On the yield point of body-centered-cubic metals

LETTERS

are observed.

In regions of the crystal which are free

from plastic deformation, and collapse

the excess vacancies

to form dislocation

class of materials homogeneous vacancy

TO

loops.

cluster

The second

is similar to the first except

nucleation

of

dislocation

that

loops

from

clusters does not occur rapidly at room tem-

perature after quenching.

Hence dislocation

loops are

only observed in regions where dislocations have moved during quenching.

This may account for the structure

of quenched Cu and Ni where micrographs loops associated with dislocation

nucleation.

However

dislocations

seems to be difficult,

cancies

loop

in the latter case, cross-slip of perhaps because of

solute pinning, and hence the distribution

typefied

of loops is

on definite slip planes than in Cu

by concentrated by dislocations

1121

5. K. H. WESTMACOTT, R. S. BARNES, D. HULL and R. E. SMALLMAN, Phil. Mug. 6, 929 (1961). 6. J. TAKAMURA and J. GREENFIELD, J. Appl. Phys. 33, 241 (1962). 7. R.E.SMALLMAN,K.H.WESTMACOTT~~~J.A.COILEY, J. Inst. Met. 88, 127 (1959-60). 8. S. MADER, A. SEECER and E. SIMSCH, Z. Metallk. 52, 7% (1961). 9. J. TAKAMURA, Acta Met. 9, 54’7 (1961). 10. A. H. COTTRELL, Creep an/l Bructure of Metals at High Tempwatures p. 141, H.M.S.O. (1954). * KerttiredApril 28. 1962.

only show

t’he structure of some quenched dilute Al alloys where

and Ni (e.g. Fig. 3(b)).

EDITOR

tangles, and also for

the solute atoms appear to hinder homogeneous

more concentrated

THE

On the yield point of body-centered-cubic metals * It is well known that b.c.c. metals will, in general, exhibit

the phenomenon

consequent

upper

of abrupt

yielding,

and lower yield

point,

with a

and that

In the final class of alloys,

there is a temperature below which yield strength rises

Al alloys, absorption

sharply

of va-

occurs but the redistribution

process appears bo be prevented.

Hence the frictional

as temperature

is decreased.

planations

for these phenomena

literature,

e.g. Refs.,+@

ex-

but it can hardly be stated

force caused by the absorbed vacancies soon stops the

that

dislocation

theories can be divided into two main classifications,

moving

and more

dislocations

generated to relieve the applied stress. vacancies

distribute

themselves

must

be

The absorbed

evenly along the dis-

location to form a helix and hence the microstructure consists of a high density ( 10s-lO1o lines/cm2) of helical dislocations

unanimity

Numerous

have appeared in the

of thought

exists.

Basically,

depending on whether static or dynamic effects control yielding.

The purpose of this letter is to present evi-

dence in support of the dynamic

viewpoint.

If the same mechanism is responsible for yielding in all b.c.c. metals, it should be possible,

and very few prismatic loops.

In this summary we have only considered the micro-

the

by the use of

suitable parameters such as elastic modulus and melt-

Slower quenching rates or ageing after quenching must clearly

ing temperature,

alter t)he structure

plotted the ratio of yield strength to elastic modulus

structure

of

nucleation materials

quenched

e.g. it may

of dislocation discussed

deformation hitherto

rapidly

periments

We believe

quenching

unrecognised

structure of quenched

cause homogeneous

loops in the second class of

above.

during

materials.

parameter

that plastic

is an important, affecting

metals and alloys.

the microFurther ex-

are being carried out to test the validity

the general ideas expressed

above

of

and to ascertain

the precise nature of the vacancy absorption tribution

and

and redis-

to plot the observed yield strengths

curve.

to Professor A. H. Cottrell, F.R.S.,

Wessel, and France@)

for W, Cr, MO, Ta, Nb, and V,

but found a separate curve for each metal.

However,

all the group V-a metals had similar slopes, as did the VI-a metals.

Although

the grain size was not consid-

ered in their curves, the yield strength of b.c.c. metals is related to d?,

where d is the grain diameter, through

the well known Petch equation.(2>10) Utilizing plots of yield strength vs. d-$, along with some yield strength data, the present author selected a

grain size that was within the range of the available results, i.e. ~1300

for helpful discussions.

Bechtold,

as a function of TIT,

vs. temperature

process on dislocations.

We are grateful

on a common

grains/mm2

to find parameters

(d-h = 6 mm-i),

J. D. EMBURY

attempted

Department of Metallurgy

C. M. SARGENT

strengths for this grain size could be plotted

University of Cambridge

R. B. NICHOLSON

curve.

References 1. D. KUHLMANN-WILSDORF, Phil. Nag. 3, 126 (1958). 2. For review see A. KELLY end R. B. NICHOLSON, Progress in Mate&&- Science Vol. 10, Pergamon Press, Oxford (1962). 3. H. G. F. WILSDORF and D. KUHLMANN-WILSDORF, J. Appl. Phys. 31, 516 (1960). 4. G.THoMAs~~~M.J.WHELAN, Phil. Mag.4,511( 1959).

on one

Strain rate is another variable that is known to

affect yield strength;

England

and

such that all the yield

at comparable magnitude.

however, all data were obtained

strain rates. i.e. within

an order of

It has been suggested that dislocation velocity is an important factor in the yield phenomenon.(6-8~11~12) There are no data for dislocation metals considered

here;

however,

velocities

in the

it can be assumed

1122

ACTA

METALLURGICA,

VOL.

10,

1962

that some of the factors that control dislocation veloc-

yield strength

ity are the same as the factors that control the pro-

creased.

pagation

or yield strength when a yield point was not, observed.

of elastic

which represents

waves.

For this reason

a longitudinal

(E/p)*,

wave velocity.

was

rapidly

selected as a parameter

that might correlate all the

data.

modulus and p is the density

so that,

$!P,

E

ii,P, gs =const. -T

Figure 1 shows the ratio of yield stress to (~~~)~ REF

&SEC-'

I3 7 I5 16 17 18 $9 20 21 22,23

2B.10‘~ 6 95x10-3 33x10-4 2 6.10“ 7 2erto-4 3.3x10-3 2.6xio-* 15x10-3 ,x!O-~

.

In obtaining data from a large number of sources, it is

14 088rlo-4

ONb Nb

0 Fe

only natural to find some disagreement, and one does not. A

completely

satisfactory

interpretation

the dislocations

released at yielding

some fraction of the velocity the

limiting

2

of the lattice.(l)

velocity.

Another

FIG, 1. Ratio of yield strength to (E/p)‘12 as a function of homologous temperature.

plotted as a function

of the homologous temperature, TIT,, for Nb (1394) Fe,'?' W,'15,1"' Ta,(ll) ~o,U8-Z0, V,@n and 0.11 C stee1.(22,B) Tensile data are not available for Cr with a grain size comparable

to that con-

sidered here. The metals were all of fairly high purity

creased sharply as temperature

possible

in the form of elastic with the scatter-

Metals of high (~~p)~ can be expected

to dissipate the energy of a moving ,v

condition. yield

at

ing of sound waves, caused by the natural vibrations

,033

in which

are moving

is that it is related to the energy dissi-

waves, or to the damping associated

to the region

the

Since

of sound, it may simply

pated by the moving dislocations

confined

of

quantity (E/~ip)~in (1) has not been made as yet.

explanation

and were in the recrystallized

as for example,

with tungsten, where one set of data falls on the curve

represent

v

de-

well by a straight line with a slope of ---1,

of t,he metal.

IO5

as temperature

As may be seen in Fig. 1, the data are represented reasonably

Here, E is Young’s

increased

Values of G, represent the lower yield point,

readily,

so that higher applied

quired

to keep the dislocation

decreased.

more

moving

at constant

velocity. The observation lates the available annealed,

b.e.c.

that the parameter yield

data

(E/P)~ corre-

for relatively

metals lends strong support

idea that yielding

pure, to the

in these metals is related to dis-

location velocity. The author is indebted

to Dr. J. L. Lytton

many helpful and stimulating

for his

discussions.

Data were strength

dislocation

stresses would be re-

M.I.

in-

JACOBSON

A log-log

plot was chosen because it was felt that this depicted most fairly the sea&r

at low values of ~~/(E~p)~. The

values used for E, p and T,

are shown in the table

below :

_-E

Material

T m, “K

dyn/cm2 x lo-l2

P g/cm3

Nb FO MO Ta

2740 1800 2880 3270 3680 2170 1765

1.03 2.06 3.30 1.86 4.08 1.2S 2.11

8.57 7.87 10.2 16.6 19.3 6.10 7.87

7 0.11 c steel

-.

The modulus, E, and density, p, were assumed not to vary with temperature, since the temperature intervals were relatively short, namely, the int,erval in which the

References 1. A. H. COTTRELL, Dislocations and Elmtic Flow in Crystnb Clarendon Press, Oxford (1953). 2. A. H. COTTRELL, Trccns.Amer. Inst. Min,. (Netall.) Engrs. 212 192 (19581. Twns. Amer. Inst. Xrlin. (X&U.) Engrs. 3. E. T. W&EL: 209, 930 (1957). and N. J. PETCH, A&t Met. 3. 186 (19561. 4. A. CRACKNELL ,- G. SCIIOECK and A. SEEQER,Acta &let. 7, 469; (195$). ’ ;: H. CONRAD, d. Iron S’f. Inst. 198, 364 (1961). H. CONRAD and G. SCHOECK, Acta Met. 8, 791 (1960). (Metall.) Engrs. :: A. N. HOLDEN, Truns. Amer. Inst. Min. 192, 182 (1952). 9. J. El. BETCHTOLD, ET. WESSEL, and L. 1,. FRANCE, Re,fractoq Metals and Alloys (Ed. by M. SEMCHYSEN and J. J. WAR~~OOD). p. 25. Interscience, New York (1961). 10. 1\;.J. PETCH, Progress in Metal Physics (Ed. by B. Cu&MERS). Vol. 4, p. 1. Pergamon Press, London (1953). J. A&. Phys. 30, 129 Il. TN. G. JOHNSTON and J. J. GILMAX, (1959).

LETTERS

TO

12. D. F. STEIN and J. R. Low, Jr., J. Appl. Phys. 31, 362 (1960). 13. M. A. ADAMS, A. C. ROBERTS, and R. E. SMALLM.AN,Acta ii: 16. 17.

ii: 20. 21. 22. 23.

.Met. 8, 328 (1960). A. A. JOHNSON, Acta Met. 8, 737 (1960). J. W. Pua~, Pmt. Amer. Sot. Testing Materials 57, 906 (1957). J. H. BECHTOI.D and P. W. SHEWXON, Trans. Amer. Sot. Metals 46, 397 (1954). W. S. OWEN, etal,Sub&u&we. and Mechanicat Properties of Refractory Metals Manufacturing Laboratories Prog. Rep. No. 3, Nov. 15, 1961. AF 33(616)-6838. A. WRONSKI and A. A. JOHNSON, Phil. Mag. 7,213 (1962). J. W. PUGH, Trans. Amer. Sot. Metals 47, 984 (1955). J. H. BECHTOLD, Trans. Amer. Inst. Min. (M&U.) Engrs. 19'9, 1469 (1953). J. W. PUGH, Trans. Amer. In.&. .I@&. (Metall.) Engrs. 209, 1244 (1957). J. HESLOP and N. 5. PETCH, Phil. Xag. I, 866 (1956). N. J. PETCH, Phil. Mug. 3, 1089 (1958).

* Raceivcd

April 11, 1962;

revised June 7, 1962.

THE

1123

EDITOR

much higher, the valence bonding should be considered basically

ionic.

Table

1 shows that the ionic

radii

sums agree with the observed

distance

not in TiN.

has the ionic size of

Oxygen

therefore

in TiO but

1.40 A (or 1.33 A) in TiO, and herein lies a possible explanation

of the reporG3) that,

whereas TiO dis-

solves 60 mol. oA TiN, TiN takes very little oxygen into solid solution, which is unexpected

since the unit

cell edges of TiO and TiN are the same to within 14 per cent.

Nitrogen

can dissolve

in TiO either

with the size of anion or with the size of a covalent atom without restriction,

but oxygen

in the interstitial compound

cannot dissolve

TiN as a covalent-me~llic

atom (r = 0.74 A) because of its demand to become an ion and adopt its ionic size (r = 1.40 A) in Ti, consistent with

the electronegativity

difference

and

ionicity

of TiO.

Comments

on “Evidence of metallic bonding in TiN”*

TABLE

The experimental results of Philipp(l) indicating metallic bonding in TIN are entirely in agreement with expectations

from consideration

of structural

chem-

1.

Compound

Observed interatomic distance in ip

Calculated ionic interatomic distance in A

TiO TiN

2.090 2.123

2.08 2.39

istry. Atoms definite

in the solid state behave as if they have a size ; two scales of atomic

recognized suitably

as

an

corrected

empirical

for coordination

within a few percent in crystals.

fact,

observed

accounted

since

bonding,

the

sums

etc. reproduce

interatomic

to

distances

Either the ionic scale, or the covalent-

metallic scale of radii is appropriat,e for a particular compound.

Covalent-metallic

which

must

be regarded

phase

of the HBgg type,@

covalent the

apply

permissible

The covalent-metaIlic

appropriate

to

as an interstitial

ratio

of

0.60

TIN

metallic

since the value

radius ratio TN/rTi is appropriately

lnaximum

phases.

sizes

Only the metallic conductivity

radii have been

of the

for,

such

radius of 0.74 A is thus

for N in TiN.

In TiO on the other hand, where the ionicity

is

of TiO remains to be

the basic

ionic

valence

this must arise from the wide extent

overlap of the occupied

and

(tzsf2 orbitals of the Ti atoms

which, in the octahedral structure,

ligand field of the rocksalt

point towards neighboring

Division of Pure Physics

Ti atoms. W. B.

PEARSON

National Research Council Ottawa, Canada

less than for

and despite

References 1. W.

PHILIPP, Acta iWet. 10, 583 (1962). 2. G. HXGG, Z. Phys. Chem. B 6, 221 (1930). 3. 0. SCHMITZ-DUMONT and K. STEINBERG, schaften 41, I17 { 1954). * Received

June 4. 1962.

Natwwissen-