The surface self-diffusion of copper as affected by environment

THE

SURFACE

F. J.

SERF-DIFFUSION OF COPPER ENVIRONMENT* 3RADSHAW.t

R.

H.

AS

AFFECTED

BY

and C. WHEELER?

BRANDONt

Using mass-transfer methods, the surface self-diffusion of copper has been shown to depend on environment. An increase of oxygen pressure increases the surface diffusion rate, but interpretation on the basis of adsorbed oxygen is not simple. There was evidence of impurity effects in hydrogen environBetween 800°C and 400°C diffusion ments, with measurements in vacua being the most consistent. occurred with an activation energy (-20 koal) lower than that previously reported for temperatures above 800°C. EFFET DE L’ENVIRONNEMENT SUR L’ACJTO-DIFFUSION EN SURFACE DU CUIVRE En utilisant la m&hode du transport de masse, il est possible de montrw quo l’auto-diffusion en surface du cuivre est affect&e par l’environnement. Une pression d’oxyg&ne plus grande augment0 la en 88 basant SW la quantitb d’oxygine diffusion en surface mais l’interpr&ation du ph&om&ne, absorb& n’est gu&re simple. Des mesures fortes dans un environnement hydrogkne semblent prouver de8 mesures sous vide ont d’ailleurs confirm+5 ce point. Entre 800 et que les impure& ont une influence: 4OO”C, la chaleur d’activation ( ~20 kcal) du ph&om&ne de diffusion est plus basse que oelle annone& pr&%demment pour des tempbratures sup&ieures B 800°C. DIE

OBERFLBCHENSELBSTDIFFUSION DER

VON KUPFER UMGEBUNG

IN IHRER

ABHANGIGKEIT

VON

Mit Hilfe von Messungen der iibartragenen Substanzmenge wurde gezeigt, daIJ die OberflBchenselbstErhiihung des Sauerstoffdrucks erhijht die diffusion von Kupfer von der Umgebung abhiingt. Oberfliichendiffusions-Rate; eine Deutung auf Grund der Adsorption des Sauerstoffs ist jedoch nicht In Wasserstoffumgebung gab es Anzeichen fiir Verunreinigungseffekte; die Messungen in einfaoh. 800°C und 400°C erfolyte die Diffusion rnit einer vncuo stimmten am besten z.u8ammen. Z&when Aktivierungsenergie (-20 kcal), die geringer war, als friiher fiir Temperaturon oberhalb 800°C berichtet.

1. INTRODUCTION

Estimates

of the surface

in hydrogen

self-diffusion

have been made by mass-t.ransfer(l-~) tracer(5) methods.

The mass-transfer

of copper

and radioactive

di~cult.

method involves

data have been obtained The diffusion

coefficient,

obtained

were

surface

for copper, using grain boundary

by

Mullins

and

Shewmon(l)

gen with 10 % hydrogen. not give reproducible Gjostein(2) -45”C,

point

was

the

temperature

extended

dew

states that

points

down

to

using the grain boundary

with bicrystals,

measured

D, over surfaces

(110) and (11 I} and three surfaces of higher index at temperatures between 1069 and 847%. For all six surfaces $

was found to be between 48.6

and

The

52.2

kcal/moIe.

extreme

limits

of their

results, shown as two lines in Fig. 1: illustrate the fact

at 830°C did

that D, varied by no more than a factor of three over

at atmospheric

that

with

oxide

of nitro-

results and were omitted.

using hydrogen

a dew

experiments

though

measurements

near to {loo},

who

a .D,% of 13.5 x 10e5 cm2/sec at 1035°C and

3 x 1O--5 cm2/secat 930°C in an atmosphere

with

self-

atmospheres

and Shewmon,(3)

technique

of D,, the

first measurements

grooving

Choi

this way.

made

give the same values of D,.

-90°C

ing of scratches under surface energy forces and most

pitting

In his recent review Gjostein@)

hydrogen

a study of the grooving of grain boundaries or smooth-

at the same temperature, and surface

formation

between

I&er

the orientations

pressure,

checked

-12°C

and

range

from

found

studied.

Shewmon

and Choi(*) later

these results using a scratch technique good

agreement,

scratch smoothing

though

D, obtained

and from

was always slightly higher than that

D, could be expressed in the usual form, D, = D, exp (-Q,/kT) with a fixed value for Q, his results were D, = 6.5 x

at 870°C and have found values 4.5 times larger than

lo2 cm2 xec--I and Q, = 40.8 kcal/molo.

those

1070°C to 720°C.

Assuming

that

However

his

points on the Arrhenius plot can be fitted more closely with a curve Below

and this has been

780°C Gjostein

obtained

drawn

in Fig.

December 2, 1963. t Ministry of Aviation, Chemistry, Dept., Royal .4ircraft Establishment,

1.

some surface pitting

ACTA METALLURGICA,

Physics and Metallurgy Fernborough, Hants.

VOL. 12, SEPTEMBER

1964

measured

technique These

by

the

grain

boundary

grooving

for the same surface orientation. results+*)

temperatures

and t,he spread of his results increased. Specimens heated at 720°C in oxygen at 1O-3 torr showed no great increase in groove widths over t,hose measured * Received

from thermal grooving. The same authorsc5) have used a tracer technique to determine the D, for CuG8

indicate that in hydrogen for above 0.73 T,, t-he melting temperature,

Qs, is 4 to 8 of AHs,,, the heat of sublimat.ion. Below this temperature surface contamination stopped the diffusion process. However it is relevant that Inman et a1.(7) in their experiments on the creep of copper wires found

that their copper in hydrogen

at 950°C

would not change shape under surface energy forces 1057

1058

ACTA

alone

even though

mass-transfer

was occurring

means of the less surface-sensitive process.

volume

by

not

affected

by

even where measurable

impurities.

Earlier Menzel@) at the disappearance of etch

had shown, by looking

pits in copper surfaces during annealing, that changing the environment Although

altered

the surface

he could not obtain

diffusion

an absolute

rate.

value for

D,$, he found that between 650°C and the melting point in a vacuum

of 3 x 10e4 torr, Q, was 13 kcal/mole In air at 2 x 1O-3 torr D,

(i.e. Q, = 0.16 AH,,,). was greater hydrogen

by a factor

were variable,

of 2 to 3.

His results in

the end state after annealing

depending on temperature, obvious

why

the more

recent

work

should give values of Qs/AHsub so much higher than Menzrl’s. have

More

found

platinum T,.

low

in

recently, values

the

Blakely for

and

Qs/AHsuh

temperature

Mykuratg)

(=0.21)

range

for

0.57?‘,-0.78

Because of this and because of the indications

impurity

effects in hydrogen

of D, on the oxygen measure

the

transfer

method

principally

self-diffusion in

(Po2), we decided to

of copper

different

the grain

of

and of the dependence

pressures

by the mass-

environments

boundary

grooving

using

technique

and to a lesser extent scratch smoothing. 2.

The

principles

boundary

grooving

are,

briefly, as follows. If a polycrystalline piece of copper with flat surfaces is annealed, grooves are developed at the intersection surfaces;

of the grain boundaries

face.

with the

this is the result of local equilibrium

set up between the grain boundary The

volume

grooves

diffusion

metal atoms. diffusion,

can form

surface

diffusion,

and condensation

If the mechanism

then a “hill”

the groove.

being

and the free sur-

by

or evaporation

of

is surface or volume

is developed

If the mechanism

on each side of

is surface

diffusion

and w:: is the width between the top of the “hills”

then

Mullins has shownoO) that (1)

where B = D,vQ2 y,lkT D, = surface self-diffusion

coefficient ( cm2 se&)

v = surface density of atoms (cm-2) Q = atomic volume k = Boltzmann’s

constant (“K)

t = time of anneal (set).

process’ll)

the width

20, = 5.0 (A#

(2)

and

D, = volume diffusion coefficient.

In practice,

thermal

and surface

diffusion

volume

diffusion

mentally

grooving

contribution

measured

can occur

simultaneously. width

by volume

Provided

is small,

the

the experi-

can be corrected

to that

which would have occurred by surface diffusion alone, using the procedure given by Mullins and Shewmon.(l) This method was adopted at the higher temperatures, when necessary, quoted

using the volume

diffusion

results

by Le Claireu2) i.e.

D, = 0.62 exp [-49.56 In all our experiments, and condensation

(kcal)/RT]

cm2 set-l.

mass-transfer

by evaporation

can easily be shown to be negligible

and is not considered

further.

The essence of the scratch smoothing if a scratch consisting

method is that

of a depression

with a mound

on each side is made in the surface of a metal, and the metal

is heated,

the scratch

broaden with time. that

if smoothing

width-time

will smooth

out

and

King and Mullins(i3) have shown is by surface

dependence w24 -

diffusion

then the

is WI4 = (6.90)4 Bt

(3)

where wi and tu2 are the initial and final widths of the Similarly if smootjhing is by volume diffusion :

w2 3 - ~113 = (6.22)3 At. (4) This method lends itself to a study of the orientation dependence

of D,.

Although

grain boundary

can be used for this it involves

growing

grooving bicrystals.

The remelting involved

could lead to impurity pick-up

and

simpler

in our

case the

scratch

chosen.

It is necessary

liminary

anneal after scratching

the deformed

method

to give the specimen

was a pre-

in order to replace

region near the scratch

with a single

crystal and to smooth out the small scale irregularities in the profile. ing scratches

The orientations were found

of the grains contain-

using (111) surface traces,

i.e. slip lines and annealing

twins,

present,

microhardness

produce

(111) slip traces.

as described

by

twin traces were

indentations

were made

to

In both methods, depth rather than width measurements can be used but we found it more reliable to use the latter.

(cm-3)

ys = surface free energy (erg cm-2) T = temperature

diffusion

Takeuchi et aZ.(14) When insufficient

II), = 4.6 (Bt)* and

1964

where A = ys ClD,jkT

scratch.

METHOD

of grain

12,

Similarly for a volume

with no diffusion occurring

below 700°C. It was not

VOL.

diffusion

With such impurity effects it is difficult to be

certain that surface diffusion is

SIETALLURGICA,

(erg deg-l)

All mass-transfer methods need a knowledge of ys to obtain D,. In this work we have used Udin et aZ.‘s(15) value

of ys as determined

ys = 2445 - 0.5875 T ergs/cm2. The of ys on environment is discussed later.

in vacua i.e. dependence The surface

BRADSHAW,

density

BRANDON

WHEELER:

AND

of atoms is taken to be simply P”.

That is,

that

D, is a mean ~oe~~ient

surface atoms even if mass-transfer ring by means of a small fraction

by Johnson,

and maximum

environments

with increasing values of PO,. For all ex-

is actually Occur-

periments

; (e) and (f) low pressure

except those in (d) the same apparatus was

used with small modifications.

It consisted of a grease-

free glass system which enclosed the boat containing the specimens; copper

and Co. Ltd.

supplied

During

anneals

it was connected through a liquid nitro-

gen trap to a silicone oil diffusion pump. The specimens were placed breaking

in a silica

end

tube

A furnace

face to face but not touching,

anneals. Dealing with the environments

in a boat with a loosely

fitting lid made from the same material. the

specimens

purit,y yet permit Changes

ready

with

access

The aim was

copper

of similar

to the atmosphere.

in surface profiles were measured

IIilger and Watts interference photographic

methods

microscope

or a micrometer

with a

using either eyepiece.

surfaces

were

mechanically

finishing with rouge and then chemically

polished,

polished in a

solution consisting of 55 ‘A by volume orthophosphoric acid (density nitric

acid

1.75 gm/cc), (densit’y

~lectropolished (density

25 % acetic acid and 20 %

1.4 gm/cc).

in a bath

1.38

gm/cc)

Mullins and Shewmon(l)

washed

in 107:

(density dueo”)),

were

procedures

then acid

similar

(the cell potential

until the grain boundaries in t#he interference

They

of orthophosphoric

using

to

was 1 V)

were smooth when viewed They were finally

microscope.

by volume

1.75 gm/cc)

of orthophosphori~

(to minimise

acid

phosphate

resi-

distilled water and “Analar” aeetone. anneals, for 34 hr at approximately

Preliminary

lOOO”C, were carried out in an atmosphere that used in the subsequent

grooving

to stab&se the grain boundaries to permit purities.

surface

segregation

The specimens

and then annealed

similar to

anneal in order

in the specimen of any

internal

were electro-polished

in one of the following

and im-

again environ-

ments: (a) hydrogen

g760

(b) hydrogen

~5

(e) vacuum (d) vacuum

tube

during

in order.

of 99.9 7; purity (impurities 0, ~500

p.p.m.:

N,

p.p.m.)

was passed through

~500

p.p.m.,

carbon

compounds

two platinised

~20

asbestos

perchlorate oxygen-removing units, a magnesium drier and a liquid nitrogen trap. It was then led into aperture in the copper to silicon monoxide

boat.

most

of our work

alumina

the

of gas

evacuation

at one atmosphere operating.

occur anneal

polishing

at

experiments apparatus widths.

failed to

it, was then necessary 1000°C

and

then

analysis appropriately.

to

by a short

at the lower temperatures,

ing the mathematical

uithexperi-

pressure

Grooving

anneal in vacua followed

hydrogen

in

without

fmther

at atmospheric

difference.

in some specimens;

give a preliminary

was maintained

However,

hydrogen

showed no significant

to

After a of the system a steady flow

of hydrogen

in static

the

~otltamination.

preliminary

ments

temperatures,

was used (in this case only)

risk

out the pumps

at one atmosphere

near 1000°cl and although

at lower

was

feed tube

minimise

The r~d~~ctiorl of silica

in hydrogen

is possible at temperatures

reanneal correctIn some

the specimens were wit#hdrawn from the after the 1000°C anneal to check groove

This did not appear to affect the results and

we conclude

that the 1OOO’C anneal was helping to

remove impurities left by polishing.

~5

was t~rap

x 10m5torr. (c) The vacuum

by simple

x 1OW torr

(e) water va~ourlhydro~en with Prro ~3.6 torr, PN, -7 X lop5 torr (f) oxygen ~5

the silica

directly into the pumped system to give a pressure of

1O-5 torr

~81 X 1O-7 torr ~1

(a) Hydrogen

over

and

were used.

(b) Hydrogen, cIeaned and dried as above, led via a controllable leak and liquid nitrogen

torr x

was drawn

making

seals

the apparatus via an alumina tube right up to a small

3. I Ci?Yzin~~ou.~~~~;r~ ~~o~v~~~~~ Specimen

by

a glass seal, i.e. no organic

these were suspended, with the surfaces to be measured

to surround

opportunity

This also

of them.

Standardised”

Matthey

1059

Cu

for all of the

I.5 cm by 0.5 cm by 0.05 cm were

‘~S~eetrogr~~phically

contamination

IN

volatilization

3. EXPERIMENTAL The specimens,

impurity

SELF-DIFFUSION

for impurity

12, is based on an average surface density. implies

SURFACE

at temperatures x 10-B

X 1O-5 torr.

Environments (a) and (b) were aimed at providing low values of PO, ; (c) and (d) the minimum gas

of ~1

pumping

x 1O-i torr was provided

alone.

below

Grooving

500°C

unless,

atmospheric hydrogen experimenm, anneal was given in* vacua at 1000°C; in removing the inhibiting factor.

did not occur as with

the

a preliminary t’his succeeded

(d) The vacuum of ~1 x 10-s torr was produced in another glass apparatus. This included improved pumping,

two liquid

nitrogen

traps in series and a,

ACTA

METALLURGIC.4,

specimens.

These were

1060

gold wire seal for introducing driven

into

the

silica

end-tube

surrounded

furnace by means of a magnetically

by

a

operated push rod.

VOL.

12,

1964 4. RESULTS

4.1. Grain boundary grooving The

results

obtained

from

the

boundary

grooving

the specimens were heated. The whole apparatus, with specimens inside but not in the furnace, was

showed the largest scatter.

pre-baked

the limits between which the results lay and each point

initially

to

pressures of ~10-~

-400°C.

torr.

This

resulted

in

method are summarised

grain

In this way the minimum material was outgassed when

The results in hydrogen

in Figs 1. and 2.

at atmospheric

pressure

The vertical bars represent

is the mean, on average, of 5 results. The t* dependence

The pressure rose to -lo-’

torr when the specimens were driven into the furnace

of groove width was checked down to 700°C.

but rapidly fell again t$o -10-s

torr, the average for

600°C grooving

the run. (e) A

distilled

connected

filled

with

to the apparatus

surrounded -lo-’

round

was

in (b) and

After evacuation

to

x 10e5 torr.

The liquid

the side arm was then replaced

solid CO, in acetone;

by

this gave a low pressure

en-

with PHzOIPH, of 5.111.

vironment

(f) Oxygen H, < 50

of 99.5 % purity

p.p.m.,

carbon

hydrogen

the

<20

argon?

value

at atmospheric

ceased at 550°C.

a single boundary,

with some evidence

was responsible

which occurred. environments hydrogen

used.

Further,

at atmospheric

pressure separate measure-

present

the water in a section of the

The measurements

somewhat average,

of 3 results.

each point

The tf dependence

(this

vapour pressure after the liquid nitrogen surround~g

at 700°C.

would

present in the hydrogen

be converted

copper some

oxygen,

into

and subsequently scatter

water

vapour

detected.

in the water

vapour

initially,

by the hot

upper limit for PE,o/FH,

specimens

down to 500°C.

or given no further

scratched an L.P.

with a modified record

diamond

tip radius of -12p. anneal

in a vacuum

polished and electro-

polishing,

microhardness

cleaned

and

tester using

stylus which had a special

They were then given the initial of lo-’

torr at 1000°C to re-

crystallise t~~roughout the scratch and to smooth out small scale irregularities in the profile. measurements of

scratch

subsequent

widths

were

made

before

and

after

a

anneal in vacuum ; some measurements

were also made using one atmosphere both anneals.

of hydrogen

After the preliminary

ture anneal for experiments

below

for

high tempera-

5OO”C, grooving

persisted to the limits of measurement.

polished

PEzo/P,

then

the tf dependence of grooving was confirmed

readings;

was found to be XO-4.

as before, then either chemically polished

an over-estimate)

This implies a PO2 of <1O-25 atm!

coherent and reliable with well-formed Each point is the mean, on average, of 3

but no

were mechanically

we assume that all the

grooves.

showed The

did

If, in estimat-

Results is vaaezrowere, by com~)arison with those in hydrogen,

Results

3.2 Scratch smoothing Cold-rolled

is certainly

fraction

significant, change after passing over the copper.

below 500°C.

on

of groove

down to 750°C and grooving

ing Pcjz for this environment,

would be <10m2.

that any

showed

is the mean,

residual pressure under vacuum is due to water vapour

flow line with liquid nitrogen, pumping out the section,

untrapped

Here after

of water vapour

in low pressure hydrogen

less scatter,

sealing off and using a Pirani gauge to read the water It was considered

pressure (at 650°C) did we

45 hr it ceased.

width was checked

the t.rap was removed.

in the other

only once and then in

not to progress steadily.

The observations

of PO2 for the runs in

pressure of the water vapour

of the grooving

observe grooving

not occur at temperatures

by trapping

for most

along

that volume

was not observed

This

and after pa,ssing over the heated specimen. The partial

above,

at low tem-

peratures variable groove widths were observed

men& were made of the water content of the gas before

was found

Typically,

content implied that at 700°C the PO2 was m1O-2s atm.

p.p.m.)

a8 in (b).

was dried and introduced determine

(main impurity

compounds

effectively

diffusion

was opened to the hydrogen

torr the apparatus

nitrogen

water

as described

wit.h liquid nitrogen.

leak to give a pressure of ~7

To

anneal as described

use of a short preliminary side-arm

Below

became very variable and despite the

Estimating

an

effective Paz for the vacuum environments

is difficult.

Equilibrium

not estab-

lished. not

with the copper

However,

oxidised

is probably

it was observed that the copper was

at 7OO”C, so,

using

Richardson

Jeffesces’17) data, PO2 wa,s less than IV1

and

at,m.

The wet hydrogen point is the mean of two virtually identical results. The value of Paz of this environment at 700°C is lo-l9 atim. The results in low pressure oxygen more scatter;

the vertical

agai:l showed

bars cover extreme

read-

ings, the points are the mean, on average, of four observations. Oxidation was probably responsible for some of the variability. at the grain which,

boundaries

Oxide formed preferentially giving

if seen, were rejected.

anomalous

However,

profiles

some of the

6-

,4 -

\!\ \

\\‘\

HYDROGEN

A

8

HYDROGEN

+

9 FIG. 1

:

(

9

0

\

II FIG. 2

104/T”K

Tcrr

_.

4,

k Tom

IO

P-5xlC?lorr

P-IO-’

P-IO-’

\

I

.

I

600 5(

TEMP ‘C 7‘00

FIGS. 1 and 2. The surface self-diffusion of copper in different environments.

8

x

IO-‘Torr I2

OXYGEN

0

Torr

=760 II

VACUUM VACUUM

0

Torr

El

0.

.

, 890

F \g )

\I

900

’ P"zo/P"z =5.1

0

4

P

1001

=760

IO 4/T”K

IO

PH* P-5x

pHZ

I

n t

5(

I *. I

600

c

:

PHz -7 6(

, 700

TEMP ‘C

9?0

AND SHEWMON

\

\8“ \ \t \’

‘\

900

___GJOSTEIN

---CHOI

+

‘\

---

1000

I2

13

\ 0

a

ACTA

1062

METALLURGICA,

readings may have been slightly affected by

accepted

The t* dependence of grooving was confirmed over

this.

the whole temperature

range.

faces and this was attributed at,mospheres on a few

etching

crystals,

to oxidation.

rarely occurred, so that

In other

and then only

it could

at,tributed to contamination. Summarising, the t* dependence was confirmed

reasonably

of groove

be

width

in all cases where checks were made,

except at low temperatures in hydrogen at 1 atm. The straight line portions of the Arrhenius plots could be tabulated _~

thus: Q,

D,(cm2 set-1)

PIY?SSUIY 560 torr NT, x 10-S tom -1 x lo-‘t’orr -5 x 10-b tom

Hydrogen Hydrogen VWUUrn Oxygen ______

method

1 7 3 2

x x x x

22 19 17 18

10-l 10-Z 10-Z 10-l

was

only

used

with

and vacuum

The results in hydrogen

hydrogen

at at

at 700°C gave a low between

vacua

showed

no correlation

D,

and surface orientation.

D, seemed more dependent

on the particular anneal;

some gave all high and some

all low values.

If a scratch

was drawn through

of different orientations,

t,here was no marked

all

and then annealed,

change in smoothing

rate from

grain to grain.

In general the results obtained by this

method

less reliable

were

boundary

grooving.

than

Perhaps

not electropolish

those

from

grain

this was because

the specimen

one

after the pre-

liminary anneal and thus remove any impurities which might have segregated to the surface. X-ray

orientation

pronounced (by

measurements

showed

a fairly

texture of (110) planes lying in the sur-

However, the (1 ll}

was measured

of 0, that

a stereographic trace

method)

plot of orientations of crystals

by scratch smoothing

whose

D,

showed a fairly

broad spread from the (110) pole up to (112). Planes not effectively covered were those round the (001) and (111). 5.

DISCUSSION

Oxygen is readily adsorbed on the surface of copper. If adsorption is in the form of a monolayer of oxygen atoms, the reaction is, 0, + 2 cu = 2(Cu-0)

and AS == -30 adsorption

cal/mol/deg.

should

take

place

rogen and in wet hydrogen at 700°C should have been oxygen.

we do not know whether to have should

mation

Calculations

for the other

used show that this should still be so. oxygen

environments:

been

long enough

surface

environments

Qs]

(tl > 4) for Paz > lo-l8 atm. at 700°C. Referring to the estimates of Po2, this implies that the copper surface in hydrogen at 1 atm., in low pressure hyd-

Given

Results

face.

kcal/mole indicates

certain

measurable.

could

-110 This

Gjostein,

pressure

In [82/Po2(1 -

coverage and PO is the oxygen pressure in atmospheres. Using the same data as Gjostein,(2) AH =

sorbed in the vacuum

value for U, which was not accurately in

T A5’ = -RT

where AG, AH and A# are the free energy, enthalpy and entropy of adsorption, 8 is the fractional surface

Whereas

(kcal/mole)

smoothing

atmospheric

crystals

represents an oxygen atom on a surface

Then

calculating

Scratch

700°C.

site.

temperatures

Atmosl~her~~

This

where (Cu-0)

1964

free of adsorbed

__~

4.2

12,

AG = AH -

after annealing in oxygen ( PO2 ~10~’ was observed on some specimen sur-

As expected, atm.), etching

VOL.

in the low pressure

in this environment

have

been

adsorption

was ad-

it was virtually

covered

oxygen.

the whole

with

Cu,O.

AS as being equal to the entropy of Cu,O,

but for a mobile

could be appreciably Shewmon(is)

near

environment

{ill},

of forlayer it

Robertson

and

that for a copper

surface

Po2

of the

increasing

the

beyond a certain level causes changes in

the torque term (i.e. the variation with orientation). is responsible at 1000°C.

adsorbed

less than this.

have shown

orientation

In

pressures we have taken, with

Assuming

we deduce

of surface energy

that adsorbed

that AG = -97

Taking as before, AH = -110

A&’ becomes

-10

cal/mole/deg.

This

characteristic

pressure, for the formation

oxygen

kcal/mole kcal/mole leads

to

a

of a mono-

layer, of 1O-23 atm. at 700°C and one should now expect

adsorption

of

oxygen

in the

wet

hydrogen

environment’. However,

regardless of this WC have (a) that where

diffusion

occurred

pressure

hydrogen,

agree within even between lo-’

the values of D, obtained in wet hydrogen

the accuracy

in low

and ilr, uacuo

of measurement

and (b)

the whole range of PO, from lo-30 to

atm. D, only changed by a factor of 7 at 700°C.

The Gibbs formula for dependence of surface energy on gas pressure, where adsorption is occurring, is Po2(dy/dPo2)

= --r

kT

where r is the number of molecules adsorbed/ems. From this one would expect, when 8 LY I, a reduction in ys of -300 erg/cm2 for every tenfold increase in pressure. As we have not so far allowed for this we might expect an apparent increasing Paz, but we have effect.

reduction

in D, with

observed

the reverse

13RADSHAW, 6.

BRANDON

SURFACE

and our few

SELF-DIFFUSION

IS

Cu

1063

ACKNOWLEDGMENTS

CONCLUSIONS

At high temperatures gether

WHEELER:

AND

all results tend to come to-

observations

agree reasonably

We

wish to thank J. N. Eastabrook

orientation

measurements

for the X-ray

and also N. J. Wadsworth

well with previous ones. At lower temperatures (i.e. < 900%) in all environments there seems to be

and D. M. Gilbey for their helpful discussions.

clear evidence

1. W. W. MULLINS and P. G. SHEWBIOX, Act<& ,%fet. 7, 163 (1959). 2. N. A. GJOSTEIN, Trains. A.Z.M.E. 221, 1039 (1961). 3. J. Y. CHOI and P. G. SHEWMON, Trans. A.Z.M.b’. 224, 589 (1962). 4. P. G. SHEWMON and J. Y. CHOI, to be published. 5. J. Y. CHOI and P. G. SHEWMON, to be published. 6. N. A. GJOSTEIN, to be published in Proceedings of BSMAIME Symposium, Surfuces: Structure, Energetics and Kinetics, held in New York in October 1962. 7. M. C. INMAN, D. MCLEAN and H. R. TIPLEK, Proc. Roy. Sot. A2*93, 538 (1963). 8. E. MENZEL, 2. Physik 132, 508 (1952). 9. J. M. BLAKELY and H. MYKURA, Acta Net. 10, 565 (1962). 10. W. W. MULLINS, J. Appl. Phys. 28, 333 (1957). 11. W. W. MULLINS, [I’rans. A.Z.M.E. 218, 354 (1960). 12. A. D. LE CLAIRE, Phil. Mag. 7, 141 (1962). 13. R. T. KING and W. W. MULLINS. Actu Met. 10.601 (19621. 14. S. TAKEUCHI, T. HONMA and S.‘IKEDA, S”ci~-~e~. !bohok’u Univ. 11,81 (1959). 15. H. CUIN, &fetal Interfaces, p. 114. Amer. Sot. Metals (1951). 16. tip.A.‘JA~QUET and M. JEAN, Rev. M&. 48, 537 (1951). 17. F. D. RICHARDSON and J. H. E. JEFFES, J. Iron. St. Inst. 160, 261 (1948). 18. W. M. ROBERTSON and P. G. SHEWMON, J. Chem. Phys. 39, 2330 (1963).

of a lower activation

(i.e. Q, RS 0.2 AH&. at the

lowest

surface

Diffusion

temperatures

contamination.

agreement hydrogen

energy

process

in VICCUO proceeded

and

showed

Because

of

the least

this

and

the

between results in vacua and low pressure one might suggest that this is characteristic

of clean copper, but because of uncertainties adsorption

and the possibility

the evidence

is not

of other

conclusive.

in oxygen impurities,

Increasing

oxygen

partial pressure increases surface diffusion under these conditions.

Limited experiments

showed no marked dependence 7OO”C, though come

moro

on orientation

at lower temperatures

important.

derived to account

Theoretical

this could models

at be-

can be

for both large and small values of

Q, and D, but discussion

of these is of limited value

unt’il a clearer idea of conditions obtained.

effects

of D, on orientation

at the surface

is

REFERENCES