The size effect in radiation-induced segregation of solutes in binary metallic alloys

Journal of Nuclear Materials North-Holland, Amsterdam

LETTER

77

126 (1984) 77-78

TO THE EDITORS

THE SIZE EFFECT IN RADIATION-INDUCED METALLIC ALLOYS

A net between binary

has

correlation the volume

metallic

induced

Ring

volumes

which

allotropes

the volume misfit

atomic

volume

solvent,

misfit

normalized

established

[3]. In ref. 3 a brief

summary

of radiation-induced

segregation

these

alloys

volume

obey

size misfit

results

sink) solute transport three exceptions, element

(RIS) stating

in a negative

to the

of the solute observations

in binary

alloys

majority

that

of

a positive

(away

from

(Al-Ge,

Ni-Ge

and Cu-Fe;

is the solvent).

the

the first

It is difficult

why the mean atomic

volume

for these three alloys;

hence here we redefine

to see

misfit rule is violated

in terms more applicable

only

the volume

to atomic

E,,(V)

diffu-

OF SOLUTES

prevails

therefore

within

the tendency

From least

pseudopotential

for simple

the metal

metals

(alloy),

theory

it is known

and alloys)

the total

E, can be presented

that

(at

energy

of

in the following

form

the total

E,(V). When

one characterizes

stacking

fault

and solute

in fact, the diffusivity is a process

What

appropriate

atom

leaves

matters

is the mutual

the solute

forms

atom

dle-point Forming

model

that excellent

metallic

lattice

etry. Therefore, a volume from

parameter

of atomic

migration

agreement

between

metals

the magnitude implicitly

of the volume

on the structure,

coordinates

The remaining

sensitive

E,(V)

energy

is the dominant a relation

dependent

E,,(V)

energy

pseudoatoms term. From the

energy

term. Within

this frame-work

stand

why enthalpies

of allotropic

tion

and

allotropic

the

atomic

transformation

0022-3115/84/$03.00

(North-Holland

volume

i and j. the volume

structure

sensitive

it is easy to undertransformations

are much less than the enthalpy why

+,, is

the minimal

exists between

and

part

part and is presented

between

energy requirement

an element

of the

sum over all atom pairs in the crystal;

the interaction Usually

not depend

i.e. is independent

of the “pseudoatoms”.

of energy is the structure as a double

V, but does

to

of sublima-

differences

are so small.

for during

The explanation

0 Elsevier Science Publishers B. Physics Publishing Division)

metallic

radii

closed-packed

processes

coincide We

list

of the atoms

solute/solvent

bee,

on mean

table

1 that

atomic

the

to volume

atom and direction eliminated

1 the misfit

metallic

based respect

the volume

radii

hcp)

volumes. based

of solute

elements

It can

[8]. on

it to that

be seen in

on mean misfit

radii or half

based

compare

noted

the

respecor nearly

distance

segregation

by using the volume

misfit

these

parameter

and

discrepancies misfit

atoms,

for closed-packed, (fee,

rather

in the unit

rsO, and rsolv are

of the corresponding

in table

from the effec-

of the atoms,

with half the nearest-neighbor

the bond length

in a geom-

one should utilize

and solvent

above,

structures

[4-61 theory

can be achieved

which follows

of the solute

sad(Void

of pseudoatoms

- 1, where

tively. As mentioned

when

defect

the VFF

volumes

(r,,,/r,,,,)3

the effec-

atoms

relaxed

dimensions

the mean

crystal atomic

from nearest-neighbor

for diffusion

misfit parameter

the

between

dimensions

are defined

of

from

in close packed

is,

however,

of solute

and solvent

Starting

Fluctuation)

and experiment

volume

a completely

configuration.

it was shown

Diffusion,

interrelation

of the solute

and solvent.

what matters

in the case

tive dimensions

of an

characteristic

transport the

of

(e.g., density,

of the solute

of the solutes.

which

unchanged. diffusivity

the

volumes

cell [7]. This can be done by defining which is sensitive

behavior

behavior

of total energy,

creation)

will be the atomic

than

where E, is that part of the energy

expres-

is to change

The close-packed

the atomic

alloy from the standpoint

tive nearest-neighbor

“I

energy

in the crystal

rather than volume.

when the saddle-point

sion.

IN BINARY

of metals and alloys is also a result of the domination

But for RIS

and vice versa. There are however,

in the couple

misfit concept

transition

The prevailing

the rule

atomic

with respect

sion,

structure

by

as the mean

of reported

26 alloys.

(23)

in the

to the concentration

is given containing

the

was defined

of the solute

in a

obtained

that

little

factor

atom

of its radiation-

the results

change

points,

is that

established

of a solute

[l]. Following

[2],

of

previously

factor

alloy and the direction

migration

H.W.

been

misfit

SEGREGATION

ref.

volume

under RIS based

from

1 with per are

on atomic

size. Partial R.A.

Welch

support

for this work was obtained

Foundation.

from the

78

L. Komhlit,

A. Ignatieri

/

Radiation

-induced

segregation

of solutes

Table 1 Volume misfit parameters based on atomic size ( rs,,,. rs~~iy)or mean atomic volume (King) determined for a number of solute/solvent systems. Note that the discrepancies in the direction of segregation (under RIS) predicted from the King volume misfit parameter are removed when the atomic size volume misfit parameter is used. Structure

Alloy

‘SO,(A)

Structure of the solute when crystal

Volume misfit % (r_, /T$~,,~)~ - 1

1.3775

fee

Pd-Cu Pd-Fe Pd-Mo Pd-Ni Pd-W

1.278 1.24115 1.36255 1.2458 1.37095

fee bee bee fee bee

-20 -27 -3 -26 -2

1.4315

fee

AI-Ge Al-Si AI-Zn

1.2249 1.17585 1.3347

diamond diamond

-37 -45 - 19

Cu-Ag Cu-Be Cu-Fe Cu-Ni

1.4447 1.1130 1.24115 1.2458

fee

?&-AI Ni-Au Ni-Be Ni-Cr Ni-Ge Ni-Mn Ni-Mo Ni-Si Ni-Si Ni-Ti

1.4315 1.44205 1.1130 1.2490 1.2249 1.36555 1.36255 I .450 1.17585 1.4478

fCC

hcp

+52 +55 -29 +1 -5 i32 +31 +58 -16 +57

Ti-Al Ti-V

1.4315 1.3112

fee fee

-3 -26

Fe-Cr Mg-Cd

1.2490 1.4894

bee hcp

+2 -19

r,,,,(A)

Direction of segregation

Volume misfit W after King [2]

Discrepancies

(from ref. 1)

1.278

fee

1.2458

fee

14478

hcp

1.24115 1.59855

bCC

-

hcp

hcp

144 -34 -8 -7

hcp bee fee

fee hcp bee fee (y-phase) bee rhomboh. diamond

References L.E. Rehn, in: Metastable Materials Formation by Ion Implantation. Eds. ST. Picraux and W.J. Choyke (Elsevier, Amsterdam, 1982) p. 17. H.W. King, in: Alloying Behaviour and Effects in Concentrated Solid Solutions, Ed. T.B. Massalski (Gordon and Breach, New York, 1965) p. 85. L.E. Rehn and P.R. Okamoto. Phase Transformation and Solute Redistribution in Alloys during Irradiation, Ed, F.V. Nolfi, Jr. (Eisevier, Amsterdam, 1983). Received 3 February

1984; accepted

- 19 - 12 -4 - 14 -4

+ + 4

+ + + + + + + + +

*

+13 - 16 -6 +44 -26 +5 -8

*

+15 +64
*

-20 -15 +4 - 21

Phys. Rev. B 16 [41L. Lornblit, J. Pelleg and A. Rabinovich, (1977) 1164. I51 L. Kornblit, Phys. Rev. B 17 (1978) 575. 161 L. Kornblit. Phys. Rev. B 20 (1979) 601. ]71 See, for example, W.B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley-Interscience, New York, 1972) p. 144. (81 Handbook of Chemistry and Physics, 54th Ed. (CRC press, 1973) p. F197.

L. Kornblit

4 May 1984

Physics Depcrrtment,

* On sabbatical leave from the Materials Engineering ment, Ben-Gurion University of the Negev, Israel.

Depart-

* and A. Ignatiev University

Houston,

of Houston,

Texas 77004, USA