Internal friction in solid solutions of tantalum

INTERNAL

FRICTION R.

W.

IN SOLID and

POWERS

SOLUTIONS

MARGARET

V.

OF TANTALUM* DOYLEt

The internal friction in tantalum arising from the diffusion of interstitial oxygen ca.n be described as the sum of two peaks. The peak at 137°C (applied frequency - 0.6 c.p.s.), whose height is directly proportional to the oxygen concentration, is interpreted as arising from the diffusion of free, non-interacting interstitial oxygen. On the other hand, that at 162”C, whose height is a quadratic function of the oxygen concentration, is believed to arise from the diffusion of oxygen atoms, each of which is interacting with anot)her oxygen atom in its neighborhood. In a very similar manner, t,he internal friction arising from the diffusion of nitrogen can also be described as the sum of two peaks, one at 334°C and the other at 362°C (Y - 0.6 c.P.s.). The peak at 362°C is shown to be a quadratic function of the nitrogen concentration. a peak appears at 175”C, whose height is With both oxygen and nitrogen present in tantalum, This peak is described as arising proportional to the product of the oxygen and nitrogen concentrations. from t,he diffusion of oxygen atoms, each of which is interacting with a nitrogen atom in its neighborhood. The act,ivation energy associated with the diffusion of free oxygen atoms was found to be less than those measured for the diffusion of oxygen interacting either with other oxygen atoms or with nitrogen. These interactions between interst,it,ial solute atoms in tantalum are believed to take place over short atomic distances.

FROTTEMEST

INTERNE

DANS

LES

SOLUTIONS

SOLIDES

DE

TANTALE

Lr frottement intorne du tantale di1 & la diffusion de l’oxyg&ne interstitiel est d&-it comme la somme de doux pits. Celui & 137” (frhquenre de 0,6 c.p.s,), dont la hauteur est proportionnelle B la concentration Par contre, celui & 162’, dent tn oxvg&ne, est explique par la diffusion des atomes interstiticls libres. la hautour est une fonct)ion quadratique de la concentration en oxyghne, est attribuG & la diffusion d’atomes d’oxyg&ne en interaction avec un autre atorne d’oxygkne situP dans le voisinagc. De la mSme manitire, le frottement interne dii B la diffusion de l’azote pout Btrc expliquG comme la somme de deux pits, l’un & 334”, l’autre k 362” (v de l’ordre de 0,6). Le pit B 362” est une fonction quadretique de la concentration en azot,e. &and l’oxpgitne et l’azot,e sont pr6sents simultan~ment dans le tant,ale, un pit apparait & 175O, dont la hautour est’ proportionnelle au produit des concentrations il est explique comme dO & la diffusion des atomos d’oxygPne cn intrrart,ion pn oxygene rt en azote; avec un atome d’azote situ& dans son roisinage. L’bnergie d’actiration associCe & la diffusion des atomes libres d’oxyg&ile est plus petite que celle mesurbe pour la diffusion de l‘oxygilne en interaction. tant aver l’oxyg&ne qu’avoc l’azotr. Ccs interactions entre atomes interstitiels dans le tantale seraient & courte distance.

i’Bl
DIE

ISNERE

REIBUNG

BE1

TAST_4L

MISCHKRISTALLER’

Die innere Reibung van Tantal, die durch die Diffusion van eingelagertem Sauerstoff hervorgerufcn w-ird, kann als die Summe zweier Maxima bcschrieben werden. Das Maximum bei 137°C (angewandtc -0.6 cm/s), dessen Hiihe direkt proportional der dauerstoffkonzentration ist, wird der DifFrequenz fusion van freiem, eingelagerten Sauerstoff zugeschrieben, der keinerlei Wechselwirkungen unterliogt. Auf der anderen Seite scheint das Maximum bei 162”C, dessen Hiihe eine quadratische Funkt,ion der Saue&offkonzentration ist, van der Diffusion ran solchen Sauer&offatornen herzuriihren, van denen ein jedes mit einem anderen aus seiner Nachbarschaft in Wechselbeziehung steht. In iihnlicher Weise kann die innere Keibung, die durch die Diffusion des Stick&offs hervorgerufen wird, ebrnfalls als die Summe zweier Maxima beschrieben werclen, van denen das eine bei 334°C und das andere bei 362°C liegt (v - 0.6 cm/s). Es wird gezeigt, dass das Maximum bei 362°C eine quadratische Funktion der Stickstoffkonzentration ist,. Bei Anwesenheit van Sauerstoff und Htickstoff in Tantal entsteht bei li.?‘C ein Maximum. dessen Hb;he proportional dem Produkt aus der Sauerstoff- und cler stickstoffkonzontration ist. Dieses Maximum wird der Diffusion van Sauerstoffatomen zugeschrieben, l-on dcnen tin jedes mit ~illem St,ickstoffatom aus seiner Xachbarschaft in Wechselwirkung steht. Die ,4ktivierungsenergie des Diffusionsvorganges van freien Sauerstoffatornm hat eiuen niedrigoren 1Vcrt als die des Diffusionsvorganges van Sauerstoff, der entweder mit Sauerstoffoder rnit Stickstoffatomen in Wechselwirkung steht. Die gegenseitige Beeinflussumg der eingelagerten, geliisten Atome in Tantal reicht anscheinend nur iiber kurze Atomabst&nde.

* Received Julv 20, 1955. t General Electric Research iZCTA

METBLLURGICB,

Laboratory,

VOL.

4, MAY

Schenectady, 1956

New

York. 233

ACTA

234

METALLURGICA,

VOL.

4,

ID,76

0.9 0.8 0.7 0.6 0.5 -

0.3 :: iE _e &J 0.2 t-

‘l/J I

al -

TO SPECIMENWT. PERCENT

0.09 -

0.07 1 0.06 /f 1 f 460 440 420 400

1’

I

I 1

360

380 I I

RECIPROCAL

diffusion of i~lterstitially dissolved time.(l)

However,

t,he experimentally (Q-i

vs. l/T)

oxygen at. low con-

at higher oxygen

concentrat’ions,

internal friction

broadened

considerably time.

280

I

II

1.7

26 0 L I’.*

1.8

f103/Tt”Kfl

kind is not, confined

curve

and skewed,

At

with

tantalum,

to solid solutions

but, is found

solid solutions

in all oxygen

of the five-B

element,s.

of oxygen

in

and nitrogen Part of the

evidence for this general behavior is illustrat’ed by the influence

of nitrogen

concentration

on the shape of

t,he int’ernal friction peak associated with the diffusion of nitrogen in tantalum.

higher on t#he high-

temperat,ure side of the peak than that computed a single relaxation

1I

TEMPERATURE

with a single relaxation

determined

becomes

the int,ernal friction

I

300

1. Sorrnalizod internal friction peaks of nitrogen in tantalum.

in t,antalum arising from the

can be described

\Y 320

1.6

INTRODUCTION

centrations

t (“Cl 340

II

I

I.5

1.4 Fx.

The internal friction

0 1% 85 28f72 45155

NONE OB38 0.076 0.114

0.08 -

0.05

CALC’O USING I?-

for

least one additional,

longer relaxation time is needed to represent> the data at these higher concentrations. In this report we present additional ~xperimelltal evidence t,hat concentration broadening in oxygentantalum solutions is brought about by an interaction between interst’itial oxygen atoms. Moreover, there are indications that concentration broadening of this

THE

TANTALUM-NITROGEN FRICTION PEAK

INTERNAL

In order to reveal the influence of nit’rogen concemration upon the shape of the internal friction peak, we measured the damping in four specimens, containing different quantities of nitrogen, as a, function of temperature in a low-frequency torsional pendulum. The internal friction in t’hese specimens, as well as that in all others discussed in this report,, was strictly

POR’ERS

AND

independent

DOYLE:

INTERNAL

of the strain-amplitude

at least 2 . 10m4. The samples manner analogous

solutions.(l)

of nitrogen

to loading

was about

normalized

damping

They

arc similar

oxygen width

solutions. of

measured nitrogen

t’o those

nitrogen

prior

per cent.

previously

peak,

r 004

t

The

in Fig.

reported

in terms

or nitrogen

the internal

1. for

of

A(l/!P)

corresponding

peak height.

At

frict,ion for small amounts

can be described

with

a single

to a peak at 334°C.

of

relaxation At’ higher

a second relaxation time corresponding

t’o a second peak at 362°C is needed to fit the experimen-

n

“0

tal data. The solid lines in Fig. 1 have been computed for various combinations

of the 334” and 362” peaks.

The ratio of the height, of the 362” peak to that of the 334’ peak is indicated

on t’he graph.

0.1 n-eight’ per cent nitrogen, experimental

dat’a using combinations

However,

for a specimen

containing relaxation

concentrations.

of curve fitting, an activation

to fit the

of only

two about

the fit is imperfect,,

the presence of additional

at’ very high nitrogen

times

For purposes

The nitrogen internal frict,ion peak is not as stable If a specimen is aged above 45O”C,

t,he int~ernnl friction

arising

nit’rogen declines noticeably.

from

the

diffusion

Similar observations

of

have

been made bv Ke.c2) Because of this inst’ability, which it, seems reasonable

I 0.03

I

I 0.01

002

WEIGHT

PERCENT

OXYGEN

I 0.05

I

004

IN

TANTALUM

3. The height of the normal tantalum-oxygen damping peak as a function of oxygen concentration. FIG.

of tantalum

to associate with the precipitation

nit’ride, our study

has not been as comprehensive

of the nitrogen

peak

as that of the oxygen

peak. THE

energy of 37.5 kcal was

used for the 334” peak and 40.0 kcal for the 362” peak. as that for oxygen.

Ld

Up to roughly

it is possible

0.12 weight’ per cent nitrogen, indicating

235

TXSTALUM

at half the peak height, increases with the

concentrations

peaks.

OF

Thus, as can he seen in Fig. 2, the

nitrogen

concentration

0.6 c.p.s., time

the

weight

SOLUTIONS

0.05

in detail

We estimat’e that

curves are presented

SOLID

in a

in the specimens

0.005

IS

up to strains of

were prepared

to that’ already described

for oxygen-tant~alum the concentration

FRICTION

EFFECT OF CONCENTRATION ON HEIGHT OF THE NORMAL (137°C) TANTALUM-OXYGEN PEAK

THE

By Snoek’s theory, t3)the height of an internal friction peak should be proportional atom concentrat’ion, the solute atoms.

to the interstitial

if no interaction

Consequently,

solute

occurs between

we thought it. would

be of value to check this aspect of Snoek’s theory for solutions

of

tantalum

concentrations. specimens varying

containing

A large

number

were prepared

with the oxygen

over a fifteen-fold of known

at

low

content

range from 0.003 to 0.045

weight’ per cent’. The preparation alloys

oxygen

of tantalum-wire

interstitial

of tantalum-oxygen

atom

content

has been

described previously. (l) The results of measurements

of

the peak heights at 0.6 c.p.s. in a torsional pendulum are shown in Fig. 3. The equation

of t’he least-square

line that best represents these data is Q-l = 1.10 (concentr. in weight per cent) -

0.0020.

With the exception of the lowest points, all points fall within ten per cent of this line. Some of t)his scatter may be associated

with variations

in grain-size

and

orientation from specimen to specimen. Usually most of the cross-section of a wire specimen is occupied by FIG. 2. Half-width of tantalum-nitrogen damping peak its a fuxtion of peek height.

one grain with, however, lying along the periphery.

a number of’ smaller grains

ACTA

236

METALLURGIC.!,

VOL.

4,

1956

In a completely

analogous manner, we interpret the

362” peak as arising from the diffusion 200

atoms,

-

each

of which

is interacting

nitrogen at)om. This assumption y

SLOPE

are presented similar to those for oxygen in Fig. 4a. The internal friction was measured at 417”C, where t,he

=2 I

+ IOO-

“0 7 0

BO-

:r/i ], WEIGHT

OXYGEN

of the height) concentration.

CONCENTRATION

EXTRAORDINARY

OXYGEN

(162”

As reported for

somewhat

AND

previously, higher

ON

AND

362”)

with neighboring THE

the tail of the 334” peak,

of the nitrogen concentrat’ion.

solute at’oms.

INFLUENCE THE

THE

Not’ only

NITROGEN

PEAKS

OF

OXYGEN

NITROGEN

ON

PEAK

does increasing

nitrogen

concentration

broaden t)he nitrogen peak, but nitrogen also broadens

the internal

concentrations

tant,alum can be represented

from

The slope of 1.9 indicates that the 362” peak

convernional manner. They arise from diffusion of free oxygen or nitrogen atoms that are not interact’@

015

4a. Plot showing quadratic dependence of the oxygen interaction peak on the oxygen OF

(334”) peak

These data have been corrected

Tl’e int*erpret t)he peaks at 137” and 334°C in the

FIG.

EFFECT

small.

is a quadrat’ic fun&ion

0.10

PERCENT

from the tail of the normal

however.

( , , , , (,

006

contribution is relatively

for the contribution

/

006

THE

another

is justified in Fig. 4b,

where data for nitrogen in tantalum (taken from Fig. 1)

‘50_

2

4

of nitrogen

with

friction of

empirically

data

oxygen

in

as the sum

of t,wo peaks,

the oxygen

peak,

concomitantly

with reducing its The damping

height, as shown in a previous report.(l)

data can be fitted fairly well as the sum of the normal

one of which occurs at 137” and the We have just shown other at 162°C (Y = 0.6 c.P.s.). that the height, of the normal peak at 137°C varies

that given the 162”C, is that it arises from the diffusion

linearly with concentration.

of oxygen

In Fig. 4a, t’he logarithm

peakat137’Candasecondpeakat

An int’erpretation

nitrogen-atom

specimens

be correct’, we would

against

oxygen concentration.

the logarithm

of the

The oxygen concentration

varied from 0.05 to 0.125 weight per cent. the internal friction is due principally

was

At 192”C,

to t’he 162” peak,

neighbor.

peak t’o be proportional

and nitrogen concentrat,ions. this point, was conducted with the same amount cent), but, with varying

this contribution

been adjusted

from the 137” peak, as indicated

Table 1. The slope of 2.1 indicates of t,he extraordinary funct’ion

for

peak

of t’he oxygen

in

t’hat the height

at 162°C is a quadratic

concentration.

These

oxygen

concentration

interaction

this interpretation

the height

t’o the product

small.

data have

Should

expect

that from the tail of the 137” peak being relatively The measured

with

atoms, each of which is int)eracting with a

of the internal friction found at 192% in a number of is plotted

175”C(~=0.6c.p.s.).

of this latter peak, consistent

of the 175”

of the oxygen

An experiment on

specimens

of oxygen quantities

to check all loaded

(0.0225 weight per of nitrogen.

The

was kept low in order that, the

between oxygen atoms might be neglected.

The internal friction data obtained from measurements

facts

suggest that t,he 162’ peak may arise from diffusion of oxygen atoms, each of which has another oxygen at’om in its neighborhood with which it is interact,ing. TABLE 1. Internal friction data on tantalum-contairling oxygen at relatively high concentrations. All internal friction data observed at 0.6 c.p.s.

Weight, ~ per cent i ox)-gen

Height peak

, -fJ,-,‘,. I

0.050 ~ 0.075 0.100 0.125

~

of

oxygen

410 599 x33 913

104

Measured internal friction at 192°C. 10”

77 145

~

258

i

347

Calculated contribution from 137” Peak lo4

40

;

Internal friction from 162” Peak . 10”

37 0 I

I

002 WEIGHT

1 I1 1111111111 0.04 006 0.10 015 PERCENT NITROGEN

FIG. 4b. Plot showing quadratic dependence of the height, of the nitrogen interaction peak on the nitrogen concentratiol,.

0.5 r 0.4 c

0.3 !-

;;

TE 0.2

_-e b

/If

/

OXYGEN\y

N iTROGEN

r

.0876

If

SINGLE

FREQUENCY

.0131

.030? .0137

.0167 .0207

.0043

.0212

RELAXATION TIME

(VI = 0.89

PEAK z 2.408

/,

.0096

.0514

1 (“Cl

160

CYCLES/SEC

(142°C)

),

i

i,

I40

120

I I.9

2.0

2.1

2.2

2.3

RECIPROCAL

2.4

TEMPERATURE

2.7

2.6

2.5

2.8

(103/T(“K),

ying mnounts of nitrogen.

are shown in Fig. 5a.

made on these specimens

dat,a in Fig. 5a have been normalized normal oxygen peak (142% The oxygen considered

dissolved

at 0.9 c,p.s.).

From

with nitrogen

mass-action

can be

and those &at

considerations

itself

as a measure

The magnitude

we

are

would

expect

at this temperature peak is relatively

is the

co~~(~entration of

interacting

The

oxygen

small.

measured

at 215°C. where the contribution

CXI is the concentration

of free nitrogen.

content

condition

peak is negligible,

from the against

of the heighm of the normal oxygen peak

with nit’rogen, of free oxygen,

nitrogen

since

from the lT5’C

atoms

Coi is the concentration

as-received

~oilcentration,

the contribution

tail of the normal oxygen CoX

concentration.

at. 142°C can ho used

In Fig. 5b there is presented a plot of t,he damping

t’he product where

of the nitrogen

of the damping

as a measure of t,he free oxygen

in t’hese specimens

dist)ributed between two classes of atoms,

those il~teracting free.

The

t,o unity at the

of

the

specimens

varies considerably,

in

and

the

as indicated

by variat’ions in t,he nitrogen peak height from 0.002 to 0.014. Since t’his nitrogen is difficult to remove, requiring temperat,ures above 2500°C and pressure of about 10e6 mm, the amount of nitrogen subsequently loaded into the specimens good

measure

of the total

cannot

be used as a very

nitrogen

content,.

It is

perhaps bettes to use the height of the nitrogen peak

FIG. 5b. Plot illustrating linear dependence of the height of the li5”C peak on the product of oxygen and nit~rogen concel1trations.

ACTA

238

METALLURGICA,

VOL.

4, 1056

THE UNIQUE POSITION OF THE INTERACTION PEAKS AND THEIR RESOLVABILITY

1 0.9 -

0.8 -

We shall now refer to the 162, li5,

Ol-

as int,eraction

0.6-

trariness

0.5 -

of this

questions

and 362°C peaks

To reduce the apparent

description,

need

concerns

0.4-

peaks. be

perhaps

considered

the uniqueness

arbi-

at least two

further.

The first of an inter-

of the position

action peak at, a fixed frecprency of vibration. position

0.3-

of an imeraction

tinuously

:: TE $ 0.20

with

centration,

changes

peak

in interstitial

the term “peak”

If the

were to vary solute

concon-

would be a description

of

lit,tle value. In Figs. ‘ia, Sb, and ‘ic there are shown plots of the interaction peaks at various concentrations. It can be seen that, t’hrough a range of concentration, the interaction-peak concentration.

.0615 .0610

0 FREOUENCY AMOUNT

OF

nitrogen interaction

.06

(vj’O.6

*

06

WEIGHT

positions

%

changes by 4 degrees. 0.05

400 II

360 I

360 II

1.5

14

340 I

320 II

RECIPROCAL

TEMPERATURE

d 50

300 I 17

1.6

I

I I.8

I.9

(103/T(“K,)

FIG. 6a. The influence of oxygen on the nitrogen-tantalum darnping peak-higher nitrogen level. and of the nitrogen observed

between

those concentrations proportionality

peak.

A linear relationship

damping

and this product

at which deviations

between

nitrogen

peak

is

up to

variation peak.

interaction

obtained

t,he

by

is relatively

greatest.

peaks in Figs. 5a, 7b, and Tc were

subtracting

a damping

curve

of unit

1.0 0.9

and

08

ON

0.6

was found capable of affecting

t,o study

the influence

0.5

both

the complementary of oxygen

I

case, to

different amounts of nitrogen. The results of damping

measurements

are to be found

0.4

on the nitrogen

peak. Four samples were prepared, with high and low oxygen concentrations in samples containing two

test specimens

where

and oxygen

peaks are more nearly of the same mag-

The interaction

the height and breadth of the oxygen peak, it was of some interest

from the 162°C

concentrations,

0.7

THE INFLUENCE OF OXYGEN THE NITROGEN PEAK

investigate

nit’rogen

nitude, this contribution

occur in the height

low

On the

A large part of this apparent

arises from the contribut’ion

At

and

peak (175°C)

relative magnitude of the oxygen-nitrogen

nitrogen concentration.

Since nitrogen

t,he oxygen

peaks at! 162°C and 362°C respec-

other hand, that for the oxygen-nit’rogen

t (“a I

do not vary with

of

tively appear constant wit’hin about a degree.

CYCLES/SEC.

NITROGEN

temperatures

The

on the four

0.3

7: 7’ 0

B 0.2 1

in Fig. 6a and 6b.

At neither nitrogen level, 0.06 nor 0.04 weight per cent nitrogen,

was oxygen

damping

peak.

found to broaden

On the contrary,

the nitrogen

t’he influence

of

oxygen was to decrease slightly the breadth of the nitrogen peak. The fact that oxygen does not broaden the nitrogen peak is perhaps not too surprising if it is borne in mind that oxygen diffuses about 25,000 times faster than nitrogen at 350°C. In t’he t,ime-interval required for a nitrogen atom to diffuse from one site t,o an adjacent one, any interaction influence of oxygen might be smeared out.

FREQUENCY AMOUNT

(VI = 0.6 OF

r 4fO I4

CYCLES/SEC

NITROGEN

- 04

WEIGHT

%

t (“C) 400I.

380I

I.5 RECIPROCAL

360I,

I I.6

340/

TEMPERATURE

320

I I.7

300I 1

200 ./ 0 1.6

(103/T(“K,,

Frc,. 611.The influence of oxygen on the rlitrogorl-tttrlt,alum dan+ng peak-lower nitrogen level.

I’O14T’EHti

height,

3~11

DOYLE:

corresponding

INTERSAL

to the

IN

FRICTION

“normal”

peak,

the experimental

damping

at it*s maximum.

There can be objection

curve normalized

SOLID

from

IO

to unity

peak to be subtracted

04 -

should be somewhat’ less than

be shown by the following If a hypothetical

is normalized

is subtract,etl from t)he synthesized peak

0.3-

02 -

from

to unity at

and if one of the peaks of unit height

of the second

; 0

curve, the position

can be determined

within

%9ooe00721

the positions

of the interaction

I 2.2

I 23

RECIPROCAL

1.5

I

24

TEMPERATURE

(lS3/T(‘K))

FIG. 5~. Detorminution of the position of the ox>-gen interaction pedc.

degrees. Although

-

argument’:

damping curve is synthesized

two peaks of equal height: its maximum,

as can

239

07 0.6 05

of its precise height is not’ required,

TANTdLUl\I

-

cedure on the grounds that the height of the normal

knowledge

OF

:“8-

to this pro-

unity. However, the precise height of the normal peak that should be snbt’racted is unknown, Moreover,

SOLUTIOSS

peaks in

Figs. ia, ib, and 7c are well est’ablished, little can be said about

their shapes from

sequently,

this procedure.

Con-

the fact, that the curves shown in Figs. 7a,

7b, and 7~1sre skewed reveals nothing about t’he shape of the interaction

peaks.

It is true that, at’ extremely the position in the

of the interaction

direction

of higher

interpret1 as an indication one neighboring jumping

high concentrations,

peak appears to move This we temperatures.

of the presence of more t’han

soliit’e atom

in the

vicinity

of a

atom.

The second question with respect to the interaction peaks concerns the possibilit,y mental

int,ernal

distinct

normal

internal-friction energy

friction 2nd

into

interaction

peaks.

of about

a,nd

Since

25 kcal, has a half-width

an

separation

of about

of the 162’ inter-

peak and the 137” peak is possible.

other hand, a partial separation peak

an experi-

separate

peak near 15O”C, with an activation

35 degrees, no distinct action

of resolving

curve

Inspection

readily discernable

inflection

2.1

23

2.2

RECIPROCAL

TEMPERATURE

(I03/T(‘K))

FIN. Sh. Determination of the position of the oxygen-nitrogen interaction peak.

of the 137” oxygen

and the nit,rogen-oxygen

175°C is possible.

On t)he

01

interaction

peak

at

of Fig. 5a discloses

a

point, which is the best

that can be done with respect

to the resolution

of

distinct peaks. ACTIVATION

Relaxation

ENERGY

times

usually be described exp

(E/R?!').

relaxatjon peaks

It is

times

are longer

for

MEASUREMENTS

diffusional

processes

in the exponential

of interest to find out whether the corresponding to the interaction than

those for

the normal

because of differences in the pre-exponential T,,, or in the activation Therefore,

can

form, 7 = 70

activation

energy E, or perhaps in both. energies for diffusion in various

specimens have been determined in peak temperature

peaks

constant 0.04 1.45

varying

the

I

I

155

16

RECIPROCAL

by noting the change

that results from

I 15

FIG.

‘ic.

TEMPERATURE

(103/T(oK))

Determination of the position of the nitrogen int,eract’ion peak.

TABTX 2. Fundamental -..

Freq. of applied stress C.P.S. __, ----- .----.

System _.--

-_

-

-

--.

--

0 in Ttt

1 (low cont. 0.016 weight, per cent) 1

/

energies

!

O..i

..-- -I__ 37.8

E = “5.9 kc*1 from ]:ea.khroadt~h nwtts.

,_.~ 0.1

___~~ \‘alue E = 2i.A issome average of that, for normal and interact ion peaks

2.35i

2.191 ?.14i -_.-__-_.-

0.235 0.570

cent)

25.8

- ___

Comment

1% SCC

"._27;j

1.722

/ (low Cone. cn. 0.03 weight per 1

/

2.492 2.408

0.393

N in Ta

I

2.431 2.381 2.305

!

0.891

1.68!) 1.652 1.625 1.596

0.927 1.662

vibration

of the tantalum

is greater

Results of these measurements

are summarized

containing

only a little oxygen.

interaction

peaks are too close to resolve well enough

frequency

of t#he torsional

in Table 2, and are depicted Sb, and 8~. plots

friction

is a maximum

of t’he midpoint

tern~)~rat,~lr~

in Figs. 8a,

was determined

of t,he low-

t,he precision

has been described

and high-

of the measurements,

in detail in a previous

Data taken on specimens are shown in Fig. 8a. t,he measured

at which

sides of the damping peak versus the Such a procedure, which damping.

normalized enhances greatly

specimen

graphically

In all cases, the temperature

the internal from

2.494 2.438 2.358

j

0.293 0.891 1.722

0 cont.

High S COIN. (0.0225 weight per cent, 0 0.08 weight per cent pu’)

wire.

activation

I / Reciprocal ) Activation 1 peak temp. ene*g) I/T . lo” , kcal/mole

0.%5

0.612 1.673 ___.-_ 0.266 0.559 : 1.541

___._---__.___l_~ 0 in To, (high cont. 0.12 weight, per cent)

Low

data used in computing

-.

containing

The significant

activation

energy

report.(4)

only oxygen result is that

(27.8 kcal)

for the

co~lt,ail~i~lg a high concer~t,ratiorl of oxygen

than

for our purpose resent

some

that

(25.8 kcal)

for

since

broadened,

specimen

here, t,he value 27.8 kcal must rep-

average

activation

energy

the normal and that for the interaction over,

the

Since the normal and

t,he experimental

of t’hat for peak.

high-oxygen

Norcpeak

as precisely

as t’hat for the low-oxygen

peak.

There

can be no doubt., however, that, the activation is greater for the interaction normal peak.

It is doubtful

set, are si~nificaiitl~

that the values obtained see and 0.1 . 10--l*

different.

Data on a specimen Fig. Sb.

energy

peak t,han that for the

for rr, in the two cases, 0.5 . lo-r4

oxygen

is

its act,ivation energy cannot8 be measured

containing

and a large amount

a small amount

of

of nitrogen are shown in

This sample is the same as the one corre-

s~olldillg t,o the largest amount3 of nitrogen in Fig. 5a. For this sample,

the interaction

peak

separated by 38” from the normal peak. t,o measure separately, the normal with

changes

position

reasonably

and the interaction in the frequency

at 175’C

well, the shifts in peak

temperat,ures

of vibration.

of the int,eraction peak was located

tract,ing from

the experime~ltal

is

It is possible

curve,

The by sub-

a calculated

damping peak corresponding t,o normal peak, The data obtained for the normal peak are in good agrcement with those found with the specimen cont,aining -25

’ 2.30

150 / 2.35 FIECIPROCAL

PEAK

MC

1 240 TEMPERATURE

I

> 265 i103~‘/T(*K~~

Frci. 8a. Activation energy determination diffusion of oxygen in tantalum.

oxygen

Ix, / 2.50

for the

alone in small amounts

(26.1 vs 25.8 kcal in

t’he act’ivation energy and 0.5 vs 0.3 . 10-r* ser in rO). The activation energy for t’he oxygen-nitrogen interaction peak was found to be greater than that: for the

normal

oxygen

peak,

values obtained sig~fi~antly

27.3 against

26.1 kcal.

for rO, 0.3 vs. 1.0 - lo-i4

The

see, are not

different, wit.hin our e~~erinleI~ta1 error.

The act-ivation energy for the diffusion in tantalum

at. low

concentration

of nitrogen

has

also

been

measured. The resuhs are shown in Fig. 8~. We obtained a value of 37.6 kcal for the act,ivation energy and 0.S X lOPi4 set for -ra with a specimen in which the nitrogen peak height was about 0.019. The activation peaks,

energies

measured

for the normal

25.8 and 26.1 kc.al for oxygen,

for nitrogen, obtained

should

be compared

and 37.5 kcal

with some values

by an entirely different met,hod.

shown t,hat the half-breadt,h,

caorresponding to a single relaxation following

relationship

It has been

WIjp, of a damping peak process, bears the FIG. 8b. Activation energy detwrnination for the diffusion of oxygen in tantalum as &fected by nitrogen.

to the activat,ion energy.(i)

E (keal) = 5.28/Wri,. If a plot of t’he half-breadth various

interstitial

concentrat,ions

zer0 ~on~ent,ratioll,

the

value

of a damping

curve f’or

is ext’rapolated

to

where illtera~t~ions do not occur,

of t,he half-breadth

so obtained

one relaxation

should

correspond

to that for only

Previously,

we reported a value of 25.0 ktal for oxygen

in t~antalum by t,his method.(l) obtained

by an extrapolation

zero oxygen polation

This

process.

number

of a half-breadth

concentrat,ion.

More properly

the extra-

Wihh the dam available

tain unambiguous

in Fig.

results, actjivation-energy

SOME

ON THE NATURE OF THE BETWEEN INTERSTITIAL SOLUTE ATOMS

COMMENTS

INTERACTION

It has been shown that,, over a range of concemration, the hnernal friction

associated

with the diffusion of a

single solute element can be described only t.wo relaxatJion times.

Moreover,

5a, we can now correct for t,he broadening

arising from

the two peaks appear t’o be constant

amount

left

composition.

. ‘oxygen”

specimens.

A llalf-breadth

is thus obt’ained corresponding of 25.9 kcal.

An

extrapolated

of 0.204 + 10-s

to an activation

energy

a&ions

as a functiou

half-breadth

of

between

solute atoms can t-ake place from a

rather limited number of relative configurations,

to an activation

number

should

37.5 ken1 obtained

be

0.143 . 10P3 is

in t,antalum.

energy

compared

of 37.0

with

from the measurement

in the peak temperature

the

This kcal. value

of the shift

with changes in the frequency

of vibration. The:

compilation

Sivertsen’“)

made

by

Marx,

shows a wide variation

energies for the diffusion

Baker,

and

in the activation

of oxygen

and nitrogen

niobium workers.

and t’antalum, as measured by Undoubtedly a factor contributing

variation

is that due t,o concentration

in

various to this

which has not,

always been controlled very well. The extra relaxation times found as a result of interactions at the higher concentrateions have higher activation energies, and thereby increase the average act.ivation energy as

of

These facts suggest perhaps that inter-

in t,he more con~ent,ional

from Fig. 2 for nitrogen

corresponds This

in the

rather well by the posit,ions of

This is in good agreement w&h the values

25.8 and 26.1 kcal obtained

obtained

nitrogen

measure-

int*erstit.ial solute atoms at low ~o~lce~~t.ratiol~s.

the small

of residual

Therefore, t,o ob-

ments should be carried out on specimens containing

was

plot to

should have been made to zero total inter-

stitial concentration.

measured in a damping experiment,.

FIG. 8~. Activation energy determinatiorl diffusion of nitrogen in tantalum.

for the

and

ACTA

24”

METBLLURGICA,

VOL.

4,

oxygen

atoms.

atomic distances.

The second peak, whose height is proportional

to the

Other experimental observations lend some support to this viewpoint. Should a strain interaction occur

square of the oxygen

arising from the diffusion

over relatively

which is interacting

t.hat the interaction

that plastic

forces

extend

large distances,

deformation

number of precipitate

over

only

short

it might be expected

or the presence

part,icles would alter the breadth

was 0.105

week in a furnace from

whose

600”

and

was aged further

400°C.

examination

specimen

loaded

of the half-width have

correspond breadth quantity The

height

to 0.186 . 10-3.

compared

with that in a

damping was 0.10. The values

subsequent

been

plott’ed

with

2.

These

data

It is seen that the a large amount

is no greater than those containing

of

When

both

tantalum, varies

have

been

described

nitrogen

and nitrogen

are present

a nitrogen

whose height

of the oxygen

and nitrogen

This peak is interpreted

atom with which

The activation oxygen

as arising

it is interacting

energies found

in its

for the diffusion

interact’ing with ot’her oxygen

of

atoms or w&h

nitrogen atoms are higher t’han that measured for the diffusion of free, non-interacting The interactions

between

oxygen.

interstitial

solute atoms from a

limited number of relative configurations. ACKNOWLEDGMENT

oxygen in tamalum can be represented as the sum of two peaks, one occurring at 137°C and the other at N 0.6 c.P.s.).

is directly

in

at li.YC,

neighborhood.

manuscript.

concentration,

with another

is found

The authors are indebted

arising from the diffusion

frequency

as the

from the diffusion of oxygen atoms, each of which has

of

oxygen

oxygen

a peak

as the product

report.(l)

friction

137”C, whose height

is interacting

concent’rations.

stimulating

162°C (applied

can also be represented

atom in its neighborhood.

CONCLUSIONS

The internal

oxygen atom.

appear to occur over short at’omic distances

experiments

briefly in a previous

in tantalum

each of which

no such

of prccipitatc. cold-work

wit’h a neighboring

preted as arising from the diffusion of nitrogen atoms,

to the two aging treaton Fig.

to the shaded circles.

for this specimen

precipitate

peak

with 0.12 weight per cent nit’rogen

for which the maximum ments

for a

disclosed the presence of

a large amount of precipitate

nitrogen

was lowered

The

declined to 0.0676 and the half-width Metallographic

The

the half-width

temperature

to

as

atoms, each of

(v N 0.6 c.p.s.). The second peak, whose height varies as the square of the nitrogen concentration, is inter-

and aged at’ 600°C for one day.

gradually

of oxygen

with 0.20 weight per

cent nitrogen

This specimen

is interpreted

sum of two peaks, one at 334°C and the other at 362°C

wire was loaded

0.211 . 10P3.

concentration,

Neither do,

however. A tantalum

damping

of free, non-interacting

Similarly, t’he damping arising from the diffusion of

of a large

of an experiment,al internal friction peak.

maximum

the diffusion

1956

The peak at

proportional

is interpreted

to the

as arising from

conversations

to J. C. Fisher for many and

for

reviewing

the

REFERENCES 1. 2. 3. 4. 5.

R. W. POWERS, _4ctaMet., 3, 135 (1955). T. H. KE, Phys. Rev., 74, 914 (1948). J. L. SNOEP, Physica, 8, 711 (1941). R. W. POWERS, Acta ilfet., 2, 604 (1954). MARX, BAKER, and khVERTSEN, Acta Xef.,

1, 193

(1953).