Holographic study of crystal growth

Journal of Crystal Growth 13114 (19"/2) 68-72 Cc~North-Holland Publishing Co,

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H O L O G R A P H I C S T U D Y OF CRYSTAL G R O W T H *

M. E. GLICKSMAN and R. J. SCHAEFER

Metalhcryy Division, Naval Research Laboratory, Wa~hinyton, D.C, 20390, U,S.A. and J. A. BLODGETT

Optical Sciences Division, Ntwal Research Laboratory, Washin,qton, D.C. 20390, U.S.A. Holography has two main advantages over conventional microscopy for studies of crystal growth. Fi ~t. the hologram records the object in great depth, so that events occurring at unpredictable locations can be studied in the reconstructed image. Second, the hologram records :he phase as well as the amplitude of hc light scattered from the object, thus making possible several interferometric techniques. A holographic microscopy system has been constructed to study the growth of transparent crystals. H¢;io. grams were made of initially planar solid/liquid interfaces developing into cellular or dendritic morpholog,es, ! Several interferometric techniques were used to measure the development of interface features. The techm. =~ ques included double exposure holography, ~,hieh revealed the crystal growth between the two exposures, i and interference of the reconstructed image with a plane wave, which revealed surface contours. The use I of a relatively high-powered argon laser permitted exposure times as short as 30 microseconds, so thai i l rapidly growing crystals could be studied. lnterferograms of reconstructed holograms are shown, illustrating the development of micromorpholog.~ on solid/liquid interfaces. The measured shape of a dendrite tip is compared to that predicted by a ~heo:etical model.

1. Introduction

Studies of the micromorphoiogy of growing crystals ha~e usually been qualitative or, at best, limited to mczt,urements of the grosset features of such crystals. [:xpcrimental techniques for the detailed mapping of •,urface morpholog3, have simply not been availab!c. Thus. ~hile several detailed theories ~-8) have been developed to describe the steady-state or transient morphologies of solid/liquid interfaces, very little experimental data exist with which to compare the theoretical lesults, it is thus difficult to judge the validity of the ~e,~eral competing theories. Two areas of crystal growth in which there is a particular need four experimental measurements are the ~lctcrmination of the exact shape of the tip of growing dendrites, and the ob,,erv~!~i~m ~f the breakdown of an trustable planar solid:'liquid interface. Experimental ,.h~ta in these areas have until n ~ been too crude to differentiate bet~een the vario,,s c'~:.~peting theories ~vhich ~rv to explain these phen<)mcna. The new technique of holograph?,, now provides a I Ills paper ~as pl-esented w.i~il the :ollowing one as ~ combined in'~lted paper hy Nt. F. (ilick,,man.

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tool whereby extremely detailed quantitative data ca~, be obtained from ;~ single image of a solid/liquid interface. In order to make clear the a(,~antages of hoh,graphy over conventional photography, several of th~ principles and techniques available for making and re. constructing holograms will b.~ briefly described hcr~' 2. Holographic techniques

A hologram records tile amplitude and phase of c0' herent light scattered from an object illuminated by a'! laser. A high-resolution tilm may be used as the rec~,rd.~ ing medium. After development, the hologram is IIt,.i~ minated by coherent light to produce, by diffractio 1. ~ reconstructed ima e of the original obiect When t~c~ morphological features of interest occur on a mi :r¢'l~ scopic scale, it is important that this reconstru t:~~ili image have a spatial resolution commensurate witl tl~ff! scale of these features. The attainment of high re, ~it~i!! tion is possible only with very careful attention to ta~ .d.-!i anical stability of the holographic apparatus, qu ,Lt. of its optical components, exposure and processil z ,'~ the film, and alignment of the hologram for recons ut¢ii~ tion. These requirements combine to make hologr: ph!i!I considerably more exacting (and expensive) than "0~'~

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HOLOGRAPHIC

STUDY OF CRYSTAL G R O W T H

:ational photography. However, the image reconrutted from a hologram has several unique characterits which, for certain purposes, make it more useful an an image recorded by conventional photographic :ans. The three-dimensional qualities of a holograi c image a r e well'known - a microscope can be :used at any depth within the image to reveal features sharp detail. Less widely known, but perhaps even ~re useful, is the fact that the hologram reconstructs : phase, as well as the amplitude, of the light scattered i ~,m the original object. This phase information can be ~ r a c t e d by a variety of interferometric methods, to reveal precise dimensional measurements of the origimti object. Only if one takes advantage of these char~cteristics is holography advantageous over conventional photography.

TtON X RECONSTRUC BEAM

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A second useful technique involves comparing a reconstructed image from a single-exposure hologram with a coherent optical plane wave. A beam splitter is used to combine the reconstructed image and the plane wave (fig. l), and fringes then appear along lines of constant optical path difference. By changing the angle o f incidence of the plane wave, one can align the fringes in such a way as to facilitate the measurement of interesting features. Both of these techniques were used in a study of the growth ofcrystals of two low-entropy-of-fusion organic materials, camphene and succinonitrile. These materials have solidification behavior similar to that of metalsg), with cubic crystal structures and unfaceted solid/liquid interfaces. The transparency of these organic materials makes them superior to metals for optical crystallization studies.

3. Experimental procedure and results

A glass specimen chamber, with flat windows on the top and bottom surfacesl°)~ was filled with the test material. A nichrome wire heater warmed the trip of the chamber, melting all of the material except a thin layer on the bottom of the chamber. Freezing and melting were then controlled by varying the heater power. I . The specimen was illuminated by a collimated "'object . ~ y ~ - iI OLOGRAM beam" passing vertically down through the specimen chamber, then reflecting from a 4 5 mirror onto the ............................... --'+i+'--"~'~, SPLITT[R lilnl. A collimated "'reference beam" forming an angle of approximately 25 with the object beam. simuhancI ously struck the flint to form the hologram. Exposure times were in the range of 30 to 150 lasec, using the I. Opticalarrangement for producing interferencefringes 5145 ,~ line of an argon ion laser. For reconstruction. ecn reconstructed image of growing crystals and phme wave the hologram was illuminated to produce a real image. once beam. which was examined through a conventional microne useful techniqt,e for extracting phase informa- scope. The reconstructed image is seen as if one were from a hologram is double-exposure holography. looking tip through the bottom surface of the specimen holograms are recorded in sequence on the same chamber, i.e., through the solid. Fig. 2 shows a rcconstrtlction of a double-exposure of film, without mcving the film or the object. If ,hape of the object changes slightly in the interval hologram of solidifying succinonitrile. The first expoeen the two exposures, two images of the object sure was made .lust as the power to the specimen chamhe reeonstrtlcted, and optical interference effects ber heater was switched off and the second exposure be seen between these two images. This technique after one minute of crystal growth. The growth during ~les an observer to measure minute changes of this interval has resulted in changes in the optical path ies with highly irregular shapes, and, thus double- length for light transmitted through th ~ chamber, since '~sttre holography can be used to map out the in- solid and liquid have different indkes of refraction. ~logeneities in growth rate on the surface of a crystal. The two reconstructed images, therefore, show inter-

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M. -E. G L I C K S M A N , R. J. S C H A E F E R A N D J. A, B L O D G E T T

when reconstructed, one can examine features withiv bulk liquid with a microscope 6bjeetive o f short work ing distance and high numerical aperture, and thu achieve best resolution. The holographic image suffer:

Fig. 5. Fringes on tip o f growing dendrite, and comparison o f f r i n ~ traced from photograph wit h fringes calculated by as,um,ng dendrite is a paraboloid of revolution.

retlcal contours calculated by assuming that the den.. drite tip is a paraboloid of revolution. The experimental contours are difficult to follow where they bend sharply, as at the edge of the dendrite, nonetheless, the overall agreement between the theoretical model and these observations is satisfactory. There is no suggestion that branching has started anywhere within ten times the tip radius from the dendrite tip.

4. Discussion The results shown here illustrate some of the measurements ~ hich can be made only through holography. (_onvenuonal interference microscopy does not allow comparison of an object with itself at a later time, as ~n double-exposure ho!lography, nor ~.locsit ;qlow alignn:ent of fringes with rapidly changi~.g features. Moreo',,er, because the hologram can p r o d u c e , real image

These e x ~ r - i ~ e n t s illustrate the use of holograpl-~ c techniques to measure dendfile tip shapes and t e breakdown of unstable planar solid/liquid interfac~ ~. The studies of dendrites have shown that, near the ti ~, the dendrite does not differ greatly from a parabolo d of revolution. The crystal anisotropy is not strong enough to produce a detectable four-fold axial sy~,l. metry of the crystal in this region. Subsequent studies will measure the initial phases of side-branch development. The observations of ridges on the solid/liquid interface adjacent to grain boundaries and sub-boundaries have shown no indication that this disturbance propagates outward from the boundaries as a wave. other than as a very slight secondary ridge. Thus, the boundaries do not generate periodic structures in adjacent regions. The primary advantage of holography as a tool for crystal growth studies lies in its use for the detailed measurement of transient crystal shapes. These measurements are providing the first experimental data of sufficient detail to provide a rigorous test of many theories of crystal growth.

References I) G. P. Ivantsov, Dokl. Akad. Nauk USSR 58 (1947) 567. 2) D. E. Temkin, Dokl, Akad. Nauk USSR 132 (1960} 13 ~7. 3) M. E. Glicksman and R. J. Schaefer, J. Crystal Growth' I ~1967) 297. 4) G. R. Kotler and L. A. Tarshis, J. Crystal Growth 3,4 ~19 8~ 603. 5) W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34 I I~ 3) 323. 6) R. F. Sekerka, in: Crystal Growth, Ed. H. S. Pciser t Pel ninon, Oxford, 1967) p. 691. 7) S. R. Coriell and R. L. Parker, rcf. 6, p. 703. 8) G. R. Kotler and W. A. Tiller, tel'. 6, p. 721. 9) K. A. Jackson and J. D. Hunt, Acta Mel. 13 (19651 [2 2. 10) R. J. Schaefer and M. E. Glicksman, Met. Trans. I Il~ 01 ! 973.

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