Role of composition in metallic glass formation

Role of composition in metallic glass formation

ROLE OF COMPOSITION C. H. BENNETT,S;$ IN METALLIC D. E. POLKfsll GLASS FORMATION* and D. TURNBULL? This paper surveys some ideas on the glass ...

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ROLE

OF COMPOSITION C. H. BENNETT,S;$

IN METALLIC D.

E.

POLKfsll

GLASS

FORMATION*

and D. TURNBULL?

This paper surveys some ideas on the glass forming tendency of monatomic systems. According to the free volume model, glass formation in such systems would result primarily from “jamming” due to the action of repulsive forces. From this viewpoint the metals most prone to glass formation should be those in which the repulsive part of the pair potential is, relatively, the largest; these are the noble, transition and polyvalent metals. Actually t.he most stable metal glasses formed so far are alloys of noble or transition metals (A) with compositions predominantly in the range A,23 to A,B where B is a metalloid. The A elements may form a skeleton having a Bernal dense random packed structure which may be somewhat stabilized by filling its holes with metalloid atoms in the manner suggested by Polk. Some additional ideas on the effect of alloying on metal glass forming tendency are discussed. ROLE DE LA COMPOSITION DANS LA FORMATION DES VERRES METALLXQUES Les auteurs examinent quelques id&s au sujet de la tendance a la formation d’un verre presentBe par les systemes monoatomiques. D’apres le mod& du volume libre, la formation dun verre dans ces systemes resulterait, d’abord d’un “6crasement” dQ a l’action des foroes de repulsion. Lcs metaux les plus enclins a la formation dun verre seraient done ceux dans lesquels la partie repulsive du potentiel de paire est relativement la plus importante, cad les metaux nobles, 10smetaux de transit,ion et les metaux polyvalents. En r&alit& les verres metalliques les plus stables form&s jusqu’~maintenant sont des alliages des m&aux nobles et des metaux de transition (A), avec des compositions comprises surtout emre A,3 et A,B, oit B est un metalloide. Les elements A peuvent former un squelette ayant une structure dense de Bernal dist,ribui?e au hasard pouvant etre quelque peu stabilisee par remplissage de ses trous par les atomes de metalloide de la maniere suggeree par Polk. Quelques id&es eomplementaires au sujet de l’effet de la formation de l’alliage sur la tendance a former un verre metallique sont discutees. DER

EINFLUR

DER

ZUSAMMENSETZUNG GLASER

AUF

DIE

BILDUNG

METALLISCHER

Die vorliegende Arbeit gibt einen Uberblick iiber einige Vorstellungen iiber die Tendenz monoatomarer Systeme zur Bildung eines glasartigen Zustandes. Im Model1 des freien Volumens ist die Glasbildung in solchen Systemen hauptsachlich eine Folge des “jamming” aufgrund der Wirkung abstofiender Kriift. Unter diesem Gesichtspunkt wiirde man Gl~bildung in solchen Metallen erwarten, bie denen der abstoi3ende Term des Paarpotentia~ relativ am gri%ten ist, d.h. bei den Edel-, ~bergangs-und mehrwertigen Metallen. TatsiLchlich sind die stab&ten, bisher bekannten Metallglaser Legierungen der Edel- und Ubergangsmetalle (A) mit Zusammensetzungen im Bereich A,B bis A$? (B ist ein Metalloid). Die A-Elemente kennen ein Skelett bilden, das durch Ausfiillen der Hohlraume durch Metalloidatome in der van Polk vorgesohlagenen Weise stabilisiert wird. Einige weitere Vorstellungen tiber den Einflul3 des Zulegierens auf die Bildung van Metallglasern wird diskutiert. ROLE

OF

COMPOSITION IN GLASS FORMATION

METALLIC

Certain metallic alloys have been put into the amorphous solid form by various deposition technique&5) or by quenching their melts.f64~ Also it has been established that alloys with compositions near Pd,Si or Au,Sir,,Ge,,s can exhibit both the thermal and rheological manifestations(g-ll) of the glass t+ liquid transition. However, it appears that amorphous solid bodies, consisting of a pure metal, have been made in only a few instances and they exhibit quite a low resistance to c~stal~zation, even at very low temperatures. This paper will describe some ideas on how composition affects the tendency towards amorphous solid formation in metal systems. CEassform+

tendency iw rpuremanatamic systems

Cohen and Turnbu~(13) suggested that the Bernal dense random packed (DRP) structure may properly model an amorphous monatomic Van der VVaalssolid. * Received June 23, 1971. t Harvard University, Division of Engineering and Applied Physics, Cambridge, Massachusetts. $ Now at: Solid Stato Division, Argonne National Laboratory, Argonne, Illinois. 8 Now at: Allied Chemical Corporation, Box 3004. Morristown, New Jersey 07960. /IXerox Corporat,ion Fellow 1970-1971. ACTA

METALLURGIC&

VOL.

19, DECEMBER

1971

Experimentally, a DRP structure of uniform hard spheres appears to be internally stable, but there is no theo~tical proof of this. Bernal and coworkers pointed out that, ideally, the DRP structure can be described as an admixture of crystallographic and non-crystallographic Voronoi polyhedra (or WignerSeitz cells). Apparently, it is the non-crystallographic configurations, such as pentagonal dodecahedra, which tend to stabilize the amorphous structure. With these configurations present, crystallization can occur only by a reconstructive process. If the atomic cores are not infinitely hard, there also will be an energetic contribution to the stability of the DRP structure. In particular, when only two-body nearest neighbor interactions are considered, Franku5) showed that the minimum potential energy of an atom is substantially less when it is in icosahedral coordination than when it is in either of the local coo~inations found in crystalline close-packing. This result contrasts with that for a two-dimensional system of semi-hard discs where the minimum energy configurationof adisc would correspond to that in crystalline close-packing, It has been shown’16s17)that a structure, closely approximating the DRP in configuration and density is generated by sequentially adding uniform spheres to an initially very small cluster of spheres, where each 1295

ACTA

1296

sphere

is added

closest

to the center of gravity

at the surface

structure so generated

METALLURGICA,

position

which

lies

of the cluster.

by Bennett’l’)

The

contained

4000

spheres, and its density was within 4 per cent of that, 86 per

cent

of

the

ideal

crystalline

close

packed

VOL.

crudely, free

19,

1971

the system

volume

must

model

the jamming

of

is associated

decreasing

one option for the placement

diffusivedisplacements,

that

the

of the next sphere.

configurational

system is indeed very small. with the described

entropy

It is also important

procedure,

the formation

ity is much greater for the amorphous crystalline

structure.

This

of

the that,

This reflects the rather special

nature of the local configurations

in crystalline

close

(to the crystal)

density

though high, is not as high as those of the of tetrarandom network structures(1s-20)

ideal

hedrally

coordinated

systems

which

per cent of the crystal values.

are within

the

random

differences

This suggests that the

network

and crystalline

However,

glasses.

in energy and volume close packed

between

smaller the softer is the pair repulsive

i.e.

owing to

Indeed,

Weaire

et a1.‘21’ have shown, assuming a pair potential

having

the form

of the Morse function,

in volume becomes

out by Frank.‘15)

between

the DRP

substantially

hard sphere systems and is only potential

that the difference and

CCP

as the potential

assignments

is made softer

of 0 to 5 per cent

considered

plausible

with for

a

number of metals. is determined

model

by the volume

This means

that in any phase

would

stay

constant

would

shift.

for metals,

Actually,

change

the volume

the

of the system. the volume

while the interatomic

change in transformations

spacing

and energy

do

from one metallic phase to

another, but the changes, especially for the metals which conform best to the free electron model, are relatively

small.

by the interatomic

We expect,

therefore,

repulsive

centers, the higher the interatomic potential

tude of the order of a few kT. are the atoms,

at a given

spacing

reaches a magni-

That is, the ‘Lharder”

temperature

and atomic

the smaller is v~.

atoms are probably transition

the “hardest”’

metal forming

those which form the noble and

metals.

These

elements

have the largest

bilities are considered to be determined core-core

interactions

density.(24)

that the in-

principally

Thus, they would be expected T,,

high glass temperatures,

here defined

as the temperature

viscosity

the

of

by

rather than by the free electron

liquid

reaches

to exhibit

where

T, is

at which the shear a specified

value,

e.g. 1013 P. In metals, such as Na and Al, which conform

more

nearly to the nearly free electron model, the repulsive of

the

pair

the decreased lombic

potential

screening

repulsion

ion pair separation decreases. problem.

acting

ions.

tendency

This

primarily

from

of the interionic

by the conduction

tion of this potential difficult

arises

out

electrons

The theoretical

has proved Qualitatively,

increase with the product

In the simple free electron energy

low

with decreasing vuf.The magni-

is at which this repulsive

part

structures

less than the 16 per cent for

of the order

of critically

to be essential for

potential and it will be less, at a given average density

relatively

will be

potential,

the less steeply it rises with pair separation, the effects pointed

the

the DRP

(CCP) structures

of the

ratios of ion core to atom radii and their compressi-

2-3

relative stability would be much less for the DRP than for

with the vanishing

presumed

From this viewpoint,

of the DRP

structure,

In the

Turnbu11,(22~23)

of occurrence

tude of V~ is determined

volume,

packing. The relative

probability

values of local density,

of atomic

probabil-

than for the

“jammed”. and

correlation factor for atomic transport with decreasing average free volume, vf. This effect follows from the

density, reported for DRP. Bennett noted that at all stages in the assembly of this structure, there was only indicates

have

Cohen

couas the

evalua-

to be an extremely it is expected

to

of the charges on the inter-

means

that

the

glass

forming

and T, of these metals should increase with

increasing metallic valence ; for example,

T, should be

higher for Al than for Na. The viscosity

behavior

with these qualitative

of liquid metals is in accord considerations.

the order of the viscosities,

In particular

as well as their temper-

ature dependences. of liquid meals is: transition and noble metals, polyvalent metals, alkali metals.(25) The

crease in energy and volume accompanying the transformation of a good metal from the crystalline to

thermodynamic

a DRP

too is stabilized, in part, relative to the liquid by the core jamming tendency.

positioning

of atomic

small, as indeed they process of melting.

centers would be quite

are in the somewhat

However, the formation

similar

of a metal glass with a DRP

structure requires not only the proper positioning of atomic centers, but also that the shear viscosity have reached

a value in excess

of 1015 P;

i.e. to put it

melting temperatures

also are roughly

in this order which reflects that the crystalline

solid

Effects of alloying on glass forming tendency Actually,

experience

had indicated

that the amor-

phous solid alloys which resist crystallization

to the

BENNETT

highest temperatures and

transition

[email protected],a)

et al.:

are principally

metals.

found

COMPOSITION

For

that

metals often deposit

Mader

admixtures

as amorphous

resist crystallization

based on noble

example,

vapor

AND

and

of these

solid films which

to room tem~rature

and above.

METALLIC

CLASS

1297

FORMATION

suggested that this effect might be the primary one for stabilizing

alloys in their amorphous

However,

solid form.

the stability of the amorphous

of alloys of the A,B-A,B for so easily

type cannot

in terms

solid state

be accounted

of the hard sphere

concepts.

have generally

range

constit,[email protected])

metal

well as those of NisP to N&P, differ only by 5-10 per

A,B to A,B

fallen

within

the composition

where A is a noble or transition

element and B is a “metalloid”

such as B, C, Si, Ge

For example,

packing

Also, the alloy glasses formed by quenching liquids(6-8)

cent.‘26)

of the amorphous

Moreover,

the density

by Cargill showed

or I?. It is well known interpret

the

systems

that it is extremely

diffra&ion

definitively.

of

The behavior

uniquely a particular exclude

behavior

difficult

to

amorphous

cannot

establish

structural model though it may

certain ones.

Cargill(26) tested carefully

the

the rnetal~~c volumes

that

solid

of the

[email protected],

measurements

the volumes

as made

of amorphous

N&P to N&P are only B-14 per cent larger than the values

calculated

by simply

summing

volumes of the constitutents. the ion cores of B type

the metallic

However, the volume of atoms

are small

relative to their metallic atom volumes,

enough,

so that they

agreement of some selected models with the reported

could be placed in the larger holes of the DRP structure

X-ray interference

without appreciable

alloys, including Ni,P-N&P.

functions

of some amorphous

He found

t,hat the results

models.

Later,

the pair distribution recent

determination(2s)

(PDF) calculated

that the split in the second which

that from

agreement with Pinney’s of the PDF of the DRP

The most impressive

solid PDF,

in

of the defective

Cargill(27) demonstrated

functions

these results are in good structure.

are not

feature of this test is

peak of the amorphous

does not appear

in the PDF

of

liquid metals, is well fit by the DRP model. admixture

greatly

of metals toward amorphous

increases

the tendency as well as

solid formation

the resistance of these solids to crystallization? following (1) the

two possibilities degree

solid, relative position,

decrease

crystallization According solid

by

the

kinetic

of amorphous

const.ants

the

for

the

cording to Polk’s

analysis,

holes to accommodate atoms

with

one B atom for every four A

interatomic

A-B

will

be

Ac-

there are enough of these spacings

which

are

quite close to those observed in the 14-B intermetallic crystalline

compounds.

For example,

Pd,Si

is only

sponding holes

3-4

per cent

separations

of the DRP

showed

the average of

separations(~) larger

in crystalline than

with Si placed structure.

Thus,

the optimum

state stability would seem

accord

that Cargill’s

the eorre-

in the idealized

with experience.

density

observations

Polk

on Ni-P

can be accounted

for, w&h the reported average Ni-Ni

nearest neighbor

spacing, if up to 60 per cent of the

large holes are filled with P atoms;

in alloys with a P

to Ni ratio greater than that] (0.15) permitted spacing

solids,

are placed in the larger holes of this structure.

in good

(21

amorphous

A,B

is formed primarily by the A atoms while the B atoms

to be A,B,

solids.

interatomic

to

A,B

in turn:

to our model in the regime of amorphous

formation,

of

for amorphous

addit,ion ;

overlap.

to which the skeleton of the DRP structure

composition

of the amorphous

impurit,y

structure

according

The

to t,he stable crystal at the same eom-

is decreased

impurities

will be considered

of metastability

the

the six shortest8 Pd-Si

We non consider the problem : why is it that some impurity

core-core

This is the basis of a model proposed by Polkur9) for

his own results on electro-deposited

agreement with the selected vacations crystal

solid

arrangement incorporated

the

excess

P

was

in the DRP skeleton.

considered

by this to

be

Thus in this model

contlrolled principally by two body repulsive forces rather than by the free electron density. Thus, a pure metal in an amorphous solid state would be prevented

with “soft” atoms, having strong interactions with A, in a manner analogous to the st,abilization of the well-

from min~izillg

known clathrate structures by putting inert molecules

the energy of coulombic

interaction

the DRP

structure is stabilized

by stuffing the holes

between the free electrons and ion cores by the large

in the larger holes.

two body repulsive

not imply that the AA repulsive potential is infinitely

potent’ial.

In this situation,

the

We note that Polk’s model does

energy of the amorphous solid might be reduced by impurity admixtures which would increase the atomic packing density. Mader and Nowick(3) pointed out

hard. It only requires that’ it be much harder than that between AB pairs.

that certain amorphous assemblies of hard spheres in which the sphere diamet,er is non-uniform may have

type alloys, from their pure metallic have quite large negative values.(9-11)

substantially higher densities of sphere centers than an amorphous assembly of uniform spheres and they

systems (e.g. Au-Si, Ni-P, Pd-Si) exhibit abnormally deep eutectics at compositions near A,B. The relatively

Actually

the heats of formation

of the A,B-A,B liquid states, Most of these

ACTA

1298

high

amorphous

state

compositionmay

stability

METALLURGICA,

of alloys

with this

reflect the geometric stabilizing factor

noted by Polk as well as strong A-B interactions.

Their

very low eutectic temperatures bring these alloys much closer to the temperature regime of glass formation while still in their range of liquid stability. We have noted that amorphous apparently crystal

offer

little

seeds but impurity

retards this growth. some

impurity

spacing

occur.

had been

have

tional disorder,

for

suggested

of

greatly

than

at least

one

crystallization

to

that glass forming

to a large degree of composi-

may actually

amorphous

often

to move

in order

alloys, when constrained their

to the growth

admixture

This difference may reflect that

atoms

interatomic

It

films of pure metals

resistance

have a lower energy in

in their

crystalline

state.(ss)

Crystal growth might then be limited to the rate at which impurity atoms jump from one equilibrium position

to another

which

higher degree of local order.

leads, for example, to a The time constant for this

process would

to scale as the time con-

be expected

stant for diffusion or viscous flow.

We expect that it

would be much larger than that for the motion crystal-amorphous

solid

interface

which may occur by much

in pure

smaller atomic

of the

systems displace-

ments. ACKNOWLEDGEMENTS

We are pleased to acknowledge with Dr. Denis Weaire.

helpful discussions

This research was supported

in part by the U.S. Navy under contract No. N0001467-A-0298-0009

and by the National

ation under contract the Division Harvard

of Engineering

University.

Science Found-

No. NSF-GP-13888, and

and also by

Applied

Physics.

VOL.

19, 1971 REFERENCES

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