Piezoelectric and ferroelectric properties of SrBi2(Nb1−χTaχ)2O9 ceramics

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Materials Science and Engineering B 135 (2006) 60–64 Piezoelectric and ferroelectric properties of SrBi 2 (Nb 1χ Ta χ ) 2 O 9 ceramics Lin Sun a,b,, Chude Feng a , Lidong Chen a , Shiming Huang a , Xiaowei Wen a a State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, PR China b Graduate School of Chinese Academy of Sciences, Beijing 100039, China Received 7 July 2006; received in revised form 1 August 2006; accepted 15 August 2006 Abstract SrBi 2 (Nb 1χ Ta χ ) 2 O 9 (0 χ 1.0) bismuth layered structured ferroelectric (BLSF) ceramics were prepared by the conventional solid-state reaction sintering method. XRD analysis indicated that a single phase of SrBi 2 (Nb 1χ Ta χ ) 2 O 9 was formed for all compositions. The substitution of Ta for Nb decreases Curie temperature (T c ), maximum permittivity (ε m ), remnant polarization (P r ) and coercive field (E c ), whereas temperature coefficient of resonance frequency (TCF) increases with the increase in Ta content for SrBi 2 (Nb 1χ Ta χ ) 2 O 9 . All of compositions have a low permittivity (ε r ), a low electromechamical coupling coefficient (K p ) and a high mechanical quality factor (Q m ), which are advantageous to be used in piezoelectric resonator device. © 2006 Elsevier B.V. All rights reserved. Keywords: Bismuth layer structure ferroelectric; SBN; SBT; Piezoelectric property 1. Introduction Bismuth layered structured ferroelectrics (BLSFs) materi- als including SrBi 2 Ta 2 O 9 (SBT), Bi 4 Ti 3 O 12 and SrBi 2 Nb 2 O 9 (SBN) have attracted much attention of researchers due to their fatigue-free properties in nonvolatile ferroelectric thin film ran- dom access memory (FE-RAM) applications [1–4]. Despite its technological importance, the understanding of the fundamen- tal nature and crystal chemistry of SBT or SBN is far from complete because of the complexity of this layered structure. In an attempt to clarify the nature of resistance to fatigue and the origin of ferroelectricity, many material scientists have stud- ied the crystal structures and ferroelectric properties of SBN and SBT based materials using electron and neutron diffraction techniques [5–7]. The study for the structure of BLSFs revealed that SBN or SBT consists of [Bi 2 O 2 ] 2+ layers interleaved with perovskite-like blocks [Nb 2 O 7 ] 2or [TaO 6 ] 2. On the other hand, considerable work has been performed on the doping effect on the enhancement of the properties of BLSFs [8–10], and there are some papers, which reported the ferroelectric and piezoelectric properties of SBN and SBT based Corresponding author. Tel.: +86 21 52411049. E-mail address: [email protected] (L. Sun). materials [11,12]. However, although Ando and Kimura reported that SrBi 2 Nb 2 O 9 ceramics has a small TCF and can be used in the fine-tolerance oscillator applications in recent years [13–15], studies on their piezoelectric properties regarding practical res- onator applications are still limited. Therefore, it is expected that the solid solution SrBi 2 (Nb 1χ Ta χ ) 2 O 9 (0 χ 1.0) (here- inafter abbreviated SBNT) will yield tunable properties on TCF and piezoelectric properties because the structure of SBT is sim- ilar to that of SBN. In addition, to date, there have been few reports concerning the detailed study of the TCF and piezoelec- tric properties of SBNT for practical resonator applications. In this work, we have investigated the ferroelectric and piezoelec- tric characteristics of SBNT ceramics. 2. Experimental procedure Samples of SrBi 2 (Nb 1χ Ta χ ) 2 O 9 (χ = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0) ceramics were prepared by a conventional solid-state reaction sintering. The starting raw materials with an analytical purity were SrCO 3 , Bi 2 O 3 , Nb 2 O 5 and Ta 2 O 5 . The powders of starting chemicals were admixed by ball milling for 24 h, and then were pre-sintered at 900 C for 2 h. The pre-sintered powders were ground and ball-milled into the fine powders for 24 h. The obtained powders were admixed with 0921-5107/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2006.08.034

Transcript of Piezoelectric and ferroelectric properties of SrBi2(Nb1−χTaχ)2O9 ceramics

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Materials Science and Engineering B 135 (2006) 60–64

Piezoelectric and ferroelectric properties of SrBi2(Nb1−χTaχ)2O9 ceramics

Lin Sun a,b,∗, Chude Feng a, Lidong Chen a,Shiming Huang a, Xiaowei Wen a

a State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics,Chinese Academy of Sciences, Shanghai 200050, PR China

b Graduate School of Chinese Academy of Sciences, Beijing 100039, China

Received 7 July 2006; received in revised form 1 August 2006; accepted 15 August 2006

bstract

SrBi2(Nb1−χTaχ)2O9 (0 ≤ χ ≤ 1.0) bismuth layered structured ferroelectric (BLSF) ceramics were prepared by the conventional solid-stateeaction sintering method. XRD analysis indicated that a single phase of SrBi2(Nb1−χTaχ)2O9 was formed for all compositions. The substitutionf Ta for Nb decreases Curie temperature (T ), maximum permittivity (ε ), remnant polarization (P ) and coercive field (E ), whereas temperature

c m r c

oefficient of resonance frequency (TCF) increases with the increase in Ta content for SrBi2(Nb1−χTaχ)2O9. All of compositions have a lowermittivity (εr), a low electromechamical coupling coefficient (Kp) and a high mechanical quality factor (Qm), which are advantageous to be usedn piezoelectric resonator device.

2006 Elsevier B.V. All rights reserved.

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eywords: Bismuth layer structure ferroelectric; SBN; SBT; Piezoelectric prop

. Introduction

Bismuth layered structured ferroelectrics (BLSFs) materi-ls including SrBi2Ta2O9 (SBT), Bi4Ti3O12 and SrBi2Nb2O9SBN) have attracted much attention of researchers due to theiratigue-free properties in nonvolatile ferroelectric thin film ran-om access memory (FE-RAM) applications [1–4]. Despite itsechnological importance, the understanding of the fundamen-al nature and crystal chemistry of SBT or SBN is far fromomplete because of the complexity of this layered structure.n an attempt to clarify the nature of resistance to fatigue andhe origin of ferroelectricity, many material scientists have stud-ed the crystal structures and ferroelectric properties of SBNnd SBT based materials using electron and neutron diffractionechniques [5–7]. The study for the structure of BLSFs revealedhat SBN or SBT consists of [Bi2O2]2+ layers interleaved witherovskite-like blocks [Nb2O7]2− or [TaO6]2−.

On the other hand, considerable work has been performed

n the doping effect on the enhancement of the properties ofLSFs [8–10], and there are some papers, which reported the

erroelectric and piezoelectric properties of SBN and SBT based

∗ Corresponding author. Tel.: +86 21 52411049.E-mail address: [email protected] (L. Sun).

0sapfpp

921-5107/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.mseb.2006.08.034

aterials [11,12]. However, although Ando and Kimura reportedhat SrBi2Nb2O9 ceramics has a small TCF and can be used inhe fine-tolerance oscillator applications in recent years [13–15],tudies on their piezoelectric properties regarding practical res-nator applications are still limited. Therefore, it is expectedhat the solid solution SrBi2(Nb1−χTaχ)2O9 (0 ≤ χ ≤ 1.0) (here-nafter abbreviated SBNT) will yield tunable properties on TCFnd piezoelectric properties because the structure of SBT is sim-lar to that of SBN. In addition, to date, there have been feweports concerning the detailed study of the TCF and piezoelec-ric properties of SBNT for practical resonator applications. Inhis work, we have investigated the ferroelectric and piezoelec-ric characteristics of SBNT ceramics.

. Experimental procedure

Samples of SrBi2(Nb1−χTaχ)2O9 (χ = 0, 0.1, 0.3, 0.5,.7, 0.9 and 1.0) ceramics were prepared by a conventionalolid-state reaction sintering. The starting raw materials with annalytical purity were SrCO3, Bi2O3, Nb2O5 and Ta2O5. The

owders of starting chemicals were admixed by ball millingor 24 h, and then were pre-sintered at 900 ◦C for 2 h. There-sintered powders were ground and ball-milled into the fineowders for 24 h. The obtained powders were admixed with

and Engineering B 135 (2006) 60–64 61

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L. Sun et al. / Materials Science

olyvinylalcohol as a binder and pressed uniaxially into pelletsith 16 mm in diameter and 2 mm in thickness. These pelletsere sintered at 1100–1200 ◦C for 2 h in a sealed alumina

rucible. All of the ceramic pellets were polished to 1 mmn thickness, painted by silver pastes on both sides and firedt 750 ◦C to form electrodes. The samples for piezoelectriceasurement were poled in a silicon oil bath at 180 ◦C under

lectric field of about 8–10 kV/mm for 5–15 min.The crystal phase of SBNT ceramics powders, which were

btained by crushing the sintered ceramics, was determined by-ray diffractometer (D/max2500 V, Rigaku, Japan) at a scan

peed of 4◦/min and a step width of 0.02◦. The dielectric proper-ies were measured by a LCR meter (Model HP 4284A, Hewlett-ackard, Palo Alto, CA). Microstructures of the ceramic samplesere observed on polished and thermally etched surfaces by

canning electron microscopy (SEM; Model JSM6700F, JEOL,okyo, Japan). The P–E hysteresis loops were measured by a TFnalyzer (Model 2000, aixACCT Systems, Germany) at the tem-erature of 150 ◦C with a frequency of 1 Hz. The piezoelectriceasurements were performed 48 h after the poling. The piezo-

lectric constants, d33, were measured using a quasi-static d33eter (Model ZJ-2, Institute of Acoustics, Chinese Academy

f Science). The planar coupling factor Kp and the mechanicaluality factor Qm were determined using the resonance–anti-esonance method. Resonance and anti-resonance frequencies inhe temperature range from −20 to 100 ◦C were measured usingrecision Impedance Analyzer (Agilent 4294A, USA) combinedith a temperature-controlling oven (VT7004, Germany). TCFas calculated using

CF = �fr

fr20◦C × 100, (1)

here �fr is the variation of the resonance frequency within theemperature range from −20 to 80 ◦C, and fr20◦C is the resonancerequency at 20 ◦C.

. Results and discussion

The X-ray diffraction patterns of SBNT samples are shownn Fig. 1. The XRD peaks were indexed and the indexed resultsndicated that the pure single phase was obtained for all SBNTamples. The strongest diffraction peak for all SBNT samples is1 1 5), which is consistent with the (112m+1) highest diffractioneak in Aurivillius phase [16]. It is noticeable that the diffractioneak (0 0 4) decreases gradually with the increase in Ta contentχ), while the diffraction peaks (1 1 1) and (0 0 6) increase grad-ally with increasing Ta content (χ). The change of intensity for0 0 4), (0 0 6) and (1 1 1) peaks just reflects the change of Nbr Ta content for SrBi2(Nb1−χTaχ)2O9. Furthermore, the XRDeaks shifts cannot be observed, which is in good agreementith the fact that the radius of Ta5+ (0.064 nm) is equal to that ofb5+ (0.064 nm) [17]. The above observations reveal that the Ta

on can substitute for Nb ion in the whole compositions without

ltering the layer perovskite structure for SBNT ceramics.

Fig. 2 shows the SEM images of the polished and thermallytched surfaces of SBNT (χ = 0, 0.5 and 1.0) ceramics. The plate-ike morphology, which is one of the characteristics of BLSFs, is

cTiχ

Fig. 1. X-ray diffraction pattern of SrBi2(Nb1−χTaχ)2O9 ceramics.

ery obvious for these SBNT samples. The grain growth behav-or of BLSFs that are anisotropic materials is different fromhat of ordinary isotropic materials. The driving force for grainrowth along the c-axis direction, which is perpendicular to thea–b) plate plane, is much smaller than that along a- or b-axisirection [18]. So the sintered SBNT ceramics as one of BLSFsisplay the plate-like morphology.

Fig. 3(a) and (b) shows the temperature dependence of theielectric constant and dielectric loss of SBNT ceramics, respec-ively. Both dielectric constant peak and dielectric loss peak shiftradually towards low temperature direction as the Ta contentχ) increases, and the value of dielectric constant peak (εm)ecreases monotonically with the increase in Ta content (χ).he observed gradual changes in both εr and tan δ spectrums also

eveal Ta ion successfully substitutes for Nb ion over the wholeange of χ. In addition, Fig. 3(c) shows the changes in Tc as theunction of Ta content (χ) for SBNT ceramics. Tc decreases lin-arly with increasing Ta content up to χ = 0.7, and only a slightecrease in Tc is observed when 0.7 < χ ≤ 0.9. However, theres a little increase in Tc when 0.9 ≤ χ ≤ 1.0.

The Curie temperatures of SBN and SBT are about 440 and10 ◦C, respectively. So it is easy to understand that Curie tem-erature Tc decreases when Ta gradually substitutes for Nbn SBNT solid solution. Furthermore, from the viewpoint oftructure distortion, the substitution of Ta for Nb decreases thetructural distortion of (Nb, Ta)O octahedron, which leads to theecrease in Curie temperature [5]. However, it is hard to clar-fy the increase in Tc when 0.9 ≤ χ ≤ 1.0 for SBNT system. Weuppose that it may be related to the partial substitution of Sr2+

or Bi3+ in the Bi2O2 layers [19].The P–E hysteresis loops of SBNT ceramics under an

pplied electric field of 80 kV/cm were shown in Fig. 4(a). Itan be seen that all the hysteresis loops approach saturationnder the driven field. The dependence of 2Pr and 2Ec on the Ta

ontent (χ) at an applied field of 80 kV/cm is given in Fig. 4(b).he coercive field (2Ec) decreases monotonously with the

ncrease in χ. For instance, 2Ec decreased from 97 kV/cm for= 0 to 33 kV/cm for χ = 1.0. This result presumably arises

62 L. Sun et al. / Materials Science and Engineering B 135 (2006) 60–64

Fig. 2. Scanning electron microscopy micrographs of polished and thermally etched surfaces of different ceramics samples: (a) SrBi2Nb2O9 (b) SrBi2(Nb0.5Ta0.5)2O9

and (c) SrBi2Ta2O9.

Fig. 3. (a) Temperature dependence of the dielectric constants of SrBi2(Nb1−χTaχ)2O9 measured at 1 MHz. (b) Temperature dependence of the dielectric loss ofSrBi2(Nb1−χTaχ)2O9 measured at 1 MHz. (c) Tc changes with Ta content for SrBi2(Nb1−χTaχ)2O9 ceramics and Tc is defined as a temperature which gives themaximum value of dielectric constant (εmax). (d) Dependence of εmax on Ta content for SrBi2(Nb1−χTaχ)2O9 ceramics measured at 1 MHz.

L. Sun et al. / Materials Science and Engineering B 135 (2006) 60–64 63

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Fig. 4. Hysteresis loops of SrBi2(Nb1−χT

rom a smaller structural distortion in TaO6 octahedron inrBi2Ta2O9 than that of SrBi2Nb2O9 [5]. The value of 2Prlso reduces gradually with the increase in Ta content (χ)xcept for χ = 0.3, which gives the maximum of 2Pr there.ccording to the calculation of Ps by Shimakawa et al. [5],

pontaneous polarization (Ps) decreases monotonously withhe increase in χ also because the increase of Ta content lowershe structural distortion of (Nb, Ta)O6 octahedron for SBNTeramics. Although the Ps for x = 0.3 is lower than that for x = 0n their calculation [5], the measured 2Pr for x = 0.3 is higherhan that for x = 0 in our experiment. This discrepancy may beelated to the insufficient saturation of the P–E hysteresis loopor x = 0 or the switching behavior of domain wall.

Furthermore, it should be noted that the P–E loops of SBNTre evidently asymmetric and shift toward the direction of neg-tive electric field. Similar phenomena were also observed inrBi2(Nb1−χTaχ)2O9 thin-film capacitors [4] and SrBi2Nb2O9eramics prepared by Wu and Cao [20]. This phenomenon wouldeem to be attributed to the internal bias field caused by thexistence of oxygen vacancies [21]. In recent years, the pos-ibility of cation disordering in BLSFs, such as SBN, SBT andi2Ln2Ti3O12 (Ln = La, Pr, Nd and Sm) systems has been inves-

igated and the exchange of cations between Bi2O2 layers and Aite has also been confirmed using a combination of X-ray andeutron powder diffraction [19,22,23]. For SBN, the significantmounts of cation disorder, i.e. the exchange of cations betweeni2O2 layers and A site (A = Sr), were detected. From Palan-uz’s viewpoint, cation disordering is necessarily accompaniedy the presence of oxygen vacancies in SBN [24]. So, in SBNTolid solution, there exist oxygen vacancies due to the exchangef cations between Bi2O2 layers and A site, and the internal

eld is possibly induced by these oxygen vacancies. However,

he exact reason for the internal field still remains unclear andeeds to study further.

g(T

able 1iezoelectric characteristic of SBNT ceramics

rBi2(Nb1−χTaχ)2O9 χ = 0 χ = 0.1 χ = 0.3

r (at 1 kHz, RT) 142 140 145

33(pC/N) 12 13 11

p (%) 4 5 6

m 4320 4320 3200

9 (χ = 0, 0.3, 0.5, 0.7 and 1.0) ceramics.

Table 1 shows the piezoelectric and dielectric properties forBNT ceramics. The d33 values of BLSFs are very low in com-arison with those of other piezoelectric materials, such as leadirconate titanate (PZT) and lead titanate (PbTiO3) ceramicsusually d33 ranged from several tens to several hundred pC/N)).he possible reasons for it are the two-dimensional orientation

estriction of their spontaneous polarization Ps and their highoercive fields Ec [25]. Note that these d33 values of χ < 0.5 com-ositions are higher than those of χ > 0.5 compositions, which isresumably due to higher 2Pr of χ < 0.5 than those of χ > 0.5 ashown in Fig. 4. For all compositions of SBNT ceramics, bothheir dielectric constants (εr) and the electromechanical couplingoefficients (Kp) are very low, whereas their mechanical qualityactor (Qm) are higher than 3000. Piezoceramics materials thatave low εr and high Qm are suitable for the high-frequencypplication. Furthermore, a low Kp is necessary for piezoceram-cs used in fine-tolerance resonator applications because a high

p will result in large changes in frequency when resonator cir-uit conditions change. The word “fine-tolerance” means thathere is only a very slight deviation from designed frequency,nd the fine-tolerance piezoelectric ceramics resonators for thescillator applications are considered as one of the most impor-ant among many piezoelectric ceramic applications [15]. So wexpect that SBNT ceramics can be regarded as promising can-idate materials for fine-tolerance oscillators applications sincehey have a low εr, a low Kp and a high Qm.

In addition, a low temperature coefficient of resonance fre-uency (TCF) is also one of the important requirements forne-tolerance oscillators applications. Fig. 5 plots resonancerequency changes of SrBi2(Nb1−χTaχ)2O9 (χ = 0, 0.5 and 1.0)gainst temperature. As shown in Fig. 5, TCF value increases

radually with the increase in Ta content (χ), and SBN ceramicsχ = 0) has the smallest TCF value. In terms of formula (1), theCF value of SBT (−55.2 ppm/◦C) is nearly two times as large

χ = 0.5 χ = 0.7 χ = 0.9 χ = 1.0

145 141 142 1309.5 9.5 9.5 97 7 7.8 8

3140 4230 4210 4170

64 L. Sun et al. / Materials Science and E

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ig. 5. Temperature dependence of resonance frequency of SrBi2(Nb1−χTaχ)2-

9 (χ = 0, 0.5, 1.0) ceramics.

s that of SBN (−29.3 ppm/◦C). TCF of piezoceramics mighte related to its Curie temperature for the reason that a higherurie temperature possibly tends to bring about a smaller TCF

13]. So TCF of SBN (Tc ∼ 440 ◦C) is smaller than that of SBTTc ∼ 310 ◦C). Therefore, SBN is a good candidate material forne-tolerance oscillator application, whereas for SBNT ceram-

cs the substitution of Ta for Nb increases the TCF value, whichay limit their application on piezoelectric resonance devices,

uch as piezoelectric filters to some degree.

. Conclusions

The dielectric property, ferroelectric property and piezoelec-ric characteristics of SBNT ceramics, which are prepared byraditional solid reaction sintering method, have been investi-ated. A single phase of Bi-layered perovskite was confirmed

or all compositions by means of XRD measurement. Theubstitution of Ta for Nb decreases the Curie temperature (Tc)ue to the decrease in the structural distortion of (Nb, Ta)O octa-edron. The Pr and Ec also lower with the increase in Ta content

[[[

ngineering B 135 (2006) 60–64

or SBNT ceramics. In addition, SBN ceramics is a promisingaterial for fine-tolerance oscillator application because it has a

ow Kp, a high Qm and a small TCF. Other SBNT ceramics alsoave these advantages, but the substitution of Ta for Nb increasesCF value, which maybe affects their application more or less.

cknowledgement

This work was supported by the Ministry of Sciences andechnology of China through 973-project under Grant No.002CB613307.

eferences

[1] B.H. Park, B.S. Kang, S.D. Bu, et al., Nature 401 (1999) 682–684.[2] A.K. Amamum, T. Hase, Y. Miyasak, Appl. Phys. Lett. 66 (1995) 221–

223.[3] H. Watanabe, T. Mihara, Jpn. J. Appl. Phys. 34 (1995) 5210–5244.[4] A. Furuya, J.D. Cuchiaro, J. Appl. Phys. 84 (1998) 6788–6794.[5] Y. Shimakawa, Y. Kubo, et al., Appl. Phys. Lett. 77 (2000) 2749–2751.[6] Y. Shimakawa, Y. Kubo, et al., Phys. Rev. B. 61 (2000) 6559–6564.[7] Y. Shimakawa, H. Imai, et al., Phys. Rev. B. 66 (144) (2002) 110-1-5.[8] A. Garg, A. Snedden, P. Lightfoot, et al., J. Appl. Phys. 96 (2004)

3408–3412.[9] Y. Noguchi, M. Miyayama, et al., J. Appl. Phys. 95 (2004) 4261–4266.10] M.J. Forbess, S. Seraji, et al., Appl. Phys. Lett. 76 (2000) 2934–2936.11] J.A. Cho, S.E. Park, et al., J. Electroceram. 13 (2004) 515–518.12] A. Ando, M. Kimura, et al., Jpn. J. Appl. Phys. 42 (2003) 520–525.13] A. Ando, M. Kimura, et al., Ferroelectrics 268 (2002) 65–70.14] A. Ando, M. Kimura, et al., Jpn. J. Appl. Phys. 42 (2003) 150–156.15] A. Ando, M. Kimura, et al., Int. J. Appl. Ceram. Technol. 2 (1) (2005)

33–44.16] X.F. Du, I.W. Chen, J. Am. Ceram. Soc. 81 (1998) 3253–3259.17] R.D. Shannon, Acta Cryst. A 32 (1976) 751–767.18] H. Watanabe, T. Kimura, et al., J. Am. Ceram. Soc. 74 (1991) 139–147.19] R. Macquart, B.J. Kennedy, J. Solid State Chem. 160 (2001) 174–177.20] Y. Wu, G.Z. Cao, J. Mater. Res. 15 (2000) 1583–1590.21] S. Takahashi, Ferroelectrics 41 (1982) 143–156.22] S.M. Blake, M.J. Falconer, et al., J. Mater. Chem. 7 (1997) 1609–

1613.23] N.C. Hyatt, J.A. Hriljac, et al., Mater. Res. Bull. 38 (2003) 837–846.24] A.C. Palanduz, D.M. Smyth, J. Electroceram. 11 (2003) 191–206.25] R.E. Newnham, R.W. Wolfe, J.F. Dorrian, Mater. Res. Bull. 6 (1971)

1029–1039.