PHONON POLARIZATION FROM PHONON IMAGING

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PHONON POLARIZATION FROM PHONON

IMAGING

J. Wolfe

To cite this version:

JOURNAL DE

PHYSIQUE

Colloque C10, supplement au n012, Tome 46, decembre 1985 page C10-821

PHONON POLARIZATION FROM PHONON IMAGING

J.P. WOLFE

Physics Department

and

Materials Research Laboratory, University

of

Illinois at Urbana-Champaign, Urbana. Illinois 61801, U.S.A.

Resume

-

Les interactions selectionnee's par la pol arisation des phonons de

hautefrgquences (1011 Hz) avec les dgfauts de crystaux peuvent &re

characterisegs par "phonon imaging1'.

Abstract

-

Polarization-selective scattering of high-frequency(l0ll~z)

phononsby defects can be characterized by phonon imaging.

rhe type of method one chooses to study propagation and scattering of acoustic

1

honons depends greatly on the desired frequency range. For example, ultrasonic

xperiments generally employ megahertz to gigahertz waves generated coherently by

f transducers. In contrast, phonons in the gigahertz to terahertz (1012 Hz) range

re frequent1

y studied by thermal conductivity and heat-pulse methods. The

peat-pul se technique involves time-of-f 1

i ght detection of incoherent,

i

on-equilibrium phonons, as first demonstrated in solids by von Gutfeld and

ethercot /I/ in 1964. Heat-pulse experiments are generally conducted at low

:

emperatures

( <

10 K) in order that the ball istic mean free path of high-frequency

honons exceeds the dimensions of a macroscopic crystal.

to good approximation both ultrasonic pulses and ballistic heat pulses travel at

,$he same velocity. despite their three-order-of magnitude difference in frequency.

21

Ultrasonical lyone produces a particular acoustic mode, wavevector, and

01

ari zation, whereas, in a heat pulse a1 1 modes, wavevectors, and polarizations

re generated. One of the features of the heat-pulse method is that longitudinal

nd transverse modes can be separated by their differing time of flights across the

rystal. This is an advantage over thermal conductivity measurements, which

nvolve an average over all modes. But strictly speaking the polarization, or

isplacement vector, of a given phonon is not selectable in a conventional

ime-of-f

1

ight experiment. Thus, the use of heat pulses to study

01 arization-sensitive scattering processes would seem to be limited.

his limitation can

be

overcome by examining the angular distribution of heat flux.

asically, the energy flux emanating from a point source of heat is highly

nisotropic, due to phonon focusing,

131

and the resulting intense structures in

he heat-~ulse Dattern can be readilv identified with ~honons

of qiven mode,

--

avevector-direction, and 01 arization

The identification requires a

flux, based simply on continuum elasticity

heory and the known elastic constants of the particular crystal.

he experimental measurement of phonon flux versus propagation angle is achieved by

recent extension of the heat-pulse technique known as phonon imaging.

/4/

In

his method a heat source (laser pulse) is raster-scanned across one face of the

rystal and a small bolometer detects the phonons arriving at a fixed point on the

pposite face. Experimental detai 1s may

be

found in the references. /4,5/

C10-822 JOURNAL DE PHYSIQUE

A phonon image o f L i F reported by Northrop, Cotts, Anderson and Wolfe 151 i s shown i n Fig. la. From a phonon focusing c a l c u l a t i o n o f t h i s c r y s t a l , it i s known t h a t t h e intense h o r i z o n t a l (H) and v e r t i c a l ( V ) r i d g e s are due t o f a s t transverse (FT) phonons, and t h e b r i g h t diamond a t t h e center is' due t o slow transverse (ST) phonons. This c a l c u l a t i o n also gives p o l a r i z a t i o n information. For example, t h e p o l a r i z a t i o n vector o f t h e h o r i z o n t a l ( v e r t i c a l ) FT r i d g e i s v e r t i c a l ( h o r i z o n t a l )

,

as i n d i c a t e d by t h e w h i t e arrows.

Fig. 1

-

(a) B a l l i s t i c phonon image o f heat-pulses i n undeformed L i F a t T = 2.2 K. (Ref. 5.) The center o f t h e photo corresponds t o phonons propagating al-ong

[loo].

The image spans 80' i n propagation d i r e c t i o n from l e f t t o r i g h t . The b r i g h t e s t regions demark f l u x singul a r i t i e s r e s u l t i n g from phonon focusing, as discussed i n Ref. 4. Hidden-line drawing shows r e l a t i v e i n t e n s i t i e s . ( b ) Image o f L i F c r y s t a l deformed as i n Fig. 2.

I f a selected o r i e n t a t i o n o f d i s l o c a t i o n s are introduced i n t o t h e c r y s t a l by p l a s t i c deformation, q u a l i t a t i v e changes occur i n t h e b a l l i s t i c h e a t - f l u x patern, 151 as shown i n Fig. lb. This sample was deformed 10% along t h e

[loo]

axis, which introduces [110] and [ l l O ] s l i p planes, as i n d i c a t d i n Fig. 2. The r e s u l t i n g h e a t - f l u x p a t t e r n d i s p l a y s a complete absence o f ST phonons. Also missing are t h e FT phonons i n the v e r t i c a l r i d g e . Remarkably, t h e h o r i z o n t a l FT r i d g e remains, i n d i c a t i n g t h a t these phonons w i t h v e r t i c a l p o l a r i z a t i o n are r e l a t i v e l y unscattered b y t h e d i s l o c a t i o n s . I n e f f e c t , t h e deformed c r y s t a l i s a c t i n g as a phonon

p o l a r i z e r . A d e t a i l e d analysis by Northrop e t a1 151 showed t h a t t h i s behavior was p r e d i c t a b l e using Granato's f l u t t e r i n g - s t r i n g model f o r phonon-dislocation

Ej-J

roo11

I

I

,'

.

.

'

Expansion

Fig. 2

-

I l l u s t r a t i o n o f s l i p planes induced by compressive f o r c e along

[loo],

w h i l e t h e c r y s t a l i s allowed t o expand along [OlO]. Loops o f edge and screw d i s l o c a t i o n s are shown. I n the phonon imaging experiments, t h e f r o n t (100) face i s covered w i t h a metal f i l m , and a superconducting bolometer i s deposited a t the center o f the r e a r (100) face.

This type o f experiment i n d i c a t e s t h a t t h e phonon imaging method has g r e a t p o t e n t i a l f o r probing t h e i n t e r a c t i o n o f high-frequency phonons w i t h extended defects. One drawback, however, i s t h a t t h e heat-pulse method involves a r a t h e r broad d i s t r i b u t i o n o f phonon frequencies; t h e maximum frequency i n a 10 K Planck d i s t r i b u t i o n i s 600 GHz. P o t e n t i a1 l y , superconducting tunnel - j u n c t i o n s o r o p t i c a l d e t e c t o r s can be used t o achieve frequency s e l e c t i o n .

This research was supported i n p a r t by the National Science Foundation under the MRL Grant DMR-83-16981.

REFERENCES

111 von Gutfeld, R. J., and Nethercot, A. H., Phys. Rev. L e t t .

2

(1964) 641. 121 Actually, under special c o n d i t i o n s i t i s p o s s i b l e t o observe slower heat pulses due t o phonon dispersion.

131 Taylor, B., Maris, H. J., and Elbaum, C., Phys. Rev. Lett.

23

(1969) 416. 141 Northrop, G. A., and Wolfe, J. P., Phys. Rev.

522

(1980) 6196. See also, Wolfe, J. P., Physics Today 33 (1983) 44.

151 Northrop, G. A., Cotts,T. J., Anderson, A. C., and Wolfe, J.

P.,

Phys. Rev 827 (1983) 6395.

/m

Granato, A. V., Phys. Rev.

111

(1958) 740.