Solidification of copper-rhodium alloy single crystals

,bfarenals

Chemistry

and Physics,

SOLIDIFICATION

OF COPPER-RHODIUM

Chimie

Analytique,

Received

ALLOY

SINGLE CRYSTALS

and F. BOUILLON

Fat. Sci., C.P. 160, Brussels

27,

August

225

225-233

M. JARDINIER-OFFERGELD

DELPLANCKE,

M.P.

27 (1991)

1990;

accepted

1,

October

University,

Brussels

(Belgium)

1990

ABSTRACT Preparation method

of copper-rhodium

is described

in this

process

solidification

to characterize the

the

and

of

are

in agreement

of

1.5,

electron

(microindentation,

thermal

single

solute

4, 8.15

and and

of

the

by

structures 15 at.%

Rh

scanning A study

distribution.

existing

crystals

Dendritic

microprobe

stability

with

alloy

paper.

structures

the vertical are

microscopy)

the

is also

Bridgman

during

Various

alloys.

Auger of

formed

formation

the

methods are

used

conditions The

presented.

results

models.

INTRODUCTION The properties of the

the most elements For

cess. senting

in the a given

both

alloys,

turbines

In the

tation

over of

samples

surface of

the

02%0584/91/$3.50

of

can

of

last

these

segregation

exposed

are

be obtained

face.

related

the

Due

of many

five

copper-rhodium

and

years

Many

oxidation

A fundamental

the

or

sample

prop

parame-

in pure

melts

importance

machine

parts and

of

prey

solidification

theoretical

and

of like

experimental

[l-t?]. system,

properties rates

TWO

distribution

solidification

occur

of critical

thirty

alloys.

to the

factors.

the

to the practical

of

the

and

structures

properties subject

on various

material

by varying

solidification

been

a study

depend structure

homogeneous

non-metallic.

have

the

them

a completely

cellular

they

context

homogeneous

Both

and

materials

the crystalline

in the mechanical

blades,

investigations

energy,

bulk.

metallic

wrought

are

system,

and

structures

and

ones

microsegregation Dendritic

ters.

these

of cast

important

such

depend

study

0 Elsevier

of

on

we

tried

as

surface

to prepare free

the crystalline

the mechanisms

Sequoia/Printed

orien-

controlling

in The Netherlands

226

these phenomena line

requires

the preparation

of well

characterized

single

crystal-

samples.

A preliminary prepared

by

study,

the

performed

vertical

in this

Bridgman

method

laboratory presented

[91 showed visible

that

the

samples

solidification

struc-

tures. The

main

purpose

structures,

methods

dium system. the phase

this

paper

to characterize

analytical

system

of

and

published

is characterized

a partition

solute

to apply

the

1101.

of the solute towards

samples

of

are mainly

(rhodium) higher agents

these

by various

to the copper-rhoobtained

The copper-rhodium

gap between

chemical

stability

models

for this last point

by a large miscibility

coefficient

in the

theoretical

by Raub and al.

in the reactivity

thermal

distribution

existing

The data necessary

diagram

difference

the

is to examine

from

binary

20 and 90 at.% Rh, by

than 1 and by a great

as a function

of the rho-

dium concentration.

THEORIES The

growth

processes These

factors

the diffusion

imply that the crystal

ones

have

rate been

to allow

growth

in space.

the

the effects

of gravity

The oldest model,

slow rates of solidification.

of

true

proposed

by Chalmers

Our experimental

: diffusion

liquid-solid limited

in the solid is negligible,

interface

during

the partition

face. cooling

for very

(solidification

rates

Three main assumptions

equilibrium

is maintained

the study stats, and transport

the solute distribution

In these conditions,

induces

The recent

are

at the

in the liquid

is

to that by diffusion.

rate (R), the diffusion

phases.

the

with those ob-

I151 is valid

conditions

lower than 10-2cm s-l) allow the us8 of this model. made

results

with

Different

in alloys.

and compare

:

phenomenon

equilibrium.

the microsegregation

of

transformations.

is a non-equilibrium

establishment

to modal

proposed

Ill-141 introduce

tained

by the coupling

fluid flux and phase

rate of the solute in the solid is too low in comparison

solidification theories

from its melt is characterized

of a crystal

such as heat and mass transfer,

coefficient

The rejection the formation Tiller

coefficient

of one of the constituent

a criterion

on the solidification

in the liquid phase

(k,) of the solute between

of a supercooled

established

depends

of the solute

(D) and

the solid and the liquid

elements,

in our system copper,

zone in front of the solid-liquid of apparition

inter-

of the constitutional

super-

:

G E+(T) S R where G = the imposed

thermal

gradient

m = the slops of the liquidus C,= The

presence

the mean composition. of

lar or dandritic,

the

supercooled

dependent

tions wsrs developed

zone allows

the development

on the experimental

to model

the spacing

conditions.

of structures Precise

cell"-

calcula-

and the size Of these structures

14.

227 They are mainly

7,161.

based on the observation These

succinonitrile-acetone. drite as

li

studies

of transparent

established

systems

that the spacing

to 6 G and that the radius of the dendrite

arms is proportional

like

of the dentip varies

c,. d--

Despite

the practical

few studies model

interest

have been performed

based on a sinusoidal

the concentration concentration

repartition

treme values

is considered

Under

value.

ted by the relation

of the solute,

Another

area.

as completed

of the concentration

of the structured

Flemings

1171 developed maxima

the

(if k, > 1) and the minima

in the dendrites

of the interdendritic

homogenization

initial

of the homogenization

on this topic.

is reduced

representing

representing was made,

when the difference

in the sample

these conditions,

assumption

alloys,

a simple

between

the

that the

the ex-

to one tenth of its

the homogenization

time can be calcula-

:

L is the size of the cell, AC H,e/ACR,t is the ratio of the concentration

where

difference

at t = 0 and after an annealing

terdiffusion

of t hours and 6 represents

the in

coefficient.

EXPERIMENTAL The apparatus method

for the solidification

was designed

was the movement

of the oven along

The rate of the oven displacement a pumping

device

(mechanical

was measured

the alumina

the melting

by a Pt-PtRh

A more detailed

[18j.

was machined

and purified To obtain

macroscopically

crucible, a cavity.

it was necessary

first to prepare

in the graphite

of four fusions were necessary

99.999%

and origin of Hoboken

of Johnson-Matthey, The orientation

face, mina

rhodium wire

ning phosphoric

rod and machine

(Fig. 1).

to obtain

with the it to form

The assembly

was

samples.

Alloys

satisfactory

by this method.

was

determined

the following 99.9% and

: 'specpure' 99.997%

by Laue back reflection

the rods along

polished

isopropanol,

the desired

on metallographic

by a short electrochemical

acid, ethanol,

the mean concentra-

crucible.

rhodium powder

After cutting

the samples were mechanically ($4 lnm), followed

purity)

99‘99% of Ventron.

of the alloy rods

of one degree.

The

rod.

of the components

a copper

of the pure metals were (Belgium),

of

the alumina

(spectroscopic

that presented

The cavity was then filled with rhodium

The purity

precision

rod

of a copper

samples

processes. between

with

a pressure

can be found in the literature

out of a graphite

at 1.5, 4, 5.75 and 15 at.% Rh were prepared

copper

placed

part and to avoid any reaction

then fused and solidified A minimum

description

is equipped

able to maintain

thermocouple

Bridgman criterion

the crucible.

The system

and solidification

homogeneous

design

tube containing

pumps)

by the fusion and solidification

tion in their central

important

could be varied.

tube and the oven. The crucible

and the most

and diffusion

7 x 10-3 Pa at 1273 K during temperature

of the alloys by the vertical

in this laboratory

polishing

urea and water

with a

crystalline

papers

and alu-

in a bath contai[19].

228

Rhodium. m

Copper

rod.

m

Graphite

mould.

Fig. 1. Scheme of the graphite single crystals.

The bulk composition was used to determine The solution tion, scanning Energy

was monitored

distribution

X-ray

X-ray diffraction

: microindenta-

by three methods

(SAM) and electron

microprobe

analysis

(EDXRF,

system

(m = 15

Fluorescence).

of the Tiller

criteria

to the copper-rhodium

Rh. k, = 1.85) shows that in our experimental

stable

for rhodium

gradient

concentrations

Fig. 2, to prevent the formation lidification

Experimentally

the preparation

of materials

as it is very difficult structures dendritic

obtained

or dendritic.

the copper-rhodium are, of

influence

in a 1.5 at.% Rh alloy, the so-

course,

structures

: FCC.

dependent

of the structures of the crucible

rates that also allow

are not interesting

in our case

under these conditions.

The

at 1.5, 4. 8.15 and 15 at.% Rh are cellular-

The growth direction

alloys

at a rate of 5.5 x 1W5 cm s-1

single crystals

for the alloys

re-

by one order of magnitude.

without

are the axes of the crystals

regularity

interface

As shown in

The high solidification

to obtain

(solidification

lower than 0.18 at.% Rh.

a 1.5 at.% Rh alloy solidified any structure.

conditions

20 K cm.l) the solid-liquid

of structures

rate has to be reduced

does not present

drites

fluorescence.

present.

was characterized

rate = 8 x 10-4cm s-l, thermal mains

by X-ray

of the alloy

AND DISCUSSION

The application K/at.%

used for the preparation

the number of phases

Auger microscopy

Dispersive

RESULTS

mould

of the dendrites

in agreement The geometry

and of the arms

with the crystalline of the figures

on the examined

crystalline

over the whole crystal

system of

formed by the den-

face (Fig. 3). The

(Fig. 3b) indicates

wall is small in our experimental

device.

that the

229

cm”

G=20K

C.

4 R= 6.1E4 cm 1s

IO2 -

12.

I

1

'1 I

1

I

I

I

1

R (cm/s

1

+ 12

1-d' Ii3 ci2

11

1

10

IO2

IO3

Fig. 2. Representation of the formation conditions of the different types of solidification structures in function of the rhodium concentration (Co) and the solidification rate (R) for a temperature gradient of 20 K cm-'.

Fig. 3. a) Cu-Rh alloy, 15 at.% Rh single crystal, face (111) solidification structures magnification : 15 X Fig. 3. b) Cu-Rh alloy, 4 at.% Rh bicrystal, face (110) for the main crystal lidification structures magnification : 5 X.

so-

230

Table I.

Average size of dendritic arme L as a function of the rhodium

concentration. C (at.% Rh)

(cm)

L

3.1x10-2

1.50

(111) face

2,7x10-'

4.00

(110) face

2,5x10-*

a.75

(111) face

2.0x10-*

15.00

(111) face

Table II. Calculated and experimental time for homogenization. C(at.% Rh)

L (cm)

1.50

3.1x10-*

D (~rn~.s-~)

t theor.

3X16'O

(h)

t exper.

210

4.00

2.7x10+

3xl6'O

157

114

a.75

2.5~16~

3x1ci'"

135

138

15.00

1.9x16*

3xuY0

78

93

An average

size of the dendrite

for each alloy. the rhodium

arms

(L) was measured

Table I shows the evolution

concentration.

this is related

to the higher

which

allows

Table

II presents

concentration

from microscopy

of this parameter

The size decreases

pictures

as a function

with increasing

gradient

(h)

98

of

concentration;

in front of the interface,

for the growth of a higher number of dendrites.

time necessary

the results

to obtain

at 1263 K either

in vacuum

tion is the bette;

of the annealing

homogenization.

or under atmospheric

one as it reduces

experiments

The thermal

and the calculated

treatments

pressure

copper evaporation

of

Hz.

were performed The later condi-

(vapor pressure

of cop-

per at 1300 K is 1.3 x 1O-2 Pa). The lack of diffusion

data required

obtain

times.

the calculated

fusion coefficient mate

To estimate presenting

is barely

coefficient

fulfilled

it is not credible

proximation,

the error similar

induced

earlier

and extrapolations

to

for highly

dilute

solid solution.

by the 1.5 at.% Rh alloy

in a first ap-

for the alloys at 4, 8.75 and 15 at.% Rh.

by this shortcoming,

characteristics,

system, whose

copper-nickel were studied tion

of rhodium

that of the interdiffusion

If this condition

some approximations

The only published value is that of the heterodifcu in copper DRhe 1201. This value could approxi-

which

solidification

in our laboratory

we looked

for a binary

was studied more extensively. morphological

and structural

[21,221, seems to fit with

system The

aspects

this descrip-

: the solute diffuses much more slowly in copper than copper itself does.

The evolutions solutes

CU of DRh*

and

dir* with temperature

are in the same group in the periodical

For the copper-nickel

system,

the literature

ween D and the solute concentration.

are similar

1231 and the two

table. [231 reports

the relationship

At 1273 K, for a Ni concentration

than 1 at.%, D = 5 x 10e10 cm2 se1 but at the same temperature to 5 x 10.11 cm2 s-1 for a Ni concentration

of 50 at.%.

bet

SmallSr

the D value drops

If the evolution

is si-

milar for the copper-rhodium system, we can expect an error induced by the use cu This factor could explain the longer Of DRh* in place of b as high as 150%.

231 time necessary

to homogenize

theory and experiment rection.

This could be due to the estimation

is well defined

for a cellular

structure,

The use of the size of a dendrite

one.

The

tance.

second power

ment between Rhodium penetration variations

theory

presence

regions,

arm overestimates relation

size.

di-

Although

the diffusion

amplifies

of the two factors

in copper

increases

This effect

I,

dis-

the influence

contributes

the resistance

increases

as high as 30% can be observed A line scan, crossing

clearly

of the dendrite

of the

to the disagree-

and experiment.

of the tip.

tion of the tip.

between

are in the opposite

this is not the case for a dendrite

in the Flemings

The combination

approximation.

But the differences

the 15 at.% Rh alloy.

for the 1.5 and 4 at.% Rh alloys

indicates

of the solute distribution

an oscillation

to the

concentration.

depending

in our samples,

the dendrite

was established

of the material

with the rhodium

on the posi-

arms and the interdendritic

of the hardness

value

(Fig. 4).

A man

by this method.

dendrite

Fig. 4. vickers hardness variation along a line crossing the interdendritic regions. 15 at.% Rh alloy.

A more precise EDXRF.

Figure

isoconcentration with

description

of this distribution

5 shows simultaneously lines.

Scanning

the scanning

Auger microscopy

of

the dendrites

arms and

the solute was obtained

electron

microscopy

at low magnification

by

and the agrees

these results.

Among

the three methods

the microindentation surface

and better

used to characterize

is the least sensitive represents

the solidification

to the preparation

the bulk mechanical

properties

structures,

procedure

of the

of the samples.

232

Fig. 5. Scanning electron microscopy of a dendrite in 8.15 at.% Rh alloy, face lines obtained by EDXRF are represent ed simulta(111). The isoconcentration neously.

CONCLUSIONS The copper-rhodium

system presents

constitutional

supercooling

solidification

structures

8.75 and 15 at.%. a drastic vations

To prevent

structure

the validity

Microindentation,

the absence

of structures

rate is required. models

dendritic

of 1.5, 4,

in the dilute

alloys,

The experimental

obser-

predicting

Auger microscopy

the conditions

and electron

the solute distribution

of the samples

This problem

of homogenization

the error induced

of the interdiffusion diffusion

homogenization Another

concentrations

of

microprobe

analysis

that is in agreement

with the

model.

The homogenization

rhodium

the formation

of existing

scanning

to characterize

cult to model.

timate

at rhodium

range where

conditions,

formation.

are useful Flemings

concentration

In our experimental

were observed

drop of the solidification

confirm

an extended

prevails.

error

by annealing

is mainly models

treatments

for dendritic

structures.

by the use of the heterodiffusion

coefficient

behaviour

in the Flemings

is the determination

data and to

In order

coefficient

model, we compared

with that of the copper-nickel

time as high as 150% could be induced factor

is long and diffi-

due to the lack of diffusion

system.

the copperError in the

by the shortcoming.

of the diffusion

distance.

to es-

in place

233

ACKNOWLEDGEMENTS This

work was financially

(Grant 48.81)

and the

of the authors la Recherche

supported

like to thank the 'Institut

(MPD) would

dans 1'Industrie

The authors

by the North Atlantic

*Fends de la Recherche Fondamentale

are indebded

Organization One

pour 1'Encouragement

de

for three scholarships.

et 1'Agriculture' to P. Delcambe

Treaty

et Collective'.

and L. Binst for their technical

as-

sistance.

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