QUASICRYSTALLINE AND CRYSTALLINE ATOMIC STRUCTURES OF Al4Mn

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QUASICRYSTALLINE AND CRYSTALLINE ATOMIC STRUCTURES OF Al4Mn

M. Audier, P. Guyot

To cite this version:

M. Audier, P. Guyot. QUASICRYSTALLINE AND CRYSTALLINE ATOMIC STRUCTURES OF Al4Mn. Journal de Physique Colloques, 1986, 47 (C3), pp.C3-405-C3-414. �10.1051/jphyscol:1986341�.

�jpa-00225753�

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JOURNAL DE PHYSIQUE

Colloque C3, supplbment au n o 7, Tome 47, juillet 1986

QUASLCRYSTALLINE AND CRYSTALLINE ATOMIC STRUCTURES OF Al,,Mn

M. AUDIER' and P. GUYOT

Laboratoire d e Thermodynamique et Physico-Chimie MBtallurgiques (UA-CNRS n o 29), E.N.S.E.E.G., BP. 75, P-38402 Saint-Martin- d l H & r e s Cedex, France

Resume

-

Une approche de l a n o d e l i s a t i o n s t r u c t u r a l e de l a phase decagonale e t de l a p h a s e t r i g o n a l e d a n s l ' a l l i a g e AlgoHnpo e s t presentee, s u r l a base d ' u n i t e s icosaedriques e x i s t a n t dans l a phase icosaEdrique e t l a phase c u b i - que a (WltinSi). Des s t r u c t u r e s en anneaux sont propos@es. Des mesures de den- s i t & de l a phase icosaPdrique e t de l a phase T suggerent p a r a i l l e u r s l ' e x i s - tence de t r i a c o n t a e d r e s concentriques aux icosaedres dans ces deux phases.

A b s t r a c t

-

An approach o f t h e s t r u c t u r a l m o d e l l i n g o f t h e decagonal phase and o f r i g o n a l phase i n Al&oPln20 i s given, i n terms o f t h e icosahedral u n i t s e x i s t i n g i n the icosahedral phase and t h e c u b i c a phase (AlNnSi). S t r u c t u r e s o f r i n g s a r e proposed. Measurements o f t h e d e n s i t y o f t h e icosahedral and T phases suggest furthermore t h e existence o f t r i a c o n t a h e d r a c o n c e n t r i c t o t h e icosahedra i n b o t h phases.

I n previous papers /1/ /2/ /3/, a s t r u c t u r a l m o d e l l i n g o f t h e icosahedral phase (i-phase) i n Al+ln o r AlMnSi has been g i v e n i n terms o f a b a s i c Mn s k e l e t o n obtained by t h e connection o f double Al-t;n icosahedra, maintained i n p a r a l l e l o r i e n t a t i o n by octahedral bonds along t h e icosahedron 3 - f o l d axes. This skeleton i s e v i d e n t l y loose, due t o a n icosahedra average c o o r d i n a t i o n number o f o n l y 5.5, and has t o be f u r t h e r dressed i n o r d e r t o achieve t h e c o r r e c t d e n s i t y .

I n t h e f i r s t p a r t o f t h e paper we present new r e s u l t s o f measurements o f t h e i-phase density, which shows t h a t i t s p r e v i o u s l y determined values /4/ /5/ a r e underestima- ted. A p o s s i b l e r o u t e t o dress t h e s k e l e t o n i s then o u t l i n e d , i n r e l a t i o n w i t h a de- c o r a t i o n g i v e n i n /3/.

I n t h e second p a r t , we propose a d e s c r i p t i o n o f t h e decagonal o r T phase i n Alqtln, on t h e basis o f l a y e r s o f icosahedra t r i a c o n t a h e d r a u n i t s and r i s e some questions about Penrose t i l e s i n t h e s t r u c t u r e .

A t t h e end we r e l a t e t h e probable t r i g o n a l s t r u c t u r e o f Alq?n, formed by c r y s t a l l i - z a t i o n o f t h e i- and T-phases,to a p e r i o d i c s t a c k i n g o f icosahedra, as i n t h e i- phase, which b r i n g s a common concept i n m o d e l l i n g q u a s i - c r y s t a l s and c r y s t a l s i n t h i s system.

I 1

-

DENSITY AND BlODEL STRUCTURE OF THE 1-PHASE

The d i f f i c u l t y t o measure c o r r e c t l y t h e d e n s i t y o f t h e i-phase i n Allln o r i g i n a t e s i n t h e presence o f an unknown volume f r a c t i o n o f a f c c AlMn s o l i d s o l u t i o n i n as- quenched AlggMn14, and t h e coexistence o f i- and T-phase i n as-quenched A1 011

(which has t h e same c a n p o s i t i o n as t h e i- o r T-phases, i .e. w i t h o u t o r negf,gf6Pe f c c . A l ) Schaefer e t a l . /6/ have shown, i n t h e l a s t case, t h a t t h e T phase f o r m a t i o n

l e a v e a t PCchiney-Cegedur. C e n t r e de Recherches. BP 24, F-38340 Voreppe (France)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986341

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C3-406 JOURNAL DE _PHYSIQUE

i s favoured by low quenching r a t e and i t s f r a c t i o n i s reduced w i t h r e s p e c t t o t h e i-phase a t i n c r e a s i n g quenching r a t e .

iie have t h e r e f o r e measured t h e d e n s i t y o f melt-spun A l g ~ M n ~ ~ v a r y i n g t h e quenching c o n d i t i o n s , and determined i n each case by transmission e l e c t r o n microscopy t h e r e - l a t i v e p r o p o r t i o n o f b o t h phases : a t low quenching r a t e , t h e ribbons a r e n e a r l y pure T phase, whereas f o r t h e h i g h e s t quenching r a t e used, i t s volume f r a c t i o n was estimated up t o .5. The values obtained i n Algg?lnl4, AlggMn20, A174.2Mn20Si5.8.by two techniques, immersion weighting, and pycnometry t o helium gas a f t e r c l e a n i n g t h e samples by outgassing under vacuum a t v a r i o u s temperatures, a r e gathered i n Table 1. The pycnometry was a l s o used due t o t h e i m p o s s i b i l i t y o f p e r f e c t c l e a n i n g o f t h e very b r i t t l e ribbons f o r t h e f i r s t method.

Table 1

I t appears from these r e s u l t s : A1 1 oys

A186Mn14 A 1 8 ~ M n 2 ~

A174.2Wn20Si5.8

4

i- i and T phases i n A180iIn20 have the same d e n s i t y (and stoichiometry Alqkln)

.

ii- t h e d e n s i t y measured f o r AlggMnl4 i s t h e same as t h i s p r e v i o u s l y measured /4/ /5/, which g i v e s a volume f r a c t i o n o f about 60 % f o r t h e f c c A1-3 at.% Mn m a t r i x /7/.

Quenching r a t e

h i g h middle

1 ow

iii- i f one takes 3.75 g f o r t h e b e s t e s t i m a t e o f the d e n s i t y o f t h e i- phase i n Iln Si5 8, i t s d e n s i t y i n Algolln20 should be a t l e a s t 3.7 g cm-3.

From cooper erZkoZPnsori /8/, t h e d e n s i t y o f t h e a-phase i s 3.64 g cm-

.

d e n s i t y ( g

immersion weighting technique 3.27

+

0.01

3.57

+

.02 3.55

+

.01 3.57 ? .02 3.63 t 0.02 He pycnometry

3.64 (outgassing 48h.

a t 100°C) 3.75 (outgassing 48h.

a t 400°C)

The a n a l y s i s o f t h e double A1-Rn icosahedra s k e l e t o n shows t h a t i t s d e n s i t y i s equal t o 1.

a

7 o r 1.34 g depending on t h e chosen rhombohedra1 edge l e n g t h 4.6 o r 4.85 (see / 3 / ) . This d e n s i t y becomes equal t o 3.20 o r 2.7 g cm-3 r e s p e c t i v e l y , f o r the A14Efn stochiometry, which i s approximately s a t i s f i e d f o r t h e rlackay d e c o r a t i o n (A13.5Mn)/3(. There

i s

therefore a need t o add more atoms i n t h e modelled s t r u c t u r e . The suggestion t o p o s i t i o n these atoms on t h e v e r t i c e s o f a rhombic t r i a c o n t a h e d r o n surrounding the b a s i c icosahedron /3/, as shown i n F i g . 1, seems t o be t h e b e s t way t o achieve the r e q u i r e d d e n s i t y . Such a decoration, w i t h reference t o d i f f r a c t i o n data and d e n s i t y wi 11 be pub1 i s h e d elsewhere.

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F i g . 1 : a) P r o l a t e and o b l a t e rhombohedra1 t i l e s , decorated by icosahedra

b) A d d i t i o n of one triacontahedron on each icosahedt-QtI. (See r e f . /3/ f o r d e t a i l s ) . I 1 1

-

DECAGONAL PHASE

Tne atomic s t r u c t u r e o f t h e decagonal o r T phase i s s t i l l unknown. From t h e forma- t i o n c o n d i t i o n s and t h e i r r e s p e c t i v e e v o l u t i o n upon heating, i t i s nevertheless c l e a r t h a t i- and T-phases a r e c l o s e l y r e l a t e d and t h e atomic u n i t s used w i t h suc- cess t o model t h e i-phase should be h e l p f u l 1 t o e l u c i d a t e t h e T phase s t r u c t u r e . we make here two suggestions about t h e T s t r u c t u r e :

i- t h e f i r s t one concerns t h e p e r i o d i c i t y o f t h e T phase d i f f r a c t i o n p a t t e r n p a r a l l e l y t o i t s 10 f o l d - a x i s , which from o u r study o f t h e o r i e n t a t i o n r e l a t i o n - ships w i t h t h e i-phase / 9 / appears t o be 12.69

A .

F i g . 2 shows a buckled r i n g o f 8 t r i a c o n t a h e d r a a l t e r n a t i v e l y connected through a common f a c e and a comnon o b l a t e a rhombohedron. I n terms o f t h e i n t e r n a l double A1-Mn icosahedra, t h i s means t h a t tLey a r e e i t h e r f i r s t - n e i g h b o u r s o r second neighbours (see /3/). Such a r i n g i n t r o - duces i n p r o j e c i o n a p e r i o d P = 2ar$ ($I = golden number) along t h e 10 f o l d - a x i s . K i t h ar = 4 - 8 5

k,

^P⁼²^{x 12.69}

^11,

i . e . t h e double o f t h e observed p e r i o d i c i t y , which means t h a t a f t e r completion o f t h e s t r u c t u r e a m i r r o r plane can be found ?

ii- p e r p e n d i c u l a r l y t o t h e 10 f o l d - a x i s , t h e h i g h r e s o l u t i o n transmission

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JOURNAL DE PHYSIQUE

Fig. 2 : Ring o f 8 rhombic t r i a c o n t a h e d r a s h a r i n g a f a c e o r a p r o l a t e a r rhombohedron. Cormon faces and c o n o n rhombohedra a r e dashed. The p r o j e c t i o n a x i s i s a 2- f o l d a x i s o f t h e T phase

e l e c t r o n micrographs a r e a p e r i o d i c /9/ and s i m i l a r i t y w i t h a 2 dim- Penrose t i l i n g i s a p r i o r i expected. To t h i s respect, some i n f o r m a t i o n s a r e brought i n F i g . 3, which i s a h i g h r e s o l u t i o n image taken along t h e 10 f o l d - a x i s o f an heterogeneous T phase d e n d r i t e t i p . The d i f f r a c t i o n p a t t e r n has a unique 10 fold-symmetry, w i t h however i n t e n s e d i f f u s e s c a t t e r i n g r i n g s i n d i c a t i v e o f d i s o r d e r . As shown i n t h e micrograph, p a r t o f t h i s d i s o r d e r o r i g i n a t e s i n t h e coexistence o f r o t a t e d T domains and p e r i o d i c dots domains. On t h e very t h i n edge o f t h e sample, f i v e branches s t a r s are d i s t i n g u i s h e d , which correspond t o t h e l a r g e s t w h i t e d o t s i n t h e t h i c k p a r t s . An enlargement o f t h e s t a r s r e g i o n i s shown i n F i g . 4 ; except i n t h e r e g i o n A, t h e image appears as a t i l i n g o f s t a r s and f l a t t e n e d hexagons, which can themselves be subdivided i n t o elementary Penrose rhombi

.

However, and w i t h r e f e r e n c e t o Levine

/ l o / ,

such a rhombi p a t t e r n does n o t s a t i s f y t h e dual Ammann g r i d r e q u i r e d by a Penrose t i l i n g .

I V

-

TRIGONAL Al,bln PHASE

Both i and T phases t r a n s f o r m a t T > 750°C i n t o a unique phase r e p o r t e d t o be hexagonal w i t h a = 28.4

A

and c = 12.43

8

/11/. A s e l e c t e d area d i f f r a c t i o n p a t t e r n o f t h i s phase i s shown i n F i g . 5, taken w i t h t h e e l e c t r o n beam p a r a l l e l t o t h e c a x i s ; the almost superimposition o f t h e i n t e n s e d i f f r a c t i o n spots w i t h those o f t h e i- phase i n a 3 f o l d - o r i e n t a t i o n , suggests t h a t t h e phase should be t r i g o n a l i n s t e a d o f hexagonal. I n t h i s perspective, a s k e l e t o n o f icosahedra connected by octohedral bonds along t h e i r 3 fold-axes, as i n t h e i-phase, must support t h e t r i g o n a l s t r u c - t u r e . Such a s k e l e t o n i s drawn i n F i g . 5d) and i s superimposed on t h e h i g h r e s o l u t i o n micrograph o f F i g . 6 taken w i t h a beam p a r a l l e l t o t h e c a x i s . I n t h i s skeleton, t h e icosahedra c o o r d i n a t i o n number i s equal t o 4, and some p l a n a r s t r u c t u r a l f a u l t s , f r e q u e n t l y observed i n t h e t r i g o n a l phase may be explained i n terms o f changes o f icosahedra connections, as shown i n F i g . 6 and 7.

V

-

CONCLUSION

We have shown t h a t t h e icosahedron, a t t h e basis o f t h e s t r u c t u r e o f t h e cubic a

phase AlMnSi and o f t h e icosahedral phase i n AlMn and AlMnSi /3/, can a l s o be consi- dered as a packing u n i t i n t h e decagonal phase and t h e presumably t r i g o n a l c r y s t a l A1 $.In.

buckled r i n g s o f 8 icosahedra, w i t h 4 octahedral f i r s t neighbours bonds, seem t o be r e l a t e d w i t h the T phase p e r i o d i c i t y along t h e 10 f o l d a x i s , whereas i n t h e t r i g o n a l phase r i n g s o f 6 icosahedra, a l l connected i n f i r s t neighbouring p o s i t i o n s by octa-

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F i g . 3 : Heteregeneous T phase d e n d r i t e . 36' r o t a t e d a p e r i o d i c domains and p e r i o d i c domains a r e i n d i c a t e d .

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F i g . 5 : D i f f r a c t i o n o a t t e r n s o f A14Mn c r y s t a l a l o n g t h e c a x i s ( a ) and o f t h e i- ohase along a 3 f o l d a x i s ( b ) . S u g e r i m ~ o s i t i o n o f t h e two n a t t e r n s ( c ) : t h e i-nhase 2 f o l d - a x e s a r e i n d i c a t e d i n c a p i t a l l e t t e r s , i t s i n t e n s e r e f l e x i o n s a r e c i r c l e d . Icosahedra s k e l e t o n o f t h e t r i q o n a l nhase n o r m a l l y t o t h e c axis(d).

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C3-412 JOURNAL DE PHYSIQUE

Fig. 6 : High resolution micrograph of t h e trigonal A14Mn phase. Its proposed ico- sahedra skeleton is suoerimposed with a faulted region indicated by arrows. In insert : model of the icosahedra skeleton for the centered 6 white dots rings.

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F i g . 7 : S t r u c t u r a l d e f e c t s i n the A14Wn t r i g o n a l phase seen edge on. They a r e con- s i s t e n t w i t h v a r i a t i o n s i n t h e icosahedra connections.

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J O U R N A L DE PHYSIQUE

REFERENCES

/1/ Guyot, P. and Audier, M., P h i l . Mag. B 52 (1985) L15.

/2/ Audier, M. and Guyot, P., P h i l . Mag. B (1986) L43.

/3/ Guyot, P., A u d i e r , M. and Leauette, R . , T h i s workshoo.

/4/ K e l t o n , K.F., and Wu, T.W., A o o l . Phys. L e t t . 46 (1985) 1059.

/5/ Chen, H.S., Chen, C.H., Indue, A. and Drause, J;f., Phys. Rev. B

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(1985) 1940.

/6/ Schaefer, R.J., Bendersky, L.A., Shechtman, D., B o e t t i n g e r , W.J. and Bianca- n i e l l o , F.S., Met. Trans. ( o r e p r i n t ) (1986).

/7/ Guyot, P., J . M i c r o s c . Spectrosc. E l e c t r o n . , 10 (1985) 333.

/8/ Cooper, M. and Robinson, K., A c t a C r y s t .

20

( m 6 6 ) 614.

/9/ Guyot, P. and Audier, M., J. Y i c r o s c . Spectrosc. E l e c t r o n . ,

10

(1985) 575.

/ l o / Levine, D., T h i s workshoo.

/11/ Bendersky, L., Schaefer, R.J., B i a n c a n e l l o , F.S., B o e t t i n q e r , W.J., Kaufman, M.J. and Shechtman, S c r i p t a Met.

19

(1985) 909.