X-ray and TEM studies of Al-Fe-Cu dodecahedral particles : characterization of their microcrystalline state of pseudo-icosahedral symmetry

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X-ray and TEM studies of Al-Fe-Cu dodecahedral

particles : characterization of their microcrystalline state

of pseudo-icosahedral symmetry

F. Dénoyer, G. Heger, M. Lambert, M. Audier, P. Guyot

To cite this version:

651

X-ray

and TEM studies of

Al-Fe-Cu dodecahedral

_{particles :}

characterization of

their

_{microcrystalline}

state

of

pseudo-icosahedral

_symmetry

F.

_Dénoyer

_(1),

G.

_Heger

_(2),

M. Lambert

_(2),

M. Audier

₍₃₎

and P.

_Guyot

₍₄₎

(1)

Laboratoire de

_Physique

des Solides

_(*),

Université Paris-Sud, Bât. 510, 91405

_Orsay

Cedex,

France

(2)

Laboratoire Léon Brillouin

_(**),

C.E.N.

_Saclay,

91191 Gif sur Yvette Cedex, France

(3)

Laboratoire de

_{Thermodynamique}

et

_{Physico-Chimie Métallurgiques}

_(***),

ENSEEG

BP 75, 38402 Saint Martin d’Hères, France

(Reçu

le 27

_septembre

1989,

accepté

sous

_{forme de finitive}

le 11 dgcembre

₁₉₈₉₎

Résumé. 2014 Des

particules

dodécahédriques

d’alliage

AlFeCu, obtenues par solidification lente,

ont été _{étudiées par diffraction des rayons} X et _par

_{microscopie électronique}

en transmission. Leur structure microcristalline

_{particulière}

de

_{symétrie globale pseudo-icosaédrique,}

préalable-ment identifiée par des

images

haute résolution et par diffraction

électronique

est confirmée par l’indexation des

diagrammes

de

_précession

_{rayons X. Le}

_système

cristallin est

_{rhomboédrique}

et a

pour

paramètres

de maille

a = 32,16 Å et 03B1 =

36°. Le

_problème

_{de pavage de l’espace} à l’aide d’une seule maille

_{rhomboédrique}

conduisant à un _{ordre moyen}

_{icosaédrique parfait}

est discuté

sur la base de résultats

_{préliminaires}

obtenus par

_{microscopie électronique}

à haute résolution.

Abstract. 2014 Dodecahedral

particles

of Al-Fe-Cu

_alloy,

obtained

_by

slow _{solidification,} have been studied

_{by X-ray}

diffraction and transmission electron

_microscopy.

Their

_{peculiar microcrystalline}

structure of overall

_{pseudo-icosahedral}

_symmetry,

_previously

identified

_{by high}

resolution

imaging

and electron diffraction, is shown to be conformed

_{by indexing}

of

_{X-ray precession}

patterns. The

_crystal

_system is rhombohedral with cell _parameters a = 32.16

Å

and 03B1 = 36°. The

space

tiling problem

of mean

_perfect

icosahedral order,

using only

one rhombohedral cell, is

discussed on the basis of some

_{preliminary investigations}

in

high

resolution electron

microscopy.

J.

_Phys.

France 51

₍₁₉₉₀₎

651-660 1er AVRIL _1990,

Classification

Physics

Abstracts

61.55H

Introduction.

The Al-Fe-Cu icosahedral

_phase

has been first

_{reported by}

Tsai and Masumoto

_[1,

_2]

as a

stable icosahedral

_phase.

The

_indexing

of

_{powder X-ray}

diffraction

patterns

by

Ishimasa et

al.

_[3]

has revealed that the

scaling

(or

self

_{similarity ratio)}

_along

the

5-fold,

3-fold and 2-fold

(*)

Associ6 au CNRS.

(**)

CEA-CNRS.

(***)

UA CNRS n° 29.

axes was the

_golden

mean T instead of

T 3.

More

_recently,

Ebalard and

_Spaepen

[4]

have

identified the

_quasilattice

with a face-centered

_{6D-hypercubic}

lattice and the structure has been described

_{by Devaud-Rzepski et}

al.

_[5],

as an ordered

_{F-superstructure}

of the usual

primitive quasilattice

with at least two motifs in the

_{6D-representation.}

The new

quasicrystal-line

_phase

has been observed in micron size

_grains

in

_rapidly

_{quenched alloys}

as well as in

as-cast

_alloys,

_therefore,

the structural studies have been limited to electron diffraction on

_single

grains

[1-6]

and

_X-ray

diffraction on

_{powder samples}

_{[1-5, 7].}

Recently, large single

«

grain

»

samples

have been grown

by

slow solidification.

The

_samples

were

_prepared

at the

_P6chiney

Research Center : an

_alloy

of chemical

composition A165CuzoFel5

was cast at _{1 200 °C under argon}

_atmosphere

and then solidified

under vacuum at a

_cooling

rate lower than 1 °C

_min-’,

down to room

_temperature.

Once

broken,

the

_ingot

_{exhibited many}

_prismatic

dendrites and

_just

a few small brilliant

dodecahedral

_particles.

The chemical

_composition

of the

latter,

presumed

to be of icosahedral

structure, is

homogeneous

and

corresponds

to

_{A163.5Cuz4FeIZ.5,}

as determined

_by

electron

probe microanalysis

[8].

Figure

1 shows such a

_{typical particle}

with a diameter size of a few

100 >m which is very suitable for a

_precise

_exploration

of the

_reciprocal

_space

by X-ray

diffraction,

i.e. a

_study

of the

_type

_already

carried out on the

_Al6CuLi3

stable

_{quasicrystalline}

phase,

where

_large

triacontahedral

_particles

were available

[9, 10].

Fig. 1. - Typical particle

found inside the

_ingot,

with a

_pentagonal

dodecahedral

_{morphology ;}

its orientation is almost

_following

a 2-fold axis in

a)

and a 5-fold axis in

b).

In _{this paper,} we

_report

the

_X-ray

diffraction results obtained on Al-Fe-Cu dodecahedral

particles

and some of their Transmission Electron

_Microscopy

_(TEM)

characteristics. The

interpretation

of these

X-ray

diffraction results appears to be in

good

agreement

with those obtained

_{previously by}

electron diffraction on

_slowly

solidified

_samples.

This Al-Fe-Cu

intermetallic

_compound

of a

_{single-phase periodic}

structure

_gives

rise to the _appearance an

overall

_{pseudo-icosahedral}

_symmetry

due to its

_{peculiar microcrystalline}

state.

Results.

In order to compare

directly

the diffraction

_peak

distribution in

_reciprocal

_{space with the}

calculated diffraction

_pattern

for an icosahedral

_quasicrystal

with a face-centered

6D-hypercubic

lattice,

given

by

Devaud-Rzepski et

al.

_[5],

we have

_performed

_X-ray

653

Fig.

2. - Monochromatic

X-ray precession photographs

obtained for the zero-level

_{reciprocal plane}

with

_successively

the 5-fold, 3-fold and 2-fold axes

_parallel

to the

_precession

axis :

a),

b)

and

_c)

shown the results obtained with an incident beam

wavelength

A = 1.542

A

(CuKa

radiation),

for the zero level and with

_successively

a

_5-,

3- and 2-fold axis

_parallel

to

_{the’precession}

axis. Each

_pattern

can be

_directly

_compared

with the results obtained for an

icosahedral

_A16CuLi3

quasicrystal

(Figs.

2d,

e and

_{f) :}

the

intensity

distribution of reflections is

_quite

_different,

but the icosahedral orientational

symmetry

is

_{perfectly angularly respected}

without any deviation in the two cases. For

_Al6CuLi3,

it has been shown

_previously

[10]

that all the reflections could

be indexed

_using

a

primitive 6D-hypercubic

lattice with a direct 6D-lattice

_parameter

A = 7.13

A.

For the Al-Fe-Cu

sample,

the measured d values

(dmeas.),

obtained from

peak

positions along

the 2- 3- and 5-fold axes are

_{respectively given}

in tables

la,

b and c. A list of

some of the main calculated reflections has been

_published

in reference

_{[5] ;}

their indices

h/h’ k/k’

Q/Q’ (I /f ’ = 0 /0 )

and their

_{correspondin N = h2 + k2 + Q2 + h’Z + k’2 + Q’2,}

M =

h’2 + k’2

₊

£,2

+

_{2 (hh’}

+

kk’ + QQ’ ), QII =

N + M?

and

_Ql

=

~ (N7 - M )

_{are also}

given

in table I.

_Using

a direct 6D F-lattice

_parameter

_AF

= 2 x 6.312

A,

the

_{corresponding d}

Table I. -

Indexing

o f

Bragg

reflections along

the

_{2- fold}

axis

_(a),

the

_{3- fold}

axis

_(b)

and the

5-fold

axis

_(c).

Table Ia. -

655

values

_{(d~an. )}

have been

_{calculated ;}

all are listed in tables

_la,

b and c, from which it appears

that :

i)

for many diffraction

peaks,

a

_good

_agreement

is found between the

dmeas.

and

dcalc.

values ;

I

ii)

a number of diffraction

peaks,

observed

_by

electron

_microscopy

_(see

for

example

Ref.

[5]),

are not observed in our

_X-ray

_experiments

in

_spite

of the extreme

_sensitivity

of the

photographic

method,

for which it is

_possible

to

_distinguish

between different

_peak

intensities

up to a ratio of more than 1000. This is the case, for

instance,

for

1/1

1/0, 1/0 0/1,

2/0

0/2,

0/2

2/2,

2/1

1/3,

0/3

3/3, 2/2 0/0,

2/0

_0/0,

0/4

_0/0,

4/2

_0/0,

...

reflections ;

iii)

additional diffraction

_peaks

of weak or medium

_intensity

are observed but

_they

cannot be indexed

_{reasonably using}

the 6D F-lattice

_parameter

_{A F}

= 2 _x 6.312

A.

Table Ib. -

3-fold

axis.

Therefore,

although

this

_slowly

solidified Al-Fe-Cu

_product

shows an overall icosahedral

symmetry, the

_indexing

of its

_{corresponding}

diffraction

_pattern

is

_incompatible

with a

face-centered

_{6D-hypercubic}

lattice.

Simultaneously

to this

_{X-ray study,}

electron

_microscopy

_experiments

have been

_performed

on

_fragments

of dodecahedral

_{particles coming}

from the same

_ingot

[11].

The electron

diffraction

_patterns,

as those with

2-,

3- and 5-fold zone _axes, shown in

_figure

3,

exhibit

_large,

split

spots ; moreover, the 5-fold axes were not

_always

found

_{strictly equivalent}

for different

fragments

of a same dodecahedral

_particle.

The

_{perfect equivalence}

of the six 5-fold axes of

the

_sample,

studied in the

_{X-ray precession experiment}

has been checked

_{carefully using}

a

Table Ic. -

5-fold

axis.

measured in the

_Burger

_{method) :}

all were found to be

_equivalent.

Furthermore,

cv

/2

0 scans of the reflections

_along

the different _symmetry axes have revealed a remarkable

sharpness

of the diffraction

_peak,

_indicating

a

_high

_coherency

in the

_spatial

_{interferences,}

comparable

to the one encountered in

_crystals

of small mosaic

spread.

Figure

4 shows the

657

Fig.

3. - Electron diffraction _patterns of 5-, 3- and 2-fold zone axes, observed on the

_fragments

of a

dodecahedral Al-Fe-Cu

particle slowly

solidified.

Electron diffraction

_patterns

have been

_interpreted

as

resulting

from a

_periodic

microcrys-talline structure

_[8,

_12],

the unit cell of which has been found to be rhombohedral with cell

parameters a = 32.08

A

and a = 36° .

By

comparison,

the

_X-ray

reflections of tables

la,

b and c, observed

along

i)

2-fold,

ii)

3-fold and

_iii)

5-fold axes can be

_interpreted

as

_arising

from the

_{i) (110),}

_{(220), (550),}

_{(880), ii)}

(333),

(555),

(888),

(13

13

₁₃₎

and

_iii)

_(100),

_(200),

_{(300), (500), (800), (900)}

reflections

respectively

of the rhombohedral Bravais lattice of refined cell _{parameters a =} 32.16

A

and a = 36°. The found

agreement is remarkable.

It is

_interesting

to note that such a

_primitive

cell can be related to a

_larger

face-centered rhombohedral unit cell with

_{parameters a}

= 37.71

A

and a =

63.43°,

whose

shape

then

becomes identical to a

_prolate

rhombohedron of the Ammann

_type.

Note furthermore that its

edge length

is

_equal

to 2 .

_{T 3(4.45 )}

A,

where 4.45

A

_corresponds

to the smallest

rhombohed-ron

_edge

_length

of the

_perfect

Al-Fe-Cu

quasicrystal [1, 8]

and

T3 to

a characteristic inflation. Discussion and

_concluding

remark

’

From these _present

results,

an obvious

_question

arises : how can _{space be} tiled with

_only

one

rhombohedral cell in order to create a mean

_perfect

icosahedral orientational order ? A

Fig.

4. -

w /2

0 scan of the « 2I2 0/0 0/0 » and « 214 0/0 0/0 » reflections.

priori,

the task of

_explaining

this is rather difficult.

However,

as a

_guide

for further

investigations,

an answer is

partially given

with 2-dimensional models

_presented

in

refer-ence

[14],

in which a consideration of the size of coherent domains

_permits

an

_{understanding}

of the

_origin

of some of the differences encountered between electron diffraction

_experiments

on small

_fragments

_[8,

11,

12]

and

_X-ray

diffraction on

_{macroscopic samples.}

_Moreover,

structural defects may occur at

_grain

boundaries in such a case.

Fig.

5. - Stellate

_polyhedron

constituted of 20 Ammann

_prolate

rhombohedra. Note that each

rhombohedron can also be viewed as a

_{microcrystalline}

domain of

_prolate

rhombohedra. The different

crystallographic

orientations of the Al-Fe-Cu

_grains

of rhombohedral structure

_correspond

to the 10

659

Previous theoretical work

_[13]

and

_high

resolution electron

microscopy

investigations

[8]

tend to confirm this view. It has been shown

_[13]

that in order to

_respect

an overall

pseudo-icosahedral

_symmetry,

the different orientations of the rhombohedral cell must

_correspond

to those observed between the 20

_prolate

rhombohedra

_constituting

a stellate

_polyhedron

(Fig. 5).

The total number of different orientations is

10,

since

_prolate

rhombohedra are

parallel

two

_by

two in such a stellate

_polyhedron.

These orientational

_{relationships}

have been identified in the Al-Fe-Cu

_product

_{by high}

resolution electron

_microscopy

_[8].

The

microtex-ture of the

_product

is thus

_quite

_{peculiar ;}

it is

_{microcrystalline}

but each

_grain

exhibits the

same

_{crystallographic}

orientational

_{relationships}

with the other

_grains.

For

_example,

the

micrograph,

shown in

_figure

_6,

is obtained from a thin

_fragment

of dodecahedral

_particle

Fig.

6. -

High

resolution TEM

_micrograph

of the Al-Fe-Cu

_product

observed

_following

a

pseudo-icosahedral 5-fold zone axis

_{(a) ;}

some

_grain

boundaries

_{converging nearly}

to a same

_point

are arrowed.

Partial

_indexing

of the

_{corresponding}

electron diffraction _pattern is realized _by the

_{superimposition}

of five _{calculated patterns of}

_[111

_{] zone}

axis of the

_primitive

_cell, each one

_being

rotated of 72° with _respect

observed

_along

a

_{pseudo-icosahedral}

5-fold axis : its

_analysis

has revealed that the different domains are

_mainly

oriented

_following

a rational

[100]

zone axis of the Ammann

_type

_prolate

rhombohedral cell

_(which

is

_equivalent

to a

[111 ]

zone axis for the

primitive

rhombohedral

cell)

and with 72° rotations in the observation

_plane.

The

_{corresponding}

electron diffraction

pattern

compares well with a schematic

_{diagram representing}

the

_{superimposition}

of five

calculated

_patterns

of

_[111

zone axis

_(cf.

Ref.

_[13]),

each one

_being

_successively

rotated

_by

72° with

_respect

to the

_previous

one. The

_{triangular shape}

of the

_spots,

also observed on the

precession photographs,

is thus due to a small

_splitting

between different

reflections,

_e.g.

202,

330,

352,

253 and 033 form one

_triangular

_spot.

Several domain boundaries can be identified on the

_micrograph,

_e.g.

_following

the arrows ; some of them can be

_interpreted

as

simple {110}

twinning

planes

[8] ;

others are common boundaries but the rotational order is

preserved

when

_{crossing through}

the

_boundary.

Finally,

it has to be stated that the structure, presented

here,

is

_basically

different from the

perfect

icosahedral structure

_reported

_by

other authors

_[1-6]

on

_{rapidly quenched samples.}

This

_apparent

_discrepancy

is

_probably

related to the occurrence of a transformation which was

observed for this

_alloy

at about

_{860 °C,}

where the rhombohedral

_crystal

structure transforms into a

_{perfect quasicrystalline}

state

_{[8, 12].}

Acknowledgements.

The authors would like to thank J. M.

_Lang

and P. Duroux for the

_preparation

of the Al-Fe-Cu

_ingot.

References

[1]

TSAI A. P., INOUE A. and MATSUMOTO T., J. Mater. Sci. Lett. 6

₍₁₉₈₇₎

1403.

[2]

TSAI A. _P., INOUE A. and MATSUMOTO _T.,

_Jpn

J.

_{Appl. Phys.}

26

₍₁₉₈₇₎

L1505.

[3]

ISHIMASA

T.,

FUKANO Y. and TSUCHIMORI M., Philos.

_Mag.

Lett. 58

₍₁₉₈₈₎

157.

[4]

EBALARD S. and SPAEPEN F., J.

_of

Mater. Res. 4

₍₁₉₈₉₎

39.

[5]

DEVAUD-RZEPSKI J., QUIVY A., CALVAYRAC Y., CORNIER-QUICANDON M. and GRATIAS _D., Philos.

_{Mag. B}

₍₁₉₈₉₎

_preprint.

[6]

HIRAGA K., ZHANG B. P., HIRABAYASHI M., INOUE A. and MATSUMOTO T.,

Jpn

J.

_{Appl. Phys.}

27

₍₁₉₈₈₎

L951.

[7]

BOUCHET-FABRE B., LARIDJANI _M., CHENOUFI A. and DIXMIER _J., in

_{Quasicrystalline}

_Materials,

Eds. C. Janot and J. M. Dubois

_(World

_Scientific)

_(1988),

_p. 136.

[8]

AUDIER M. and GUYOT P., AAR Conf., ICTP, Trieste

_(July

₁₉₈₉₎

to be

_published.

[9]

DÉNOYER F., HEGER G., LAMBERT M. et LANG J. M., C.R. Acad. Sci. Paris Sér. II, 304 12

(1987)

625.

[10]

DÉNOYER _F., HEGER G., LAMBERT _M., LANG J. M. and SAINFORT P., J.

_Phys.

France 48

₍₁₉₈₇₎

1357.

[11]

DÉNOYER F., HEGER G., AUDIER M. and LAMBERT M., French National

_Colloquium

on

Quasicrystals, Nancy (March 1989).

[12]

AUDIER M. and GUYOT _P., Third Int.

_Meeting

on

_{Quasicrystals ;}

Incommensurate Structure in Condensed _Matter, 27

_May-2

June _1989, Vista _Hermosa, Mexico, to be

_published.

[13]

AUDIER M. and GUYOT _P., Acta Metall. 36

₍₁₉₈₈₎

1321.