The deformation of amorphous palladium-20 at.% silicon

Materials Science and Engineerino American Society for Metals, Metals Park, Ohio, and Elsevier Sequoia S.A., Lausanne-Printed in the Netherlands

153

The Deformation of Amorphous Palladium-20 at.% Silicon R. M A D D I N School of Metallurgy and Materials" Science and The Laboratory for Research on the Structure of Matter, Universi O' of Pennsylrania, Philadelphia, Pa. 19104 (U.S.A.j

and T. M A S U M O T O The Research Institute for Iron, Steel and Other Metals, Tohoku University, Sendai (Japanj (Received October 4, 1971)

S u m m a r I, t

The time-dependent mechanical properties of amorphous Pd-20 at.% Si, i.e., fracture-strain rate effect, load relaxation, creep and elastic after-effect characteristics, were determined as a function of both stress and temperature. On the basis of the kinetics' developed from these tests, the viscous nature of the amorphous phase has been explained, and a qualitative model for the change from the amorphous to the crystalline phase has been sugyested. This model requires atoms to transfer from a Bernal random close packed arrangement to crystalline islands which 9row with the application of temperature, stress and time.

In a recent publication I we reported the deformation characteristics (those not predominantly dependent upon time) of Pd 20 at.% Si quenched from the liquid state to an " a m o r p h o u s " phase. Deformation and fracture occur by the stabilization of cracks through plastic flow followed shortly thereafter by the propagation of these same cracks in a manner not dissimilar from behaviour in brittle crystalline solids. However, a viscous type tearing exists at the fractured interface. In these "amorphous" materials there is no well-defined regular crystal structure and hence no slip systems; consequently, the deformation is "apparently homogeneous" with no strain hardening. Strain should be, therefore, a linear function of stress and time. An indication of this type of behaviour was given with For French and German translation of the Summary, see p. 162.

:~tater. Sci. En#.. 9 (1972)

the observation of the viscous nature of the material adjacent to the fractured surface. In the present paper we shall report on the "time dependent" properties and from these results comment on the structure of the " a m o r p h o u s " phase, particularly with regard to the manner of the transformation to the crystalline state. If a crack is accompanied by some viscous flow, we may expect that the fracture stress will be dependent upon strain rate. This relationship is shown in Fig. 1 where it is seen that the fracture stress decreases with increasing strain rate. It appears that at low strain rates the fracture stress increases and more energy is needed to continue the propagation of the crack. At the high temperature, at which the a m o r p h o u s phase changes to a crystalline structure, the opposite effect is observed, as is seen in Fig. 2. We believe that this difference is due to a change in the fracture mechanism, i.e., to one where a shear tearing mechanism is the primary fracture mode. The effect of temperature and strain rate on the fracture stress and mode is shown in Fig. 3. The broken line indicates the boundary between brittle and ductile behaviour. Relaxation studies in crystalline metals show the stress to relax from its value a o at the initial flow stress according to a logarithmic relation ao - a = S (a, T) x log (t + t o)

(1)

where S(a, T) is a time-independent parameter of the relaxation and to is a constant in a given relaxation test. In order to check the relation for a m o r p h o u s Pd-20 ~oSi, the load relaxation versus the logarithm of time for various temperatures and initial loads is

154

R. M A D D I N , T. M A S U M O T O xlO3

,0

El40

0.5-

/

120 03 q

~. 100

_~

YO_UUNG'SMODULUS

-o"

n-

I

10-4

F"0 = 21b (68Kg/mm 2) i

Z50°C

•

//

/)~ /~."

/

/}#200%

sill

x

d

(,,b~J

,.,

-

F--

10-z

iI

/

~) 0.3

4

I

iO -~

~P°~¢1~

(21b)

d

STRAIN RATE (sec -11

"' 11:

Fig. i. Relationship between the strain rate and the strength properties of amorphous Pd-20 at. % Si alloys.

0.2

// p /

..,,,d8

..~o...~ .s."J' . . . ~

SOOARE TYPE

.~,~ j B "

//


o.,APPEARANCE OF FRACTURE SLANT TYPE q

l/

2

5

t

.....

,e

b. i

6

=~ 8o

6o

F0 = t ib (54Kg/rnm 2)

- 0.4

X

~"


o.~.o

~"

~

.

200oC

(lib) ~ oS d

~

,5ooc

~

(21b) •

,~

"

IOO I

TESTED AT 300"C

cuE

E

I

•

5(-

MAXIMUM

FRACTURE STRESS

0

•

r--

c

-

IO ¢~

STRESS

I ii / i

~.

~, x "~ ..... ~J ~ 0 L ~

~.

Y,ELD 0 STRESS . . . . . .

~.--

~ x. . . . . . . . . ~7~

x. . . . . . . . . . . . . . . . YOUNG'S MODULUS

10-4

~.~

X

ELONGATION

"~

|

o

~_~

al 0 0 i0 -E

i0 -z,

STRAIN RATE (sec d) (HELD 15 MINS AT TEMPERATURE;HEATING RATE 200°D/MIN)

Fig. 2. The effect of strain rate on the mechanical properties of amorphous alloy at 300 ° C. 150 * MAXIMUM STRESS 0%

E 140

o 120

-

1 5 0 % ~ ~'''" "--------=--~. ~~

A~,A A . ~ "

n "--"

2000C/

/

X

o

"\

o

:. I IIIII[ I iO-5

°

o

,, I/I I1111] I ~l~lllll] I I 1 1 llllI l I l IO -4 iO-5 iO-2

STRAIN RATE (sec -1}

Fig. 3. The effect of strain rate on the fracture stress at various temperatures.

Mater. Sci. Eng., 9 (1972)

extended linear the relaxation of a crystalline type behaviour,

(2)

where e is the strain, E Young's modulus, (r the stress, t the time and q the viscosity. For our relaxation experiments t/>0, e = e o and the above equation becomes cr jr/

+ =- = o

(3)

for which a solution is

7o

50

a 3r/

+ --

a = ao e x p ( - A t ) ,

80

,,m 60

d~ 1 da dt - E dt

"

I00

•~IE 9o

shown in Fig. 4. Since there is no relationship, we conclude that mechanism is different from that metal. If we further assume a Maxwell then we may write

d~

o

IO00

Fig. 4. Load relaxation as a logarithmic function of time for various temperatures.

1 da

o

o2a~____~~-_.....o~

w I10

,oo~ ~"~"---o

I

I00 TIME (sec)

A ---

E

3t/"

(4)

There is shown in Fig. 5 a plot of In ao/a versus t for various initial loads. At this temperature (250 ° C) as well as at a lower temperature (200 ° C) (not shown) non-linearity is apparent at loads in excess of 0.5 pound. The conclusion that the behaviour for higher loads is not that of a simple Maxwell solid seems justified. Another indication of this type of behaviour is seen in Fig. 6 where the amount of load relaxation decreases for repeated load-

155

D E F O R M A T I O N OF A M O R P H O U S Pd-20 at. % Si 0.8

0.7

CONTROL SCREW

OALLBEAR,NG/

250 °C

--

--STEEL PIN

0.6

0.5

u_

z~ °

-

b-

_

0.4

. . . . . STAINLESS ROD

o/0,1010102,bo." STEEL WIRE

3 0.3

/ _ ~o/,

-

-STAINLESS TUBE

ul u

F PIN

0.2

!-

0.1

0 ~ / I 0

200

I

I

I

400

600

800

TIME

I000

(sec)

Fig. 5. Load relaxation curves replotted by assuming a Maxwell type solid. VACUUM~ BOTTLE

/

0,5

/I 250°C

0.4

/

bIo LL v

J

Fig. 7. Schematic diagram of creep testing device.

i"

!

.7

0.3 F< x

1

I 7"

F 0 = lib (42 Kg/mm 2) -

./

./

0.2 _

/

oU

7

o,o oloI

123

11I

0 -J

0.1

D

~

u

o I0

J

u

I

I

I00

I000

TIME (rain)

Fig. 6. Repeated load relaxation tests on the same specimen at 250 ° C.

relaxation tests on the same specimen. This behaviour may be due to some change in the atomic arrangement during testing. An alternative approach to the understanding of the deformation and structure of "amorphous" alloys would be its creep characteristics. Accordingly, filaments (0.5 mm wide and 30 # thick) cast from the liquid state by a modified P o n d - M a d d i n 2 Mater. Sci. Eng., 9 (1972)

I; ,~

technique were subjected to creep in an apparatus shown schematically in Fig. 7. The strain was measured with a dial gauge to within an error of 4- 2 x I0- s m m / m m and the temperature was controlled in a silicone oil bath to within _+0.5 deg C. Creep tests were made at a series of stresses (15 kg/mm 2, 28 kg/mm 2, 48 kg/mm 2, 53 kg/mm 2, 67 kg/mm 2) and at different temperatures (100°C, 125 ° C, 150° C, 175° C, 200 ° C). Since very little is known about the stressdependent thermal stability of the amorphous phase, this aspect of the amorphous structure was determined for an arbitrary stress of 48 kg/mm 2 and is shown in Fig. 8. X-Ray and isothermal electrical resistivity measurements were made to monitor the transformation. As Fig. 8 shows, load markedly affects the beginning of crystallization and hence, the creep testing conditions should be fixed at below 200°C for times shorter than 1000 min, i.e., for loads~< 48 kg/mm 2. We were also aware that the time for crystallization decreased with increasing load. For example, as may be seen in Fig. 9, 1000 min at 225 ° C with a load of 48 kg/mm 2 produces a granularity with "grain size" of about 150 ,& with a f.c.c, structure *(a o = 3.93 A.). The lower conditions of the creep test are, on the other hand, fixed at * Corresponding to the metastable phase I reported in ref. 1.

156

R. MADDIN, T. M A S U M O T O xlO ~= --

/---BEGINNING LINE OF ' ~ /CRYSTALLIZATION ' % \~~ , , , ~ , ~ , ~ ~ " WITHOUT STRESS

\

L =' Q: 2 0 0 -

I

i

i0 I-

-

[3

~\

to/

It- / /

-FCC METASTABLE PHASE

BEGINNING LINE OF CRYSTALLIZATION (ABouTWITSTRESS H ~ 48 Kg/mrnZ' 0

%.

0

/

[

I

~..=/°

t

°/,~

2 / 4aKg/m~%.~ ° o

~

°I"°

5

t,J

~

o AMORPHOUSPHASE t, FCC METASTABLE PHASE

i/67K~/mm2

~-

300

"~

°/

175"(:

15~

Z8 Kg/mmz ~°.......o~o ~ o _,----.----- o.O~

\N~

° 0

O0

%'\

L~Y_L..

\ 0 AMORPHOUS PHASE

I00

0

0~'~ El ~,

--

I till[

I

I

I

I iitil

102

I

105

I

I

15Kg/mm2

. . . . . . . . .

~

-

_ ...........

A

200

o ~

- 23~%Cmm____~

.....

..................

400 600 TIME (rain)

800

IO00

Fig. 10. Creep curves of amorphous alloy at 175° C. (The creep curve for a crystalline alloy is also shown.)

0 I

0

-

.__..~.-o----~'-

I I III

104

TIME (rain)

xlO-3

..........

Fig. 8. Effect of stress on the beginning line of crystallization in the amorphous phase.

125 °C 64Kg/mm 2

E3 z I0

EO 5

65 /

0

I I00

I 200

I 500

I

I

~

I

400 500 600 TIME (rnin)

I 7'00

800

I

900

I000

Fig. 11. Creep curve and strain relaxation curve of amorphous alloy at 125 ° C and 64 kg/mm 2.

Fig. 9. Transmission electron micrograph of the quenched alloy after creep testing for 1000 min at 225°C and 48 kg/mm 2.

stresses above 15 k g / m m 2 and temperatures above 100 ° C. For measurable creep strains, temperatures in excess of 100 ° C are required. Figure 10 shows typical creep curves at 175 ° C. For comparison there is also shown in this Figure the creep curve for Mater. Sci. Eng., 9 (1972)

crystalline Pd-20 a t . ~ S i (in its f.c.c, structure1). Creep data for the amorphous phase were obtained for 100° C, 125°C, 150°C, 175°C and 200°C. Data of this sort show the creep curves all to consist of an instantaneous part, a transient part and a steadystate part. Since an amorphous structure should show anelastic behaviour recoverable when the load is removed, the anelastic after-effect was examined at 125°C and 150 ° C. Typical results are shown in Fig. 11 where it may be seen that the anelastic component e4 is not equal to the transient component e 1. Table 1 gives the changes in each component of the creep strain shown in Fig. 11 when creep and relaxation are repeated alternately; % is the instantaneous strain (elastic), % is the instantaneous strain reduction on removal of the load, e I is

157

D E F O R M A T I O N OF A M O R P H O U S Pd 20 at. % Si TABLE 1 The effects of repeated testing on creep and recovery 125° C, 67 kg/mm 2, 500 min

No. of cycle

1 2 3

co

et

c2

83

~,~

e5

~h

c4

c1+82

xlO 3 12.35 12.36 12.25

xlO a 3.96 1.60 1.44

xlO 3 1.28 1.07 1.05

xlO 3 12.17 12.31 12.29

×10-3

x l O -3

2.01 1.56 1.35

3.41 1.16 1.10

1.95 0.04 0.09

×10 3 5.24 2.67 2.49

El

82

83

E4

85

81 _c;,$

E1 +":2

xlO. 3 5.07 1.92

xlO-3

xlO

2.50 2.10

9.76 9.62

x l O -3

150 ° C, 53 kg/mm 2, 800 min

NO. QI' cycle

~;0

I 2

9.99 9.71

xlO

3

3

X10-3

xlO

2.21 1.90

5.59 2.21

150 *C

N2"% ", k

:

3

81 = go [1 - e x p ( -

".o.

--

\°.o °x2"o x' oo ,

\,

I00

200

×I0

t/~)]

500

TIME (rain)

Fig. 12. Relationship between the logarithm of strain for transient creep and the time at 150°C and various stresses.

a = 8o+g1,~+81,/~+~ 2

•°[1 81,a = 8~

-exp(-

t/~)]

e,,~ = e~ [1 - e x p ( - t/z~)] the transient creep strain and 82 is the steady-state creep strain. For the " a m o r p h o u s " alloy to be ideally visco-elastic, 81 =e,4 and 82 =85. As seen in Table i, 8~ is about twice 84. However, the difference e I - e 4 .~dater. Sci. En#., 9 (1972)

3

7.57 4.02

(5)

where r is the relaxation time and co is the equilibrium strain as time t - , vc. The relation between the logarithm of the strain 81 and the creep time at 150 ° C for various stresses is shown in Fig. 12. The data are linear except for times shorter than about 60 min. Using the data for a stress of 53 k g / m m 2 (as example), the point of intersection between the extrapolated linear portion at t = 0 and the actual data at t = 0 gives the strain as 2.2 x 10 3 m m / m m which agrees quite well with the irreversible strain 81-84 shown in Table 1 (2.8 x 10 3 m m / m m for this same stress). The irreversible part was represented by an exponential function (eqn. (5)). The creep curve, therefore, consists of the following :

"%o \ ~.'%^ - o \

Xo

0

xlO

2.86 0.02

goes to zero when the experiment on the same specimen is repeated. We, therefore, consider that the transient creep consists of a reversible part (81,~) and an irreversible part (e~,,). The reversible part, if it is due wholly to anelastic behaviour, should be given by

-5 -

~,

3

a2

= ~,t.

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

~ is the strain rate. These individual values have all been obtained at

158

R. M A D D I N , T. M A S U M O T O

TABLE 2 Creep parameters at various conditions of temperatures and stresses Temperature

°C

o e=

Applied stress

e~

~

1/z~

sec-

1

sec

i/zp i

sec-

1

( kg/mm 2)

100

49.4

x10 3 0.55

x10-3 0.56

x10-3 1.02

125

28.1 47.7 64.0

0.76 1.30 2.12

0.32 0.94 1.84

1.00 2.17 4.33

x l O -4 1.08

xlO 4 9.0

150

18.0 27.9 48.5 66.7

0.65 1.08 2.27 4.18

0.25 0.57 1.66 2.82

1.00 2.08 4.75 9.33

1.32

11

175

15.0 28.2 47.7 67.6

0.78 1.69 4.37 7.54

0.49 0.92 2.33 5.26

1.45 4.17 9.42 25.8

1.53

12

200

15.0 28.0 46.2

1.05 3.20 6.42

0.60 1.20 3.97

3.00 7.50 17.3

1.75

14

xlO-8

30

In considering the flow behaviour of the "amorphous" alloy, it is possible that a single thermally activated process is the rate-controlling step and hence the creep strain ~ should be given as follows: The coefficient of viscosity under an applied stress z is given by reaction rate theory as

[]

/

20

17 = B 1 z e x p

o 0

_zoo I0

20

:50

40

50

~ = Z/r I = B 2 60

70

APPLIED STRESS ( K g / m m 2 )

Fig. 13. Relationship between the strain rate at steady state creep and applied stress at various temperatures.

various stresses and temperatures and are shown in Table 2. The steady-state creep rate was plotted against the applied stress for various temperatures (Fig. 13) and shows a parabolic relationship, i.e., ~ = A a " with n g l . 6 . This again indicates a non-linear viscous behaviour. Mater.

Sci. Eng., 9 (1972)

(10)

where B 1 is a constant at a given absolute temperature T, H~ the activation energy for flow, k the Boltzmann constant, A the projected area of the unit of flow on the shear plane, and ! the distance the shear stress acts iri surmounting the potential barrier. Accordingly, the shear strain rate becomes

,/ /°

10--

(H~/kT)s i n h - 1 (AH/kT)

exp(-H~/kT) s i n h ( A l z / k T ) .

(11)

In the case where the structure of the system is fairly rigid such as in the case of the amorphous phase (non-Newtonian flow), the value of z is large and hence Alz becomes greater than kT, i.e.,

sinh(Alz/kT) ~- exp

Alz kT

(12)

Accordingly, eqn (11) becomes

~y=B2exp[(-H~+vz)/kT)],

v=Al.

(13)

If the strain rate for steady state creep ~ is given by

D E F O R M A T I O N OF A M O R P H O U S Pd-20 at. % Si

159

TABLE 3 Activation energies for each of the creep components and calculated n(G,T)/N

Stress (kg/mm 2)

Steadystate HT(a )

Irreversible transient H,,a

H2, ~

n(a, T ) / N x 10 3 100° C

15 28 48 67

0.50 eV 0.46 0.43 0.41

150

175

200

0.16 0.47 0.92

0.12 0.28 0.83 1.41

0.24 0.46 1.16 2.63

0.30 0.60 1.99

-Average 0.09 eV

TEMPERATURE (°C) 175 150 ~) I

200 I

-15

0.26 eV 0.26 0.29 0.32

125

125 I

0.27

The stress dependence of the activation enthalpy is usually expressed by the activation volume, i.e.,

I00 a

~)~ __ _dn~.

\,

do Hence

-'°

",o, r',

\

_,-,_

r',

R,_ ",o, \%o

,8_ 20

(~ In i7~

\ t 21

v=kT\~.a

",%

\

"

\

=1

J 22

23

2.4

2.5

2.6

xlO-5

"~ (°K)

Fig. 14. Arrhenius plot of the strain rate for steady state creep at various stresses.

eqn. (13), one may write for i~ i 7 = A 2 exp

kT

(14)

The plots of In ir versus 1/T for various stresses (Fig. 14) show good linearity with a small stress dependence of the enthalpy. The values of H~(a) shown in Table 3 are all about 0.5 eV which is about one-sixth the self diffusion energy for Pd (2.8 eV) 3. This value is also close to that of the activation energy (l 2.0 kcal/mol 4) for viscous flow in liquid Ni. Because of the proximity of Ni to Pd in the periodic table, the value for liquid Pd is not expected to differ markedly. Mater. Sci. Eng]. 9 (1972)

/T.

(15)

The activation volume so calculated was 15 cm3/ mol (25 /~3) or about the volume of one atom. Considering these values for the activation energy and activation volume, it is reasonable to assume that steady-state creep of the amorphous phase is due to the transfer of atoms from those in the heap arrangement (Bernal sense 5) across distances of or just less than one lattice spacing in order to relax the applied stress. We will have more to say about this process in later pages. On the other hand, the transient creep consisting of a reversible part and an irreversible part will be explained in the terms of an amorphous structure. Investigations on a number of amorphous alloys indicate that these solids are indeed glasses which differ from microcrystalline solids in that their structures are quite similar to those of liquid metals 6 - 10 It has been shown by Scott et al. 11 that an assembly of randomly packed spheres can represent certain features of the geometry of simple liquids. Thus, a box, constructed with hinged end plates and walls dimpled to prevent initiation of regular packing at these surfaces, packed with 16,000 ~-inch steel balls at random in '~loose" packing was oscillated. They noted that the volume of packing decreased after about 100 oscillations and reached a constant value. The mean density above the random close packing indicated the presence of "regular" packing which grew as crystals in a "liquid" (Fig. 15). While an array of steel balls either as random

160

R. MADDIN, T. MASUMOTO OBSERVED PACKING DENSITY AFTER IOO SHEARING OSCILLATIONS OF VARIOUS SHEAR ANGLES

>" I.- 0.66

0~0-.~0%.

- -

w

0.64

/

\o

F

RANDOM LOOSE PACKING

--~ 0.62 I-.J

0.60 1 I0

I

20

I

50

I

40

I 50

MAXIMUM HALF ANGLE OF SHEARING, 0 (deg)

Fig. 15. Corrected mean packing density after shearing showing evidence for regular packing only for limited range of maximum shear angle.

loose packing or as random close packing both in the Bernal 5 sense will not have many of the characteristics of an amorphous structure, the fact that alloys such as Pd-20 at. ~Si are able to form the solid amorphous structure requires that the atoms pack together in a manner similar to the hard spheres of Scott et al. and Bernal. Polk 12 considers that the jamming of atoms can be expected to be more probable for the noble and transition metals with their relatively large cores than for other metals. Polk goes on to state that the introduction of another kind of atom, e.9., Si (in Pd-20 at. ~Si), into the holes of the Bernal structure should further mechanically stabilize the structure. We, therefore, consider it reasonable to adopt a structural model of this type in order to understand the time-dependent characteristics of the flow. The electron diffraction results of the amorphous phase aged into the stage showing "incipient crystallization" indicated a "granularity" of about 50 A in diameter 1. This increase in the intensity of the granularity on aging is considered to be due to the fact that regular regions present in the amorphous alloy acquire a stronger contrast as a result of some degree of ordering of the atoms within their boundaries. With the application of stress at temperatures below the crystallization temperature, the "granularity" grows to reach a constant size for a given temperature and stress, as indicated from the Scott et al. experiment. Consequently, we start with a random close packing of palladium atoms with holes in which there are located Si atoms. The application of a stress Mater. ScL Eng., 9 (1972)

induces atoms from the random close packing to transfer forming "regular" crystalline arrays which grow with time as the stress is applied. Accordingly, we consider that the irreversible transient creep occurs by the movement of atoms which transfer to a more stable position, resulting in an increase in the size of "regular" packed regions. This occurs in a relatively short time, i.e., less than 60 min, as seen in Fig. 12, and creates an arrangement in which these same atoms can no longer take part in the irreversible flow (as shown in Table 1). Using a model for the irreversible flow based upon this mechanism, the total number of movable atoms per unit volume moving in the direction of shear by action of temperature, T, and stress, a, is n(a, T); the points exhausted with time without new ones appearing. The change in n(a, T) for time, t, becomes

dn(a, T)/dt = - k n (a, T).

(16)

Consequently, the number of atoms which have moved at a time t is n(a, T ) [ 1 - e x p ( - k t ) ] ,

k = 1/z

(17)

where z is the relaxation time and is given by z = z o exp (H2/kT)

(18)

Here, if the motion of each atom contributes the same amount of strain, the strain is given by

= a2b/2n(a, T)[1 - e x p ( - t/z)]

(19)

where b is the distance moved by one atom and a is the atomic diameter. Since b ~ a and, hence, a 2b~- 1/N where N is the total number of atoms per unit volume,

e = n(a, T)/2N [1 - exp ( - t/z)].

(20)

Here, n (a, T) for unit time is given by

n(a, T) = N O exp [ - H, (a)/kT]

(21)

where No is a constant. From plots of the logarithm of e~ values versus 1/T (Fig. 16), the values for H1,p were determined (Table 3), being about 0.3 eV. In a similar way, plots of the logarithm of the relaxation time versus 1/T give the values H2, p (shown also in Table 3) being about 0.1 eV with relaxation times in the range of 15 ,-~20 min for 100° C ~ 200° C. On the basis of these values n(a, T) is calculated and shown at various temperatures and stresses in Table 3. Consequently, the total atoms contributing to the irreversible strain is in the ratio of a few atoms per 1000.

DEFORMATION OFAMORPHOUS TEMPERATURE 200

-5 - -

175

I

Pd 20 at. °', Si

(°C)

D : dkT/tlA

150

I

125

I00

I

I

I

0

\ -6

-.... 20

[

I

I

I

I

I

21

22

23

24

25

26

x l O "3

/ (OK) T

Fig. 16. Arrhenius plot of the equilibrium strain for the irreversible strain component at various stresses.

On the other hand, it will be considered that the reversible flow takes place in "regular" regions and can relax only after longer times (r~ = 170 ~ 300 rain in the range of tested temperatures). The "regular" regions are strained only elastically since they are stronger than the array of randomly packed atoms. The relaxation of these elastic strains will occur by the relaxation of the surrounding randomly packed atoms. As previously mentioned, the steady-state creep will be induced by the migration of atoms in a randomly packed array. From the values of these strain rates, the viscosity, t/, was calculated as l 01 5 ~ 1016 poises. For example, q at 500 ° K without stress is 1.0× 101~' poises, somewhat lower than those for common crystalline metals, 1022~102s poises. This value, however, is near the value at the boundary between solid and liquids ~3, i.e., rL= l01¢~ - 1 0 ~s poises. The diffusion coefficient can be estimated by REFERENCES T. M a s u m o t o and R. Maddin, Acta Met., 19 (1971) 725. R. B. Pond, Jr. and R. Maddin, Trans. AIME, 245 (1969) 2475. N. U Peterson, Phys. Rev., 136 (1964) A568. M. F. Culpin, Proc. Phys. Soc. (London), [B] 70 (1957) 1069, 1079. 5 J. D. Bernal, Proc. Roy Soc. (London), 2804 (1964) 299. 6 H. S. (?hen and D. Turnbull, Acta Met., 17 (1969) 1021.

I 2 3 4

Mater. Sci. E,lg., 9 (1972)

161

(22)

where d is the average distance between layers of flow and A is the projected area of the unit of flow on the shear plane. Using this equation, the diffusion coefficient in the amorphous phase was calculated to be 2.3 × 10 - 2 2 cmZ/sec at 500° K (5 × 10 29 cm2/sec at 500° K in crystalline palladium). We also obtained 0.5 eV as the activation energy of the steady-state creep and about 0.3 eV as that for the irreversible flow. These values are quite low compared with the activation energy for selfdiffusion of Pd atom. Unfortunately, the measured value of the activation for flow in liquid palladium was not available but from the fact that the elements are relatively close and in the same group in the periodic table as Ni, it seems justified to say that the activation energy for viscous flow in amorphous Pd Si alloy will be about 0.5 eV (i.e., using, as comparison, the value for liquid nickel ( - 0 . 5 2 eV)). Considering this viscous nature of the amorphous phase, it seems reasonable that the region adjacent to the cracks in the amorphous alloy, that is, in the highly stressed parts of the failed section (as shown in the earlier paper1), shows traces of viscous appearances. For example, the strain rate at a stress of 500 kg/mm 2 and 0°C was estimated as about 5 x 10 ¢ sec- 1, a value for which viscous flow does occur.

We, therefore, conclude that the "amorphous" state of these alloys is characterized by an arrangement of atoms in a random close-packed structure within which there are regular packed regions. The action of a stress at an elevated temperature produces an anelastic strain accompanied by a reversible, an irreversible and a viscous flow. ACKNOWLEDGEMENT

This work was sponsored in part by the Navy through the Office of Naval Research, Contract No. N00014-67-A-0216-0019, and by the Advanced Research Projects Agency of the Department of Defense. 7 B. Bagley, H. S. Chen and D. Turnbull, Mater. Res. Bull., 3 (1968) I59. 8 S. C. H. Lin, Phys. Status Solidi, 34 (1969) 469. 9 P. L. Matrepierre, .I. Appl. Ph)s.. 40 (1969) 4826. 10 G. S. Cargill, J. Appl. Phys., 41 (1970) 12. l 1 G. D. Scott, A. M. Charlesworth and M. K. Max, Letters to the editor, J. Chem. Phys., 40 (1966) 611. t2 D. E. Polk, Scripta Met., 4 (1970) I17. 13 E. U. C o n d o m Am. J. Phys., 22 (1954) 43.

162

R. MADDIN,T. MASUMOTO

DOformation d'un alliage amorphe palladium-20 a t . ° silicium

Die Verformung yon amorphem Palladium-20 A tomprozent Silizium

Les auteurs ont 6tudi6 l'influence de la contrainte et de la temp6rature sur les propri6t6s m6caniques qui d6pendent du temps: effet de la vitesse de d6formation sur la rupture, relaxation de contrainte, fluage et tra~nage 61astique. A partir de la cin6tique d6termin6e au moyen des essais pr6c6dents, ils ont propos6 un mod61e qualitatif expliquant le passage de l'6tat amorphe ~ l'6tat cristallis6. D'apr~s ce mod61e, les atomes se r6arrangent en ~lots cristallis6s ~ partir d'un empilement compact d6sordonn6 du type de Bernal. Ces Tlots croissent ensuite sous Faction de la temp6rature, de la contrainte et du temps.

Die Zeitabhangigkeit mechanischer Eigenschaften von amorphem Pd-20 At.~o Si, d.h. der Zusammenhang von Dehngeschwindigkeit und Bruch, Spannungsrelaxation, Kriechen und Eigenschaften der elastischen Nachwirkung wurden sowohl als Funktion der Spannung als auch der Temperatur untersucht. Auf der Grundlage der aus diesen Versuchen entwickelten Kinetik konnte die viskose Natur der amorphen Phase erklart und ein qualitatives Modell ffir den Obergang von der amorphen zur kristallinen Phase vorgeschlagen werden. Dieses Modell geht davon aus, dab Atome aus einer Bernal r.c.p. Anordnung in eine Anordnung kristalliner Inseln fibergehen, die mit zunehmender Temperatur, Spannung und Zeit wachsen.

Mater. Sci. Eng.,9 (1972)