Icosahedral AlCuFe alloys : towards ideal quasicrystals

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Submitted on 1 Jan 1990

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417

Icosahedral AlCuFe

_{alloys :}

towards ideal

_{quasicrystals}

Y.

_Calvayrac

_(1),

A.

_Quivy

_(1),

M. Bessière

_(2),

S. Lefebvre

_(2,1),

M.

_{Cornier-Quiquandon (1)}

and D. Gratias

₍₁₎

(1)

C.E.C.M./C.N.R.S.,

15 rue G. Urbain, F-94407

_Vitry

Cedex, France

(2)

L.U.R.E., Bât 209d, F-91405

Orsay

Cedex, France

(Reçu

le 18 août 1989, révisé le 8 novembre 1989,

accepté

le 20 novembre

₁₉₈₉₎

Résumé. 2014 Le désordre

_topologique

et l’ordre

_chimique

à

_grande

distance ont été étudiés par diffraction des rayons X sur

_poudre

dans

_{l’alliage i-Al65Cu20Fe15}

brut de _trempe. Le

perfectionne-ment

_{spectaculaire}

de l’état

_{quasicristallin,}

_{obtenu par recuit d’échantillons}

_{hypertrempés,}

a été mesuré

_{quantitativement ;}

le matériau recuit final

_correspond

aux

_{prévisions théoriques}

du

modèle

_{quasicristallin}

idéal dans les limites de la résolution instrumentale.

_Après

recuit à 1 073 K,

l’alliage

de

_composition

nominale

_Al65Cu20Fe15

est

_biphasé.

La

_{composition Al63Cu25Fe12}

conduit

quant à elle à une structure

_{icosaédrique}

_monophasée

_qui

convient à

l’analyse

par diffraction des rayons X ou des neutrons sur un mono

_{quasi-cristal.}

Abstract. 2014 The

_topological

and chemical

_long

_{range orders in the icosahedral}

_Al65Cu20Fe15

_alloy

have been studied

by X-ray

powder

diffraction. The

_spectacular

enhancement of the

quasicrystal-line state

_{by annealing}

of

_{rapidly quenched samples}

have been

_{quantitatively}

measured

showing

that the final annealed

_product

fits the theoretical

_predictions

of the ideal

_quasicrystal

model within the instrument resolution. Whereas, after

_annealing

at 1 073 K,

Al65Cu2oFe15

is

two-phased

2014

that makes difficult any fine

study

of the structure and the

_properties

of the ideal icosahedral

phase

2014 a close

_composition

_Al63Cu25Fe12

leads to a

_{single-phased}

icosahedral structure suitable for

_single

_quasicrystal

_X-ray

and neutron diffraction

_analysis.

J.

_Phys.

France 51

₍₁₉₉₀₎

417-431 ler MARS 1990,

Classification

Physics

Abstracts 61.10F - 81.30 - 81.40

Introduction.

High quality quasicrystal making

has been one of the basic

_topics

of research in

_metallurgy

for

providing samples

suitable for the

_study

of the structural and

_{physical properties}

of

quasicrystals.

Most of the available materials are metastable

phases

issued from

rapid

quenching

and contain an

_important

fraction of

_topological

disorder that obscures the intrinsic

quasiperiodic

nature of the icosahedral

_{phases. Topological}

disorder has even been considered as an intrinsic

property

of these

_phases

after the

_discovery

of the first stable i-AlLiCu

_{[1, 2]}

and

_GaMgZn

_[3]

_alloys

_which,

_initially

obtained

_{by rapid quenching,}

transform

by subsequent annealing

into a more disordered state.

The announcement, two _{years ago,}

_by

Tsai et al.

_[4]

of a new stable icosahedral

_phase

in the

A16sCu20FelS

alloy

has been the

_{starting point}

of an intensive research where it has been shown that this structure can indeed be described as a

_high

_quality

ordered

_{F-superstructure}

of the

Experimental.

Master

_alloys

of

_compositions

_A16sCu20Fe15

and

_Al63Cu25Fe12

have been

_prepared

from the pure elements

(Al :

99.99

%,

Cu : 99.99

%,

Fe : 99.95

%)

by

levitation

melting

in a controlled

helium

_atmosphere.

The

_alloys

have been

_{subsequently rapidly quenched}

_{by planar}

flow

casting

on a _{copper wheel under} a helium

_atmosphere

_(quenching

_{temperature :}

1 423

K,

tangential speed

of the wheel : 25

_m/s).

The flakes were

_ground

and sifted

_through

a 32 itm

sieve for

_{powder X-ray}

diffraction

_pattern

measurements.

High-resolution X-ray experiments

have been done

_using

the

_synchrotron

radiation on the

line D23 of

LURE-DCI,

which is

_equipped

with a

_{double-crystal}

monochromator

(Si 111)

in

the incident beam and an

_{analyzer crystal}

_{(Ge 111)}

in the diffracted beam

_[13].

The resolution

Aq,

measured on the

(111)

_{Bragg peak}

from a standard Ni

_{powder sample,}

was

3 x

10- 4 A -

1

_(the

diffraction vector _q

_being

defined as _q = 2 sin 6

/ À).

Due to lack of allocated beam time at the

_synchrotron

source,

peak

width measurements of the

_{as-quenched samples}

have been

_performed

on a conventional diffractometer

_equipped

with a curved LiF monochromator in the diffracted

_beam,

_using

the

_CuKJ3

radiation. The resolution was about 2 x

10- 3 Â- 1.

The intrinsic

_{broadening à}

0 has been obtained

_through

the

_{Taylor expression}

_[14]

where B is the observed full width at half maximum and b is

_{representative}

of the instrument

broadening.

The use of this formula is

_{justified by}

_satisfactory

_agreement

with the

high-resolution data.

Integrated intensity

measurements have been made

_{taking advantage}

of the variation in the atomic

_scattering

factors near the

_absorption

_edges

of Cu and

Fe,

using

the

_synchrotron

radiation and also classical

_targets

_(CoKa

and

_CuKp

_radiations).

Results.

1. IDENTIFICATION OF THE PHASES IN THE

_A165Cu20Fe15

ALLOY.

As

_quenched.

- All the

peaks

of the

_X-ray

_spectrum

can be indexed

_using

an icosahedral 6D

_I-reciprocal

lattice with a

_(primitive)

6D lattice

_parameter

of the icosahedral

_phase

of 6.320 ± 0.008

Â.

A few additional weak

_peaks

_{indicate the presence of} a small amount of a

simple

cubic

_{FeAl-type phase}

_(a

= 2.90

Â)

[7].

Annealed. - After

annealing

for 30 min at 1 073 K the intensities of the fundamental lines decrease

_by

about 30

_%,

and the

_{precipitation}

of a monoclinic

_Al3Fe-type

_phase

is observed

(Fig. 1).

There is no

_companion

decrease in the

intensity

of the

_{superlattice peaks}

which

419

Fig.

1. -

X-ray powder

diffraction _pattern of the

_Al65CuwFe15

_alloy.

The

alloy

has been

_quenched

_by

planar

flow

_casting,

then the flakes have been annealed for 30 min at 1 073 K

_{«V) Al3Fe-type phase).}

phase. Correlatively

the

_(primitive)

6D lattice

_parameter

decreases

_slightly

to

a6 = 6.3146 ± 0.004

Â.

The

_Al3Fe

_compound,

as studied

_by

Black

_[15],

has the lattice

parameters : a

= 15.489

Â,

b = 8.083

Â,

c = 12.476

Â

and 13 =

107.68°. The

Al3Fe-type compound

we observe has the lattice

_{parameters : a}

= 15.535

Â,

b = 7.993

Â,

c =

12.509 À

and 13 =

107.96°. These values

are similar to those measured

_by

Ishimasa et al.

_[5]

in an

_A165Cu2oFe15

_alloy

annealed for

65 hours at 1 073 K.

2. TOPOLOGICAL DISORDER IN THE

_A165Cu20Fe15

ICOSAHEDRAL PHASE.

_{- During}

the heat-treatment, a considerable increase in the structural

perfection

of the icosahedral

phase

occurs

which is observed

_by

both a

_{perfectioning}

in the

_{peak positions}

and a

_narrowing

in the

_peak

widths of the

_{X-ray powder}

diffraction

_spectra

_{(Fig. 2).}

2.1

_Displacement

_from

the i-deal 6D I

_{reciprocal lattice.}

- The

_indexing

of the

_as-quenched

icosahedral

_phase

has been

_performed

in the scheme

_proposed

_by

Cahn et al.

_[16]

with a 6D F-direct lattice

_parameter

_{aF = 6.32} x 2 = 12.64

Â.

Table I

gives

the measured

peak positions

and the deviations

_(Aqll

from those calculated for an ideal

_{quasicrystal.}

The

_largest

difference reaches

10- 3 Â- 1.

These results have been obtained from

_{experiments performed}

using

the

_CuKp

radiation. In order to check the intrinsic values of

_Oqp

we have done the same

Fig.

2. - Increase in the structural

_perfection

of the icosahedral

_phase,

in an

_A165Cu2oFel5

_sample

annealed for 30 min at 1 073 K. The arrows

_give

the calculated

positions,

for the ideal icosahedral

phase

(A

= 1.746

Â).

Table 1. - Observed

positions

of

the

_reflections

_{(qll ),}

deviation

_fiom

the calculated values

421

Fig.

3. - Deviations from the theoretical icosahedral

positions

of the reflections, for the different

experiments performed :

in the

_as-quenched

state,

systematic

déviations occur, which are released

by

annealing.

An

_annealing

at 1 073 K for 30 min leads to drastic

_changes

in the

_peak

_{positions :}

although,

in the annealed state,

only

those few

_peaks

which do not

_superimpose

with diffraction lines of the monoclinic

_A13Fe-like

_phase

can be measured with accuracy, the

displacements

from the

_expected

values decrease

_by

a factor of ten or more and fall within the

uncertainty

domain of the

_experimental

measure

_(see

_Fig.

_3).

2.2 Peak widths. - Intrinsic

peak

widths

_(full

width at half maximum :

fwhm,

noted

W p ) ,

measured on

_as-quenched

_samples,

are

_given

in table 1 and have been

_{plotted according}

to two

_possible

_types

of disorder

_{suggested by}

Hom et al.

_{[17] :}

icosahedral

_glass

_{(Fig. 4)}

and frozen-in

_phason

strain

_{(Fig. 5).}

Fig.

4. - Icosahedral

glass

model :

_plot

of the

peak

width

_(fwhm)

as a function of the

perpendicular

Fig.

5. -

Frozen-in

phason

strain

model : y

=

(fwhm/q,

)2@ X

=

(q@ /qj

)2, a

= 1.36

x10-5 , b

= 0.0033.

There is a wide scatter from the

_straight

line

_{predicted by}

the icosahedral

_glass

model. A much better fit is obtained if a

_dependence

on both the

_parallel

and the

_{perpendicular}

components

of the 6D-wave vector is considered. The

_least-square

fit of the

_quadratic

law :

leads to

a = 1.36 x 10- 5

and

b = 3.3 x 10-3 .

These values are of the same order of

magnitude

as those found for

_as-quenched

i-AIMnSi

[10]

_except

that the relative

_importance

of the

_parallel

contribution is here four times smaller than in the case of AIMnSi. That

explains

the

_difficulty

to

_put

it into evidence : in fact the difference between the

_agreement

ratios of the fits

_{corresponding}

to the two models results

_essentially

from a few reflections with very small values for q1 and

large

values for qi .

Table II. - Intrinsic

_peak

widths

_for

the icosahedral

_phase

in a

_{A165Cu2OFe 15 sample}

annealed

for

30 min at 1 073 K

_(instrument

resolution

_Aq

= 3 _x

10-4

A -1).

An

_annealing

at 1 073 K for 30 min leads to a

_{striking sharpening}

of the

_peaks

_(see

_Fig.

_2).

The intrinsic

_peak

width reduces

_by

a factor of 10 as seen in table II

_showing

the values obtained from those

_single

_peaks

for which there is no

_{superimposition}

with reflections from

Al3Fe.

After this short

_annealing

treatment, the

_{« high}

resolution »

_X-ray

measurements

show that a small

_{peak broadening}

still

survives,

which

_corresponds

to

_coherently

_reflecting

regions

the size of which is

_roughly

_{1 / W h}

2 800

Â.

The intrinsic

_peak

width is now

independent

of

_{both qll}

and _{q, .} It is also

_independent

of the nature of the

_{peaks :}

both odd indices

_peaks

-

corresponding

to

_{superstructure}

reflections - and

423

3. CHEMICAL LONG RANGE ORDER IN THE ICOSAHEDRAL

_A165Cu20Fe15

PHASE. - The

structure of the icosahedral F-AlCuFe

_phase

can be described as a chemical

_ordering

P (A) -. F (2 A),

with two

_{superlattices displaced by}

half an unit vector of the F cell in 6-D. The _presence of smooth

_antiphase

boundaries

_together

with the relative low intensities of the

superstructure spots

are

_good

indications that the two

_{superlattices}

are decorated

_by

_very

similar atomic surfaces with

_altemating

chemical

_species.

The intensities of the

_superlattice

peaks

depend

on the contrast between these atomic

_species.

A crude estimate of which kind of atoms orders can be obtained

_{by using X-ray}

anomalous

_{scattering phenomenon :}

the variation of the

_scattering

factor with

_wavelength

near the

_{absorption edges}

of the constituent

elements

_produces

a variation of contrast in the

_intensity

that is

_directly

related to the nature

of the elements.

Assuming

in the

_simplest

case that the atomic surfaces at the two sublattices have the same

geometry

and differ

_{only by}

the atomic

_species,

we can write the

_global

form factor

F (K )

in 6D as :

where

f a

and

_fp

are the form factors of the atomic

_species

that order between the

a and

_/3

sublattices with the associated

_geometric

factor

_G,,,,,e

(K.L) supposed

to be the same

for both

sublattices,

/0

and

_{GO(K_L ) designates}

all the orbits that are common to both

sublattices,

T is the 6D

_primitive

translation that relates the two sublattices

(T

=

[1,

0,0,0,0,0

]).

Superstructure

reflections

correspond

to half

integer

values of the

phase

factor K . T whereas fundamental

spots

correspond

to

integer

values of this

phase

factor. The

ratio of the

_{integrated intensities $}

of a

_{superstructure}

versus a fundamental reflection is

If

therefore

_proportional

to

Assuming

fo Go

to be much

_larger

that the

_ordering

terms and

_{approximately independent}

on the

_wavelength,

we

_finally

obtain an

_intensity

ratio that varies like

_{(la -}

_{f p}

₎₂

with

_varying

the

_wavelength.

Measurements of the

_(7-11)

_{superlattice peak}

and of the

_(20-32)

fundamental

peak

have been made at four different

_wavelengths

near the

_{absorption edges}

of Fe and Cu.

They

lead to the ratios

_given

in table III. A

_long

_{range chemical}

_ordering

between Fe and Cu

can be ruled out because the

_{experimental intensity}

ratio does not vanish near the Cu

absorption

edge

(À

=

1.3923,

second _raw in Tab.

III).

The best linear trend is obtained

by

choosing

as one of the

_{ordering species}

a random mixture of Cu and Fe in the nominal

composition

and Al as the other

_(see

last column in Tab.

_III).

These

_preliminary

results

suggest

that the

_long

range chemical order occurs between an Al orbit and one or several

orbits where Fe and Cu are distributed in the

proportion

of the nominal concentrations. No

additional information can be extracted from these sole results

_concerning

a

_possible

short

range order between the Cu and Fe atoms.

4. THE SINGLE-PHASE ICOSAHEDRAL ALLOY. - The AlCuFe

_ternary

_{phase diagram}

was

extensively

studied

_by

_Bradley

and Goldschmidt

_[18].

A

_{systematic investigation,}

around the

compositions corresponding

to the three

_temary

_phases

called

_.p,

lù, and

¢

in their

original

paper, led us to the conclusion that

the gi

phase

is indeed the icosahedral

_phase

discovered

_by

Tsai et al.

_[4]

in the AlCuFe

_system.

This

_phase

has a small

_single-phase

domain,

around the

difficult to obtain in a _pure state and in true

_{equilibrium : they}

did not succeed in

_obtaining

a

single-phase gi alloy

which would

_{give sharp X-ray peaks.}

Trying

to

_{reproduce Bradley}

and Goldschmid’s

_results,

we had to

_{slightly displace}

the boundaries of the

_{single phase}

domain

of gi

by

a 2.5 % increase in Cu content and a 2.5 % decrease in Al content.

_During

the solidification of the master

_alloy,

we observed a

tremendous

_{macrosegregation}

which can be

_responsible

for

_{large compositional}

inhomogenei-ty

in the final

_ingot.

The safest way we found to avoid this

_{compositional inhomogeneity}

was to

_produce

the

master

_{alloy by}

_{rapid quenching}

from the

_liquid.

_By

_{this way} we have succeeded in

_preparing,

in a

_perfectly

_reproducible

manner, a

_single-phase

icosahedral

_alloy

which

_{gives sharp X-ray}

lines. The

_composition

is

_{A163Cu25Fel2 ;}

the

_rapidly

_quenched

_alloy

is similar to the

A165Cu2oFe 15

alloy

quenched

in the same conditions : an icosahedral

_phase

with a small

amount of a cubic

_{FeAl-type phase}

_(referred

to as

₍₃₂

in

_Bradley

and Goldschmidt’s

paper).

After

_annealing

for a few hours at 1 093

_K,

a

single-phase

icosahedral structure is obtained

(Fig. 6).

The

_high

resolution

_{X-ray powder}

diffraction shows that the

_peaks

have intrinsic widths

_comparable

to those observed for the best standard

_{crystalline powders,}

and that the

peak positions

are identical with those calculated for the ideal icosahedral

_{quasicrystal,}

within the instrumental error.

Subsequent

annealing

between 1 133 and 1 143

_K,

_during

several

_days,

leads to a

morphology

where

_relatively

_{large single}

_{quasicrystals}

- the size of _{which may vary from} a

few hundreds of microns to several millimeters

_{- generally}

located at the bottom of the

crucible,

are surrounded

_by

a cloud of fine

_{quasicrystals}

_(see

_Fig.

_7a)

_indicating

that the

growth

process

developed

in a

_partially

melt

_{alloy by coarsening}

of the icosahedral

_grains

in the

_liquid.

The small

_grains

are almost

_{perfect regular}

dodecahedra with

_edges

truncated

_by

2-fold

_planes

and vertices truncated

_by

3-fold

_planes.

Close examination of small

_grains

show an

equivalent morphology

for all the

vertices,

and not

_only

for those related

_by

a

_single

three-fold axis

_{(Fig. 7b),}

in

_agreement

with the icosahedral

_symmetry.

Discussion.

The annealed AlCuFe icosahedral

_phase

is a stable

_phase

which

_{gives sharp}

diffraction

_peaks

425

Fig.

6. -

X-ray powder

diffraction _pattern of the

_{single-phase Al63Cu25Fe12}

icosahedral

_alloy.

The

alloy

has been

_{quenched by planar}

flow

_casting,

then the flakes have been annealed for 2 h at 1 093 K.

Fig. 7.

-

(a)

Scanning

electron

_micrograph

of the

_single-phase

_A163Cu25Fel2

_{alloy initially rapidly}

427

In a recent

_publication

Audier and

_Guyot

_[22]

identified a

_crystalline

structure

_by

electron

microscopy

in an as-cast

_ingot

of AlCuFe. This

_phase

has been identified as rhombohedral

with a

_large

unit cell that can be derived from an inflation

_by

a factor of 2

r 3

of the

_prolate

rhombohedron of the canonical icosahedral

_tiling.

This

_phase

_corresponds

to a cut

_by

a

rational 3D

_plane

_{spanned by}

the three vectors A =

_{(2 p - q, q, q, q, q, - q ),}

B=

_{(q,2p-q,q,-q,q,q)}

and C =

_{(q,q,2p-q,q,-q,q)}

_{where p=3 and q=2,}

very close to the icosahedral cut

_(in

the 5-fold 2D

_plane,

its trace is at 3.19° from the icosahedral

_one).

The rhombohedral

_parameter

is

A, = ,/’2- A6D (q 7- + p - q )

_(here,

A

= 3.786

nm) (1).

We have calculated the differences in the location of the diffraction

peaks

between the icosahedral

phase

and the

_approximant

rhombohedral

_phase

_{(Tab. IV).}

Although

the differences are

_relatively

weak,

the

_figure

_8,

where these deviations are

Fig.

8. - Relative

position

of the diffraction

_peaks

of the 3rd rhombohedral

_approximant

with _respect

to the ideal icosahedral

_phase.

The bars

_correspond

to the fwhm of the

_{rapidly quenched}

alloy. They

all fit inside the

_dispersion

cone of the rhombohedral

_phase

_showing

that the

_rapidly

_quenched

_alloy

is not a

microcrystalline

rhombohedral

_phase.

(1)

A smaller cell can be obtained

_by

the three vectors

A’ - 2 ,BI - 2 , CI - 2

that

2 2 2

corresponds

to the parameter

A’

= A,

T = 3.221 nm

_analog

to the one found

_by

Audier and

2

429

reported

as a function of

_Q,

shows that the two

_phases

can be

_{unambiguously}

differentiated

by

powder

diffraction.

_By

_{this way,} we confirm that the

_alloys

studied in this paper are

_really

icosahedral

_phases.

On

_figure

_8,

the bars are

_{representative}

of the fwhm of the

rapidly

quenched

alloy ;

they

are all inside the

_dispersion

cone of the rhombohedral

phase,

a fact

which proves that even these

_{imperfect alloys}

are not

_{microcrystalline}

rhombohedral

_phases.

Deviations from

_perfect

icosahedral

_symmetry

towards

_periodicity

have also been

_reported

in as cast AlCuRu

_[23]

and a

_major

_question

is to determine which of those

_phases

corresponds

to a

_ground

state in the

_temary

_system.

In order to check if a

_{crystalline phase}

would form from the

_{quasicrystalline}

structure at low

_temperature,

we have

performed

isothermal

_annealing

at 930 K for 65 hours of the

_single

_phased

_A163Cu25Fel2

sample

previously

annealed at 1 093 K. We did not _{observe any}

_changes

in the

_high

resolution diffraction

_patterns

nor in the overall

_morphology

of the

_{sample :}

once

_formed,

the

icosahedral

_phase

does not

_undergo

_{any structural}

_change

at low

_temperatures

even after

_long

annealing

times.

This

_apparent

_discrepancy

between Audier and

_Guyot

results and ours seems even to be

more

flagrant

with their additional recent result

_[24]

that the

_composition

of the rhombohedral

phase

is the same as the one we found for the icosahedral

_phase

_(thanks

to one of the referees for this information which was unknown to

_us).

The

_only

difference between their

_experiments

and ours, is the

metallurgical

process used

to

_produce

the

_phases.

Instead of a slow

_cooling

of the

_ingot,

we used an isothermal

_growth

of

the

_{single quasicrystals}

from the

_liquid.

From what is

_actually

observed in

_computer

simulation of

_growth

_models,

the

_growth

of an ideal

_quasicrystal

is an

_extremely

slow process as

_compared

to

_crystals

_{and is very sensitive} to the

_surrounding

environnement

_(see

for instance Elser

_[25]).

Small

_anisotropy

_{(composition/temperature}

_{gradients, anisotropic}

_stress)

during

the

_growth

can

_locally

break the icosahedral

_symmetry.

A

_possible

scenario is

that,

as

suggested by

the recent results of

_Hiraga

et al. in as cast

_AlCuRu,

a linear

_phason

strain

develops during

the slow

solidification,

due to local

_anisotropy

that locks the structure

_along

rational

_{hyperplanes leading}

to a domain structure of

_periodic

_{approximants.}

The dodecahed-ral

_shapes

of the icosahedral

_{quasicrystals}

indicate that the

_ternary

axes are the

_{« rapid »}

growth

directions. We may therefore

expect

the

_{anisotropic phason}

field to

_develop

preferentially along

one of the 3-fold axes, which is in

agreement

with an eventual

rhombohedral

_approximant.

This

_periodic

structure, obtained in

_slowly

cooled

_samples,

would therefore be a metastable

_phase

_{very close} to the icosahedral

_phase

with the same

composition :

a

_{subsequent annealing}

is needed to eliminate the

_phason

strain for

_eventually

restoring

the ideal icosahedral

_symmetry.

Audier and

_Guyot

_(and

_Hiraga

_{et al.)}

results indicate that

_phason

fields are

_{preferentially}

linear and

_along

rational

_hyperplanes.

Conclusion.

Two AlCuFe

_alloys

were studied here :

_A165Cu2oFe15

and

_{A163Cu25Fel2.}

After

_{quenching by}

planar

flow

_casting,

both

_alloys

have the same structural state :

_essentially

_icosahedral,

with a

few

_percents

of a cubic

_{FeAl-type phase}

(named

₍₃₂

in

[18]).

_However,

their state of

equilibrium

at 1 073 K is different :

_A165Cu2oFe15

is

two-phased,

_A163Cu25Fel2

is a

_single-phase

icosahedral

_alloy.

This latter is the ideal

_alloy

for the

_{investigation}

of structure and

_properties

of the icosahedral

_{quasicrystals.}

In both

_alloys,

the icosahedral

_phase

_{may be obtained with} no

_long

distance

_diverging

phason

disorder : after

_annealing

at 1 073

_K,

there is no

_dependence

of the diffraction

_peak

width with

_phason

momentum.

_Hence,

this kind of disorder is not an intrinsic character of the icosahedral structure.

We think

_that,

in order to

_{produce single quasicrystals,}

it is crucial to _{grow the} material in

an

_isotropic

medium at constant

_temperature

_{by coarsening.}

This is what is achieved in the process we used to obtain the

_{quasicrystals}

_isothermally

from the

_liquid

_by

a slow

_coarsening

of

_preexistant

icosahedral germs.

The fact that we did not _{observe any}

_phase

transformation from

_quasicrystal

to

_crystal

and that all

_actually

available results

_{unambiguously}

_{agree that}

_annealing

of as cast or

rapidly

quenched

samples

lead to a

_{perfectionning}

of the icosahedral

_phase

is a

_{strong support}

to the

hypothesis

of a true thermal

_stability

of the icosahedral

_phase

which makes it a

good

candidate as

_{possible groundstate}

of the

_ternary

AlCuFe

_system.

The chemical

_long

_range

order,

in the icosahedral

_phase

of the

_asquenched

_A165Cu20Fe15

alloy,

was studied

_by

_{X-ray diffraction,}

taking advantage

of the contrast variation between the atomic

_scattering

factors of Cu and Fe near the

_{absorption edges}

of these elements. We

suggest

that the chemical

_long

range order results from a substitution of Al

_by

Cu and Fe on

primitive orbit(s)

in 6D. A Cu/Fe

_long

_range

_ordering

is excluded.

Acknowledgments.

We

_{gratefully acknowledge}

our

_colleagues

S.

_Peynot

and A. Dezellus for the

_preparation

and the

_rapid

_quenching

of the

_alloys.

We thank S. Ebalard and F.

_Spaepen,

C. L.

Henley

and M. Audier and P.

_Guyot

for

_having

sent us their

_{preprint prior}

to

_publication.

One of us

(D . G . )

is

very

grateful

to C. L.

_Henley

and D. DiVincenzo for

_stimulating

and

_enlighting

discussions.

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