MICROSPECTROSCOPY

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MICROSPECTROSCOPY

P. Piera_ski, B. Pansu

To cite this version:

P. Piera_ski, B. Pansu. MICROSPECTROSCOPY. Journal de Physique Colloques, 1985, 46 (C3), pp.C3-281-C3-293. �10.1051/jphyscol:1985322�. �jpa-00224639�

JOURNAL DE PHYSIQUE

Colloque C3, suppl6ment a u n03, Tome 46, mars 1985 page C3-281

MICROSPECTROSCOPY

P. p i e r a h s k i a n d B. P a n s u

Laboratoire de Physique des Solides, Universi t& Paris-Sud, B8t

.

91 405 Orsay Ceder, France

Resume - Nous proposons une n o u v e l l e methode d 1 6 t u d e des C r i s t a u x ColloFdaux, l a q u e l l e c o n s i s t e a u t i l i s e r un microscope r 6 f l e c h i s s a n t a s s o c i e avec un mo- nochromateur. Nous avons e n r e g i s t r e des s p e c t r e s des r e f l e t s de Bragg p r o - d u i t s p a r des m o n o c r i s t a u x C.C. e t c.f.c. en c o e x i s t e n c e dans un m6me 6chan- t i l l o n . Nous d i s c u t o n s egalement l e s f r a n g e s d ' i n t e r f e r e n c e p r e s e n t e s s u r l e s s p e c t r e s p r o d u i t s p a r l e s m o n o c r i s t a u x e t i n d i q u o n s comment l e s u t i l i s e r pour d e t e r m i n e r l e s formes c r i s t a l l in e s .

A b s t r a c t - We propose a new niethod o f s t u d y i n g C o l l o i d a l C r y s t a l s . The method c o n s i s t s i n an a s s o c i a t i o n o f a r e f l e c t i n g microscope w i t h a monochromatic i l l u m i n a t i o n . U s i n g t h i s e x p e r i m e n t a l set-up we o b t a i n e d t h e s p e c t r a o f Bragg r e f l e c t i o n s f r o m bcc and f c c s i n g l e c r y s t a l s c o e x i s t i n g i n t h e same sample o f C o l l o i d a l C r y s t a l . tle a l s o p o i n t o u t t h a t shapes o f s i n g l e c r y s t a l s , i n e q u i - l i b r i u m w i t h t h e l i q u i d phase, can be deduced f r o m Pendelltisung f r i n g e s o c c u r - i n g i n s p e c t r a o f Bragg r e f l e c t i o n s .

I - INTRODUCTION

I

-

-

( 3 " ) B l u e Phases o f c h o l e s t e r i c l i q u i d c r y s t a l s

a r e t h r e e examples o f systems, where l o n g - r a n g e c r y s t a l l i n e o r d e r o c c u r s on c o l l o i - d a l scales. Although t h i s o r d e r o c c u r s f o r d i f f e r e n t reasons i n t h e s e t h r e e examples, i t s consequences a r e s i m i l a r so f a r as o p t i c a l p r o p e r t i e s o f t h e s e systems a r e con- cerned. The " i r i d e s c e n c e " o f l a r g e samples ( o f a t e s t - t u b e s i z e , shown i n F i g . 1) i s p r o b a b l y t h e most obvious o f t h e s e p r o p e r t i e s and has been mentioned i n a number o f papers on c o l l o i d a l suspensions o r on opals, which a r e a v a i l a b l e i n such l a r g e quan- t i t i e s .

...

W

F i g . 1 - I r i d e s c e n c e o f l a r g e samples o f c o l l o i d a l c r y s t a l s : shadowed

c r y s t a l l i t e s " s p a r k l e w i t h f i r e s o f pure s p e c t r a l c o l o r " .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985322

C3-282 JOURNAL DE PHYSIQUE

Blue Phases, on t h e o t h e r hand, have been t r a d i t i o n a l l y studied i n very small samples of l i q u i d c r y s t a l s and t h i s a d j e c t i v e has not been used t o q u a l i f y t h e i r external aspect. On1 y very r e c e n t l y , i n experiments on v i s c o e l a s t i c p r o p e r t i e s of Blue Phases / I / , such l a r g e , t e s t - t u b e - s i z e samples have been slowly cooled from t h e i s o t r o p i c phase and t h e occurence of small c r y s t a l 1 i t e s , spark1 ing with f i r e s of pure s p e c t r a l c o l o r , was noted.

The i r i d e s c e n c e of a given s p e c t r a l c o l o r is a r e s u l t of Bragg r e f l e c t i o n s of v i s i b l e l i g h t on a p a r t i c u l a r system of c r y s t a l planes ( h , k , l ) . The use of l i g h t d i f f r a c t i o n f o r s t r u c t u r a l s t u d i e s of c o l l o i d a l c r y s t a l s ( I o t o 3") i s t h e r e f o r e just as common a s t h e use of X-rays t o study t h e s t r u c t u r e of ordinary c r y s t a l s .

I - 2 - Light d i f f r a c t i o n experiments

Numerous papers d e s c r i b e l i g h t d i f f r a c t i o n experiments / 2 , 3 / , which i n t h e i r p r i n - c i p l e s ressemble X-ray d i f f r a c t o m e t r y (Fig. 2) : a collimated source of l i g h t (X- rays) i s i n c i d e n t on a sample and t h e i n t e n s i t y I ( A ) of t h e r e f l e c t e d l i g h t (X-rays) i s measured a s a function of t h e wavelength A , f o r d i f f e r e n t incidence ( e i n ) and r e f l e c t i o n (aout) angles.

SAMPLE

h

FROM MONOCHROMATOR TO DETECTOR

Fig. 2 - Typical c o n f i g u r a t i o n of a l i g h t d i f f r a c t o m e t e r used f o r s t u d i e s of Colloidal c r y s t a l s .

In t h i s arrangement, t h e diameter of t h e l i g h t beam, a s i t p e n e t r a t e s i n t o t h e sample, i s u s u a l l y much l a r g e r than t h e dimensions of c r y s t a l l i t e s and t h e s p e c t r a I ( A ) may contain several Bragg p i c s correspondin? t o c r y s t a l l i t e s of d i f f e r e n t o r i e n t a t i o n s . The i n t e r p r e t a t i o n of d a t a from p o l y c r y s t a l l i n e samples i s d i f f i c u l t when t h e crys- t a l s t r u c t u r e i s not known. For example, an unambiguous d i s t i n c t i o n between S . C . and b.c.c. l a t t i c e s can only be nade when more than seven Bragg p i c s a r e p r e s e n t on t h e (X-ray) spectrum I (A). The d i f f i c u l t y of i n t e r p r e t a t i o n of t h e (1 i g h t ) s p e c t r a I ( h ) of Colloidal C r y s t a l s i s even l a r g e r due t o t h e f a c t t h a t t h e r e f r a c t i v e index n(h) i n t h e Bragg formula :

2dhk1 s i n e = Ahkl/n(x)

cannot be s e t 1, a s i n t h e case of X-rays /4/. In a l l t h r e e types ( I o t o 3') of Colloidal C r y s t a l s , t h e average r e f r a c t i v e index n(A) i s of t h e o r d e r of 1.3 t o 1.5 and i t s dependence on h cannot be neglected.

I - 3 - O p t i c a l microscopy

An o p t i c a l microscope i s a n o t h e r t o o l , w h i c h has been used f r e q u e n t l y t o s t u d y C o l l o - i d a l C r y s t a l s . Because i t s r e s o l u t i o n i s p r a c t i c a l l y l i m i t e d t o a b o u t 0.3 pm, a d i r e c t d e t e r m i n a t i o n o f t h e c r y s t a l s t r u c t u r e f r o m p o s i t i o n s o f i n d i v i d u a l p a r t i c l e s i s r e - served t o t h e case o f suspensions o f l a r g e (> 0.3 ym i n d i a m e t e r ) polymer o r m i n e r a l p a r t i c l e s . I n a l l o t h e r cases, t h e image seen i n t h e microscope i s a r e s u l t o f i n t e r f e r e n c e s o f w a v e l e t s f r o m many p a r t i c l e s ( u n i t c e l l s ) . Due t o t h e l o n g - r a n g e c r y s t a l l i n e o r d e r , t h e s e i n t e r f e r e n c e s g i v e r i s e t o a f o r m a t i o n o f monochromatic c o l o u r s . The u s e f u l i n f o r m a t i o n a b o u t t h e c r y s t a l s t r u c t u r e i s , t h e r e f o r e , c o n t a i n e d i n n a r r o w bands o f t h e v i s i b l e spectrum, c o r r e s p o n d i n g t o Bragg r e f l e c t i o n s o f wave- l e n g t h hhkl f r o m d i f f e r e n t systems o f c r y s t a l p l a n e s ( h k l ) .

When a t u n g s t e n lamp i s used as t h e l i g h t source i n t h e microscope, t h i s u s e f u l i n - f o r m a t i o n w i l l be masked by s c a t t e r i n g o f a l l o t h e r wavelengths ( A

+

I - 4 - P r i n c i p l e o f m i c r o s p e c t r o s c o p y

The aim o f t h e p r e s e n t paper i s t o o u t l i n e p r i n c i p l e s o f an a s s o c i a t i o n o f an o p t i c a l microscope w i t h a s p e c t r o m e t e r (monochromator) i n one e x p e r i m e n t a l set-up, which f o r b r i e f n e s s , can b e c a l l e d a microspectroscope. T h i s s e t - u p was b u i l t i n a manner t o correspond t o f o l l o w i n g o p e r a t i n g f e a t u r e s :

( I 0 ) - The monochromatic i l l u m i n a t i o n s h o u l d b e made t h r o u g h an o b j e c t i v e o f a m e t a l l u r g i c a l ( r e f l e c t i n g ) microscope, i n o r d e r t o a l l o w t o s e l e c t one c r y s t a l 1 i t e o f some p a r t i c u l a r o r i e n t a t i o n ( o r o f some p e c u l a r shape) and t o measure t h e spectrum o f l i g h t r e f l e c t e d by t h i s p a r t i c u l a r c r y s t a l l i t e .

( 2 " ) - D i r e c t o b s e r v a t i o n s s h o u l d be p o s s i b l e under monochromatic i l l u m i n a t i o n i n o r d e r t o e l i m i n a t e t h e broad-band " n o i s e " mentioned i n s e c t i o n 1-3.

( 3 " ) - We expected a l s o t h a t t h e monochromatic i l l u m i n a t i o n w i l l r e v e a l c r y s t a l d e f e c t s such as g r a i n b o u n d a r i e s and screw o r edge d i s l o c a t i o n .

The s e t - u p d e s c r i b e d i n t h e n e x t s e c t i o n , s a t i s f i e d t h e s e requirements. I t s p r a c t i c a l performances have been t e s t e d and a r e r e p o r t e d i n s e c t i o n 11-2. The use o f t h e m i c r o - s p e c t r o s c o p e i s i l l u s t r a t e d i n s e c t i o n 111 by two examples :

( I 0 ) - Coexistence between f.c.c. and b.c.c. c r y s t a l l i t e s i n suspensions o f p o l y s t y - r e n e spheres and

(2') - "PendellSsung" f r i n g e s i n c r y s t a l 1 i t e s o f f i n i t e t h i c k n e s s .

I n c o n c l u s i o n , ( S e c t i o n I V ) we w i l l i n d i c a t e o t h e r problems where t h e use o f t h e m i c r o s p e c t r o s c o p y has been s u c c e s s f u l o r i s p r o m i s s i n g .

I 1 - EXPERIMENTAL SET-UP I 1 - 1 - C o n s t r u c t i o n

A schema shown i n F i g . 3 d e p i c t s t h e p r i n c i p a l elements o f t h e e x p e r i m e n t a l set-up, d i s p o s e d on a g r a n i t o p t i c a l t a b l e ( f r o n M i c r o c o n t r B l e ) : t h e microscope i s o f an i n v e r t e d type, d e s t i n a t e d m a i n l y f o r o b s e r v a t i o n s b y l i g h t r e f l e c t i o n (Olympus PME). A t u n g s t e n lamp ( a p a r t o f t h e s t a n d a r d equipment o f t h e microscope) i s used as t h e l i g h t source. A small monochromator (Jobin-Yvon 20 VIS) i s o f h o l o g r a p h i c g r a t i n g t y p e and i s equiped f o r n u m e r i c a l c o n t r o l o f t h e wavelength A. The monochro- m a t o r and a n imaging l e n s L1 ( a c h r o m a t i c d u b l e t , f = 20 cm) a r e disposed on an

C3-284 JOURNAL DE PHYSIQUE

o p t i c a l bench (X95 from ~ i c r o c o n t r 6 l e ) which can be placed a t d i f f e r e n t heights, con- venient f o r i l l u m i n a t i o n o f t h e sample from above (transmission) o r from below ( f o r r e f l e c t i o n s t u d i e s ) . I f necessary, t h e sample can a l s o be i l l u m i n a t e d by a He-Ne l a s e r beam.

MONOCHROMATOR

6 ,SAMPLE LAMP

Fig. 3 - General view o f the microspectrometer.

7

The o p e r a t i o n o f t h i s set-up i s d e t a i l e d i n Fig. 4 :

- CHOPPER MONOCHROMATOR LAMP

-

f I - ~ ~ ~ - [ & ]

Fig. 4 - Scheme e x p l a i n i n g p r i n c i p l e s o f o p e r a t i o n o f the microspectrometer

i l l u m i n a t i o n : the w h i t e l i g h t beam from t h e lamp i s focused onto t h e i n p u t s l i t Sin o f t h e monochromator. The images o f Sin, formed i n t h e plane o f t h e o u t p u t s l i t Sout by t h e s p h e r i c a l g r a t i n g , are dispersed alono t h e h o r i z o n t a l a x i s A ( F i g . 5). The o u t p u t s l i t SOut i s then p r o j e c t e d through a l e n s L1 i n t o the plane o f t h e f i e l d diaphragm o f t h e microscope. F i n a l l y , the condenser and t h e o b j e c t i v e p r o j e c t t h e image o f Sout onto t h e plane o f t h e sample. For t h e o u t p u t s l i t w i d e l y open, t h e area o f .the sample i l l u m i n a t e d by t h i s means has roughly a form o f a trapeze (ABCD i n Fig. 5) and t h e c o l o u r o f 1 ig h t v a r i e s along t h e a x i s A . Using t h e f i e l d diaphragm

o r by changing t h e o u t p u t s l i t t o a narrower one ( f . ex. EFGH i n F i g . 5 ) , one can s e l e c t a v e r y sniall a r e a o f t h e sample. T h i s i l l u m i n a t e d area ( f . ex. ABCD o r EFGH

F i g . 5 - Area o f t h e sample, i l l u m i n a t e d by t h e l i g h t beam f r o m t h e monochromator, as seen i n t h e microscope.

i n F i g . 5 ) l o o k s ( i n t h e microscope) a l w a y s . t h e same when one changes t h e o b j e c t i v e b u t i t s r e a l dimensions a r e i n f a c t i n v e r s e l y p r o p o r t i o n a l t o t h e m a g n i f i c a t i o n s o f o b j e c t i v e s (see s e c t i o n 11.2).

D e t e c t i o n : t h e sample, i l l u m i n a t e d w i t h t h e monochromatic l i g h t , can be observed t h r o u g h t h e e y e p i e c e o r , a l t e r n a t i v e l y , t h e r e a l image o f t h e sample can be formed i n t h e p l a n e o f t h e p h o t o g r a p h i c camera. A photodiode, which i s s i t u a t e d t h e r e , mea- sures t h e i n t e n s i t y o f l i g h t IpD o f a p o r t i o n o f t h i s r e a l image, which s u r f a c e area and shape a r e s i m p l y t h o s e o f t h e p h o t o s e n s i t i v e a r e a o f t h e p h o t o d i o d e ( f o r example a c i r c l e of s u r f a c e . 1 cmZ). I n most cases, when one wants t o o b t a i n a quasi-normal i n c i d e n c e o f t h e i l l u m i n a t i n g beam, t h e a p e r t u r e diaphragm o f t h e microscope i s a l m o s t c l o s e d and, t h e r e f o r e , t h e l i g h t i n t e n s i t y IpD i s v e r y low. A synchroneous d e t e c t i o n (EGG 5206) was a p p l i e d t o measure a c c u r a t e l y t h e s e s m a l l l i g h t i n t e n s i t i e s . I 1 - 2 - S p e c i f i c a t i o n s

Wavelength range : t h e c h o i c e o f t h e elements o f t h e m i c r o s p e c t r o s c o p e was made i n f u n c t i o n o f i t s a p p l i c a t i o n f o r o b s e r v a t i o n and measurements u s i n g v i s i b l e 1 ig h t ; t h e l i g h t s o u r c e i s a t u n g s t e n lamp, t h e monochromator p e r m i t s t o scan between 200 and 900 nm, t h e p h o t o d e t e c t o r i s a s i l i c o n photodiode. The o v e r a l l s e n s i t i v i t y o f t h e m i c r o s p e c t r o s c o p e depends on s p e c i f i c a t i o n s o f t h e s e elements as w e l l as on c h a r a c t e r i s t i c s o f mu1 t i p l e lenses, m i r r o r s o r g l a s s p l a t e s i n t h e t r a j e c t o r y o f t h e l i g h t . A p r a c t i c a l t e s t o f t h e s e n s i t i v i t y was made b y p l o t t i n g t h e l i g h t i n d e n s i t y , measured b y t h e photodiode, when t h e sample was r e p l a c e d by a m e t a l 1 i c m i r r o r . The c o r r e s p o n d i n ? p l o t , shown i n F i g . 6a, has a maximum a t 590 nm and f a l l s o f f s y m e t r i - c a l l y t o a b o u t 10 % o f i t s maximum v a l u e a t

bin

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P a r a s i t i c l i g h t : The l i g h t i n t e n s i t y , measured by t h e photodiode ( i n t h e c o n f i g u r a - t i o n o f F i g . 4 ) , has two c o n t r i b u t i o n s : t h e u s e f u l ' o n e , f r o n t h e sample (whatever i t i s ) and t h e p a r a s i t i c one, f r o m r e y l e c t i o n s a t d i f f e r e n t i n t e r f a c e s i n t h e o p t i c a l path. Two t e s t s o f a l e v e l o f t h i s p a r a s i t i c l i g h t were made : f i r s t o f a l l , t h e

sample i n t h e g l a s s c o n t a i n e r was r e p l a c e d by p u r e water. The i n t e n s i t y o f l i g h t I ~ D was a b o u t 7 % ( f i g . 6b) as compared w i t h t h e r e f l e c t i o n by t h e m i r r o r . I n t h e second

t e s t , t h e g l a s s c o n t a i n e r was c o m p l e t e l y removed, so t h a t o n l y t h e o p t i c a l system c o n t r i b u t e d t o I ~ D . The i n t e n s i t y IPD measured i n such a c o n d i t i o n , was n e g l i g i b l e

( f i g . 6 c ) so we have concluded t h a t t h e r e f l e c t i o n a t t h e l o w e r s u r f a c e o f t h e g l a s s c o n t a i n e r was t h e p r i n c i p a l s o u r c e o f l i g h t i n t h e p l o t o f f i g . 6h. The o b v i o u s way t o suppress t h i s p a r a s i t i c r e f l e c t i o n c o n s i s t s i n u s i n g an o i l immersion o b j e c t i v e . I n p r a c t i c e , a 40X o b j e c t i v e (Olympus AP040) has been f o u n d t o work p r o p e r l y . S p e c t r a l r e s o l u t i o n : The d i s p e r s i o n power o f t h e monochronator i n t h e p l a n e o f t h e o u t p u t s l i t Sout i s 4 nm/mm. U s i n g a s l i t o f w i d t h 0.5 mm (EFGH i n f i g . 5 ) t h e expected r e s o l u t i o n o f t h e m i c r o s p e c t r o s c o p e s h o u l d be 2 nm. We have t e s t e d t h i s expected r e s o l u t i o n by r e p l a c i n g t h e t u n g s t e n lam? b y a He-Ne l a s e r . The p l o t , enre- g i s t e r e d u s i n g t h e l a s e r i l l u m i n a t i o n , i s shown i n F i g . 6d. As expected, i t i s o f a t r i a n g u l a r shape and i t s h a l f w i d t h i s 2 nm.

S p a t i a l r e s o l u t i o n : The dimensions W ' o f t h e a r e a o f t h e sample, i l l u m i n a t e d and observed t h r o u g h t h e o b j e c t i v e , depend on c h a r a c t e r i s t i c s o f t h e vihole o p t i c a l sys- tem ( l e n s L1, condenser and o b j e c t i v e ) w h i c h forms t h e image o f Sout i n t h e p l a n e o f t h e sample. A s i m p l e t e s t has shown t h a t , i n p r a c t i c e , W ' % W/M, where M i s a no- m i n a l m a g n i f i c a t i o n o f t h e o b j e c t i v e and W i s t h e w i d t h o f Sout.

F i g . 6

-

monocrystal o r i e n t e d w i t h (110) planes / / S.

U s i n g t h e o i l immersion o b j e c t i v e , M = 40 x, and t h e n a r r o w e s t o u t p u t s l i t (W=0.5 mm) one g e t s W ' = 12.5 Dm. W ' can be c o n s i d e r e d as a measure of t h e s p a t i a l r e s o l u t i o n of t h e m i c r o s p e c t r o s c o p e . I n o t h e r words, u s i n g t h e microscpectroscope, rre can measure s p e c t r a o f l i g h t r e f l e c t e d ( o r t r a n s m i t t e d ) by c r y s t a l l i t e s as s m a l l as 12,5 urn.

I t i s c l e a r t h a t t h i s s p a t i a l r e s o l u t i o n r e q u i r e s t h e use of a f i n i t e a p e r t u r e A % X / W 1 . Using Bragg r e l a t i o n ( I ) , one e s t i m a t e s t h a t , due t o t h e f i n i t e a p e r t u r e A , t h e r e f l e c t i o n p i c s w i l l have an "instrumental width" 6X/X % ( A / W ' ) ~ . With X = 500 nm and W ' = 12.5 11m one g e t s 6Xinstr. % 1 nm which i s l e s s than t h e s p e c t r a l width of t h e monochromator ( 6 ~ ) ~ ~ ~ . = 2 nm

111 - APPLICATIOI.IS OF- THE MICROSPECTROSCOPE 111.1. b.c.c.-f.c.c. phase coexistence

I t has been o f t e n mentioned /5,6,7/ t h a t in c e r t a i n suspensions of srnall polystyrene p a r t i c l e s (0.1 Dm i n diameter) dispersed i n water, h.c.c.-type c r y s t a l s may c o e x i s t with f.c.c.-type c F y s t a l s . Thus f a r , t h i s r e s u l t was obtained e i t h e r from d i f f r a c - t i o n p a t t e r n s , of a l a s e r bean!, from p o l y c r y s t a l l i n e samples /5/ o r from Kossel diagrams /7/. In both c a s e s , the s t u d i e s required t h e presence of l a r g e d e f e c t l e s s c r y s t a l 1 i t e s .

The microspectroscopy not only o f f e r s p o s s i b i l i t y of n!onitoring t h e processus of c r y s t a l growth b u t , a l s o , p e r n i t s an immediate d i s t i n ~ t i o n between t h e c r y s t a l l i t e s of d i f f e r e n t s t r u c t u r e s .

Let us consider an example of a sample shown i n f i g . 8. This suspension wade of polystyrene spheres 0.1 um i n diameter, dispersed i n water a t concentration

n = 9 x IOl3 part/cm3 was c r y s t a l l i z e d , f o r t h e f i r s t time, using an i o n i c exchange r e s i n and, then, was poored in a g l a s s r e s e r v o i r shoern i n f i g . 7. The temperature of t h e sample was p r o g r e s s i v e l y r a i s e d u n t i l a complete me1 t i n g of t h e c o l l o i d a l c r y s t a l occured and, t h e n , was s l o ~ r l y cooled down. The melting of t h e c o l l o i d a l c r y s t a l and i t s subsequent r e c r y s t a l l i z a t i o n has a l s o been obtained a t c o n s t a n t temperature by t h e following method : a very small c r y s t a l of saccharose was dropped i n t h e sample. Once f a l l e n a t t h e bottom of t h e r e s e r v o i r , t h e c r y s t a l disolved slowly. The saccharose d i f f u s e d slowly and, where i t s concentration n s was l a r g e r then some c r i t i c a l value n g r l t , t h e melting of t h e c o l l o i d a l c r y s t a l occured. Once t h e c r y s t a l of saccharose was completely d i s s o l v e d , t h e concentration ns decreased progressively due t o t h e continuing d i f f u s i o n . For ns

<

Fig. 7 - Cell used f o r t h e c o n t r o l l e d growth of t h e f c c and bcc c r y s t a l s : c - water c i r c u l a t i o n

The r e c r y s t a l l i z a t i o n always s t a r t e d a t t h e g l a s s s u r f a c e S so t h a t t h e c r y s t a l l i t e s had p r e f e r e n t i a l o r i e n t a t i o n s with r e s p e c t t o S. Figs 8 a and b show two views of t h e same portion of t h e sample, obtained under monochromatic i l l u m i n a t i o n of d i f f e r e n t wavelengths Xa % 527 nm and X b % 542 nm. As t h e c o n t r a s t i s reversed in t h e s e two

C3-288 JOURNAL DE PHYSIQUE

photographs, i t i s c l e a r t h a t t h e sample i s made o f two types o f c r y s t a l l i t e s g i v i n g Bragg r e f l e c t i o n s o f d i f f e r e n t wavelengths ha and Xb.

Fig. 8

-

+

The same r e v e r s a l o f t h e c o n t r a s t i s observed i n f i g s 9 a and b, which were taken u s i n g a h i g h e r m a g n i f i c a t i o n . The s i z e o f t h e l a r g e c r y s t a l l i t e i s about 200 pm.

I n o r d e r t o measure p r e c i s e l y t h e wavelengths Xa and Xb o f Bragg r e f l e c t i o n s from t h e two types o f c r y s t a l l i t e s , t h e f i e l d diaphragme o f t h e microscope was closed i n a manner t o s e l e c t one c r y s t a l l i t e ( o f type a o r b). The i n p u t and o u t p u t s l i t s were s e t t o t h e i r minimum widths (0.5 m) and t h e a p e r t u r e diaphragme was almost closed. The Bragg spectra, p l o t t e d i n such conditions, are shown i n f i g . 10. One measures

XFX

XrX

L e t us suppose now t h a t t h e c r y s t a l l i t e s o f t y p e a have t h e b.c.c. s t r u c t u r e and a r e oriented, as u s u a l l y /7/, w i t h t h e i r (110) planes p a r a l l e l t o S. As these c r y s t a l l i t e s c o e x i s t w i t h t h e c r y s t a l l i t e s b, we can suppose t h a t t h e i r d e n s i t i e s n a r e

s i m i l a r ( t h e same). If t h e c r y s t a l l i t e s b had f.c.c. s t r u c t u r e and were o r i e n t e d w i t h t h e i r planes (111 p a r a l l e l t o S, from nbcc = nFcc one would g e t :

. i i n

A f ~ ~

This t h e o r e t i c a l value i s i n agreement w i t h t h e r a t i o Xa/Xb = 0.972 measured i n f i g . 10. This agreement was v e r i f i e d i n many o t h e r samples, each time, when t h e coexistence o f two types o f c r y s t a l s occured. The i d e n t i f i c a t i o n o f bcc and f c c s t r u c t u r e s as w e l l as t h e p e c u l a r o r i e n t a t i o n s ( ( l l ~ ) ~ ~ ~ , (1 11 lf c c / / s ) o f c r y s t a l s

\rere confirmed by observation of defects c h a r a c t e r i s t i c o f these s t r u c t u r e s .

Fig. 9

-

Fig. 10

-

XY;

C3-290 JOURNAL DE PHYSIQUE

This p a r t i c u l a r a p p l i c a t i o n o f t h e microspectroscope t r e a t e d as an example, r a i s e s an i n t e r e s t i n g q u e s t i o n concerning t h e r e l a t i o n s h i p between t h e s t r u c t u r e o f a c r y s t a l and and t h e growth r a t e . Indeed, r e have observed t h a t t h e b.c.c. cr:lstals have grown p r e f e r e n t a i l l y under r a p i d c o o l i n a from t h e i s o t r o p i c phase, w h i l e t h e growth o f t h e f.c.c. c r y s t a l s always occured under v e r y slo\.r c o o l i n g . This problem i s o u t o f t h e scope o f t h e p r e s e n t paper and w i l l be considered elsewhere /8/.

111.2. "Pendell6sung" f r i n g e s

During t h e growth o f bcc o r f c c c r y s t a l s , we have observed, under monochromatic i l l u - n i n a t i o n , systems o f f r i n g e s (shown i n f i g . 11) "decorating" each c r y s t a l l i t e . A t f i r s t i n s i g h t these f r i n g e s were s i m i l a r t o those which would occur i n a t h i n l i q u i d l a y e r , where two l i g h t waves, r e f l e c t e d a t two i n t e r f a c e s o f t h e l a y e r , i n t e r f e r e . I f t h e f r i n g e s shown i n f i g . 11 were produced by an i n t e r f e r e n c e o f two \.laves, t h e i r o r d e r p should be r e l a t e d t o t h e l o c a l thickness h and t o t h e wavelength X by t h e formula :

p = 2hn ; where n i s t h e r e f r a c t i v e index ( s 1.33) ( 2 )

Fig. 11

-

As X % 500 nm, according t o t h i s r e l a t i o n , t h e c r y s t a l 1 i t e "a" i n f i g . 11 would have t h e t h i c k n e s s h = 0.564 vm, which i s j u s t enough t o c o n t a i n two l a y e r s o f p a r t i c l e s . Obviously, t h i s was n o t t r u e , because Bragg r e f ! e c t i o n g i v e n by t h i s c r y s t a l l i t e was v e r y i n t e n s e i n d i c a t i n g a presence of a t l e a s t few dozens o f c r y s t a l planes. Another experimental f a c t was a l s o i n c o n t r a d i c t i o n w i t h t h e equation (2) :

I n f i o . 12 a t o d, we show another b.c.c. c r y s t a l l i t e , i l l u n i n a t e d w i t l r t h e m o n o c h r o ~ t i c l i g h t o f d i f f e r e n t wavelengths A. For X = Amax t h e r e a r e no f r i n g e s a t a l l , w h i l e

f o r X = Xmax + 15 nm, two c o n c e n t r i c f r i n g e s decorate t h e c r y s t a l l i t e . It i s c l e a r t h a t such a m o d i f i c a t i o n o f t h e i n t e r f e r e n c e p a t t e r n cannot be explained by form.

(2).

We have found t h a t t h e f r i n g e s i n Figs. 11 and 12 r e s u l t from t h e i n t e r f e r e n c e o f waves r e f l e c t e d by l a r g e b u t f i n i t e number M o f c r y s t a l l i n e l a y e r s (110). This

"Pendell6sung" phenomenon i s e x p l a i n e d simply i n r e f /9/ : t h e i n t e n s i t y I o f l i q h t r e f l e c t e d from M c r y s t a l planes, d i s t a n t by dbCc, i s g i v e n by : 110

where Ak = 2.k0 = 2.7X/nr 2n

Fig. 12

-

110

C3-292 JOURNAL DE PHYSIQUE

Let X = X

Bragg - 61, where 6X/X

Bragg

<<

and

s i n 2 ME I %

For a given E, i n t h e c r y s t a l l i t e o f thickness h = h(x,y) o r M = Pl(x,y), t h e

i n t e n s i t y of t h e r e f l e c t e d l i g h t w i l l show minima corresponding t o f r i n g e s of o r d e r p, f o r :

110

2n

'bee

M(X,Y) = p(x,y) =

.

with 6X % 10 nm, Abcc 110 = 500 nm and p = 1 ( i n f i g . 12 c ) , one c a l c u l a t e s M = 50.

Knowing t h e p a t t e r n p(x,y) one can c a l c u l a t e t h e l o c a l thickness h ( x , y ) i n t h e whole c r y s t a l l i t e and, by t h i s means, determine i t s three-dimensional h a b i t .

In p a r t i c u l a r c a s e s . o f f i g s 11 and 12, we have concluded t h a t t h e i n t e r f a c e c r y s t a l / melt must have been smooth and rough and t h a t t h e o v e r a l l shape of t h e c r y s t a l ressembl ed a pl ane-convex 1 ens. ( f i g

.

4 .

, CRYSTAL \,

Fig. 13

-

The l o c a l t h i c k n e s s h(x,y) can a l s o be determined even when t h e whole p a t t e r n p(x,y) i s not known. This can be done by nieasuring t h e spectrum I ( x ) of l i g h t r e f l e c t e d from a very small (compared t o i n t e r f r i n g e d i s t a n c e s ) a r e a o f t h e c r ~ l s t a l The p l o t shown i n f i g . 14 shows such "PendellBsunq" o s c i l l a t i o n around t h e c e n t r a l

"Bragg" pic.

From p o s i t i o n s o f t h e minima one c a l c u l a t e s :

IV - CONCLUSION

Although t h e a s s o c i a t i o n of t h e r e f l e c t i n g microscope with t h e monochromator i s so simple i n i t s p r i n c i p l e and s o easy t o r e a l i z e , i t s i n t e r e s t f o r s t r u c t u r a l s t u d i e s of systems showing Bragg r e f l e c t i o n s of l i g h t , was not obvious thus f a r .

We aimed i n t h i s paper t o prove t h e u t i l i t y of t h e microspectroscope f o r such s t u d i e s . Besides t h e two examples of i t s a p p l i c a t i o n , given i n t h e previous s e c t i o n , we

would l i k e t o mention study of c o l o r s i n t h i n l a y e r s of c o l l o i d a l c r y s t a l s /10/ and r e c e n t works /11,12/, given independently, concerning t h e determination of s t r u c t u r e s of Blue Phases. The p o s s i b i l i t y of measuring wavelengths of Bragg r e f l e c t i o n s , from c r y s t a l l i t e s of

known

these s t r u c t u r e s and, p r e c i s e l y , t h e microspectroscopy o f f e r e d t h i s p o s s i b i l i t y .

Fig. 14

-

F u r t h e r s t u d i e s o f d i f f e r e n t types o f c o l l o i d a l c r y s t a l s by means o f t h e microspec- troscopy should b r i n g i n t e r e s t i n g c o n t r i b u t i o n s t o t h e understandino o f e q u i l i b r i u m and non e q u i l i b r i u m c r y s t a l shapes /12/. I n p a r t i ~ u l a r ~ ~ p h e n o m e n o n o f c r y s t a l growth deserves more d e t a i l e d s t u d i e s by nieans o f t h e microspectroscope.

REFERENCES

1. CLADIS P.E., JOANICOT M. and PIERANSKI P., submitted t o Phys. Rev. L e t t . 2. TAKANO K. and HACCIISU S., J. C o l l . I n t . Sc. 66 (1978)

3. HILTNER A. and KRIEGER I.M., J , Phys. Chem. 73 (1969) 2386

4. GUINIER A., "Theorie e t Technique de l a r a d i i F r y s t a l l o g r a p h i e " , Dunod, P a r i s 1956 5. WILLIAHS R., CRANDALL R.S., Phys. L e t t . 48A (1974) 225

ti. CLARK N.A., HURD A. J., ACKERSON B. J., N a c e , 281 ( 1 979) 57

7. PIERANSKI P., DUBOIS-VIOLETTE E., ROTHEN F. anTTRZELECK1 L., J. de Phys.

42

(1981) 53

8. PIERANSKI P., t o be published

9. KITTEL Ch., " I n t r o d u c t i o n t o S o l i d S t a t e Physics" WILEY (1966)

1G. PANSU B., DUBOIS-VIOLETTE E., PIERANSKI P. and ROTHEN F., Proc. o f Workshop on C o l l o i d a l C r y s t a l s , Les Houches 1984

11. MARCUS M., Phys. Rev. A 25 (1982) 2272

12. CLADIS P.E., BARBET-MASSm R. and PIERANSKI P., Phys. Rev. A

-