Inelastic neutron scattering study of acoustic modes in a monodomain AlCuFe quasicrystal

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Inelastic neutron scattering study of acoustic modes in a

monodomain AlCuFe quasicrystal

M. Quilichini, G. Heger, B. Hennion, S. Lefebvre, A. Quivy

To cite this version:

1785

LE

JOURNAL DE

PHYSIQUE

Short Communication

Inelastic

neutron

_{scattering study}

of

acoustic modes

in

a

monodomain AlCuFe

_quasicrystal

M.

_{Quilichini(1),}

G.

_Heger(1),

B.

_Hennion(1),

S.

_{Lefebvre(2,3)}

and A.

_Quivy(2)

(1)

Laboratoire Léon Brillouin

_{(CEA-CNRS), CEN-Saclay,}

91191 Gif-sur-Yvette

_Cedex,

France

(2)

CECM/CNRS, 15

rue G.

Urbain,

94400

_Vitry

Cedex,

France

(3)

LURE,

bât.

_209D,

Université

_Paris-Sud,

91405

_Orsay

_Cedex,

France

(Received

on 21

June,1990,

accepted

on

_27June,1990)

Abstract. 2014 Inelastic neutron

scattering

results evidenced for the first time that acoustic

_phonon

modes can be observed for a

_{quasicrystal.}

The

_{triple-axes experiments}

have been

_performed

on a

small monodomain

_{Al63Cu25Fe12 sample.}

The obtained TA and LA

_dispersion

curves near to _strong

Bragg peaks

do not show _any variation with

_respect

to different _Q values. Their

_slopes

are

_isotropic

and do not

_depend

on

_special

_{symmetry directions;}

_they

are

_comparable

to those of

_{corresponding}

curves for _pure aluminium. We have not been able to observe _{energy gaps} in our measurements.

1

_Phys.

France 51

_{( 1990)}

1785-1790 ler SEPTEMBRE

_1990,

Classification

Physics

Abstracts 61.12 - 63.20

Introduction.

A stable icosahedral

_phase

in the AlCuFe

_ternary

_alloys

was obtained

_by

slow solidification

_by

l%a1 et aL

_{[1, 2].}

Ebalard and

_Spaepen

_[3]

have identified the

_quasilattice

with a face centered

6D-hypercubic

lattice and the structure has been described

_by

_{Devaud-Rzepski et aL}

_[4]

as a F

superstructure

with ordered domains and

_antiphase

boundaries.

_Depending

_upon

the

_preparation

conditions and the thermal

_history

of these AlCuFe

_alloys,

it has been

_observed,

even at room

temperature,

either a

_{perfect quasicrystalline}

state without _any indication of

_phason

strain or a

microcrystalline

twin state with an overall

_{pseudo-icosahedral}

_symmetry

_[5-7].

In this

_paper

we show for the first time

_phonon

_dispersion

curves for a monodomain

_quasicrystal

of

_{Al63Cu25 Fe12.}

_{Dynamical properties}

of

_{rapidly quenched}

as well as

_slowly

cooled and annealed icosahedral

_Al65Cu20Fe15

have been

_already

studied

_by

inelastic neutron

_{time-of-flight}

experi-ments

_{[8] .}

The obtained

_generalized

vibrational densities of states show

_only

very few structure

and the low _energy modes are related to atomic disorder introduced

_{by rapid quench.}

1786

In the

_large

class of

_{quasiperiodic}

structures, incommensurate modulated

_phases

have been the

most studied

_{(both experimentally}

and

_{theoretically)}

as

_regards

to their

_{dynamical properties.}

For

quasiperiodic

systems

it is

_{generally expected}

to observe acoustic

_phonon

branches with the usual

linear

_slopes.

In an incommensurate modulated

_crystal

where one can define a basic

_{(or average)}

lattice and an associated Brillouin zone, the modulation and its harmonics lead to an infinite

number of wave vectors within the Brillouin zone, and therefore an infinite number _{of energy}

_gaps

in the

_{frequency dispersion}

relation is

_expected

_{[9, 10].}

In

_fact,

_only

those which

_correspond

to the q vectors of the modulation itself and its lowest order harmonics

_{give experimentally}

detectable

effects,

similar to what is

_usually

observed at the Brillouin zone

_boundary

of a normal

_crystal.

In a

_quasicrystal

no _average lattice can be defined. Nevertheless acoustic modes should be ob-served around the

_Bragg

reflections,

and their

_intensity

should fulfill the usual

_relationship

which

exists for

_crystals

between the

_{Bragg intensity}

and the acoustic mode

_intensity.

Furthermore,

be-cause of the dense set of

_{Bragg peaks,}

one

_expects

_{energy gaps}

in the

_{frequency dispersion}

of the

acoustic

_phonons.

As an

_example

of a 1D

quasiperiodic

_system,

a Fibonacci chain was treated in numerical model calculations

_by

Benoit et aL

_[11]

in order to show the existence of

_{pseudoacoustic}

_dispersion

curves.

_They

have

_pointed

out that it is

_possible

to define for

_stronger

_{Bragg peaks pseudo}

Bril-louin zones

_analogous

to those of normal

_crystals.

Experimental

conditions.

The

_alloy

of

_composition

_{Al63Cu25Fëi2}

was

_prepared

from the

_pure

_{elements(Al99.99Cu99.99}

and

_{Fe99 95)}

_by

levitation

_melting

in a hélium

_atmosphère,

followed

_{by a quench}

from 1150° C

_by

planar

flow

_casting,

as is described in

_{[5] ;}

_part

of the brittle flakes were annealed

_during

_many

_days

in an alumina crucible under vacuum, at 860°

_C,

_just

below the

_peritectic

transformation and then

slowly

cooled. The

_{quasicrystals}

_{grown from} the melt are surrounded

_by

small

_grains

of

_slightly

différent

_composition.

The

_sample

used in our inelastic neutron

_study

consisted of a 2 mm diameter monodomain

quasicrystal

of dodecahedral

_shape

with

_pentagonal

faces. It was characterised

_by

a

_complete

neutron diffraction

_study

on a four-circle instrument. A set of

_symmetry

related

_Bragg

reflec-tions was

_investigated

with

_respect

to their

_precise

orientations and intensities in order to check the icosahedral

_symmetry,

and no deviation was observed. The

_{high perfection}

of the

_sample

was ascertained

_by

_studying

the reflection

_profiles

which

_correspond

to almost the instrumental

resolution obtained

_by

measurements on an ideal

_{germanium single crystal.}

These results

_imply

a

_perfect

_quasicrystal

without

_any

_phason

strain,

_especially

when

_comparing

them to those

ob-tained on monodomain icosahedral AlLiCu

_samples

where the best ones show a

_"mosaïcity"

of

about 0.8° and a

_strong

and

_{typical dependence}

of the reflection

_profiles

on

_Q1,

which is

com-pletely

absent for the AlCuFe

_sample.

A data collection of the intensities of all

_Bragg

_peaks

_up

to

Q

=11.6

Â- 1

has been achieved to allow a

_complète

structure

_analysis

of the AlCuFe icosahedral

phase.

First results have been

_published

elsewhere

_{[12] .}

Additional

reflections,

observed for the

microcrystalline

state

_{Of A43.5CU24Fel2.5}

_{by X-ray}

_precession

_photographs

_[6]

were

_checked,

but

no

_intensity

could be detected.

_{Finally, X-ray}

measurements on

_{powdered single crystals}

of iden-tical

_preparation

show reflections of the F icosahedral

_{phase, only.}

Even with the

_good

resolution

Inelastic neutron

_scattering

measurements have been carried out on the three axis

spectrome-ters 4F1 and

1T,

_respectively

on cold and thermal sources at the

_Orphée

reactor in

_Saclay.

In order

to measure

_phonon

_dispersion

curves for the main

_symmetry

directions of the icosahedral

_phase,

the

_sample

was oriented with a

_{scattering plane}

defined

_by

two

_orthogonal

two-fold axes. This

plane

also contains a three fold and a five fold

_axis,

and its schematic

_diagram

is shown in

_figure

1.

Fig.

1. -

Scattering phase:

circles locate

_Bragg

reflections. Dark

_large

circles indicate

_{high intensity peaks}

around which acoustic modes were looked for. In

_calculating

irrational

_pseudo

indices

H,K,L

with H =

h +

_h’r,

h’ = _{k +}

k’r,

L =

É + É’r

(r: golden

mean),

we took a

_pseudocubic

lattice _parameter a = 16.944

Â.

Here

_{Bragg peaks}

are labelled

_following

the

_indexing

method of icosahedral

_{quasi periodic}

_crystals

_by

Cahn et aL

_[13].

Arrows indicate

_typical

_phonon

scans.

1788

or normal to

_symmetry

axes around

_Bragg

_positions

which have different

_QIB

values.

On both

_{spectrometers}

_{pyrolytic graphite}

_(PG[002])

has been used as monochromator

(ver-tically bent)

and

_analyser.

On 4FI

_spectrometer

constant

_kj

= 2.662

A-1

scans allowed us to

measure

_phonons

in neutron _energy

_gain,

with a

_horizontally

bent

_{analyser (energy}

resolution: -0.23

THz,

_FWHM).

On 1T

_spectrometer

constant

_kF

=

2.662,

3.85 or 4.25

A-1

scans were used

to measure

_phonons

in neutron

_energy

loss with a flat

_analyser.

Phonon modes have been detected in

both,

transverse and

_{longitudinal, configurations}

and found to follow the usual linear

_dispersion.

_Systematic

data

_{analysis, accounting}

for the

convolu-tion of the instrumental resolution with the observed linear

_dispersion

indicates that these

_phonon

modes have no intrinsic linewidths within

_experimental

_accuracy. An

_example

of

_typical

neutron

groups

is shown in

figure

2.

Fig.

2. -

_Typical

neutron _groups for the transverse acoustic mode

_emanating

from

_{(0/0 4/6}

_0/0).

Experi-mental

_points

are shown

_along

with the fitted _responses

_{(full lines).}

According

to the

_signal

to

_background

ratio we were not able to ascertain

_any

_phonon

_peaks

at

_{energies higher}

than about 2.5 THz. The

_slopes

of the linear

_dispersion

curves of transverse

acoustic

_(TA)

and

_longitudinal

acoustic

_(LA)

branches are

_independent

of the direction of

prop-agation

and of the

_QiB

values. This is

_clearly

seen in

_figure

3 where the fitted measured values are

reported

(together

with the

_slopes

for

_pure

_aluminium).

We wish to

_emphasize

that the

_independence

of the results with

_respect

to

_QB

values

_supports

the

_concept

of the existence of a

_pseudo

Brillouin zone introduced

_by

Benoit et aL

_[11]

for a

Fibonacci

chain,

and that the

_isotropy

of the

_slopes

of

_phonon

branches

_(LA

and TA

_modes)

for diffferent

_symmetry

directions is not _very

_surprising,

due to icosahedral

_point

_group

_symmetry.

But since this first

_experiment

was

_performed

on a

_very

small

_sample

_(N

7

_mm3),

a small

_anisotropy

of the

_slopes

_may have not been detected.

We have found that we could follow all the studied TA modes

_up

to 0.44

A-1

with no

_significant

Fig.

3. -

a)

Unique

TA

_dispersion

curve.

b) Unique

LA

_dispersion

curves : 0

_{2/3 5/8 0/0;}

+

_0/0

4.6

_{0/0; A 4/6}

2.4

_0/0.

Full lines are

_guides

to

1790

in real _space without

strong

scattering.

We have not found _any evidence for _{energy gap} in our

measurements.

Furthermore,

the

_comparison

between results obtained in _very different

_experimental

condi-tions on the two

_{spectrometers}

favors the

_assumption

that the lack of observation in the

_higher

en-ergy range is due to

_{expérimental}

limitations rather than to

_physical

reasons. as described

_above,

this first

_experiment

on a monodomain

_sample

does show that at leat acoustic modes exist in a

quasicrystal,

in

_agreement

with the

_{quasiperiodicity}

of the

_lattice;

but

_{larger high quality samples}

are needed to obtain more

_complete

_data,

_especially

when one wants to observe _energy

_gaps

and

optic

modes.

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