Guinier-Preston zones in Al-3 at.% Ag

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Guinier-Preston zones in Al-3 at.% Ag

B. Schönfeld, A. Göcmen, G. Kostorz

To cite this version:

B. Schönfeld, A. Göcmen, G. Kostorz. Guinier-Preston zones in Al-3 at.% Ag. Journal de Physique

I, EDP Sciences, 1992, 2 (6), pp.1075-1081. �10.1051/jp1:1992197�. �jpa-00246589�

Classification

Physics

Abstracts

61.55H 81.30M

Guinier-Preston

_zones

in Al-3 at.fli Ag

B.

Sch6nfeld,

A. G6cmen and G. Kostorz

Institut flit

Angewandte Physik,

ETH Zorich, CH-8093 Zorich, Switzerland (Received 7

Janua~y

1992, accepted in

final form

17

Februa~y

1992)

Rdsumk. on _a mesur£ la diffusion de rayons X aux

grands angles

_pour un monocristal d'Al- 3 9bat.

Ag.

L'£chantillon _a £t£ vieilli pour produire ^des zones de Guinier-Preston (« zones E »). A

pant

d'une combinaison des intensit£s diffuses

correspondant

h l'ordre h _courte distance, qui ont

£t£

s£parses

des intensit£s mesur6es, _avec des rdsultats ant£rieurs de diffusion de rayons X _aux

petits angles,

des cristaux ont £t6 simul£s _sur ordinateur.

L'analyse

de la

disposition

des atomes dans _ces cristaux semble supporter ^la

proposition

r£cente d'un enrichissement

d'argent

dons _une

couche extdrieure des _{zones E,}

Abstract. Diffuse wide-angle X-ray

scattering

has been measured from _an Al-3 at.9b

Ag single

crystal.

The

sample

was

aged

for 4 min at 453 K to

produce

Guinier-Preston _zones (« e-zones »).

Combining

the

separated short-range

order

intensity

with

previous small-angle X-ray scattering

results,

crystals

_{were computer} modelled. An

analysis

of the atomic arrangements in these model

crystals

tends to support ^the recent

suggestion

of _a silver enrichment in the shell of the _E-zones.

Introduction.

Guinier-Preston _zones

(GP zones)

_are metastable

phases

found

during

the

early

_stages of

decomposition.

In

Al-Ag they

_were first observed

by

Guinier

[II

with

small-angle X-ray scattering (SAXS).

His basic model of these _zones as silver-rich

spheres

has been refined _over the years

(for

a recent review, _{see, e-g-}

[2]).

In

subsequent investigations

the existence of _two types ^{of GP} zones was

introduced,

so-

called q-zones below about 443K and _e-zones for

higher temperatures.

^{This idea} was

supported by

SAXS and

atom-probe

^field ion

microscopy (AP-FIM),

where _a

significant change

in the _zone

composition

_was ^determined around 443 K

(Baur

and Gerold

[3],

Osamura _et al.

[4]).

Naudon and Caisso

[5]

and also

Dubey

et al.

[6], however,

did not observe such _a distinct

change

in the zone

composition

with

aging

temperature. ^{But from the} presence of two

peaks

in _a Porod

representation

of SAXS data for the _e

regime,

both groups

suggested

a different silver distribution in _~- and _e-zones- The _q-zones are

homogeneous (possibly short-range ordered),

and the _e-zones have _{a more}

complex

structure : while _a silver-enriched

core and _a

depleted

shell _were

suggested by

Naudon and Caisso

[5],

_a

depleted

core and _an

outer shell of

nearly

_pure silver tumed out to be _more

appropriate [6],

based _{on a} detailed

comparison

of simulations with

experimental

results.

1076 JOURNAL DE PHYSIQUE I N° 6

Small-angle scattering

is suited for _an

investigation

on a

larger

than atomic scale. It _was found useful to also include

wide-angle

diffuse

scattering

in order _to determine _more

reliably

the small-scale

Ag

distribution within the _e-zones.

One

quantitative wide-angle scattering study

on

Al-Ag

has been

performed by Gragg

and

Cohen

[7]

who

investigated

_an Al-5

at.fbAg single crystal aged

for 14h at 383 K and

observed _no intemal order within the silver

agglomerates

that _were

reported

to be octahedral in

shape

and to have _{an average}

Ag

content of 68 at.9b. It is

tempting

_to

_accept

these results _as

being fully

characteristic for _q-zones. But _as noted

by Dubey

et al.

[6],

the heat treatment

chosen _was too short, ^and

quenched-in

silver

agglomerates

are

probably

still

dominating.

That _{zones are} octahedral and bounded

by ( ii1) planes

is

supported by high

resolution

electron

microscopy [8]. Using

transmission electron

microscopy

_a

faceting

_on

(100) planes

in addition to the dominant

(111)

facets _was found for somewhat

larger

zones

by

Alexander _et al.

[9]

and followed _{as a} function of temperature. ^With

increasing

temperature

faceting

decreases and the

shape

of the _zones

changes

from _a truncated octahedron to a

truncated

sphere.

Similar results _were deduced from SAXS

[6],

with _a

slightly higher

percentage ^of

( ii1)

facets than

given

in

[9].

For _a

wide-angle

diffuse

scattering experiment

it had _to be

kept

in mind that the _e-zones should _not be _too

small,

in order to be able to demonstrate _a

possible

silver

inhomogeneity

within the _zones in

computer-modelled crystals,

but small

enough

to avoid that the

modulation in the diffuse

scattering

would be too

sharp

close to the direct beam and the

Bragg

reflections.

Furthermore,

_a combination of the

wide-angle scattering

with the SAXS data of

Dubey

et al.

[6]

_was to be

attempted.

Theory.

The

diffusely

scattered elastic coherent

intensity

from _a

binary alloy

has two contributions _:

one due _to the presence of two

types

^{of elements}

(short-range order/decomposition)

and the other due _to the static

displacements

of these atoms from the _mean lattice sites

(size effect).

The

displacement scattering

cannot be

represented

in closed form and is

usually

_as in the present case

approximated by

_a series

expansion

_up to terms

quadratic

in the static atomic

displacements (Bone

and

Sparks [10],

_see also Schwartz and Cohen

[11]).

For _a cubic substitutional solid solution the chemical order which will

only

be of interest in the

following, gives

rise to a

scattering intensity Is~o according

to

~SRO

(h)

"

£ £ £

_{"fmn C°S}

("hl

_C°S (

"h2

m

)

_CDS

(Wh3

_n

)

t

m n

where h=

(hi h~h~)

^is the

scattering

vector in

reciprocal

lattice units

(r.I.u.)

and

ai~~ are the

Warren-Cowley short-range

order parameters

[12]

defined

by

"fmn " 1~

P©/CB

P£$

is the conditional

probability

of

finding

_a B atom

(the

concentration of B _atoms is

c~)

at an

imn site,

if _an A atom is at

position

000.

Thus,

_door has _to be

equal

to one. For _a

homogeneous

solid solution ai~~~~y~~ =

0,

and

Is~o(h)

is the monotonic Laue

scattering (defined

as one Laue

unit).

A

short-range

ordered fcc

alloy

has aj _Jo <

0,

but _a

~~o ^~ 0 for _a

decomposed

_one.

The various

scattering

contributions _can be

separated taking

into _account their different

symmetries

in

reciprocal

_space. For

X-rays

^this

technique

was introduced

by Georgopoulos-

Cohen

[13]

who extended the

Borie-Sparks

evaluation

[10] by explicitly including

_a variation

of the form factor ratios for

X-ray scattering.

The

Georgopoulos-Cohen technique

was

applied

in the present

investigation.

Experiment.

An Al-3 at.fb

Ag single crystal

_{was grown}

by

strain

annealing [6].

A slice 9 _mm in diameter and 2.5 _mm thick _was cut

by spark

erosion. The

sample

_was

homogenized

at 848 K for 2

h, quenched

into water and

aged

at 453 K for 4min in _a silicon oil bath. With such _a heat treatment, the formation of the

subsequent

metastable

y'-phase

^is still avoided. The

sample

surface _was

finally polished using

_a 3 ~m diamond spray.

The

wide-angle scattering

_was measured _on a four-circle

diffractometer, using

Mo

K~ radiation,

_a

pyrolitic graphite

monochromator and _a

high-purity

Ge detector. The

sample

was mounted under _an evacuated

Be-hemisphere

to reduce air

scattering.

For _a detailed

description

of the

set-up,

see Klaiber _et al.

[14].

Data _were taken _at about 8 000

positions

in

reciprocal

_space

(I.e.

diffractometer

settings),

with _more than 10 000 counts per

position.

The various

settings

_were chosen

appropriate

to _a

Georgopoulos-Cohen analysis,

with about 50

symmetry-equivalent positions

for _one

position

within the minimum

separation

volume for

short-range

order

ion

a

grid

of 0.I

r-I-u-)-

The data _were corrected for

background,

^{thermal diffuse}

scattering

and

Compton

scattering.

Thermal diffuse

scattering

_up to third order _was calculated

using

the interatomic force constants up ^to

eight neighboring

shells _as determined

by

Gilat and Nicklow

[15]

for pure aluminum.

Compton scattering

was calculated from the data of Cromer

[16]

and Cromer and Mann

[17].

The atomic

scattering

factors were taken from

Doyle

and Tumer

[18]

with

dispersion

corrections

given by

Sasaki

[19].

Absolute intensities _were calculated

using

the

scattering

of

polystyrene

at sin MIA

=0.5A~' _(&

_{is half the}

_{scattering angle}

_and

A the

wavelength).

The calibration before and after the

experiment agreed

within 2 9b.

Results and discussion.

The

separated short-range

order

intensity

is

partly (there

is _a total of 153 data

points

in the present

case)

shown in

figure

I. It tumed out to be

appropriate

to

plot

the intensities _versus the

magnitude

of the

scattering

vector, h. This could

already

be

anticipated

because the SAXS

experiment

showed _a rather

isotropic intensity

distribution

[20].

The data _are in

good

agreement ^{with the} SAXS results obtained from _a

sample

with _a

comparable

heat _treatment.

These intensities _were

averaged

within _a

(110) plane. Surely, they

_are not

just short-range

order

intensities,

but the static atomic

displacement scattering

for such small values of h is small for _an

alloy

with _a small lattice misfit of 2 _to 3 _x

10~~ [21].

12

iQ O

O

8

d °.

£ ₆

o 2

°$Y

0

0.2

h

Fig. I.- _SAXS [20] (.)

of

1078 JOURNAL DE

PHYSIQUE

I N° 6

The

separated short-range

order intensities _were fitted with the

Warren-Cowley

short- range order parameters. ^{About 20 to} 30 of them could thus be determined. As the standard deviations

steadily

increased for _a

larger

^number of

parameters,

a set of 23 ai~~ was chosen

(weighted

R-value

=

0.045, x~=1.4). _Figure

2 compares the

intensity

from

small-angle scattering

with the recalculated

short-range

order

intensity.

It is obvious that _a distinct

underestimation is observed close _to the

origin

which is reflected

by

_a~y~~

=

0.831(7).

If _one adds the SAXS data _to the

separated short-range

order

intensity,

about 90 _{ai~~ can} be fitted

(weighted

R-value

=

0.086, x~

=

7.2).

With _a

larger

number of ai~~ the

system

^of

equations

now becomes

unstable, indicating

that _a volume and not

just

_a

plane

of SAXS data

might

be

required

for the

least-squares fitting.

With

91ai~~

the recalculated

Is~o(h) reproduces

the

general

behaviour of the SAXS

data,

but not

unexpectedly

fails to

reproduce

the interference

peak.

With door =

1.038(12)

the theoretical value is reached within three times the standard deviation that _was

solely

determined from

counting

statistics. The _{a i~~}

~~y~~ ^are all

positive, decreasing monotonically

within _one standard deviation towards _zero, the value for _a

statistically

uncorrelated

arrangement.

Figure

2 also allows the radius of

gyration R~

to be estimated

(for spherical particles

the

particle

radius is

R~

=

fi _R~).

_The

experimental

value from SAXS is

R~

=

14. 5

(6) A,

and

the value determined from

Is~o(h)

recalculated from

91ai~~

is

only slightly

lower

(R~

= 11.8

1).

_{For such}

a

particle

size _a model

crystal

with 32 _x 32 _x 32 unit cells

(the

lattice parameter ^{is 4.05}

A)

will be

sufficiently large.

Several

crystals

were modelled with all «i~~ _~~y~~

starting

from _a random

arrangement

^and

using periodic boundary

conditions. An

algorithm

_was used to

exchange

Al and

Ag

atoms if _a

closer

approach

to the

experimental

a i~~ is

reached,

_a

procedure

first realized

by

Gehlen and Cohen

[22].

All the 90 _ai~~

finally

obtained _were within the standard deviation of their

experimental value,

with _a

typical agreement

^{of 0.1 9b} or better.

s

4

- *O

j °@

~ ₃ ~O

~ °m

- ~

*ii

Do

_ *,

* ~.

- O *

c O ^~ *O~

~ ^* _{_}

l °

O ° _O ^* * .

O o ~ ^*° ~

b J

0 o

0 0.03 0.06 0.09 0.12 0.15

h~,(r.I.u.)~

Fig.

2. Guinier

plot

of the SAXS

intensity

[20] (.), the

short-range

order

intensity

from 23 _ai~~ (*) and from 91 ai~~ (o).

Figure

3 shows _a

plot

of

eight

consecutive

(100) planes

of _a modelled

crystal,

where each

figure _represents

two

planes.

One finds that the size of _{the e-zones}

corresponds

to the radii found from _a Guinier

plot (Fig. 2). However,

the modelled

particles

_are not

really spherical.

Especially,

it _seems difficult _to define _a

precise interface,

and thus the

particle composition

cannot be

given exactly.

The value of

71(10)

at.9b

Ag

determined

by Dubey

et al.

[6]

from the

integrated intensity

of

SAXS,

is

surely

consistent for the _zones shown.

Conceming

the

a b

c d

Fig.

3. Four consecutive (100) double

planes

of _a

crystal

modelled from 90 ai~~ (. _;

Ag,

o : Al).

discussion about the intemal structure of the _{e-zones, a} silver

depletion

in the _cores is found to be _more

plausible

_even if the

particle

surface is _not

precisely

known.

Thus,

the

three-phase

model of

Dubey

_et al.

[6]

should represent ^the _average characteristic

particle

structure. It is obvious that the

present

^atomic

type

^of

modelling

is _{on a} scale too fine to

give

the _«

typical

_»

structure of the _zones in _an easy way. A different

algorithm

for

modelling involving

not

just

atoms but

appropriately

chosen

agglomerates

is _more

promising

and will be

developed.

For

comparison

consecutive

(100) planes

of _one out of several

crystals

modelled with all the

Warren-Cowley short-range

order parameters ^of

Gragg

and Cohen

(Tab.

II of

[7])

_are shown in

figure

4.

Up

to the shell index

imn

=

510,

the agreement ^{between the modelled and the}

experimental

_{ai~~ was} « 3 9b. Beside the

expected

difference in the

particle

size

(the

radius of

gyration

is 5.9

A _[7])

_{it is}

striking

that these

particles

have _a

higher

silver concentration

(nearly

100

9b)

than

given

in

[7].

Thus

they

represent ^silver

agglomerates. Surely

the silver

1080 JOURNAL DE PHYSIQUE I N° 6

a b

c d

Fig.

4. Four consecutive (100) double

planes

of _a

crystal

modelled with the 26 ai~~ of [7] (. _: Ag, O

Al).

content can be reduced to about 70 9b if additional

assumptions

about the

shape (sphere

_or

truncated octahedron) _are

imposed.

Acknowledgement.

The authors thank Ph. A.

Dubey

for

making

available the

single crystal

and for communicat-

ing

the SAXS data.

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