48
Journal o,1"Crystal Growth 13/14 (1972) 48-56 ~:, North-Hoihmd Publishing Co.
FORMATION OF MULTIPLY-TWINNED PARTICLES ON ALKALI HALIDE CRYSTALS BY VACUUM EVAPORATION AND THEIR STRUCTURES SHIRO OGAWA and SHOZO INO The Rest'arch Institute for Iron, Steel and Other Metals, Tohoku Unh~ersity, Sendal, Japan
During studies on the epitaxy and film growth of metals evaporated onto alkali halide crystals curie particles causing anomalous I I I electron diffraction spots and showing unusual shapes and contrasts n electron micrographs have been found. They have mainly been studied for Au on NaCI. As a result ,f analysis it has become clear that they have multiply twinned structures and are divided into three kin, ,. i.e., a pentagonal decahedron particle composed of five distorted tetrahedral twins, an icosahedral parti composed of twenty distorted tetrahedral twins and a rhombic shape particle consisting of five distort d t~ins. Stability of these multiply-twinned particles that have inherently strained structures is discussed, ~e total energies of them being calculated and compared with those of a fcc tetrahedron and a fcc Wu. rpolyhedron. There is a good agreement in sizes of multiply-twinned particles between calculalion and c ~ser~ation. Behavior of the particles during film growth of various metals on NaCI and KCI is describ, d. Finally, the origin of the particles is discussed, most of them being presumed to form by nucleation at tae earliest .,,rage of film growth.
I. Introduction
stages o f fihn g r o w t h were b a c k e d by c a r b o n evapo,'a. tion a n d isolated f r o m the substrates. As the mo~t reliable d a t a c o n c e r n i n g m u l t i p l y - t w i n n e d particles have been a c c u m u l a t e d for Au on N a C I , results o f observations on this system will be described. Fig. I is a typical diffraction p a t t e r n obtained from a film 25 ,,~ thick f o r m e d at 290 C. F o u r {2001 sp,,l, represent (001) orientation, a n d t w e n t y - f o u r {220} sp~f~ ari,,e f r o m t w o sets o f (111) orientation. However.
Allpress and Sanders~). a n d M i h a m a a n d Y a s u d a 2) f o u n d a b n o r m a l I I I spots on electron diffraction patterns o f epitaxial Au films, a n d the latter r e s e a r c h e r s a~cribed them to some c o m p o u n d particles which s h o w ed curi~u,, contrast~ on e~,,ctron m i c r o g r a p h s , b u t they did not elucidate the s t r u c t u r e of such particles. In o u r taborator~ the~e particles ~ e r e studied in detail m a i n l y u,,ing d a r k licld electron micn~scops, and it was reveal.:d that the\ dr¢ com+.osed o f rib, totted l e t r a h e d r a l tv, in~. and are called " m u l t i p l y - t w i n n e d particles"3'4). In the present paper we describe o b s e r v a t i o n s o n three kind., o f multiply-twinned particles by electron diffract+on and electron m i c r o s c o p y , detailed analyses o f their ,,tructure,,, discu,,sion on the stability o f the particles ba,,ed on the calculation o f energies, b e h a v i o r o f the particles during lilm gn~wth in various rnetals, and finally some considerali~ms a b o u t the origin o f the parlicle,,.
2. Electron dilfraction p a t t e r n s and electron m i e r o g r a p h s in the initial growth stages of ~old films formed by ~acuum evaporation on clea,agt: tace of rocksalt In the present w(~rk N a C I and KC.I were u',ed as substrafes, and were cleaved in an uitrahigh v a c u u m o f pressure 10 ~ ' 10 ~0 m m Hg. [!vaporated lilms that ~ e r e c o m p o s e d of m a n y small discrete p a r 6 c l e s at early
| -9
Fig. 1.
A typical electron diffraction pattern taken from ~, ~';
film 25 A thick deposited at 290 'C on NaCI (001) fi~ce de, c,! in ultrahigh vacuum. Abnormal twenty-four III spot'~ arc ~ ,,I
F O R M A T I O N OF M U L T I P L Y - T W I N N E D
P A R T I C L E S ON A L K A L I H A L I D E C R Y S T A L S
49
O
|
F! I
s'il tO00 ~
Iig. 2. A bright li¢Id electron micrograph taken from a Au lilm I00 .at thick formed at 350 C, .~hm~ing discrete particles ~i111 ~,arious shapes.
twenty-four somewhat elongated III spots which are divided into two groups ~1" twelve, one strong and one ~cak. result neither from normal ;,u particles with ,n0l) orientation nor from those with ( i i 1) orientation. Fig. 2 shows a bright field electron micrograph taken rrom a tilm 100 A thick evaporated at 350 C. A square e~,'~rtiele S and triangular ones T are normal particles ith (001) and t i l l ) orieatations, respectively. There :e, however, many hexagonal particles H, some pent:treal ones P and a rhombic one R on this micrograph. ~is last particle only appeared infrequently. These rticl~s have unusual shapes and were suspected 1o 'ate to abnormal { ! ! I] diffraction spots. In ligs. 3 a a n d 3e there are a bright tield image anti a ffraction pattern of a lilm IOOA thick formed at .t) C (b), (c) and (d) are dark field images corre~,anding to (a), formed by t, sing I I ! spots b, c and d , (e), respectively, it is remarkable that butterfly-like mtrasts are rotated by 6 0 each time f|'om (b) to (c) tttl from (c) to (d) and a line combining a head with tail of it butterfly is parallel to a linc combining the I
direct spot x~ith tile diffraction spot used to Form the image. Bright contrasts are often observed" at a head and a tail of a butterfly. Figs. 4a and 4b are a bright lield and a dark lield image of a pentagonal particle, the latter being formed by using one of II ! spots. !11 the latter image only a rhombic part is bright inside which a dark striation is scen, while in the former image contrasts of the thornbic part are reversed, and a triangular dark contrast appears in the lower part of the pentagon. Thus, pentagonal particles are also responsible for the appearance of abnormal I 1 I diflYaction spots. II1 (c) and (d) dark lield images of a pentagonal particle are seen. Thex were I\mned by using two different 220 .',pots. Fig. 5 shows bright ticld images of a rhombic particle in (a) and (a') and its dark field images m (b) and (b' (ct and it'), and [d) alld (d'). The fihn was 100 A thick and formed at 350 C. The three types of dark field images were i\mned by using a 200 spot, a 220 spot and a II1 spot, respectively. Different characteristic contrasts are observed for different diffraction spots -" 9
~0
SHIRO O G A W A AND S H O Z O I N O
O
darkfield image (b) formed by using a I|1 spot and (c) and ~t;J by using two different 220 spots.
l
t t g . 3.
Electron m l c r o g r a p h s a n d an electron d i f f r a c t i o n pat-
tern '~aken from a A u film 100 A thief. !ormed at 350 C . (a) A
~,r~',[ ticld image. (b), h.> a n d (d.b: I ' a [ ' : i k , J images o f t h e s a m e Iickl a~ In (a), formed by using l h o s e I I I spots ~,,,hich arc m a r k e d h: small circles h, c a n d d o n the ~.lifi:',~cOon p a t t e r n in (c), rc,pccti~ el',.
(d') Fig, 5. E l e c t r o n m i c r o g r a p h s o f r h o m b i c particles. (a~ a n d ~ Bright field images. (b) a n d ( b ' ) : 200 d a r k field images. (d) , ~J (d'): l I I d a r k tield images.
FORMATION OF M U L T I P L Y - T W I N N E D
F
PARTICLES ON ALAKL1 HALIDE CRYSTALS
F
L
B
~.
C
C
B
(at
(b)
0
0
0
Produced by nucleus
0
o
0
o
9~
~
OOO
0
llJ
220
o o
222
0
Produced by pr;mary twins
Produced by secondoty tw,ns
0
2o+
©
I ig, O. A slrucltll'¢ model I'or a pentagonal particle. (a): I)iling-lir) Of lixe tclrah~:dral t~ins. (b): A fi~e-I'old s)mmctr~ of{me set +,I fly(: distorled lulrahCdra ~sithout the gap. ~.i¢~(.'d along ()& diro:tion, I,.'): A diffraction p~lllcrH to b¢ expect+2d l'rom the 'rtlCttlrC
ill (;,1),
,:d. Also in this ca,,e a h n o r n m l I I I shot+, are related the structure oI' rhonll+ic particlc~,. %lrueture o f multiply-twimlcd particles
h e ,,,haws and dark fluid images oi" pcnhtgonal and igonal particle~, enpcci-dly the t r i a n g u l a r cotltrast ,-. pat t l ~ l C " ) i'll[IV D{." COIllpO-,¢ti 'ctrahedra. B;.tscd on II1F, ,,uggestmn, m u h i p l y +ned particle rm)du, b, were proposed For Ihe,,e parli• and also l'or a rhombic particle. i~ '. ~IRUI"IURI' ()I" I)INIAC;()NAI+ PAI{II('I.IS
i
+!!'+! \ structure rnodel in lig. 6a i,+ proposed fbr a , ntagonal particle. On a t c l r a h c d r , ) n ( ) A B C xvl+lt)se
ABC face adhcr+~, to the sub.',trate surface two t+trahedral twins O A B F and O A C I . pile up p r i m a r i l y , and on these further tv, o Ictrahedral IV,m s OAt:t:+ and OAI+I) pile up >,econdarily, resulting in the l'ormation o l ' a gap O A t ! I t . If this gap is lilled, the pile-up of tkc Ictrahcdra will look like a pentagon just as oh,served in it,, 5a. Actually no gap has ever been observed. A lattice imperfection resulting from disappearance of the gap ,.hould distribute inside the particle and gixc rise It) a straining o1" Ih+ structure, t:ig. 6b is a shape of such a particle viev, cd along OA direction. Bagley has tmcc ctmsid,.'red such a decahedron consisting of fix'e distorted telrahedra ~). In fig. 6c an electron diffraction p:+ttlerl~ resulting
i il
I.
t)
.52
SHIRO O G A W A AND S H O Z O I N O
E P0
F , --'''-
"'-'i"
F , "'-S-
'
,/
R
(a}
(b)
Fig. 7. A structure model for a hexagonal particle. (a): An icosahedron composed of twenty distorted tetrahedral txvin,, ~b~: A structure resulting from a simple pile-up of thirteen tetrahedra.
from a decahedral particle when the electron beam is incident perpendicularly upon the substrate surface is shown. It is clear that 111 reflections occur from secondary twins and two adjacent I l l spots, separated because of the gap, merge into a diffuse elongated spot as a result of the strain left by the disappearance of the gap. A consideration of possible orientations of the present structure results in the diffraction pattern actually observed. The dark field contrasts in fig. 4 are ~atisfactorily explained by the present model consisting nf tire twins of distorted tetrahedra. 3.2. SIRUCIURE OF HEXAGONALPARTICLES The pile-up of twinned tetrahedra is further continued until a structure composed of twenty tetrahedra is completed, as shown in fig. 7a. Many more gaps come from a simple pile-up of tetrahedra than in the case of a decahedral particle, but as before when these gaps disappear they leave strain in the particle. Thus this icosahedron is a structural model based on a hexagonal particle. A structure composed of thirteen tetrahcdra, as shown in fig. 7b, is used for explanation. The icosahedral structure can explain all the observed facts related to hexagonal particlc~. !!1 diffraction spots are diffused and elongated ow'ng ~o ,he strained { I I ! } planes as a result of the disappearance of the gaps. The characteristic contrast change obser ~,.,d !n fig. 3 isclearly understood. By using one of ! I I spots to form a dark field image, for instance, secondary twim O A E F and
O A D L and tertiary twins O H I U and OJIV in fig. 7b become bright at the same time producing butterfly. like contrasts, because they cause the I II reflection. and use o f other Ill s p o t s c a u s e s rotations of the contrasts. Contrasts corresponding to a head and a tail of a butterfly can be explained by double diffraction of a secondary and a tertiary twin neighboring along the incident beam direction, in fig. 3e many extra diffr.'tction spots are seen, and all of these extra ~,pots are also satisfactorily explained by double diffraction fron~ neighboring twins. A diffraction pattern to be expected from the above model is in good agreement with the observed diffr:tction pattern in fig. I, as is the case with a pentagonal particle. The strained structure of an icosahedral particl~ i~ considered to be no more than the one already desc, bed by Mackay as a dense non-crystallographic pack ng of equal spheres°). 3.3. S'IRUCTURE OF RHi)MBIC' PAR'tICLIThe structure of a rhombic particle is not as sin ,I,: as it appears. A structural model propo,ed in ti.,. explains well the external shape and the observed c x. tron microscopic contrasts o f a rhombic particle A i!: cube O ' B A ' C O D A E in (a), truncated at two ( I I l ) fa c,. adheres with its (001) faces to the substrate, and i ,ur I~ tetrahedra pile up on it, as shown in (c). A gap wl ch I~ should result from a simple pile-up disappears as in h¢
FORMATION A
OF MULTIPLY-TWINNED E
°
PARTICLES
ON ALKALI
HALIDE
CRYSTALS
5.~
A T ; Tetrohedron 0 ; Octahldron W ; Wulff-Polyhedron
I ; Icosahedron 0 ; Decahedron
&
l
0
Y
w
(c) o A P
D
0 G o
F
2~
2
~
r 1"4.*
! 1. . . . . . . . . . .
r,~,
r;,
Fig. 9. Depiction of the stability of an icosahedral and a decahedral particle.
L
mechanism. The term "'nucleus" was used here only for an easier understanding of the structures.
4. Stability of multiply-twinned particles
C
B (d) I.ig. 8.
A slructurc model for a rhombic particle. (a): A n cxtcrnal form of a nucleus with (001} orientation. (b): A projection
of Ihe nucleus on the film plane. (c}: A lop view of a particle c,,~sisUng of five twins showing a rhombic shape. (d): A ~iew ,,! the particle showing a pentagonal shape.
!,
,cs of a pentagonal and an icosahedral particle, leav.... the strain inside the particle. The shape viewed ,~g the OA direction appears as a pentagon in (d). re is thus a close resemblance between a pentagonal a rhombic particle. A diffraction pattern to be ex:d from the present structure agrees well with the rvation. The present structure explains well the field images in fig. 5 which were formed by using 220 and I I I spots. e above-mentioned particles o f three kinds with ~cteristic structures are given a general name "multwinned particles" in consideration of their twin,tructures. This name has been given only because structures are composed o f units having a twin-' relation with one another, it does not necessarily ,n that they are formed by some real twinning
Some theoretical treatments have been made in order to explain the stability of multiply-twinned particles in comparison with normal fcc particlesT"S). Here. ino's investigation will be introduced°). The total free energ} U including the cohesive energy, the surface energy, the adhesive energy, the elastic strain energy and the twin boundary energy was calculated for a decahedral and an icosahedral particle in comparison with a fcc tetrahedron, a fcc octahedron al~d a fcc Wulff-polyhedron. The elastic strain energy is characteristic of multiply-twinned particles that have heavily strained structures. In this calculation various energy values characteristic of each metal were estimated from experimental data. Fig. 9 depicts results ot" the calculation. The abscissa r is tile edge length of a polyhedron and a measure of the particle size, and in tile ordinate U-L,', is the sum of the energies less the cohesive energy U~. T, O, W, I and D mean a tetrahedral, an octahedral, a Wulff-pt, lyhedron, an icosahedrai and a decahedral particle, respectively. A Wulffpolyhedron particle has the lowest energy per volume of all the crystalline polyhedra, but for r <_ r~*,,an icosa-
!-9
SHIRO OGAWA
54
AND SHOZO
INO
T,~,n,E 1 Calculated critical diameters 2r,~*, 2rlt ° and 2rdt ° for essentially stable and quasi-stable states ;..~ = O (in free space) 2tit 0 2rd,°
2r,,,) ~
Au Ag Cu Ni Pd Pt Pb AI S, Ge -:,-Ve I~-Co
7~ ; 0 ton NaCI) 2riw* 2rt, ° 2rdl0
~At
<,%)
(A)
(A)
(A)
(A)
106.8 75.6 67.(, 43.1 49.0 56.3 97.5 29.3 27.6 15.5 44.0 97.6
436.3 306.9 279.1 212.6 263.9 238.4 446. I 486.1 133.7 109.8 200.6 375.9
3961 2905 2833 3385 2447 3784 2258 2199 830 725 1727 1574
102.1 69.8 63.2 39.0 44.8 51.9 89.2 15.4 25.1 13.3 40.2 90.9
409.4 273.5 259.2 189.4 234.6 213.4 398.5 406.4 119.2 96.9 179.2 337.8
3550 2373 2404 2765 1992 3118 i 852 1602 679 583 1417 1305
hedral particle is more stable than a Wulff-polyhedron particle. The reason for this lies in the a b n o r m a l strttclure o f the former. The condensation process of evaporated flints is not considered to be in equilibrium, and a tetrahedral particle is frequently found in e v a p o r a t e d films. Therefore. icosahedral particles with r <_ r ° are con~,idercd to be able to be quasi-stable. A decahedral particle is not stable for any size. bt, t quay, i-stable for =: r0,. It is suggested that a decahedral particle can grow larger than an icosahedral particle. -Fable I show~ values of calculated critical diameters _r,,,. :r,~ and --'u, ~ "" for particles of various metals grown m frec ~pacc and on Nuf..'l. ,'~, means the adhesive energ.~. There is no large difference in diameter values betx~een those in free space and those on a substrate. 0 (a~culated values of r~°, and rat should be c o m p a r e d x,.~th observed values of m a x i m u m sizes. There seems a g o o d agreement between observation and calculation. For in,,tance, the largest diameter of icosahedral particles o f Au formed on NaCI is about 400 A and diameter,, most freqt,ently observed converge into about 290 .\. and these values correspond to calculated values l',~r 3"!J,~ ;A!!d =.Vit "~ m = ~r?3 ,. "l'here_ is also an a~reement~ for :~ decahcdrat particle between the I~trgest observed dia.
.
.
.
.
.
l~lcter
;.It]t]
3t'udT"
--
#, Behavior of multiply-hvinned gro~vth
e.articles during film
" [ h e t':~rm;.tlio!l of mtdtipl~-twinned particle~ can be kno~vn from abnormal II] diffraction sDots, even if the\ ~.re n~,t direcllv observed on electron micrographs.
I
Fig. 10. A sequence o f e l e c t r o n diffraction patterns and bright field electron micrographs sho,.,,ing various stages of gro~th ol Au films deposited on NaCI cleavage fat:e ill 300 C. l ' h e mc:tT, thicknesses are 5 A, 20 A. I00 ,% and 500 A for la), (b), to) aml (dj, respectively,
Fig. I0 shows diffraction patterns and correspond micrographs o f Au tilms f o r m e d Oll NaCI at 300 C !~ 5 A, 20 A, 100 A and 500 A in m e a n thickness. Mt ply-twinned particles appear ah'eady in earlier st:, 'c~ !! of deposition, many more at 100 A and they aln disappear at 500 A as a result ot*"coalescence and ii ! stability o f these particles. {I I I } spots arising from multiply-twimled parl~ were f o u n d also from Ag tilms formed on NaCI as oil as KCI. In the case of Ni and Pd lilm~ lormed o,i lx, (! as well as KCI diffraction spots originated from rh tl~" bic particles were observed F r o m AI lilms grow, NaCI as well as KCI diffraction spols originaled 1 H l l multiply-twinned particles have never been obser :d Fig. I I represents the relation between the dcusil 9
FORMATION
I
n
OF M U L T I P L Y - T W I N N E D
• mean thickness
PARTICLES
ON A L K A L I
HALIDE CRYSTALS
55
5~
o
•
25~.
,
"
~OOa
o
5 3 ,D ;3
(a)
A
L
"
I00
200
(b)
4
300
40o
...... particle size (/~)
Fig. I I. A histogram of particle size of icosahedral particles in Au lilms 5 A, 25 A and I00 ,~,in the mean thickness.
(c)
the number of icosahedral particles observed on elec-
tron micrographs and the particle size for Au tilms 5 A, 25 A and 100 A thick Ibrmed on NaCI at 350 C. In Ihe thinnest lilm the greater part of Ihe isolated p:~rticles are icosahedral and the mean particle size is less than 100 A. With increasing tilm thickness the mean particle size increases but the total number of the particles decreases. The largesl and the mean particle size m the l i l m I00 A thick are abouI 4 0 0 / ~ and about 290 A, respectively. The cur,~cs in lig. I I show approximately the way the nt, mber of ico,~ahedral particlc~ decreases by coalescence. '.. Origin of formation of multiply-twinned particles Fig. I I shows that a large number of icosahedral rtieles are formed at a very early stage of lilm growth, 'smallest one being about 20 A in size. This Fact rgests that multiply-twinned particles may be formed nucleation from deposited atoms. On tile other hand, ~ilar observations by cine lilms have been reported, I here the multiply-twinned particles are formed by ,~slh or coalescence of normal particles t o. ~~). Such ,topics were, however, very few, and most of multi-twinned particles usually observed are not considerto form by such processes. It wilt be natural to ~ider that most of them nucleate at the earliest stage tilm growth. tig. 12 explains the formation proce',,scs o f an icosadral nucleus in (a) and (b), decahedral nucleus in (c) I-9
,
(d)
Fig. 12. Structures of nuclei of multiply-tv~inned particles, lb): A nucleus of an icosahedral particle, the process o f its formation being sho~n in (a). (c): A nucleus of a dccahedral particle. (d): A t+ucleus of a rhombic particle.
and a r h o m b i c particle in (d). The plane of illustration is parallel to tile substrate surface. OABC in (a) is a tetrahedral nucleus, but positions D, E and F are those ~hich are not permitted in a fcc lattice, and when the adhesive lbrce between metal atoms and subqrate ions i~ smaller than the cohe.~i~e l\~rce bet~secn metal atoms.
these positions will be occupied. Po.silions G, H and i are also abnormal positions. Thus a v,ucleus forms which is composed of O and tweh'e atoms surrounding it, as shown in (b). This nucleus has two xalues of bond length, one of which connects O with the ,~urrounding atoms and tile other of which connects, e.g., A with B and is about 5°. longer. An icosahedral nucleus possesses, therefore, essentially a strained structure. This is due to the fi~Cl thai an energy increase caused by the straining is overcome by an surface energy decrease caused by its shape. This nucletis can grow tip to an icosahedral particle having lhe spontaneously slrained structure. In (c) a nucleus of a decahcdral particle is shown. This nucleus has also a strained structure with three kinds of bond length represented by CO, OA and AB. In ld) the growing process of a nt~cleus of a dlombic particle is shov, n. This has also a strained structure.
56
SHIRO OGAWA AND SHOZO | N O 3) 4) 5) 6) 7)
It is very interesting t h a t t h e r e are those a n o m a l o u s a t o m i c distanc¢~ in the s t r u c t u r e s o f m u l t i p l y - t w i n n e d particles w h i c h are n o t f o u n d in the n o r m a l lattice, as c a n be u n d e r s t o o d f r o m the a b o v e . This m a y b e the r e a s o n f o r the unusual a t o m i c distances t h a t h a v e s o m e times b e e n observed ~2).
8) 9) 10)
References D J. G. Allpress and J. V. Sanders, Phil. Mag. 10 (1964) 645. ~) K. Mihama and Y. Yasuda, R e a d before the Meeting of Phy.~,. Soc. Japan held October 1964; J. Phys. 3oc. Japan 21 ~1966) 1166.
1-9
11) 12)
S. Ino, J. Phys, Soc. Japan 21 (1966) 346. S. Ino and S. Ogawa, J. Phys. Soc. Sapan 22 (1967) 1365. B. G. Bagley, Nature 208 (1965) 674. A. L. Mackay, Acta Cryst. 1$ (1962) 916. Y. Fukano and C. M. WaYman, J. Appl. Phys. 40 (1969) 1656. J. G. Allpress and J. V. Sanders, Australian J. Phys. 23 (1970} 23. S. Ino, J. Phys. Soc. Japan 26 (1969) 1559; 27 (1969) 941. G. Honjo and K. Yagi, Read before the Intern. Conf. or Thin Films held in Boston on 28 April-2 May, 1969. Private communication. H, Morimoto and H. Sakata, J, Phys. Soc. Japan 17 (1962 136.