Interface hardening and softening in dissociative solute solutions

Scrtpta METALLURGICA

Vol. 2, pp. 509-514, 1968 Printed in the United States

Pergamon Press, Inc.

INTERFACE HARDENING AND SOFTENING IN DISSOCIATIVE SOLUTE SOLUTIONS T. R. Anthony General Electric Research and Development Center Schenectady, New York

(Recetved July 3, 196~ Introduction An increase in hardness over bulk hardness near free surfaces and grain boundaries has been observed in many dilute solld solutions following a high temperature quench and a low temperature anneal.

Most of these observations

have been explained by models in which free surfaces and grain boundaries act as vacancy sinks.

Several different types of solute interactions with the

resulting vacancy gradients have been suggested to account for the observed hardening.

One of these was the dissociative solution mechanism proposed by

Seybolt et al to explain the grain boundary and free surface hardening of NiGa and NIAI by small amounts of oxygen (1). Later Aust and Westbrook suggested this mechanism as a possible alternative to their vacancy drag model to explain grain boundary hardening in zone refined lead containing parts per million of dissolved gold (2). In the following discussion, it will be shown that the model of Seybolt et al can lead not only to solution hardening of vacancy sink zones in some cases but to softening by solute depletion of these same zones in other cases. Which alternative occurs depends upon the ratio of the vacancy diffuslvity to the interstitial solute diffusivity.

In particular, this model predicts that

small concentrations of copper and gold in lead should cause a decrease in grain boundary hardness from bulk values rather than the increase that is observed.

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Discussion In a dissociative solute solution, solute atoms occupy both interstitial and substitutional sites.

The distribution of solute atoms between these two

types of sites can be considered in terms of a defect reaction involving vacancies, substitutional solute and interstitial solute atoms.

If V, N

s

and

N. are the mole fractions of vacancies, substitutional solute and interstitial solute, respectively, then the equilibrium concentration of the various species may be written as

Ns = K N i V

(i)

where K is an equilibrium constant (3). Before quenching, it is presumed that the spatial distribution of vacancies, substitutional solute and interstitial solute is homogeneous with ratio of their concentrations being given by equation (i).

On quenching, the

equilibrium concentration of vacancies falls from V(TI) to V(T2).

If free

surfaces and grain boundaries are efficient vacancy sinks, then vacancy gradients will develop normal to these interfaces during the subsequent vacancy equilibration.

While vacancy gradients persist, a solute interaction

with these gradients, of the type suggested by Seybolt et al, may cause either boundary hardening or boundary softening. Case I - Boundary Hardening D v >> Di, D s If the vacancy diffusivity, D v, is much larger than the interstitial solute dlffusivity, Di, and substitutional solute diffusivity, Ds, then long range vacancy gradients will develop without any simultaneous long range movement of solute atoms.

The equillbriumdenoted by equation (I) will be

complied with everywhere since this reaction can occur without long range motion of solute, requiring only that vacancies are available for the interstltial-to-substitutional reaction direction.

Thus the steady state interstitial

and substitutional solute concentrations in the presence of a vacancy gradient away from a vacancy sink will be given by v = v(x)

(2)

NI/N s = I/KV(x)

(3)

N i + N s = N T ~ f(x)

(4)

where x is the distance from a vacancy sink and N T is the local total solute

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HARDENING AND SOFTENING IN SOLUTE SOLUTIONS

concentration.

511

Since the local total solute concentration is constant and in-

dependent of x, the only effect of the vacancy gradient is to vary the ratio of interstitial to substitutional solute atoms from a high value near the boundary to a lower value away from the boundary as depicted in Figure I. Although neither solute enrichment nor solute depletion of the vacancy sink zones occurs, hardening of these zones will take place if the interstitial solute causes proportionately more solution hardening than the substitutional solute (4).

NT = Ni + Ns

OW

8 - V(T,

~ -

V

Z¢~, •

0

/V(T ) I

I

I

I

I

I

2

4

6

8

I0

12

DISTANCE FROM VACANCY SINK

FIGURE I Grain Boundary Hardenlng Case II - Boundary Softening D i > D v >> D s In most cases the substitutlonal solute dlffuslvity, Ds, is much less than the vacancy diffusivlty, D v.

However in many instances (3,5,6), the

interstitial solute dlffusivity, Di, is much greater than the vacancy dlffuslvity, Dv, and consequently the interstitial solute concentration will remain level as the vacancy gradient develops.

In this case, the conditions

imposed by equations (i), (2) and (3) will again hold but equation (4) will be

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H A R D E N I N GAND SOFTENING IN SOLUTE SOLUTIONS

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replaced by the requirement that V Ni = 0

(5)

In the presence of a vacancy gradient thenl the steady state interstitial and substitutional solute concentrations and their sum, the total solute concentration, will vary as depicted in Figure 2.

The total solute concentra-

tion, NT, is now a function of the distance from the vacancy slnk with solute depletion occurring in the sink region.

Hence in this case, grain boundary

and free surface softening relative to bulk hardness values would be expected following a quench and anneal.

Because the conditions D i > D v >> D s are

applicable to dilute solutions of copper and gold in lead (5), grain boundary and free surface softening would be expected if Seybolt et al's model were applicable to these systems.

The contrary observations of Aust and Westbrook

(2) imply that this particular model is invalid for these systems.

wl..-

Ns Ol.u

8

~La.I

I

2

,

I

1

I

I

4

6

8

I0

i

12

DISTANCE FROMVACANCYSINK FIGURE 2 Grain Boundary Softening

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513

References (1)

A. U. Seybolt, J. H. Westbrook and D. Turnbu11, Acta Met ~

1456 (1964).

(2)

K. T. Aust and J. H. Westbrook, Lattice Defects in ~uenched Metals, p.

(3)

F. C. Frank and D. Turnbu11, Phys. Rev. 104, 617 (1956).

(4)

R. L. Flelscher,

(5)

B. Dyson, T. R. Anthony and D. Turnbull, JAP 37, 2370 (1966).

(6)

T. R. Anthony~ B. F. Dyson and D. Turnbu11, JAP 39, 1391 (1968).

711, Academic Press (New York) 1964. Strength of Metalsj Chap. IV, Reinhold Press (1964).