HAL Id: jpa-00223232
https://hal.archives-ouvertes.fr/jpa-00223232
Submitted on 1 Jan 1983
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
PHOTOACOUSTIC MEASUREMENTS OF THERMAL DIFFUSIVITY OR THICKNESS OF
MULTI-LAYER SOLIDS
S. Yun, H. Seo
To cite this version:
S. Yun, H. Seo. PHOTOACOUSTIC MEASUREMENTS OF THERMAL DIFFUSIVITY OR
THICKNESS OF MULTI-LAYER SOLIDS. Journal de Physique Colloques, 1983, 44 (C6), pp.C6-
459-C6-462. �10.1051/jphyscol:1983673�. �jpa-00223232�
J O U R N A L D E PHYSIQUE
Colloque C6, supplement
au nO1O,Tome 44, octobre 1983 page C6-
459PHOTOACOUSTIC MEASUREMENTS OF THERMAL D I F F U S I V I T Y OR THICKNESS OF MULTI-LAYER SOLIDS*
S . I . Yun and H . J . Seo
Department of Physics and I n s t i t u t e of SoLid State Physics, Busan ~ a t i o n a z University, Busan
60 7 ,Korea
&sumd.- Le p r i n c i p e e t l e s r g s u l t a t s expe'rimentaux pour l a mesure photoacoustique de l a d i f f u s i v i t 6 thermique ou de l 1 6 p a i s s e u r de chaque couche d'une m u l t i p l e couche s o l i d e s o n t d e ' c r i t s dans c e t t e Qtude
.
A b s t r a c t = - The p r i n c i p l e and experimental r e s u l t s f o r t h e photo- a c o u s t i c measurements of thermal d i f f u s i v i t y o r t h i c k n e s s o f each i n d i v i d u a l l a y e r of a m u l t i - l a y e r s o l i d a r e d e s c r i b e d .
I . INTRODUCTION.
Adams and K i r k b r i g h t / l - 3 / , and o t h e r s / 4 / measured t h e thermal d i f f u s i v i t i e s of cop- p e r , aluminum and polymer from t h e phase l a g observed i n t h e p h o t o a c o u s t i c s i g n a l from t h e s e samples. A n a l t e r n a t i v e way of measuring t h e thermal d i f f u s i v i t y of s o l i d m a t e r i a l s was r e p o r t e d independently by two group, Lepoutre and Charpentier/S, 6 / , and S u g i t a n i and Fujinami/7/, They measured t h e thermal d i f f u s i v i t y o f m a t e r i a l s by a n a l y z i n g t h e p h o t o a c o u s t i c s i g n a l i n t e n s i t y a s a f u n c t i o n of t h e l i g h t chopping frequency. Here we r e p o r t t h e p h o t o a c o u s t i c measurements of thermal d i f f u s i v i t y o r t h i c k n e s s o f each i n d i v i d u a l l a y e r o f a m u l t i - l a y e r s o l i d sample by t h e e x t e n s i o n o f t h e p r i n c i p l e employed by a u t h o r s of r e f e r e n c e s 5 . 6 and 7 .
11. THEORY OF THE METHOD.
According t o ~osencwaig-Gersho p h o t o a c o u s t i c theory/8/ t h e photoacoustic(PA) signal.
i n t e n s i t y Q f o r t h e o p t i c a l l y opaque s o l i d ( u a < < l l l ) , a s long a s pl>pa, i s given by
1
( a . I 3 / ( 2 r f k . )
,
f o r t h e r m a l l y t h i n c a s e o fu
. > t .Q OL { ]+I 3+1 3 3
( a j ) / ( 2 1 ~ f k
'I
.),
f o r t h e r m a l l y t h i c k c a s e o fu
<II.3 1 3
I n t h e above e x p r e s s i o n s , pa i e t h e o p t i c a l a b s o r p t i o n l e n g t h o f r e g i o n ( 1 ) i n F i g . 1.
Fig. 1.- Simple p h o t o a c o u s t i c INSIDENT c e l l w i t h a m u l t i - l a y e r s o l i d
LlGHT sample.
*
P r e s e n t s t u d i e s were supported by t h e Basic Science Research I n s t i t u t e Program, M i n i s t r y of Education, The Republic o f Korea, 1982.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983673
C6-460
JOURNAL DE PHYSIQUE
R j ,
u . ,
a j and k . a r e t h e t h i c k n e s s , thermal d i f f u s i o n l e n g t h , thermal d i f f u s i v i t y , and d e r m a l c o n d i c t i v i t y of ( j ) t h region o f t h e sample ; f i s t h e chopping frequency.From E q . ( l ) it i s c l e a r t h a t , f o r p j > R j , t h e thermal p r o p e r t y o f ( j + l ) t h r e g i o n o f t h e sample comes i n t o t h e e x p r e s s i o n f o r PA s i g n a l i n t e n s i t y . Whereas, f o r p . < R .
3 ' t h e PA s i g n a l depends on t h e thermal p r o p e r t y o f ( j ) t h r e g i o n o f t h e sample.
knee
t h e thermal d i f f u s i o n l e n g t h i n ( j ) t h m a t e r i a l i s given by
t h e thermal d i f f u s i o n l e n g t h can be changed by changing t h e l i g h t chopping frequency.
Thus, we e x p e c t t o have a b r u p t changes i n PA s i g n a l i n t e n s i t y a s we s c a n t h e chopping frequency. Whenever t h e thermal d i f f u s i o n l e n g t h i n t h e m u l t i - l a y e r s o l i d sample r e a c h e s t h e boundary of t h e m a t e r i a l with d i f f e r e n t thermal p r o p e r t y , a d i s c o n t i n u - i t y of t h e PA s i g n a l i n t e n s i t y can be observed. Therefore, i t i s p o s s i b l e t o o b t a i n t h e thermal d i f f u s i v i t y of m a t e r i a l j o f known t h i c k n e s s R . by f i n d i n g a s e r i e s of chopping f r e q u e n c i e s f c a t which t h e PA s i g n a l i n t e n s i t y changes d i s c o n t i n u o u s l y . I Let c a l l t h i s chopping ?requency a s t h e c h a r a c t e r i s t i c frequency.
On t h e o t h e r hand, we can o b t a i n t h e t h i c k n e s s R. of each i n d i v i d u a l l a y e r of a m u l t i - l a y e r s o l i d sample through t h e knowledge o? t h e thermal d i f f u s i v i t y a . and t h e
corresponding c h a r a c t e r i s t i c frequency f c j . 7
111. EXPERIMENTAL
The experimental arrangement i s s i m i l a r t o t h o s e o f Adams e t a l . / l - 3 / . The micro- phone was an AKG CK-22 condenser microphone w i t h a r a t e d open c i r c u i t s e n s i t i v i t y o f 8 mV/pa. The l i g h t source was a 1000 w a t t t u n g s t e n lamp. The l i g h t beam from t h e microphone was chopped with a v a r i a b l e l i g h t chopper(^^^ 1 9 2 ) . The s i g n a l from t h e microphone was a m p l i f i e d by an AKG C451E p r e a m p l i f i e r and a Keithley 429 c u r r e n t a m p l i f i e r , and t h e n f e d i n t o an ITHACO 391 Dynatrac l o c k - i n a m p l i f i e r .
I V . RESULTS AND DISCUSSION.
Fig. 2 and 3 show t h e P A s i g n a l s from 520pm t h i c k copper p l a t e and 357um t h i c k alumi- num p l a t e , r e s p e c t i v e l y . The samples were mounted on t h e copper sample h o l d e r use- i n g a quick s e t t i n g adhesive. From Fig. 2 t h e c h a r a c t e r i s t i c frequency i s found t o be 125Hz. Since p(copper)=R(copper) a t t h i s chopping frequency, we have 0.052(cm) =
l a (copper) /l 2 5 n I f . Therefore t h e measured thermal d i f f u s i v i t y o f copper i s a (copper)
FREQUENCY ( H z )
I
I
I I. I
6 01
o - ~
~ INVERSE OF FREQUENCY (HZ" ) Fig. 2.-
PA s i g n a l v r s t h e i n v e r s e o f F i g . 3--
PA s i g n a l v r s t h e i n v e r s e of t h e chopping frequency f o r a copper t h e chopping frequency f o r an aluminump l a t e . Thickness: 520um. p l a t e . Thickness: 357pm.
= 1.061 cm2/sec. S i r i l a r l y t h e thermal d i f f u s i v i t y o f aluminum can be determined from t h e c h a r a c t e r i s t i c frequency i n Fig. 3 and found t o be 0.87 cm2/sec. F i g . 4 shows t h e PA s i g n a l from a t r i p l e - l a y e r s o l i d sample o f /460um copper/8pm adhesive/
1.5 mm copper/. We can c a l c u l a t e t h e thermal d i f f u s i v i t i e s of f i r s t and second l a y e r s of t h e sample from two c h a r a c t e r i s t i c f r e q u e n c i e s , 160 H z and 68 H z . They
m
200 150 100 80 60
518
Ll l l r r l
I I I1
I I IY
INVERSE
O F
FREQUENCY(HZ")Fig. 4.
-
PA s i g n a l v r s t h e i n v e r s e o f t h e chopping f r e - quency f o r a t r i p l e - l a y e r sample of Cu/adhesive/Cu.a r e a ( c o p p e r ) = 1.064 cm2/sec and a ( a d h e s i v e ) = 0.00114 cm2/sec, r e - s p e c t i v e l y , and i n good agreement w i t h d a t a found i n t h e l i t e r a t u r e s 9 The adhesive used i n t h i s measurement was c y a n o a c r y l a t e Type EE from Alpha Techno Co. Because of t h e l i m i t a t i o n o f o u r microphone i n t h e lower frequency range, i t was impossible t o measure t h e c h a r a c t e r i s t i c f r e - quency f o r t h e t h i r d l a y e r of t h e sample. On t h e o t h e r hand, if we know t h e thermal d i f f u s i v i t y i n s t e a d of t h e t h i c k n e s s o f e a c h i n d i v i d u a l l a y e r of t h e m u l t i - l a y e r sample, we can o b t a i n t h e t h i c k n e s s o f e a c h
Fig. 5.
-
The r e l a t i o n s h i p between PA and micrometer determined t h i c k - n e s s e s of copper p l a t e s .10
102103
FREQUENCY (Hz)
i n d i v i d u a l l a y e r o f t h e sample from F i g . 6.- The r e l a t i o n s h i p among t h e t h e c h a r a c t e r i s t i c frequency d a t a . thermal d i f f u s i v i t y and t h i c k n e s s of Fig. 5 shows t h e r e l a t i o n s h i p between m a t e r i a l s , and t h e chopping frequency PA and micrometer determined t h i c k -
n e s s e s of copper p l a t e s with s e v e r a l
d i f f e r e n t t h i c k n e s s . This f i g u r e shows c l e a r l y t h e r e l i a b i l i t y of o u r method i n measuring t h e t h i c k n e s s of s o l i d samples. F i n a l l y Fig. 6 d e p i c t s t h e measurable range o f t h e t h i c k n e s s of t h e m a t e r i a l s c a l c u l a t e d from Eq. ( 2 ) a s a f u n c t i o n of t h e
JOURNAL DE PHYSIQUE
t h e t h e r m a l d i f f u s i v i t y and t h e chopping frequency.
V. CONCLUSION.
The above T e s u l t s demonstrate t h a t it i s p o s s i b l e t o measure t h e t h e r m a l d i f f u s i v i t y o r t h i c k n e s s o f each i n d i v i d u a l l a y e r o f a m u l t i - l a y e r s o l i d sample, a s l o n g a s t h e f i r s t l a y e r of t h e sample i s o p t i c a l l y opaque, from t h e p h o t o a c o u s t i c c h a r a c t e r i s t i c frequency d a t a .
REFERENCES.
-.
Adams, M. J . , K i r k b r i g h t , G. F . , S p e c t r o s c . L e t t . 2(1976)255.
Adams, M. J., K i r k b r i g h t , G. F . , A n a l y s t =(1977)281.
Adams, M. J . , K i r k b r i g h t , G . F., Analyst =(1977)678.
Park, K. O., Yun, S. I . , S o l , C. S . , New P h y s i c s 21(1981)183.
Lepoutre, F . , C h a r p e n t i e r , P . , Boccara, C . , F o u r n i e r , D.,Technical D i g e s t o f 2nd I n t e r n a t i o n a l T o p i c a l Meeting on P h o t o a c o u s t i c Spectroscopy (Berkeley)
,
1981, p . MA3.C h a r p e n t i e r , P., Lepoutre, F., J. Appl. Phys. =(1982)608.
S u g u t a n i , Y . , Fujunami, M., B u l l . Chem. Soc. Japan =(1981)722.
Rosencwaig, A., Gersho, A., J . Appl. Phys. %(1976)64.
Touloukian, Y. S . , e t a l . , The TPRC Data S e r i e s Vol. 1 0 , Thermal D i f f u s i v i t y (Plenum, New York)
