www.elsevier.com/locate/ssi

Solid State Ionics 172 (2004) 25–30

Solid state batteries with sulfide-based solid electrolytes

Kazunori Takadaa,b,*, Taro Inadaa, Akihisa Kajiyamaa, Masaru Kouguchia, Hideki Sasakia,Shigeo Kondoa, Yuichi Michiuea, Satoshi Nakanoa, Mitsuharu Tabuchic, Mamoru Watanabea

aAdvanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanbCREST, Japan Science and Technology Agency, Japan

cSpecial Division for Green Life Technology, National Institute of Advanced Industrial Science and Technology, 1-8-31 Midorigaoka, Ikeda,

Osaka 563-8577, Japan

Received 9 November 2003; accepted 8 February 2004

Abstract

Inorganic solid electrolytes are promising for the solution to the safety issue of lithium batteries. In spite of this advantage, solid state

lithium batteries are, in general, lower in energy density than organic electrolyte systems. This paper presents two points, to which we have to

direct our attention: compatibility of solid electrolytes with electrode materials and novel electrode materials functional only in solid systems.

The consideration for the compatibility lead us to a unique construction of a solid state lithium battery employing two kinds of solid

electrolytes, which enabled us to realize C/LiCoO2 solid state batteries with a high energy density. Ion-selectivity of solid electrolytes made

materials that are not available in liquid system functional in solid ones. Some examples are also presented in this paper.

D 2004 Elsevier B.V. All rights reserved.

PACS: 85.70.Dg; 82.45.+z

Keywords: Lithium battery; Solid electrolyte; Sulfide; Graphite

1. Introduction

Since the invention of rocking chair-type ‘‘Li-ion bat-

teries’’ [1] with a construction of C/LiCoO2, rechargeable

lithium batteries have widely spread to be used in portable

equipments today. Although they have been on market for

more than 10 years, they still have a safety issue. This is one

of the intrinsic problems that should be solved since their

birth, because the electrolytes used in them contain com-

bustible organic solvents. Lithium ion-conductive solid

electrolytes are attractive for their application to lithium

batteries, because they are nonflammable and will give a

fundamental solution to the safety issue associated with

flammable organic electrolytes.

Another remarkable feature of solid electrolytes in addi-

tion to their contribution to the safety issue is their ion-

selectivity; i.e., only Li+ ions are mobile in them. They do

not accommodate any mobile species other than Li+ ions,

0167-2738/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.ssi.2004.02.027

* Corresponding author. Tel.: +81-29-860-4317; fax: +81-29-854-

9061.

E-mail address: takada.kazunori@nims.go.jp (K. Takada).

e.g., counter anions and molecules of the solvents as liquid

or polymer electrolytes, which can diffuse to the surface of

the electrodes and may cause side reactions there. Therefore,

side reactions hardly occur in solid-state systems. In other

words, the employment of solid electrolytes will solve the

problems including capacity fading, self-discharge caused

by the side reactions. In fact, solid state batteries showed

remarkably long cycle life over 20000 cycles [2], and self-

discharge was very small even in the storage at an elevated

temperature [3].

In spite of these advantages, the performances of the

solid state lithium batteries including lower energy den-

sities or smaller current drains compared to liquid systems

have been preventing them from practical use. In the

present paper, we present the performance of our solid

state battery recently developed on the basis of the

careful consideration for the compatibility of the solid

electrolytes with the electrode materials. The ion-selectiv-

ity brings about more than the improvement of the

reliability. Solid electrolytes sometimes make the materi-

als that no-one regard as electrode materials available.

Three examples of such ‘‘unexpected’’ electrode materials

are also presented.

Fig. 1. Charge–discharge curves of graphite in solid electrolytes. Li3PO4-

Li2S-SiS2 glass (upper) and with LiI-Li2S-P2S5 glass (lower) were used as

electrolytes.

K. Takada et al. / Solid State Ionics 172 (2004) 25–3026

2. Battery performances

2.1. Compatibility of solid electrolytes to electrode

materials

Solid electrolytes for lithium batteries are required to

have not only high ionic conductivities but also wide

electrochemical windows, because they should be stable to

both the highly oxidative cathodes and the highly reduc-

tive anodes. Sulfide glasses, Li2S-P2S5 [4], Li2S-B2S3 [5],

Li2S-SiS2 [6], etc., have been regarded as a suitable solid

electrolyte for solid-state lithium batteries. They show high

ionic conductivities of the order of 10� 3 S cm with doped

LiI and do not contain any transition metal elements easily

reduced in contact with low potential anodes. LiI forms

microdomains; that is, I� ions are not covalently bonded

to the glass network [4]. Therefore, the isolated I� ions

tend to be oxidized in contact with high-voltage cathodes,

having limited the cell voltages of solid state batteries

using the sulfide glasses. However, without the doping of

LiI, conductivities of the sulfide glasses had been of the

order of 10� 4 S cm� 1. The findings of the conductivity

enhancement by doping oxysalts [7–10] instead of LiI

have lead way to high-voltage solid state batteries.

Only sulfide glasses have been candidates of solid

electrolyte for the application to lithium batteries for a long

time. Since sulfide ions are essentially preferred as frame-

work anions for high ionic conduction because of their large

polarizability, highly conductive solid electrolytes will be

found also in crystalline materials. Recently, crystalline

sulfides with LISICON structure have reported to have high

ionic conductivities [11–13].

Although solid state lithium batteries have high reliabil-

ity including safety and long cycle life, they are, in

general, lower in energy density than lithium ion ones

with organic electrolytes, which should be improved for

their practical application. Combination of graphite anode

and LiCoO2 cathode is employed in lithium ion cells and

affords them high energy density. However, solid state

batteries with this construction have not been reported so

far. Several kinds of solid-state lithium batteries were

embodied, where LiCoO2 or LiNiO2 was used as cathode.

On the other hand, indium–lithium alloy [14,15], Li2FeS2[16], or Li4/3Ti5/3O4 [17] was used as the negative elec-

trode material; carbon materials including graphite [18]

have never used in spite of the high performance with a

low potential (ca. 0.1 V vs. Li/Li+) and a large theoretical

capacity (372 mA h g� 1).

A series of Li+ ion conductive sulfide glasses were found

in the 1980s. Interest on them has been mainly focusing on

their ionic conductivity. In the batteries mentioned above,

SiS2-based glasses were used as electrolyte. Only the SiS2-

based glass can be prepared under the atmospheric pressure

owing to the low vapor pressure of SiS2 [19]. This feature is

suited to a large-scale preparation of the glass; and hence,

the solid state batteries adopted the SiS2-based glasses. The

reason why graphite has not been used in solid state

batteries may be that most of the studies have been done

with the SiS2-based glass.

Fig. 1 displays the discharge–charge curves of graphite

electrodes in the cells with Li3PO4-Li2S-SiS2 glass and with

LiI-Li2S-P2S5 glass. As for the former cell, the graphite had

a potential plateau at ca. 0.15 V vs. Li/Li+. It did not reach

down to 0 V at the end of reduction with an applied

electricity (Q) of 372 mA h g� 1 for graphite. The Q

observed in the following oxidation was only 125 mA

h g� 1. In case of the LiI-Li2S-P2S5 glass, the potential of

the graphite reached to 0 V vs. Li/Li+ at Q = 344 mA h g� 1,

and the Q in the following oxidation was recovered up

to 292 mA h g� 1. The results of X-ray diffraction and

Raman spectroscopy indicated that the Li3PO4-Li2S-SiS2was reduced instead of the intercalation of Li+ ions to

graphite during the reduction. In contrast, the LiI-Li2S-

P2S5 glass demonstrated that the lithium intercalation–

deintercalation process proceeded without any significant

side reactions.

2.2. Solid state battery using two kinds of solid electrolytes

Much attention has not been paid for the compatibility

of the solid electrolyte with electrode materials. However,

the above results show clear difference between the

compatibilities of the solid electrolytes.

K. Takada et al. / Solid State Ionics 172 (2004) 25–30 27

When the LiI-Li2S-P2S5 glass was used as an electrolyte,

graphite was available as an anode material. However, the

glass was unstable in contact with a high-voltage cathode

such as LiCoO2, because I� ions in the glass may be

oxidized at the surface of the electrode material. Removal

of LiI stabilizes the glass to the high-voltage cathode, but it

decreases its Li+ ionic conductivity to the order of 10� 4 S

cm� 1. Consequently, in order to construct a high-voltage

battery using graphite and LiCoO2, we should use two kinds

of lithium ion-conductive glasses, i.e., one stable to anode

and another to cathode. When the above-mentioned two

kinds of glasses are used, the anode should consist of a

mixture of the graphite and LiI-Li2S-P2S5 glass, and the

cathode of a mixture of LiCoO2 and Li3PO4-Li2S-SiS2glass. Both electrodes should be separated by a double-

layered electrolyte, that is, the battery should be constructed

in the form (graphite + LiI-Li2S-P2S5 glass)/LiI-Li2S-P2S5glass/Li3PO4-Li2S-SiS2 glass/(LiCoO2 + Li3PO4-Li2S-SiS2glass).

Recently discovered Li2S-GeS2-P2S5 with LISICON

structure has activation energy for conduction lower than

the sulfide glasses [13]. The usage of this crystalline

electrolyte instead of the SiS2-based glass much improved

the battery performance. Fig. 2 shows the discharge curves

of a cell with a construction of (graphite + LiI-Li2S-P2S5)/

LiI-Li2S-P2S5/Li2S-GeS2-P2S5/(LiCoO2 + Li2S-GeS2-P2S5)

at various discharge rates and 25 jC. The energy density of

the battery was calculated to be 390 W h l� 1 and 160 W

h kg� 1 per total volume and weight of the anode layer (the

mixture of graphite and LiI-Li2S-P2S5 glass) and cathode

layer (the mixture of LiCoO2 and Li2S-GeS2-P2S5), respec-

tively. These values do not directly correspond to the energy

density of the solid-state battery, because the volume and

weight of the electrolyte layer and the battery case are

excluded. However, one will realize that this solid-state

lithium battery has an energy density comparable to those of

commercialized Li-ion batteries; a recent review on lithium

batteries [20] reported that these energy densities were 250–

400 W h l� 1 and 110–170 W h kg� 1.

Fig. 2. Discharge curves of the solid electrolyte battery with a construction

of (graphite + LiI-Li2S-P2S5)/LiI-Li2S-P2S5/Li2S-GeS2-P2S5/(LiCoO2 +

Li2S-GeS2-P2S5). Discharging current densities are indicated in the figure.

3. Novel electrode materials in solid state batteries

Ion selectivity suppresses side reactions, endowing high

reliabilities to solid state batteries including long cycle life

[2], small self discharge [3], and long shelf life [21]. It also

allows us to use a large variety of materials as electrode

material. That is, a material that can not be used in a liquid

system sometimes becomes available for electrodematerial in

a solid system. Three iron compounds, Li2FeCl4 [22],

Li2FeP2S6, [23], and Li2FeS2 [14,24], are presented here as

examples. The Li+ ion conductive solid electrolyte used in the

following studies was 0.01 Li3PO4–0.63 Li2S–0.36 SiS2[25].

3.1. Halide spinel

The most easy-to-understand example showing that

‘‘unexpected’’ materials can be used in solid state batteries

is halide spinels. Lithium transition metal halides with

spinel structure are known as Li+ ion conductors [26].

Their high ionic conduction and contained transition metal

elements that act as redox couple are considered to make

them available for electrode materials. However, their

ionicities are so high that they are easily dissolved in

liquid electrolytes and cannot be used as electrode materi-

als. To the contrary, any materials are never dissolved into

solid electrolytes.

Fig. 3 indicates a potential profile of Li2FeCl4 in the

oxidation process in the solid electrolyte. It showed a

potential plateau at ca. 3.5 V vs. Li/Li+. Our structural

studies revealed that the reaction was based on the extrac-

tion of Li+ ions from Li2FeCl4, and more than 1.4 Li+ ions

were extracted from Li2FeCl4. These results suggest that

Li2FeCl4 may be available for electrode materials in lithium

batteries.

3.2. Lithium iron sulfide

Iron sulfide (FeS2) has been investigated as a positive

electrode material in thermal batteries [27–30]. The theo-

retical capacity of FeS2 is 894 mA h g� 1 corresponding to

4e�/FeS2, and it shows two potential plateaus at 2.3 and 1.6

V [31]. The former was assigned to reaction (1), and the

latter to Eq. (2).

FeS2 þ 2Liþ þ 2e� ! Li2FeS2 ð1Þ

Li2FeS2 þ 2Liþ þ 2e� ! Feþ 2Li2S ð2Þ

In liquid electrolyte or polymer electrolyte [31,32], the

electrode reaction was reversible through the 2.3 V plateau,

but irreversible through the 1.6-V plateau, because the

resultant Fe metal (a-Fe) is electrochemically inactive in

the electrolytes. However, when we used a solid electrolyte,

Fig. 4. Potential profile of Li2FeS2. The reduced sample was re-oxidized

after a rest period of 1 h (solid lines) and after the annealing at 210 jC(dashed lines).

Fig. 3. Potential profile (quasi-open circuit voltage) of Li2FeCl4 during the

oxidation in the Li+ ion conductive glass.

K. Takada et al. / Solid State Ionics 172 (2004) 25–3028

the electrode reaction at the 1.7-V plateau was reversible

[33].

Solid lines in Fig. 4 indicate the voltage profile of

Li2FeS2 during reduction and re-oxidation. The re-oxidation

profile consisted of two plateaus at 1.7 and 2.3 V. The

higher plateau is ascribed to extraction of lithium from

Li2FeS2. On the lower, the reaction was formation of Fe

metal and should be its re-oxidation, although Fe metal was

thought to be inactive. The plateaus were connected at x = 0,

indicating that the Fe metal was completely re-oxidized to

Li2FeS2.

The product at x = 2 did not show any distinguishable

reflections attributable to Fe metal in its XRD diffraction

pattern. An absorption at d = 0 mm s� 1 with a small

quadrupole splitting observed in its 57Fe Mossbauer spec-

trum was assignable to superparamagnetic Fe0 (u SP Fe0)

[34]. According to the literature [35,36], small particles of

Fe0 exhibit superparamagnetism, when they are sufficiently

distant from each other that their magnetic moments have

little interaction. The particles at x = 2 should grow upon

annealing. Annealing the sample at x = 2 at 210 jC for 30

days gave reflections for Fe metal in its XRD pattern and the

strong sextet absorption in its Mossbauer spectrum. These

evidenced that the SP Fe0 grow to a-Fe. Recovery of the

capacity upon the re-oxidation became smaller as indicated

by dashed lines in the figure, because the electrochemically

active SP Fe0 was partially transformed into inactive a-Fe.

TEM observation suggested that Fe atoms would exist in

small particles of nanometer dimension even after anneal-

ing, and therefore, the electrochemically active Fe particles

would be much smaller before annealing.

Poizot et al. [37] also reported similar ‘‘unexpected’’

activities in nano-sized particles of Co, Ni, Cu, or Fe.

According to their study, cycling performances of such

materials were extremely sensitive to their degree of divi-

sion or aggregation. On the other hand, that of FeS2 in the

solid electrolyte was steady. The reason should be that the

solid electrolyte prevents the diffusion of the nano-sized

particles of Fe0, so that they do not aggregate into larger

particles.

3.3. Thiophosphate

Studies on lithium intercalation compounds started with

TiS2 [38]. After the finding of TiS2, many sulfides have

been reported as intercalation hosts for Li+ ion. However,

their intercalation potentials have been below 2.7 V vs. Li/

Li+, which are considerably lower than those of oxides.

From the viewpoint of application to batteries, fast ionic

diffusion is also important. In this respect, sulfides generally

show faster ion-diffusion than oxides, because sulfur has

larger polarizability than oxygen. If a certain sulfide gen-

erates a high electrode potential, it will be a good candidate

for cathode materials in lithium batteries because of its high

potential and high ionic diffusion.

The way to raise the potential can be found in oxides

having polyanions including LiFePO4 [39]. The redox

couple of Fe2 +/Fe3 + in LiFePO4 shows an unusually high

redox potential. In the material, the FeO6 octahedron is

linked to the PO4 tetrahedra. Electrons of O2� ion in the

Fe–O–P linkage are polarized towards more covalent P–O

bonding, and the polarization reduces the covalency of the

Fe–O bonding via the inductive effect. The decrease in

covalent mixing lowers the energy of antibonding orbital,

raising the Fe2 +/Fe3 + redox potential. If we introduce such

covalent bonding in the polyhedra neighboring to those

containing transition metal, we may enhance the redox

potential of the transition metal element also in sulfides.

Metal thiophospates (Me2P2S6; Me = Fe, Ni, Co) were

first reported by Hahn and Klingen [40]. Many isomorphs

have been found so far [41]. The Me2P2S6 has a layered

structure; each layer is build up from MeS6 octahedra

surrounded by three P2S6 octahedra, sharing their edges

with them each. If we introduce Li+ ions in the structure

Fig. 5. Potential profile of Li2FeP2S6. Circles and solid lines indicate that

obtained by coulombic titration and cycling operation at a constant current,

respectively.

K. Takada et al. / Solid State Ionics 172 (2004) 25–30 29

with remaining the divalent state of Me ion, they will be

electrochemically deintercalated at high voltages on the

analogy to polyanion oxides, because the covalent bond of

P–S will raise the redox potential of Me ion in the

neighboring octahedron.

Even if the sulfides generate high voltages, we may not

be able to use them as cathodes in lithium batteries. Sulfides

tend to form polysulfides upon the oxidation, which are

soluble species in organic electrolytes. The dissolution

prevents them from being charged in lithium batteries.

When we use solid electrolytes, they will completely

suppress the dissolution, allowing us to use the high-voltage

sulfides in lithium batteries.

When we synthesized a substitution product, Li2FeP2S6,

and investigated its crystal structure, we found that it has

an intermediate structure [23] between Li4P2S6 [42] and

Fe2P2S6. Fig. 5 shows the results of coulombic titration

and cycling test of Li2FeP2S6. Its potential increased from

2.5 to 3.1 V with a plateau at ca. 3.0 V vs. Li/Li+ upon

deintercalation of lithium. This is the highest potential

given by sulfides and significantly higher than that in

Li2FeS2 (2.3 V) [43].

4. Summary

The results on graphite anode in the solid electrolyte

system clearly showed the difference between the compat-

ibility of solid electrolytes with electrode materials, al-

though little attention has been paid to the compatibility

of solid electrolytes to electrode materials so far. Such

compatibility is quite important to gain energy density of

batteries by raising their cell voltages. However, as far as we

use the same kinds of electrode materials as those used in

liquid system, their energy densities will not largely exceed

those of liquid systems. The three examples of ‘‘unexpect-

ed’’ electrode materials may lead us to the discovery of

high-performance electrode materials. For example, ionic

crystals have never been investigated as electrode materials.

Acknowledgements

This work has been supported by the ‘Combinatorial

Materials Exploration and Technology’ joint project from

Science and Technology Agency Japan. The authors also

thank Denki Kagaku Kogyo K.K., Toda Kogyo, and Japan

Storage Battery for their collaboration.

References

[1] T. Nagaura, K. Tozawa, Prog. Batteries Sol. Cells 9 (1990) 209.

[2] S.D. Jones, J.R. Akridge, Solid State Ionics 86–88 (1996) 1291.

[3] K. Iwamoto, M. Fujino, K. Takada, S. Kondo, Denki Kagaku 65

(1997) 753.

[4] R. Mercier, J.-P. Malugani, B. Fahys, G. Robert, Solid State Ionics 5

(1981) 663.

[5] H. Wada, M. Menetrier, A. Levasseur, P. Hagenmuller, Mater. Res.

Bull. 18 (1983) 189.

[6] J.H. Kennedy, Y. Yang, J. Electrochem. Soc. 133 (1986) 2437.

[7] S. Kondo, K. Takada, Y. Yamamura, Solid State Ionics 28–30 (1992)

726.

[8] K. Hirai, M. Tatsumisago, T. Minami, Solid State Ionics 78 (1995)

269.

[9] M. Tatsumisago, K. Hirai, T. Hirata, M. Takahashi, T. Minami, Solid

State Ionics 86–88 (1996) 487.

[10] A. Hayashi, M. Tatsumisago, T. Minami, Y. Miura, J. Am. Ceram.

Soc. 81 (1998) 1305.

[11] R. Kanno, T. Hara, Y. Kawamoto, M. Irie, Solid State Ionics 130

(2000) 97.

[12] M. Murayama, R. Kanno, M. Irie, S. Ito, T. Hata, N. Sonoyama, Y.

Kawamoto, J. Solid State Chem. 168 (2002) 140.

[13] R. Kanno, M. Murayama, J. Electrochem. Soc. 148 (2001) A742.

[14] K. Takada, N. Aotani, K. Iwamoto, S. Kondo, Solid State Ionics

86–88 (1996) 877.

[15] R. Komiya, A. Hayashi, H. Morimoto, M. Tatsumisago, T. Minami,

Solid State Ionics 140 (2001) 83.

[16] K. Takada, K. Iwamoto, S. Kondo, Solid State Ionics 117 (1999) 273.

[17] K. Iwamoto, M. Fujino, K. Takada, S. Kondo, Denki Kagaku 67

(1999) 151.

[18] D. Billaud, F.X. Henry, P. Willmann, Mater. Res. Bull. 28 (1993) 477.

[19] S. Sahami, S.W. Shea, J.H. Kennedy, J. Electrochem. Soc. 132 (1985)

985.

[20] J.-M. Tarascon, M. Armand, Nature 414 (2001) 359.

[21] B.B. Owens, B.K. Patel, P.M. Skarstad, Solid State Ionics 9&10

(1983) 1241.

[22] A. Kajiyama, K. Takada, T. Inada, M. Kouguchi, S. Kondo, M.

Watanabe, M. Tabuchi, Solid State Ionics 152–153 (2002) 295–302.

[23] K. Takada, Y. Michiue, T. Inada, A. Kajiyama, M. Kouguchi, S.

Kondo, M. Watanabe, M. Tabuchi, Solid State Ionics 159 (2003)

257.

[24] K. Takada, Y. Kitami, T. Inada, A. Kajiyama, M. Kouguchi, S.

Kondo, M. Watanabe, M. Tabuchi, J. Electrochem. Soc. 148

(2001) A1085.

[25] N. Aotani, K. Iwamoto, K. Takada, S. Kondo, Solid State Ionics 68

(1994) 35.

[26] R. Kanno, Y. Takeda, O. Yamamoto, Solid State Ionics 28–30 (1988)

1276;

H.J. Steiner, H.D. Lutz, J. Solid State Chem. 99 (1992) 1.

K. Takada et al. / Solid State Ionics 172 (2004) 25–3030

[27] Z. Tomczuk, B. Tani, N.C. Otto, M.F. Roche, D.R. Vissers, J. Electro-

chem. Soc. 129 (1982) 925.

[28] S.K. Preto, Z. Tomczuk, S. von Winbush, M.F. Roche, J. Electro-

chem. Soc. 130 (1983) 264.

[29] D. Bernardi, J. Newman, J. Electrochem. Soc. 134 (1987) 1309.

[30] R.A. Guidotti, F.W. Reinhardt, Proc. 9th Int. Symp. Molten Salts 1994

(1994) 820.

[31] R. Brec, A. Dugast, A.L. Mehaute, Mater. Res. Bull. 15 (1980) 619.

[32] R. Fong, J.R. Dahn, C.H.W. Jones, J. Electrochem. Soc. 136 (1989)

3206.

[33] K. Takada, K. Iwamoto, S. Kondo, Solid State Ionics 117 (1999) 273.

[34] C.H.W. Jones, P.E. Kovacs, R.D. Sharma, R.S. McMillan, J. Phys.

Chem. 94 (1991) 832.

[35] S. Mørup, J. Magn. Magn. Mater. 37 (1983) 39.

[36] J.W. Niemantsverdriet, A.M. van der Kraan, W.N. Delgass, M.A.

Vannice, J. Phys. Chem. 89 (1985) 67.

[37] P. Poizot, S. Laruelle, S. Grugeon, L. Dupont, J.-M. Tarascon, Nature

407 (2000) 496.

[38] M.S. Whittingham, Science 192 (1976) 1126.

[39] A.K. Padhi, K.S. Nanjundaswamy, J.B. Goodenough, J. Electrochem.

Soc. 144 (1997) 1188.

[40] H. Hahn, W. Klingen, Naturwissenschaften 52 (1965) 494.

[41] R. Brec, Solid State Ionics 22 (1986) 3.

[42] R. Mercier, J.P. Malugani, B. Fays, J. Douglade, G. Robert, J. Solid

State Chem. 43 (1982) 151.

[43] R. Brec, A. Dugast, A. Le Mahaute, Mater. Res. Bull. 15 (1980) 619.