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NBS

463

Mossbauer Effect Study

Of Magnetic Ordering in

Copper-Rich Cu-Ni-Fe Alloys

S

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
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UNITED STATES DEPARTMENT OF COMMERCE

C. R. Smith, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 463

ISSUED AUGUST 1968

Mossbauer Effect Study of Magnetic Ordering

in Copper-Rich Cu-Ni-Fe Alloys

LJ. Swartzendruber

Metallurgy Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

Sponsored by the Department of the Interior Office of Saline Water, Contract No. 14-01-0001-1091

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402

Price $1.25.
ABSTRACT

The Fe Mossbauer effect has been observed in a series of

copper rich Cu-Ni-Fe alloys, and for two samples of gold rich

Au-Fe. At low temperatures most of these alloys order magnetically

and the Mossbauer effect spectra develop typical six-line hyperfine field structure. For dissolved Fe the room temperature Cu-Fe

and Au-Fe spectra consist of a doublet superimposed on a central

line. In Cu-Ni-Fe the spectra at room temperature consist of a

doublet with no evidence of a central line when the Ni concentration

is above 10 atomic percent. The doublet separations at room temperature (and their estimated uncertainties) are 0.69 + 0.02, 0.58 +

0.02 and 0.22 + 0.04 mm/ sec in Au-Fe, Cu-Fe, and Cu-Ni-Fe respectively. By observation of the spectra in a magnetic field the

doublet structure is shown to be due to magnetic interactions between Fe and other Fe or Ni atoms. Isomer shifts, metallurgy in

Cu-Ni-Fe alloys, sample preparation techniques, and the Mossbauer

effect equipment developed are also discussed.

Key words: alloys; copper; nickel; iron; gold; Mossbauer effect;

magnetism.

11
TABLE OF CONTENTS

Chapter Page

I. INTRODUCTION 1

II. BACKGROUND 3

A. Related Measurements on Au-Fe, Cu-Fe and Cu-Ni .... 3 B. Origin of 5'Fe Mossbauer Effect Line Structure .... 5 C. Metallurgy of the Cu-Ni-Fe System 13

III. EXPERIMENTAL PROCEDURE 19

A. Sample Preparation 19

B. Mossbauer Effect Spectrometer 23

C. Magnet and Dewar System 26

D. Data Analysis 27

IV. EXPERIMENTAL RESULTS 30

A. Preliminary 30

B. Alloys Containing 0,5 Atomic Percent Fe 32

C. Source Experiment 33

D. Cu-Fe Alloys 33

E. Magnetic Field Results 34

F. Other Results and Summary 36

V. DISCUSSION OF RESULTS 38

A. Metallurgical Considerations 38

B. Origin of the ^-Fe Doublet 43

C. Discussion of- the "V^-Fe Doublet . .- 48

D. Isomer Shifts 52

E. Conclusion 53

REFERENCES 55

in
LIST OF TABLES

Table Page

III-l. Impurities detected by spectrochemical analysis

of starting Cu-Ni alloy foils 64

III-2. Impurities detected by spectrochemical analysis

of Fe enriched Fe_0„ 65

III-3. Absorption spectrum of Fe calibration sample 66

IV-1 . Parameters for quenched (Cu., Ni )_ __ r Fe^ __ r 1-x x 0.995 0.005

alloy spectra analyzed as a sum of separate

Lorentzian lines 67

IV-2 . Parameters for quenched (Cu., Ni ). „„,_Fe„ „^ r 1-x x 0.995 0.005

alloy spectra analyzed as a six-line hyperfine

pattern 68

69

IV- 3 . Parameters for Cu., Fe alloy spectra analyzed

1-y y

as a sum of separate Lorentzian lines

IV-4 . Parameters for annealed Cu n n

-

l Fe _ spectra

at 205°K with and without an applied field 70

IV- 5 . Parameters obtained for 298°K spectra from

three quenched samples of (Cu_ ^Ni. , ~), Fe . . . . 71

0.90 0.10 1-y y

IV-6 . Summary of Mossbauer effect spectra for

(Cu, Ni ). Fe alloys 72

1-x x 1-y y

IV
LIST OF FIGURES

Figure Page

II-l. Ternary and binary diagrams for Cu-Ni-Fe alloys. ... 77

Ill-l(a). Electron-probe scan of annealed Cu Q

-,Fe 78

0.9/ o

.

Oj

Ill-l(b). Electron-probe scan of annealed Cu_ ~,Fe_ _, 78

0.94 0.06

III-l(c). Electron-probe scan of annealed

(Cu0.90

Ni

0.10 ) 0.92

Fe

0.08

78

III-2. Block diagram of Mossbauer effect spectrometer 79

III-3. Schematic of driver electronics 80

III-4. Iron calibration spectrum. 81

III-5. Fixed temperature dewar. 82

III-6. Superconducting magnet and dewar system. 83

III-7. Detail of sample holder and source chamber. 84

IV-l(a). Sample no. 1 of CuA on Je. _ at 298°K fitted

u . y y_> u . uu_> to three Lorentzians 85

IV-l(b). (Cu099Nl

_ 01 ) 0-995

Fe0005 at 298"K fitted to

three Lorentzians 86

IV-l(c). (% 95

Ni005 ) 995

Fe

0()05

at 298°K fitted to

one Lorentzian 87

IV-l(d). (Co090Ni

1Q ) 995

Fe0005 at 298°K fitted to

two Lorentzians 88

IV-l(e). (%_ 79

Ni021 ) 995

Fe0005 at 298'K fitted to

two Lorentzians 89

IV-l(f). (Cu067Ni _33) _ 995Fe

_ 005

at 298°K fitted to

90 two Lorentzians. ;u
IV-Kg). <Cu

. 53

Ni

. 47 ). 995

Fe

0Q5

at 298°K fitted to

two Lorentzians 91

IV-l(h). (Cu0>47

Ni

0>53 ) 0>995

Fe0>005 at 298°K fitted to

two Lorentzians 92

IV-2(a). (Cu0t99Ni0i01 ) 0>995

Fe0005 at 298°K fitted to

two Lorentzians plus a central unresolved sixline hyperfine field pattern 93

IV-2(b). (Cu

Q 95

Ni

05 )

_ 995

FeOiO05 at 298°K fitted to

two Lorentzians plus a central unresolved sixline hyperfine field pattern. 94

95

IV-2(c). (CV90Ni

0>10 ) 0>995

Fe 0005 at 298°K fitted to

an unresolved six-line hyperfine field pattern. • • •

IV-2(d). (Cu079Ni

0>21 ) 0>995

Fe0f005 at 298°K fitted to

an unresolved six-line hyperfine field pattern. .... 96

IV-2(e). (Cu 067Ni

0> 3 3

) 0>995

Fe0>005at 298°K fitted to

an unresolved six-line hyperfine field pattern 97

IV-2(f). (Cu6>53

Ni

0#47 ) 0>995

Fe0i005 at 298°K fitted to

an unresolved six-line hyperfine field pattern 98

IV-2(g). (Cu047Ni

. 53 ). 995

Fe

_ 005

at 298°K fitted to

an unresolved six-line hyperfine field pattern 99

IV-3. Spectra of (Cu, Ni ) n nnc Fe n nni- alloys at 298°K. . . . 100

1-x x 0.995 U.UUd

IV-4. Cu. ,-,Ni,. „„( Co) source, metallic Fe absorber,

l) . b/ U . jj

both at 298°K 101

IV-5. Sample no. 2 of Cu n QQC-Fe n ___ at 298°K fitted

to three Lorentzian lines. 102

IV-6. Sample no. 2 of Cu

g95

Fe at 4.2°K fitted

to three Lorentzian lines. 103
IV-7. Annealed Cu

9y

Fe at 298°K. Fit is to

two Lorentzian lines. 104

IV-8(a). Annealed Cu

9?

Fe at 4.2°K fitted to

two Lorentzians. 105

IV-8(b). Annealed Cu

9?

Fe at 4.2°K fitted to a

six-line hyperfine field pattern. 106

IV-9. Splat cooled sample of Cun Fe noc_ at 298°K. • • • • 107

IV-10. Quenched sample of Cun Q

-,Fe n __ at 298°K. 108

u.y/ u.Uj

IV-ll. Cu-Ni-Fe alloy spectra at 205°K with zero field

and an applied field of 50 kG. - 109

IV-12. Au-Fe alloy spectra at 205°K with either zero

field or an applied field of 50 kG. HO

IV-13(a). Annealed sample of Cu. Q7 Fe at 205°K taken

u.y/ o.uj

in magnet with H=0. HI

IV-13(b). Annealed sample of Cun Q -,Fe n

__ at 205°K taken

u.y/ u .

u

j

in magnet with H = 50 kG. 112

IV-14(a). Quenched sample of ( Cu

.90

N1

. 10^ . 97

Fe

0.03

at 205°K taken in magnet with H = 0. H3

IV-14(b). Quenched sample of (Cu

Q 90

Ni

Q 1Q ) 97

Fe

Q 03

at 205°K with H = 50 kG. H^

IV-15. Spectra of four furnace cooled samples taken

at 298°K. II 5

IV-16. Spectra of four furnace cooled samples taken

at 78°K. II 6

IV-17(a). Spectrum of quenched (Cu

Q 90

Ni

Q 1q )q 9 7 Fe

Q 03

at 298°K fitted to a six-line hyperfine field

pattern. H'

vn
IV-17(b). Spectrum of quenched (Cu

Q 9Q

^±

Q 10 ) Q g?

Fe

Q3

at 298°K fitted to two separate Lorentziarts 118

IV-18(a). Spectrum of quenched ( Cu

. 90

Ni0.10') 0.94

Fe

.06

at 298°K fitted to a six-line hyperfine field

pattern 119

IV-18(b). Spectrum of quenched ( Cu

<90

Ni .k^o. 94Fe

0. 06

at 298°K fitted to two separate Lorentzians 120

IV-19(a). Spectrum of quenched ( Cu

0> 90

N1

o.lO^O. 92

Fe

0.08

at 298°K fitted to a six-line hyperfine field

pattern 121

IV-19(b). Spectrum of quenched (Cu

Q 9Q

N±

Q 1Q ) 92

Fe

08

at 298°K fitted to two separate Lorentzians 122

IV-20. Isomer shifts in Cu-Ni alloys with respect to

pure Fe metal at room temperature 123

V-l. Theoretically generated spectra for combined

longitudinal magnetic field and randomly

oriented electric field gradient 124

vixx
CHAPTER I

INTRODUCTION

Recoilless nuclear gamma-ray resonance in solids was discovered

1 2 in 1958 by R. L. Mossbauer and is generally referred to as the

Mossbauer effect. Mossbauer effect spectroscopy has since proven

itself a useful tool for studies in solid state physics. Many review

articles and books covering the principles and applications are

3-17

presently available. The influence of the electronic environment

on the nuclear gamma-ray transition energy of a Mossbauer nucleus

causes observable hyperfine structure in a Mossbauer effect spectrum.

The possibility of interpreting this structure in terms of the electronic and magnetic properties of the solid in which the Mossbauer

nucleus is embedded is responsible for the large number of current

solid state studies utilizing the Mossbauer effect.

One interesting application is the study of the formation and

interaction of local moments in metals and alloys. The isotope Fe

is well suited to this study since it forms interacting local moments

in many systems, has an easily observable Mossbauer effect with a

narrow linewidth, and has a relatively long lifetime parent isotope

( Co) . The combination of nuclear properties and Mossbauer effect

linewidth gives spectra in which it is possible to resolve magnetic

fields on the order of a few kG. The nuclear properties of Fe also

make possible the observation of electric field gradients in a solid.

18 57

One recent application of the Fe Mossbauer effect has been
the study of the localized moment behavior of very dilute (<0.1%) Fe

impurities in a series of nonmagnetic pure elements. The values for

the localized moments found were in qualitative agreement with the

19

moments derived from magnetic susceptibility measurements. As the

iron concentration is increased in those matrices where it forms a

local moment, the interaction of these local moments brings about

transitions to an ordered magnetic state at low temperature. The

Mossbauer effect spectrum can be used to study the details of this

transition.

20 Since the time Zener suggested that magnetic ordering in some

metals might arise from indirect magnetic coupling via the conduction

electrons, there has been considerable interest in the magnetic properties of alloys in which the magnetic centers are dilute. Extensive

21-25

measurements have been performed on the Cu-Mn system by a number

of techniques. Accordingly a great deal of theoretical work on

magnetism in dilute alloys has been directed toward a description of

this system. The " Fe Mossbauer effect offers a sensitive technique to extend these studies to dilute magnetic alloys containing Fe.

In this thesis the Fe Mossbauer effect was used to study Fe

dissolved in copper-rich Cu-Ni alloys. Some experiments were also

performed in the related AuFe system. The AuFe , CuFe and copper rich

CuNiFe systems were found to possess many similarities in their magnetic behavior as observed by the Mossbauer effect. In addition to a

transition to a low temperature magnetically ordered state they all

appear to retain magnetic structure at higher temperatures. This magnetic structure manifests itself by the appearance of a poorly resolved

doublet in the Mossbauer effect spectra of these alloys.

2
CHAPTER II

BACKGROUND

A. Related Measurements on Au-Fe, Cu-Fe and Cu-Ni . In their

31 MSssbauer effect investigations of the Au-Fe system, Borg et al

.

found magnetic transitions in alloys with as little as 0.84 atomic

percent Fe. This was in disagreement with the earlier investigations

32 33

of Kaufmann et al . ' who concluded that AuFe alloys containing less

than about 6.5% Fe were paramagnetic at all temperatures, while the

more concentrated alloys appeared to have definite Curie temperatures.

34

From the measurements of Kaufmann et al., Arrott calculated a

27 critical concentration for the Au-Fe system of 12% Fe. Sato et al.

took this to be in reasonable agreement with the theoretical value of

17% based on their cluster variation model for a dilute alloy with

only nearest-neighbor interactions.

35

Lutes and Schmit measured the magnetic susceptibility of several

AuFe alloys and found a maximum in the reciprocal susceptibility suggestive of antif erromagnetic ordering. This interpretation is supported by the low induced moment of 0.63 u per Fe atom measured by

D

Of. Henry at 4.2°K in an applied field of 95 kG. This contrasts with the

2 u per Fe atom for very dilute Fe in Au indicated by Lutes and

35 Schmidt as well as by the Mb'ssbauer effect measurements of Kitchens

O ~l o o et al. Also, a Mossbauer effect spectrum for a 5% Fe in Au alloy

at 4.2°K in an applied field of 30.8 kG exhibited very little change

from the spectrum observed at zero field. All these measurements

indicate that, on the average, the magnetic ordering for AuFe with low
Fe concentration is antif erromagnetic . However, they do not specify

the precise nature of the local ordering.

39 40 Mossbauer effect measurements ' for dilute Fe in Cu have

s'hown similar effects. However the study in Cu-Fe is more difficult

due to the limited solubility of Fe, about 3% at 1000°C compared to

40

about 60% for Fe in Au. It appears that the ordering temperature

is higher in Cu-Fe than in Au-Fe for equal Fe concentrations. However, in contrast to the Au-Fe system, the Mossbauer spectra in Cu-Fe

remain complicated and unresolved well below the magnetic transition

41

temperature. As pointed out by Housley this is not expected from

a model which utilizes a distribution of molecular fields which has a42

reasonable temperature dependence, such as the one proposed by Liu.

From the measurements in Cu-Fe and Au-Fe it appears that the

magnetic interaction must be longer range than first nearest neighbor,

and oscillatory in sign. This is similar to the previously observed

28 29 measurements in Cu-Mn alloys. Klein and Brout ' have proposed a

model in which the magnetic interaction couples the solute atoms within small clusters by means of an interaction of the RKKY type. This

model proved successful in explaining the low temperature specific

heat of Cu-Mn, Cu-Fe and Cu-Co . No well defined transition temperature

exists in this model. Instead the randomly oriented moments become

increasingly correlated in an antif erromagnetic manner as the temper43 ature decreases. While this is not inconsistent with the observations on the Cu-Fe system, it is not in agreement with the relatively

OQ / / well defined transition temperature found for Au-Fe.

In further study of the Au-Fe system, Violet and Borg found
structure in their Mossbauer effect spectra at high temperatures.

This structure consisted of a doublet superimposed on a central

singlet. The doublet was interpreted as being due to quadrupole

effects arising from Fe-Fe pairs. The measurements made here have

revealed that this doublet also exists in CuFe and Cu-Ni-Fe alloys at

high temperature. It also appears that this doublet is of magnetic,

rather than quadrupole origin. Since the interpretation of structure

in Mossbauer effect spectra and the metallurgy of the Cu-Ni-Fe

system are important to this study, they are discussed in some detail

below in Sections B and C.

The properties of Cu-Ni alloys have been extensively studied

46-79

by a number of techniques. Of particular interest here are the

49 50 79 conclusions of Goldman ' and of Lang and Ehrenreich ' that the

80 simple rigid-band model gives a poor approximation to the properties of Cu-Ni alloys. They propose a model in which d-holes are

79

present on Ni atoms at all concentrations. Lang and Ehrenreich

emphasize, however, that a real justification of this model in terms

of band theory for nonper iodic systems remains to be given.

B. Origin of Fe Mossbauer Effect Line Structure . In iron

the Mossbauer effect is observed for gamma-ray transitions between the

ground state of the Fe nucleus and its first excited state. The

first excited state has a half life of 0.14 y sec, a magnetic dipole

moment y = -0.155 nuclear magnetons, a quadrupole moment Q = 0.33 b,

and a spin I = 3/2. The gamma-ray transition energy to the ground

state is 14.4 keV. The Fe ground state has a spin I = 1/2 and a

magnetic dipole moment y = +0.0903 nuclear magnetons.
57 The nuclear properties of Fe allow the observation of Mossbauer

effect line structure due to three interactions. The electrostatic

interaction between the distributed positive charge of the nucleus

and the electronic charge density that interpenetrates it gives rise

to the isomer shift. The interaction between the nuclear magnetic

dipole moment and the effective field at the nuclear site gives rise

to magnetic hyperfine field splitting. Finally, the interaction between the nuclear electric quadrupole moment and the electric field

gradient at the nuclear site gives rise to quadrupole splitting. These

three interactions, along with their angular dependences and time and

space fluctuations, are predominately responsible for the line structure

observed in Fe Mossbauer effect spectra.

1. Line Shapes . Mossbauer effect absorption lines are expected to be Lorentzian in shape, with a width determined by the lifetime of the excited level. However if the absorber is of finite

thickness the shape of the energy distribution in the gamma-ray beam

will be distorted as it passes through the absorber. This has been

81 studied in detail by Fraunfelder et al. They found that for t < 10

the shape of the absorption line is Lorentzian to within about 1/2%

but has an increased linewidth, r, that can be approximated by

T = 2T (1.00 + 0.135t) for < t< 5 o —

= 2T (1.01 + 0.145t - 0.0025 t 2

) for 4 < t < 10 II-l

where t = fna is the absorber thickness with f the recoil free fraction

o of the absorber, n the number of Fe nuclei per unit area, and c the

resonance absorption cross section for a single nucleus.
2. Isomer Shif t. This is a nuclear volume effect and results

from the fact that the ground and excited states of the nucleus have

different effective charge radii. The electrostatic interaction

energy due to the overlap of electronic and nuclear charge is therefore different for the two levels and the y-ray energy is shifted.

Neglecting relativistic effects, one obtains for the isomer shift, s,

the expression

4tt _ 2 r

I , . 1 2 | ,.

1 2 , _,2 AR TT _ s = — Ze [ j ij> (o) j - I * (o) ] R — II-2

j a s k.

where AR is the increase in nuclear radius of the excited state over

the ground state (assumed << R) , Z is the nuclear charge, and

2 2

| \\> (o) | and ty (o) | are the electron densities at the nuclear

3. S

site in absorber and source respectively. Correction factors taking

into account relativistic corrections to the electron wave functions

82

have been given by Shirley. These corrections can be as high as 30

percent for heavier nuclei. The centroid of the Mossbauer effect

spectrum is also shifted by the second order Doppler effect.

Thus if a doublet is observed in a Mossbauer spectrum one possible

origin is a non-homogeneous specimen. This could give Fe in two

different environments, each with a different isomer shift.

3. Magnetic Hyperfine Splitting . The Hamiltonian for the

interaction between the nuclear magnetic moment and a magnetic field

can be written

H = - y T

' H ,, H-3

m I eff

where H _- refers to the effective magnetic field at the nucleus. In

eff

Fe the spin 3/2 excited level is split into four sublevels while the
spin 1/2 ground level is split into two sublevels. This gives rise to

eight possible transitions, two of which are forbidden by the selection

rules for Ml transitions. The six remaining transitions, along with

their angular distributions are listed below in order of increasing

energy

:

Transition Angular Distribution

-3/2 -> -1/2 3(1 + cos

2

6 )

-1/2 + -1/2 4 sin

2

6

-1/2 -> +1/2 1 + cos 8

+1/2 + -1/2 1 + cos

2

6

+1/2 * +1/2 4 sin

2

6

+3/2 -> +1/2 3(1 + cos

2

6 )

Here 6 is the angle between the magnetic field and the direction of

propagation for the gamma-ray. This gives rise to the familiar sixline absorption pattern for iron metal (see Fig. III-4) . A magnetic

field oriented at random to the line of observation of the gamma-ray

gives an intensity ratio of 3:2:1:1:2:3 for the six lines. If the

magnetic field is longitudinal, i.e. points in the same direction as

the direction of gamma-ray travel, the six lines will have an intensity

ratio of 3:0:1:1:0:3 and only four lines will be observed. Finite

thickness effects, instrumental broadening, and field distributions

can serve to modify these theoretical ratios somewhat.

The effective field at the Fe nucleus is usually large for Fe

in a magnetic material below its transition temperature, -330 kG for

Fe in metallic form at room temperature. The origin of this field has

Q O Q A been discussed by Watson and Freeman and by Marshall and Johnson.

The large value observed in iron metal is almost entirely due to core

polarization.

8
4. Quadrupole Splitting . The Hamiltonian for the interaction between a nucleus with quadrupole moment, Q, and an electric

field gradient, eq, at the nuclear site can be written

% - ztohr [ 3I

Z

2 - I(I +1» +

\

" »+

2 + *3 i «-*

where _

9 v eq = V = ZZ 3z Z II-5

with V the electric potential. The asymmetry parameter n =

(V - V )/V and I, = I +il . The z direction in the above xx yy zz + x — y

Hamiltonian is taken in the direction of the principle axis of the

electric field gradient. If the field gradient has axial symmetry

V = V and n = 0. Thus n is a measure of the deviation from axial xx yy

symmetry. For cubic or spherical symmetry each of the V.. =0 and

the quadrupole interaction vanishes.

Consider the case of axial symmetry. The ground state of Fe

has Q = and thus is not affected. The excited state, with spin 3/2

is split into two levels with separation

A = eQV /2 II-6

zz resulting in two possible transitions and a Mossbauer spectrum with

two lines. The angular distributions for the two transitions are

given by:

Transition Angular Distribution

2

+3/2 -> +1/2 1 + cos 9

+1/2 -* +1/2 5/3 - cos

2

9

Here 9 is the angle between the principal axis of the electric field

gradient and the direction of gamma-ray propagation. If the electric

field gradient is randomly oriented the average intensity is the same

9
for both transitions. However if the recoil free fraction were to

have an angular dependence, the average intensity could be different

for the two transitions. This would result in a Mossbauer spectrum

with the appearance of an asymmetric doublet. This is generally reo c f erred to as the Goldanskii effect.

The origin of electric field gradients in metals has been discussed by Watson et al. ' They can be expressed as

« = <latt (1 " *-> + «loc (1 " R

n> II-7

where q.. is the field gradient due to charges outside an atomic

sphere centered at the nucleus in question, and q.. is the field

gradient due to conduction electrons within the atomic sphere. The

go

factors Y and R^ are Sternheimer antishielding factors. In this

0° Q

°

thesis we will not be preoccupied with the source of field gradients.

Main interest will center on determining if a given interaction is

of magnetic or quadrupole origin.

5. Combined Magnetic and Quadrupole . If the principal

axis of the electric field gradient tensor is not in the same direction

as the magnetic field, no closed form solution is possible for this

case. In general the magnetic substates will be mixed by the quadrupole interaction and all eight possible transitions will be allowed,

2 yielding complex spectra. If e qQ/yH<<l and the electric field gradient

is axially symmetric the energy levels of the excited state will be

given by

E = -y

eHM

z + (-1) l Mll +1/2 Sja 3 co « 2e -1 H-8

10
where 9 is the angle between the magnetic field and the electric field

gradient

.

2 For the more complex situations where e qQ and yH are comparable

and the angle between the electric field gradient tensor principal

axis and the magnetic field may be at random, it is advantageous to

use machine computations . Computer methods for performing such computations for a wide variety of experimental situations have been

89 developed by Gabriel and Ruby. The use of these calculations for

the case of Fe has been described in detail by Collins and Travis

.

6. Relaxation Effects . The effect of fluctuating magnetic

fields and electric field gradients on Mossbauer effect spectra have

been recently considered by a number of authors. The presence

of these relaxation effects can, for example, distort the shape of a

quadrupole doublet giving it an asymmetric appearance, cause a magnetic field splitting to be observed in a paramagnetic material, and

distort the shape of a six-line magnetic hyperfine pattern.

Consider Fe in a matrix in which there are a number of unpaired

electrons at the iron site giving a resultant spin S along the axis

of quantization. The presence of this spin results in an effective

field H at the nucleus, established mainly through the mechanism of

87 core polarization. Even in a magnetized material the spin S will

undergo a constant motion, due to spin-spin and spin- lattice relaxation mechanisms, which can be characterized by a spin flip frequency

a. In a magnetized material S will spend, on the average, more time

in one direction than in the other. The magnetization is expected to

be proportional to <S >, and hence <H > to the magnetization. If the

11
spin flip frequency is much greater than the Larmor frequency

co = yH /-ft then the observed energy level splitting will be proportional to <H > and hence to the magnetization. If the spin flip

frequency is very small compared to the Larmor frequency then the

observed energy level splitting will be proportional to H rather than

to <H >. Thus even in paramagnetic materials in which <H > = it

z z is possible to observe a magnetic hyperfine splitting if the spin flip

frequency is very low. In the intermediate case, where the spin flip

frequency and Larmor frequency are of comparable magnitude, complex

91

spectra with broad lines are expected. These expected spectra are

very similar to those obtained in the presence of a hyperfine field

distribution.

Q

For the case of pure Fe metal we have H = -330 kG, to = 1.6 x 10

Z i-i Q

rad/sec for the excited state and to = 2.8 x 10 rad/sec for the

ground state. Thus if the spin relaxation time is much less than

_o

about 10 sec one expects the magnetization and observed magnetic

hyperfine splitting to be proportional. In metals this is usually

assumed to be the case. In pure Fe metal the careful measurements of

102 Preston et al . have shown that the observed H is closely proportional

to the magnetization, and that there is no observable broadening of

the individual lines as a function of temperature. Thus no relaxation

effects are apparent in pure Fe metal. Although there are hints '

that relaxation effects might be present in, for example, dilute Fe

in Pd or Au, their existence for Fe in metallic form has been definitely

established only in the case of large super paramagnetic precipitates. ' In this case the Mossbauer effect spectra show changes

over a wide temperature range. Such behavior has not been detected

12
in this study.

C. Metallurgy of the Cu-Ni-Fe System . Because of its importance

to this study the metallurgy of the Cu-Ni-Fe ternary alloy system

will be discussed briefly. This system has the simplifying feature

that it contains only body-centered-cubic (bcc) and face-centeredcubic (fee) crystal structures (with the exception of the composition

Fe„Ni which attains the ordered Cu„Au (Ll~) structure). However, the

metallurgy of the system is quite complex and cannot be considered to

be completely understood at present. We will first consider the

associated binary systems and then the ternary system. The binary and

ternary diagrams are shown in Fig. II-l.

1. The Cu-Ni Binary System . The Cu-Ni binary system forms

107 only a fee structure and has a complete range of solid solubility.

Homogeneous solid solutions at any composition can be prepared by a

melting, quenching, and homogenizing procedure. However, a number

of studies have indicated a tendency for a small amount of clustering

to occur. The tendency towards clustering has recently been

studied in a neutron diffraction experiment by Mozer et al . They

found that, for a Cu„ __ c Ni_ ..,,. sample, furnace cooled from 1021°C,

0.525 0.4/5

the probability of finding a Ni atom in the first coordination shell

of a given Ni atom was enhanced from the random probability of 0.475

to 0.542. In the second coordination shell the probability of finding

Cu atoms was enhanced. On the basis of small angle X-ray scattering

lift a much larger clustering tendency was reported by Kirdon. Thus, although the amount is an open question, it is clear that there is some

tendency for clustering in Cu-Ni alloys.

13
2. The Fe-Ni Binary System . Face-centered-cubic y-Fe is

completely soluble in nickel which is also fee. Equilibrium is

difficult to achieve in the mixed bec and fee (a + y) field (.Fig. II-l)

since the a + y transformation on heating or cooling is the martensitic

type. It is possible to maintain Fe7

-.Ni in the fee phase down to

about 0°C. The order-disorder transformation around FeNi~ (which

attains the ordered Cu~Au structure) covers a wide range of composition,

about 50-80% Ni.

117

3. The Cu-Fe Binary System . The solubility of Fe in Cu or

of Cu in Fe is small. According to the copper-rich end of the diagram the solubility of iron in copper reduces from about 3.0 at.%

at 1060°C to practically zero at room temperature.

Only a small amount of Fe can thus be retained in solid solution

in pure Cu. At room temperature the equilibrium structure is almost

pure Cu and a-Fe. Precipitation of Fe in a copper-rich Cu-Fe solid

solution consists first in the formation of coherent particles

(Guinier-Preston zones) of y~Fe which can later transform to a-Fe if

they reach sufficient size or if the alloy is cold worked. The

formation of the y-~Fe precipitates was first suggested by Bitter

. 118,119 , ,_ . . .,_.,. et al. on the basis of magnetic susceptibility measurements.

The realization that the initially paramagnetic Fe precipitates

could be made ferromagnetic after cold working or extended aging at

120 elevated temperatures led Smith to suggest that the paramagnetic

precipitate might well be fee and coherent with the Cu matrix, while

the ferromagnetic precipitate could be identified with the more stable

bec a-Fe structure.

14
121 122

In an attempt to confirm Smith's suggestion, Denney '

studied a Cu-2.4% Fe alloy. His samples were first solution annealed

at 1060°C, then quenched. The samples were then precipitation

annealed at temperatures up to 800°C. Magnetization measurements revealed no ferromagnetic precipitates. After cold working at room

temperature to start the y

-> a transformation the samples were again

raised to the annealing temperature for one minute to complete the

Y > a transformation. The samples were now ferromagnetic and their

saturation magnetization was measured in a field of 10 kG. Denney

concluded that the precipitation process proceeded as a diffusion

limited growth process characterized by an activation energy of 1.65

+ 0.1 eV.

The precipitation behavior of Cu-rich Cu-Fe was also studied by

123 Newkirk who combined X-ray diffraction, hardness measurements, and

optical and electron microscope observations on a Cu-2.5% (wt.) Fe

alloy. After solution treatment at 1050 °C for one hour and quenching

the sample in wire form the Debye-Scherrer X-ray patterns indicated

o a single fee phase with a = 3.615 A. After an anneal at 600°C for

o 600 hours a weak fee phase with a = 3.590 A was indicated identically

o

o oriented with a strong fee phase with a = 3.616 A. After cold working

at 20 °C evidence for the weak fee phase weakened and faint bec lines

o with a = 2.864 A were observed,

o The y * a martensitic transformation was further studied by

Easterling and Meik-Oja124 in a Cu-1.95 wt.% (2.21 at.%) Fe alloy

using rough magnetic measurements and electron microscope observations.

They showed that precipitation of the Y

-phase for this composition begins

15
at all temperatures in the range 550 - 750°C. Nucleation was found to

occur homogeneously leading to fully coherent spherical precipitates.

With a prolonged precipitation anneal, y~Fe precipitates were found to

grow, lose their full coherency and take on a cubic shape. Finally,

after prolonged annealing, stable yprecipitates would nucleate from

large cubic Y~Prec ipitate s or directly on dislocations of the matrix

as well as at grain boundaries. The rough magnetic measurements showed

a drop in magnetic force upon precipitation of y-Fe, which would

indicate, as did Bitter et al.'s measurements ' that the y^ value

D

of y-Fe is only a fraction of that for Fe dissolved in Cu.

125

4. The Ternary System . Bradley et al. studied the Cu-Ni-Fe

phase diagram using X-rays. The criterion used for a single phase

alloy was, as in most X-ray studies, that only a pattern typical of the

single phase is detected, for a two-phase alloy the superimposed lines

for both phases would be detected, etc. The ternary diagram determined

by Bradley et al . for slowly cooled alloys (from 900°C to 300°C at

20°C/hour) is shown in Fig. II-l. The alloys within the dotted line

did not give a normal two phase pattern, but showed indications that

decomposition of the original single-phase structure had already begun.

The positions of the single phase boundaries at several elevated

temperatures were also determined by Bradley et al.

Palmer and Wilson studied the solubility of Fe in Cu-Ni alloys

containing 2 to 10 percent Ni by using the metallurgical techniques of

etching, magnetic colloids, and polarized light microscopy. Their results did not confirm the increased solubility hump around 10 percent

125 Ni shown in the results of Bradley et al. Their alloys contained

16
about 0.3% Mn as an impurity and it is not known what effect this

127 1 28 would have on the Fe solubility. Kneller et al . ' studied

Cu

Q 7 ANiQ 2 A Feo 02 after a 8ing at 600°C by electron microscopy and magnetic susceptibility. The results indicated that Fe-Ni rich ferromagnetic particles of essentially spherical shape were coherently and

randomly precipitated in a Cu-rich paramagnetic matrix. The alloy was

first solution heated at 1073°K and quenched. No precipitation for

this treatment was reported. Aging for 25 minutes at 873°K was reo ported to produce particle sizes about 40 A in diameter. The limit

o of resolution was reported to be about 20 A diameter. This result

appears consistent with the trends shown for Fe solubility in Cu-Ni

alloys by Palmer and Wilson.

129

Ham et al. during a study of fatigue in Cu-Ni-Fe alloys made

electron microscope observations of precipitation in Cu-17.3 Ni-17.3 Fe.

The alloy was first solution treated at 1000°C and then quenched.

After aging for one hour at 640° C large numbers of small precipitates

o less than about 250 A in diameter were observed uniformly distributed

throughout the sample. After aging 2.5 hours at 640° C a modulated

structure developed with the particles appearing to be linked into a

o lattice of rods spaced about 250 A apart.

130 Hillert et al. studied the formation of side bands in the X-ray

patterns of Cun (Ni^ _,Fe rt „) alloys. (These side bands were first

1-x 0.7 0.3 x observed by Bradley et al. within the dotted line region of Fig.II-1.)

They interpreted their results in terms of the formation of modulated

structures with periodic variations in composition brought about by the

simple interchange of atoms (spinodal decomposition)

.

17
The precipitation in these Cu.. _ (Ni_ 7 Fe _) alloys was also

131 studied by Najarajan and Flinn using the Mossbauer effect. They

showed that the segregation of these alloys into two phases includes,

at any stage of decomposition, only two rather definite compositions

and not a continuous range of compositions. They interpreted this

as evidence against the formation of a modulated structure.

18
CHAPTER III

EXPERIMENTAL PROCEDURE

A. Sample Preparation . Samples were prepared by plating a

starting foil with iron isotopically enriched in Fe followed by

diffusion and heat treatment.

The Cu-Ni starting foils were prepared from 99.999 percent Cu

and 99.99 percent Ni arc melted together in the required proportions

132

in an argon atmosphere. The resulting alloys were cold rolled

to thicknesses of 12 and 25 ym. Pure Cu foil and seven compositions

of Cu-Ni foil were prepared. The Cu-Ni foils were analyzed chemi133 cally to determine the Ni concentration. The Ni concentrations

found were 0.9, 5.1, 10.7, 21.0, 33.4, 46.6, and 53.2 atomic percent.

To check homogeneity, four pieces were selected at random from the

10.7% foil and each piece was analyzed chemically. The measured

compositions agreed within the precision of the chemical analysis

which was judged to be 0.3%. The pure Cu and Cu-Ni foils were spec134 trochemically analyzed for impurities. Those impurities detected

are listed in Table III-l. The starting foil for the Au-Fe samples

135 was 99.99% pure Au 12 ym thick.

A stock solution containing 2.0 mg/ml of Fe was prepared by dissolving a sample of isotopically enriched Fe„0„ into hydrochloric

acid. The Fe_0» sample was enriched to 90.7% " Fe. The results of

a spectrochemical analysis of this sample is given in Table III-2.

The stock solution was used to place the required amount of Fe into

19
the plating bath.

137

A depletion plating technique was used to deposit the required

quantity of Fe onto the surface of a foil. The plating bath was prepared in a 30 ml beaker by dissolving 0.65 g of (NH.).C 0, in about

15 ml of water. The desired amount of Fe stock solution was measured

and added to the plating solution with a pipette. The pH was then

adjusting to about 5 by adding dilute ammonium hydroxide. Two platinum

strips, each about 1 by 3 cm, were placed on opposite sides of the

beaker for use as anodes. A piece of the foil to be plated was cut

to about 2 by 3 cm, cleaned by scrubbing with 0.3 um A1„0„ abrasive,

rinsed and masked to leave a bare central region about 1.5 cm square

on both sides of the foil. This foil was then placed in the plating

bath, equidistant from and parallel to the anodes. A plating current

2 of about 0.015 amp/cm was used. The solution was stirred by an

electric motor which would periodically strike the wire holding the

foil. The plating uniformity was checked during the initial stages

of plating while the plated layer was thin enough to be transparent.

Any tendency not to plate uniformly could then be seen visually. About

0.1 cm along the edge of the plated region tended to plate slightly

faster than the remainder of the foil. Therefore only the central

region about 1.3 cm in diameter was used for obtaining Mossbauer

effect spectra.

Several tests made by weighing the amount of iron plated onto the

foil showed that about 90% of the iron added to the bath was recovered.

Thus, to obtain a given iron concentration, an extra 10% of iron

stock solution was added to the plating bath. No chemical analysis

20
was made of the foils after diffusion of the plated iron. It is

estimated that the iron concentrations are accurate to + 20% of the

stated concentration.

The diffusion treatment consisted of holding the plated foil at

1000°C in a hydrogen atmosphere for 16 hours. The diffusion coefficient,

D, as a function of temperature is given by D = D exp(-Q/RT), where Q

is the activation energy, R the gas constant, and T the absolute

temperature. For the diffusion of iron in Cu between 720 and 1060°C,

138 2, Mullen gives the values D_ = 1.01 cm /sec and Q = 50.95 kcal/mole.

Then using R = 1.99 cal/mole and the above parameters we obtain a diffusion length L = N Dt ', where t is the diffusion time, of 103 urn or

about four times the thickest sample used. Thus, assuming solubility

and good plating uniformity, the diffusion treatment is expected to

give a uniform iron concentration throughout the sample.

The heat treatments used resulted in four types of samples:

(1) "Furnace cooled" samples - cooled by turning off furnace

power - After diffusion the furnace power was turned off and

sample and furnace were allowed to cool together.

(2) "Quenched" samples - gas quenched from 1000° C - Following

diffusion at 1000° C the foil was withdrawn rapidly from the

furnace and blasted on both sides with a room temperature

jet of gas containing 95 percent helium and 5 percent hydrogen.

(3) "Annealed" samples - "quenched" sample held at 650°C, then

gas quenched - After diffusion and quenching from 1000° C the

furnace temperature was lowered to 650°C. The foil was replaced in the furnace and retained at 650°C for 16 hours in

21
a hydrogen atmosphere. The foil was then withdrawn rapidly

and blasted on both sides with a room temperature jet of gas

containing 95 percent helium and 5 percent hydrogen.

(4) "Splat cooled" samples - rapidly quenched from the melt -

This was performed following diffusion and furnace cooling.

The apparatus and technique used were essentially as described

,139 140

by Goldstein et ai. and Duwez and Willens. The sample

was placed in a boron-nitride crucible and induction melted.

Using helium gas with 5 percent hydrogen under high pressure

the sample was rapidly expelled through a small hole in the

crucible onto a rotating copper hearth at room temperature.

Both crucible and hearth were maintained in an atmosphere

of helium five percent hydrogen. The resulting sample was

in the form of a flake 100 to 200 ym thick. It was etched

to a thickness of about 50 ym.

Several samples prepared using the above procedures were observed

141

metallurgically by electron-probe microanalysis. An annealed sample

of Cu

q 7 Fen n o showed iron segregated into small particles less than

about 2.0 ym in diameter. An annealed sample of Cu_ ^.^e- n , showed

0.94 0.06

iron segregated into particles with diameters up to about 6 ym.

Quenched samples of both Cu_ ,.,Fe_ __ and Cu. „, Fe_ _, indicated homo0.97 0.03 0.94 0.06

geneously distributed iron. In both a quenched and an annealed sample

of (Cu_ qqNIq -iq)q oo Fe

o 08 no segre8ation of either iron or nickel

could be detected by the electron probe. Fig. III-l shows electronprobe scans of three of these samples.

Sources were prepared by plating Co onto a matrix and diffusing

22
at 950°C in an argon atmosphere, followed with quenching by flushing

the furnace with room temperature argon gas. Two single line sources

were used for studying absorbers, one had 10 mCi Co in Pd and the

other 50 mCi Co in Pd. No difference in the Mossbauer effect linewidth for these two sources was detected. One source for study was

prepared with 5 mCi Co in a Cu_ _ Ni matrix.

u . y / u . jj

B. Mossbauer Effect Spectrometer . A variety of designs ~* for

Mossbauer effect spectrometers have been published. The spectrometer

used here was of the constant acceleration electro-mechanical feedback

type. In such a spectrometer, which is velocity controlled, a problem

arises because the system does not respond to a shift in its neutral

position. This is often overcome by letting a fairly stiff suspension

spring determine the neutral position. If this is done the total

linear displacement of the driving rod must be small, requiring a rather

high fundamental vibration frequency. When driving a source on the

end of a long rod some of these higher frequency harmonics might

excite acoustic vibration modes in the rod, thereby degrading the observed spectra. If, however, the neutral position is held fixed by

the use of a position sensor such as a limit switch or photocell, a

very weak driving rod support spring can be used, resulting in a much

lower fundamental vibration frequency. Good velocity fidelity can then

be obtained with a lower overall frequency response. A suitable system

152 of this type has been described by Reugg et al. and their design is

the one used here. Several modifications were made aimed at reducing

drift and increasing velocity fidelity when driving a gamma-ray source

at the end of a long vertical rod. Those details not given below are

23
152 153 essentially as described by Reugg et al.

For reference, a block diagram of the entire system is shown in

Fig. III-2. To give additional drive power the Doppler-ef feet

154 modulator was fabricated using two speakers , one on each end of the

Velocity transducer. A schematic of the modified section of the driver

electronics is shown in Fig. III-3. This circuit is dc coupled and

hence very sensitive to voltage drifts. Components and circuits were

selected to reduce this drift and also to provide the best possible

linearity. A stable reference voltage, V , is provided by the Zener

diode Dll. Any drift of this reference voltage results in a proportional drift in the velocity calibration of the spectrometer. The

diode selected had a Zener voltage of 9.3 volts and a temperature coefficient of 0.005% per °C. A sawtooth ramp voltage, applied to J10,

is added to the reference voltage through the operational amplifier

A10 to provide a velocity sweep waveform. The source of this ramp

voltage is provided by the multichannel analyzer as a voltage proportional to the channel address number when the analyzer is operating

in the multichannel scaling mode. Overall linearity will suffer if

this ramp voltage is not at least as linear as the velocity transducer.

The multichannel analyzer for this system was modified to have a

linearity of 0.1% in this respect. The potentiometer R1A is used to

vary the total number of channels used to accumulate the spectrum.

Potentiometer R15 varies the total velocity range. If the multichannel

analyzer ramp voltage is accurately zero for channel one there will be

no interaction between the two potentiometer settings. The velocity

transducer LI had a rated sensitivity of 23.5 mV sec/mm and a

linearity of better than 0.1% over a displacement range of one cm. 24
1 Sfi Wertheim has commented that the velocity calibration of

Doppler-ef f ect modulators has been an unexpected challenge to

the experimentalist and no attempt was made here to obtain absolute

calibration. The procedure used was to calibrate the velocity

102

scale using the data given by Preston et al. for pure iron metal.

A sample was prepared from iron with a purity of 99.99% crushed

to a -200 mesh powder. Enough powder was bound in a lucite disc

57 2 to give an areal density of " Fe of 0.32 mg/cm . This sample

was used for all subsequent calibrations.

A spectrum of the iron calibration sample after a 14 hour run

with a 10 mCi Pd( Co) source is shown in Fig. III-4. A listing of

the line positions, widths, and areas is given in Table III-3.

102 Assuming the data of Preston et al. is correct, the linearity

of the spectrometer is better than +0.01 mm/sec.

The theoretical linewidths given in Table III-3 are based

81 on the formula given by Fraunfelder et al. for the linewidth of

an absorber with finite thickness (Eq. II-l) . Based on the lifetime of the excited nuclear state of Fe, 2r - 0.194 mm/sec. For

computing the theoretical linewidths in Table III-3 the value

-18 2 157

a = 2.42 x 10 cm given by Hanna and Preston was used.

Instrumental broadening of the linewidths is seen to be small, about

0.007 mm/sec for lines 3 and 4, increasing to 0.020 mm/sec for lines

1 and 6

.

Calibrations over a period of about a year showed that long term

drifts in the velocity calibration were on the order of one percent

25
per month. To retain an accuracy of better than one percent in the

velocity scale, calibration runs were made at least once a week.

C. Magnet and Dewar System . Two dewars were used for obtaining

spectra at low temperatures, one a fixed temperature dewar and the

other a variable temperature dewar with provision for obtaining spectra

in the presence of an externally applied magnetic, field.

The fixed temperature dewar is shown in Fig. III-5. The sample

is immersed in liquid nitrogen or liquid helium contained in the inner

158

well. The dewar body is basically that described by Hersh except

the inner well was not narrowed at the top but continued straight.

This reduces the holding time for liquid helium somewhat but was

necessary to prevent vibration of the sample. The magnetic field at

the sample due to the bar magnets used is negligible. The liquid

capacity of the inner well was 800 ml and gave a holding time of

eight to ten hours for liquid helium.

The equipment used to obtain spectra in the presence of an exter159 nally applied longitudinal field is shown in Fig. III-6. The temperature of the source and absorber are controlled independently. The

source and Doppler-ef feet modulator share a common vacuum. This removes the need for the double bellows type of arrangement usually required to transmit the source motion into the dewar. The source chamber

and sample holder are shown in more detail in Fig. III-7 . The sample

is held at the temperature of the sample holder by helium exchange gas

trapped inside the sample holder.

26
D. Data Analysis . Many of the spectra obtained in this study

were analyzed by the use of computerized least squares fitting techniques. The techniques used were adapted from the computer programs

of Polinger et al. and Chrisman and Tumollilo. Three types of

curves were used in fitting the experimental data. The first was a

sum of separate Lorentzian shaped lines , the second a six-line hyperfine field pattern, and the third a hyperfine field distribution.

The experimental spectra often contained a curved background due to

the variable source absorber distance when the source was moved to

Doppler shift the gamma-ray energy. In the first type of fitting the

background was fitted to a quadratic equation at the same time the

Lorentzians were being fitted. For the second and third methods a

background spectrum was obtained by tuning the single channel analyzer

off the 14.4 keV gamma-ray to spoil the resonance. Before proceeding,

the background was least squares fitted and the fitted curve subtracted from the original data to remove the background. The three

fitting methods are outlined below. All three methods utilized an

automatic plotter to plot the data and fitted curve.

1. Individual Lorentzians . In this method of fitting a sum

of independent Lorentzians plus a curved background was least squares

fitted to the data. The equation used was

N

L A. , y (v) =

I + a + bv + cv III-3

±=1 (2/r.)2 (v _ Ci )2 + x

27
where y(v) is the amount of absorption at velocity v, c. the centroid

of the i Lorentzian, N is the number of Lorentzians used, and r . is

La -*- the linewidth of the i Lorentzian. All fitting parameters were

varied independently.

2. Six-Line Hyperfine Pattern . In this method the data,

with the curved background removed, were fitted to an equation of the

form ,6 Ar

.

y(v,H) =

I III-4

i=l (2/D (v - Hg. - Qa. - c) + 1

where H represents the magnetic field, Q the quadrupole splitting,

assumed small, and c the center of the spectrum. The six parameters

r. represent the relative strength of the six lines and were generally

given the ratio 3:2:1:1:2:3. The six parameters g. represent the

relative splitting of the six lines and were given the values -0.01615,

-0.00934, -0.00254, 0.00254, 0.00934 and 0.01615 mm(sec kG)

_1 respectively. The parameter a. is +1 for lines 1 and 6 and -1 for lines

2, 3, 4 and 5. All parameters except r., g. and a. were allowed to

vary independently.

3. Hyperfine Field Distribution . In this method the data,

with the curved background removed, were fitted to an equation of the

form M

max

y(v) = I p(mAH) y(v,mAH) III-5

m=0

where y(v,mAH) is given by equation III-4, and p (mAH) is the field

distribution function. The field increments, AH, are taken small

enough to give a smooth y(v). The distribution is cut off at a field

M AH. The field distribution function was chosen to be a two max

28
parameter function such as a Lorentzian. For this fitting procedure

the parameters r, r., g. and M were not varied and Q was set equal

to zero.

29
CHAPTER IV

EXPERIMENTAL RESULTS

A. Preliminary . This chapter describes the Mossbauer effect

results obtained from various Cu-Ni-Fe alloys studied as absorbers,

for one source of Cu_ ^Ni^ „_( Co), and for two Au-Fe alloys studied

U. b/ U

.

jj as absorbers. The Cu-Ni-Fe alloys will be designated by the formula

(Cu. Ni ). Fe , 1-x x 1-y y

where x and y are atomic fractions. The values of x ranged from to

0.53. The values of y ranged from 0.005 to as high as 0.08 in one

alloy which had x = 0.10. Sample preparation has been discussed in

Section III-A which describes the heat treatments used in preparing

the alloys. Here we refer to the alloys as being either furnace cooled,

quenched, splat cooled or annealed.

The Mossbauer spectra observed for these alloys are complex and

for purposes of discussion they are divided into components due to four

types of Fe. Further justification for this division is given in

Section V-A. The four types of Fe are:

(1) a-Fe: Fe in bcc precipitates. This iron normally yields

a six-line pattern similar to that observed in pure Fe

metal. The six-line pattern seen in the "wings" of Fig.

IV-15(a) is an example of a-Fe. It arises from bcc Fe

precipitating from a Cu matrix. The separation of the

outer two absorption peaks is 10.7 mm/sec which is the

same observed in pure Fe metal at room temperature.

(2) y -~Fe: Non-magnetic or paramagnetic Fe in solution. This

30
Fe is characterized by a single, relatively narrow, absorption line at room temperature. The large peak in

Fig. IV-l(a) is an example of Yn_Fe and is characteristic

of Fe in solution in Cu. It has a linewidth of 0.22 mm/

sec which is very close to the natural linewidth of 0.20

mm/sec based on the lifetime of the Fe isomeric state.

(3) Y-i~Fe: Fe in fee Fe-rich antiferromagnetic precipitates.

This Fe is generally characterized by a single relatively

narrow absorption line above liquid nitrogen temperature.

Fig. IV- 7 shows the spectrum of a sample of Cu_ Q7 Fe_ _„

annealed to precipitate the fee y.-Fe which appears as

the prominant single peak on the left. The smaller peak

on the right is y -Fe.

(4) Y 9 ~Fe: Fe in fee regions generally characterized by an

unresolved Mossbauer effect structure at room temperature

having the appearance of a doublet . The doublet structure

at the base of the central peak in Fig. IV-l(a) is an

example of y „-Fe.

Spectra were obtained for a series of alloys with y = 0.005.

These results are described in Section IV-B. One source with x = 0.33

was studied and the results are described in Section IV-C. Except for

this source all alloys were studied as absorbers. The experiments performed on some alloys with x = are described in Section IV-D. Results

obtained in a magnetic field are described in Section IV-E. A series

of other results for various compositions and heat treatments are

described in Section IV-F.

31
B. Alloys Containing 0.5 Atomic Percent Fe . Spectra were obtained for a series of alloys with the formula

(Cul-x

NVo.995Fe0.005'

where x varied from to 0.53. Each of these spectra were least

squares fitted to a sum of individual Lorentzian lines whose position,

height and width were allowed to vary independently. The spectra and

the fits obtained by this technique are shown in Fig. IV-l(a) through

(h) . Table IV- 1 lists the parameters obtained.

In the second fitting method a six-line hyperfine field pattern

was least squares fitted to the spectra. The center of this six-line

pattern, its intensity, the hyperfine field value and the linewidth

varied independently. A 3:2:1:1:2:3 intensity ratio was used for the

six lines. A small amount of quadrupole splitting was included in the

six-line pattern and this is the source of the asymmetry in some of

the fitted patterns such as seen in Fig. IV-2(c). For the two samples

^Vg^o.oPo.ggs^o.oos and c S.95Nl

o. 05*0; $95^0.005 two Lorentzian

lines were also included in the fit. These lines were assumed to be

in the same position as the y doublet of Fig. IV-l(a). Also, for these

two samples only, the linewidth was not allowed to vary during the

least squares fit and was held constant at 0.22 mm/sec. The spectra

and the fits obtained are displayed in Fig. IV-2(a) through (g) . The

values of the parameters obtained by the fitting procedure are listed

in Table IV-2

.

The spectra, without any fits, are all displayed in Fig. IV-3

.

This figure illustrates the evolution of the Mossbauer effect absorption

pattern as the Ni concentration is gradually increased.

32
C. Source Experiment . One source of Cu_ .-,Ni n _ ( Co) was

. b / . j J prepared as described in Section III-A. The room temperature spectrum

of this source, using the central two lines of metallic Fe as an absorber, is shown in Fig. IV-4 . Each of the two absorption patterns in

this spectrum have been least squares fitted either as two Lorentzians

or as a hyperfine field. The theoretical line shown in Fig. IV-4 is

for a hyperfine field. The averaged parameters obtained for these fits

are listed in Tables IV-1 and IV-2 along with the results for the 0.5

atomic percent Fe absorbers.

D. Cu-Fe Alloys . Fig. IV-15(a) shows the room temperature

spectrum of a furnace cooled sample of Cu„ Q7C.Fe n9q. (2.5 atomic percent Fe) . Three types of Fe are evident in this spectrum. The most

prominent central peak is y -Fe. The smaller central peak is y -Fe.

The six-line pattern in the "wings" of the spectrum corresponds to

a-Fe. The splitting of this six-line pattern corresponds to 330 + 5 kG,

the same field value found in metallic Fe at room temperature. This

sample showed evidence of f erromagnetism, it was strongly attracted to

a permanent magnet at room temperature.

Fig. IV-1 (a) shows the room temperature spectrum of the first of

two quenched samples of Cu Fe n ^. The prominent central peak,

u.yy_> u . uu j

comprising 73 percent of the absorption area, is y n

- Fe. The two remaining peaks are the y 9 ~Fe doublet. Fig. IV- 5 shows the room temperature

spectrum of the second of two quenched samples of Cu_ Fe_ qqc- This

spectrum appears identical to that for the first sample except that

the central y peak contains slightly less of the total absorption area.

Fig. IV-6 shows the spectrum of the second sample of quenched

33
Cu Fe at 4.2°K. There is no apparent increase in the yn linewidth or in the splitting of the y„ doublet and no shift of the

relative position of the yn peak and y 9 doublet. The centroid of the

pattern has been shifted by 0.13 + 0.03 mm/sec by the second order

Doppler effect. This shift is, within experimental error, the same

101

as reported by Preston et al. for pure Fe metal.

Fig. IV-7 shows the room temperature spectrum of an annealed

sample of Cu Q-,Fe n_. As described in Section III-A, the annealing

u • y / U . u j

procedure yielded Fe precipitates about 2um in diameter. The prominent peak is due to these Y-,~Fe precipitates. The smaller peak is

due to y -Fe. The spectrum of this sample at 4.2°K, fitted to two

Lorentzian lines is shown in Fig. IV-8(a).

Fig. IV-9 shows the room temperature spectrum of a splat cooled

sample of Cu Fe n0l-. The central peak represents Y n~Fe * The Pea^ u.y/j u.uz_> u at higher velocity is one peak of the y doublet. The absorption peak

at lower velocity is the sum of one peak of the y~ doublet and the y-i

peak. The spectrum of Fig. IV-10 is for a quenched sample of

Cu_

q 7 Fe and, except for a slightly greater percentage of Y-i~Ee,

is essentially the same spectrum as for the splat-cooled sample.

E. Magnetic Field Results . The absorption spectra for three

Cu-Ni-Fe alloys and for two Au-Fe alloys were obtained in a field of

approximately 50 kG at a temperature of 205°K. The spectra for the

Cu-Ni-Fe alloys are displayed in Fig. IV-11 and those for the Au-Fe

alloys in Fig. IV-12. Each sample was placed in the magnet, the abaorber was brought to a temperature of 205°K and the source to 255°K,

and a spectrum was obtained first for zero field and then for a field

of 50 kG. As discussed below, one spectrum indicates that the applied

34
field, which was not precisely measured, may have been slightly less

than 50 kG. However, the same magnet current was used for each

spectrum labeled with H = 50 kG.

The spectrum of annealed Cu o-yFe with H = is shown least

squares fitted to two Lorentzians in Fig. IV-13(a). The spectrum of

this sample with the applied field is shown in Fig. IV-13(b) least

squares fitted to two hyperfine field patterns with a 2:0:1:1:0:2 line

ratio. Lines 2 and 5 are missing due to polarization effects. In the

fitting procedure the linewidth, hyperfine field, and line ratios were

assumed the same for each of the two patterns and lines 2 and 5 were

assumed to be absent. All other parameters were allowed to vary

independently. The lines for each of the two patterns are labelled in

Fig. IV-13(a) and (b) . The parameters obtained in the least squares

fitting procedure for this sample are listed in Table IV-4. Although

a field value slightly less than the applied field is expected, the

field of 45.6 kG obtained indicates that the applied field may have been

slightly less than 50 kG. The discrepancy between the y linewidth in

zero field and in the applied field is due partly to the least squares

fitting procedure which gave an equal linewidth to both the y~ and y..

linewidths while fitting the applied field spectrum.

The spectrum of quenched (Cu

go

Ni 10 ) g7

Fe

o 03 at 205 ° K with

no applied field is shown in Fig. IV-14(a) least squares fitted to two

Lorentzians. The two lines were located at -0.07 + 0.03 and +0.29 +

0.03 mm/sec and each had a linewidth of 0.39 + 0.03 mm/sec. Fig. IV14(b) shows the spectrum of this sample when a field of 50 kG was

applied. The spectrum has been fitted to the field distribution shown

35
in the inset. This distribution has the shape of a cut-off Lorentzian

For this fit a line ratio of 2:0:1:1:0:2 was assumed. The amount of

polarization and hence the proper line ratio to use is not certain.

Since the field distribution obtained will change when the line ratio

is changed, the field distribution obtained cannot be considered unique.

F. Other Results and Summary . Spectra obtained at room temperature

and at liquid nitrogen temperature on several furnace cooled samples of

(Cun Ni ). n ^Fen rtOC are displayed in Fig. IV-15 and Fig. IV-16. The

1-x x 0.975 0.025

samples used to obtain the spectra of Fig. IV-15 (c) and (d) were the

same used to obtain Fig. IV-16 (a) and (b) respectively.

Room temperature spectra for three quenched samples of

(Cu_ onNin ) Fe are shown in Figs. IV-17, IV-18, and IV-19. Part

u.yu u

.

±\j i—y y

(a) of these figures shows each spectrum fitted to a six-line hyperfine

field pattern with a 3:2:1:1:2:3 line ratio. Part (b) shows each

spectrum fitted to two separate Lorentzians. The parameters obtained

by the least squares fitting technique are listed in Table IV-5.

Table IV-6 gives a summary of the Mossbauer effect spectra obtained

in this study. Where a resolved hyperfine field splitting was present

its value has been estimated. All the six line hyperfine spectra observed were characteristic of a hyperfine field distribution with broad

lines such as shown in Fig. IV-16 (c) in contrast with Fig. IV-4.

All line positions have been measured with respect to a pure Fe

absorber at room temperature. The isomer shifts for alloys containing

0.5 atomic percent Fe are plotted in Fig. IV-20. Also plotted are the

results of Wertheim and Wernick " for Cu-Ni alloy sources at 4.2°K.

Their results have been corrected to use pure Fe as a reference.

36
Considering the uncertainty in this correction, the results are

in good agreement

.

37
CHAPTER V

DISCUSSION OF RESULTS

A. Metallurgical Considerations . The study of copper rich

Cu-Ni-Fe alloys with even small amounts of Fe presents severe metallurgical problems. Since the metallurgy and physics problems are

intimately related a certain amount of effort has been devoted to gaining an understanding of the metallurgy. The work here, and elsewhere '

, has shown that the Mossbauer effect is quite sensitive to

phase segregation in the Cu-Ni-Fe system. No attempt has been made

here to carry out a systematic study of the phase boundaries and

kinetics in this system, though it appears that the Mossbauer effect

would be a powerful tool for such a study.

on -I co

1. Cu-Fe . In a study of the Cu-Fe system Gonser et.al. '

identified three types of Fe; that in solution, that precipitated in

a fee phase, and that precipitated in a bec phase. The precipitated

bec iron, or a-Fe, has a six-line Mossbauer effect spectrum with the

same hyperfine field splitting as pure iron. The precipitated fee Fe,

commonly termed y~Fe, has a single narrow absorption line at room

temperature with its centroid displaced by - 0.35 mm/sec from the

single narrow line corresponding to Fe in solution in Cu. The fee Fe

precipitate line is easily recognized by its tendency to grow upon

annealing a sample which contains Fe in excess of that soluble in Cu

at the annealing temperature. These precipitates are Fe held in fee

form by the Cu matrix and thus can be called Guinier-Preston zones.

38
They transform to a-Fe upon reaching sufficient size or upon cold

working.

The experimental results here are in agreement with those of

Gonser et.al. ' However we recognize another type of Fe in the fee

phase in Cu. This is Fe in solid solution that interacts with other

Fe in solid solution in the Cu matrix. This interaction results in the

formation of a doublet superimposed upon the central singlet, as seen

in Fig. IV-5 for a quenched sample of 0.5% Fe in Cu. One peak of this

doublet, that at lower velocity, is almost in the same location as

the absorption peak for Fe in fee y-Fe precipitates . Thus the two are

unresolved if both are present. The doublet seen in Fig. IV-5 is

also evident in the well resolved spectrum of 0.6% Fe in Cu shown in

-1 £Q

Fig. 1(a) of Gonser et.al. They interpreted one line of this

doublet as precipitated fee y~Fe and reached the conclusion that complete solid solution had not been achieved in spite of severe quenching.

Instead we believe that this line did not represent precipitated y-Fe

but rather one peak of a doublet, and hence complete solid solution

had been achieved.

The doublet formation for Fe in Cu is analogous to that for Fe

in Au as observed by Violet and Borg. The increased solubility of Fe

in Au over that for Fe in Cu allowed a study of this doublet over a

wide range of iron concentration. In both Au-Fe and Cu-Fe the position

and separation of the doublet appears relatively independent of Fe

concentration. For both Au-Fe and Cu-Fe the doublet behaves in the

same way when a magnetic field is applied. This helps confirm a common

physical origin for the doublet structure in both.

39
We are thus led to distinguish three types of fee Fe in Cu.

Because all three are Fe in an fee form the notation y is appropriate

in each case. The iron in solid solution which forms a single line

at room temperature is denoted y -Fe. The Fe which precipitates into

fee regions and forms a single line at room temperature is denoted

y,-Fe. The Fe in solid solution which forms a doublet at room temperature due to interactions with other Fe in solid solution is denoted

Y

2"Fe.

Thus we can picture what happens to the Fe in Cu Mossbauer

effect spectrum as the iron concentration is increased keeping the heat

treatment constant. In the very dilute region only the single Y ~Fe

line will be observed. This is a narrow line with near natural linewidth and hence Co in Cu is often used as a source in Mossbauer

effect studies. As the Fe concentration is increased the Y 9 ~Fe doublet

will appear. When solid solubility is exceeded the Y1 ~Fe line will

appear superimposed on one of the y-Fe doublet peaks. Finally, at

very high concentrations, some of the Y-i~Fe precipitates will grow

large enough to transform into a-Fe and the six-line pattern of a-Fe

will also be present in the Mossbauer effect spectrum.

The spectrum obtained for a splat cooled sample of Cu-Fe is shown

in Fig. IV-9 and that for a quenched sample is shown in Fig. IV-10.

The shapes of these two spectra are identical and hence can be regarded

as characteristic of the Cu-Fe system and not of the particular heat

treatment used. These spectra can then be interpreted as consisting

of a central y^-Fe peak for isolated Fe in solution, a Y 9 ~Fe doublet

which has two peaks of roughly equal intensity, and a Y-i~Fe peak which

40
is superimposed on the Y 9 ~Fe doublet peak at lower velocity. Referring

to Table IV-6, for an iron concentration of 3 atomic percent Fe in Cu

about 1/3 is precipitated as Y-i~ Fe ' The remaining 2/3 is present as

Yn

_ and Y 9 -Fe « This compares with a solubility of about 3 percent at

the quenching temperature of 1000°C indicated by the phase diagram in

Hansen and Anderko . Although both methods of rapid quenching used

yielded roughly equivalent results it is still possible that more

severe quenching, perhaps to liquid nitrogen temperatures, might reduce the amount of y-i _Fe and give results closer to the phase diagram.

We have attributed the Y 9 -Fe doublet as due to an Fe atom in

solid solution interacting with other Fe atoms in solid solution. It

is thus possible that the relative amount of y„-Fe present may result

from a tendency for a clustering of Fe, i.e. the formation of small

regions containing greater than the average amount of Fe but not yet

identifiable as a Y-, -Fe precipitate. In this case the relative amount

of y„-Fe present could be sensitive to the heat treatment of the sample.

2. Cu-Ni-Fe . A series of Mossbauer effect spectra for

(Cu n Ni )_, nnr Fen nnr for x from to 0.53 are shown in Fig. IV-3 . As

1-x x 0.995 0.005

the Ni content is increased from zero the spectra are consistent with

a disappearance of the Y 9 -Fe doublet characteristic of Fe in Cu and an

increase in a Y 9 ~Fe doublet characteristic of Fe in Cu-Ni. At x = 0.10

the Cu-Ni type of Y 9 -Fe appears as the major component. For Fe in Cu-Ni

the y 9 doublet can be associated with Fe atoms in solid solution that

interact with Ni atoms in solid solution.

When the solid solubility of Fe in Cu-Ni is exceeded fee precipitates form that contain Ni as well as Fe. This is because Ni and

41
Fe have a complete range of solid solubility with a fee form stable

at room temperature for greater than 30 percent Ni. These precipitates,

which will also contain some Cu, can be ferromagnetic at room temperature or below. Fig. IV-15(b) is an example of a Cu-Ni-Fe alloy containing these fee precipitates ferromagnetic at room temperature.

Fig. IV-15(c) and Fig. IV-16(a) show a Cu-Ni-Fe alloy with fee precipitates ferromagnetic at 78°K but not at room temperature.

The results obtained here for Fe added to Cu_ onNi^ , n are in

126

agreement with the solubility diagram derived by Palmer and Wilson

if it is assumed that the furnace cooling treatment used here is

roughly equivalent to quenching from a temperature of 650°C. The

results on alloys with Ni fractions larger than 0.10 are consistent

with an increasing Fe solubility as the Ni concentration is increased.

131 Nagarajan and Flinn found by use of the Mossbauer effect that an

alloy of Cu_ , .Ni,. „,-Fe- , , did not exhibit a two phase region after 0.64 0.25 0.11

quenching from 1050°C but did develop two distinct phases when annealed

at 600°C. The fraction of the spectrum in a six-line hyperfine

pattern was found to be independent of temperature from 73°K to 143°K.

The spectra obtained here for a furnace cooled sample of

(Cu0.79Ni

0.21 ) 0.975

Fe0.025 and a <l uenched samPle of (Cu

.79

Ni0.21 ) 0.97

Fe

03 sh°wed segregation in the former but not in the latter.

These results, along with the microprobe studies mentioned in

Chapter III, indicate that all the quenched samples studied here, except

the Cu with Fe concentration of 2.5 percent or more and the ^U

90

Ni 10^0 92

Fe 08 samPle > were solid solutions. However, the

possibility of deviations from uniformity due to clustering remains.

42
This means that, for example, in a Cu-Ni-Fe alloy, an Fe atom may

have a larger probability for having Ni neighbors than would be

expected in a perfectly random solid solution. This form of nonrandomness might not be observable by ordinary metallurgical techniques, including electron microscopy and X-rays, but could have a

large influence on the Mossbauer effect spectrum and on the magnetic

properties of the alloy.

B. Origin of the y~-~Fe Doublet. In the previous section we have

identified a "doublet" that is present in the Mossbauer effect spectra

of Cu-Fe, Au-Fe, and Cu-Ni-Fe. This doublet has been termed y -Fe.

In this section we will consider the origin of this doublet. We

are led to the conclusion, mostly by the behavior of the spectrum

when an external magnetic field is applied, that the y^-Fe doublet is

mainly magnetic in origin.

There are three possible origins for the observed doublet:

(1) The doublet is really two separate lines due to a separation

of alloy phases giving Fe in two different environments

with different isomer shifts.

(2) The doublet is really a quadrupole split line arising from

the non-cubic environment of the Fe atoms. The non-cubic

environment results from a given Fe atom having both Cu and

Ni or Fe near neighbors.

(3) The doublet is really an unresolved six-line hyperfine

pattern due to a weak magnetic field at the nucleus.

Possibility (1) is ruled out for several reasons including the

metallurgical considerations presented in Section V-A. Further, the

43
y -Fe doublet is present in Cu-Ni alloys down to very low Fe concentrations. Thus a Cu,. ^-.Ni,. __ alloy containing 5 mCi of Co used as

U • b / L) . J J

a source gave a spectrum identical to the same alloy containing 0.5

atomic percent Fe and used as an absorber. These spectra are compared

in Table IV-2. The presence of the y -Fe doublet in Cu-Ni alloys at

very low Fe concentrations shows that its origin must be in Fe-Ni

interactions. In Cu-Fe and Au-Fe, where the relative amount of y 9 ~Fe

increases with increasing Fe concentration, the y„-Fe doublet must be

due to Fe-Fe interactions.

Since a poorly resolved doublet, such as obtained for y -Fe, has

the appearance of a quadrupole splitting it might at first glance be

assumed that this is the origin of the doublet . The small temperature

dependence for the y -Fe doublet separation seems to favor this interpretation. However a poorly resolved doublet can also be due to an

unresolved six-line hyperfine field pattern. In the case of the y ? -Fe

doublet, which is poorly resolved in Au-Fe, Cu-Fe, and Cu-Ni-Fe,

further examination is necessary to distinguish between the two possibilities .

A number of spectra have been least squares fitted assuming first

that the quadrupole splitting (2) is dominant and then that the magnetic origin (3) is dominant. For Cu-Ni alloys containing 0.5 atomic

percent Fe room temperature spectra are shown fitted to separate

Lorentzians in Fig. IV-1 . These same spectra are shown fitted to sixline patterns in Fig. iv -2. Both of these methods give reasonable

fits. Hence it is not possible on the basis of these spectra alone to

distinguish between a quadrupole or magnetic effect. There is a

44
slight asymmetry in the doublets, both in those observed here for

45 Cu-Ni-Fe and those observed for Au-Fe. In the case of a quadrupole

origin the Goldanskii effect provides a mechanism to give the asymmetry,

In the case of a magnetic origin a very small amount of added quadrupole effect will produce an asymmetric doublet. In either case the

asymmetry could be due to a small amount of Yn -Fe present but not

resolved. Spectra for an alloy of Cu n QNin.. with 3, 6, and 8 atomic

percent Fe are shown in Figs. IV-17, IV-18, and IV-19. Again it is

impossible to distinguish whether two Lorentzian lines or a magnetic

field interaction gives a better fit to the data.

It is interesting to compare the above with a doublet structure

in a material which neutron diffraction has shown to be magnetic.

164

From neutron diffraction data Abrahams et al. concluded that y -Fe t

formed by annealing a Cu-Fe alloy, is antif erromagnetic at 4.2°K

with a moment per iron atom of 0.7 y. A spectrum of an annealed

D sample of Cu Q

-,Fe at 4.2°K is shown in Fig. IV-8 analyzed both

as two Lorentzians and as a six-line magnetic hyperfine pattern. A

room temperature spectrum showed this sample to be about 80% y-i ~Fe

and 20% Y n~Fe. Although it is known that a magnetic effect is being

observed, it is difficult to tell by the shape of the spectrum alone

whether the doublet structure is quadrupole or magnetic in origin.

Also the yn-Fe > which is not resolved at 4.2°K, could be the source

of the asymmetry in the spectrum.

To help determine the origin of the Yo -Fe doublet several samples

were observed in an externally applied longitudinal magnetic field of

50 kG. The spectra were all obtained at a temperature of 205°K. The

45
39 44 164 samples studied and their expected transition temperature,

T , are listed below:

c Sample T

c , °K

Annealed Cu q 7 Fe

n no < 77

Quenched Cu^^Fe^ 12

Quenched (C*

. 90

Ni

0>10 ) 0>97

Fe

0>03

< 77

Quenched Au^^Fe,^ 35

Quenched Au_ 0/ Fe_ . , 180

.84 .16

Except for the latter sample the temperature used is considerably

above the transition temperature.

The annealed sample of Cu Q

-,Fe contained about 80 percent

y -Fe and the rest Y n-Fe • A spectrum at 205°K with H = is shown in

Fig. IV-13(a) and with H = 50 kG in Fig. IV-13(b). With the applied

field the spectrum is the sum of two four-line patterns. These two

four-line patterns have the proper centroids and area ratios (when

corrected for finite thickness) to be identified as the y and Y n-Fe

observed at H= 0. This is further confirmation that these two spectral

lines represent Fe in two distinct environments.

Consider next the sample of (Cu QANi» ln ) n Q7 Fe. __ . A spectrum

u.yu u . xu u.y/ u.Uj

of this sample at 205°K with H = is shown in Fig. IV-14(a). This

spectrum is shown least squares fitted to two Lorentzians. Using the

linewidth and line separation obtained in this fit, and assuming the

doublet is of quadrupole origin, several theoretical spectra for the

results expected when a magnetic field is applied are shown in Fig.

V-l(a) through (d) . These spectra have been calculated using the method

of Gabriel and Ruby.

The spectrum obtained when a 50 kG longitudinal field is applied

46
to the (Cu

Q 9Q

Ni

10 ) Q g7

Fe Q3 samPle is shown in Fig. IV-14(b).

This spectrum more closely resembles a magnetic hyperf ine field distribution than the spectrum expected from a combined magnetic field

and electric field gradient.

The quenched sample of Cu Q7 Fe has been shown to consist of

three types of Fe, roughly 14% Y

2 "Fe, 33% y^-Fe, and 52% Y n ~Fe. Spectra

for this sample with and without an applied field are shown in Fig.

IV-ll(c) and (d) . Subtracting out of the spectrum obtained with a

magnetic field those four-line spectra expected for the Yn

-Fe and

y -Fe must result in a spectrum that closely resembles Fig. IV-ll(f).

This is evident since such a subtraction will remove less from the

central region of the spectrum, leaving an enhanced central region.

Again this is not the spectrum expected from the y -Fe doublet in Cu

if it were due to a quadrupole interaction.

The spectrum for the Aun QnFen in sample with no applied field,

u . y U u . j-U

shown in Fig. IV-12(a) consists of about 1/3 Y n_Fe singlet and 2/3

Y 9 ~Fe doublet. Using the approximate linewidth and line separation of

the doublet, theoretically generated spectra for the appearance of an

equivalent quadrupole doublet are shown in Fig. V-l(e) and (f ) . If a

four-line pattern expected from the Yn~ Fe is subtracted from the magnetic field spectrum, Fig. IV-12(b), a spectrum with a shape similar

to Fig. IV-ll(f) would be obtained. This is a spectrum with the central

region much enhanced over that expected from a combined magnetic field

and electric field gradient.

Spectra obtained for the sample of Au

g^

Fe

Q 16

with and without

an applied field are shown in Fig. IV-12(c) and (d) . The temperature

47
205°K, was very close to the transition temperature of 180°K ex39 45 pected ' for this alloy. The spectrum observed in a magnetic field

is characteristic of a broad hyperfine field distribution with a

maximum much greater than the applied field. The large fields indicate

a large internal field and hence a considerable alignment of Fe

moments by the external field. This is to be expected in a high field

for a material near a magnetic transition temperature. Although

poorly resolved, the spectrum appears symmetric which would not be

expected if a quadrupole interaction were present.

C. Discussion of the y-Fe Doublet. When Fe in dilute quantities

is dissolved in Au, Cu, or copper-rich Cu-Ni the Fe Mossbauer effect

reveals a similar behavior in each. At room temperature the spectrum

consists of a central Y n~Fe singlet and a poorly resolved Y 9 ~Fe

doublet. In Cu-Ni, with more than about 10 atomic percent Ni, only

the Yo""Fe doublet appears to be present. At low temperature all three

systems have a relatively broad transition temperature, T , below

which a large magnetic splitting develops in the Mossbauer spectrum.

This transition temperature is a different function of Fe concentration

in each matrix. For a given Fe concentration the transition temperature appears to be slightly lower in Cu than in Au. For example

39 Gonser et al. found T = 13 + 2 °K for 1.6 percent Fe in Cu, whereas

2 percent Fe in Au was required for the same transition temperature.

Although the evidence is scanty, it appears that as Ni is added to Cu,

keeping the relative Fe concentration constant, T first decreases,

c and then increases again as the critical composition of 40 percent Ni

is approached.

48
Below T the hyperfine spectrum indicates a distribution of hyperfine fields. This distribution is much broader in Cu-Fe alloys than

in Au-Fe or Cu-Ni-Fe alloys. If any difference exists for the spectrum

of Y«~Fe and Yn~Fe below T , it cannot be resolved in the observed

2 c Mossbauer spectra. Above T the separation of the Y 9 ~Fe doublet has

a very small dependence on both temperature and Fe concentration. In

45

Au-Fe Violet and Borg measured a Y 9 ~Fe doublet separation of 0.77

+ 0.02 mm/sec at 77°K and 0.69 + 0.02 mm/sec at 294°K. In Cu-Fe the

Y 9 ~Fe doublet separation was 0.57 + 0.02 mm/sec at 4.2°K and 0.58 +

0.02 mm/sec at 298°K. In Cu_ ,-,Ni_ __ the Yo~Fe doublet separation

U . b/ U . JJ z was 0.28 + 0.02 mm/sec at 4.2°K and 0.23 + 0.02 mm/sec at 298°K.

One of the objections to a magnetic origin for the Y 9 ~Fe doublet

is the above mentioned temperature region over which the magnetic

splitting remains small and relatively constant. Though not expected

to be the exact physical picture here, one model which illustrates

that this behavior is possible in principle has been given by Brout

.

This model is based on a dilute ferromagnet with a strong first neighbor interaction and a weak second neighbor interaction. The magnetization versus temperature curve given by Brout is shown below.

Fig. V-2. Magnetization vs. temperature for

model with strong first neighbor and

weak second neighbor interaction.

49
The plateau above T represents a region where a portion of the sample

is aligned due to the strong first neighbor interaction. Below T

the second neighbor interactions become important and a standard magnetization curve results.

1. Ferromagnetic-Ant if erromagnetic Model . Of interest in

considering possible models to explain the Mossbauer effect results is

ic i (if: -I f. -i the ferromagnetic-antiferromagnetic model proposed by Kouvel ' '

for Cu-Mn, Ag-Mn and related alloys. Mn appears to form a local moment

in Cu of about 4 y . For concentrations greater than about 1 atomic

B 21 22 percent Mn in Cu, Ag and Mg, Owen et al. ' found, on the basis of

electron-spin resonance and susceptibility measurements, that the magnetic properties were dominated by short range Mn-Mn interactions such

as direct and super exchange. Kouvel found that the magnetization of

dilute Mn in Cu or Ag displayed a displaced hysteresis loop at low

temperature when cooled in a magnetic field. When cooled in zero

field a hysteresis loop centered about the origin with a relatively

small remanence was observed. The displaced hysteresis loops have a

thermoremanance which decreases with increasing temperature. The

phenomenological model proposed by Kouvel to explain this behavior was

that of very small ferromagnetic regions (or domains) coupled antiferromagnetically through nearest-neighbor Mn atom pairs. This sort

of model requires the sign of the magnetic interaction between Mn

atoms to depend critically on their distance of separation. The type

of interaction proposed was strong short-range magnetic forces such as

direct exchange or superexchange involving intervening Cu atoms. It

is tempting to apply a modified model of this type to the Au-Fe,

Cu-Fe, and Cu-Ni-Fe Mossbauer results. The existence of the Y 9 -Fe 50
could perhaps be correlated to magnetic clusters which are coupled

together below T and uncoupled above T . Further Mossbauer and

magnetic measurements would be necessary to verify any such model.

2. Invar Effect Model . Another interesting model that deserves mention here is that proposed by Weiss ' as an explanation

for the "invar" effect in Fe-Ni alloys. The so-called invar region

in fee Fe-Ni alloys occurs around 30 percent Ni. In this region the

thermal expansion coefficient changes rapidly with composition and

undergoes a minimum with a near zero coefficient. The presence of

small amounts of Cu or other elements can shift the position of this

minimum. This phenomenon has proven useful, for example, for making

low expansion alloys for absolute standards of length, watch balance

wheels, etc. The model proposed by Weiss appears to explain this

coefficient expansion minimum and a number of other anomalous properties of Fe-Ni alloys in the invar region. These include magnetization and pressure dependence of the Curie temperature.

Weiss proposes that Fe in a face centered cubic structure (y-Fe)

has two electronic structures y-i an<i Yo • We retain this notation

although it is by no means certain that these can be identified with

the Y-i~Fe and Y 9 -Fe described earlier. However, the analogy is suggestive. The proposed y n electronic structure is antif erromagnetic

with a moment of about 0.5 y„ and a transition temperature around 80°K.

The Y 9 electronic structure is ferromagnetic with a moment of about

2.8 u_ and a transition temperature around 1800°K. It is further proB

posed that the energy separation of these two structures is a function

of alloy composition. A small volume change of about 8% is proposed,

Mot

51

with y ? having the larger volume. Mott has speculated that according
to the model of Friedel et al. the low moment structure of Fe with

about 0.5 y could be stabilized if there were a minimum in the density

B of states situated at a valence electron-to-atom ratio of about 7.

That Fe can actually be antiferromagnetic in fee structure is supported

164

for example, by the neutron diffraction evidence of Abrahams et al.

on y.-Fe precipitated in Cu, by the susceptibility measurements of

172 stainless steels by Kondorsky and Sedov, and by the neutron dif173 fraction studies on fee Fe-Mn alloys by Ishikawa and Endoh.

The application of this model to explain the spectra observed here

would be a complex task. However, if it is admitted that the model is

actually operative in Fe-Ni alloys, then it is likely that it plays a

role in some of the observed Cu-Ni-Fe spectra, especially if a

tendency existed for Fe and Ni to cluster together and form small

regions with compositions close to Fe

n 7 Ni_ _. Around this composition

one could have ferromagnetic regions with very small hyperfine fields,

174

as has been observed in Fe-Ni alloys by Johnson et al. and by

Nakamura et al. This might, for example, be the explanation for the

quenched alloy of 8% Fe in Cu QNi . This sample had indications of

f erromagnetism at room temperature, but its spectrum did not show a

resolved six-line pattern (Fig. IV-19) at that temperature.

D. Isomer Shifts . The isomer shifts bear no obvious relation to

the observed magnetic properties of Cu-Ni-Fe alloys. However, for

completeness, they are considered briefly here. Using the data pre-

-1 -j £ sented by Walker et al. the 0.20 mm/sec isomer shift decrease on

going from Fe in Cu to Fe in Ni (Fig. V-20) corresponds to a 3.8%

increase in s-electron density at the Fe nucleus. This increase is the

52
sum of a number of contributions, some of which may be of opposite

sign and tend to cancel. A decrease in 3d-electron density around the

Fe impurity would give in increase in s-electron density at the

nucleus. A decrease in 4s-electron density would have the opposite

1 7 ft effect. Also, the 2.6% decrease in lattice parameter from pure

Cu to pure Ni, corresponding to a 7.4% decrease in atomic volume,

could have a considerable effect

.

Isomer shift data are also available for both Sn and

197

Au as impurities in Cu-Ni alloys. The results are consistent with

a net decrease in d-character around an Fe or Au atom, and a net decrease in s-character around a Sn atom, as the Ni concentration is

increased. On the basis of a simple rigid band model, the addition

of Fe, which has fewer atomic electrons than Ni, should have a larger

effect on the isomer shift than the same amount of Ni. However, the

addition of 6% Fe to Cu QNin i reduced the Fe isomer shift only

o . y u . l

0.01 mm/sec, compared to a reduction of 0.025 mm/sec expected for the

addition of 6% Ni. This tendency of the isomer shift to be relatively

44

independent of Fe concentration has also been observed in gold-rich

Au-Fe alloys

.

Further work appears necessary to obtain an understanding of the

various contributions to the isomer shifts in these alloys.

E. Conclusions . The major result presented here has been the

discovery of a doublet structure in the high temperature Mossbauer

effect spectra of Cu-Fe and Cu-Ni-Fe alloys. This doublet is responsible

1 ft? for the line broadening observed by Wertheim and Wernick in their

study of Cu-Ni ( Co) sources, and one peak of the doublet is the

53
unidentified line in the Cu-Fe spectra previously presented by Gonser

et al. ' This doublet is similar to the one observed in gold-rich

45

Au-Fe by Violet and Borg, who proposed a quadrupole interaction as

the origin of the doublet. We have shown here, by observation of the

spectra in an externally applied magnetic field, that in both Au-Fe

and Cu-Ni-Fe the doublet is of magnetic origin. This implies that

some form of magnetic order persists above what has usually been considered the magnetic transition temperature in these alloys.

Two phenomenological models for the magnetic behavior of these

alloys appear worthy of further consideration. They are the ferromagnetic - antiferromagnetic model of Kouvel ' ' and the invar

1 to -i £n

effect model of Weiss. ' Further experimental work, especially

magnetic susceptibility measurements, would be helpful in this regard.

Also, it would be interesting to extend the Mossbauer effect measurements above room temperature since a second ordering temperature

should exist.

Using the identification presented here for the types of Mossbauer

effect spectra present in Cu-Ni-Fe alloys, it appears that the Mossbauer

effect could be a very useful tool for further study of the metallurgy

of this system. For example, a study of the relative amounts of y^j

Y, and Yo~Fe in Cu-Fe as a function of heat treatment could provide

information about the kinetics of precipitation in Cu-Fe.

54
ACKNOWLEDGEMENTS

The author wishes to thank, first of all, his adviser Dr. L. H.

Bennett, who provided essential ingredients of knowledge, enthusiasm,

and intuition. Dr. R. E. Watson provided several profitable and

interesting discussions. Useful advice was contributed by Drs . I. D.

Weisman, B. Mozer, M. Kuriyama, B. W. Christ, J. C. Travis, J. J.

Spijkerman, A. W. Ruff, H. Yakowitz, J. A. Manning, J. R. Cuthill,

R. W. Mebs, A. J. McAlister, N. M. Wolcott, R. A. Falge, T. A. Kitchens

and R. M. Housley.

I also wish to thank D. P. Fickle and G. 0. Queen for their aid

in sample preparation, F. C. Reugg for advice on instrumentation, R. L.

Parke, R. D. Robbins, and G. P. Spurlock for technical assistance, and

Katie Walder for typing the manuscript.

Thanks are also due to the many staff members of the University of

Maryland and the National Bureau of Standards who provided encouragement

and assistance. The research was performed at the National Bureau of

Standards and received support from the Office of Saline Water, Department of the Interior. Relevance of this work to desalination is discussed elsewhere.

55
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61
133. I thank E. R. Deardorf and E. J. Marenthal of the National Bureau

of Standards, Gaithersburg, Maryland, for performing the

chemical analysis.

134. I thank E. K. Hubbard of the National Bureau of Standards,

Gaithersburg, Maryland, for performing the spectrochemical

analysis.

135. The Au foil was obtained from Leico Industries Inc., New York.

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154. University Loudspeaker, Oaklahoma City, Oaklahoma, model UL6114.

This and further references to commercial components are for

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63
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64
Table III-l

Impurities detected by spectrochemical analysis of

starting Cu-Ni alloy foils. Metallic impurities not

listed were not detected to a sensitivity of better

than 0.001%.

Element Amount

at.%

Element Amount

at.%

Ag < 0.001 Mg 0.001 - 0.01

Al 0.001 - 0.01 Mn < 0.001

Ca < 0.001 Si 0.001 - 0.01

Cr < 0.001 W 0.001 - 0.01

Fe 0.001 - 0.01 V 0.001 - 0.01

65
Table III-2

Impurities detected by spectrochemical analysis

of Fe enriched Fe„CL.

Element Amount

at.%

- - - Element Amount

at.%

Ag <0.01 Mo <0.02

Al <0.05 Na <0.01

B <0.01 Nb <0.05

Ba <0.01 Ni <0.05

Be <0.001 Pb <0.02

Bi <0.02 Pt <0.05

Ca 0.01 Rb <0.02

Cd <0.05 Sb <0.05

Co <0.05 Si 0.02

Cr <0.05 Sn <0.02

Cu 0.05 Sr <0.01

Ge <0.05 Ta <0.05

Hg <0.01 Ti 0.02

K <0.01 V 0.02

Li 0.005 W <0.05

Mg <0.01 Zn <0.2

Mn <0.02 Zr <0.05

66
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CO < H T3 CU

CO CU rH

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70
Table IV-4

Parameters for annealed Cu Q-^Fe _ spectra at 205°K

with and without an applied field (source at 255°K).

Field Splitting

kG

Position

mm/sec (+ 0.03)

r mm/sec (+ 0.03)Relative

Area

Y Y

l y

o Y

l Y Yl

0.25 -0.07 0.31 0.41 0.29 0.71

45.6 + 1.0 0.25 -0.06 0.30 0.30 0.22 0.78

71
mI >

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CO H

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CD

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barely

resolved 6-line

pattern

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very

broad

unresolved

structure

very

broad

unresolved

structure

>> H xl

CU CU n >

CO H

-Q O

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and

y

spectra

superimposed

H

for

6-line

pattern kG

m

+ 1 o

en

CO

oCN+ 1 o

m

o

CN+ 1 o

H

m

+ 1 00H

Estimated

Fractions

of

Spectral

Compositions

resolved

6-line

pattern o

unresolved splittingunresolved splittingunresolved splitting

Y2

doublet CNO

CNO

o o o o o

onoCOO o

o

o O o

COo

CNo

m

o

m

o

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t4 H o 00ON

CN 00

CTi CN

00

CM

00o^

CN

00

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00

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CNST

00

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CN

x>

4-1 d

CU6

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cO CU CU U

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CO O" a- <J <

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a

composition

^ o

o

o

m

o

o

o

m

o

o

o

m

iHo

o

m

CNo

o

m

CNO

o

m

CNO

o

m

o

o

coo

o

coo

o

COo

o

X o o o o o o o o o o o

73
T3

CU3

C

I >

CU rH

cfl H

COH

cOe

A

V

00+1

o

CO

00+1

CM

CN

00+ 1

rH

resolved 6-line pattern r» r-« o

rH

Y

2

doublet rHO

lHo

O

rH o

rH OrH o

rH

co co O

rH OrH OrH

rH o O

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00

CN

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CN

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o

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co

00

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CN

CXi CN

resolved 6-line pattern COo O o

rH

O

Y2

doublet CNO

O

rH

mO [ o

rH orH o

rH o

rH o O

T-i

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CMOoCOOO

COOO

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T-I o orHo

rH

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CNO

CNO

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CNO

rH

CNO

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75
XI

<D3C

•H

4-1 coo>

XI

ccj H

CO

s-l coe

<u Pi

EC

00+ 1 m

00

iH

00+m

CO

CM

resolved 6-line pattern oH o

rH

Y2

doublet o

iH

O o

rH oH orH orH o

rH orH orH orH

H^O>- H

00 CM 00

CM

00

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00

CM

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CTi CM

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4-1 c

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rHoo X

t-I CMO

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CMo HCMO

coo

co

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co

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COo

CO

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76
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4-> coOI >

43

CO H

CO

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cu PiA

PCV

00+1

rHCN

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CN

00+1

CN

CN

CN

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O

rH

O

rH

O

rH

Y2

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rHoH

00 CO

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00 00

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CN

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77
1000-

2000 -J

Figure II-l, Ternary and binary diagrams for Cu-Ni-Fe

alloys . The ternary diagram is as given

by Bradley et al.125 for slow cooling.

The notation of Bradley et al . has been

changed so that a refers to bcc structures

and y to fee structures.

78
Figure Ill-l(a). Electronprobe scan of annealed

Cu

0.97

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Figure Ill-l(b). Electronprobe scan of annealed

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Figure III-l(c). Electronprobe scan of annealed

(Cu

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using FeKa X-ray.

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