Influence of Composition on the Structur

Influence of Composition on the Structure and Properties of Fe-Pd-P and Ni-Pd-P Amorphous Alloys - CaltechTHESIS
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Influence of Composition on the Structure and Properties of Fe-Pd-P and Ni-Pd-P Amorphous Alloys
Citation
Maitrepierre, Philippe Louis
(1969)
Influence of Composition on the Structure and Properties of Fe-Pd-P and Ni-Pd-P Amorphous Alloys.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/8VCG-6E08.
Abstract
Ternary alloys of nickel-palladium-phosphorus and iron-palladium-phosphorus containing 20 atomic % phosphorus were rapidly quenched from the liquid state. The structure of the quenched alloys was investigated by X-ray diffraction. Broad maxima in the diffraction patterns, indicative of a glass-like structure, were obtained for 13 to 73 atomic % nickel and 13 to 44 atomic % iron, with palladium adding up to 80%.
Radial distribution functions were computed from the diffraction data and yielded average interatomic distances and coordination numbers. The structure of the amorphous alloys could be explained in terms of structural units analogous to those existing in the crystalline Pd
P, Ni
P and Fe
P phases, with iron or nickel substituting for
palladium. A linear relationship between interatomic distances and composition, similar to Vegard's law, was shown for these metallic glasses.
Electrical resistivity measurements showed that the quenched alloys were metallic. Measurements were performed from liquid helium temperatures (4.2°K) up to the vicinity of the melting points (900°K-1000°K). The temperature coefficient in the glassy state was very low, of the order of 10
-4
/°K. A resistivity minimum was found at low temperature, varying between 9°K and 14°K for Ni
-Pd
80-x
-P
20
and between 17°K and 96°K for Fe
-Pd
80-x
-P
20
, indicating the presence of a Kondo effect. Resistivity measurements, with a constant heating rate of about 1.5°C/min,showed progressive crystallization above approximately 600°K.
The magnetic moments of the amorphous Fe-Pd-P alloys were measured as a function of magnetic field and temperature. True ferromagnetism was found for the alloys Fe
32
-Pd
48
-P
20
and Fe
44
-Pd
36
-P
20
with Curie points at 165° K and 380° K respectively. Extrapolated values of the saturation magnetic moments to 0° K were 1.70 µ
and 2.10 µ
respectively. The amorphous alloy Fe
23
-Pd
57
-P
20
was assumed to be superparamagnetic. The experimental data indicate that phosphorus contributes to the decrease of moments by electron transfer, whereas palladium atoms probably have a small magnetic moment. A preliminary investigation of the Ni-Pd-P amorphous alloys showed that these alloys are weakly paramagnetic.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
(Materials Science) ; amorphous metallic alloys
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Duwez, Pol E.
Thesis Committee:
Unknown, Unknown
Defense Date:
17 March 1969
Funders:
Funding Agency
Grant Number
Atomic Energy Commission
UNSPECIFIED
Record Number:
CaltechTHESIS:02192014-085423804
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DOI:
10.7907/8VCG-6E08
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8084
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INFLUENCE OF COMPOSITION ON THE STRUCTURE
AND PROPERTIES OF Fe-Pd-P AND Ni-Pd-P AMORPHOUS ALLOYS

Thesis by
Philippe Louis Maitrepierre

In Partial Fulfillment of the Requirements
For the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California
1969
(Submitted March 17, 1969)

A MA FEMME ET
MES PARENTS

iii

ACKNOWLEDGMENTS

It has been a privilege to work under the direction of Professor
Pol Duwez, and I want to express here my deepest gratitude for the
guidance and encouragement with which he provided me.

I also thank

R. Hasegawa and Dr. Tsuei for stimulating discussions, and P. Bourgain,
L. Cyrot and R. Binst for assisting in some of the experiments.
I am grateful to the technicians of this laboratory for their
help and to Mrs. Sue Williams for her care and diligence in the typing
of my thesis.
The financial support of the Atomic Energy Commission during this
doctoral work is gratefully acknowledged.

iv
ABSTRACT

Ternary alloys of nickel-palladium-phosphorus and ironpalladium-phosphorus containing 20 atomic % phosphorus were rapidly
quenched from the liquid state.

The structure of the quenched alloys

was investigated by X-ray diffraction.

Broad maxima in the diffraction

patterns, indicative of a glass-like structure, were obtained for 13
to 73 atomic % nickel and 13 to 44 atomic % iron, with palladium adding
up to 80%.
Radial distribution functions were computed from the diffraction
data and yielded average interatomic distances and coordination numhers.

The structure of the amorphous alloys could be explained in

terms of structural units analogous to those existing in the crystalline Pd P, Ni P and Fe P phases, with iron or nickel substituting for
palladium.

A linear relationship between interatomic distances and

composition, similar to Vegard's law, was shown for these metallic
glasses.
Electrical resistivity measurements showed that the quenched
alloys were metallic.

Measurements were performed from liquid helium

temperatures (4.2°K) up to the vicinity of the melting points (900°K1000°K).

The temperature coefficient in the glassy state was very

low, of the order of

10~/°K.

A resistivity minimum was found at low

temperature, varying between 9°K and 14°K for Nix-Pd

_x-P

and

between 17 K and 96 K for Fex-Pd _x-P , indicating the presence
20
80
of a Kondo effect.

Resistivity measurements, with a constant heating

rate of about 1.5 C/min,showed progressive crystallization above
approximately 600°K.
The magnetic moments of the amorphous Fe-Pd-P alloys were

measured as a function of magnetic field and temperature.
ferromagnetism was found for the alloys Fe

True

-Pd -P
and Fe -Pd -P
48 20
36 20
44

with Curie points at 165 K and 380 K respectively.

Extrapolated

values of the saturation magnetic moments to 0 K were 1.70
2.10

respectively.

The amorphous alloy Fe

to be superparamagnetic.

-Pd

-P

~and

was assumed

The experimental data indicate that phosphorus

contributes to the decrease of moments by electron transfer, whereas
palladium atoms probably have a small magnetic moment.

A preliminary

investigation of the Ni-Pd-P amorphous alloys showed that these alloys
are weakly paramagnetic.

TABLE OF CONTENTS

Page

Part
I.

INTRODUCTION

II.

ALLOYS PREPARATION

Composition ranges and sintering

Quenching technique

Verification of the structure of quenched

specimens
III .

STRUCTURE INVESTIGATION BY X-RAY DIFFRACTION

Scattering of X-rays by an amorphous solid

Scattering X-rays by a polyatomic system

Radial distribution function, interatomic

distances and coordination numbers
3.

Direct interpretation of the diffraction

spectrum
B.

Experimental procedure

Treatment of data

Error treatment

Results

Nickel-palladium-phosphorus alloys

Iron-palladium-phosphorus alloys

vii

Part

Page
IV.

ELECTRICAL RESISTIVITY

Experimental procedure

Results

Low temperature measurements

High temperature measurements

CRYSTALLIZATION OF Fe-Pd-P AND Ni-Pd-P ALLOYS

VI.

MAGNETIC MOMENTS

Experimental procedure

Results

DISCUSSION

VII.

Structure of the quenched Fe-Pd-P and Ni-Pd-P
alloy phases

Magnetic moments in amorphous Fe-Pd-P alloys

103

Electrical resistivity of amorphous Fe-Pd-P

108

and Ni-Pd-P alloys
VIII.

SUMMARY AND CONCLUSIONS

114

REFERENCES

117

APPENDIX I

122

APPENDIX II

126

-1-

INTRODUCTION

During recent years a growing interest has been shown in the
study of non-crystalline solids, which have been alternately qualified
as ''glassy" or "amorphous''.

The main difference between amorphous and

crystalline solids resides in the absence of long range order in the
amorphous structure , although some type and degree of short range order
2 3 4
can generally be recognized ' '

In this respect, glasses may be

characterized as supercooled liquids

Differences between glasses

and supercooled liquids arise when other properties such as thermal
and electrical conductivities, density, etc. are considered.

Hence,

glasses constitute a type of solids with specific characters differentiating them from both crystalline solids and undercooled liquids.
Whereas silicate glasses have been known and investigated for
a long time, new developments have extended the field of amorphous
inorganic materials.

Experimental techniques such as high vacuum

6 7 8 9

vapor depos1.ti-on '

electrodeposition

and chemical deposition

have been successful in yielding amorphous phases of normally crystalline materials.

Direct attempts to obtain glasses by drastic cooling

from the 1 iquid state 12,13,14 at rates o f a b out 106o CI sec, have b e en
successful in yielding glassy structures in Au-Si
Fe-P-C

, Pd-si

alloys as well as in several tellurium base alloys (with

Ge, Ga, In)

Glass forming in these rapidly quenched alloys seems

to be closely related to the existence of d eep eutectics as well as
rather high viscosity in the liquid state.

However, only rathe r

-2-

narrow ranges of composition have yielded amorphous structures in
these systems.

This turned out to be a serious restriction in studying

the changes in the amorphous structure with composition as well as the
effect of composition on electrical and magnetic properties.
Alloys whic·., would contain at least one s t rongly ferromagnetic
element (Fe, Co or Ni) and would give reasonable chances of structural
continuity with changing composition were considered for this investigation.

The existence of rather low eutectics in the binary systems

Fe-P, Ni-P and Pd-P at about 20% atomic phosphorus (cf. Appendix I),
as well as the complete solid solubility of iron and nickel in palladium, was an important criterion for ·s tarting the investigation of
Fe-Pd-P and Ni-Pd-P ternary alloys.

Amorphous structures were success -

fully obtained by rapid quenching from the liquid state for Fe

-Pd

-P

to Fe -Pd -P
alloys and Ni -Pd -P
to Ni -Pd -P
alloys .
67 20
44
36 20
13
73
7 20
Strong ferromagnetism was shown in Fe
amorphous alloys.

-Pd

-P

and Fe

-Pd

-P

A study of the influence of composition on the

structure and properties of these amorphous Fe-Pd-P and Ni-Pd-P alloys
is the object of the present investigat i on.

-3II.

ALLOYS PREPARATION

Composition ranges and sintering
Ternary alloys of Ni-Pd-P and Fe-Pd-P were prepared from 99.99%

palladium powder from Engelhard Industries Inc., 99.9% nickel and
iron from Charles Harvey Inc., and red amorphous phosphorus from
Allied Chemical.

The phosphorus was kept in a dessicator to prevent

it from being hydrated.

After different trials, the composition in

phosphorus was set at 20 atomic % (except in one case were it turned
out to be only 15%), whereas the ranges of Ni-Pd and Fe-Pd were
explored .

The extent of the range of compositions was from 13 to 73

atomic % nickel and from 13 to 44 atomic % iron, for r e asons which
will be explained below.
prepared from carefully

Samples of 2 to 8 g in total mass were
weighed powders.

A thorough mixing of the

powders was performed before agglomeration under a pressure of 60,000
psi.

Phosphorus improved greatly the coherency of the pressed

briquets .

These briquets were sintered in two stages, in order to

insure an op t imum d e gree of bonding between phosphorus and the metallic
elements .

The following procedure was found to b e succe s s ful i n

reaching this objective.

The samples, placed in evacuated pyrex

tubes,we r e slowly h e at e d up to 350°C and kept for two days at temperature.

The py rex tub e s were subs e que ntly ope n e d to rel e as e whatever

gas pressure might be present , and the sample s were placed in evacuate d
quartz tubes.

The y we re h e at e d up to about 550 C for two more days,

to comple t e t h e sinte ring process.

The sintere d brique ts we r e the n

melt e d in a quartz crucible under arg on gas (induc tion furna ce ) and

-4-

the melted alloys were cast into rods by sucking the liquid alloy
into capillary quartz tubes 2 mm in diameter.

The absence of reaction

between the melted alloy and the quartz tubes attested to the high
degree of bonding between phosphorus and metallic elements .
B.

Quenching technique
The "piston and anvil" technique used to quench the alloys from

the melt is described in references 12 and 13 and a schematic drawing
of this apparatus is given in Fig. 1.

The alloy is contained in a

fused silica tube 3 mm in diameter having a small opening at its
bottom end .

The alloy is melted by induction through the susceptor E.

The liquid globule is ejected by application of a small helium
pressure and quenching is achieved by squeezing the liquid drop
between the fixed anvil A and the moving piston B.
lined with copper-beryllium discs C.

Both A and B are

When the globule is released,

it cuts a light beam between a source G and a photocell H and an
appropriate delay circuit triggers the releas e of the finger F which
retains the piston B, which is actuated by a gas pressure of 200 psi.
The rat e of cooling is of the order of 10

C/sec

The resulting

samples are thin foils of about 2 em in diameter, and 30 to 40
thickne ss.

Typical sample appearanc e is shown in Fig. 2.

The se foils

ar e suitable for X-ray diffraction inv estigations as well ·as for
magnetic and electric al measurements.

The "lace like" edges of the

foils can b e d ire ctly used for transmission e l ec tron-mic roscopy,
though f or s uch inv e s t i g ations i t is pr e f e rabl e to thin down the
cente r o f t h e foil , whic h is mor e r e pres entative of the bulk o f the

-5-

(!)
........
II
II
II
II
II

,I
I'
II

9 •

II
II

I'
I'
II
II

""' r

:I:

I'
II

J :::::..

-6-

Fig. 2.

Typical quenched foil app earance

-7-

quenched sample.
C.

Verification of the structure of quenched specimens
The main drawback of the piston and anvil technique resides

in the difficulty to duplicate exactly the rate of cooling from one
sample to the other, though the order of magnitude is usually main~
tained.

Consequently, each quenched foil was checked by X-ray dif-

fraction with CuK

0.05 ) •

radiation and step scanning (one point every 2e

The foils were then classified as ''good", ''doubtful" and

''rejected''.

By ''good" it was implied that the diffraction spectrum

exhibited no definite crystalline peaks (Bragg reflections) but
instead large amorphous bands.

"Doubtful" were the samples with some

evidence of small crystalline peaks superimposed on the amorphous
bands.

"Rejected" were samples exhibiting well-defined crystalline

peaks.

In some cases, it appeared possible to suppress the crystal-

line peaks by removing a small layer from the top of the foil (about
1 to 5

~).

This result seemed to indicate that some small crystals

might have been nucleated on the surface of the quenched globule,
during the early stages of the quenching.
power of CuK

The lack of penetrating

radiation makes it particularly sensitive to surface

effects on the quenched specimen .

As expected, MoK

radiation was less

sensitive to the presence of such surface crystallites.

Consequent ly ,

these two radiations were used concurrently to assert the truly amorphous character of the quenched specimens.

Only some ranges of compo-

sition yielded amorphous diffraction bands.

For Nix -Pd _xP
alloys
80
20

-8-

the range of x allowed varied from 13 to 73 (Pd consequently going
from 67 to 7 atomic %) whereas for FexPd _xP
the range appeared
20
80
smaller with x varying from 13 to 44 (Pd consequently ranging from
67% to 36 atomic%).
The chemical composition of some of the samples was checked
after quenching from the melt, and found very close to the initial
composition before sintering.

Table I gives the result of the chemical

analysis performed on about 0.5 g to 1 g of quenched samples in each
case, as well as the complete range of amorphous structure in both
Fe-Pd-P and Ni-Pd-P systems.

-9-

TABLE I
AMORPHOUS ALLOYS IN THE IRON-PALLADIUM-PHOSPHORUS
AND NICKEL-PALLADIUM-PHOSPHORUS SYSTEMS

Alloy designation

Initial composition

Actual compositior

before sintering

a·f ter quenching

(at.%)

Ni32-Pd53-Pl5

32.2

52.8

15.0

Ni43-Pd37-P20

42.8

36.9

20.3

Ni53-Pd27-P20

53.0

27.5

19.5

Ni63-Pd17-P20

62.2

16.5

21.3

Ni73-P7-

72.6

7.4

20.0

Fe13-Pd67-P20

Fe23-Pd57-P20

Fe32-Pd48-P20

32.4

47 . 6

20.0

Fe44-Pd36-P20

43.9

35.7

20.4

-Pd

-P

p20

-10-

III.

STRUCTURE INVESTIGATION BY X-RAY DIFFRACTION

The amorphous Fe-Pd-P and Ni-Pd-P alloys under consideration
allow rather large variations of composition.

Interatomic distances,

in these alloys, may be expected also to vary substantially with
composition, yielding valuable comparisons with possible models.
Diffraction studies with X-rays are particularly suitable for investigating disordered structures because of the informations they provide
on interatomic distances as well as on the average ligancy of the
atoms.

The diffraction s~ctrum of amorphous alloys leads, after the

appropriate corrections, to an interference function.

This function

can then be used, through a Fourier transformation, to yield an atomic
or electronic radial distribution function.

This is a rather straight-

forward procedure in a monoatomic system, but requires some approximations in binary and ternary systems.

In any case, the numerical

Fourier inversion of the diffraction data requires the use of a
computer.

The program used for the computation of the radial distri-

bution functions (RDF) of Fe-Pd-P and Ni-Pd-P amorphous alloys is
described in appendix II.
A.

Scattering of X-rays by an amorphous solid
The total scattered intensity It (in arbitrary units), at a

given angle, consists of the coherently scattered intensity I

plus

the modified intensity Iin(Compton scattering) and a background intensity Ib.

All of these are also affected by a polarization factor P(2e)

and an absorption factor A(2e).

It is given by the following equation:

-11-

The most important term is the coherently scattered intensity I

, which

leads to the radial distribution function .after the derivations described in the following paragraphs.
1.

Scattering of X-rays by a polyatomic system
The formula for coherent scattering was given by Debye

under the assumption of equal probability for all orientations of
any given interatomic vector.

The scattered intensity, in electron

units, is:

= ~ ~ f n f m(sin srnm/sr nm )

(1)

n m

where s

= 4~ sin S/A and r nm is the interatomic distance between atom

n and atom m, the summation being extended to the entire solid.
Equation (1) can be rewritten as:

I h (s)

= N [ ~ x. f.

+ ~ x.

~ f.1 f.J (sin sr 1]
.. I sr .. ) J
1]

(2)

j~i

where N is the total number of atoms in the sample and xi is the atomic
concentration of element i.

In the present case i goes from 1 to 3

(that is P, Ni, Pd) and j means all the atoms in the system except
the chosen atom i.

The atomic density functions pij(r), which

give the number of atoms of type j at a distance between r
from an atom i, can be introduced through the integral
dr.

• rl

and r

4nr pi.(r)

The p .. (r) are obviously spherically symmetrical by definition,
1]

-12-

which is consistent with the assumptions of the Debye's formula.
Equation (2) becomes:

(3)

where i = 1,2,3 an6 k = 1,2,3 also, with l=P, 2=Ni and 3=Pd.

Intro-

ducing p , which is the average density of atoms, it is possible to

correct equation (3) in the following way:

where the last term is the small angle scattering of the uniformly
dense material and is not experimentally observed: hence, it must be
subtracted from I h to give I
h' which can then be related to the
co
experimentally observed coherent intensity.

Finally, the structure

sensitive intensity is (per atom, in electron unit):

-(~ x.fi)

J0 4rt rp 0 sin sr dr
sr>

All the fi and fk are functions of s, so that all the integrals in the
double sum depend

on s in a diffe rent way.

It is the refore impossible

to g et the distribution function as a result of a dir e ct Fourier

-13-

inversion, as in the case of a monoatomic system.
solution was provided by Warren

An approximate

and has since been commonly used

It consists of assuming that a reduced scattering factor f
defined and used for different

elen~nts

22,23

(s) can be

such that:

where Ki is approximately equal to Zi, number of electrons of the
scatterer i .

A typical selection is:

(s) = ~ xif.(s)/~ xizi

This is usually a rather good approximation, as it was found in the
present investigation.

Equation (5) becomes:

- (~ xiK. )

This equation shows that s(I

f' 4:J(rp sin sr dr

(6)

h(s) - ~ x f. )/f
= sl(s) is the
co
i ~

Fourier transform of:

Performing the Fourier transformation leads to:
4:J(r~ x ~ K.K pik(r)
ik ~ k

Let:

W(r)

4:J(r(~ xiK.) 2 p + 2/:J( J= sl(s) sin sr ds

(7)

(8)

-14-

The maxima of the function W(r) will corres pond to the averag e interatomic distances.

However, the interpretation of these interatomic

distances will require a more careful look at the distribution
sum of partial distribution functions .Z •

function, since it is a weighed
2.

Radial distribution function, interatomic distances and
coordination numbers
Equation (8) can be rewritten as:

W(r) =

4~r(p(r)

- p )

x.K.)

= ~I: wikpik(r)

with

(9)

x. K. K /(I: x.K.)

-1<

Hence p(r) appears as · an atomic density function which is simply
the weighed

sum of all the partial density functions pik (r).

The

actual radial distribution function is obtained by multiplying
equation (7) by r so as to y ield:

2r/n

• 0

si(s) sin sr ds + 4nr (:E x.K.) p

(10)

The interatomic distances can b e obtained by conside ring the maxima
6 23
of W(r), which is the Fourie r transform of s I(s) •

It i s W(r),

and not the final radial di s tribution function rW(r), which yields
the actual interatomi c distances, as its p e aks are left symmetrical
and unshifted by the us e o f modification factors such as 1/f
a damping factor exp(-a s ) in th e functions I(s).
cons eque nc e o f the d e finition

o f p(r)-p

45 .

(s) or

This also is a

Howev e r, some authors

-15-

have sometimes considered the maxima of r W(r) as meaningfur ,
especially when the peaks of the RDF appear rather symmetrical.

These

can be related to the center of the shell represented by the peak and
the ·mean interatomic distances given by this procedure will also be
and r ,
.r2
from the definition of p ,pik(r) and p(r), the integral
4:rrr p (r) dr
can be related to the number of atoms at distances between r and r
considered.

If there is a discrete peak in the RDF between r

from an atom taken as origin.

Actually, the meaning of this number

appears more clearly by writing p (r) explicitly:

A =

Let J~~ 4:rrr

.r 2 4:rrr 2 p(r)dr
Jrl

pik(r) dr = nik' that is the number of atoms k at a

distance between r

and r

from an atom i.

Then

In this expression, the nik are the coordination numbers, A is an
experimental ~antity equal to the area under the peak divided by
(~

x.K) , and the w.k can be computed from equation (9).
1.

From here

on, the nik can be obtained through certain assumptions or approximations .

A rather frequent case is the one for which the peak in the

RDF is believed to be only due to ij pairs.

Equation (11) then reduces

to:

(n . . xi + nJ.i xJ.) K. K./ (L: x.K . )
1.]

-16-

which, if there is no short range order (ni/xj = nj/xi), reduces
further to:

Another assumption (which will be used later) is that of equal atomic
densities of j and k around atoms j and atoms k.

Namely:

Then the following relationships are verified:

It can be noticed that nkj = njj and njk = ~k' which is consistent
with the h y pothesis of no short range orde r for atoms j and k.
Equation (11) bec omes then (assuming that only j and k atoms are
involved):
A=

One can therefore obtain from the area unde r

(12)

the RDF curve, an average

coordination numb e r n for the pairs (j or k) -

25
(j or k)

This reduced

formula (12) will be u s ed later for Ni-Pd or Fe-Pd type pairs.

In the

case s of ov e rlapp i ng distributions, assumptions ar e made on the relative importance of, for instance pij and pjk' as it wi l l app e ar lat e r

-17-

in the case of phosphorus as i, and j and k as Ni and Pd (or Fe and Pd).
3.

Dir¢ct interpretation of the diffraction spectrum ·
The direct interpretation of the broad diffraction peaks

has sometimes been attempted, but it has often been a deceiving, if
not completely erroneous

27,28

, procedure.

This can be readily seen

from the Debye's formula giving the coherently scattered intensity
(equation 1):
Ich(s)

= ~ ~ f m(s) f n (s) (sin srmnIs r mn )

(1)

m n

where the summation is extended to all the atoms of the sample, and

is the interatomic distance between atom m and atom n.

To obtain

the maxima of Ich(s), equation (1) must be differentiated, which
yields a complicated :.f unction depending on all the r

Some simpli-

fications can be made, like neglecting the variation of the scattering

29
factor with s and considering only one interatomic distance r 22 •

Then: 4rc sin e r/A. = A where A = 4rc/E, E = 1.627 is the Ehrenfest's
constant and 4rc sin e /A. = s

its first

maxi~um;

1 is the value of s for which Ich(s) has

This r e lation is very approximate and a different

approach seems preferable.

The interference function I(s), defined

in III-A.l, is a function of the product sr only.
first maximum of I(s) occurs for s
verifies s

Then s

Suppose

vary with composition according to the same law,

for instance all the ratios r

= s 1 for a given alloy.

rmn = Amn' with a different Amn for each rmn

also that all the r

let r'
mn

Suppos e that the

stay constant.

For another alloy,

(l+a), and a be a small per <;: e ntage .

Then I (s) will have

-18-

its first maximum for s ' = s /(l+a) and s ' will satisfy s' r' =A
1 mn
mn
for all m and n.

If such an hypothesis stands, it will then be

sufficient to obtain only one r

and the corresponding s

give A , and any r' , provided s' is known.
mn
mn

; this will

Another immediate conse-

quence of such a situation will be the invariance of the ratios s /s ,

s /s , etc. from one composition to the other.

Reciprocally, if these

ratios are constant, it will be a strong indication of the invariance
of the ratios r

from one composition to the other.

The direct

interpretation may consequently yield valuable information on the
ratios of the interatomic distances, and on the interatomic distances
provided some of the interatomic distances are already known through
other channels such as the Fourier inversion of the interference
function, leading to the radial distribution function.
B.

Experimental procedure
The thickness of the foils obtained by the piston and anvil
~·

quenching method varied between 30 and 45

In order to avoid any

angular dependent absorption correction, several foils were stuck
together with duco-cement on a bakelite substrate.

Table II gives

the mass absorpti •:>n coefficients for the compositions investigated,
for both CuK

~/p,

and MoK

radiation.

It can be seen from the values of

and the knowledge of the density of the alloys (around 9 g/cm ),

that only three or four foils were necessary in the case of MoKa
radiation, and more than necessary for CuK

radiation, to eliminate

the necessity of including an absorption factor in the pres ent analysis.

-19-

TABLE II

MASS ABSORPTION COEFFICIENTS OF THE Fe-Pd-P
AND Ni-Pd-P ALLOYS FOR CuKa AND MoKa RADIATIONS

Composition

CuKa

(at.%)

IJ./ p (em /g)

MoK
!J./p(cm /g)

183.0

27.2

159.7

30.1

138.9

32.4

120.8

34.6

97.6

37.1

72.7

40.1

207.2

26.3

215.4

27.1

224.0

27.9

236.4

29.1

-20-

The specimens so prepared were mounted on the sample holder of
a G.E. diffractometer with vertical axis.

Two similar units were

used, one for MoKa radiation and the other for CuKa radiation.

The

units were run under 45 kV and 38 rnA, to provide a sufficient intensity.
The incident beam was collimated by a system of slits which allowed
different beam divergences.

A LiF monochromator with double curvature

was placed in the diffracted beam to eliminate K~, the white spectrum,
the fluorescent scattering

31 32

though not completely

and most of the incoherent scattering,
A combination scintillation counter and

pulse height analyzer was used as a detector.

For the experiments

performed with MoKa leading to the determination of radial distribution
functions, the pulse height analyzer was adjusted to eliminate ~/2,
which is let through the monochromator.

The contribution of intensity

due to ~/2 was checked to be of the order of 15 counts/sec to 10,000
counts/sec for Ka, which is indeed negligible (in the absence of pulse
height analyzer, the ~/2 contribution was still small, though about
10 times the above value).
Since a complete scanning of the diffraction pattern of an
amorphous alloy required as long as ten days, the reliability of the
data depended on the stability of the intensity of the incident X-rays,
as well as that of the counter.

First, the stability of the counter

was checked by using a radioactive source.

Different levels, in the

range of intensity used for the diffraction experiments, were checked.
These tests showed stability within 1% for periods of time up to 120
hours.

The same experiments were repeated with the MoK

radiation

-21-

and an amorphous Ni-Pd-P specimen.

The same levels of intensity were

again checked and no appreciable fluctuations recorded for periods
of time up to 120 hours.

For MoKa diffraction experiments, the experi-

mental data were obtained with a rate of scanning of 0.02°/100 sec in

2e.

A printer gave a reading of the accumulated counts every 200

seconds, which yielded 25 prints/degree (2e).
For 2e going from 2

used were:

to 20 : 0.1

The beam divergences

divergence.

Restart at

2e = 10 0 with 1 0 divergence and match curves on common range of 2e
(10

to 20 ) until 2e

= 62 0 .

Restart from 48

with one data point every 1000 sec up to 160

with 3

divergence,

and matching of the

curves on the range 58° to 62°.

Treatment of data
In order to determine the coherent intensity in electron units,

the experimentally obtained intensity It(2B) must be corrected for
absorption, polarization, fluorescent scattering, Compton scattering
and background.

These corrected data must then be scaled to the units

of~. x.f. 2 for the computation of the interference function.
].

Since

the specimens used for recording the diffraction patterns could be
considered as infinitely thick, the absorption correction is independent of angle and can be included in the scaling factor.

The pol-

arization correction is angle dependent and results in dividing the
experimental intensity by a factor P (2e) such that:

P(2e)

(1 +cos

2~ cos

2e)/(l +cos

2~),

-22-

where 13 is the Bragg angle for the radiation considered, incident on

(200) plane of LiF.

Actually, one need only take into account the

angular dependence of P(2B) and the factor 1/(1 +cos

213) can be

included in the scaling constant.
In the present investigation, the fluorescent radiation is
practically negligible, as a consequence of the presence of the monochromator in the diffracted beam, as well as the use of a pulseheight analyzer with the counter.

The use of a monochromator in the

diffracted beam introduces, however, some difficulties as far as the
evaluation of the Compton (or incoherent) scattering is concerned
This problem has been rather thoroughly studied by Ruland

•·

Ruland

showed that the elimination of the incoherent scattering requires
the evaluation of an attenuation function Q (2B) (or Q (s), where

= 4~ sine/~).

The determination of Q (s) requires a knowledge of

the "pass-band" of the monochromator.

The value of Q (s) decreases

with increasing s to become essentially negligible above a value of
s which depends on the integral width of the pass-band.

However, Q

(s) depends on several unknown parameters , and we will only be able
to evaluate Q (s) I.

(s), where I .

(s) is the Compton scattering,

by approximations which will be justified by the good fitting of

a Ic(s) to~ xi fi 2 , as well as by the b ehavior of the Fourier

transform of s I(s) in the region in which r < 2j.

Experiments wer e

performed with the same apparatus on a monocrystal o f silic on, and a
qualitativ e shape o f the v ariation of Q (s) Iin (s) was d e duced from
the se exp e riments.

A similar variation was assumed to hold for the

-23-

Fe-Pd-P and Ni-Pd-P alloys, and a trial and error process was used
to adjust the contribution of the incoherent scattering (cr. III-D).
The background electronic noise was substracted from the measured

intensities.

For 29 angles less than about 10 , the background

increased with decreasing angle because of the divergence of the
incident beam.

Measurements below 10° were considered unreliable and

the experimental intensity curve was extrapolated to zero at 29

= 0°.

The scaling of the experimental data to electron units was
performed on the coherent fraction of the experimental scattered
intensity.

The atomic scattering factors were corrected for anomalous

dispersion.

That is:

= f 0 + M + i ilf''

and
= (f

The values of f

I::J.

+ I::J. f') 2 + (I::J. f 11 ) 2

f' and I::J. f" were taken from reference 33 and

checked with the values given in the International Tables for X-ray
Crystallography

The experimental corrected intensity I

scaled by making use of the fact that Icoh(s) - ~ xifi

(s) was

converges

toward 0 for large enough s (that is, interatomic interferences become
negligible at high angles).

This procedure has been most commonly

25 35
used by earlier investigators of liquid and amorphous structures '
and is quite appropriate when experimental data can be obtained up to

= 10 x-l and above.

This is the situation with MoKa radiation, for

which s goes up to 17.4 x-l for 29

= 160°.

A fitting factor a can be

-24-

o-1

(s) Ic(s) = ~ xifi (s) for s = 13A

found such that: a

to s

= 17.4 Ao-1 .

Provided all the corrections have been done properly, the fitting is
quite good.

One must especially look for drifts in a

cations of errors in I

(s).

(s) as indi-

An average value is taken for a at the

conclusion of the scaling process.

The functions I(s) which is then

going to be Fourier transformed is finally: si(s) =s(a I

(s)-~ x.fi 2 (s))/

(s).

The Fourier inversion of s I(s) was done on a 7094 IBM computer
through a program written in Fortran~IV language (see Appendix II).
intervals in s values were taken small enough so that ~s ~ ~/r

max
36
being the distance beyond which the RDF has no significant variations
In the present case, taking r

max

~ 20

A, led

to~

was well satisfied over the whole range of s values.

max

The

o-1
0.16 A
which

Plots of the

fitting of .Ic(s) to~ xifi, of I(s), of the Fourier transform
4~r(p(r)-p )(~ xiK.)

= W(r) and of the final RDF were provided

together with the printed output of the program.
D.

Error treatment
Several causes of errors can greatly diminish the amount of

information yielded by the radial distribution function, especially
with respect to the det e rmination of coordination numbers.

These

errors are mainly normalization (or scaling) errors, e rrors on the
scattering factors and termination errors.

Several authors have dis-

cussed the errors involved in the d e t e rmination of radial distribution
functions, but ref e rence is mainly b e ing made h e r e to the ext e nsive
. 30
review of Kaplow et al . .

The caus e s of ; e rrors in the RDF (or in

-25-

W(r), the Fourier transform of s I(s)) are numerous and are always
present.

However, each type of error usually has some specific

features which make it recognizable.

Also, the relationship of

Fourier transformation which relates s I(s) and W(r) is of great use,
as the back Fourier transformation of corrected W(r) can be used to
check s I(s) and eventually trace down the range of erroneous data.
In the following argument, F(s)

J F(s) sin

s I(s) and W(r) = 2/rr.

sr ds, as previously defined.
Considering first the normalization error, let the error on a
be 6a.

The resulting error

~F(s)

on F(s) is then:

~(s) = s 6a I c (s)/f e 2
or

~F(s)=(6a/a)F(s) + s (L xi fi 2 /fe2 )6a/a

The resultant ~W(r) is then the true W(r) multiplied by 6a/a, plus the
transform of a ramp of slope (L xi Ki ) baJa.
ramp has the form:

where s

The transform of such a

is the upper boundary of integration in the Fourier integral.

The analytical behavior of

~W(r)

with r is shown in Fig. 3, for

The effects of errors on the scattering factors were specifically studied in reference 30.

The present case, however, is more compli-

cated due to the use of the reduced scattering factor f

(s).

This is

0.6

-040

~ 0.2

....-

X 04

r<>

1.0

Fig. 3.

Error on W(r) due to 1% scaling error for a Ni

-Pd

-P

alloy.

-27-

only an approximation and, consequently, will necessarily generate
An error of the form 6F(s) = e(s)

some error.

sa I c (s)/f e 2 (s) is

rather likely, with e(s) being a slowly varying function of s.

The

error 6F(s) can also be expressed as 6F(s) = e(s) F(s) + (~ xiKi )s

e(s).

The first term of the transform of 6F(s) will consist of the

convolution of the cosine transform of e(s) with the true W(r), which,
if e(s) varies slowly, will only be comparable to a change of scale.
The second term will, as in the case of normalization error, give a
transform with its most significant features obtained for small value
or r, and dying off rather rapidly.
Termination errors arise from termination of experimental
data at s = s

instead of s = 00 ,

peak portion of the RDF

23 37
and usually quite small if s

enough (which is our case, with s
But the use of f

They are maximum around the main

is large

= 17.4 ~-l for MoKa radiation).

(s) in the interference function I(s) amplifies

the oscillations of s I(s) at large values of s and consequently increases the termination errors.
The procedure of error corrections made use of the fact that,
physically, no interatomic distances smaller than approximately 2 ~
can exist.

Consequently, for r < 2 ~. the function W(r) should be
(~

equal to -4nrp

xiK.) .

plot of W(r) versus r.

Such a function is a straight line in a

Any deviation from such a straight line is an

indication of error and it is possible to recognize the type of error
involved.

In the present investigation, the errors were found to

consist mainly of scaling errors and errors at large values of s, due

-28-

to the sharpening effect off

(s).

A commonly used procedure to

reduce the influence of errors at large s is the use of an artificial

"temperature" factor exp(-as ), so that the function which is Fourier
transformed is s I(s) exp(-as ).

The value of a is usually chosen of

the order of 0.01, so that the exponential factor does not affect too
much the main peaks of s I(s).

The use of a temperature or damping

factor whereas it compensated spurious details due to errors at high
s, also decreased the resolution of the final W(r) and rW(r)

though

it did not affect the location of the maxima of W(r) and the area

6 23

under the peaks, '

but simply modified the peaks width and height.

The scaling errors, which could sometimes be large due to an unprecise
knowledge of the incoherent scattering going through ' the monochromator,
were corrected in the following way:

a trial and error method was

used to adjust the contribution of the incoherent scattering such
(s) would give a good fitting along ~ xifi and the final
transform W(r) would show only reduced oscillations along the straight

that 0: I

line -4rrrp (~ xiK . ) .

When the spurious details at small r became

small enough to indicate no important error on 0:, the procedure was
stopped.

In some cases, an additional verification was performed:

the small r part of W(r) was approximated to a straight line and a

Fourier inversion performed giving F' (s) = J ~(r) sin sr dr

F'(s) was reasonably close to F(s) (apart from an inevitable termination effect)W(r) and subsequent r W(r) were the accepted distribution
functionsfor the composition investigated.

An additional e rror was

-29-

always present, due to the uncertainty on p , the atomic density.

From experimental measurements, the value of p

was known with an

uncertainty of ± 5%.
E.

Results
1.

Nickel-palladium-phosphorus alloys
Six different compositions were investigated (cf. Table I).

For two of them, MoKa radiation was used and the diffraction patterns
were analyzed to yield electronic radial distribution functions.

For

the other compositions, CuKa radiation was used for the diffraction
experiments and the pattern was restricted to the first amorphous
band.
Diffraction experiments with MoKa radiation were performed on
Ni

Pd P
and Ni Pd P
alloys.
32 53 15
53 27 20

pattern for Ni

The uncorrected diffraction

is shown in Fig. 4, as an example.
53 15

amorphous bands (or peaks) are easily recognizable.

Several

A comparison of

the diffrac:tion patterns of these two Ni-Pd-P amorphous alloys reveals
that the amorphous peaks are displaced towards larger values of 2e with
increasing percentage of nickel.

The fitting to ~ xifi

of the

corrected coherent intensity is shown in Fig. 5 and the r e sulting
interference function I(s) is plotted in Fig. 6 (in both cases for
Ni
Ni

32
32

-Pd
-Pd

53
53

-P
-P

15
15

, as an example).

All the numerical results for both

and Ni

are gathered in Table III, concerning

-Pd

-P

both the actual diffraction spectrum and the interf e renc e function.
The Fourier inver sion of F(s)

= s I(s) was performed ac cording to the

20~

010

Fig. 4.

I-

(/)

-200

;::,

'2300

(/)

~Jo

500l

600

!\ 30r

ANGLE 28 ( )

-Pd

-P

100

alloy (MoK0 radiation)

Experimental diffraction pattern of an amorphous Ni

I \

0::

(f)

:j
aj

->-

alloy (MoKa radiation).

S c&- 1)
Coherently scattered intensity from an amorphous Ni

Fig . 5.

5 6 7

3 4

'\ I \

0o I

·~~~l

-Pd

-P 15

......

XIC\1

·-

C\1

f()

-I

Fig. 6.

3 4

5 6 7

sc&-

8 9 10 II

(MoK

radiation).

-Pd

-P 15 alloy

12 13 14 15 16 17

Interference function I(s) for an amorphous Ni

-33-

TABLE III

VALUES OF 29 AND s CORRESPONDING TO THE TWO
FIRST PEAKS OF THE DIFFRACTION PATTERNS AND
TO THE MAXIMA OF THE INTEREFERENCE FUNCTIONS
(MoKO: RADIATION)

Composition

Ni32-Pd53-P15

Ni57-Pd23-P20

18.70

19.35

2.888

2.961

2 . 95

3.25

29 (deg.)

32.15

33.18

s(Ao-1)

4.90

5.07

1st

2.890

2. 980

2nd

4.92

5.11

3rd

7.32

7.50

4th

9.66

9.87

First peak

29(deg.)
s(K- 1 )

Half width of
first peak (29)

Second peak

Successive
maxima of I (s)

-34description given in III-C.

The resulting functions W(r) and r W(r)

are shown in Fig. 7 and 8 for the Ni
for Ni

-Pd

-P

-Pd

obtained for Ni

-Pd

alloy, and in Fig. 9

fact~ exp(-0.01 s 2 )

correct the oversharpening effect of 1/f
53

-P

The interference function of Ni

multiplied by a temperature

function of Ni

-Pd

-P

s~ows

-P

-Pd

-P

was

(cf. III-D) to

The radial distribution

consequently less details than the RDF

which did not require the use of a tempera-

The upper value in r was chosen to be 10 R for practical

ture factor.

purposes, since a sufficient number of interatomic distances are
smaller than 10
-4~rp

In both cases, the theoretical straight line

(~ xiK.) 2 is shown on the graphs of W(r).

Spurious oscil-

lations can be observed for r
to remaining small errors.

< 2 R, on all W(r) plots, corresponding

Their amplitude is however small and, as

it can be seen on the plot of W(r), these spurious oscillations seem
to be damped rather fast with increasing r.

As it was explained in

III-A.2, the interatomic distances can be either related to the radius
of symmetry r of the function W(r) or to the radius r' corresponding
to the maximum of r W(r).

Both rand r' are given in Table IV.

The

third peaks are rather ill defined and the values given are only
approximate.
The area under the first peak of the RDF has been evaluated in
each case by using a gaussian approximation.
appears in Fig. 10 for Ni

-Pd

-P

This procedure, as it

as an example, gives a satis-

6 26
factory fitting of the first peak of the RDF •

In addition, the

width of the peak at half height gives an indication on the mean square

C\J

Fig. 7 .

- 0

X 5

f"()

r(A)

Distribution function W(r) for an amorphous Ni 32 -Pd

-P 15 alloy.

8~--------------------------------------.

I,.)

1.11

C\J

.....-

·-

C\J

....ct_60

I_/

Fig. 8 .

Radial distribution function for an amorphous Ni

I --- 2

:::t::~

4 1r r (Lxi Ki) Po

-Pd

-P 15 alloy .

-374~----------~------------------------------------.

-2

-I

C\J

~ 0 ',
x.(..oo.l

'"C -1
1:::

o;;t

-2

,...,

Q..

C\J

~- 40

C\J

1=::

o;;t

0 o~--~~-?--~3~--~4--~5~--~6--~7~--~8----~9--~lo·

r(A)
Fig. 9.

Amorphous Ni

-Pd -P
alloy: a) func tion W(r);
53
27 20
b) radial distribution function.

-38-

TABLE IV

INTERATOMIC DISTANCES IN Ni
AND Ni

Composition

-Pd

-P

-Pd 27 - P20 AMORPHOUS ALLOYS

Ni32-Pd53-P15

Ni53-Pd37-P26

r(K)

r' (K)

r(K)

r ' cK)

1st

2 . 79

2.81

2 . 72

2 . 74

2nd

4 . 62

4.65

4.52

4 . 57

3rd

(5 . 40)

(5. 36)

(5 .17)

(5.13)

4th

6.90

6.94

6 . 75

6.83

Successive peaks
in the RDF

-3930.-------------------------------------~

-X

!o...

C\J

4.0
Fig. 10.

First peak of the radial distribution function
of th e amorphous Ni

-Pd -P
alloy, with
32
53 15
Gaussian approximation (dash e d-line ).

-40-

deviation of r

(orr'), assuming always a gaussian approximation.

Then

the first peak can be analytically represented by:
r W(r) = [ A 1 exp(-(r-r ) /4(cr1+a))J

/[4:rr(cr1+a)J~

where 2cr is the mean square deviation of r
and a(= 0.01) is the
constant in the temperature factor exp(-as ), when such a factor is
used to counterbalance the oversharpening due to 1/f
under the first peak, is then A .

2 (s).

The area

Hence, if B is the width at half

height, the following relationship is verified:

(B /8 Log 2) -2a
--

Average values for A

(6~2 ) 2 are listed in Table V, together with

and

the coordination numbers for the first atomic shell.

The average

coordination number, N , was computed under the assumptions that all

types of pairs were contributing to the first peak and that there
were equal atomic densities of Ni, Pd and P atoms around any atom
(cf. III-A.2).

Consequently, N

was defined as:

The metallic coordination number, N , was computed by
me

subtracting

the contributions due to phosphorus-metal and phosphorus-phosphorus
pairs.

This was performed by assuming that the ligancy of phosphorus

. meta 138 .
was equal to 9, as in most transition metal phosphides rich 1n
The value of N
was the n computed by dir ec t application of equation
me
(12) (cf. III-A.2).

An e rror of about + 0.5 atom on N

and N
was
me

-41-

TABLE V

COORDINATION NUMBERS,

Composition

RATIOS

OF s VALUES AND OF INTERATOMIC

Ni32-Pd53-P15

Ni53-Pd27-P2C

16000

12300

0.22

0.23

12.7 ± 0.5

13.3 ± 0.5

Nme

10.5 ± 0.5

10 . 1 ± 0 . 5

1.00

1. 70

2 .53

2.52

3. 34

3 . 32

1.00

1. 655

1 . 660

1. 90

1. 89

2.47

2.48

A (e1ectrons)
~ ~
(flr ) "2

Ratio s/s

Ratio r / r

-42-

considered likely, due to the remaining errors in the experimentally
determined distribution functions W(r) and r W(r) and to the error
on Po
It appeared of interest, in the light of the remarks made in
III-A.3, to compute the ratios of s values corresponding to the maxima
of the interference function I(s), and the ratios of interatomic
distances, which were determined by taking the average value of r and
r'.

The references were s

and r

, corresponding to the first maxima

in I(s) and in the distribution function respectively.

These succes-

sive ratios are also given in Table V.
All Ni-Pd-P amorphous alloys (6 compositions) were used for
diffraction experiments with CuKa radiation, using the same diffractometer as for the experiments with MoKa radiation.

Only the first

amorphous band was recorded, as this appeared to be sufficient to
investigate the influence of large variations of composition on the
diffraction pattern, and subsequently on the interatomic distances.
For increasing values of the ratio Ni/Pd, the first amorphous peak
decreased in intensity and was shifted towards higher angles.

The

results of the investigation with MoKa radiation, showing rather
constant ratios of ri/r
si/s

together with an invariance of the ratios

with varying compositions, led to make use of the argument

developed in III-A.3.
and Ni

-Pd

-P

The product s r was calculated for Ni -Pd -P
1 1
32
53 15

and was found quite constant and equal to 8.11

± 0.02.

The relation: s r = 13.11 was used to compute r
for all 6 compositions .
1 1

-43-

As previously defined, s

is the value of s at the first peak of the

diffraction pattern and can be taken as a good approximation of s for
the first maximum of the interference function.
The results are given in Table VI and the variation of r
composition is shown in Fig. 11.

with

The linear dependence of r with the

ratio Ni/(Ni+Pd) where Ni and Pd are in atomic%, appears quite clearly,
except for the Ni
than expected.

-Pd

-P

alloy which gives a value of r

smaller

This is not surprising, considering that this alloy

contains only 15 atomic % phosphorus compared with 20 atomic % for the
other compositions.

This result suggests that the Ni-Pd-P alloys

present some strong structural similarities with the transition metal
phosphides.

In these phosphides, homogeneity ranges exist around the

. compos1t
. i on38,39 , an d t h e average i nteratomi c d'1stances
stoech 1ometr1c

decrease with decreas i ng phosphorus content, probably because of a
better packing of the metallic atoms .

A point corresponding to Ni

83 17
11
amorphous electrodeposited Kanigen nickel studied by Guinieret al.
is

also shown in Fig. 11.
2.

Iron-palladium-phosphorus alloys
Three different compositions were investigated.

-Pd

-P

and Fe -Pd -P
were both studied with MoKa and CuKa
36 20
44

radiations, whereas the alloy Fe
radiation.
on Fe

The alloy s

-Pd

-P

was studied only with CuKa

The diffraction experiments performed with MoKa radiation

-Pd -P
and Fe -Pd -P
showed several amorphous peaks, as
36 20
44
48 20

in the case of Ni-Pd-P alloys.

The position of these peaks was also

-44-

TABLE VI

s VALUES FOR THE FIRST AMORPHOUS PEAK AND
FIRST INTERATOMIC DISTANCE r 1 IN NICKELPALLADIUM-PHOSPHORUS AMORPHOUS ALLOYS

Composition

S1(_R-1)

r1 (_R)

Ni13-Pd67-P20

2.79

2.90+0.01

Ni32-Pd53-P15

2.89

2.8Q±0.01

Ni43-Pd37-P20

2.92

2.78±0.01

Ni53-Pd27-P20

2. 98

2.73+0.01

Ni63- Pd17-P20

3.02

2 . 68(5)±0 . 01

Ni73-Pd7- p20

3.07

2.64±0.01

Fig . 11.

0.1

0.2

0.3

Ni+Pd

0.4 Ni

0.5

0.6

0.7

o.a

0.9

! _ _+_ _ +_ _ ,

Nearest neighbors interatomic distance in Ni-Pd-P amorphous alloys.

----------+

1.0

3.3,...--------------------------..._,

\.JI

-1:'-

-46-

displaced toward larger values of 29(or s) with increasing percentage
of iron.

Table VII gathers the numerical results with respect to the

diffraction patterns and to the maxima of the interference function
I(s).

The Fourier transformations leading to the radial distribution

functions were performed in the same way as for the Ni-Pd-P alloys
(cf. III-A).

The resultant distribution functions W(r) and r W(r)

are given in Fig. 12 and 13.

In both cases a temperature factor equal

to exp(-0.01 s ) was used in an effort to reduce the oversharpening

effect of 1/f

The values of rand r', referred to W(r) and r W(r)

respectively, are given in Table VIII for the first four atomic shells.
As in the case of Ni-Pd-P alloys, the fitting of the first peak of
the RDF to a gaussian shape was quite satisfactory.

The coordination

--::2

numbers N and N , as well as the mean square deviation ~\
me
as in III-E.l.

These numbers, as well as the ratios si/s

are defined

and ri/r

are given in Table IX.
Only the first amorphous peak was recorded in the experiments
performed with CuKa radiation.

This first peak is shown in Fig. 14

for the three compositions investigated.

As expected, the amorphous

band is displaced towards larger angles and decreases in intenstiy
with increasing iron content.

As in the case of Ni-Pd-P alloys, the

good invariance of the ratios ri/r 1 and si/s 1 led to establish a
relation between s

and r

for the alloy Fe

(cf. III-A.3).

s r
= 8.08.
1 1

this relation was:

-Pd

-P

For the Fe-Pd-P alloys,

This relation was used to compute
The results for all three compositions

-47-

TABLE VII

VALUES OF 29 AND s CORRESPONDING TO THE TWO FIRST
PEAKS OF THE DIFFRACTION PATTERNS AND TO 'IRE MAXIMA
OF THE INTERFERENCE FUNCTIONS (MoKa RADIATION)

Composition

Fe32-Pd48-P20

Fe44-Pd36-P20

29 (deg.)

18.58

18.77

s(R- 1 )

2.851

2.887

2.84

3.02

29 (deg.)

31.81

32.04

4.85

4.88

1st

2.85

2.88

2nd

4.89

4.92

3rd

7.22

7.28

4th

9.55

9.60

First peak

Half width of
first peak (29)

Second peak

Successive maxima
of I (s)

-48-

f(')

--w

?-2

"'-

Q..

-I

x- 0

"'-

1:::: -1
'¢

-2
100

90
f(')

b 80

"'-

-60
Q..

""":':.. 50

"'-

1::::
'¢

w 40

oo
Fig. 12.

Amorphous Fe

50
r( A)

-Pd -P
alloy: a) function W(r);
32
48 20
b) radial distribution function.

-49-

,..,

-ti:2

--I

"'-

Q..l

C\1

-x- 0

~ -1

o;;t

-3

,.., 80

-"'-

70
60

Q..
~50

4TTr 2 (Lx; K/Po

x-40

.........
C\1

"'-

t:::

o;;t

20
10
0o
~--~--~~--~3--~4~--~5~--~6--~7~--~8~--~9--~
IOo

r (A)
Fig. 13.

Amorphous Fe

-Pd -P
alloy: a) function W(r);
36 20
44
b) radial distribution function .

-50-

TABLE VIII

INTERATOMIC DISTANCES IN Fe 32 -Pd -P 20
48
AND Fe -Pd -P
AMORPHOUS ALLOYS
36 20
44

Composition

Fe32-Pd48-P20

Fe44-Pd36-P20

in the RDF

r(.~)

r' (R)

r(R)

r' (R)

1st

2.82

2.855

2 . 775

2.825

2nd

4.66

4. 70

4.675

4.685

3rd

(5.38)

(5.35)

(5.25)

(5.28)

4th

7.03

7.20

6.97

7 . 20

Successive peaks

-51-

TABLE IX

COORDINATION NUMBERS, RATIOS OF s VALUES AND
OF INTERATOMIC DISTANCES IN Fe

-Pd

-P

AND Fe -Pd -P20 AMORPHOUS ALLOYS
44
36
Composition

Fe32-Pd48-P20

Fe44-Pd36-P20

A (electrons)

14700

14000

(l1r;) ~

0.24

0.23

13.2±0.5

14.6±1.0

Nme

10 . 2±0.5

11.6±1. 0

1.00

1.71

2.53

3.37

3.33

1.00

1.66

1.67

1.90

1.87

2.52

2 .53

Ratio s/s 1

Ratio r / r 1

-52-

IOOOr--------------------------------------------------------------------------------------~

(/)

a.
(.)

>r500
(f)
rz

28 (deg.)
Fig. 14.

First amorphous peak in Fe-Pd-P amorphous alloy s:
- - Fe23-Pd57-P20; ---- Fe32-Pd48-P20; Fe44-Pd36-P20'

·- · -

-53-

are given in Table X and plotted in Fig. 15 versus the ratio
Fe/(Fe+Pd).

As in the case of Ni-Pd-P alloys, a linear relationship

with composition can be recognized.

-54-

TABLE X

s VALUES FOR THE FIRST AMORPHOUS PEAK AND
FIRST INTERATOMIC DISTANCE r

IN IRON-

PALLADIUM-PHOSPHORUS AMORPHOJ S ALLOYS

Composition

sl(R-1 )

Fe23-Pd57-P20

2.82

2.87

Fe32-Pd48-P20

2.85

2.84

Fe44-Pd36-P20

2.88

2.80

(R)

oc::r_.
+_ _+______ !

~---

--- ------..

0.2

Fi g . 15.

0.1

0.5

Fe
Fe+Pd

0.4

0.6

0.7

0.8

0.9

1.0

Nearest neighbors interatomic distance i n Fe-Pd-P amorphous alloys .

0.3

2 . 5~----~----~--------~----~----~--------~----~--------~----~----~

2.6~

2.7~

2.8t-

2.9t-

3.01--

-- ----------

t::. __ _

3.1t-

3.2,---------------------

1./1
1./1

-56-

IV.

ELECTRICAL RESISTIVITY

The amorphous alloys which are the object of this investigation
exhibit rather characteristic transport properties.

The study of

electrical resistivity and specifically its variations with temperature
and composition, is of particular interest.

The presence of ferro-

magnetic elements (Fe and Ni) in th~se alloys suggested low temperature
experiments in order to investigate whether or not a Kondo effect existed
in these alloys.

High temperature resistivity measurements yielded in-

formations on the transformation from the amorphous to the crystalline
state.

Direct comparison of parameters such as temperature coeft icient

of resistivity and res idual resistivity of amorphous and crystalline
phases was
A.

also obtained.

Experimental procedure
Small rectangular samples of about 15 x 5 mm were prepared by

electro-discharge machining of amorphous foils under oil.

Current

and potential leads made of 0 . 063 inch in diameter nickel or platinum
wire were spot welded on the specimens.
were measured, by a null technique.

The currents and potentials

Only potentials were measured,

the currents being obtained from the potential drop across a standard
resistor of 0.10.
reversal.

Thermal g radient effect were minimized by current

The resistivit y

~easurements

are presented on a relative

scale and are given as a fraction of the resistivity of the amorphous
phase at room temp erature.

Consequently, if p(T) is the resistivit y

at a temperature T, the relative resitivity r(T) is defined as

-57-

p(T)/p(294°K).

A few absolute resistivity measurements were performed

at room temperature on samples representative of each composition.

The

dimensions of these samples were carefully determined by use of a
Precision was about + 3%

microscope equipped with a filar eyepiece.

on thickness and± 2 to 4% for the other dimensions, yielding about
± 10% error on the absolute value of the resistivity.

Results
The Ni-Pd-P and Fe-Pd-P amorphous alloys investigated showed

metallic conduction.

At room temperature their electrical resistivity

was between two and three times the resistivity of the corresponding
stable crystalline phases obtained by annealing at temperatures
around 550°C, for periods of time ranging from one day to one month.
The values obtained for the resistivity of the amorphous alloys ranged
from 100 to 175

~~em

for the Ni-Pd-P alloys and from 160 to 180

~~em for the Fe-Pd-P alloys.

The dispersion of values was too large

to show clearly the influence of composition.

However, in the Ni-Pd-P

system, which offered the largest range of compositions, the largest
value (175 ~~em) was obtained for the alloy Ni

-Pd

-P

and the

resistivity seemed to decrease on both sides of this composition.

The

order of magnitude of these resistivity values is the s ame as that
previously reported for amorphous

.40

Pd-S~

and Fe-P-C

alloys.

They

also compare favorably with the resistivity of both iron and nickel
measured just above the melting point (110
tively41).

~0-cm

and 85

~0-cm

respec-

-58-

Low temperature measurements
The most striking feature of the behavior of · the resistivity

of Fe-Pd-P and Ni-Pd-P alloys at low temperatures was the occurrence
of a minimum in the resistivity curve.

This minimum appeared at

temperatures rang i ng f rom a b out 9°K to 96°K, d ependi ng on t h e system.
Moreover, for temperatures between the minimum temperature (T ) and

about 140°K - 150°K, r(T) assumed a T

behavior.

Typical low tempera-

ture behaviors are illustrated in Figs. 16 and 17 for Ni-Pd-P alloys
and in Figs. 18 and 19 for Fe-Pd-P alloys.

The existence of a

resistivity minimum, and the presence of iron and nickel in the systems
under investigation, led to consider a possible Kondo effect.

There-

fore r(T) was tentativ ely approximated by a function of the form:

r(T)

with r

, 6r ,

+ ~ T 2 + 6r 0 - a Log T

(1)

a and ~ depending only on the composition and the

structure of the amorphous alloy.

The determination of these param-

e ters was performed by plotting r (T·) versus T
then by plotting the difference r(T)-r

to obtain r

and

~, and

= r 2 (T) versus Log T.

Examples of such plots are given in Figs. 20 and 21 for Ni-Pd-P alloys
and Figs. 22 and 23 for Fe-Pd-P alloy s.

Several sample s of e ach campo-

sition were used for low temperature measurements, and the dispersion
in experimental res ults was probably due to small differences in
structure from one sample to the other.
the experimental

r es~lts

Tables XI and XII summarize

for Ni-Pd-P and f e-Pd-P systems r e spectively .

I-

Fig. 16.

0.9600

100

T(°K)

150

helium temperature to room temperature.

-Pd

200

Relative electrical resistivity of amorphous Ni

-P

300
alloy, from liquid

250

I.Jl

-60-

97.6

97.5

'b 97.4
I-

.....

97.3

97.2

--- ---

T (° K)
Fig. 17 .

Re lativ e e l e ctrical n •sistivity at low
te mp c·rature o f

four sp ec ime ns of amor-

-61-

O~O·L-------L-------~------~------J_------~----~
0~5.---------------------------------------------~

0945o
~----~~
~----~,±
oo~----~,~~----~~~------2~5~o----~3oo

T("K)

Fig. 18.

Relative e l ectrical resistivity of Fe-Pd-P
amorphous alloys at low temperature.

-62100.0 0 . . . . - - - - - - - - - - - - - - - - ,

C\J

....

96.00

Fig. 19.

100

150

Relativ e e l ect rical r esist ivi ty at low
temperature of six specimens of amurph o uH

-63-

96.9

r.....
96.8

Fig. 20.

500

1000

1500

Relative electrical resistivity versus T
specimens of amorphous Ni

-Pd

-P

of f our

-64-

50r--------------------------------------

C\J

Fig. 21.

Residual relative resistivity versus Log T f or
four specimens of amorphous Ni

-Pd

-P

-65-

100.0 r - - - - - - - - - - - - - - - - - - - - - - - .

-X

95·0 o~...~.....-_,__.....~..-.....L.::s~o'="oo-=-'----'-__._---L_Io....~.,o__o__,o----li..--L...-J....I_5.L,o-o..Lo---L_j
T2 (oK)
Fig . 22 .

Re lative electrical resistivity versus T
specimens of amorphous Fe

-Pd

-P

of six

-66-

140r-------------------------------------------------~

Fig . 23.

(T) v e rs u s Log T f or
six spe cime ns of amorphous Fe -Pd -P .
32
48 20

Residual relative resistivity r

Ni63-Pd17-P20

Ni53-Pd27-P20

Ni 43~Pd37-P 20

Ni32-Pd53-P15

Composition

3.890
4.30

96.830
96.894
97 . 600
96.580
98.198
98.662
97.526
97 . 196
97.316
97.558

-~--

2.31

2.75

5.05

5.2

4. 70

4.18

6.35

5.35

3.255

96.816

3.820

96.657

a:(x104 )

r (x10 )

0.89

1.11

0.89

0.93

0.38

0.63

1.5

0.973

1.22

1.33

1.53

1.34

~ (x106 )

10.5

11.0

13.5

14.5

15.5

12.5

13.5

15.0

10.5

9.8

9.3

9.5

T (°K)

97.576

97.348

97.220

97.549

98.673

98.213

96 . 632

97.664

96.917

96.849

96.835

96.674

r (x10 )

LOW TEMPERATURE RESISTIVITY DATA FOR NICKEL-PALLADIUM-PHOSPHORUS ALLOYS

TABLE XI

2.6

4.1

5.0

5.6

4.9

4.1

8.2

10.0

2.4

1.4

1.0

1.6

llr(x104 )

-..J

(1\

Fe44-Pd36-P20

Fe32-Pd48-P20

Fe23-Pd57-P20

Composition

0.16

0.39
1.60
1.20

65.0

49.8
51.5
53.4
44.7
52.0
31.8
11.55
8 . 35

99.480

97.640
97.940
98.620
96.900
98.380
95.480
98.050
94.512

1.23

0.81

0.43

0.64

0.69

~(x10 6 )

r (x10 )

a:(x10 )

17.5

T (°K)

94.665

98.150

95.570

98.600

97.150

98.890

98.290

97.990

99.580

r (x10 )

LOW TEMPERATURE RESISTIVITY DATA FOR IRON-PALLADIUM-PHOSPHORUS ALLOYS

TABLE XII

8.9

15.0

39.5

110

82.5

116

100

150

6r (x104 )

-69-

These tables give a,

as well as T

and r(T ) = r .

Also given

is 6r = r(S.O)-r , which is a measure of the depth of the minimum.

Without anticipating the discussion, the following remarks can
already be made.

First, though all the amorphous alloys showed a

minimum, the effect is strikingly more pronounced in Fe-Pd-P alloys.
This can readily be seen by comparing the 6r which are about 10 to 100
times higher in the Fe-Pd-P alloys than in the Ni-Pd-P alloys.

For

all the alloys, r(T) showed a reasonably good fit to equation (1),
but the dispersion was quite large as it appears in Fe
instance (cf. Figs. 22 and 23).

a, T

-Pd

-P

-Pd _P
for
48 20

No noticeable law of variation for

and r . appeared in Ni-Pd-P alloys.

decreased from Fe

to Fe

-Pd

For Fe-Pd-P alloys both a and T
-P

, but the large dispersion

of data for these compositions prevented from checking accurately the
composition dependence.

High temperature measurements
The high temperature resistivity measurements were performed

at constant rates of heating of approximately 1.2 to 2.0 C/min.

Under

these conditions the resistivity vs. temperature curve of all the
amorphous alloys had the same general shape.

The resistivity increased

with temperatur e , with a small temperature coefficient of the order
of 10

-4 0

I C, until a crys tallization temperature t cr was r e ached .

this temperature the resistivity dropped sharply at first, then
reached a minimum befor e incr e asing again up to the melting point of
the alloy .

Typical b e haviorsof r(t) with t are giv e n in Fig. 24 for

-701 .0011-----------~

1.00~-~~~------

Eo.eo

...

0.60

Fig. 24.

Relative e l ectri c al resis tivity of six Ni-Pd-P
amorphous alloys measured with an avera ge h e ating
rate of 1.5°C/min.

-71-

Ni-Pd-P alloys.

Only one composition (Fe

-Pd -P ) was investigated
47 20

for the iron-palladium-phosphorus system (cf. Fig. 25), as attempts
to investigate Fe

-Pd

-P

alloy were deceived by the great brittle-

ness of foils of this composition.
data for the alloys studied.

Table XIII summarizes the important

For each composition, the following

characteristic parameters are given: temperature coefficient

termined between 20°C and 220°C; crystallization temperature t
with its dispersion 6t

de-

cr'

, and temperature tN, which is related to the

small increase in resistivity which appears for most Ni-Pd-P alloys
shortly before crystallization.

More precisely t

is the temperature

characterizing the beginning of this anomalous deviation from a linear
relationship of the type r(t)
itself.

= 1 + ~ t, prior to the crystallization

From the data of Table XIII, it appears that t

is rather

well defined, varying between 305°C, and 340°C for all the amorphous
alloys.

For slow rates of heating (10 to 5°/min), t

appreciably.

did not var y

The existence of a small increase in the resistivity

prior to crystallization was found in Ni-Pd-P alloys oniy.
zling behavior has been noticed in other amorphous alloys
tentative explanation will be given in the discussion.

This puzand a

The temperature

tN is characteristic of this pre-crystallization stage: usually tcr-tN
is the order of 20°C to 40°C.

The possible reversibility of the pr e-

crystallization stage was inves tigat e d, by stopping th e heating at
temperatures intermediat e between tN and tcr for a Ni

- Pd

-P
alloy.
53 20
Wher e as the truly amorphous range (< tN) showed reversibility, cooling
32

-s

r:- /'\

Fig. 25.

0.20

0.30

0.40

0.50

·-

0.60,

0.70

0.80

0.90

1.00

1.10~

1.20

It:"/'\

nr"\r"\

nL/'\

T (°C)

300 350

with an average heating rate of 1.5°C/min.

Relative electrical resistivity of an amorphous Fe 32 -Pd 48 -P 20 alloy measured

I /'\ /'\

-...!

-73-

TABLE XIII

ELECTRICAL RESISTIVITY OF AMORPHOUS Fe-Pd-P
AND Ni-Pd-P ALLOYS ABOVE ROOM TEMPERATURE

Composition

~-~.CI 0c)x104

Ni32-Pd53-P15

1.5 - 3.0

335 (±10)

290(±10)

Ni43-Pd37-P20

1.4 - 0.4

305 (±5)

280

Ni53-Pd27-P20

1.0- 0.5

325

295

Ni63-Pd17-P20

1.0 - 0.6

340

320

Ni73-Pd7- p20

0.7

325

---

Fe33-Pd47-P20

0.4- 0.7

315 (±5)

---

(°C)

-74-

from temperatures t such that tN < t
character of this

< t cr made obvious the irreversible

pre-crystalli~ation

transformation.

The crystalliza-

tion takes place in several steps, as it appears in Figs. 24 and 25 .
These steps are especially well defined in nickel-palladium-phosphorus
alloys.
Ni

-Pd

The intermediate crystalline step which is very clear in
53

-P

regresses in importance as the amount of nickel increases.

It was found, by X-ray studies that this intermediate stage corresponded
to metastable crystalline phases.

Stable crystalline phases were

attained, in all cases, before 550 C.

The temperature behavior of

r(t) for these stable crystalline phases was investigated for
Ni

-Pd

-P

and Fe

-Pd -P
alloys by measuring the resistivity
47 20

during slow cooling from temperatures above 550°C.

The crystalline

alloys exhibited, as expected, larger temperature coefficient than
the amorphous (l0- /°C compared to 10- /°C).

A change of slope,

probably connected with a Curie point, appeared at 260°C for Ni

and 345 C for Fe

-Pd

-P

-Pd

The room temperature resistivities of

the stable crystalline phases were respectively 32% and 52% of the
values for the amorphous phases, in good agreement with previous
40,42
o b servat~ons

-P

-75-

CRYSTALLIZATION OF Fe-Pd-P AND Ni-Pd-P ALLOYS

A limited effort was devoted to the study of the rate of
crystallization of the amorphous alloys and the structure of the
corresponding crystalline phases,

When these alloys are rapidly

heated (at rates of about 400 C/min and above) crystallization occurs
rapidly at a certain temperature, as previously reported for Pd
and Fe

-P

-c 7 17 .

16
20

This temperature can be easily measured by spot

welding thermocouple wires (0.005" in diameter) to a small alloy
foil (about 5 x 5 mm) and immersing the specimen in a furnace.
typical temperature-time curve is shown in Fig. 26.

From the height

of the heat pulse, an approximate value for the heat of crystallization
can be obtained.

An average value for all the specimens investigated

was about 700 cal/mole.
340

The sudden crystallization temperature was

± 5 0 C for the Fe-Pd-P alloys and 375 0 ± 100 C for the N1-Pd-P

alloys.

Within the experimental uncertainties, this temperature did

not vary with the ratios Fe/Pd and Ni/Pd.
Experiments were also performed in an effort to find what
structural transformations might be responsible for the rather abrupt
changes in the slope of the resistivity-temperature curves such as
those shown in Figs. 24 and 25.

Specimens suitable for X-ray diffrac-

tion analysis (lx2cm) were heated for a fixed time (20 min) at various
temperatures with steps of 20°C.
taken after each step.

An X-ray diffraction pattern was

This isochronal heat treatment corresponds

to an average rate of heating of 1°C/min which is comparable with that

-76 -

600

500

-u

...........

400

300

200

Tl ME (sec)
Fig . 26.

Thermal analy sis of an amorphous Ni

-Pd

-P

alloy.

-77-

used for measuring electrical resistivity changes with temperature.

Up to about 280 C, the diffraction pattern did not show any change
(dotted line in Fig. 27).

At 300°C, the width of the broad amorphous

band of the pattern slightly decreased and the maximum of this band
shifted to higher 2e values (dash and dot curve in Fig. 27).
additional sharpening occurred (dashed curve in Fig. 27).

At 320°C,

At 340°C,

rather sharp diffraction peaks were present although the amorphous
band can still be recognized.

At this state of transformation, the

alloys consists of an amorphous matrix, in which crystals are embedded.
The crystal structure of the crystalline phase (or phases) is not
known, but it is most probably that these are metastable intermediate
phases .

This statement is based on the fact that, as the temperature

was increased, the intensity of most of the reflections shown in
Fig. 27 decreased and disappeared at about S00°C.

At the same time,

new reflections corresponding to the equilibrium phases became visible
and increased in intensity.

At 550°C, equilibrium was achieved and

further annealing of the specimen for more than one month at this
temperature did not bring any change in the diffraction pattern.

I-

(f)

I-

:::1

t/)

...........

t/)

42
28 (0 )

·················

::...:....-==-~~·-~-

- - .. -

--·· ..• -

·- ·- · 300 c;-------- 320 c;

340 c.

-Pd -P
amorphous alloy after diffe rent
32
53 15
stages of isochronal heat treatment, 20 min every 20°C : . . . . . . room temperature;

···---

Diffraction pattern (CuKa radiation) of a Ni

~12/

.........-...,..--

Fig. 27.

100

200

300

400

500~-----------------------------------------------------------------

.....I
00

-79-

VI.

MAGNETIC MOMENTS

Experimental Procedure
The magnetic moments of Fe

-Pd

-P 20 and Ni

-Pd

-P

-Pd

-P

, Fe

-Pd

-P

were measured with a low temperature

magnetometer, which is described in reference 43.
is of the null-coil pendulum type.

This magnetometer

The pendulum is made of a fused

silica rod bearing a small coil located at its bottom and the sample
is placed close to the coil.

The upper part of the rigid pendulum

is connected to a bronze beam with silicon strain gages bonded to
its surface.

The output voltage of the strain gages is entered in

an a.c. bridge circuit utilizing a lock-in amplifier as detector.
Uniform magnetic fields up to 8.4 kOe can be obtained at the sample
location .

Direct currents ranging from 0 to 100 rnA can be sent

through the pendulum coil, which is adequate to attain an equilibrium
under the highest field.

Coil currents were calibrated with a pure

nickel sample as reference.

Additional checks were made by measuring

the susceptibilities of diamagnetic Bi and paramagnetic Hg Co(SCN) .
Small samples were cut out of quenched foils and carefully
weighed with a microbalance.

Weights of 2 to 5 mg were sufficient for

ferromagnetic samples, whereas about 50 mg were used in the case of
paramagnetic samples.

The magnetic moments of the alloys were meas-

ured from liquid helium temperature up to room temperature.

This

range was, when n eces sary , extended towards lower t e mpe ratures by
pump i ng t h e h e 1 ~urn
and tempera t ures down to 1.6°K were obtained by

-80-

this procedure.

Temperatures were measured with a germanium resistor

up to 50 K and a copper-constantan thermocouple up to room temperature.
Between 1.6°K and 4.2°K the vapor pressure of helium was used for
temperature determination.

An automatic temperature control helped

to attain good thermal stability.
B.

Results
Two alloy compositions, Fe

-Pd -P
and Fe -Pd -P , showed
48 20
36 20
44

a clear ferromagnetic behavior at low temperatures, though they gave
evidence of substantial magnetic "hardness" since, even in the highest
magnetic field (8.4 kOe), saturation was not completely reached.
alloy Fe

-Pd

-P

The

had a rather complex behavior which, at first,

could be mistaken for normal ferromagnetism.

For reasons explained

later in this paragraph this alloy was assumed to exhibit superparamagnetism.
For each measurement in the ferromagnetic range of temperatures
the saturation was evaluated by assuming a law of approach of the
type:
(J

H,T

where crH T is the magnetization per unit mass under the field H and

at a temperature T and cr
is the saturation magnetization, for all
ro,T
. d oma i ns or~ente
d ~n
. t h e same d i rect i on44 ' 4 S . A t 1 east t h ree
magnet~c
values of the field were used and a least square fitting yiel4,ed crro ,T
in each case.

0 K(cr00

In order to obtain the saturation magnetization at

), values of CJ00 T were fitted along a law in T

least square procedure (a T

3/2

through a

fitting was less satisfactory):

-81-

The saturation moment was then evaluated in units of Bohr magnetons.
The variations of magnetic moments (per unit mass of iron) with
temperature are given in Fig. 28.

Whereas a clear ferromagnetic

region can be recognized at low temperatures, a pronounced tail effect
occurs for the transition from ferromagnetism to paramagnetism.

was consequently rather difficult to determine a Curie point with
preci.sion.
method.

The Curie points were determined using the following

First the inflexion point of the curve crH T = f(T)

(for H

8.35 kOe) was considered to give a good approximation of the ferromagnetic Curie temperature.

A more elaborate analysis was subsequently

used to check these values.

In the vicinity of the Curie point, on
l.

the ferromagnetic side, crH,T behaves like (T-Tc)~; on the paramagnetic
side, assuming a Curie-Weiss behavior, crH,T/H behaves like 1/(T-Tc).

Consequently a plot of crH T versus H/crH T should yield a straight line

through the origin forT= T

The intercepts of these straight

lines with one of the axis of coordinates are then used for a more
precise determination of T , by interpolation or extrapolation.
procedure confirmed that Fe

-Pd

-P

and Fe

-Pd

-P

This

were normal

ferromagnetic alloys, in spite of the important tail effect apparent
in Fig. 28.

The alloy Fe

-Pd

-P

had a Curie point which was

extrapolated to about 380 K, whereas a Curie point of approximately
165°K was obtaine d for the alloy Fe

-Pd

-P

The intercepts of the

straight lines crH,T = 1 H/crH,T with the axis H/crH,T = 0 we r e always

----

Fig. 28.

100

TtK)

150

200

250

300

-Pd

-P

4- - - - - -

for Fe

(circles), Fe

-Pd

-P

(squares) and Fe

-Pd

-P

(triangles).

Magnetization (per unit mass of iron) in a field of 8.35 kOe versus temperature

250r-----------------------------------------~

-83-

negative for Fe

-Pd

-P

, down to 6,5°K, and linear extrapolation

confirmed that no Curie temperature existed for this alloy, thus implying a lack of long range ferromagnetism for this composition.
fact was confirmed by the magnetization curves obtained for Fe

This
-Pd

-P

(cf. Fig. 29), which revealed a magnetization still far from saturation,

even at the lowest temperature (6.5 K).
Fe

-Pd

-P

The magnetic behavior of

appears to be similar to the "superparamagnetism" recognized

in AuFe alloys by Crangle et al.

A paramagnetic behavi or following

a Curie-Weiss law was recognized above 135 K (cf. Fig. 30).

The con-

stant C in the Curie-Weiss relation X= C/(T-135) yielded a moment of
5.98

per atom of iron, giving therefore some backing to the assump-

tion of superparamagnetic behavior for this alloy.

The saturation

magnetization was obtained for this alloy by extrapolation to l/H=o
All three values of cr

and T

m, 0

(Curie temperature) are given in Table XIV.

Preliminary experiments show that all the amorphous Ni-Pd-P alloys
are paramagnetic at room temperature.
g ated down to 1.6 K.

Only Ni

-Pd

-P

was investi-

Paramagnetism, with a very approximate 1/T

d e pende nce, was observed down to 1.6 K though

a small permanent

moment, probably due to some iron impurities in palladium, wa s observed.
The gram susceptibility (Xg) was 1.45 x 10ture for Ni

-Pd

-P

e.m.u . at room tempera-

, increasing to 10.0 x 10-

e.m.u. at 1.6°K.

(])

........

at d~fferent temperatures.

-Pd

-P

. H(KOe)_

Magn~tization of an amorphous Fe

Fig. 29.

10
alloy versus magnetic field

,._-------~ 145.5 °K

93.5°K

61 °K

6.5 °K

.p.

Fig .

9oo

~ 5L

f()

30.
Cur ~ e - We ~ ss

Inv~rse ~ ram

T (°K)

200

250

susceptib ility of Fe - Pct - P
versus temperature, showing the
57 20
23
temperature dependence.

150

/,/

300

-86-

TABLE XIV

SATURATION MOMENTS AND CURIE POINTS
OF AMORPHOUS Fe-Pd-P ALLOYS

Composition

C1oo•O{~)

Fe23-Pd57-P20

1.07

135 {paramagnetic)

Fe32-Pd48-P20

1. 70

165 {±5)

Fe44-Pd36-P20

2.16

380(±10)

T (OK)

-87-

VII.

DISCUSSION

During the last decade, a considerable amount of research has
been devoted to the study of amorphous solids, resulting in a better
understanding of the amorphous state.

Amorphous or glass-like struc-

ture does not imply randomness of the atomic arrangement.

Some degree

of local order may prevail, though the true characteristic of crystallinity - namely the invariance of the atomic structure under translation in three directions defining a space lattice - is absent.

The

number of translations of a unit cell required to define a solid as
crystalline is a controversial subject.

Consequently, amorphous and

crystalline solids have a common boundary which is the smallest microcrystalline state in which the size of the microcrystals is of the
order of magnitude of the unit cell size.
A.

Structure of the quenched Fe-Pd-P and Ni-Pd-P alloy phases
Most of the experimental information on the structure of the

Fe-Pd-P and Ni-Pd-P alloys resulted from the X-ray investigations
leading to the radial distribution functions reported in section III-E.
The X-ray diffraction patterns of the quenched foils showed broad
maxima and no sign of crystalline Bragg reflections.

It can, of

course, be argued that small grain size and stresses can broaden the
Bragg peaks of crystalline solids.

By applying the Scherrer formula

to the observed width of the diffraction peaks. the crystal size for
the Fe-Pd-P and Ni-Pd-P alloys would be about 13 to 15

Since in

the rapidly quenched foils internal stresses are undoubtedly present,

-88-

they also contribute to the broadening of the peak and consequently
the crystal sizes given above might be slightly less than the actual
values.

Additional evidence for the lack of crystallinity was ob-

tained by electron microscopy.

Whereas previous investigators

utilized the "lace like" edges of the quenched foils for transmission
electron microscopy, this investigation was performed by using the
center of quenched foils thinned by electropolishing until they reached
a suitable thickness .

No evidence of microcrystals was found at a

magnification of 80,000.

The remarkable lack of contrast of bright as

well as dark field images and the broad diffraction patterns (cf. Fig.
31) are strong indications of lack of well-defined crystallinity.
The X-ray diffraction patterns (cf. Fig. 4) exhibit a
first relatively sharp peak and subsequent oscillations around the
coherent homogeneous scattering curve Exif ..

obtained between the values of r

The linear relationship

and alloy compositions (cf. Figs. 11

and 15) suggests that a continuity of structure exists through the
whole range of metallic concentrations and that Ni or Fe atoms can be
substituted for Pd atoms without drastic changes in the structure,
just like in a crystalline solid solution.
Ni

-Pd

-P

The point corresponding to

in Fig. 11 does not fall on the straight line, and this

can be explained by the fact that this particular alloy contained only
15 at.% P instead of 20 at.%.

The linear relationship between r

and

concentration can be cor1.sidered as an extension of Vegard's law to
amorphous alloys.

It is unfortunate that the amorphous range does not

-89-

Fig. 31.

Electron diffraction patt ern of an amorphous
Ni

-Pd

-P

alloy.

-90-

include the binary alloys Pd-P, Fe-P and Ni-P.
of r

for these compositions, however, can be obtained by extrapolat-

ing the straight lines of Figs. 11 and 15.
for Pd-P and r

The approximate values

This leads to r

= 2.97 K

= 2.61 K for Ni-P, based on the Ni-Pd-P results and

= 2.95 K for Pd-P and r 1 = 2.68 K for Fe-P, based on the Fe-Pd-P

results.

The usefulne ss

of the extrapolated values on the choice of

possible models for the amorphous state will be considered later .

The

radial distribution functions established for the Fe-Pd-P and Ni-Pd-P

alloys yield additional indications of continuity of structure all
through the amorphous range.

The invariance of the ratios ri/r

(for

= 2,3,4) throughout Fe-Pd-P and Ni-Pd-P alloys also implies simi-

larity of structural arrangement.

As explained before, only the first

peak of the radial distribution functions can yield meaningful information on coordination numbers.

Though some errors, partly due to an

imperfect knowledge of the densit y of the amorphous alloys,were
involved, the coordination numbers were found to be aropnd 13 for the
overall coord1nation and 10 to 11 for the me tallic coordination
(cf. Tables V and IX).
The diffraction patterns and radial distribution functions of
Fe-Pd-P and Ni-Pd-P alloy s show some resemblance with those obtained

f or 1 1.qu

id 49,50,51

The successive "shells" corresponding to increas-

ing interatomic distanc e s around an arbitrary atom become less and less
marked after the "neare st neighbors" shell.

The smoothness of th e

oscillations of the radial distribution function around the homogeneous

-91-

parabola 4~r p (~ xiK.) , shows a dispersion of interatomic distances

obviously more "liquid like" than "crystal like", making appropriate
the

qualification

of "frozen liquids" sometimes applied to the

quenched amorphous alloys.

Palladium, nickel and r-iron are fcc metals

but, unfortunately, only iron has been studied in the liquid state.
Ruppersberg

found a coordination close to 8 which seems to indicate

an arrangement comparable with a bee structure in the crystalline
state.
gol;

51
More truly fcc types in the liquid state, are copper
and
(cf. Fig. 32).

When compared with the radial distribution of

these metals, the amorphous Fe-Pd-P and Ni-Pd-P

alloys show a sharper

"nearest neighbors" peak and a clear splitting of the RDF in two
shells between 4

K and 6 K (cf. Fig. 8 in particular).

This splitting

is an interesting and real feature .of the radial distribution function
of

t h 1s
. category o f quenc h e d amorp h ous a 11 oys

17 40 54
• •
and h as .1 1 so

been observed in Ni-P amorphous alloys obtained by electrodeposition
l d epos1t1on
. . 11
or c h em1ca

The shape of the first peak in the amorphous

Fe-Pd-P and Ni-Pd-P alloys is also rather different from the shape
exhibited in the RDF of liquid metals.

To a good approximation the

first peak of the RDF:' of the amorphous alloys is ga\.\ssian, which
suggests atomic displacements centered around an average interatomic
distance more sharply defined than in a liquid metal.

The deviations

of atomic distances around an ideal interatomc distance corresponding
to the first peak in the RDF are given in Tables V and IX and correspond to mean square clisplacements of the order of 0.06 K

This

value is larger for the second shell though overlapping of the second

- 92 -

,......
(")

U'"'\
Q)

'-"

(\j

"0
......

tl()

"0
"M

::l

0'
"M

......

o<(

t::

::l

"M
,...

.w
til

"M
"0

......

('(!

"M
"0

('(!
,...

·M

(")

tl()

"M
f:z;

I{)

f'()

(J)d zJ.lL t7

-93-

and third shells prevents an accurate determination.

Thermal dis-

placements obviously cannot account for more than a small fraction
of the mean ~quare displacement which is, consequently, essentially a
static displacement.

The large value of this mean square displacement

for the first atomic shell is an argument against the hypothesis of
microcrystallinity with microcrystals of the order of 15

K, since such

crystals would yield a sharper "nearest neighbors" peak.

Independent

experiments by Lesueur

on a rapidly quenched Pd

alloy (believed

to have a structure close to Ni-Pd-P and Fe-Pd-P alloys) confirm the
existence of important displacement disorder.

Lesueur observed that

under irradiation by fission products, the amorphous structure of the
quenched Pd

was unaltered whereas irradiation would produce a

progressive amorphization of the stable crystalline phases in the
equilibrium crystalline Pd

alloy.

A suitable model for the amorphous state of Fe-Pd-P and
Ni-Pd-P alloys must, obviously, take into account the role played by
phosphorus since, without phosphorus, the quenched binary alloys Fe-Pd
and Ni-Pd are always crystalline.
deposited amorphous Ni

-P

In their study of an electro-

alloy Dixmier et al.

suggested a model

consisting of regularly spaced but randomly oriented layers of atoms
arranged as in the (111) plane of an fcc structure.

Their model, un-

fortunately, does not show the role of phosphorus.

In a separate

investigation, however, Legras

showed that the chemical bonding

betweenNi and Pin the electrodeposited Ni
th e bonding

l~Xisting

in Ni P.

83 -P 17 was identical to

lnformatlons on the bonding b e tWl~ en

-94phosphorus and metallic atoms can be obtained from the study
of transition metal phosphides.

The transition metal phosphides have

b e en studied thoroughly by Rundqvist
facts concerning their structure.

who pointed out some interesting

In the crystalline state, transition

metal phosphides with less than 40% atomic phosphorus exhibit tetradecahedral arrangements with phosphorus atoms at the c enter and metallic
atoms at the corners of the polyedron.

A t e tradecahedron is a polye dron

with fourteen triangular faces, which can be better described as mad e
of a square triangular prism with three half octahedron sharing its
rectangular sides.

The number of metal neighbors varies from 8 to 10

(usually 9) around one phosphorus atom.

The tetradecahedral unit for

Fe P, as an example, is shown in Fig. 33.

Whereas the average phos-

phorus-metal ligancy revolves around 9, the metal-metal ligancy vari e s
between 10 and 12 indicating a rather good packing, not too remote f rom
fcc clos e packing .

On the other hand, the chemical bonding b e twe e n

phosphorus and metal atoms s eems rather strong
the metal-metal bonds.

, at l e ast stronger than

Besides their importance in the structure of

transition metal phosphides, the tetradecahe dra have be en mentioned as
possible structural units in liquids,from a geome trical standpoint
(Bernal poly edra

59 60
).

An attempt will now b e mad e to d e scrib e th e amorphous

structur ·~

of the Fe-Pd-P and Ni-Pd-P alloy s in terms of the struc tural units
which exist in crystalline phosphides of corresponding phosphorus
content.

In binar y alloys of F e , Ni, Pd with P, the stable metal rich

39
phosphides are Fe P, Ni P, Ni P and Pd P · These compounds are either
12 5
orthorhombic (Pd P) or t e tra g onal (Fe P, Ni P, Ni P ) b ut all exhibit
12 5

-95-

Fig. 33.

Tetradecahedral e nvironment of phosphorus in the
Fe P structure:
are iron atoms.

C is a phosphorus atom; A]_. and B.]_

-96-

tetradecahedral structural units more or less deformed
phase shows a range of homogeneity from the
''Pd P".

stochiometric Pd P to

The decrease in phosphorus is accompanied by a decrease in the

volume of the unit cell, and has been accounted for by phosphorus

. 61
vacanc1.es

On the other hand the eventuality of continuous solid

solution (Fe,Pd~P and (Ni,Pd) P must be considered as such continuous
62
solid solutions have been reported in the Fe-Ni-P ternary system
Let
us consider the "nearest neighbors" shell in the crystalline Fe P,
Ni P, Ni P and Pd P compounds.
12 5

The mean interatomic distances for

"nearest neighbors" (both around a metal atom and a phosphorus atom)
and the average ligancy for the type of pairs consider e d (which is not
n e cessarily an even number sinc e we consider the a v erage ligancy
around non-equivalent atomic positions) are giv en in Tabl e XV .
previously mentioned; the extrapolated value of r
Pd

-P

would be about 2.96

for the binary alloy

K, which is quite close to the nearest

neighbors distance in "Pd P" (Pd rich Pd P phase),though slightly
larg e r.

This is to be expe cte d since the amorphous alloy s ar e mor e

disordered than the corre sponding crystalline phases.

Another experi-

me ntal fa c t corroborates the usefulness of the extrapola tion of r
the palladium side of the diagram.

Que nche d Pd

-P

binary all.oy

consiste d almost exc lusive l y of the c ry stalline phase "Pd P" (Palladium
rich Pd P).

In the light of th e se facts a model based on the atomic

arrangement in ''Pd P" wt ,s considered.
The model was c onsidered f rom the q u asi- c ry s talline appr oach
starting with the atomic sh e ll distances and oc c up ati on numb e rs o f an

-97-

TABLE XV

NEAREST NEIGHBORS INTERATOMIC DISTANCES r

AND COORDINATION NUMBERS N IN METAL RICH PHOSPHIDES

Compound

Metal-Metal

Phosphorus-Metal

rl(~)

Fe P

2.72

10.66

2.34

Ni P

2.68

10.66

2.29

Nil2p5

2.60
(2. 67)

7 .66
(9 .00)

2.39

Pd P
(P-rich)

2. 965

11.33

2.49

Pd P
(Pd-rich)

2.905

11.33

2 .44

-98-

assumed lattice

30 so

A gaussian broadening function was then applied

to each shell to account for mean-square displacements around the center of the shell (thermal or disorder displacements).

Finally a

correlation function provided an increasing damping of the oscillations
due to the different shells with increasing radial distance.

Each

atomic shell is represented by the function

and the quasi-crystalline atomic radial distribution function is:

4rcr p

where:

radial distance to the i th shell

c.1 = number of atoms in i th shell
cri

mean square displacement around ri

critical correlation distance

D(r,d)= damping function depending on the critical
corr e lation distance

= homogeneous density (atoms/g

The quasi-crystalline approach was first applied to a simple fcc mode l
in which metal-metal i nt era tomic distances only wer e consid e r e d and
complete substitutional disorder between iron or nickel and palladium
atoms was assumed.

Wh en multiplied by the appropriate average numb e r

of electrons per meta l atom, the e lectronic radial di st ribution

-99-

function based on the fcc model was unable to give even an approximate
fitting of the 2nd and 3rd shells of the amorphous alloys.

Even an

average of the 2nd and 3rd shell, as suggested by some authors

yielded a poor fit t ing since the 2nd and 3rd she l ls in the amorphous
alloys revealed shorter interatomic distances.

The quasi-crystalline

model based on Pd P (Pd-rich) yielded a much better approximation.
Metal-metal shells only were considered since their contributions are
preponderant in the outcome of the radial distribution function.

The

analytical form of the damping function D(r,d) was evaluated as a
function of r/d according to the method outlined by Kaplow et al.

Xwas deduced from the

A critical correlation distance of about 18

experimental radial distribution functions of Ni-Pd-P and Fe-Pd-P
alloys. corresponding to the distance beyond which no appreciable
oscillations around the homogeneous parabola 4~r
observed.

(~ xiK . )

can be

The cri were also approximated from the experimentally

determined radial distribution functions.
The radial distribution function 4~r
4~r(p(r)-p

p(r) and the function

) for such a quasi-crystalline model are shown in Fig. 34.

Both the radial distribution function and the distribution f unction
W(r) compare well with the results obtained for the four different
amorphous alloys shown in Figs. 7, 8, 9, 12 and 13.

The qualitative

features of the model show a rather sharp first shell, quite well
isolated from the second and third shells which are hard to separate,
especially on the atomic radial distribution curve.

The coordination

for the third shell appears slightly larger in the mode l than actually

-100-

-·
02

Fig. 34.

Atomi c RDF (a) and function W(r) (b) for quasicrystalline models with d
d = 18 K (dotted lines).

(solid line s) and

-101-

observed in the amorphous alloys, but this can be attributed to having

chosen too small a value for cr (that is, underestimating the amount
of displacement disorder for the third atomic shell).

Quantitatively

the metal-metal coordination number for the first shell was about 10.5
which compares quite well with 10.6, the average value obtained for the
amorphous alloys.

More striking were the similarities of the ratios

r /r and r /r .
3 1

The model gave r /r = 1.68 and r /r = 1.91,
2 1
3 1

while the average values for the amorphous alloys were 1.66 and 1.89
respectively.

The structure of the amorphous Fe-Pd-P and Ni-Pd-P

alloys can, therefore, be described quite satisfactorily by a quasicrystalline model based on the Pd P (Pd-rich) structure.

As an example,

Fig. 35 shows the comparison between the distribution functions W(r)
obtained for Ni

-Pd

-P

and for a quasi-crystalline model.

was computed by assuming a linear dependence of r
as the one observed for the amorphous alloys.

The model

which was the same

The progressive substi-

tution of iron or nickel for palladium does not change the structural
disordered network based on the Pd P structure.

The extrapolation on

the nickel side of the diagram indicates a nearest neighbors distance
of 2.61 j which can be considered as the nickel-nickel distance in a
nickel-rich Ni P (''Ni P 11 ) , though such a compound is not ordinarily
stable.

The extrapolation on the iron side is more dubious because of

the lack of data for alloys containing more than about 44 at.% Fe,
which is the end of the amorphous range.

The existence of a small

range in phosphorus content without change in the amorphous structure
can be accounted for by phosphorus vacancies in the tehadecahedral

V\1

C\1

Q..
..._.,

..._.,
"""'

-·.

Q..

Fig. 35.

;:/

...

.... L

-Pd -P
(solid line) compared with
32
53 15
quasi-crystalline mode l (dotted line).

r (A)

Distribution function W(r) for Ni

.....I

-103-

arrangements61 leading to shorter metal-metal interatomic distances.
This would explain the value of r

obtained for Ni

-Pd

-P

, which

is about 1.5% shorter than expected for 20 atomic% phosphorus.

The

lack of evidence of short phosphorus-metal interatomic distances in
the amorphous alloys can be accounted for by the small scattering factor
of phosphorus compared with those of Pd, Ni and Fe, as well as by
probably slightly larger phosphorus-metal distances than in the crystalline phases.

The combination of these two effects leads to the

inseparable mixing of all types of interatomic pairs in the first shell.
This fact however, was accounted for when coordination numbers were
calculated from the radial distribution functions.
The structure of the amorphous Fe-Pd-P and Ni-Pd-P alloys,
quenched from the liquid state, can be satisfactorily described by a
quasi-crystalline model based on the structure of transition metal
phosphides.

The glass-forming elements are believed to be tetradeca-

hedral units which are probably already present in the melt.

The

existence of a linear dependence of int e ratomic distances on camposition is in agreement with the proposed structure.
B.

Magnetic moments in amorphous Fe-Pd-P alloys
In the Fe-Pd-P amorphous alloys, two compositions, name l y

-Pd

-P

and Fe

the third one, Fe

-Pd

-Pd
57

-P

were found to be ferromagnetic, while

is probably superparamagnetic.

Amorphous

ferromagnetic alloys have been previously reported in Au-Co alloys
64
obtaine d by vapor d e position
and in Fe-P-C alloys quenc hed f rom the

-104-

65
liquid state

The existence of ferromag netism in amorphous solids

was theoretically predicted by Gubanov

who showed that only short

range interactions are required for ferromagnetism, and that there
is no n e ed to assumed long range crystalline .order.

Since,as ex-

plained in sectionvii, the structure of amorphous Fe-Pd-P alloys is
based on the existe nce of local order similar to that found in crystalline ferromagnetic phosphides,it is not too surprising to find that
the amorphous alloys are also ferromagnetic.
The crystalline phosphides Fe P, Fe P and FeP are ferromagneti c ,
with saturation moments of 1.84, 1.32 and 0.36 Bohr mag n e tons per iron
1 y, wh ereas F e P
atom respect1ve

. an t'f
· 45 .
1s
1 erromagnet1c

The moments

in the iron phosphides are lower than in pur e iron mainly bec aus e o f
the filling of the 3d orbitals of iron by electron transfer from
phosphorus

Simi lar filling of the d orbitals of iron group

metals have b een reported in othe r phosphide s

, as we ll as in boride s

and carbides, which also have a tetradecahedral atomic arrangement
for metal rich c ompounds around the composition Me x.

A plot of satu-

ration ferromagnetic mome nts in the crystalline iron phosphides as a
function of the ratio of the atomi c conc e ntrations of Fe to Fe+P i s
shown in Fig. 36.

The variation of the mome nt p e r iron atom with th e

concentration ratio is almo13t linear and extrapolat e s to a zero mome nt
at a conc entration ratio of about 0.44.

The saturation mome nts me as-

ured for the thr ee amorphous Fe-Pd-P alloy s also shown in Fig . 36
f all approximately on a straig ht line whic h is above that of th e
crystalline phosphid e s and seems to have a slightly larger slope .

0.4

Fig. 36.

0.3

0.5

0.6

0.7

0.8

Saturation moments in amorphous Fe-Pd-P alloys (triangles) and in iron phosphid es (circles)

Fe
Fe+ P

c 1.0

......

.........

::i.

£I)

..........

3.0 - - - - - - - - - - - - - - - - - - - - - - - - - - - . , .

-106-

The fact that for a given concentration ratio Fe/(Fe+P) the
moments for the amorphous alloys are larger than those in the crystalline phosphides can be interpreted in different ways.

The most

probable explanation, however, is the existence of simultaneous
electron transfer from phosphorus to iron and pa l ladium: the linear
decrease of the saturation moment of the amorphous Fe-Pd-P alloys with
decreasing Fe/Fe+P ratio can be attributed to the progressive filling
of the holes in the 4d band of Pd and the 3d band of Fe by electron
transfer.

In the amorphous alloys, however, the number of holes in the

d bands is probably different from the values in the pure elements,
due to a different overlap of s and d bands.

The presence of larger

moments in Fe-Pd-P amorphous alloys suggests also a possible contribution of palladium to the overall ferromagnetism.

Additional evidence

of the ferromagnetic coupling between iron and palladium is given by
the superparamagnetic behavior of the alloy Fe

-Pd

-P

The fact

that palladium may contribute to the ferromagnetism of alloys containing iron-group metals has been recognized by a number of investigators
(cf. Ref. 69 for instance).

This contribution to the bulk ferromagne-

tism has been diversely interpreted and the actual moment carried by
individual palladium atoms has been estimated anywhere from 0.1
0.7

~·

However, it seems rather well established that palladium con-

tributes to the building of ferromagnetic complexes (or 11 atmospher e s 11 )
around iron (or c obalt) atoms in ordinary [ ce alloys.
effect of favoring

Thi s h as th e

clus t e rs of iron and palladium atoms which h L' ar,

-107-

as a whole, rather large moments.

The large value of 5.98

~/iron

atom obtained from the Curie constant in the paramagnetic range of
Fe

-Pd

-P

could hardly be explained by assuming that iron is in

a triply ionized state (Fe +) with a spin moment of 5.92
pointed out by Wollan

~/atom.

, such highly ionized state are very unlikely

for conducting metallic systems.

The only other alternative consists

of clustering via polarization of palladium atoms.

Actually such an

explanation has been proposed to explain the experimentally observed
magnetic moments in Pd-Co-Si amorphous alloys

In view of the

superparamagnetic behavior of the approach to saturation at low ternperatures and of the large moment per iron atom, it seems, therefore,
probable that some clustering occurs in Fe
neutralizing effect of phosphorus.

-Pd

-P

, in spite of the

Such a clustering is all the more

likely in amorphous systems where only the closest atomic shells (and
mainly the nearest neighbors shell) contribute to the short range order.
Determination of the cluster size is not possible in the absence of
data for lower iron concentrations .

The large tail effect present in

the magnetization versus T behavior of the alloys Fe
Fe

-Pd

-P

-Pd

-P

and

before a clear bulk ferromagnetism is attained, can

probably be accounted for by the high degree of disorder of the amorphous alloys and some degree of clustering accompanied by palladium
polarization.

Some of the clusters might still act paramagnetically

while the rest of the solid already shows ferromagnetism, as it was
suggested for th e Pd-Co-Si amorphous a ll oys

Such an int e rpr e tation

might also account for the pec uliar b ehavior of the low temperatur e

-108-

resistivity of the amorphous Fe-Pd-P alloys.
The model proposed for the structure of amorphous Fe-Pd-P and
Ni-Pd-P alloys implies a short range order quite similar to that
existing in the metal rich phosphides.

The magnetic moments of the

Fe-Pd-P amorphous alloys are in agreement with such a model, in which
electron transfer from phosphorus to the metals reduces the saturation
moments.

A small moment can be attributed to the palladium atoms

which contribute to ferromagnetic ordering.
C.

Electrical resistivity of amorphous Ni-Pd-P and Fe-Pd-P alloys
The amorphous Fe-Pd-P and Ni-Pd-P alloys investigated are metal -

lie conductors.

Their resistivity at room temperature is approximately

100 to 150 ~~em, which is about two to three times that of the crystalline alloys of the same composition.

The larger resistivity of the

amorphous alloys is the result of the rather high degree of disorder
which characterizes the amorphous state.

Between 480°K and about 160°K,

the resistivity of all alloys decreases almost linearly with temperature.

The slope of the linear part of this curve is only about 10-

O-cm/°K which is of the order of magnitude of one-tenth that of the
same alloys in the equilibrium crystalline state.

This small tempera-

ture coefficient of resistivity can also be attributed to the large
disorder in the amorphous structure and to the absence of long range
periodicity, since the contribution of the phonon scatte ring is
expected to b e very small in amorphous struc tur e s

According to

Ziman's the ory, extended by Gubanov to amorphous metallic conductors

-109-

the main temperature dependent term in the mean free path of conduction
electrons is the correlation function, which is a slowly varying function of temperature.
The most striking feature of the low temperature resistivity
of the amorphous Fe-Pd-P and Ni-Pd-P alloys is the existence of a minimum at temperatures varying from 9 to 96°K, according to the alloys.
As it was shown in section IV,the low temperature resistivity can be
reasonably well described by a relation of the type:

r(T)

where r(T)

= r 0 + ~ T 2 + ~ r 0 - a Log T

= p(T)/p(294°K).

temperature T

This relation is best valid below the

of the minimum.

At temperatures above T , the T

is dominant until the linear variation is reached .

(1)

term

The variation in

can be explained in terms of the band structure of the Fe-Pd-P

and Ni-Pd-P alloys which contain 80 at.% transition e leme nts .

It has

been shown that electron- e lectron interactionsin the transition metals
contribute substantially to the resistivity at low tempe ratur e through
collisions between s electrons (conduction electrons) and d electrons
which are mainly bound electrons.
actions contribute a T

. . 71
t1v1ty

Such s-d electron-el ectron inter-

t e rm in addition to the normal lattice resis-

In the amorphous alloys where the main characteristics of

the s and d bands are expected to prevail, such a T

contribution

appears clearly at low t e mperatur e since the e lectron-phonon c ontribution to resistiv ity is small .

The r e sistivity minimum is r e lated to

-110-

the existence of a -Log T term in equation (1).

This logarithmic

contribution is indicative of a Kondo effect .

According to Kondo's

analysis

, s-d interactions in dilute magnetic alloys result in a

-Log T contribution to the resistivity, provided the exchange integral
J of the s-d interaction is negative (antiferromagnetic coupling).

This

s-d interaction is actually the coupling betwe en localized and conduction
electrons spins.
The occurrence of a Kondo effect in Fe-Pd-P amorphous alloys
constitutes a puzzling fact in several respects.

The hypothesis of

Kondo implies the existence of localized moments and requires the noncorrelation of the localized spins.

Such a picture is rather hard to

conceive for ferromagnetic alloys where strong d-d interactions take
place.

Moreover, iron could hardly be considered an impurity in alloys

containing 23 at. %, 32.4 at.% and 44 at.% iron.

However, it can b e

noticed that the importance of the Kondo effect, as charact erized b y
the depth of the minimum, decreases drastically with increasing iron
conte nt.

Though the dispersion of data is quite large, this fact

appe ars quite cle arly in Table XII.
occurs in the Fe
netic.

-Pd

-P

In addition, the larg e st effect

alloy , which is assumed to be superparamag-

It appears the refore , that the strong d-d interactions existing

in the ferromagn e tic alloys are quite detrime ntal to the occurrence of
the r e sistiv ity minimum, but cannot suppress it c omplete l y.

The mag ne ti-

zation of the amorphous F e -Pd-P alloys was shown to e xhibit lar ge tail
e f fect s at th e ons e t of f e rr o mag twt ic ord e ring .

It i s , t h e r efor e ,

-111-

likely that the bulk ferromagnetism cannot prevent the existence of
localized moments on a small fraction of the iron atom, provided, for
instance, they have a sufficient palladium environment.

Such an

hypothesis is consistent with the fact that the Kondo effect is increased for higher palladium concentrations.

The existence of localized

moments in otherwise ferromagnetic alloys has been recognized by some

. i ans 73' 74
an d t h eoret~c

~nvest~gators

alloy, the postulated clusters of iron atoms and associated polarized
palladium atoms are only partly coupled and one can therefore expect
a more pronounced Kondo effect.

Investigations on alloys with lower

iron content would be very helpful in providing more clues on the Kondo
effect in the amorphous Fe-Pd-P alloys.

Unfortunately, the amorphous

range does not appear to extend to very low iron contents.
The Kondo effect observed for the amorphous Ni-Pd-P alloys seems
to be easier to explain in terms of localized moments due to magnetic
impurities.
alloy Ni

The magnetization measurements performed on the amorphous

-Pd

-P

showed an intermediate behavior between weak para-

magnetism and Pauli paramagnetism, with a very small residual moment
even at room temperature.

Such a behavior could be explained by the

presence of a very small concentration of iron in palladium (and possibly
nickel).

Evidence that the palladium utilized for the preparation of

these amorphous alloys contains a very small conc e ntration of iron has
been confirmed by magnetic

and

r e sistiv~ty

measurcne nts.

A Kondo

effect due to v e r y small concentrations of iron has b<.!en obs e rved in

-112-

copper and gold
variations of T

for instance.

The fact that no significant trend of

or a with nickel content (cf. Table XI) was observed

confirms that iron impurities present in both palladium and nickel are
probably responsible for the Kondo effect.

If this effect were due

to localized moments on nickel atoms, one might expect a linear variation of a with nickel concentration and a variation of T

proportional

to the square root of concentration.
The high temperature resistivity measurements performed on
Fe-Pd-P and Ni-Pd-P amorphous alloys were particularly helpful in
following the crystallization process, and were correlated with X-ray
diffraction experiments.

The increase in resistivity shown by most of

the amorphous alloys in the range of 280 to 320°C seems to be related
to the formation of very small crystallites e mbedded in : the amorphous
matrix.

Evidence of very small microcrystals in an amorphous matrix

appears in the x-ray diffraction patterns of this pre-cry stallization
stage, as characterized by very broad Bragg peaks superimposed on the
amorphous band.

Such micro c rystals probably act as additional scatter-

ing centers during the e arliest stages of their dev e lopme nt, when they
are still rather far apart.

In the Fe-Pd-P and Ni-Pd-P alloys, the

crystallization t e mp e ratur e t

is always about 40°C higher than the

temperature of ons e t of the increase in resistivity tN.
in resistivity observe d at t
crystalline phases.

The sharp drop

corresponds to the rapid g rowth of

In the Ni-Pd-P alloys, th ese phas e s are metastabl e

and r evert to the stable phas e mixture at higher temperatures.

The

-113-

behavior of the resistivity of the stable crystalline phases did not
exhibit any singularities except changes of slope probably related to
a Curie point (cf. Figs. 24 and 25).

-114-

VIII.

SUMMARY AND CONCLUSIONS

The structure and properties of iron-palladium-phosphorus and
nickel-palladium-phosphorus alloys quenched from the liquid state hav e
been investigated.

Since these alloys can be obtained in the amor-

phous state within a relatively large range of concentrations for the
metallic atoms, both structure and properties could be studied as a
function of composition.

In both ternary systems, a line ar r e lation-

ship was found between the nearest neighbor interatomic distances r
and concentration.
distances (r

The ratios between the second and third neighbor

and r

) and r

also varied linearly with concentration .

These relationships constitute an extension to amorphous alloys of the
well known Vegard's law generally applicable to crystalline s olid
solutions.
The structure of the amorphous alloys was tentatively e xplained
by a quasi-crystalline model based on the crystal structure of metal
rich phosphides.

The structural unit used for the mod e l is that

found in Pd P, e xcept that it has a distorted atomic packing.

The

radial distribution functions computed for the model were in satisfactor y a g reement with those experimentally det e rmined.
The iron rich amorphous alloys Fe

-Pd

were found to be ferromagnetic, whereas the Fe
probably superparamagnetic.

-P

-Pd

and Fe

-P

-Pd

-P

alloy is

The saturation magnetic mome nt s observed

for the s e thre e alloy s we r e 2.16, 1. 70 and 1. 07 Bohr magne tons p e r
iron at om r (' spPc tiv ely.

ThL' p r o):!;r e ss i v e r L•duc tiLHl in t h e mng n e tit·

-llS-

moments with decreasing iron content was attributed mostly to electron
transfer from phosphorus to the d band of the transition metals.
Palladium atoms appeared to contribute to the overall ferromagnetism
through the formation of "atmospheres" around iron atoms which could
account for clustering in the alloy Fe

-Pd

-P

The Ni-Pd-P amor-

phous alloys investigated were weakly paramagnetic.
All the amorphous alloys were electrical conductors.

Their

temperature coefficients of resistivity were about ten times smaller
than those of the corresponding crystalline alloys.

These results

gave additional evidence for the non-crystalline nature of the quenched
alloys.

A minimum in the resistivity temperature curves was observed

for the amorphous Fe-Pd-P alloys.

This minimum was in the range from

17.5 to 96°K depending on the composi tion of the alloys, and its
importance increased with decreasing iron content.

The resistivity

minimum was tentatively attributed to a Kondo effect due to localized
moments on a small fraction of the iron atoms.

The amorphous Ni-Pd-P

alloys also showed a resistivity minimum in a range of temperatures
from about 9 to 14°K depending on composition.

This Kondo effect was

attributed to the presence of small amounts of iron impurities in
the palladium, nickel and perhaps also phosphorus used for alloys
preparation .
The validity of the model proposed for the structure of the
amorphous Fe-Pd-P and Ni-Pd-P could be further t e sted by several typ e s
of

e xp L~ riments.

Tlw

analysis

lL•adin~

to t lw radial distribuLi.on

fun,; ll.on was compl fcall'd l>y LIH· pt- t'St'llct• ol

l hn·•· kl.11d s

ur at oms.

-116-

the non-me tallic atom had a very low scattering factor (which was not
the case of phosphorus) its contribution to the diffracted intensity
compared to those of the metals, could be neglected .

Recent experi-

ments indicate that ternary Ni-Pd-B alloys might o e quenched into an
amorphous phase, and if so, this system should be considered for
further investigations. Diffraction experiments with X-rays only may
not be sufficient to establish the fine details of the structure o f
ternary amorphous alloys .

Neutron diffraction experiments would

certainly help in solving the problem. but the small size of the
quenched specimens, especially their thickness, may create experimental
difficulties.
A more detailed study of the ferromagnetic transition c ould be
done by M8ssbauer spectroscopy.

This technique would also be useful

in verifying the assumption of clustering in the amorphous Fe
alloy.

-Pd

Furthermore, some information on the postulated localized

moments responsible for th e Kondo effects observed could be expect e d
from these experime nts .

In this respect , mag n e to-resistanc e experi-

ments might also be of int e rest, since a n e gative mag netor e sistanc e
would be a strong indication of localize d moments.

-P

-117-

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10.

B. Bagley and D. Turnbull, Technical Report No. 17-Division of
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11.

J. Dixmier, K. Doi and A. Guinier, in Physics of Non-crystalline
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P. Pietrokowsky, Rev. Sci. Instr., 34, 445 (1962).

13.

Pol Duwez, Trans. A.S.M., 60, 607 (1967).

14.

Pol Duwez and R. Willens, Trans . A.I.M.E., 227, 362 (1963).

-118-

15.

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16.

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17 .

s. Lin, Ph.D. Thesis, California Institute of Technology (1968).

18.

H. Luo and Pol Duwez, Appl. Phys. Letters, 2, 21 (1963).

19 .

D. Harbur, J. Anderson and W. Maraman, Rapid Quenching Drop
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20.

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21.

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22.

R. W. James, The Optical Principles of the Diffraction of X-rays,
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23.

J. Waser and V. Schomaker, Revs, Modern Phys., 25, 671 (1953).

24.

C. Pings and J. Waser, J. Chern. Physics, 48, 3016 (1968).

25.

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26.

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27.

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28.

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29.

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-119-

s. Strong and A. Averbach, Phys. Rev., 138, Al336 (1965).

30.

R. Kaplow,

31.

s. Strong and R . Kaplow , Rev. Sci. Instr., 37, 1495 (1966).

32.

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33.

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34.

International Tables for X-ray Crystallography, Vol. III, Kynoch
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35.

K. Furukawa, Rep. Prog. in Phys., 25, 395 (1962).

36.

T. Ino, J. Phys. Soc. Japan, 12, 495 (1957).

37.

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38 .

S. Rundqvist, Arkiv Kemi, Bd 20/7, 98 (1963).

39.

W. Pearson, Hand book of Lattice Spacings and Structur e of Metals ,
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40 .

R. Crewdson, Ph.D . Thesis, California Institute of Technology (1966).

41.

N. Mokrovskii and A . Regel, Zh. Tekhn. Fiz . , 23, 2121, (1953).

42.

H . Chen and D. Turnbull, J. Chern. Phys., 48, 2560 (1968).

43.

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44.

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45.

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46.

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47.

J. Crangle and W. Scott, J. Appl . Phy s. 36, 921 (1965).

48.

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s. Steeb, Fortschr . Chern. Forsch . , Bd. 10/4, 473 (1968).

-120-

SO.

R. Kaplow ,

s. Strong and B. Averbach, in Local Atomic Arrangements

Studied by X-ray Diffraction, Metallurgical Society of the
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H. Ruppersberg, Mem. Sc . Rev. Met., LXI/10, 709 (1964).

52.

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53.

0. Pfannenschmid, Z. Naturforsch., lSa, 603 (1960).

54.

J. Dixmier and A. Guinier, Mem. Sc. Rev. Met., LXIV/1, 53 (1967).

55.

B. Bagley and D. Turnbull, J. Appl. Phys., 39, 5681 (1968).

56.

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57.

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58 .

Schonberg,
Acta Chern. Scand., 8, 226 (1954).

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60.

J. Bernal, Nature, 185, 68 (1960).

61 .

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62.

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63 .

s. Fujime, Japan J. Appl. Phys . , 5, 1029 (1966).

64.

s. Mader and A. Nowick, Appl. Phys. Letters, 7, 57 (1965).

65.

Pol Duwez and S . Lin, J. Appl. Phys., 38, 4096 (1967).

66.

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67.

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68.

P . Albert et al., J . Appl. Phys., 38, 1258 (1967).

-121-

69.

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70.

E . Wollan, Phys. Rev., 112, 1710 (1962).

71.

J. Ziman, Electrons and Phonons, Clarendon Press- Oxford (1963).

72.

J. Kondo, Prog. Theor. Phys., 32, 37 (1964).

73.

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74.

V. Jaccarino, J. Appl. Phys., 39, 1166 (1968).

75.

M. Weiner, pri.vate communication.

76.

R. Hasegawa, private communication.

77.

G. Van den Be rg, in Proceedings of the 7th International
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-122-

APPENDIX I

Phase diagrams in binary Fe-P, Ni-P and Pd-P systems
(cf. M. Hansen, Constitution of binary alloys, Mac Graw-Hill - New
York (1958)).

-123-

1600
1534°

0..
f'() _

1500 r\

1400
13900
1300

.. 1100
l.J.J
a:

I-

/1262°
40

\v/i

24.5 1166°

1050°
17.5
4 .9

1000

1400

\ I

a..
:iE

::::>
<{

'tu..

0..

I ~r\

0::

I-

1365°

1200
(.)

0..

- ~~ ~1.5~-

910°
900

'I:

1300 r-

.....

.. ~'
\ '\ .. \

.. ~,

' '\

1200 1-

1100 1-

700

.....

.. '

800

'"I

I '
,)

900~

, ./

ATOMIC PER CENT PHOSPHORUS
Fig . 3 7.

F e - P b ina ry pha se d iag ram

,,/.,."'

0 .2
0.4
WT-% P

, ///

~----_,/

4000

,.Y j

1000 r-

600 I

I '

500

0 .6

-124 -

1500

1452°

1400

1300
(.)

w 1200

<:(

a::

1'-

a::

::>
1-

z...

cf'la..
10 N

a.. ·z -z

fi+

117~

Q_N .

c[>

z- -z-

t t

rnlll0°

~·

1100

cf'
.!:P

: :32~~

1~25j ..

LLI

~ 1000

1000°

\7?~

900

880°

800

20
30
40
50
60
ATOMIC PER CENT PHOSPHORUS

Fig. 38.

Ni-P binary phase d i agram

-125-

1600
1500

.1553°

1400

c£1
"0
a..

1300

..
w 1200

a::
:::)
t-

rt'>IO

a..10

1:}-

••I

llOO

a::
a..
:::2E 1000

' 1\

900

807°

'/ v

:~
I I ~y
10

! :

/, '~0"1

78 °
'l1 f'

700
6000

1047

800

a..c£1

32.7

,"'

'" "_.,"'1150°

.,
I'

796°

PdP2+P

20
30
40
50
60
70
80
ATOMIC PER CENT PHOSPHORUS
Fig. 39.

Pd-P binary phase diagram

100

- 126-

APPENDIX II

Program used for the determination of Electronic Radial
Distribution Functions

This program is written in FORTRAN IV language for processing through
an IBM 360/75 or an IBM 7094 system.
1)

Input data
- Composition in atomic %
- Density (in atoms/X )
Experimental intensity, in counts per second: 601 readings,
corresponding to one datum every 0.2° up to 28=80°, and one
datum every 0.4

up to 28=160 .

- Background intensity, in counts/sec.
- Tables of scattering factors for the appropriate radiation.
2)

Sequence of Operations
Part 1

Input of diffraction data; correction for background;

Polarization correction.
Part 2

Computation of (f ) =

~ x.f.
for each of the 601
1 1

values

of s = 4:rc sin8
A,

computation of (f
Part 3

correction for anomalous dispersion;

= (~ x . f.) 2 /(~ x.Z.) 2

High angle fitting, yielding the coherent intensity

scaled in electron units.

Computation of the interfe r e nce

function sl(s) for all 601 values of s.

-127-

Part 4

Fourier inversion yielding W(r) and the actual radial

distribution function r W(r).

The Fourier integration is

performed by the trapezoidal method which is accurate enough

for such a large number of points.

W(r) and r W(r) are

evaluated usually for values of r increasing from 0 to 10

£,

by steps of 0.05 £.
3)

Plots
----The program provides plots of the scaled coherent intensity, the
interference function si(s) and the functions W(r) and r W(r).