K are not in the Phase diagram databasebecause Roy’s group did not publish the phase diagrams of theRE2O3­SiO2 system (See Appendix C). A revised phase diagramof the La2O3­SiO2 quasi-binary system was found in the invitedreview paper written in 1982 by Bondar, who was a researchcollaborator with Toropov9) (Fig. 6). This revised phase diagramwas presented by referring to a textbook written in Russian in1971 (See Appendix D). However, both the phase diagramsreported in the Russian textbook and in the Bondar’s review9)

are not in the phase equilibria database. In this review, thecomposition of 2RE2O3·3SiO2 was revised to 7RE2O3·9SiO2, andthis compound is stable below 1873K. Other important datareported by Roy’s group in 1967 were the Miller indices andlattice constant values (a = 0.9497 nm and c = 0.6949 nm) forSm4(SiO4)3 (2Sm2O3·3SiO2), which are close to the latticeparameters of oxyapatite [a = 0.94923 nm and c = 0.69394 nmfor Sm9.33(SiO4)6O2]30) even though it is now known that it wasnot possible to synthesize the oxyapatite single phase with thecomposition Sm4(SiO4)3.In 1971, Toropov and Kougiya revised the phase diagram of

Nd2O3­SiO2 quasi-binary system around oxyapatite composi-tion31) (Fig. 7). Neodymium silicate oxyapatite phase has a com-positionnal width with x mol% SiO2 range between x = 54.5[corresponding to Nd10.03(SiO4)6O3.045] and x = 60 [correspond-ing to Nd7.67(SiO3.9175)6] after the papers by Miller et al.26) and

Fig. 4. Optical microscope image of 2La2O3·3SiO2 copied fromreference.17) The picture was magnified 240 times. The authors onlyexplained that the contrast was generated because of the decomposition of2La2O3·3SiO2 to La2O3·SiO2 and La2O3·2SiO2. This was only one proofthat 2La2O3·3SiO2 decomposed below 1873K.

(a)

(b)

Fig. 5. Phase diagram of the Nd2O3­SiO2 quasi-binary systempresented by (a) Toropov in 196120) and (b) Miller et al. in 1964.26)

The diagrams were re-drawn from the diagrams in references.20),26)

The labels in this figure are as follows: N: Nd2O3, NS: Nd2O3·SiO2,N2S3: 2Nd2O3·3SiO2, NS2: Nd2O3·2SiO2, S: SiO2, liq: liquid phase, andliq1 and liq2 are the liquid phase with different composition in themiscibility gap.

Fig. 3. Phase diagrams of the La2O3­SiO2 quasi-binary systempresented in the fourth paper by Toropov et al. in 1961.17) The diagramwas re-drawn from Fig. 1(b) in reference.17) The labels in this figureare as follows: L: La2O3, LS: La2O3·SiO2, L2S3: 2La2O3·3SiO2, LS2:La2O3·2SiO2, S: SiO2, liq: liquid phase, and liq1 and liq2 are the liquidphase with different composition in the miscibility gap.

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McCathy et al.29) However, this composition range is too wide forthe oxyapatite structure because not only existence of interstitialoxygen but also Nd interstitial or Si vacancy are necessary forthe x = 54.5 [Nd10.03(SiO4)6O3.045] and partial dimerization of[SiO4]4­ unit is necessary for x = 60 [Nd7.67(SiO3.9175)6]. Fur-thermore, it was found that Nd2Si2O7 compound was also revisedas high temperature phase above 1668K from comparing to thephase diagram by Toropov in 196120) [Fig. 5(a)].In 1982, Montorsi reported compounds of Ho2O3 and silica

with the compositions Ho2O3·SiO2, 2Ho2O3·3SiO2, Ho2O3·3SiO2, and Ho2O3·6SiO2.32) In addition, the phase diagram ofthe Ho2O3­SiO2 quasi-binary system was proposed in the limitedtemperature range below 1873K. Furthermore, in this reportthe 2Ho2O3·3SiO2 compound had hexagonal symmetry and wasthe stable high temperature phase above 1573K.Here, it is necessary to emphasize that all the groups that

investigated the phase diagrams of rare-earth oxide-silica quasi-binary systems did not use the apatite or oxyapatite terms forthe orthosilicate compounds RE4(SiO4)3 (2RE2O3·3SiO2) before1971 (See Appendix E) and 1982, respectively, because chemistsand ceramists in the 1960s had the custom of categorizinginorganic compounds by their constituent ratio and coordination

of [SiO4]4¹ unit. At present, the orthosilicate represents olivine,garnet, zircon, and etc. In addition, referring to the paper byGrisafe and Hummel,33) McCathy et al. seemed to consider that2RE2O3·3SiO2 orthosilicate had a similar but different crystalstructure to apatite. In a review paper in 1982 by Bondar,9) thecompound RE4.67O(SiO4)3 (7RE2O3·9SiO2) was introduced asan apatite-like silicate determined by Belov et al. Belov’s paperwas published in 1965.34) Belov et al. solved the correct crystalstructure and determined corresponding chemical compositionof RE4.67O(SiO4)3 (7RE2O3·9SiO2) which had been identified asorthosilicate, 2RE2O3·3SiO2 (RE4Si3O12) compound. For cate-gorization of compounds by crystal structure in phase diagramresearch, it was necessary for ceramists to conform to the systemused in mineralogy and crystal chemistry. Considering this fact,Bondar et al.9) used a different categorization to that normallyused by ceramists, and the interdisciplinary research seemed toproceed smoothly in the Soviet Union.In 1994, Tas and Akinc investigated the phase diagram of

Ce2O3­Ce2Si2O7 between 1423K and 2243K under Ar + 10%H2 atmosphere to avoid CeO2 formation.35) In this paper,Ce4.67(SiO4)3O phase was described as cerium oxygen apatite.Based on their results, the phase relationship between Ce2O3 andCe2Si2O7 were similar to the relationship of La2O3­SiO2 quasi-binary system except for the phase transition of Ce2Si2O7. Thepolymorphic transformation exists at 1547K among tetragonallow-temperature form and monoclinic high-temperature form.In 2003, Masubuchi et al. reinvestigated the phase diagram of

the Nd2O3­SiO2 quasi-binary system by single crystal growthof Nd9.33(SiO4)6O2 with the floating zone method.36),37) Theyfound that the composition of the oxyapatite single phase was notNd4Si3O12 (2Nd2O3·3SiO2) but Nd9.33Si6O26 (7Nd2O3·9SiO2). Inaddition, decomposition of Nd9.33Si6O26 was not observed below1873K (Fig. 8).After 2003, no research on the phase diagrams of rare-earth

oxides-silica quasi-binary systems seemed to be carried out, eventhough there were still inconsistencies in the database.

3. Recognition on the crystal structureof oxyapatite before 1993

Before 1960, there had been considerable interest in thelanthanoid silicate system by mineralogists. Several mineralo-gists had already succeeded in solving the crystal structureand determining the chemical composition of fluorapatite

Fig. 7. Partial phase diagram of Nd2O3­SiO2 quasi-binary systemrrevised by Toropov and Kougiya in 1971.31) This diagram was re-drawnfrom the Fig. 1 in reference.31) The labels in this figure are as follows:NS: Nd2SiO5, Ap(ss): Oxyapatite solid solution, and N2S: Nd2Si2O7.Nd:Si indicates the mole fraction value of Nd2O3:SiO2.

Fig. 8. Partial phase diagram of the Nd2O3­SiO2 quasi-binary systempresented by Masubuchi et al. in 2003.36) They investigated the phaserelationship between 30 and 70mol% SiO2. The labels in this figure areas follows: N: Nd2O3, NS: Nd2O3·SiO2, N7S9: 7Nd2O3·9SiO2, NS2:Nd2O3·2SiO2, S: SiO2, and liq: liquid phase.

Fig. 6. Phase diagram of the La2O3­SiO2 quasi-binary system pre-sented by Bondar.9) This diagram was re-drawn from Fig. 1 in reference.9)

The labels in this figure are as follows: L: La2O3, LS: La2O3·SiO2, L7S9:7La2O3·9SiO2, LS2: La2O3·2SiO2, S: SiO2, liq: liquid phase, and liq1 andliq2 are the liquid phase with different composition in the miscibilitygap. Although LB and LBB might be two high temperature phases, therewas no explanation in reference.9)

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(Ca10(PO4)6F2) before 1946.38) In addition, they already knew thatseveral minerals, with different chemical composition to hydroxy-apatite and fluorapatite, belonged to the apatite group. Based onearly review-like papers,38),39) rare-earth silicate apatites wererecognized to be isostructural to the natural minerals britholite,abukumalite, beckelite, and lessingite. The chemical formulae ofthese minerals are as follows:Britholite: (Ce,Ca,Th,La,Nd)10(SiO4,PO4)6(OH,F)2Abukumalite: (Ca,Y)10(PO4,SiO4)6(OH,F)2Beckelite and Lessingite: (Ce,Ca)10(SiO4)3(OH,F)2Although these minerals contain rare-earth elements and sili-

con, all of the compounds seem to be categorized in the apatitegroup, in particular the hydroxyapatite or fluorapatite groupsbecause they all contain the anions OH­ and F­. Mineralogistseemed to begin the artificial synthesis of apatite compoundsinspired by the chemical compositions of these minerals.Kuźmin and Belov focused on the similarity of the powder

XRD pattern of the La and Sm silicates reported as orthosilicate(2RE2O3·3SiO2) and britholite in 1965.34) The XRD patternsof britholite [(Ce0.4Ca0.35Sr0.25)2(Ce0.86Ca0.14)3 (SiO4)3(O, OH,F)] and La9.33(SiO4)6O2 calculated using the crystallographicdata40),22) and RIETAN-FP software41) are shown in Fig. 9.From the host chemical composition of britholite [Ca5(PO4)3F],Kuźmin and Belov assumed the same chemical composition aslanthanum orthosilicates [La5­x(SiO4)3O]. Then, they used threemodels with different assumptions: (1) La had mixed valencestates of +3 and +2, (2) La had mixed valence and water wasincorporated in the structure, and (3) statistically, some of the Lasites were vacant. By careful measurement of XRD pattern using

small single crystals (0.4 © 0.2 © 0.2mm3 for lanthanum silicateand 0.3 © 0.2 © 0.1mm3 for samarium silicate), they concludedthat the lanthanum silicate and samarium silicate reported asorthosilicate (2RE2O3·3SiO2) has hexagonal symmetry andbelongs to the space group P63/m. Model (3) was confirmed tobe the most adequate based on the XRD results. By their carefulanalysis, the chemical composition was determined as RE4+2/3-(SiO4)3O, which corresponded to the 7RE2O3·9SiO2. The crys-tallographic data and the corresponding structure in this paper,which are fundamentally consistent with the present widelyaccepted oxygen-stoichiometric oxyapatite model, are shownin Table 1 and Fig. 10(a), respectively. According to Kuźminand Belov’s results, the rare-earth ions at the 4 f and 6h siteswill be hereafter denoted as RE1(4 f ) and RE2(6h) or chemical

Fig. 9. Simulated powder X-ray diffraction patterns of britholite40)

(a) and La9.33(SiO4)6O222) (b) using the crystallographic data and the

RIETAN-FP software.41)

Table 1. Coordinates of the atoms in La4+2/3(SiO4)3O and Sm4+2/3(SiO4)3O reported by Kuźmin and Belov in 1965.34) Both of the crystals have thehexagonal lattice with space group P63/m. In the original paper, the La1(4 f ), La2(6h), Sm1(4 f ), and Sm2(6h) sites in this table were labeled as LaII, LaI,SmII, and SmI, respectively. In addition, site occupancy (g) is included in the table.

La4+2/3(SiO4)3Oa = 0.955nm and c = 0.714 nm

Sm4+2/3(SiO4)3Oa = 0.933 nm and c = 0.685 nm

Site g x y z Site g x y z

La1(4 f ) 0.833 1/3 2/3 0 Sm1(4 f ) 0.833 1/3 2/3 0La2(6h) 1 0.233 ­0.013 1/4 Sm2(6h) 1 0.232 ­0.009 1/4Si(6h) 1 0.400 0.368 1/4 Si(6h) 1 0.394 0.370 1/4O1(6h) 1 0.333 0.485 1/4 O1(6h) 1 0.319 0.493 1/4O2(6h) 1 0.592 0.468 1/4 O2(6h) 1 0.595 0.470 1/4O3(12i) 1 0.346 0.246 0.073 O3(12i) 1 0.342 0.244 0.065O4(2a) 1 0 0 1/4 O4(2a) 1 0 0 1/4

(a)

(b)

Fig. 10. (a) Crystal structure of La9.33(SiO4)6O2 (7La2O3·9SiO2) usingthe structural data of Kuźmin and Belov34) and (b) the change of theLa1(4 f ) position from (1/3, 2/3, 0) to (1/3, 2/3, 0.0018), whichcorresponds to the modern model. In the Kuźmin and Belov’s model, Lasites in the 4 f position are located at (1/3, 2/3, 0) and four La positionsare located on the a-b plane. This figure was drawn using VESTA.42)

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element1(4 f ) and chemical element2(6h). The crystal structureswere drawn by Kuźmin and Belov’s model using the VESTAprogram.42) The difference between the results of Kuźmin andBelov and those of recent studies22),34) is the RE1(4 f ) position:Kuźmin and Belov’s analysis fixed the z position of the RE1(4 f )site at 0, whereas the recent structural data have the z valueslightly shifted from 0 [Fig. 10(b)]. Comparing the simulatedXRD patterns of Kuźmin and Belov’s original model and themodified model by changing the La1(4 f ) position and the latticeconstants reported by Okudera et al.22) (Fig. 11) shows that theexperimentally collected pattern is different from the simulatedpattern by Kuźmin and Belov’s model. Hence, the accuracy ofthe Kuźmin and Belov model seems to be insufficient. This mightbe because of the low analytical resolution of the instruments in1965. The difference is mainly because of the lattice constants, asexplained below.One important conclusion by Kuźmin and Belov was that

3 + 1/3 of the RE ions are statistically distributed in the RE1(4 f )site34) and they determined the chemical composition of the rare-earth silicate oxyapatite from the crystal structure analysis. Thismethodology might be the opposite route to the chemists andceramists. Chemists and ceramists at that time determined thechemical composition of new compounds from the nominalcomposition when the single phase was obtained because they didnot have effective analytical method such as electron probe micro-analysis. Then, candidate crystal structure would be selected fromthe chemical composition. On the other hand, Kuźmin and Belovwas determined the chemical composition of rare-earth silicateoxyapatites from the crystal structure. Considering that Belov hadstudied various types of silicates,43) the method would be based onboth crystal chemistry and silicate chemistry.The most important difference between the crystal model of

Kuźmin and the other studies is the assumption of the existenceof statistical rare-earth deficiency. This indicates that the chemi-cally stoichiometric composition does not indicate a perfect statecompared with its crystal structure. This concept is significantlydifferent from the model of disorder in crystals proposed byFrenkel44)­46) and Wagner and Schottky.45)­47) The concept of

defects in crystal by Frenkel, and Wagner and Schottky is thatdefects are treated as components in thermodynamic system.Therefore, formation mechanism of defects is two types: onetype of defects is formed by the thermal activation process tominimize the Gibbs energy of the crystal system (or maximize theentropy of the crystal system): the second type is formed bydoping of aliovalent ions to keep a charge neutrality of ioniccrystals. In the latter case, the defects are formed to maintaincharge neutrality in the crystals.48)­51) However, the Kuźmin andBelov model set the rare-earth deficiency as primitive existence.Although the structural model by Kuźmin and Belov was derivedfrom single-crystal XRD analysis, their suggestions seemed tonot be widely accepted in the US and Europe during the 1960s.For example, Ito agreed with the findings of Kuźmin and Belovbecause the results were consistent with the lattice parameterdependences for a large number of the monovalent and divalention-doped lanthanoid silicate oxyapatites that he synthesized andanalyzed.39) However, he stated that “The finding of cation-defectapatite opens the wide possibilities of cation deficiency in silicateapatites generally. Further investigation is indicated”. Ito synthe-sized a large number of samples, but the sample composition withRE9.33(SiO4)6O2 was not contained in his sample list. After theKuźmin and Belov’s paper, the RE9.33(SiO4)6O2 oxyapatites werefollowed in 1969 by Smolin and Shepelev52) and Felsche,53) andin 1972 by Belokoneva et al.54) and Felsche.55) The reason mightbe that the concept of primitive rare-earth deficiency was so farfrom the conventional knowledge.Below we give the modern interpretation of Kuźmin and

Belov’s analysis logic. Keep in mind that systematic research onclarifying the physicochemical properties of rare-earth oxidesstarted around 1960 and the possibility of the mixed valence stateof La ion was not confirmed experimentally until 1965. If a mixedvalence state of La ion was considered, it would be possible toexplain why the rare-earth silicate oxyapatites were only formed athigh temperature, as reported by Tropov et al.,15)­20) because theoxyapatites would be formed only when the lower valence rare-earth ions were formed, which would occur at high temperature.Estimation logic of the chemical composition of rare-earth

silicate oxyapatites was the main advance in the paper by Kuźminand Belov.34) They took into account the similarity of the XRDpatterns of lanthanum silicate oxyapatite and britholite, andthe chemical composition of lanthanum silicate oxyapatite wasestimated from the host composition of britholite (Ca5(PO4)3-(F, OH)2). The explanation in the paper was that, referring to thesimilarity of the XRD patterns between the synthetic lanthanumsilicate and britholite shown in Fig. 8, “This result led us to acceptfor the synthetic compounds a chemical formula close to theformula of britholite, La5­x[SiO4]3O, equal to the sum of the twosilicates [La2SiO5 (La2O3·SiO2) and La2Si2O7 (La2O3·2SiO2)]initially assumed plus a minimum amount of a freer La2O3:

La2O3 � SiO2 þ La2O3 � 2SiO2 þ 1=3La2O3

¼ La2SiO4 þ La2Si2O7 þ 1=3La2O3

! La4þ2=3ðSiO4Þ3O: ð1ÞThis derivation of the formula seemed insufficiently dependable”.However, the explanation of the “minimum amount of a freerLa2O3” was not given in detail, and, therefore, this equationmight be incorrect as the equilibrium chemical reaction. Kuźminand Belov would know that the compound composition was closeto equal amounts of La2SiO5 (La2O3·SiO2, 50mol% of SiO2 inLa2O3­SiO2 system) and La2Si2O7 (La2O3·2SiO2, 66.7mol% ofSiO2). In addition, they would notice that the La5(SiO4)3Ocomposition could not be given by a combination of La2O3 and

Fig. 11. (a) Simulated powder X-ray diffraction patterns based onKuźmin and Belov’s original structure data and (b) modified data with theLa1(4 f ) position changed from (1/3, 2/3, 0) to (1/3, 2/3, 0.018) and thelattice parameters using the values of Okudera et al. (a = 0.9714 nm andc = 0.7183nm).22) (c) The experimentally collected powder diffractionpattern for comparison. RIETAN-FP software41) was used for the patternsimulations.

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SiO2 if the valence of the La ion was fixed at +3. Hence, theyinitially assumed the minimum La2O3 amount and changed theCa5(PO4)3(F, OH) composition to lanthanum and oxygen. Ifone wants to adjust the number of La atoms while ignoring thechange in the number of oxygen atoms, 1/2La2O3 is necessary byfollowing equation:

La2O3 � SiO2 þ La2O3 � 2SiO2 þ 1=2La2O3

¼ La2SiO4 þ La2Si2O7 þ 1=2La2O3

! La5ðSiO4Þ3O1:5: (1B)

This equation is also probable if the existence of excess oxygenis accepted. In this case, the additional La2O3 becomes 1/2.Comparing Eqs. (1) and (1B), the smallest amount of La2O3

necessary for apatite structure formation is 1/3 La2O3. Thiswould be the meaning of “a minimum amount of a freer La2O3”.The meaning of this treatment is the estimation methodology ofthe compositional deviation of the rare-earth silicate oxyapatitefrom La8Si4O12 (2La2O3·3SiO2, 60mol% of SiO2). Therefore,Eq. (1) is not the chemical reaction equation. Actually, oxyapatiteformation from La2SiO5 and La2Si2O7 is simply given by

10La2SiO5 þ 4La2Si2O7 ¼ 3La8þ4=3ðSiO4Þ6O2: ð2ÞThe accuracy of Eq. (2) has been confirmed in papers from2011 to 2013 by modified diffusion couple experiments.56)­61)

In contrast, if one tried to analyze the kinetics of rare-earthoxyapatite formation by considering Eq. (1) based on masstransport theory in solids,62) no solution can be derived because ofthermodynamic inconsistency: Eq. (1) does not satisfy the phaserule. Kuźmin and Belov could reach the answer that the composi-tion of the rare-earth silicate oxyapatites were RE4+2/3(SiO4)3O(7RE2O3·9SiO2) by the viewpoint of the crystal chemistry.However, it would be impossible to find such a complex ratiobetween of La2O3 to SiO2 (7 to 9) without Kuźmin and Belov’sresearch. Kuźmin and Belov wrote their logic in a simple way,and, therefore, it might be necessary to read it carefully. Further-more, in Kuźmin and Belov’s paper the accuracy of the latticeconstants is poor, as pointed out by McCathy et al.29) In the caseof samarium silicate oxyapatite, the lattice parameters determinedby Kuźmin and Belov were a = 0.933 nm and c = 0.685 nm, butthe values reported by McCathy et al.29) were a = 0.9497 nmand c = 0.6949 nm. Compared with the recent data of Sm9.33-(SiO4)6O2 (a = 0.94923 nm and c = 0.69394 nm),30) McCathy’sdata is found to be more accurate than Kuźmin and Belov’s data.In contrast, McCathy et al. did not solve the coordinates ofthe atoms because they measured the powder XRD pattern, nota single-crystal XRD pattern.Cockbain and Smith reported their success of synthesizing

a number of alkaline-earth­rare-earth silicates and germanateapatites in 1967.38) The main analytical method they used waspowder XRD by applying the space group P63/m to the hydroxy-apatites and fluorapatites. In addition, an important possibilitywas introduced, namely, formation of oxyapatite, because wefound the description “Attempts to confirm the presence ofthe hydroxyl ion in the calcium lanthanum silicate apatite byinfra-red absorption spectroscopy have so far been unsuccessful,and an oxyapatite formula Ca4La6(SiO4)6O such as has beensuggested for voelckerite and oxy-pyromorphite could be pro-posed instead of Ca4La6(SiO4)6(OH)2” in their paper. Thechemical compositions of voelckerite and oxy-pyromorphite areCa10(PO4)6O and Pb10(PO4)6O, respectively. From this descrip-tion, Cockbain and Smith were careful to accept the existence ofcation- and oxygen-deficient oxyapatites, whose crystal structuremodel was proposed by Kuźmin and Belov in 1965.34)

In the same year (1967), Schwarz reported the discovery ofnew oxyapatite single-phase compositions.63) He systematicallysynthesized the solid solution of Sr3(PO4)2 and La8(SiO4)6 withthe molecular formula given by [Sr9­xLax(PO4)6­x(SiO4)x]. Bythis analysis, he found that the oxyapatite structure phase wasobtained between x = 4.5 and x = 6. After further detailed ana-lysis, he discovered the six non-doped and Sr-doped lanthanumsilicate oxyapatite compositions: (1) La8+2/3(SiO4)6O; (1a) Sr4­y-La6+2y/3(SiO4)6O, 0 ¯ y ¯ 4; (1b) Sr4La6(SiO4)6O; (2) La9+1/3-(SiO4)6O2; (2a) Sr2­yLa8+2y/3(SiO4)6O2, 0 ¯ y ¯ 2; and (2b)Sr2La8(SiO4)6O2.It was interesting that the oxyapatite type was distinguished by

the number of oxygen atoms. This categorization indicated thatSchwartz might consider that oxygen stoichiometric oxyapatite(2, 2a, and 2b) and oxygen-deficient oxyapatite (1, 1a, and 1b)were implicitly different phases.Ito published a long paper in 1968 entitled “Silicate apatites

and oxyapatites”.39) In this paper, many compositional silicatehydroxyapatites and oxyapatites were synthesized mainly byhydrothermal and conventional solid-state reaction methods,respectively. XRD and thermal analyses were used for the char-acterization of the structures. From this research, the existenceof silicate oxyapatites were clarified in the cases of monovalention-doped rare-earth silicates (RE9A(SiO4)6O2, RE = rare-earthelements and A = Na and Li) and divalent ion-doped rare-earthsilicates [RE8R2(SiO4)6O2, RE = rare-earth elements and R =Ba, Sr, Ca, and Pb]. In addition, it was clarified that cation andanion deficiencies were not the fundamental factor for formationof the lanthanoid silicate oxyapatites.In 1969, Smolin and Shepelev52) determined the crystal struc-

ture of 7Gd2O3·3SiO2 along with the Kuźmin and Belov analogy.Small 7Gd2O3·3SiO2 single crystals (0.7 to 0.15mm) were grownby the flux method using KF. Based on the single-crystal XRDanalysis, they concluded that the 7Gd2O3·3SiO2 compound hadan apatite-like structure similar to 7Ln2O3·3SiO2 (Ln = La, Sm,Eu, and Sm). The space group was P63/m. In the case ofgadolinium silicate oxyapatite, it was concluded that 1/6 of theGd(4 f ) sites were vacant.In the same year as Smolin and Shepelev (1969),52) Felsche

published a short paper reporting the success of solving thecrystal structure of cerium (III) orthosilicate [Ce4.67(SiO4)6O].53)

He synthesized the sample at 1973K under high vacuumconditions. The crystal structure was analyzed using a smallplate-like single crystal (0.1 © 0.1 © 0.02mm3) by XRD. Thecerium (III) orthosilicate was found to be the oxyapatite structurewith space group P63 or P63/m. By the analysis of the cerium(III) orthosilicate structure, the adequacy of the structure modelproposed by Kuźmin and Belov34) was confirmed.Wanmaker et al. synthesized a series of oxyapatite samples with

compositions Me2þ2þxMe3þ8�xðSiO4Þ6�xðPO4ÞxO2, Me2þ3þxMe3þ6�x-

ðSiO4Þ6�xðPO4Þx, and Me2þ4þxMe3þ6�xðSiO4Þ6�xðPO4ÞxO, withMe2+ = Ca, Sr, Ba, Mg, Zn or Cd and Me3+ = Y or La in1971.64) In this research, the powder XRD method was used forthe characterization of the samples. By analysis of the relation-ships between the chemical composition and lattice parameters,Vegard’s law was found to be well established when taking intoconsideration the ionic radii of the constituent ions.Following Felsche’s work in 1969,53) Belokoneva et al.54)

successfully synthesized small single crystals (0.1 to 0.3mm)of cerium (III) orthosilicate [Ce4.67(SiO4)3O] and dysprosiumorthosilicate [Dy4.67(SiO4)3O] by the hydrothermal method. Fromcrystal structure analysis using single-crystal XRD, both com-pounds were found to have the apatite structure with space group

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P63/m. In addition, it was reported that 1/6 of the RE1(4 f ) siteswere vacant.Felsche examined systematic composition samples of lantha-

noid-deficient oxyapatites [RE9.33(SiO4)6O2] and alkali-dopedstoichiometric oxyapatites [RE9A(SiO4)6O2, RE = La­Lu, A =Na and Li] between 1969 and 1973.53),55),65) These samples weresynthesized and their crystal structures analyzed using smallsingle crystals (10 to 200¯m) by XRD. The single crystals wereformed by cooling from the melted sample obtained by heatingup to 2173K. All of the samples were determined to have thespace group P63/m. Felsche reported that a small deviation fromthe simple Vegard law was observed in the oxyapatite system inthe small cell volume region for RE = La­Ho. Felsche discussedthe deviation from Vegard’s law by the different distribution ofRE vacancies and the site distribution of Na and Li on two REsites: RE1(4 f ) and RE2(6h). In addition, Felsche recognized theexistence of oxyapatites containing oxygen vacancies as wellas lanthanoid vacancies such as Sr2La6.67(SiO4)6, Sr3La6(SiO4)6,Sr4La5.33(SiO4)6, Sr4La6(SiO4)6O, and suggested that neutrondiffraction was necessary for the crystal structural analysis of theoxygen-deficient oxyapatites. In the review paper by Felsche in1973,65) he summarized the diagrams showing the relationshipsbetween the component ionic radius and crystal structure typesof various types of rare-earth silicate-based compounds includ-ing RE9.33(SiO4)6O2. It is necessary to note that the diagramspresented by Felsche were based on the crystal chemistry and/orsilica chemistry of the title of his review paper: “Crystalchemistry of the rare-earth silicates”. The diagrams were notbased on chemical thermodynamics, because the diagramsshowed the relationship between crystal structure type and ionicradius of components. This means that the diagram was notcontained the constraints generated from chemical thermo-dynamics. Hence, the diagrams described by Felsche were notthe phase diagram as reported by Toropov et al.8),9),15)­20) Inter-disciplinary studies by crystal chemists and ceramists have notbeen sufficient for quasi-ternary oxide systems including rare-earth oxides and silica by considering the molecular formulae ofoxygen-deficient oxyapatites by Felsche because of the lack ofknowledge whether the oxygen-deficient oxyapatite and oxygen-stoichiometric oxyapatite were the same phase. With respect tothe quasi-ternary phase diagrams including rare-earth silicates,most of the phase diagrams have not yet been solved except forY2O3­SiO2­MgO, RE2O3­SiO2­Al2O3 (RE = Y, La, Nd, andGd), and La2O3­SiO2­MgO systems.23)­25),66)­70) This lack ofthe knowledge about the phase diagrams remains at present.In 1977, Sidorov et al. reported the crystal structure of CaNd4-

(SiO4)3O using single crystal grown from solution in a meltof alkaline fluoride.71) Size of the single crystal was from 1 to10mm. They succeeded to determine the space group, atomicpositions, isotropic thermal displacement parameter, and aniso-tropic thermal displacement parameter. Checking an ellipsoidfigure using this report data, it was found that too large isothermaldisplacements were found for all of the oxygen sites. Althoughthe accuracy of the anisotropic thermal displacement parameterseemed to be low, it was interesting that anisotropic expansionof the thermal displacement of oxygen at O4(2a) site wasreported in their data. With respect to the oxygen site bondedto Si, highly rotational vibration of isolated SiO4 tetrahedronseemed to exist.In 1978, Schroeder and Mathew analyzed the crystal struc-

ture of the oxyapatite La8Ca2(SiO4)6O2 using the single crystalsupplied by Hopkins, who grew the oxyapatite single crystal byCzochralski’s method.72) The research of Hopkins et al. will be

introduced in the following section. The motivation of Schroederand Mathew was to determine whether La8Ca2(SiO4)6O2 has adifferent crystal structure to oxyapatite. In this research, La8Ca2-(SiO4)6O2 was confirmed to have the space group P63/m. Theyinvestigated the possibility of the ordered apatite structure becauseof the ordered arrangement of Ca on La2(6h) and La1(4 f ) sites,which might be the same crystallographic image as reported byMcCathey29) and Felsche.55),65) The conclusion by Schroeder andMathew was that Ca ions occupied only the La1(4 f ) site. How-ever, two La ions also occupied the La1(4 f ) site and no long-rangeordering was confirmed among the La and Ca ions on the La1(4 f )site. Hence, the crystal structure model and its space group was thesame as oxyapatite. This was the first report of the preferabledistribution of Ca ions on the La1(4 f ) site in oxyapatite.In the same year (1978), Pushcharovskii et al.73) reported the

crystal structure of KNd9(SiO4)6O2 analyzed by single-crystalXRD using a small crystal, but no description exists of the samplesize. The sample was synthesized by the hydrothermal method.Although KNd9(SiO4)6O2 was concluded to be the hexagonaltype with an apatite-like structure, the space group was P63 notP63/m. Owing to the lower symmetry than P63/m, two Nd ions inthe case of P63/m were divided among three sites. The Nd1(4 f )site in the case of P63/m becomes the two different sites Nd1(2b)and Nd2(2b). The potassium ions were reported to occupy theNd1(2b) and Nd2(2b) sites with the same ratio. With respect tothis material, Haile et al.74) also reported the same result using apowder sample synthesized by the hydrothermal method. On theother hand, Li-doped RE silicate oxyapatites (RE = La, Nd, Sm,Eu, Gd, and Dy) were analyzed using the space group P63/m bySato et al.75),76)

In 1983, de Alleluia et al.77) reported the crystal structure ofcompounds of the trivalent transuranium (An = Pu, Am, and Cm)oxide and silica system. Samples with compositions of An9.33-(SiO4)6O2, An8(SiO4)6, MeIAn9(SiO4)6O2, andMeII2An8(SiO4)6O2

formed apatite-type structures with MeI = Li and K, and MeII2 =Mg, Ca, Sr, and Ba, respectively. The structure identification wascarried out by the powder XRD method. No explanation wasfound about the space group of these apatites.In 1985, Fahey et al. reported that the crystal structures of the

oxygen-deficient neodymium silicate oxyapatites Ca2+xNd8­x-(SiO4)6O2­0.5x were analyzed by a combination of powder XRDand powder neutron diffraction analyses.78) Because of the pow-der diffraction analysis, they used the space group P63/m forthe pattern refinements. In this paper, they succeeded in clarifyingthe crystal structures of two samples: one was stoichiometricoxyapatite Ca2Nd8(SiO4)6O2 and the other was oxygen non-stoichiometric oxyapatite Ca2.2Nd7.8(SiO4)6O1.9. An importantfinding of this study was the existence of oxyapatite containinga non-integer number of oxygen atoms. Checking the previousresearch, all of the oxygen numbers in the oxygen-deficientoxyapatites were integer numbers. However, any explanation ofthis point was not found in Fahey’s paper. Instead, they clarifiedthe two facts that calcium ions were preferably substituted in theNd1(4 f ) site rather than the Nd2(6h) site, and oxygen vacancieswas observed at the O4(2a) site. The former result was consistentwith the results of Schroeder and Mathew for La8Ca2(SiO4)6O2.72)

Furthermore, it was not possible to synthesize the oxygen-deficient oxyapatites with the compositions of Ca4Nd6(SiO4)6Oand Ca6Nd4(SiO4)6 owing to the coexistence of a glass-likecalcium silicate phase, even though these compositions werereported to be the oxygen-deficient oxyapatite phase in previouspapers.38),39),55),64),65) Based on their results, neodymium andoxygen deficiency was concluded to be very small in calcium-

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doped neodymium silicate oxyapatite.78) It was interesting thatthe sample composition presented by Fahey et al. (Ca2+xNd8­x-(SiO4)6O2­0.5x) is equivalent to the modern description (Nd10­y-Cay(SiO4)6O3­0.5y) when x is replaced by y ­ 2. This indicates thatFahey et al. had produced oxygen-excess oxyapatite. However,the oxygen-excess state was beyond the knowledge of crystallog-raphy at the time, and, therefore, they did not consider thatpossibility.With respect to the RE ion ordering in RE9.33(SiO4)6O2, three

research papers with different conclusions were published: oneby Malinovskii et al. in 1990,79) the second by Yoshioka in2007,80) and the third by Kobayashi et al. in 2012.81) Malinovskiiet al. concluded that the crystal structure of La2Nd7.33(SiO4)6O2

was given by La3Nd11(SiO4)6O3 because of the ordering of thecoordination of La and Nd ions even though the space groupof La3Nd11(SiO4)6O3 was the same as oxyapatite (P63/m). TheLa3Nd11(SiO4)6O3 sample was synthesized by hydrothermalcrystallization in La2O3­Nd2O3­SiO2­Na2O­H2O at 723K under1.5 kbar. They used a well-faced isometric crystal (0.1mm © 0.1mm © 0.1mm) for the crystal structure analysis. On the otherhand, Yoshioka reported that no extra diffraction peaks owing tothe La and Nd ordering were observed using a laboratory powderXRD instrument for (La9.33Nd0.33)(SiO4)6O2.5 and (La9.33Nd0.67)-(SiO4)6O3. The latter sample contained a small amount of theLn2SiO5 phase. These samples were synthesized by the conven-tional solid-state reaction method. Kobayashi et al. also reportedthat no ordering peaks of La and Nd were observed using the(La0.46Nd0.54)9.33(SiO4)6O2 composition sample by synchrotronpowder XRD measurement. In addition, the La and Nd ions werealmost randomly distributed on Ln2(6h) and Ln1(4 f ) sites. The(La0.46Nd0.54)9.33(SiO4)6O2 sample was synthesized by the water-based sol­gel method and then heated at 1773K. Conforming tothe simulated XRD pattern with the crystal model by Malinovskiiet al. using the RIETAN-FP software41) (Fig. 12), weak but clearXRD peaks should be observed at 2ª between 10 and 21° usingCuK¡ radiation because of the La and Nd ordering. However,no ordering peaks in the low 2ª angle region were observed inthe XRD patterns by Yoshioka and Kobayashi et al. There is thepossibility that long-period annealing at relatively low temper-

ature is necessary for Ln ion ordering. Hence, further carefulexperiments are required to determine the ordering of lanthanoidions in the lanthanoid silicate solid solution containing severallanthanoid species.Furthermore, in mineral research another symmetry group was

proposed for britholite, in particular a rare-earth-rich containinggroup.82)­84) In 1990, Kalsbeek et al.82) reported the crystal struc-ture of a rare-earth element-rich mineral with chemical similarityto both cerium-rich britholite and lessingite (britholite­(Ce) andlessingite­(Ce)) collected from the Ilímaussaq intrusion inGreenland. The crystal structure of this mineral was determinedby single-crystal XRD. Although the crystal structure was closeto the apatite structure with a hexagonal cell, the symmetry groupwas concluded to be P63. The reason for the lower symmetrycompared with P63/m was the distortion of the sevenfoldcoordination of RE­O.From 1992 to 1993, Drexler’s group reported the crystal

structure of monoclinic britholite-(RE) (RE = La, Gd, Y, andCe) collected from Kipawa syenite gneiss complex andSuishoyama.83),84) The britholite-(RE) structure showed thatbritholite mineral mainly contained the (RE) elements. Thebritholite-(RE) (RE = La, Gd, Y, and Ce) structures were con-cluded to have the monoclinic cell (space group P21 setting 2,which is a subsymmetry group of P63/m, see Appendix F).Similar to the discussion by Kalsbeek et al.,82) the lower sym-metry than ideal apatite (hexagonal system, space group: P63/m)was because of the slight deviation of the RE coordination.In 1999, Wang and Weber reported the in-situ transmission

electron microscopy (TEM) and high-resolution transmissionmicroscopy (HRTEM) images using Ca2La8(SiO4)6O2 singlecrystal.85) Aim of this research was to clarify the influence ofion-beam-induced amorphization. By comparison of the observedHRTEM image and simulated HRTEM image, they confirmedthat the space group of Ca2La8(SiO4)6O2 was P63/m if no ion-beam-induced amorphization was occurred. After the Wang’spaper, Utsunomiya et al. reported the TEM and HRTEM imagesof synthetic brisolite with complex chemical compositions,Ca3.05Ce2.38Fe0.25Gd5.37Si4.88O26 and Ce1.45Zr0.78Fe0.14Nd2.15-Eu0.50Si6.02O26.86) The aim of this paper was to investigate theion-beam and electron-beam irradiation of these syntheticbritholites. Although crystal structure was not discussed in detail,they seemed to accept the space group of P63 referring to theKalsbeek’s paper.82)

In the same year by Wang and Weber, Morgan et al. reportednon-defect Sm10(SiO4)6O2 structure using single crystal grownin the evacuated silica tube put the Sm, Ga, and Bi.87)

The Sm10(SiO4)6O2 single crystal was grown as adventitiousbyproducts by chemical attack to the silica tube. The space groupwas determined as P63/m. From red color of their crystal andcrystal structure analysis, they concluded that a part of the Smions should be in Sm2+ state and the Sm2+ ions were located onthe Sm1(4 f ) site. It was interesting that Morgan’s group foundan adequacy compound that lanthanoid constituent were in themixed valence state as initially considered by Kuźmin and Belovat 1965.34)

To compare the relationships between the atomic coordinationin the three models (P63/m, P63, and P21), tables of the atomiccoordination reported in the literature22),82),84) are listed inTables 2(a) to 2(c). The site occupancy factors based on theP63/m model by Okudera et al.22) are also listed for comparison.Typical site labels are shown in the crystal structure Figs. 13(a)­13(c). The site relationships between P63/m, P63, and P21(setting 2) are shown as a tree diagram in Fig. 14. From these

Fig. 12. Simulated powder X-ray diffraction patterns using the report-ed structure models: (a) La3Nd11(SiO4)6O3 by Malinovskii et al.,79)

(b) (La9.33Nd0.33)(SiO4)6O2.5 by Yoshioka,80) and (c) (La0.46Nd0.54)9.33-(SiO4)6O2 by Kobayashi et al.81) The Miller indices are also indicatedfor each structure model. Indices of the weak peaks, which cannot beconfirmed by this figure, were omitted.

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tables and figures, the symmetry lowering is found to be becauseof not only the slight deviation of RE coordination but also thecoordination of the SiO4 tetrahedrons.Another question arose among mineralogists and physicists:

Are the different polymorphs of oxyapatite the high pressurephase? This problem has been discussed in high pressurephysics.88)­90)

The important fact was that before 1995, the consensus wasthat point defects in the silicate oxyapatites were only vacanciesof lanthanoid and oxygen, and the understanding of the defectmodel suddenly and drastically changed after 1995, and variousdefects are now accepted. These changes will be explained in afurther.

4. Initial application research of oxyapatites

4.1 New laser hostsIn the 1960s, the main research topics of the lanthanoid silicate

oxyapatites were at the fundamental science stage. In the 1970s,

Table 2. Coordinates of the atoms in La9.33(SiO4)6O2 with differentstructure models: (a) P63/m,22) (b) P63,73) and (c) P21 (setting 2).83) Thesite occupancy values were calculated based on the P63/m model.

(a)

Symmetry: hexagonalSpace group: P63/ma = b º c, ¡ = ¢ = 90°, £ = 120°

Sites Occupancy x y z

RE1(4 f ) 0.8580 2/3 1/3 0.00118RE2(6h) 0.983 0.01223 0.23921 1/4Si(6h) 1 0.40290 0.37280 1/4O1(6h) 1 0.32550 0.48730 1/4O2(6h) 1 0.52670 0.12320 1/4O3(12i) 1 0.34760 0.25640 0.06840O4(2a) 1 0 0 1/4

(b)

Symmetry: hexagonalSpace group: P63a = b º c, ¡ = ¢ = 90°, £ = 120°

Sites Occupancy x y z

RE1(2b) 0.8580 1/3 2/3 0RE2(2b) 0.8580 2/3 1/3 0.4977RE3(6c) 0.983 0.2483 0.0113 0.2552Si(6c) 1 0.3730 0.3998 0.255O1(6c) 1 0.486 0.318 0.264O2(6c) 1 0.475 0.600 0.232O3(6c) 1 0.262 0.362 0.064O4(6c) 1 0.243 0.303 0.419O5(2a) 1 0 0 0.155

(c)

Symmetry: monoclinicSpace group: P21 (setting 2)a º b º c, a/b µ 1, ¡ = ¢ = 90°, £ º 120° µ 120°

Sites Occupancy x y z

RE1(2a) 0.8580 0.33267 0.66656 0.0057RE2(2a) 0.8580 0.33415 0.66678 0.5002RE3(2a) 0.983 ­0.01483 0.23465 0.2513RE4(2a) 0.983 0.23454 0.24946 0.7484RE5(2a) 0.983 0.24944 0.01482 0.2506Si1(2a) 1 0.0289 0.6287 0.25Si2(2a) 1 0.3715 0.4004 0.248Si3(2a) 1 0.5997 0.9708 0.252O1(2a) 1 0.8366 0.5165 0.245O2(2a) 1 0.4821 0.3200 0.261O3(2a) 1 0.6783 0.1623 0.243O4(2a) 1 0.4068 0.8779 0.267O5(2a) 1 0.4704 0.5933 0.238O6(2a) 1 0.1230 0.5304 0.267O7(2a) 1 0.6364 0.8985 0.0618O8(2a) 1 0.6811 0.9258 0.422O9(2a) 1 0.2615 0.3625 0.063O10(2a) 1 0.2443 0.3189 0.425O11(2a) 1 0.0747 0.7546 0.083O12(2a) 1 0.1017 0.7373 0.444O13(2a) 1 ­0.0007 ­0.0009 0.225

(a)

(b)

(c)

Fig. 13. Crystal structure of La9.33(SiO4)6O2 with different models.Models using the space groups P63/m, P63, and P21 (setting 2) are shownin (a), (b), and (c), respectively. Typical atomic sites are also shown in thefigures. To compare the structural features, all the crystal structures aredrawn within the fractional coordinate range from ­0.2 to 1.2 of the x, y,and z axes.

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however, the interests of scientists were gradually shifting fromfundamental research to the applications of oxyapatites.The first research papers suggesting applications of the silicate

oxyapatites were published in 1971 by Hopkins et al., whobelonged to the Westinghouse Research Laboratory.91),92) Theinitial applications of the oxyapatites were alternative materialsto fluorapatite [Ca10(PO4)6F2] as solid laser hosts. Althoughfluorapatite was known to be an extremely efficient host for bothrare-earth ion fluorescence and laser action at 1.06¯m, and as acandidate as a host for the activator ion (Ho3+), the drawback wasthe low solubility limit of sensitizer ions (Er3+ and Tm3+) and theactivator ion (Ho3+).91) Therefore, they focused on oxyapatiteswith the same crystal structure as fluorapatite. In addition, variouslanthanoid ions were known to be structural constituents ofoxyapatites. Hence, it was suggested that co-doping of Ho3+,Er3+, and Tm3+ in oxyapatite hosts was a candidate for new laserhosts. Based on this strategy, Hopkins et al. successfully grewsingle crystals of CaY4(SiO4)3O and CaY2.25Er1.5Tm0.15Ho0.1-(SiO4)3O with size greater than 100¯m by Czochralski’s method.Although the quality of the single crystal was not very goodbecause of the low angle boundary development and secondaryphase precipitation, it was confirmed that energy transfer fromthe Er3+ and Tm3+ ions to the Ho3+ ion was efficient andcomplete in the silicate oxyapatite by spectroscopic measure-ments. In addition, they pointed out that the most promisingapplication for the oxyapatite host would be in high energy perpulse Q-switch systems because of the broad fluorescence linewidth of Ho3+.In the second paper,92) they grew single crystals of Nd3+-doped

CaLa4(SiO4)6O and SrLa4(SiO4)6O by Czochralski’s method. Inthis paper, surprisingly large single crystals (0.64 cm diameterand 4.6 cm length but including a 3¯m to 5¯m sized secondphase) were shown in the image (Fig. 15). The quality of thesingle crystals were quite good compared with the single crystalsof CaY4(SiO4)3O. With respect to the spectroscopic data, theycarefully discussed that oxyapatite might be superior to fluo-rapatite at a high pumping power level because of the highhardness. From the viewpoint of the mechanical properties, the

thermal and elastic properties of Ho3+-doped Ca2Y8(SiO4)6O2

single crystals were reported in 1973.93) The interesting resultswere that the temperature dependence of the thermal conductivitywas large compared with the conductivity of fluorapatite. Inaddition, the thermal conductivity did not show crystallographicanisotropy. The elastic, thermal expansion, and heat capacitybehaviors could be explained by the Debye solid model. Furtherstudies by the same group94),95) reported that the damagethreshold of Nd3+-doped CaLa4(SiO4)3O was 20 to 30 percenthigher than the threshold of Nd3+-doped yttrium aluminumgarnet (YAG). With respect to the long-pulse properties, the gainper excited Nd ion in CaLa4(SiO4)3O was at least 3.5 times lowerthan in YAG. Overall, it can be concluded that oxyapatites havean advantage over YAG as laser host materials.In 1989, de la Fuente et al.96) were successful in growing a

single crystal of (La1­xNdx)9.33(SiO4)6O2 and (Gd1­xNdx)2SiO5 bythe floating zone method. The absorption and fluorescencespectra were measured at 18K and room temperature. Based onthe spectra, the energy level diagram of Nd3+ in (La1­xNdx)9.33-(SiO4)6O2 was given for the 806 nm absorption band and lasertransition state. As a result, they concluded that lanthanumsilicate oxyapatite could be used as a Nd host with potentialapplications in diode-pumped solid-state lasers.In 2002, Druon et al.97) announced first success of diode-

pumped laser oscillation using Yb3+ doped Sr2Y8(SiO4)6O2

oxyapatite single crystal. They focused on the simpler elec-tronic structure of Yb3+ ions and oxyapatite system could bedissolved various kind of lanthanoid species. It was explainedthat single crystal growth of Yb3+ doped Sr2Y8(SiO4)6O2 wasrelatively easy by the Czocgralski method from the melt around2173K (Fig. 16). They reported that Yb3+ doped Sr2Y8(SiO4)6O2

exhibits very broad emission and absorotion bands compared tothe bands of Yb3+ doped Sr3Y (BO3)3 and Ca4Gd (BO3)3 singlecrystals and Yb3+ doped glass in range of wavelength between850 and 1150 nm. Due to this broad emission and absorotionbands, they succeeded that 1.05W of output power at 1071 nmwith an incident power of 3.6W in the continuous wave (cw)laser regime, and sub-100-femt second (fs) pulses were generatednear 1070 nm with an average power of 110mW in the fs regime.In the case of cw regime, laser operation was observed widewavelength among 75 and 1095 nm. Additional interesting resultwas the anisotropic thermal conductivities, 2.85Wm¹1 K¹1 along

Fig. 14. Schematic tree diagram of the relationships of the atomic sitesamong the models for the space groups P63/m, P63, and P21 (setting 2).The O atoms enclosed in the dashed boxes are the constituents of the SiO4

tetrahedron.

Fig. 15. Photo of the 3% Nd-doped CaLa4(SiO4)3O single crystalcopied from reference.92) The single crystal was grown by the Czochralskimethod. The diameter of this crystal was 0.64 cm. The ring-shaped patternaround the center of this photo is the Twyman­Green interference patternobserved with He­Ne laser traversing a 4.6 cm length. Reproduced withpermission from J. Electrochem. Soc., 118, 637 (1971). Copyright 1971,The Electrochemical Society.

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to c-axis and 1.6Wm¹1K¹1 for perpendicular to the c-axis. Thisanisotropy was different from the thermal conductivity of Nd3+-doped La8Ca2(SiO4)6O2 single crystal.93) After this paper, Druonet al. reported the self-compression and Raman soliton gener-ation in a photonic crystal fiber using a diode-pumped Yb-dopedoscillator in 2003,98) and pulse-compression down to 20 fs usinga photonic crystal fiber seeded by a diode-pumped Yb:SYS laserin 2004.99)

4.2 Phosphor MaterialsAlthough lanthanoid silicates were already expected to be

phosphor materials by Wanmaker et al. in 1958100) and Toropovand Bondar in 1961,21) the early luminescent experiments ofoxyapatites were carried out by Ito39) in 1968 and Maksimovet al.101) in 1969 as pure scientific research. The optical spectrawere sometimes reported with respect to the crystal structure andlocal coordination of the activator ions.33),102)­110)

In 1973, Isaacs111) reported systematic data of the emissionand excitation spectra of Eu3+-doped Ca2Gd8(SiO4)6O2, Ca2La8-(SiO4)6O2, Ca2Y8(SiO4)6O2, Mg2La8(SiO4)6O2, and Mg2Y8-(SiO4)6O2 by comparing the spectra with the spectrum of Eu3+-doped Y2O3 at room temperature. This was the first report onmaterial engineering of oxyapatite phosphors. Through detailedinterpretation of the spectra of these materials, the main emissionpeak intensity at 253.7 nm excitation of oxyapatites was foundto be much lower than the intensity of Eu3+-doped Y2O3.In 1987, Lammers and Blasse112) reported the luminescence

properties of Tb3+- and Ce3+-activated Gd9.33(SiO4)6O2, La9.33-(SiO4)6O2, and Gd2SiO5 excited by ultra-violet (UV) light andX-ray. The quantum efficiency of all the oxyapatites werereported to be low by interpretation of the energy transition ofthe emission spectra by the UV excitation. The local structure ofthe Tb3+ and Ce3+ ions was discussed combined with the crystalstructural information. On the other hand, Tb3+- and Ce3+-activated oxyapatites were concluded to be inefficient phosphors.Lin and Su113) reported a systematic study of the luminescence

properties of Ca2Gd8(SiO4)6O2 doped with Eu3+, Tb3+, Dy3+,Sm3+, Y3+, Ce3+, Pr3+, Bi3+, and Pb2+ ions in 1994. Theyconcluded that Pb2+ and Dy3+ coactivated Ca2Gd8(SiO4)6O2 wasa potential candidate for white emission under excitation by 254nm light, which corresponds to excitation by a low-pressuremercury discharge. After this work, they reported a systematicluminescent properties of M2RE8(SiO4)6O2 (M = alkali earthelements) prepared by sol­gel method and solid state reac-tions.114)­119)

After Lin’s paper, Han et al.120) reported the luminescenceproperties of Eu3+-, Ce3+-, and Tb3+-doped La9.33(SiO4)6O2

phosphor thin films fabricated by a sol­gel soft lithographytechnique in 2002. They succeeded in making a pattern arraywith linewidths of 50¯m and 20¯m, and found that strongemission with red (615 nm), green (542 nm) and blue (350­450 nm) colors were obtained by the doped Eu3+, Tb3+, and Ce3+

ions, respectively. Even though the film seems not to be theoxyapatite single phase because many peaks from the impurityphase were found by careful checking of the XRD patterns in thepaper, the luminescence properties are interesting.In 2006, Yamane et al.121) reported the luminescence properties

of Tb-activated rare-earth oxyapatite silicate MLn4Si3O13 (M =Ca or Sr, Ln = La or Gd). The molecular formula correspondsto Ln8M2(SiO4)6O2. They reported the vacuum UV radiationexcited photoluminescence spectra of Tb-doped MLn4Si3O13.It was clarified that Tb-doped MLn4Si3O13 showed the greenluminescence due to the 5D4­

7FJ transition of Tb3+. Furthermore,the photoluminescence peak intensity of the Tb3+ emission fromSrGd4Si3O13 was found to be comparable to the peak intensity ofMn-doped Zn2SiO4, which was the commercial phosphor mate-rial for plasma display panels. Hence, they concluded that Tb-doped SrGd4Si3O13 is a candidate for a green phosphor materialof plasma display panels excited by Xe discharged plasma.Improvement of the luminescent properties of Ca2(La1­xEux)8-

(SiO4)6O2 by lithium treatment was reported by two researchgroups in 2009 and 2013.122),123) Shen et al. reported that efficientbright red emission was observed by excitation of near-UV toblue light. In addition, the emission intensity was improved byaddition of Li2CO3 flux. Shen et al. suggested that the reason forthe luminescent improvement was that the Li2CO3 flux mightdecrease at the oxyapatite formation temperature and improvethe crystallinity. After Shen’s paper, Li et al. also reported theluminescent properties of a similar composition, Ca2(1­x)La7.6+x-(SiO4)6O2: Eu0.4, Lix.123) In contrast to the report by Shen et al.,122)

Li et al. proposed that the improvement of the luminescentproperties by lithium ion doping was related to oxygen ionvacancy formation.123)

Between 2011 and 2012, Lin’s group and Lu’s group reportedthe color tuning luminescence of Ce3+/Mn2+/Tb3+-triactivatedphosphor using oxyapatite.124)­126) They used Mg2Y8(SiO4)6-O2

124),125) and Ca2Y8(SiO4)6O2126) as the phosphor host. The inter-

esting results of these studies were that the luminescent color canbe changed by a dual energy transfer mechanism between theactivator ions. These oxyapatites were concluded to have potentialas single-phase trichromatic white-emitting phosphors underUV and low-voltage electron beam excitation. Furthermore, theysucceeded in fabricating a microfiber of Ce, Eu, and Tb-dopedLa9.33(SiO4)6O2 using electrospinning synthesis that has a poten-tial application in field emission displays.127) After this study,their target materials seem to shift from silicate oxyapatites tophosphate oxyapatites and/or solid solutions of silicate oxyapatiteand phosphate oxyapatite.128),129) With respect to the silicateoxyapatite and phosphate oxyapatite solid solution system, twopapers were published by Yu et al.130) and Tao et al.131) Recallingthe fact that the solid solution of silicate oxyapatite and phosphateoxyapatite was initially recognized as minerals,38),39),63),132) it isinteresting that the phosphor host seems to have changed fromartificial materials back to natural compounds.

4.3 Other applicationsThe silicate oxyapatite and quasi-ternary rare-earth oxide­

silica­alkali earth oxide system was studied as a candidate as a

Fig. 16. Photo of the 5.5% Yb3+ doped Sr2Y8(SiO4)6O2 single crystalsalong with a 1 Euro coin for scale copied from reference.97) Diameter ofthe 1 Euro coin is about 23mm.

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stabilizer of unwanted radioactive waste materials (radwastes)produced in nuclear power reactors.85),133)­138) The studies byde Alleluia et al.76) and Fahey et al.77) seemed to be motivatedby the fact that de Alleluia belonged to Karlsruhe NuclearResearch Center, School of Nuclear Technology and Institute ofRadiochemistry76) and we found the explanation “The structureand stability of rare earth silicate isomorphs of natural apatite,Ca10(PO4)6(F, OH)2, are of interest in nuclear managementbecause they can occur as actinide host phases in several high-level nuclear waste forms” in Reference.77)

In addition, the quasi-ternary Y2O3­SiO2­MgO system andRE2O3­SiO2­Al2O3 (RE = Y, Sc, La, Ce, Nd, Sm, Gd, Dy, Er,and Yb) system were investigated as sintering additives forSi3N4, SiAlON, Sic, and AlN.66)­68)

5. Summary

Although research of the rare-earth silicate oxyapatites hasfocused on their oxygen ion conductivity since 1995, manystudies were carried out from 1959 to 1993. Before 1993,research on the rare-earth silicate oxyapatites was separatelycarried out in the fields of ceramics and crystal chemistry. Afterthe fusion of the accumulated knowledge of the ceramists andcrystal chemists, the existence of rare-earth silicate oxyapatiteswas widely recognized.The idea of the rare-earth vacant model was an important

advance for the identification of the rare-earth silicate oxyapatitesand understanding their crystal structures. Although this struc-tural model has now been accepted, the model was carefullytreated from 1965 to 1980. Oxygen defective rare-earth silicateoxyapatite was first reported as Ca2.2Nd7.8(SiO4)6O1.9 in 1985.Before this paper, the oxygen number of rare-earth silicateoxyapatites was fixed at integer numbers.The engineering of rare-earth silicate oxyapatites started in

1973 for their application as optical materials such as laserand phosphor hosts. Before 1995, other applications were alsoconsidered, such as stabilizer hosts of radwaste elements andsintering additives of high temperature ceramics. Developmenton phosphor materials based on rare-earth silicate oxyapatitescontinues.

Acknowledgement Authors are grateful to Dr. Takuji Ikeda atNational Institute of Advanced Industrial Science and Technology forhelpful suggestions on the crystallography and the RIETAN-FPsoftware.

Appendix AAlthough Toropov and Bondar introduced the US atmospherereferring to the paper “Smith K M and Doningnes L P, 1958J. Am. Ceram. Soc. 37 4”, we could not find the correspondingliterature in the American Ceramics Society Bulletin or the Journal ofthe American Ceramics Society in 1958. However, we did find thereport entitled “Thermal expansion and phase inversion of rare-earthoxides” in the United States Department of Energy (DOE) office ofscientific and technical information (OSTI) in the United States. Thesponsoring and research organizations were credited as the DOE andBureau of Mines, respectively.http://www.osti.gov/scitech/biblio/4840970

Appendix BAccording to the papers by Warshaw and Roy (Warshaw I and RoyR, 1964 Prog. Sci. Tech. Rare Earths. vol. 1. (Ed. Eyring L.Pergamon Press) pp. 203­221), and Smolin and Shepelev (SmolinY I and Shepelev Y F 1970 Acta Cryst. B26 484), first investigationof rare-earth silicates were carried out by Giuscă in 1934 (Giuscă D

1934 Bull. Labor. Miner. Univ. Bucuresti. 1 27). Although we couldnot obtain a copy of the Giuscă’s paper, the brief abstract of theGiuscă’s research was found in the Warshaw’s one: they explainedthat crystallographic data accuracy was poor due to low resolution oftheir XRD instrument and low purity of the raw materials.

Appendix CKuźmin and Belov explained in their paper34) that “The mostcomplete investigations of the phase diagrams of the La2O3­SiO2

system have been made at the University of Pennsylvania and at theInstitute for the Chemistry of Silicates of the Academy of Sciencesof USSR (Leningrad)”. The research groups at the University ofPennsylvania and at the Institute for the Chemistry of Silicates aresuggested to be Roy’s group and Toropov’s group, respectively.However, we could not find the phase diagram of the La2O3­SiO2

quasi-binary system reported by Roy’s group.

Appendix DThe latest phase diagram of the La2O3­SiO2 system in Bondar’sreview paper9) referred the textbook entitled “Rare-earth silicates andtheir analogues” (Nauka, Leningrad, 1971). Compared with the phasediagram of the La2O3­SiO2 system presented in Felsche’s review,65)

the difference was found in the La2O3 and liquid coexisting region,even though Felsche specified that the phase diagram was the sameas the textbook. In the phase diagram in Bondar’s review, he seemedto consider that two different polymorphs of La2O3 appeared at about2323K and 2373K.

Appendix EWe could not obtain a copy of the textbook entitled “Rare-earthsilicates and their analogues” (Nauka, Leningrad, 1971) written inRussian. Although we could not confirm whether they used the termapatite and/or oxyapatite, we confirmed that the term apatite-likestructure was used in Bondar’s review in 1982 by referring to theabove textbook.

Appendix FAlthough the space group was presented as P21 setting 1 in theoriginal papers,82),83) the subspace group of P63/m is P21 setting 2(P1121) correctly. Hence, we employed the correct description of thespace group.

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