Small angle neutron scattering from polycrystalline Cu-2 at% Co aged and dynamically deformed

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Small angle neutron scattering from polycrystalline Cu-2 at% Co aged and dynamically deformed

P. Ancrenaz, C. Servant

To cite this version:

P. Ancrenaz, C. Servant. Small angle neutron scattering from polycrystalline Cu-2 at% Co aged and dynamically deformed. Journal de Physique I, EDP Sciences, 1992, 2 (6), pp.1113-1128.

�10.1051/jp1:1992200�. �jpa-00246592�

Classification

Physics

Abstracts

61.12 61.12B 61.12E

Small angle neutron scattering from polycrystalline Cu-2 at'Jb

Co aged and dynamically deformed

P. Ancrenaz

(')

and C. Servant

(2)

(')

DGA/CREA, 16 bis _avenue Prieur de la C6te d'or, 94114 Arcueil, France

(2) ISMA, Laboratoire de

M£tallurgie

Structurale (*), Universitd de Paris Sud, 91405

Orsay

Cedex, France

(Received 30 October J99J, revised 28 February J992,

accepted

3 March J992)

Abstract. The

unmixing

of

polycrystalline

Cu-2 atfb Co

alloy

water

quenched

then

aged

at

650 °C _was followed

by

small

angle

neutron

scattering

and transmission electron

microscopy.

The two-dimensional

scattering

pattems were

analyzed

with _a

two-phase

model which leads to the time evolution of the size, number

density

and interdistance of the

spherical precipitates

enriched in Co.

During ageing,

the

precipitates partially

lose

coherency

and their

magnetic

state evolves from

ferromagnetic

to

paramagnetic stability.

Each state was shown _to be stable down _to 10 K.

Samples aged

for 3 and 120 h _were

subsequently

deformed at 20 °C

by dynamic compression

to different strains. From _a comparison of the SANS recorded _on three faces

(perpendicular, parallel

and to 45° of the

compression

axis) and with the

help

of TEM observations,

qualitative

information _was obtained

conceming

the deformation modes of the

precipitates.

1. Introduction.

In the

literature,

_many studies have been devoted _to the Cu-Co system ^{which shows} a

simple phase diagram.

In

particular alloys

with low Co concentrations have received great ^attention.

Among them,

dilute Cu-Co

alloys

with

0.4, 0.5,

0.8 and 2 atfb

Co, aged

at 510 and 560 °C have been

extensively

studied

by Wagner [1-4] by

^small

angle

neutron

scattering (SANS).

The

existence of extended

compositional

fluctuations which

precede

the formation of stable

precipitates

of the f.c,c. Co rich _a

phase

has been established. These precursor fluctuations

seem to have considerable influence _on the reaction kinetics of _a -Co

precipitation compared

to the

prediction

of classical nucleation

theory. Furthermore,

the initial sizes of _a

precipitates

are

significantly

increased

compared

to the theoretical

prediction

of the size of critical nuclei.

SANS and

magnetic

measurements were also

performed

in Cu-I atfb Co

single crystals aged

at 600 °C

by

Abersfelder _et al.

[5]

and at 500 and 600 °C

by

Emst et al.

[6]

in order to

study

the

(*) Unit6 associ£e CNRS _n 1107.

magnetic anisotropy

_energy of the

precipitates responsible

for _a transition from superparama-

gnetism

_to

magnetically

stable behaviour.

The present paper

reports

the results obtained

mainly by

^{SANS from}

polycrystalline

Cu-

2atfb Co

previously aged

at 650°C for various times.

First,

SANS measurements were

performed

at 20 °C without

application

^of a

magnetic

field in order to

study

the

growth

kinetics of the

precipitates. Secondly, experiments

_were carried _out with _an

applied magnetic

field of

increasing strength

_up to 9kOe

(this

value is

higher

than the saturation field

H~),

^and as a function of

decreasing temperature

^{from 293} to 10

K, only

_on two

samples initially aged

for 3 and 120h in which TEM revealed coherent f-c-c- and semi-coherent

precipitates, respectively.

We

recently

determined their

respective

chemical

composition by

anomalous small

angle X-ray scattering [7]. Finally,

the

specimens aged

for 3 and 120 h at 650 °C _were studied after deformation

by dynamic compression

in order to obtain further

information _on the deformation modes of the _two

types

^of

precipitates.

In

fact,

such Cu-Co

alloys

_may become

alloys

to fabricate

chapped charges

devoted to

pierce

_armour

platings.

2. Material.

The

polycrystalline

Cu-2atfb Co

alloy

was

homogenised

at 950°C for 2h under argon

atmosphere

then water

quenched. Precipitation

treatment _was

performed

at 650°C also under argon

atmosphere

for

ageing

times

increasing

from 1/2 to 120 h.

Dynamic compression

on the

specimens aged

for 3 and 120h _was carried out with the

help

of _a

Hopkinson apparatus.

Three values of uniaxial

compressive plastic

strain

(5,

10 and 20

fb)

_were chosen and the deformation rate i _was about 103 s-'.

Samples

with

parallel

faces about I _mm thick

were cut from the deformed

specimens,

with the surface

parallel, perpendicular

and _at 45°

from the

compression

axis.

3.

Experimental.

3,1 SANS. The SANS

experiments

were

performed

at the laboratoire Ldon Brillouin in

Saclay, France,

with the

equipment

installed _{at one} of the

guide

tubes of the

Orphee

reactor and

having

a two dimensional multidetector

(«PAXY»).

We worked with _neutrons of

wavelength

A

=

1.2 _nm and AA IA

~ 10 fb. With such _a

wavelength,

far

beyond

the

Bragg

cut- off for copper (A

B ⁼ 2 d

j jijj ⁼ 0.416

nm), multiple scattering

is minimized. The

unpolarized

neutron beam had _a diameter of 7.6 mm, and the collimation _was considered to be of

pinhole

geometry.

^The scattered neutrons were counted

by

_a detector

consisting

of128 _x 128 square elements of 0.5 cm

edge length.

The

specimen

to detector distance _was either 5.19 _{m or}

6.83 _m, and the range in momentum transfer q was 0.036 _{wq w} 0.366 nm~ ^' and 0.028 _w

q w 0.245

nm~'

; q, the modulus of the

scattering

vector q, is

equal

to 4 _gr sin o/A where 2 o is the

scattering angle (the angle

between the incident and scattered

neutrons) [8].

A

magnetic

field H from 0 to 9 koe _was

applied

across the

samples

studied.

Usually,

the H direction is called the Oz direction and _a is the

angle lying

between the directions of H and q.

SANS spectra were recorded from 293 _to 10 K for different values of H, with the

specimen

in air.

3.2 TEM. -TEM and microdiffraction

experiments

were carried _out with _a JEOL120 C

microscope operating

_at 120kV. The thin foils _were obtained

by electrothinning

_at 20 °C

using

the

two-jet technique

with _a solution D2 from Struers.

4. Data

analysis.

The _neutron

scattering

intensities recorded _were treated

using

the standard computer

programs of the LLB.

Depending

on the measured

scattering,

it is then

possible

to make

isotropic

or

anisotropic regroupings using

sectors on the detector. Sectors of _ten

degrees

were

selected. For each sector, the

angle

_a between the directions of the

scattering

vector q and the

magnetic

field H

applied

_was defined from 0 to 90° every ^ten

degrees.

The chosen limits of the

angular

sectors were then

respectively equal

to 5°

~ +

5,

₊ 5° _~+

15°,

,

+ 85

~ 95°. In

general,

the scattered

intensity

from all the

samples

under consideration is sufficient to allow such

angular

sectors often

degrees

to be used with _some statistical

reliability.

The data _were corrected for local variations in detector

efficiency,

for the

background intensity

extemal _to the

sample (I.e.

the empty

sample holder)

and for the transmission. We used _{water or} vanadium _as a standard to normalize the scattered

intensity

measurements and to obtain absolute values for the

scattering

cross-sections.

The differential neutron cross-section of small

angle

neutron

scattering

is the _sum of two terms

[9]

_:

d~ ^total d~ ^nucl d~ mag

~ ~

^~

~

^~~~

>

i)

The nuclear _term consists of _two parts

The first part

(subscript incoh)

is due _to the

spin incoherency

and the natural

isotropic

mixture which constitutes each element of the

sample

^studied. It _can be

expressed

_as follows _:

ldl2

>ncoh 4

Qr

~ _{~ ~~}

~~~ _~~ ~~~~ ~~~

where

C~

^and

«~ respectively represent

^{the atomic fractions and the incoherent neutron cross-}

sections for any element

j.

For the

present

case,

Cc~

₌

^0.02,

_«c~ =

0.1042 and d _~ ^nucl+ sp>n

«c~ =

1.24 bar at~

[10],

then

= 0.105 bar sr~ at" The chemical _« incohe- dfl _>ncoh

rency » or Laue

scattering

_can been

expressed

as follows in the _case of the

fully

disordered state _:

l~"

=

I~

^C_j

b/ _{(I~ C~}

b~)~ bar sr~ ^' at ^'

(4)

dn _Laue

where b~ is the coherent

scattering length

of the element

j.

For the present

alloy, by using bc~

^and

bc~ respectively equal

to 0.76 and 0.25x10~'2cm

[10], (~"

dn _Laue =

5. I x 10~^~ bar sr~ ^' at ^'

ii)

The

magnetic

term also consists of _two

parts

:

The incoherent

part

can be

expressed

_as follows _:

0.0486F~(q) C(I C) (m~ m~)~,

where F

(q

is the atomic form factor

equal

to

unity

for very ^small q

values,

C is the fraction of

atoms of type ^A

(I.e. Cu)

and m~ and m~ are the average

magnetic

moments of type ^A and B

d~ mag

atoms

respectively (m~

= 0 and m~ = 2.I Bohr

magnetons). So,

is

equal

to

dl2 _>ncoh

4.2 x 10~^~ bar _sr~ ^' _at~ ^' The _sum of the above calculated terms is about 0.12 bar sr" ^' at~ ^'

Compared

to the values of the coherent terms

(see Fig.

3 in the _case of the Cu-2 atfb Co

alloy, aged

for 3

h,

^~"

=

10~ bar sr~ ^' at~ ^' for q = 0.25 nm"

'),

it _can then be

neglected.

It _can be d12

noted however that this _sum is

higher

than the _one

= 0.06 bar sr~ ^' at~

')

_deduced from the

extrapoled

part

(q

m 0.4 nm~ ^'

)

of the SANS _curve of Cu-2 atfb Co

alloy

water

quenched

and studied

by Wagner [4].

In the _case of the

samples

of Cu-2 atfb Co

aged

for

1/2

to 15

h,

in which

ferromagnetic

coherent

precipitates

_are embedded in _a

nonmagnetic matrix,

the

isotropic

nuclear

part

^{of the}

scattering

_was

appreciated

in the field direction when the

magnetic

field

applied

_was

equal

_or

higher

than the saturation field. In the _case of the

sample aged

for 120 h, where

paramagnetic

precipitates

_are embedded in the

nonmagnetic

_copper

matrix,

_we used _:

d~ to~l d~ nud

d12 d12

5. Results and discussion.

5.I TEM. The

alloy aged

for 3 h contains coherent

precipitates

enriched in cobalt

[7].

A diffraction contrast associated with the elastic strain around the

precipitates

is observed

(Fig. I).

This _contrast

presents

a zero-contrast line which is

perpendicular

to the

operating

"RV

?~w~

~i

#

(

Fig.

I.

Bright

field

micrograph

showing coherent

precipitates

in the

alloy aged

for 3 h at 650 °C.

Fig.

2.

Bright

field

micrograph

showing

partially

coherent

precipitates

in the

alloy aged

for 120 h _at 650 °C.

reflection vector. After 120 h of

ageing,

the

precipitates partially

lose

coherency

because of

coarsening,

and

they adopt

_a

polyhedral shape. They present

^Moird

fringes

and lattice mismatch _can be estimated from Moird

spacing

measurements.

Many

interfacial dislocations

are visible around the

periphery

of these

partially

^coherent

precipitates.

These dislocations appear ^{for the} accommodation of the

crystalline

lattice between

precipitates

and matrix

(Fig. 2).

5.2 SANS.

5.2.I SANS specti~a

of undeformed samples

_{as a}

function of ageing

time and without

application ofmagnetic field.

The two dimensional SANS

isointensity

pattems are

isotropic

whatever the

ageing

time

comprised

between

1/2

and 120 h. This result confirms the TEM observations _: the distribution of the

precipitates

is

homogeneous

^and there is _no

preferred

orientation of these

precipitates.

^The _curves ^~"

=

f(q)

obtained after

isotropic

d12

regroupings

_are shown in

figure

3.

They

_{present a} maximum _{at a} q

position

which is the lower the

higher

the

ageing

time.

Furthermore,

for _a

given

_q

value,

the scattered

intensity

is

increasing

^{with the}

ageing

time. The presence of _a maximum _on the

scattering

_curves can be associated with different

phenomena [8].

When

interpartide

interference effects _are conside-

red,

from the determination of the q~~~

position

of the

maximum,

the number of

scattering particles

_per unit volume

(NIV

_can be estimated

owing

to the relation established

by

Roth

[I I]

_:

NIV

=

1/2(q~~~/gr /)~ ₍₆₎

d _~ d Q

lo lo^~ O 2 h

~

n 3h

a lsh

~ j

~3

^{' 120h}

a

6,io3

>

R~

~'1

~

~ 2,io3

0

0

~j~ -ij

Fig.

3.

dil

The _mean interdistance D between

precipitates

can be estimated from TEM observations.

This interdistance represents ^{the diameter of the excluded}

sphere.

This excluded volume

means

that,

in the

vicinity

of _a

growing precipitate,

no other

precipitate

can grow due to the

concentration

depletion

ⁱⁿ solute element.

By assuming

identical

precipitates

^and

only

when the system ^{is dilute}

enough (so

without _a

bump

on the

scattering curves),

it is

possible

to

calculate the radius of

gyration _R~

of the

precipitates by

^the Guinier

approximation [8]

_:

d«/d12 aA exp

[- (q~R()/3] ⁽⁷⁾

The

approximation

is valid for

spherical precipitates

if

qR~~l.3 [8].

The radius R of _a

sphere

is related _to the radius of

gyration R~ by

:

R

=

fiR~. ₍₈₎

The SANS _curves

reported

in

figure

3 show _{a more} or less well defined maximum.

So, only

an estimate of

R~

can be obtained

by plotting _log (d«/d12

_versus

q~(q

~

q~~).

In this

plot, straight

lines _were obtained

only

for

ageing

times up ^to 15 h. The calculated R values from the estimated

R~

ones were in

satisfactory agreement

^{with the radius of the}

spherical

or

approximately spherical (120h) precipitates

determined

by

TEM. The three

parameters (R, lilv

_and

_D)

were used _as

input

data to fit the

experimental

_curves

by

the

two-phase

model

developed by

^Hennion et al.

[12].

In this model

applied

to _a

binary

system

A-B,

I.e.

Cu-Co in the present case,

spherical precipitates

of atomic

composition C~

are assumed _to be embedded in _a matrix of atomic

composition C~.

The

expression

of the differential neutron cross-section d«/dn

(q)

is _as follows _:

$ _(q)

= AN

~

vj jF~(q)2j jF~(q)j2 _ii -i(q)j (9)

where A

=

vj~(b~ _b~) (c) ^Cl

_)~

(10)

and

N~

=

(NIV )

_x

V~ ⁽¹¹⁾

where v~ is the average atomic volume,

b~

and

b~

_are the coherent

scattering lengths

of the elements A and

B, N~

is the volume fraction of

precipitates

and

F(q)

is the

shape

factor of

precipitate having

_a volume

V~, ( )

_{means an average over} all

possible

orientations of the

precipitates.

For

spherical precipitates

of radius

R,

(F~(q))~

=

(F~(q)2)

=

Fj(q) (12)

and F

(q

₌ 3

(sin qR qR

x cos

qR )/(qR

)~

(13)

1(q)

is the interference function defined

by

Ashcroft et al.

II 3]

and

)I (q)

I is the Fourier transform of the

pair

correlation function of the

precipitates.

According

to

[13],

1(q, N~,

D

)

₌ ^I

N~

_x B

(q, N~, D)

_(~^'

(14)

where

B

(q, N~,

D

=

4 grD ^~

j~

^ds

^s~

^~~~

^{~~~ (a}

⁺

^ps

⁺

^{ys~) (15)}

~

sqD

a,

p

and _{y are} related _to the volume fraction

7~ =

grN~ D~/6

of the excluded

spheres

_:

a =

(1

+ 2

~)~/(i

_{~ )~}

₍₁₆₎

p

= 6 _~

(i

+

~/2)~/(i

~ )~

(17)

y =

(1/2)

_~

(i

+ 2

~)2/(1- ~)4 ₍₁₈₎

In this

model,

the

dispersion

in size of

spheres

is _not considered. In the present case, this

hypothesis

can be considered _as valid because _we have

shown, by

ASAXS

experiments [7]

carried out _on the _same

alloy,

the presence of _a second maximum _on the

scattering

_curve of the

sample aged

for 3h related _to the very narrow size distribution function of the

precipitates.

In the _case of SANS

experiments,

the

wavelength dispersion (AA/A

=10

fb)

seems to be

responsible

for the less well defined first maximum _at q~~~ and the absence of the second maximum.

By

SANS

experiments

_{on a} 2 atfb Co

alloy

annealed _at 833

K, Wagner [4]

also observed the first maximum

only. However,

for _a Cu-0.8 atfb Co

alloy

annealed for short

periods (20 mn)

at 833

K,

he

really

observed _a well defined second maximum.

The parameters

resulting

from the

fitting procedure

with the model of Hennion

[12]

are

reported

in table I. The evolution of the radius R _versus the

aging

^time in _a R

=

f (t"~) plot

is showed in

figure

4. R increases first

strongly

_up to about 2-3

h,

then _more

slowly.

The _onset of the slower increase

corresponds

to the transition of _a

high

to

partial coherency

^observed

by

TEM. From 2-3

h,

the radius evolution follows _a power law _: R _cc t~ with _n

equal

to

1/3.

The number

density

of

precipitates ^(IV

follows

approximately

_a t~ ^'

dependence

and the volume fraction of

precipitates

is about constant and

equal

to 1.2 fb. Such results _are observed when the

growth

of

precipitates

is controlled

by coarsening phenomena (14)

^of the Lifshiftz-

Slyosov-Wagner type

^related to the volume diffusion of solute

(Co)

in the matrix

(Cu).

The

t"~

_{and t~} ^'

dependence

of the R and

lilv parameters

_agree ^with

Wagner

results characteristic for classical Oswald

ripening. According

to Wendt et al.

(15),

_{great care} must be taken to

Table I. Fitted parameters

of

the

tmJo-phase

^model.

~ ~~ ~ _~ ~ _~~ v~iurne

~~ing

~irn~

j~j

_q~~

inrn- ii

NV

iCIn

_x '° ~~

fraction

~~~

0.5 0.230 212.0 26.3 2.8 0.19

0.75 0.173 81.4 36.1 4.0 0.22

1.0 0.ill 42.5 56.6 6.1 0.40

1.5 0.092 26.5 66.0 9.0 0.81

2.0 0.083 18.0 75.3 11.6 1-1?

3.0 0.070 10.6 89.8 14.3 1.29

15.0 0.048 2.12 130.8 24.0 1.22

120.0 0.037 0.26 169.8 46.5 1.10

o

+ SA NS

o ASAXS C7J

+

+°

$~$ t'/3 CA'/3J

0 2 3 4

Fig.

4. Evolution of the radius R of the

precipitates

_{as a} function of

aging

time.

interpret

_power laws such _as

t"~ (particle growth)

^and t~ ^'

(number density decrease).

In

fact,

these laws may be found under many circumstances. For

example,

in _a Ni-14 atfb

Al, during

later

aging

stages

(the phase

transformations _y

~

y' being

still far from

complete)

the

y' particles

_grow in

proportion

to

t"~

_{while their}

density

decreases in

proportion

_to

t~

'.

_{This behaviour}

was

interpreted by

Wendt in terms of the classical nucleation

theory

and

by

_a modification of _a

theory

which considers

coarsening already during

the nucleation

stage.

In the _case of _our

alloy,

we can conclude without any doubt that _a

coarsening phenomenon

is

operative

because the volume fraction of the

precipitates

is _constant from 2-3 h up ^to 120 h.

In

figure 4,

we have also

compared

our SANS results with those obtained

by

ASAXS

(7).

The radius of the

precipitates

calculated from SANS

experiments

is

always slightly higher

and

so the

lilv

_{parameter is found lower.}

Furthermore,

the values of the radius of the

spherical precipitates

obtained from 2-3 h of _our Cu-2atfb Co

alloy

_are about identical to those

reported by Wagner

in _{a more} dilute Cu-Co

alloy (0.5 atfbco)

annealed _at 783 K. In such _an

alloy, dominating

_precursor

fluctuations,

indicated for _a 24 h

annealing,

tend _to increase the size of the

subsequent

_a Co

precipitates.

In

addition,

_as well _as

Wagner,

_we also observed

approximately

_a

q~~ dependence

of the

scattering

_{at very} small q, in the _case of pure copper and Cu-2atfb Co

alloy

water

quenched,

related to

sample heterogeneities (microvoids, dislocations...). Wagner

also mentioned for the short

annealings (0.25h),

_a

scattering

contribution

following approximately

a

q~' _{dependence indicating rod-shaped scattering}

centres that _we did not observe.

In _a Cu-I atfb Co

alloy

annealed _at 600 °C for 40 h, Abersfelder et al.

[5]

calculated radii of

precipitates

smaller than 18 _nm from SANS

experiments. According

to

Phillips [16],

the

precipitates

_are coherent with the copper ^matrix up to this size.

Furthermore,

when H~~~~~i~~ =

0,

the cobalt

precipitates

_grow

preferentially

in all

(100)

directions and _non-

spherical precipitates

^with a cubic

symmetry

are formed. But the directional

dependence

of the radius with the

(100), ii II)

and

(011)

directions of the Cu-Co

single crystal

is

quite small,

at most 7 fb. Such _a result confirms the

typical

diffraction contrast we observed

by

TEM in the _case of _our coherent

precipitates

and associated with the

spherical

elastic strain field.

5.2.2 SANS spectra recorded with

application ofa magnetic field

_on

undeformed samples aged for

3 and 120 h. For the

sample aged

for 3

h,

when the value of H is

increasing

from 0 _to 9

koe,

the SANS pattems ^become

anisotropic

and present ^two symmetry ^lines

(qflH

and

qi H).

The _{contours are}

elongated perpendicular

to the field direction and

they

narrow

down

along

^the field direction

(Fig.

5a and

b).

Such a behaviour is observed when

ferromagnetic precipitates

_are embedded within _a

non-magnetic matrix,

_or vice _versa

[9, 17].

For H

larger

than 3

koe,

the SANS

isointensity

contour

pattem

^does not

change

_{any more.}

The saturation field

Hs

is reached _as revealed

by

the evolution of the ratio of

anisotropy

T

(T

=

(d«/dn )jj~/(d«/dn )~ ~)

_as a function of the value of H. This result is in

satisfactory

agreement ^{with the work}

published by

Emst _et al.

[6]

which indicates that, within _an extemal field of 2.5

koe,

the

magnetization approaches

98 fb of its saturation.

For the

sample aged

for 120

h,

_an

anisotropic

behaviour is _not observed whatever the value of the

magnetic

field

(Fig. 5c).

This difference of behaviour in _a

magnetic

field between the

two

samples

can be

explained owing

to

previous

results obtained

by

ASAXS

experiments [7]

in order to determine the chemical

composition

of the

precipitates.

In

fact,

in the former

sample,

we determined that coherent

precipitates

contain 57 atfb Co within _a

copper-rich

matrix with 0.9 atfbco while in the latter

sample, partially

coherent

precipitates

contain

only

31 atfb Co within _a

copper-rich

matrix

containing

1.8 atfb Co. It _can be concluded that after 3 h of

ageing,

the coherent

precipitates

_seem to be

ferromagnetic owing

to a

high

amount of

« xx

~~ ^* _=iff( (-(- y «

« =_ =_= f ](£_=(~ f__ ^"

~5x El- ₌~[ f==~-

x

~= ~~~j~_x~

~_ ^~~

"C =f _~

=f~

~~~~ -~ ~~

£ 2

/ ^{=Q ~-}

== J-j-

" .

«

x ~ =-<£"

''

l

~

~ «

~

~

O. 64.

a)

cell

~ ~

~

"d - _i~

~

II '~ ^II

),

ii [((ii li

_~l~ ~

ix

~

~ ~O ^{- ~} _~ ^_

__

fi

~

_,

^{.. .- « ---}

=-. -~,-. ^« « « «

.~_-

X

w _{=~/_~£-£~}~ «

~

. - ~~~

O.

~

cell number

b) c)

Fig.

5.

with H

0

and T = lo _K, b) aged for 3 h at

650

_°C and ^{with =} 6 koe and T

at ₆₅₀

°C andwith H

= 4 koe _and T = _10K.

Co. Theiragnetic state does _{not own} to 10 K._After 120 h

coherent precipitates

of

larger size _are paramagnetic at

room ^mperatureand below ; _{in fact}

SANS

intensities

do

not

change as

a

unction of

decreasing

^{emperature down} o 10 K.

specimen aged for 3

h,

despite ^heir

small size

(R =

¹⁵ _nm), the recipitates do not

superparamagnetic.Indeed,isointensity

ongated

in

the field _directionhould

then

be observed _as in the Co-Ga _or Cr-Fe systems

[18, 19].

However, it is

possible

that _we failed to reveal the

superparamagnetism

because _we used _too

high

values of H

(m

I koe

).

For the

same

sample,

_we examined the evolution of the ratio

Q

^with

sin~

a for different values of q. This ratio is defined _as

[17]

_:

d~ total d~ total d~ total d~ to~l

~

dfl

a

dfl

a

~~

dfl

a «/2 dfl

a

~

~~~~

It will be

noted,

in

figure 6,

that _a linear

relationship holds,

^{with moderate}

precision,

whatever the q value.

Moreover,

within the scatter of the data the

slope

of the

plot

is

equal

to

unity.

This result demonstrates the

isotropy

of the

magnetic

correlation function in the

plane

normal to q. Such _a result _was

previously

obtained in the _case of _a Mn

maraging alloy (0.7549

Fe-0,1 249 Mn-0.0874 Co-0.0298

Mo) aged

at 425 °C for 32 h

[17].

~

h

'

~ i h

m ~

a#

_e

l _I

c~

.

, o

3 ^~'

~

Or 0.252 Q= 0.201

, Q~ 0.isi

Q~ 0.101 On 0.757 lo-I

, =0.504

0 6

(siltotj2

Fig.

6. -Variation of the ratio Q

(Eq. (19))

with sin~

a for different values of q. Note the linear behaviour with

slope equal

to

unity

for the

alloy aged

for 3 h, H

= 0 and T

=

10 K.

5.2.3 SANS spectra recorded without

application of

_a

magnetic field from samples aged

and

deformed

to

different degrees.

5.2.3. I

Sample aged

for 3 h. The

isointensity

contour

pattems

recorded from

specimens

A cut

perpendicular

to the

compression

axis _are

isotropic

while

they

_appear

anisotropic

for

specimens

B cut at 45°

(Fig. 7a)

and from

specimen

C cut

parallel

to the

compression

axis

(Fig. 7b)

for _a

compressive

strain _e

=

20 fb. The

anisotropy

is _more marked at 0° than at 45°

of the

compressive

axis. These results allow _{one to} conclude that the

spherical precipitates

within the

copper-rich

matrix do not behave like

hard,

undeformable inclusions in _a soft matrix.

Indeed,

with this

hypothesis,

the

spherical precipitates

would remain

spherical during

the deformation and all three SANS pattems

(at

0.45 and

90°)

should be

isotropic. Thus, they

seem to behave like deformable

precipitates

in _a hard matrix. The

isotropy

observed in the

sample

cut

perpendicular

to the

compression

axis shows that the deformation is

axisymmetri-

cell number

~~

~

~

~

*

~"

** ~~~

~ > ~

~ p~

~ ~

~~

~~i~i~>~ii> ~&<i

<,

V

g~ ~

i

Ii

o

""

*

*"

~

, ~ _~-=-=- == ~ ~

~~~ <_=J ~_-~3j_ ~~

~ *

G~~

~~~(/Z

§~

,~~~~ ~~

~

J j =_1 .~~~ i,.,,,

_-~ _~

f~

~~

l]~jj~f5lli~~ "p j-

~o~ ~ ~

"~

~

"

64

j[

j=-I

(i ~/jmi,~ ii ii~

64

~

' S~

~ -= ,~o ~ =- ~~ j ,

X ~__,- _{~"j_} ~~ ~f~

(~ ~~~l?I, $~i~'li

~

/~

i~'

o

~~~i~~ "-j--=~-5-=Pf-" ~1~~~

~"~*

_.

~~

/

~~~>l

w~j~~~nf~'~

^~

~

".

~

* '

~,

~

» ,o ^** _~

~ . ,

o o

32. 64, 96. 32. 64. 96.

cell number

a b

Fig.

7.

Isointensity plots

recorded for the

alloy aged

for 3 h, when _e

= 20 fb, at 45° (a) and 0° (b) to

the

compression

axis, H

=

0 and T

= 293 K.

cal and that the

precipitates

become

ellipsoids

of revolution

during

the deformation

[20, 21].

As the

anisotropy

for the

samples

cut at 45° and 0° of the

compression

axis becomes _more and

more marked when the

compressive

strain is

increased,

the

ellipsoids

become

progressively

flatter. In

figure 7b,

the

elongated

direction of the

anisotropic

pattem ^is

parallel

to the small axis of the

ellipsoids.

Isotropic regroupings

in the _case of

specimenA give

SANS _curves for different

e as

plotted

ⁱⁿ

figure

8a. It _can be noted that _:

the

shape

of the _curves

changes

_{as a} function of

e ;

all of them show _a maximum which becomes broader when

e reaches 10-20 fb _; the

position

_q~~~ shifts towards

higher

_q values when _e reaches 10-20 fb _; for _a

given

_q

values,

the

scattering intensity

for

e =

5fb is

higher

than when

e =

0 fb _; then it decreases

markedly

when _e

= 10 and 20 fb.

Anisotropic regroupings

made in the

elongated

direction of

anisotropy

in the _case of

specimens

C

give

SANS _{curves as a} function of _e

plotted

in

figure

8b.

Similar remarks _as above _can be made. However, the q~~~ of the SANS _curves shifts

towards

higher

_q values

only

when _e reaches 20 fb. Furthermore, for _a

given

_q

value,

the scattered

intensity

recorded when

e =5 and 10fb is

higher

than that obtained when

e =

0.

By TEM,

when

e =

5

fb,

_we still observe about 75 fb of coherent

precipitates

with _{a zero} contrast line both in

samples

A and C.

Therefore,

the

spherical shape

of the

precipitates

has not

changed

to a

large

extent

during

this small deformation.

Assuming

the _same value for NIV _as for _e

=

0 fb and _an increase in the

apparent

^{radius R of the}

precipitates,

it is

possible

to

justify

the increase observed in the scattered

intensity

for _a

given

_q value in the

plane

perpendicular

to the

compressive

stress.

dq d~

+ C

=

0%

1.053

lo'

* C = 5 %

, ^{» o} C

=

IO %

~~~~ ~~

» a g= 20

%

0.d20

IO'

*

*

a~04 1

4

_0.587

lo'

»

~ +

(

^0Ah

^lo'

«

~

0.355 lo'

~ o o

0,23d lo ^'

0.122

lo'

0, 006

IO'

000 366,~32 1.0Sd 1,4d4 1,d30 21S5 ?561 2527 3~253

10"~

q Cum J a)

d~

~~

O e

=

0 %

!205

~ . £ ₌ 5 _%~

* + e= lo %

L0~4

~

* ~. ^{a 20} %

940 ^"

do6

to'

_*

672

lo'

Q >

_~ 537 lo' k ,

,

f

^.403 lo 4

265 lo'

~

134 lo' 000

000.368 .7361.105 1.473 1.8412.2052577254633H 10-~

qillmJ-'

b)

Fig.

8. -SANS ^~"

f(q)

for different

compression

strains _e.

Specimens aged

for 3 h, cut dil

perpendicular

to the

compression

^axis

(a)

and

parallel

to the

compression

axis (b), ^{H=0 and} T= 293K.

When _e

= 20

fb,

the very broad maximum _may be related to a

larger dispersion

^{in the}

distance of

precipitates.

As q~~~ is

higher

than when _e

= 0

fb,

the average distance _{seems to} be

decreasing

and may indicate _a

fragmentation

of _some of the

precipitates.

5.2.3.2

Sample aged

for 120h.- The contour

plots

are

isotropic

for

samples

A' _cut

perpendicular

to the

compression

axis and

anisotropic

for

samples

^B' and C' cut at 45° and 0°

of this

axis, figure

9a and b.

96

~ x

~@-W

~

f fljfi

~~4~

f$

~*J-

£~~~~~~'~-

^~ _DC

64

~

(io

~ ) jl

( ~~ ^{64 -~} _~=

~ _i

8~. ~i~

~i~ ^~~ _~~

'&_~ ^W" ~ _'

~~

H *W WW ,-'S

' _~£

~S~ -~' @-~H~~

= _-

£~

32 ^~

32. 64 96 32 64 96.

a b

cell number

'---

"--

96

&, .l~y.

/~' _'~~"$ -j

ii iP/~#I

64 ~l ~° _SS I °8

~~ i~ $ °~

j ^o_jh~ ~~~j$._~~f

«

~ '°°ijvjt~×mlf~j

f

~_

~l'~©.,1*~""

^l

_, ,,~ ^~ i" *

~

~

~ '~~

o

0 32 64 96.

cell

number

c

Fig. 9.-Isointensity plots

recorded for the

alloy

aged for 120h, when

e = 209b, at 90° _to the

compression

axis (a), at 45° (b) and at 0° (b), H

=

o and T

= 293 K.

The SANS _curves obtained after

isotropic (samples A')

_or

anisotropic (samples

C' in the

elongated

direction of

anisotropy) regroupings

are

plotted

in

figure

10a and b.

For both

samples

A' _et

C',

and for _a

given

_q

value,

the

scattering intensity

is

always decreasing

when

e is

increasing

from 0 _to 20 fb _;

the

position

of the maximum shifts towards

higher

_q values and becomes smoother.

As _{soon as}

e reaches 5

fb,

it is _no

longer possible

to determine the

shape

of the

precipitates by

TEM

owing

to a very

high

dislocation

density surrounding

the

precipitates.

The behaviour

as a function of the deformation of the

initially partially

coherent

precipitates

in the

alloy aged

for 120h is different from that of the coherent

precipitates

in the

alloy aged

for 3 h in

particular

when _e

= 5 and 10fb. Both the

isotropy

of the contour

plots

in the

plane

d_~ dQ

»C= 0 %

6 3

Jo'

+ C- 5 %

o C- to %

5.6 to'

a C= 20 °/~

, 9 1 4,2

lo'

4

n a5

h

~ 2.8

21

1,4 az

000 ,366 732 1098 1,464 1,d30 2195 ?561 ?9273.293 10~~

a)

CumJ~~

du da d,50 lo,

7.65 o=0%

*= 5 %

~'~~ +=10%

5 .95 n = 20

1 _{5 -lo} Z

~ 4.25

(

?

3.40

u~

2.55 ,zo

o.85

o.oo

000.250.500 _.750 1,oo01,250 !5001/50 ?0002250 lo-I

b) ^{qcflm J-1}

Fig.

lo. -SANS _curves ~"

=

f(q)

for different values of _e.

Samples aged

for 120h cut dil

perpendicular

to the

compression

axis (a) and at 0° (b), H

= 0 and T

= 293 K.

perpendicular

to the

compression

axis and the

slighter anisotropy

observed in the two other

planes

seem to indicate _an

axially symmetric

deformation and that the

partially

coherent are

less deformable than the coherent

precipitates

because the latter _can be _more

easily

sheared

by

dislocations. In the _case of the

partially

^coherent

precipitates,

concentric Orowan

loops

are

emitted

by

the dislocation

piles-up

and succeed in

shearing

the

precipitates [22].

6. Conclusion.

I)

For _an

aging

at 650

°C,

from SANS

experiments,

the size and number

density

of the

precipitates

_were calculated in _a Cu-2 atfb Co.

ii)

Coherent

spherical precipitates

become

partially

coherent

polyhedral precipitates

with

increasing ageing

time.

iii)

Their

magnetic

state also is different. It evolves from

ferromagnetic

to

paramagnetic stability.

iv) Qualitative

information _on the

phenomena

involved

during dynamic

uniaxial _compres- sion _on the

alloys aged

^for 3 and 120 h _was obtained

by comparing

the results recorded

along

the

compression

axis and _at 45 and 0° of this axis. In both

samples,

the deformation mode is

axially symmetric

and the

precipitates

seem more deformable than the copper matrix.

Furthermore,

the coherent

precipitates

seem to be _more sensitive to the deformation than the

partially

coherent

precipitates

because

they

_can be _more

easily

sheared

by

dislocations.

Acknowledgements.

The authors wish to thank A.

Brulet,

M. Buzier and E. Lecoz of the Laboratoire L60n Brillouin in

Saclay,

France for

help

in

experiments.

References

ill WAGNER W., J. Phys. F 16 (1986) L 239.

[2] WAGNER W. and PETRY W., Physica ^{B 156} (1989) 65.

[3] WAGNER W., Z. Melallk. 80 (1989) 873.

[4] WAGNER W., Acta Met. Mater. 38 (1990) 2711.

[5] ABERSFELDER G., NOACK K., STIERSTADT K., SCHELTEN J. and SCHMATz N., Philos. Mag. 41 (1980) 519.

[6] ERNST M., SCHELTEN J. and SCHMATz W.,

Phys.

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[7] ANCRENAz P., SERVANT C. and LYON O., Acta

Cryst.,

to be

published.

[8] GUINIER A. and FOURNET G., Small angle

scattering

of X rays

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New York, 1955).

[9] MARSHALL W. and LOVESEY S. W.,

Theory

of thermal _neutron

scattering (Oxford,

Clarendon, 1971).

[10] BACON G. E., Neutron diffraction (Clarendon Press, Oxford, 1975).

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petits

angles, Utilisation des faisceaux de _{neutrons en}

Mdtallurgie,

Aussois (1981).

[12] HENNION M., RONzAUD D. and GUYOT P., Acta Metal. 30 (1982) 599.

[13] ASHCROFT N. M, and LEKNER J.,

Phys.

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[14] MARTIN G., Solid state

phase

transformations in Metals and

Alloys,

Aussois (Les Editions de

Physique, 1978)

_p. 337.

[15] WENDT H. and HANSEN P., Acta Metal. 31 (1983) 1649.

[16] PHILLIPS W., Trans. Am. inst. Mech. Engrs. 230 (1964) 967.

[17] SERVANT C. and BouzID N., Philos. Mag. ¹³ (1989) 659.

[18] CYWINSKI R., BOOTH J. G. and RAINFORD B. D., J. Phys. F 7 (1977) 2567.

[19] BURKE S. K., CYWINSKI R. and RAINFORD B. D., J.

Appl. Crys.

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[20] MONTHEILLET F. and MoussY F.,

Physique

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m£canique

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1989).

[21] MONTHEILLET F, and GILORMINI P., Archiwum Hutnictwa, Kwartalnick, Tom. 31,

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