Microstrain and dislocation relaxations in BCC metals

Scripta METALLURGICA

Vol. 5, pp. 875-882, 1971 Printed in the United States

MICROSTRAIN

AND DISLOCATION Alfred

Max-Planck-Institut

Pergamon

RELAXATIONS

Press,

Inc

IN BCC METALS*

Seeger

fGr Metallforschung, Stuttgart, Germany

Institut

fGr Physik,

and Bohdan ~est~k V

Institute

of Physics,

Czechoslovak

Academy

of Sciences,

*(Revised received July 16, 1971; this supersedes manuscript, Scripta Met. ~, 681, 1971)

I. In a recent that the special be reflected

nature of <111>

He attributes,

in the notation

corresponding

process

process

(5-8)

of Chambers

use of the work of Chambers starting

rather different our views

conclusions.

This prompts

remain

to be clarified

2. There

Escaig

to the

(1) bases his results

(9). Our own considerations

and his associates us to present

energy barrier the motion

evidence

<111> screw dislocations

the macroscopic

yield point [see, e.g.,

(2-4,7,10)

as Escaig a brief

(11-15)].

summary of

valley

much larger than those in f.c.c, in silicon and germanium dislocations,

i.e.,

metals are sessile

to the need to overcome requires

the transitions

core" model

(12,16-20)

and comparable

barrier

between dislocation

as the that is

with those encountered

of this large

"Peierls

metals we may expect kinks

875

and that

locally the change from the

it may be described

metals

of lowest

the associated

to the "extended

to the next over a Peierls

in b.c.c,

We hope to

that in their configuration

(21). As a consequence

of screw dislocations

experiments.

and

Predictions

According

configuration;

from one Peierls

and

(I), to

later.

in b.c.c,

is related

of such screw dislocations

to a glissile

by further

presentation

Theoretical

is now overwhelming

free energy

rier"

should

in spite of the fact that they are to some extent tentative

that several points

sessile

metals

in these metals.

and the B-peaks

from the same point of departure

be able to give a more complete

movement

processes

(2-4), the a-peak to the double-

of Rieu and de Fouquet

come,

to the fact

in b.c.c,

friction

in edge dislocations

make extensive although

previous

called attention

screw dislocations internal

in screw dislocations.

on the measurements

CSSR.

Introduction

(I) has rightly

in the Bordoni-type

kink relaxation mainly

note Escaig

Prague,

segments

bar-

in these in neigh-

876

RELAXATION

bouring potential

valleys,

tude of a few lattice

(i) Formation

to have rather

Vol.

small widths

of the order of magni-

about

the general

properties

of kinks

of pairs of kinks of opposite

signs

(double kink formation)

should be similar to the corresponding

f.c.c,

to the Bordoni

metals

energies. volume

leading

metals)

at higher

The activation

volume

(ii) On account

relaxation,

temperatures

but should occur

the kinks

"kink potential" The overcoming

at low but presumably

[For the analogous

process

(iii) kink

71°-dislocations,

<111>-directions

(Bordoni-type)

3.

Chambers those listed

between

(4,25)

but also in microstrain obtained

experiments.

tion enthalpies

H Chambers

range

4. We identify, [process

Chambers

dislocation

such as

friction

the results

processes

activain the

and that the same

found no correlation data.

He demonstrated

flow-stress

is associated

motion").

Interpretation

on the basis of a comparison

IV with the formation

effects

of the measured

are identical,

metals.

Experiments

internal

that the dislocation

for the macroscopic

("unrestricted

in f.c.c,

I and II summarize

peaks and the micro-strain

responsible

with the y-relaxation

and range

Tables

IV and the y-relaxation.

the B-relaxation

that the process

relaxation

not only through

II and in the a-relaxation

is true for range

processes

and Microstrain

From a comparison

concluded

(24).

should occur at temperatures

that dislocation

by his group and others.

temperature between

This relaxation

2 may be studied

volume

stress-independent

lying along the other close-

Internal Friction

recognized

in Sect.

tempera-

should also give rise to a double-

with those of the corresponding

Comparison

should

should give

see (8).] The activation

i.e., dislocations

(5).

if they

still accessible

b 3 and virtually

on (l~O)-planes,

relaxation.

that are comparable

of these barriers

in silicon

v should be of the order of magnitude packed

larger than one atomic

in screw dislocations

rise to a relaxation tureS.

(for other-

with period b (8,21-23)

move along the dislocations. process

in

101.b 3 to 102.b 3) and stress dependent

of their narrowness

an appreciable

processes

and with higher activation

should be distinctly

(of the order of magnitude

experience

(22) we can

predictions:

in screw dislocations wise comparable

S, No. i0

parameters.

From our knowledge make the following

IN BCC METALS

of double kinks

of Sect.

2 and 3, the y-peaks

in <111> screw dislocations

(i)], and the o-peak and range II with the motion of kinks in these

screw dislocations the magnitudes

[process

(ii)]. These assignments

of the activation

was already recognized

volumes.

by Chambers

are strongly

(The essence

and his associates,

aware of the special r61e of the screw dislocations

supported

by

of this last argument but since they were not

in b.c.c,

metals

they had

Vol.

5, No. i0

RELAXATION

IN BCC METALS

877

TABLE I Summary of Results from Microstrain Experiments

(including dependence

of micro flow stress a on temperature T and impurities for constant dislocation

strain Cd' activation volumes v, and activation enthalpies

H)

I

II

Ill

IV

Temperature range [o K]

< 5

lO-25(Fe,Mo)

30-80 (Fe ,Mo)

100-300 (Fe ,Nb ,Ta)

lO-50(Nb,Ta,W)

50-lO0(Nb,Ta,W)

lO0-500(Mo,W)

d~ ICd:const.

for T÷O

÷ 0

v [b 3 ]

large, T-independent

smaller, T-dependent

.1

H [eV]

impurity effects

~0

smal i, T-dep. weak ~50

O.l-O.15(Fe,Mo)

0.7 (Fe,Nb)

0.25-0.30(Nb, Ta,W)

1.2 (Mo,Ta) 1.6 (W)

~0

increase

increase

on

on do/dT

~0

~0

Table II Summary of Results from Internal Friction Experiments times T = T o exp(H/kT)

Metal Fe

H e [eV]

To, a [s]

Hy1 [eV]

Hy2 [eV]

To, Y [s]

~10-12.8

0.75 0.?

0.85 0.8

10-11.8

0.07

Nb

0.25

(relaxation

for a- and y-peaks)

Ta

0.15 0.18

O.95 1.2

1.15

Mo W

0.27

1.5

1.7

878

RELAXATION IN BCC METALS

difficulties energies

in arriving

for the peaks

times,

cannot endorse Escaig's (better:

dislocations;

which disregard

strain release

as for the s-process

on the motion of kinks which are compatible

tions

the microstrain

view of the crudeness

5.

of Chambers

[e.g., the differences

with the s-peak.

Our interpreta-

in Fig.

2.

Issues

is capable

et al.

(3,4),

of accounting and f.c.c,

of the high barrier

motion of the screw dislocations].

discussed,

namely

(a) the effects

hydrogen)

effects

are immobile.

virtually

including details

metals

activated

range

for screw dislocation

of impurities

and

lyhood for impurity same impurity recognition be helpful

effects.

as listed in Table

movement

(b) the dislocation

I are easily accounted exception

sites for the movement

with the double

of hydrogen.

While they are not yet understood

therefore

for: of of the

The like-

is much lar-

in detail

the

(31), the

process

should

influences.

Recently Mazzolai,

Nuovo,

in Nb, Ta and V the s-peak may be enhanced interpret

rela-

flow show essentially

that one is dealing with one and the same atomistic

In most of the earlier work insufficient effects

kink generation

and the onset of macroscopic

these

and the

Two points remain to be

(with the possible

The number of activation

in unravelling

here

(7), in which

dislocations.

II the impurities

interference

(22). The y-process

completely

not discussed

metals

kinks is so large that only rarely will an impurity atom interfere. ger

of these

region.

thermally

(a) The impurity

the results

in

in the micro-strain

there is no analogy

In the temperature

However,

curve is illustrated

between b.c.c,

with non-screw

Hartmann

the height of

our assignment.

Critical

interpretation

(27)

of kinks along screw disloca-

objection against

i shows the C-Ed-curve

of Gehlen

By contrast,

(29) estimated

of their models we do not consider

tion of the micro stress-strain

xation associated

volume

in s-iron yield results

interpretation.

and Schellenberger

for the movement

a serious

for the results

~ ,

in

[For the B-relaxa-

(26). The recent model computations

with the present

barriers

The present

data.

We

in the special case of Fe, with

in s-iron to be too small to be associated

Fig.

kink generation

gave about the same activation

in screw dislocations

(28) and Heinrich

calculations

fac-

with this interpretatior,

[s-peak = double kink generation

experiments

i0

The ratio of the activation of the preexponential

B-peak = double

of the s-peak agrees,

that of Takita and Sakamoto

the potential

S, No.

(4)].

Our interpretation

and Pegel

To, are compatible

(I) assignments

non-screw)

screw dislocations], tion process

picture.)

(Hs/H Y) and the magnitudes

tors of the relaxation edge

at a consistent

Vol.

attention

was paid to possible

and Cannelli

(32,35)

found that

by charging with hydrogen,

this peak as the socalled

cold-work

and they

peak associated

With

Vol.

5, No. i0

RELAXATION

IN BCC METALS

879

~2OK l~Ox I0-'; G

f

Io 120

,j

i

Z I

/

~ tO0

~ 8O E

I

~1/ I

60

280°K

I

/

I

L,O

processi:~o~---°

20 I

I

i

2

3

~xlO~--~ dislocat~n stroin~ d

FIG. 1

(top)

Micro stress-strain curves [semiquantitatively for W after (7,30)] with ranges I-IV indicated qualitatively. FIG.

2

(right)

The sequence of processes in the micro stressstrain curve o-c~ of b.c.c, metal crystals, illustrated for ~ dislocation segment of arbitrary orientation. I: Movement of non-screw dislocations, formation of (immobile) geometrical kinks in screw dislocations. II: Movement of kinks along screw dislocations. III: Further bending out of non-screw dislocations. IV: Nucleation of double kinks in screw dislocations, macroscopic yielding at o = Oy. (The sessile screw parts are indicated as bold lines.)

i

880

RELAXATION

hydrogen. ture,

Against

IN BCC METALS

this interpretation,

quite a number of objections

the specimens impurities.

of Weft,

gen high-temperature

annealing

charging

of niobium with hydrogen of hydride deformation.

an increase

sity. The observed increasing

In this

cracks

and the resulting

In Nb Weft et al. hydrogen,

(e.g., a-Fe)

ported by the order of magnitude that in Fe the hydrogen internal

cold-work

friction data collected

work peak in iron

after-effect

found evidence dislocations

for processes

[process

metals

and is explained (e.g.,

are more effective.

Nevertheless,

relaxation

The activation

and effects

energies

of inter-

[In metals not ca-

of molecular

hydrogen

that peak

peak occurs

the presence

volume

is sup-

(4) and by the fact By combining

(37) and Sturges and Miodownik (39) we deduce

metals

by the Peierls barriers

of non-screw

to the situation

by the notion that other flow-stress

involving dislocation

interactions

metals,

con-

or impurities)

the corresponding

in internal

friction

experiments.

[Nb: H B ~ 0.47 eV, ~o ~ 10-12"5

appear to be too large for such a process

(38)

for the cold-

one has sofar not

2]. This is analogous

for the B-peak

the

s.

of b.c.c,

as in f.c.c,

of

(which may have sub-

Such an assignment

in the B-range.

measurements

should be observable

in

may play a similar rSle.]

of the activation

controlled

with

width of the peak may be

are high.

the formation

by Gibala

acts indirectly

to higher temperatures

interactions

densities

interaction.

behaviour

trolling mechanisms Bordoni-type

the hydrbgen

temperature

to ascribe

(iii) of Sect.

is caused by

and hence also of the kink den-

H = 0.26 eV and T o = 10 -12"6

(b) In the micro-strain

in f.c.c,

density

deformation

to a hydrogen-dislocation

with recent magnetic

(36) suggests

(35) find that the B-peak does require

so that it is tempting

structure)

of high-temperature

and Weft

as well as the excessive

plastic

with

hydro-

during cooling and the accompagnying

interpretation

when the local dislocation

pable of forming hydrides

is compatible

the a-peak but gives rise to the

as being due to strong kink-kink

nal stresses

impuri-

by these other

of the a-peak by hydrogen

shift of the a-peak content

out that

(35) that in Nb containing

by Buck, Thompson

precipitates

with our pic-

also many other

study of the effect

of the dislocation

hydrogen

interpreted

detailed

that the enhancement

the formation through

and Buck

suppresses

Snoek peak. A recent

local plastic

contained

5, No. I0

(34) points

that the Rome interpretation

Thompson,

hydrogen

strongly

(32,33)

Schultz

effects may have been influenced

It is not obvious

the observation

rather

wb~ich is not in agreement

may be raised.

used by the Rome group

ties and that the observed

Vol.

[see also the remarks

s]

in the pre-

ceding paragraph]. A much better dislocations

candidate

[relaxation

for the double-kink

process

(iii)]

formation

is the socalled

in non-screw

6-peak

eV; Ta: H~ = 0.02 eV; V: H 6 = O.O12 eV; To, 6 ~ 10 -8.7 s (32,33)], tion of which had already been seen by Chambers

(71 °-)

[Nb: H 6 = 0.02 an indica-

(3) and named m'. The measured

Vol. 5, No. I0

RELAXATION

IN BCC METALS

881

frequency factor appears compatible with a Bordoni-type relaxation;

the fact

that it would be quite incompatible with the relaxation process due to kink movement supports indirectly the assignment of the a-peak to that process. The considerable

excess width of the 6-peak and the observation that hydrogen may

suppress it (presumably by dislocation pinning) a Bordoni-type relaxation,

supports its interpretation as

as already pointed out by Cannelli and Mazzolai

(33)

Acknowled@ements The authors are grateful to Dr. H. Schultz for several helpful suggestions To him as well as other members of the Stuttgart Institute thanks are due for critical discussions. References (1)

B.Escaig, Scripta Met. 5, 199 (1971)

(2) (3)

R.H.Chambers and J.Schultz, Acta Met. R.H.Chambers, Dislocation Relaxations Transition Metals, Physical Acoustics, (W.P.Mason, ed.), Academic Press, New

(4)

R.H.Chambers, T.E.Firle, T.Trozera, and G. Buzzelli, A Program of Basic Research on Mechanical Properties of Reactor Materials, Final Summary Report, General Dynamics, General Atomic Division GA-7978, San Diego (1967) A.Seeger, Phil.Nag. I, 651 (1956) A.Seeger, H.Donth, and F.Pfaff, Disc. Faraday Soc. 23, 19 (1957) G.Alefeld, Der EinfluB des Gitters auf kurzreichweitige Versetzungsbewegungen, Kernforschungsanlage, Jfllich, JH1-558-FN (1968)

(5) (6) (7) (8) (9)

10, 466 (1962) in Body-Centered Cubic Vol. III A, Chapt. 4 York and London (1966)

A.Seeger, J. Physique 32, C-2, 201 (1971) G.Rieu and J.de Fouquet, J.Physique, in the press

(10)

G.Alefeld, J.Filloux, and H.Harper, Dislocation Dynamics et al., ads.) p.191, McGraw Hill, New York etc. (1968)

(11) (12)

F.Kroupa and V.Vitek, Can. J.Phys. 45, 945 (1967) M.S.Duesbery and P.B.Hirsch, Dislocation Dynamics eds.) P.57, McGraw Hill, New York etc. (1968)

(13)

H.D.Solomon and C.J.McMahon, Jr., Work Hardening ads.) p.311, Gordon and Breach (1968)

(14)

B.~est~k and A.Seeger, 1970 (in press)

(15

H.D.Solomon and C.J.McMahon, Jr., Acta Met. 19, 291 (1971)

(16

H.Suzuki, Dislocation Dynamics (A.R.Rosenfield et al., eds.) p.551, McGraw Hill, New York etc. (1968)

(17

J.Friedel, Comments on Solid State Physics 1, 24 (1968)

(18 (19 (20

B.Escaig, phys.stat.sol. 28, 463 (1968) R.Heinrich, W.Schellenberger, and B.Pegel, phys.stat.sol.39,493 (1970) G.Diener, R.Heinrich, and W. Schellenberger, phys.stat.sol.(b) 44, 403 (1971) R.Labusch, phys.stat.sol, iO, 645 (1965)

(21

(A.R.Rosenfield

(A.R.Rosenfield et al., (H.P.Hirth, J.Weertman,

Internat.Conf. Sci.Technol. Iron and Steel, Tokyo

882 (22) (23) (23 (25) (26) (27) (28)

(29) (30) (31) (32) (33) (34) (35) (36) (37) (58) (39)

RELAXATION IN BCC METALS

V01. 5, No. i0

A.Seeger and P.Schiller, Kinks in Dislocation Lines and Their Effects on the Internal Friction in Crystals, Physical Acoustics, Vol. III A, Chapt.8 (W.P.Mason, ed.), Academic Press, New York and London (1966) G.Schottky, phys.stat.sol. 5, 697 (1964) U.Kammerer, Diplomarbeit T.H. Stuttgart (1965) R.Chambers, Nato Support Evaluation Conference in High Temperature Materials, Sandefjord, Norway, 1967 K.Takita and K.Sakamoto, Scripta Met. 4, 403 (1970) O.Hartmann and B.Pegel, phys.stat.sol. 42, 315 (1970) P.C.Gehlen, Battelle Colloquium on Interatomic Potentials and Simulation of Lattice Defects, Seattle and Harrison Hot Springs 1971, Plenum Press, to be published R.Heinrich and W.Schellenberger, phys.stat.sol. 42, K127 (1970) R.H.Chambers, T.E.Firle, J.H.Filloux, and H.T.Harper, Intrinsic Versus Impurity Barriers to Dislocation Motion in BCC Transition Metals Below 0.2 Tm, General Dynamics, Generel Atomic Division Report GA-7946 (~967) W.Frank and B.~est~k, Scripta Met. 4, 451 (1970) F.M.Mazzolai and M.Nuovo, Sol. State Comm. 7, 103 (1969) G.Cannelli and F.M.Mazzolai, J.Phys.Chem. Solids 31, 1913 (1970) H.Sehultz, private communication C.A.Wert, D.O.Thompson, and O.Buck, J.Phys.Chem. Solids 31, 1793 (1970) O.Buck, D.O.Thompson, and C.A.Wert, J.Phys.Chem. Solids, in press R.Gibala, Trans.Met.Soc. AIME 239, 1574 (1967) C.M.Sturges and A.P,Miodownik, Acta Met. 17, 1197 (1969) H.KronmUller and R.Martinez-Garcia, unpublished results