Grain boundary relaxations in iron-chromium alloys

GRAIN

BOUNDARY

RELAXATIONS P.

IN IRON-CHROMIUM

ALLOYS*

BARRAND?

Grain boundary relaxations were investigated in a series of Fe-Cr alloys in the range up to 43.1% Cr. For Cr contents up to about 2 %, two grain boundary peaks were observed; one at 500°C due to relaxation of Fe atoms and one near 600°C due to relaxation of Cr atoms. At higher Cr concentrations the 500°C peak disappeared completely and the solute peak became stronger. The peaks for all the specimens were superimposed on a steeply rising background which arises due to dislocation movement possibly mainly in the region of the boundaries. Anomalously high values of Q (activation energy) and low values of 70 for the 12.9 and 14.0 y0 Cr alloys are interpreted in terms of a contribution from a process of ferromagnetic electron spin ordering in the region of the peak temperatures. A model for the observed relaxations is described in terms of grain boundary migration under the action of the applied alternating stresses. RELAXATIONS

AUX

JOINTS

DE GRAINS

DANS

LES ALLIAGES

FER-CHROME

Les relaxations aux joints de grains ont et& examinees dans toute une serie d’alliages Fe-Cr, jusqu’a 43,l o! Cr. Pour des teneurs en Cr allant jusqu’it 27o, deux pits de joints de grains sont observes, l’un a 500% dh aux atomes de Fe, et l’autre aux environs de 600°C dii aux atomes de Cr. Pour des teneurs en Cr plus &levees,le pie de 500°C disprait et celui cause par les atomes de solute devient plus marque. Pour toutes les Bprouvettes, on a observe en m&me temps que les pies, un fond continu qui augmente fortement avec la temperature; cet effet est cuse par le mouvement des dislocations, sans doute principalement dans le voisinage des joints. Des valeurs anormalement &levees de l’energie d’activation Q et des valeurs faibles pour r,,, dans des alliages a 12,9 et 14% Cr, ont 8te interpret&escomme &ant dues a une mise en ordre ferromagnetique de spin des electrons dans le domaine de la temperature des pies. Les auteurs proposent un modele de ces relaxations en terme de migration des joints sous l’action de la contrainte alternative qui est appliquee a l’eprouvette. KORNGRENZENRELAXATIONEN

IN EISEN-CHROM-LEGIERUNGEN

Korngrenzenrelaxationen wurden in einer Reihe von Fe-Cr-Legierungen mit Zusammensetzungen bis zu 43,l o/0Cr untersuoht. Bei einem Cr-Gehalt bis zu 2% wurden zewi Korngrenzenmaxima beobachtet; ems bei 500°C aufgrund der Relaxation von Fe-Atomen und ein zweites bei 600% aufgrund der Relaxation von Cr-Atomen. Bei hiiheren Cr-Konzentrationen verschwand das 500%Maximum vollstandig und das Maximum der gel&ten Komponente wurde starker. Bei allen Proben waren die Maxima einem steil ansteigenden Untergrund tiberlagert, welcher von der Versetzungsbewegung moglicherweise hauptsachlich in den Korngrenzengebieten herriihrt. Die anomal hohen Werte fur Q (Aktivierungsenergie) und niedrigen Werte fur r0 bei den Legierungen mit 12,9 und 14% Cr werden mit einem Beitrag eines Prozesses der ferromagnetischen Elektronenspinordnung im Bereich der Maximumstemperaturen erklart. Es wird ein Model1 fur die beobachteten Relaxationen beschrieben, welches auf Korngrenzenwanderung unter Wirkung einer angelegten alternierenden Spannung beruht.

1. INTRODUCTION

Grain boundary polycrystalline

aluminium,

250 and 300”C.(1) between activation proposed

the

relaxations

at temperatures

Because

measured

and gave rise to a second

were first observed

energies for self-diffusion

energy

and activation

closer relation

boundary

and

sliding.

energies

This

then gave a for grain

diffusion.

solid solutions.

Pearson

investigated

The activation copper

in dilute alloys,

activation

energies

for

grain

in the alloys were approximately

of the

with increasing

solute

elements peak

concentration

used, (c) the

decreased

slightly

of the solute element.

energy for grain boundary

was significantly

Similar

and

less than that

Rotherham

relaxation

copper

for volume

binary

and

The significant effects

internal friction peak characteristic

of the pure copper

* Received October 22, 1965. t University of Manchester, England. VOL.

14, OCTOBER

experiments

damping in for volume

silver

and

self-diffusion,

silver

alloys

energy for grain boundary

in silver was considerably

less than that

but was in good agreement

with measured values for grain boundary

self-diffusion.

The effect of Cd, In solution in silver was damping, and to raise boundary relaxation

and Sn in substitutional solid to increase the grain boundary the activation energy for grain from 22 kcal/mole for pure

silver to 43 kcal/mole

for the solid solutions.

Work on interstitial 1966

on

showed that the activation

For example,

of alloying elements on grain boundaries in copper alloys can be summarised as follows: (a) the addition of the solute elements, e.g. Zn or Ga, suppressed the

METALLURGICA,

(b) the

relaxation

peak at a higher

causing the peaks were

the same for all the alloying

both

binary silver solid solutions.(2,3)

ACTA

that the processes

temperature

effects in pure metals

work has also been carried out on substitutional interstitial

boundary

(solute)

peaks occurred

self-diffusion.

As well as grain boundary

and

Both

independent,

the

using more

with those measured

temperature. indicating

and for creep, KB

early work was superseded by experiments much

between

there was a correlation

activation

his model of grain boundary

pure material,

in

1247

alloys has been carried out by

ACTA

1248

Miles and Leak(*) who studied of high purity

for grain boundary

iron.

damping

damping

charac-

The activation

energy

iron-nitrogen

alloys respectively.

corresponding

alloys,

Background reached

TABLE 1. Composition

Chromium

measurement.

The whole level of damping

iron-nitrogen

alloys was lower than for the iron-carbon

It was also found

raised the temperature

that interstitial

impurities

of the grain boundary

tion peak, and it was concluded

0.0022 0.004

2.94

0.003

0.004

5.26

0.0026

0.004

12.9

0.0028

0.0125

14.0

0.0026

0.0165

19.2

0.0026

0.004

27.55

0.0026

0.004

43.1

0.0084

scale.

Support

relaxa-

that the mechanism

of damping was that of reversible boundary on an atomic

migration

for this postulate

that some pure metals showed an activation

was

energy

for up to 2 hr, in situ in the damping prior to any measurements

which could be related to that for

out

grain

diffusion.

torsion pendulum.

system

would

therefore

grain boundary activation

cyclic

provide

movement,

applied

a driving

leading

that

in moving

locally

an atom

force for

rearrange-

from the lattice may

of

diffusion.(s)

the atomic

grain to the lattice of the neighbouring give rise to a strain which

stress

to an energy

identical with that for boundary

It was thought ments,

A

of one

grain, would

not have

been in

using

a free-decay

under a vacuum

was

Some work on grain boundary

damping

effects in

The

influence

Alloys containing

the

up to 45% Cr were

but the grain boundary

measurements

part of their investigation.

It

presence

magnetic

field.

the peak value for grain boundary

damping

A grain boundary

damping to higher activation

energy of

boundary

damping

aim

of the iron-chromium

of more

observed

clearly

dia.

establishing

system with the a model

for the

logarithmic

of

damping

decrement

damping

and

absence

of

an

axially

range

of

specimens,

PROCEDURE

whose

A field of about 100 Oe was used for and this appeared to saturate

for higher fields did not reduce

significantly.

Unless

otherwise

compositions

are

subsequently cold swaged to about 0.090 in. The 27.55 and 43.1 y0 Cr alloys were too hard and brittle to swage all the way down, and were reduced to size by

centreless

grinding.

The

specimen

the

indicated

therefore the results and figures will be for specimens field.

3. RESULTS

Figure

1 shows

a composite

curves for specimens 5.26 wt.%

containing

Cr respectively.

graph

of damping

0.62, 1.21, 2.94 and

All the curves

are for

of about 1 c/s, and The

main features are firstly the rapid fall of the damping

shown in Table 1, were kindly supplied by the British Iron and Steel Research Association. The material was either hot or cold rolled down to 0.25 in. and

recrystallised

in

applied

having grain sizes of between 0.05 and 0.06 mm. A

(6).

of nichrome

magnetomechanical

specimens operating at a frequency

effects. 2. EXPERIMENTAL

grip

phosphor-bronze

effects,

particularly in substitutional solid solutions, is so sparse that it was decided to undertake a detailed investigation

10”

x

in the presence of a magnetic

was recorded. grain

0.020 in.

all these measurements, the specimens,

on

The top specimen

was studied by taking measurements

was observed that the addition of chromium displaced

data

by

and to keep the level

low.

The furnace was wound non-inductively

Preisendanz.@)

The

inverted

was sealed

wire, which had itself a room temperature

contributions

93 kcal/mole

oxidation

damping

level of less than 1

alloys was carried out by Bungardt and

temperatures.

an

of better than 10” mm Hg, in order

suspended

iron-chromium

were only a subsidiary

were carried

in

The whole apparatus

to reduce specimen of background

technique

wire which is non-ferromagnetic.

phase with the applied stress.

investigated

equipment,

being taken.

All the internal friction measurements

for grain growth boundary

Nitrogen

0.0006

of

for the

Carbon

0.003

damp-

at the temperature

alloys (wt. %)

1.21

roughly to a carbon content equal to that solid solution

of the Fe-&

0.62

and

a maximum

in equilibrium

series.

14, 1966

in pure iron increased

from 46 to 60.5 and 68.5 kcals for iron-carbon ing in the iron-carbon

VOL.

the effects of carbon

and nitrogen on the grain boundary teristics

METALLURGICA,

were

then

and stress relieved by heating to 750°C

peak at 500°C and the increasing strength of the peak at about 600°C

as the proportion

of Cr increases.

A

sample of pure Fe had a grain boundary peak at 500°C having a height of 0.35 log dec. This characteristic has been reported previously for f.c.c. alloys,(2,3) but not, as far as can be ascertained, b.c.c. alloys. Figure 2 is also a composite specimens

containing

12.9,

graph

14.0 and

for the case of of curves for 19.2 wt.%

Cr

BARRAND: I

I

1

I 500

I 600

7oc

I

0 0.62% .

GRAIN

BOUNDARY

cr

I.21 ale, Cr

x 2.94%

Cr

0 5.26%

Cr

x----t 400

TEMPERATURE

I

‘C

FIG. 1. Damping curves of Fe-0

Cr.

Frequency ~1 c/s.

specimens up to 5.26 % Grain size 0.05-0.06 mm dia.

respectively. The frequencies were again about 1 c/s, and the grain sizes approximately 0.045 mm. Also included in the figure is a curve taken using a specimen of 14.0% Cr, but having a grain size of 2.0 mm. This curve does not seem to leave much doubt about the origin of the observed damping effects. The pattern of increasing relaxation strength with increasing chromium content is maintained for the 12.9 and 14% Cr specimens, but it will be noted that the strength of the 19.2% Cr peak, as may be seen also by reference to Table 2, is significantly lower. This is almost certainly due to the influence of (r phase formation and it will be discussed more fully in the next section. Figures 3 and 4 are curves for the 27.55 and 43.1 y0 Cr specimens respectively. The chief differences here are firstly that two peaks again appear to be present,

1249

RELAXATION

shown more clearly in Pig. 4, and also that the peak heights are further significantly reduced. It is thought that the lower ~mperature peaks in both cases are probably due to a substitutional relaxation effect within the lattice, while the higher temperature peaks are due to relaxations at crystals boundaries. The 43.1 y0 Cr specimen would be almost entirely Q phase at the temperatu~ of the peaks and this is again felt to have an impo~nt bearing on the low level of damping. It will be observed that in general the grain boundary peak is superimposed on a steeply rising background. Previous workers have commented on this phenomenon in other alloy systems,(2-4) and the probable reason for its presence is some sort of ~sloeation movement in the neighbourhood of the grain boundaries. Some substantiation for this can be seen in Fig. 2 where the large grained specimen has a much lower general level of background damping as well as a greatly rednced peak. Figure 5 shows a curve for a specimen of the 0.62% Cr material showing the grain boundary peaks previously mentioned, and also a maximum in the damping at a temperature of approximately 800°C. This particular peak was observed by Bungardt and Preisen~nz(~) and was ascribed to deformation effects, and also o-phase formation, since it increased in height with increased deformation, moving to lower temperatures, and vanished on annealing at high temperatures. The present measurements confirm the

9 rain

dia. 2.0 mm.

TABLE2. Summaryof results wt. % cr 1.21 2.94 5.26 12.9 14.0 19.2 27.55 43.1

--l%, 70 14.0 14.21 14.71 16.49 17.62 14.42 14.0 12.47

Tp “C 562 592 597 603 631 627 627 683

AB x IO* & I$r: 3 kcal 1.0 2.4 3.6 6.7 7.0 z7 0:32

51.5 54.3 56.3 64.1 70.8 57.3 55.5 52.3

500

700

600 TEMPERATURE

‘C

Fm. 2. Damping curves of Fe-Q specimens containing 12.9, 14.0 and 19.2% Cr. Frequency ~1 c/s. Grain size 0.045-0.05 mm. dia.

ACTA

1260

METALLURGICA.

VOL.

14, 1966

24

1

,-

2c

616

“0 x 12

!4

I

550

I

f

600

650

TEMPERATURE

t

7oc

‘C

I

I

t

I

500

600

700

8OC

TEMPERATURE°C

Fra, 3. Damping curve of a 27.55’~ Cr specimen. quency -1 c[s. Grain size 0.06 mm dia.

Fre-

FIG. 5. Damping curve of a 0.62 % Cr specimen showing the high temperature deformation peak and two grain boundary peaks. Frequency -1 c/s. Grain size 0.055 mm dia.

IS -

15-

IZ-

9-

GRAIN

6-

.

0.042

0

0.056

x

0.067

SIZES

(mm.\

3-

*

bcx3

650 TEMPERATURE

Fro.

700 ‘C

4. Damping curve of a 43.1% Cr specimen. Frequency -1 c/s. Grain size 0.05 mm dia.

L SOC>

,

I

600 TEMPERATURE

700 “C

FIG. 6. Damping curves of a 14% Cr alloy for specimens having the grain size indicated. Frequency -1 c/s.

BARRAND:

GRAIN

BOUNDARY

gained 0

by subtraction

background GRAIN

SIZES

1251

RELAXATION

of the peak from

was observed while investi-

A curious phenomenon

(m.m.1

the dotted

damping.

0

0.042

gating the 19.2% Cr alloy.

0

0.056

A and B, the first of which has a very small peak on a

.

0.067

steeply rising background

while the second has a much

more substantial

Curve A represents the level

0

of damping apparatus,

effect.

on initially from

room

Figure 9 shows two curves

heating the specimen temperature,

and

shows the resultant level of damping specimen

isothermally

matter of 2-3 hr.

.

As mentioned netoelastic

at the peak temperature

previously

B the

for a

component

and dissolution.

the presence of any mag-

to

the

total

checked by taking measurements

I-

on holding

The reason for this effect is again,

it is felt, due to u-phase formation

0

0”

in the

curve

damping

was

in the presence and

absence of an applied field of 100 Oe. A typical effect may be seen in Fig. 10 for the case of the 12.9% alloy,

-C

a small

peak

developed,

due

to

Cr

magnetic

effects, at a temperature just below the Curie temperature for the alloy.

It was impossible

accurate

of an activation

estimation

effect, but it was highly reproducible. FIG. 7. The effect of varying the grain size, of a 14 % alloy, on a plot of log,,f versus lOOO/PK.

there were also magnetoelastic lower temperatures. A summary investigated

irreversibility damping.

and

The

dislocation

exact

location

extremely difficult to determineat damping

encountered,

dependence

of

of a peak

this

but an approximate

As can be seen contributions

viz, ~c, Q, AE and

at

T,

factor in the equation I

I

I

the very high levels of

an

of the values of the main parameters for the alloys,

(where r,, is the pre-exponential

becomes

to make

energy for this

activation

energy, calculated from peak shift with change of vibration frequency,

of 64 kcals/mole was calculated.

seem possible

therefore

damping

It does

that the very high level of

plus the presence of the peak may be due to

some stress induced migration in association

of Fe and/or

Cr atoms

with dislocations.

The effect of grain size on the damping characteristics was investigated

and the results, for the case of the

14% Cr alloy, may be seen in Figs. 6 and 7. Figure 6 shows damping curves, at about the same frequency, for the three grain sizes indicated while Fig. 7 is a plot

(f

of log,,f reciprocal

is the frequency of the absolute

of vibration) temperature.

versus the The three

lines, constructed

using a least squares analysis,

are

almost

parallel

the

perfectly

thus

indicating

that

activation energy is independent of the grain size. There was a slight but inconsistent tendency for the peak temperature to increase as the grain size is The symmetry of the grain boundary increased. peaks obtained

can be seen by reference

which is a plot of the actual damping alloy plus a plot of the grain boundary

SO0

to Fig. 8

curve of 14% peak alone,

600 TEMPERATURE

FIG.

8.

700 ‘C

Grain boundary peak of a 14 ‘A Cr specimen after subtraction from the background damping.

ACTA

METALLURGICA,

VOL.

14,

1966

for the relaxation time, Q is the activation energy, A, is the relaxation strength of the peak and T, is the peak temperature at 1 c/s), are presented in Table 2. These parameters are also, with the exception of the more conoentrated alloys, presented in Fig. Il. ~om~lous results were obtained for 70 and Q, in the cases of the 12.9 and 14% alloys. Possible reasons for this are discussed in the next section. The peak temperature, with some fluctuations, can be seen to increase steadily with increase of Cr content, while up to 14% Cr, the relaxation strength of the boundary damping was almost precisely a linear function of the Cr content. 4. DISCUSSION

,

I

I

I

I

600

>

700

TEMPERATURE

‘C

FIG. 9. The effect of an isothermal treatment on the boundary peak of a 19.2 % Cr specimen.

!2-

Characteristically magnet~lastic damping effects, previously investigated by e.g. Fishba~h(~5)arise from the stress-induced migration of 90” domain boundaries (since 180’ boundaries suffer no magnetic change due to stress alone, although some will undoubtedly move due to being pinned to 90” boundaries). At low strain amplitudes the damping due to this source can be attributed to the atomic rearrangement involved s,s the walls move under the applied oscillating stress. At intermediate temperatures the magnetostriotive strain associated with domain wall movement could lag behind the stress, giving rise to the observed damping effects. Although the small damping peak obtained see Fig. 10, did show a movement to higher temperature as the frequency increased, it was impossible to measure an activation energy with sufficient accuracy or reproducibility. Further magnetic damping contributions were obtained at lower temperatures, but these were small and did not appear to take the form of well-defined peaks. 4.2 Grain boundary eJfe&

9-

t

I

500 TEMPE~TURE

I

600 “C

FIG. 10. The effect of an axial magnetic field of 100 Oe on the demping of & 12.9 y0 Cr specimen.

Prior to the investigation of the Fe-Cr alloys a sample of pure Fe whose only signifi~nt impurity was O.OO25o/oCr, was tested in order to check existing data on the iron grain boundary peak. An activation energy of 48 kc&/mole (12 kc&) was measured. This, in view of the slight impurity, compared well with previously measured data which gave an energy of 46 kcals/mole. t7) A problem encountered in the pure Fe was the fairly rapid grain growth which took place at the temperature of the peak. This made it impossible to use the s&me specimen more than once. Gradual trends in the grain boundary damping char~c~ristics with increase of Cr content, have been mentioned in the previous section. It ean readily be seen that as the Cr content increases the Fe grain

-1 3

Q

RELAXATION

I/ 560.

8

4

I2

16

I 8

’ 4

20

I 12

t 16

1253

I 20

k.calr.

WC.%

Chromium

Wt.%

Chromium

Il. The effect of composition on T,,,Q, & and ‘I’, for the grain boundary peaks of Fe-Cr alloys up to 20% Cr.

FIG.

boundary

peak rapidly

vanishes,

while the peak due to Cr atoms

the

boundaries

the

matrix

preferentially

diminishes

in size and finally

correspondingly

Figs. 1, 2. Impurity than

BOUNDARY

‘og,&

1

-“t_--_--,

at

-. . I./ .

GRAIN

BARRAND:

relaxing

increases,

see

atoms, whether larger or smaller

atoms,

segregate

can readily to

crystal

be shown

boundaries,

to the

is rather

strikingly

substantiated

Table 2 or the appropriate

by

reference

graph in Fig. 11.

to

It can

be seen that up to 14% Cr there is a linear relation between Ax and Cr concentration. It would seem reasonable the

Cr content

would

that further increases in

either

give

rise

to

higher

degree of segregation depending on the degree of misfit

relaxation

of the solute

saturation behaviour,

maintain the peak damping at a

of two peaks in dilute

high, constant

That this is not the case can be

forward.@)

seen in Table 2. The grain boundary

explanation binary

atoms

in the lattice.@)

for the presence

alloys

has been

put

A plausible When

the

strengths, value.

or,

assuming

number of solute atoms is small there will be a certain

cantly smaller for the 19.2%

proportion

ward trend

of grain

regions which contain

boundaries

or grain

no solute atoms.

dependent on the misorientation

across the boundaries.

Two damping peaks may thus be expected; movement solvent

of grain boundaries

atoms,

(a) due to

requiring

high

movement

explanation

more

of

the peak

associated

with the formation

The act of here will involve diffusion of

concentration

of solute

atoms.

of a An

strength

temperature.

is almost

An of

certainly

of the brittle

at the higher Cr concentrations. information

for the more to a continued

for this sharp change in the process

only, and (b) due to those regions in is large.

of

peak is signifi-

sharply

This is coupled

relaxation

either solute or solvent atoms in an environment relatively

upward

alloys.

increasing

movement

diffusion

is followed

concentrated

form

Cr alloy, and this down-

of

which the degree of misorientation grain boundary

boundary

This will be

some

c phase

Although

detailed

regarding binding energies etc., for this 0

phase, is limited it would seem reasonable to postulate that

the

atomic

bonding

in this

brittle

distorted

increase in the total content of solute atoms can thus be expected to lead to an increasing contribution to

hexagonal compound is significantly stronger than that between the Fe and Cr atoms in normal solid solution.

peak (b) with a decreasing

There would also appear to be some doubt regarding the structure of the Fe-& equilibrium diagram, particularly at higher temperatures. Figure 12 shows a recent attempt by Kubaschewskids) to calculate the

contribution

to peak (a).

Ultimately only peak (b) will be observed. Since each Cr atom in the region of the boundary may, as a simple approximation, be expected to make some contribution to the grain boundary peak, one would expect the relaxation

strength to bear a linear

relation to the total solute atom concentration, assuming complete solid solubility. This hypothesis

various phase boundaries

from thermodynamic

data.

If we take the dotted boundary defining the diagram under conditions of metastable equilibrium, it can be seen that below 20% Cr the (G + a)

ACTA

1254

METALLURGICA,

VOL.

14,

1966

locked in the CTphase.

There would therefore be only

a small grain boundary almost

peak.

inside the uniform

The 43.1%

(T phase region

alloy

would expect only a very small grain boundary Because it is almost entirely tures of measurement the background The

high

for

should also be very low. activation

values for r,,, associated is probably

and

low Cr

The reason for these

similar to the one offered by

Stanley and Wert,(ll) V alloy.

energy

with the 12.9 and 14%

alloys, require more explanation. anomalies

peak.

CJphase at all tempera-

with no phase re-adjustment,

damping

values

is

and one

when investigating

At temperatures

an Fe-18%

below 600°C 7s had a normal

value, but between 600 and 840°C (the Curie temperature) the r,, value was very small (~4 associated,

with

appreciably

higher than that for normal self-diffusion

(as observed

above 850°C and below 600°C).

effect was attributed

FIG.

I

20

40

CHROMIUM

ATOMIC

anomalous

1

60

limits

80

of this

energy.

transition

ture the 19.2%

ordering on the low side.

These temperature

peak tempera-

Cr alloy is in the two phase (a + a)

the

region

examined

of

710°C.

the

Curie

For

for these the

temperatures

temperatures observed

this process could be incomplete

and the diffusion of Ni into a-Fe.04)

by the time the alloy This

Borgo5) anomalous

represented

where the full grain boundary

peak only developed

after holding

the specimen

for several hours. preferentially contribute

at the peak temperature

If one assumes that the G phase is

located

the Cr atoms

at grain boundaries,

are too tightly

to the relaxation

bound

and that

to significantly

in this form, then until

the 0 phase breaks down to u the grain boundary

peak

is going to be very small. The same argument, slightly modified, could be used to explain the curves in Figs. 3 and 4. The 27.55%

Cr

alloy would still almost certainly be in the two phase (G + a) region at temperatures higher than the grain boundary peak temperatures, under the conditions of the experiment. Thus, although the proportion of G phase

would

be

continually

changing

on

heating,

contributing probably to the high observed background in this alloy, there would still be a significant proportion

of

Cr atoms

in the

boundary

temperatures.

in Fig. 9

temperature.

would explain the phenomenon

regions

dilute

are

is in alloys

760-77O”C,

are below the level of the grain boundary

single phase u. Unless the rate of heating is very slow peak

limits

while for the 27.55 and 43.1 o/o Cr alloys the Curie peak

the damping

on spin

alloys

more

Raising the temperature merely alters the region. proportion of o: u until finally the alloy becomes

has attained

the

would fit in well with the 12.9 and 14% Cr specimens

Thus at a tempera-

ture fairly close to the grain boundary

showing

effect, would be the Curie temperature

since the Curie temperature falls below 500°C.

The tempera-

region,

the high side and the point of nearly complete

PERCENT

12. A representation of some Fe-& equilibrium date due to Kubaschewski aud Chart.‘l”)

phase boundary

This

to the influence of ferromagnetic

spin ordering on the activation ture I

10-22) and was

x

energy

at temperatures

an activation

A similar

in self-diffusion has

more

diffusion

effect

has also been

measurements

recently

in a-Fe(13,13)

postulated

coefficients,

that

measured

the

on ferro-

magnetic materials in the region of the Curie temperature, are due to the unusual temperature of elastic properties

in this region,

lated that the Arrhenius sion coefficients

relationship,

and activation

other ferromagnetic

materials

dependence

Borg also posturelating diffu-

energies,

in Fe and

is applicable,

if at all,

only at temperatutes

much higher or lower than the

Curie

These

temperature.

postulates

could

also

partly explain the peculiar effects in the 12.9 and 14% Cr alloys, but there does not appear to be sufficient evidence to substantiate this at the present time. The widths of the observed grain boundary peaks were much greater than would be expected for a unique relaxation process. This must mean that the total damping is made up of a distribution of relaxations each having its own relaxation time and strength. It has been suggested spread of orientation

by Marsh and Ha11(16) that a

changes across the boundaries

in

BARRAND:

any polycrystalline

GRAIN

BOUNDARY

metal would give rise to a distri-

1255

RELAXATION

(where N is the number of grain boundary

intercepts

bution of relaxation

times and broad internal friction

made by a line of length L, 1 is the length of grain

peaks.

of the distribution

boundary

An estimate

t,imes can be obtained and

Berry.(l’)

assumed

this

a Gaussian

in the logarithm

“lognormal” which

In

distribution

A parameter

the width

is

times (a

p is specified

of the distribution,

/3 = 0 signifies a single relaxation. applied

of Nowick

of the relaxation

distribution).

expresses

of relaxation

using the analysis

e.g.

The analysis was

to the results of KB on polycrystalline

Al,(l)

on a random

micro-scetion,

area of the grains on a random grain boundary total volume

e.g. assuming a grain size of 0.06 mm dia. and boundaries made up of a dislocation edge dislocation preferential

segregation

relaxation.

each dislocation

this particular

For a single relaxation

in

case the half peak width should have

been 16”C, instead of which it was 75°C. A

precise

model

for

effects is extremely

grain

difficult to define.

due to the range of structures

relaxation

This is chiefly

and orientation

differ-

require

in grain

only

slight

boundary

14%) Cr. This

modification

structure,

for

numbers

solute atoms per atom plane of each dislocation concentration

boundary

atom per atom plane for

in an alloy containing

would

changes

one

of solute atoms to the boun-

,Q = 3.30 at 280°C for the grain boundary

picture

array containing

per atom plane, only a small degree of

daries gives one chromium

B = 5.75 was obtained.

and V the

of the grains) can be used to show that,

peak, that

the same analysis to the 12.9 alloy a value of

S the total

area (in three dimensions)

and it was found assuming a symmetrical Applying

A the total

section,

solute

of solute atoms in the alloy.

concentration

required

would

depend

principally

The actual

to saturate

of greatest misfit, in a boundary

of and

the sites

of this simple model,

on the lattice

distortion

ences which must have been present, in any specimen,

caused by the solute, and thus the degree of preferen-

at the crystal boundaries

tial

model

due

to

Mott,

investigators,(2-47)

in these experiments.

largely

discounted

has recently received

The

by

boundary

maximum

grain

some support

assuming

complete

from Brandon

et &.(22) as a result of field ion micro-

atomic

scope

of

crystal

boundaries

alloys,

solute

studies

boundaries

atomic

of tungsten

configurations

at

and tungsten-rhenium

several important

relaxation

points.(2-47) can be considered

work of edge dislocations a more

precise

it becomes easier to postulate

quantitative been

to be a net-

model.

This type of observed to move

boundary

has

previously

reversibly,

under the action of an applied

stress, into neighbouring rearrangement having

an

relaxation on

the

could

produce

dislocation

density,

and

either substitutional

effect

of the presence

atomic

relaxation These mainly

therefore

and also the presence

atoms,

A possible

a unique

associated relaxation time. characteristics would depend

misorientation, impurity

oscillating

grains.c23) Associated

the

or absence

of

or interstitial. of substitutional

impurity atoms “inside” the dislocations forming these boundaries could be to a slow down boundary movements,

due to binding

activation

energy

This, coupled

with

for

effects, grain

thus increasing boundary

an increase

the

relaxation.

in relaxation

time,

would give rise to the observed solute grain boundary peak at a higher temperature than the peak due to relaxation of solvent atoms. Relations derived by Smith and Guttman,(24) viz.

peak

solid

solubility,

V

rA

2N

X

41

at

be

different

solutes.

constrained

As the

stress the

to

follow

of relaxation

strength

tration up to a maximum

of 14% Cr (Fig. ll),

atom could be expected,

previously,

to

make

relaxation.

Some

structures

its own

high

linear

on solute conaen-

each chromium

have

the

effects.

This model would also explain the observed dependence

the

occur,

this giving rise to the observed

angle

as pictured

since

as mentioned

contribution boundaries

to may

the well

by Mott,(18) but there

does not seem to be any reason, particularly regions of good fit, why these boundaries

in the

could not

migrate in the manner visualised above and contribute to the observed peaks.

Sliding, as visualised by KG(‘)

is a more limited possibility

and it has been largely

discounted here because it fails to explain most of the observations. Previous

investigator@‘)

have

to the grain size dependence

drawn

attent.ion

of -rO. This was specifi-

cally checked in this series of experiments

only for the

14%

findings

Cr alloy.

Results

confirmed

the

of

Leak(‘) that the relaxation time was given by an expression frequency (grain size)2 exp (QIRT), although this was not a precise identity. It appears from these experiments that the grain size dependence of 70 may be merely an incidental

L

to

under an oscillating

would

network

expect

height

for different

migrated

atoms

dislocation

One would

boundary

concentrations

while KB’s model has also been found to fall down on If a grain boundary

segregation.

other

characteristic,

the more

important property being that changes in TV, apart from electronic contributions, may give a sensitive

ACTA

1256

indication

of

overall

changes

structure

as the grain

therefore

that

of

METALLURGICA,

grain

size increases.

investigation

boundary

It could

of the precise

be

way

in

which T,, changes as a function of grain growth, or as a function of misorientation

for the case e.g. of bicrystals

may give more detailed

information

of the structure

of crystal boundaries. What is obviously model

is

more

needed to fully substantiate

data

on

different

alloy

this

systems,

using internal friction techniques, and more correlation of results using these methods radio-tracer

with results using e.g.

and micro-probe

4.3 Substitutional

analysis techniques.

relax&ions

For the alloys less than 27.55%

Cr no effect was

observed which could be attributed relaxation.

to a substitutional

size and

characteristics

atoms.

As Seraphim

of the

et al. have

problem of detection crystalline specimens

Fe and

pointed

of Zener-type is particularly

relaxation provides a high background

against

a small Zener peak may be lost.

which

seem likely

grain boundary

that the positions

of Zener

relaxation content

showed

the heat of activation

particularly

that

and it is

the lower

ones are due to stressThe solute redistribution.

substitutional

picture is somewhat

complicated

by the presence of o

phase in these alloys, and it is probable that the lower peak in Fig. 4 is due to solute re-distribution phase itself.

in the o

These peaks did show a frequency

shift

and the activation energy in the case of the 27.55% Cr alloy was approximately 57 kcals, although it was not possible accuracy.

to

measure

figure

with

very

great

In order to establish the characteristics

substitutional advantage

this

relaxations

it would

to work on specimens

of

be an obvious

of single crystal

or

very large grained material. 5.

The characteristics a

number

of Fe-Cr

SUMMARY

of grain boundary alloys

have

been

relaxations

Cr, while

the peak

The 12.9 and 14%

the

Cr alloys

values for T,, and the activation in terms of ferromagnetic

damping effects were briefly investi-

and commented

on.

A model

relaxation

is described

boundary

migration

rather

appearance

of possible

for the grain

in terms

than

substitional

in the more concentrated

sliding,

of grain and

relaxation

the

peaks

alloys are indicated.

ACKNOWLEDGMENTS

I would provision Leak

for

stimulating

like to thank of laboratory his interest

Professor

facilities, in the

C. R. Tottle

for

and also Dr. G. M.

work

and

for

many

discussions. REFERENCES

in

established.

T. S. K$, Phys. Rev. 71, 533 (1947). and S. PEARSON, Trans. Am. Inst. Min. metaE2. Engm 206, 881 (1956). L. ROTHERRAM and S. PEARSON, ibid. 206,894 (1956). G. W. MILES and G. M. LEAK, Proc. phys. Sot. Lond. 78, 1592 (1961). P. FELTHAM, Acta Met. 5, 97 (1957). K. BUNGARDT and H. PREISENDANZ, Arch. Eisenhiittwes. 27, 715 (1956). G. M. LEAK, Proc. phys. Sot. Lond. 78, 1520 (1961). D. MCLEAN, Qrain boundaries in Metals. Oxford (1957). G. M. LEAK, Prog. appl. Mater. Res. No. 4 (1963). 0. KUBASCKEWSKI and T. G. CHART, J. Inst. Metals 93, 329 (1965). J. STANLEY and C. WERT, J. appl. Phys. 32, 267 (1961). R.J. BORG~~~C.E.BIRCHENALL, Trans. Am.Inst. Min. met&Z. Engrs 218, 980 (1960). F. S. BUFBINGTON, K. HIRANO end M. COHEN, Acta Met. 9, 434 (1961). K.HIRANO,M.COHEN and B. L.AVERBACH, ibid.9,440 (1961). R. J. BORG, J. appl. Phys. 35, 567 (1964). D. R. MARSH and L. D. HALL, Trans. Am. Inst. Min. metall. Engrs 197,937(1953). A. 8. NOWICK and B. S. BERRY. I.B.M. J. Res. Dew 5. No. 4, 297 (1961). N. F. MOTT, Proc. phye. Sot. Lond. 60, 391 (1948). T. S. K$, J. appl. Phys, 20, 274 (1949). D. P.SERAPHIM,A.S.N~WICK~~~B.S.BERRY, ActaMet. 12, 891 (1964). C. WERT and J. MARX, ‘bid. 1, 113 (1953). M. 8. PH,S. RAKGANATHAN~~~ D. G. BRANDON,B.RA WALD, ibid. 12, 813 (19 4). J. WASHBURN~~~E.R.PARKER, J.MetaZs.4,1076( 1952). C. S. SMITH and L. GUT h MAN, ibid. 5, 81 (1953). D. FISHBACH, Acta Met. 10,319 (1962).

;: L. ROTHERHAM

Cr alloy in

peaks have already relaxations,

14%

to increase throughout

boundary

of a relaxation

clear for the 43.1%

been assigned to grain boundary postulated induced

anomalous

Magnetoelastic gated

this.

The higher temperature

of

spin ordering effects.

Both of the curves in Figs. 3 and 4 show two small Fig. 4.

alloys

also tended

energy, this being explained

at which the maximum

occurs, substantiates

The

It

scale. Reference to a work and Marx,(22) on the linear relation which

process and the temperature

of Cr atoms.

showed a linear increase with Cr

range of alloys tested.

peaks in some Fe-Cr alloys, are very

exists between

peaks,

up to

temperature

in the more dilute alloys,

to the relaxation

strength

and

close on a temperature

relaxation

one attributable

out’21) the

effects in polyacute since the

1966

T wo peaks were observed

Cr

grain boundary

by Wert

14,

The main reason for this may lie in the

similar

would

VOL.

9.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.