NEUTRON SMALL ANGLE SCATTERING FROM THE ALLOY Al-Zn ABOVE THE CRITICAL POINT

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NEUTRON SMALL ANGLE SCATTERING FROM

THE ALLOY Al-Zn ABOVE THE CRITICAL POINT

D. Schwahn, W. Schmatz

To cite this version:

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JOURNAL DE PHYSIQUE

NEUTRON SMALL ANGLE SCATTERING FROM THE ALLOY

Al-Zn

ABOVE

THE CRITICAL POINT

(*)

D. S C H W A H N a n d W. SCHMATZ

Institut fur Festkorperforschung der Kernforschungsanlage Julich 5170 Jiilich, Postfach 191 3, Germany

RCsumC. - La fluctuation cohkrente de composition d'un alliage AI-Zn a 6tk mesurke par diffusion-aw petits angles des neutrons, dans un domaine de tempkrature de 435 OC et 324 OC. Aucune diffusion critique n'a pu btre dktectke au point critique incohkrent. L'intensitk des neutrons diffusks augmente continfiment lorsque la temperature dkcroit de 435 QC

a

324 QC. Au-dessous de T = 324 OC les courbes de diffusion diffhrent essentiellement des autres par leur grande intensitk a petit K et leur dkcroissance rapide aux grandes valeurs de K. Les rksultats sont en accord avec la thtorie de Cahn qui prtdit une diminution du point critique rCel a cause de la formation d'tnergie Clastique par la fluctuation de composition. La forte augmentation d'intensitk au-dessous de T = 324 OC est due au comportement de dkcomposition rapide dans l'ktat instable du systhme.

Nous avons trouvk un dkplacement d'environ AT = 28 degrks en bon accord avec une kvaluation thkorique AT = 25 degrts.

Abstract. - The coherent composition fluctuation in the system AI-Zn was measured by neutron small angle scattering in the temperature range between 435 and 324 QC. No critical scattering could be detected at the incoherent critical point. The intensity of the scattered neutrons increases conti- nuously by decreasing the temperature from 435 to 324 QC. The scattering curves below T = 324 OC

differ from the others essentially by their high intensity for small K and their strong decrease to larger K values. These results agree with Cahn's theory which predicts a decrease of the real critical point due to the elastic energy built up by composition fluctuation. The strong increase of intensity below

T = 324 OC is due to the rapid decomposition behaviour in the unstable state of the system. A shift of about AT = 28 degrees was found which is in good agreement to a theoretical estimate of A T = 25 degrees.

Introduction. - We measured (

1

C(K)

l2

) i.e. the absolute square of the coherent composition fluctuation C(K) of a binary alloy above the critical point as a function of temperature by neutron small angle scattering. We chose the system AI-Zn with the critical composition c,, = 0.395 (figure 1). We intended t o demonstrate experimentally :

1) Whether or not elastic energy cp,, due t o the size difference of the components influences the stability of the system against decomposition. Following Cahn (1961) the additional elastic energy lowers the spinodal phase boundary (inside the spinodal is the unstable region): By this the metastable region becomes continuous from the low t o the high composition side a n d therefore the critical point touches n o more the stable region. An estimate gives a temperature shift of about 25 degrees for the critical point.

2) The singular behaviour of the composition fluctuation in the neighbourhood of the critical point.

( * ) I heae results w11l be publ~shed in greater deta~l m Acta Met.

LOO I I I I l I

Cr,itical Point

'

Spinodal

haseboundary

\

1

100b 10 I 20 I 30 I 10 I 50 I GO I

Atomic Percent Zinc

FIG. l. -Aluminium rich side of the phasediagram of Al-Zn with the two phase boundary and the spinodal.

Scattering Law. - In a neutron small angle scattering experiment we measure the diffuse scattering cross

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C7-412 D. SCHWAHN AND W. SCHMATZ

do of the system in the unstable state. As one can see the

section

-

dQ (K) which is proportiona1 to (

I

'(K)

I2

)

Value of the critical temperature is about 324 oC. This

(Krivoglaz, 1969). is a shift of about 28 degrees due to elastic energy.

It should be mentioned that the curves measured do

-

_dQ(K) (

l

C(K)

l2

) (l) in the metastable region are not so accurate as those _{measured in the stable region. In the metastable State} beside the built-up of concentration fluctuations the

(

I

C(K)

1'

) can be expressed for small K-values _{system decomposes by nucleation and growth mecha-} by thermodynamic functions as follows (Krivoglaz, _{nism and therefore it is difficult to measure the}

1969) : _{coherent composition fluctuations. Thus, these curves}

kT

were measured during the incubation time, when the

<

I

C(K)

l2

) =

l

(2) decomposition mechanism is not yet of great influence.

v [ g

(g

+

qe3

+

2 ~ ~ 2 (A detailed description is given by D. Schwahn, 1977.) ,B is the gradient energy coefficient. The term contain-

a2

1

ing B is due to the surface energy.

-

(

+

v,,)

the

ac2

g Irnb/sterl x=o

second derivative of the Gibbs potential (g

+

v,,) with respect to the composition c, determines the stability of the system as defined by Gibbs. g is the

Gibbs potential per unit volume of the unstressed Calculated

a2

system.

-

(g

+

q,,) is positive in the stable region of Measured ac2

the phasediagram. It becomes zero at the spinodal and negative in the unstable region. Therefore (

1

C(K)

1'

)

do

and

-

(K) increases by lowering the temperature and dQ

become infinite for K = 0 at the critical point which is a point of the spinodal.

FIG. 2. - Summary of the measurements of the coherent composition fluctuation. The change of the shape of the curves below 324 OC is due to the decomposition behaviour of the system in the

unstable region.

Results. - Indeed, as shown in figure 2 and as predicted by eq. (2) the scattered intensity bows continuously as the temperature is lowered from 400 to 324 OC. The two curves measured below 324OC differ from the others by their shape. Their intensity is much higher for small K-values and their decrease to greater K-values is much more pronounced. The behaviour of these curves is due to the decomposition

du

FIG. 3. - - (0) and K; between 324 OC and 435 OC reflect the dQ

d o

result of this experiment. At about 324 OC

-

(0) becomes infinite d o

and K; zero which is due to the behaviour of the system at the critical point. The critical behaviour of both curves is classical. The fulldine curves are calculated independently from the neutron data. K: depends sensitively on the range of the interaction potential as can be seen from the different slopes of the straight lines which are calculated from nearest neighbour interaction- ,and Lennard- Jones (6-12) potential (Cahn and Hilliard,-1958). The experimental values for the interaction potential range is in between the two

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NEUTRON SMALL ANGLE SCATTERING FROM ALLOYS AI-Zn C7-4 1.7

Discussion. - To discuss the results we write the 1) It can be concluded that the elastic energy

scattering law in a different form do

produces the expected behaviour.

dS2

(0) becomes

do do

d

singular and K: becomes zero at about 324 OC and not

-

(U) =

-

(0)

dQ dQ K;

+

K~ at 351.5 OC, which is the highest point of the two phase

boundary. This point would be the critical point if the

with elastic energy cp,, is zero. The difference of 27.5 degrees

do

kT

is in good agreement to theoretical calculations with

-

(0) a

,,

dQ the result of 25 degrees.

2

(9

+

'P.I) _{2) The critical behaviour of both parameters is} the cross section in forward direction and

do

classical.

-

(0) which is proportional to the suscepti- dS2

bility has a critical exponent of y = 0.95 f 0.12. The

a2

- ( g

+

( ~ e l ) correlation length ( = 1/~, has a critical exponent of

,c2 v = 0.5 f 0.03. Near T, this behaviour can only be

K, =

2 B understood if long range interaction energies are

acting. This interaction is obviously caused .by elastic the reciprocal square of the correlation length. energy. Finally, it should be mentioned that the full

do

As can be seen from (3)

-

(0) and K; completely line curves in figure 3 are calculated without any

dQ relation to the neutron data. There is a reasonable

describe the scattering law. They are plotted as- a agreement between these curves and the measured

function of temperature in figure 3. values.

References

CAHN, J. W. and HILLIARD, J. E., J. Chem. Phys. 28 (1958) 258. CAHN, J. W., Acta Met. 9 (1961) 795.

KRIVOGLAZ, M. A., Theory of X-Ray and Thermal Neutron Scatter- ing by Real Crystals, New York (Plenum Press) 1969. SCHWAHN, D., Berichte der Kernforschungsanlage Julich Jul-