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ULTRASONIC STUDY OF TWO-LEVEL
TUNNELING SYSTEMS IN SINTERED SiC
A. Hikata, C . Elbaum, Y. Inomata, G. Orange, Y. Takeda
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C10, suppl6ment au n 0 1 2 , Tome
46,
d6cembre 1985 page C10-557ULTRASONIC STUDY OF TWO-LEVEL TUNNELING SYSTEMS IN SINTERED Sic
A. HIKATA,
C.
ELBAUM, Y. INOMATA',G.
ORANGE+'AND Y. TAKEDA+'*Brown University, Providence, RI, 02912, U.S.A.
'National Institute for Research in Inorganic Materials,
Ibaraki, Japan
++Institut
National des Sciences Appliquees, Villeurbame,
France
"'Hitachi
Research Laboratory, Hitachi-shi, Japan
~e'sume' - Nous avons 6tudiB (aux basses tempe'ratures; T
<
lK), la vitesse du son, en fonction de la tempe'rature, dans le carbure de silicium fritte' contenant trois additifs de frittage diffe'rents,1
savoir, les oxydes de be'ryllium et de bore, ou le ni trite d'aluminium. Les r6sultats sont interpre'te's suivant le modsle de l'effet tunnel dans des syst&nes1
deux niveaux.Abstract - We investigated the temperature dependence, at low temperatures (< lK), of sound velocity in sintered silicon carbide samples, containing three different sintering additives, boron or beryllium oxide or aluminum nitride. The results are interpreted in terms of Two Level Tunneling
System (TLS)
.
I
-
INTRODUCTIONA special feature of disordered materials is the temperature dependence of sound velocity at low temperatures; i.e., the velocity increases linearly with InT (T is the temperature) [1,2]. This and other low temperature properties of glasses are well explained by a phenomenological model called two Level Tunneling Systems (TLS)
[3]. The detailed structure or configuration of TLS, however, has not been estab- lished. We utilized this property and investigated at low temperatures the
effects of three different additives, aluminum nitride (AlN), boron (B), and beryl- lium oxide (BeO) on Sic. In case of B additives, effects of grain growth are also studied. From these investigations, it becomes apparent that the glass-like prop- erties manifested by TLS exist in sintered Sic, and these TLS reside not at the g r a b boundaries but inside the grains.
I1 - EXPERIMENTAL METIrOD
Samples used are sintered Sic with three different additives, AIN, B, and BeO. The ones with
B
were supplied by the National Institute for Research in Inorganic Mate- rials, and the ones with A1N and Be0 were supplied by the tlitachi Research Lab. The samples have rectangular cross sections, approximately 0.4 cm x 0.3 cm, and 0.9 cm in length. The weight percent of additives, sintering temperatures, grain sizes, densities and shear wave velocities for each sample are shown in TABLE I. The details of sintering of these materials are reported in [4] for SiC:AlN, in [5] for SiC:BeO and in [6] for SiC:B. The SiC:B samples are subsequently heat treated at 2050°C for 15, 30 and 60 minutes to allow grain growth and densification.JOURNAL
DE
PHYSIQUE weight s i n t e r d e n s i - g r a i n s h e a r nM2 % i n g t Y . s i z e wave e r g temp. g cm-3 v e l . cm-3 cm/sec TABLE I Comparison of A d d i t i v e s t o S i n t e r e d S i c .A p u l s e echo system combined w i t h phase d e t e c t i o n i s used f o r u l t r a s o n i c v e l o c i t y change measurements.
I11
-
EXPERIMENTAL RESULTS AND DISCUSSIONFIG. 1 shows t h e v e l o c i t y change Av/v a s a f u n c t i o n o f t e m p e r a t u r e of t h r e e samples each c o n t a i n i n g r e s p e c t i v e l y A l N , Be0 and B a s t h e a d d i t i v e s , t a k e n w i t h 96 MHz s h e a r waves. A s can be s e e n , t h e v e l o c i t y change of t h e SiC:BeO samples shows v e r y l i t t l e t e m p e r a t u r e dependence i h t h e t e m p e r a t u r e r a n g e i n v e s t i g a t e d ( s l i g h t l y de- c r e a s i n g w i t h i n c r e a s i n g t e m p e r a t u r e ) . T h i s i s a t y p i c a l b e h a v i o r f o r c r y s t a l l i n e m a t e r i a l s . The sound v e l o c i t i e s of SiC:AlN and SiC:B, on t h e o t h e r hand, i n c r e a s e w i t h t e m p e r a t u r e below a p p r o x i m a t e l y 1.5K f o r SiC:B, and 3.5K f o r SiC:AlN, b o t h become p r o p o r t i o n a l t o 1nT below 0.6K. T h i s l o g a r i t h m i c i n c r e a s e of sound v e l o c i t y w i t h t e m p e r a t u r e i s t y p i c a l i n a l m o s t a l l g l a s s y m a t e r i a l s i n c l u d i n g m e t a l l i c g l a s s e s .
The TLS model p r e d i c t s t h a t a t low t e m p e r a t u r e s (w-cm >> I ) , u l t r a s o n i c v e l o c i t y change (Av/v) i s g i v e n by and a t h i g h t e m p e r a t u r e s (w-cm << l ) , where n i s t h e d e n s i t y of s t a t e s of TLS, M i s t h e d e f o r m a t i o n p o t e n t i a l , p i s t h e m a t e r i a l d e n s i t y and T i s t h e a r b i t r a r y r e f e r e n c e t e m p e r a t u r e . T i s t h e r e l a x - m a t i o n t i m e of f a s t e s t ? e l a x i n g TLS w i t h energy s p l i t t i n g ~ [ 7 ] .
Thus, a s t h e t e m p e r a t u r e i s r a i s e d , Av/v i n i t i a l l y i n c r e a s e s w i t h 1nT and t h e n goes through a maximum and d e c r e a s e s p r o p o r t i o n a l l y t o -1nT b u t w i t h a s l o w e r r a t e . The c r o s s o v e r from t h e w'rm
>>
1 t o t h e wTm<<
1 regime must t a k e p l a c e n e a r t h e v e l o c - i t y maximum. I f one simply assumes t h a t w'rm = 1 a t t h e v e l o c i t y maximum, t h e de- f o r m a t i o n p o t e n t i a l M c a n b e c a l c u l a t e d . Once M i s determined, t h e v a l u e s of n c a n be r e a d i l y deduced from t h e v a l u e s of nM2 which can b e determined by t h e s l o p e of t h e (Av/v) v s . (InT) p l o t . The v a l u e s t h u s o b t a i n e d a r e a l s o l i s t e d i n Table I. TheM
v a l u e s of 1.1 dV f o r SiC:B and 0 . 5 eV f o r SiC:AlN a r e w i t h i n t h e range r e p o r t e d f o r v a r i o u s i n s u l a t i n g g l a s s e s [ 81.
2
It should be noted that reported strengths measured by a bending test at room tem- perature also follow this sequence, i.e., 800 MPa for SiC:AlN [4], 470 MPa for SiC:B [6], and 450 MPa for SiC:BeO [5].
FIG. 2 shows the effects of heat treatment of four SiC:B samples. These samples are heat treated at 2 0 5 0 ~ ~ for
0
(as sintered), 15, 30 and 60 minutes, respectively. With this heat treatment, grain growth and densification took place. The values of grain size, density, shear wave velocity are given in Table 11.time density shear wave grain size
min. g/cm3 vel. cmlsec erglcm 3
0 2.95 7.13x105 1.4 1.43~10 7
15 3.04 7.23 3.4 1.46
30 3.05 7.35 4.3 1.71
60 3.07 7.53 4.7 1.87
TABLE I1
Effect of Heat Treatment on Sintered Sic.
As can be seen in FIG. 2, the slope of the (Avlv) vs. (InT) relation increases with increasing grain size. It is also noted that as the slope increases with increas- ing heat treatment time, the temperature for velocity maximu, Tm, shifted slightly toward higher temperatures. If one follows the procedure mentioned above, approxi- mately the same values of M are obtained for these four samples; i.e. the increase in Tm is compensated by the increase in density and sound velocity
( E ~ ~ T J
vs. pv!).2
Therefore, the increase of nM due to the heat treatment can be attributed entirely to the increase in density of states of TLS, n.
Despite the reduction of grain boundary volume due to the grain growth, the density of TLS increased. Since solid solutions seem to be prime sources of the TLS as mentioned above, this fact iridicates that the additives, originally confined to the grain boundaries during the sintering processes dissolve into the bulk (grains) as the heat treatment proceeds and consequently produce more TLS, i.e., it appears that TLS reside not at grain boundaries but inside the grains.
Although the TLS model is successful in explaining many properties of glassy materi- als, the origin of TLS has not been established. The results of the present study suggest that at least in the case of sintered Sic, the TLS are associated with atoms of the additives B and A1N dissolved in the crystalline matrix (i.e., in solid solu- tions). Furthermore, these TLS are likely to be located inside the grains rather than at the grain boundaries.
IV - ACKNOWLEDGEMENT
One of the authors (A.H.) is grateful to Professor J. Shioiri of Hosei University (Tokyo) who called attention to this subject and provided samples in the early stages of this study. This work is supported 'in part by the National Science Foun- dation through the Materials Research Laboratory of Brown University.
V - REFERENCES
1. "Amorphous Solids", ed. by W.A. Phillips, (Springer-Verlag, Berlin, Heidelberg, New York, 1981).
2. D.A. Ackerman, D. Moy, R.C. Potter, A.C. Anderson, and W.N. Lawless, Phys. Rev. B 2 , 3886 (1981).
3 . P.W. Anderson, B.I. Halperin and C.M. Varma, Phil. Mag.,
5,
1 (1972); W.A. Phillips,J.
Low Temp. Phys.7,
351 (1972).C10-560
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DE
PHYSIQUE
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5. Y. Takeda, K. Usami, K. Nakamura, S. O g i h a r a , K. Maeda, T . Miyoshi, S.
S h i n o z a k i , and M. Ura, i n "Advances i n Ceramics", v o l . 7, A d d i t i v e s and I n t e r - f a c e s i n E l e c t r o n i c Ceramics, (American Ceramic S o c i e t y , 1 9 5 4 ) , pp. 253. 6 . H. Tanaka, Y . Inomata, K. Tsukuda, and A. Hagimura, Yogyo K y o k a i s h i z , 461
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7. J. ~ g c k l e , 2. Phys.
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212 (1972).8. S. Hunklinger and W. Arnold, i n " P h y s i c a l A c o u s t i c s " , ed. by W.P. Mason and R.N. T h u r s t o n , (Academic, New York 1 9 7 6 ) , v o l . 1 2 , p p . 155.
9.
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C u t l e r , P.D. M i l l e r , W. R a f a n i e l l o , H.K. P a r k , D.P. Thompson, and K.H. J a c k , N a t u r e275,
434 (1978).10. P.T.B. S h a f f e r , Mat. Res. B u l l .
6,
213 (1969).7
-
96MHz
Shear Wave
-
TEMPERATURE
(K)
F i g . 1 : E f f e c t o f a d d i t i v e s , BeO. A%N ~ i2 ; ~E f f e c t of h e a t t r e a t m e n t on tem- .
and B* O n t h e p e r a t u r e dependence of sound v e l o c i t y i n
sound v e l o c i t y i n s i n t e r e d S i c . The v e r - s i n t e r e d
