PARAMAGNETIC RESONANCE ABSORPTION SPECTRA OF SOME
ADSORBED TRANSITION METAL IONS
By
Roger Jack Faber
A THESIS
Submitted to the School of Advanced Graduate Studies of
Michigan State University of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry
1957
P roQ uest Num ber: 10008593
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ACKNOWLEDGMENTS
The author wishes to express his sincere
appreciation to Professor M. T. Rogers for his
guidance and assistance throughout the course of
this work, to Dr. H. B. Thompson, who designed
and constructed much of the electronic circuitry
used in these experiments, to Mr. F. Betts and
Mr. R. Brigham, who assisted in the construction
of the electromagnet and its fittings, and to the
Atomic Energy Commission and the Union Carbide
Corporation for grants subsidizing this research.
VITA
Roger Jack Faber
candidate for the degree of
Doctor of Philosophy
Final examination, December 16, 1957, 2:00 P.M., Room 128, Kedzie
Chemical Laboratory
Dissertation:
Paramagnetic Resonance Absorption Spectra of Some
Adsorbed Transition Metal Ions
Outline of Studies:
Major subject — Physical Chemistry
Minor subjects — Physics, Mathematics
Biographical Items:
Born, October U, 1931, Grand Rapids, Michigan
Undergraduate Studies, Calvin College, 1959-53
Graduate Studies, Michigan State University, 1953-57
Experience:
Graduate Assistant, Michigan State University, 1953-55
Special Graduate Research Assistant, Michigan State
University, 19514-56
Graduate Fellow, Michigan State University, 1956-57
Member of American Chemical Society, Society of the Sigma Xi
PARAMAGNETIC RESONANCE ABSORPTION SPECTRA OF SOME
ADSORBED TRANSITION METAL IONS
By
Roger Jack Faber
AN ABSTRACT
Submitted to the School of Advanced Graduate Studies of
Michigan State University of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry
Year
Approved
19^7
ABSTRACT
Paramagnetic resonance absorption spectra were obtained for samples
containing manganous, cupric, and vanadyl ions absorbed on various
adsorbents.
The adsorbents included two forms of commercial sulfonic-
acid-type cation exchange resins, a carboxylic-acid-type cation exchange
resin, an anion exchange resin, silica gel, commercial zeolite, and
sugar charcoal activated at 1+00° centigrade.
The spectra were obtained by means of a paramagnetic resonance
spectrometer employing a transmission cavity which resonated at 9 *21+0
megacycles.
The microwave radiation was generated by a klystron,
detected by a silicon diode crystal, and the resulting signal was
analyzed by a lock-in amplifier and displayed on a strip-chart recorder.
Magnetic field strengths were measured by means of the magnetic resonance
frequency of the proton.
The g values and hyperfine structure intervals
were computed on the basis of measured line positions.
A study of the spectra of manganese adsorbed on various resins
enables a number of conclusions to be drawn concerning the properties
of the adsorbed ions. All the spectra of the manganese samples had g
values of 2.00.
All but the spectra obtained from the anion exchange
resin showed nuclear hyperfine structure with intervals of 96 gauss
between the various lines.
The presence of a weak fine structure in
the charcoal and cation exchange resin spectra indicated electrostatic
fields of less than cubic symmetry, probably tetragonal.
A lower
symmetry, which left the hyperfine structure barely detectable, was
present in the zeolite samples.
The electrostatic field symmetry about
the manganous ions bound to the anion exchange resin was even lower;
no hyperfine structure was resolved. The hyperfine structure interval
indicated essentially ionic bonding about the manganous ion in all the
spectra where resolution was obtained. The line width of the unresolved
spectrum of manganese on an anion exchange resin suggested approximately
fifty percent covalent bonding between the manganese and the resin.
The most useful information was obtained from the study of adsorbed
cupric ion because variations in the g values and hyperfine structure
constants were observed in the copper samples.
These quantities depended
upon both the nature of the adsorbent and upon the coordinated ligands
about the cupric ion.
Higher g values and smaller hyperfine structure
intervals were present in the spectra of hydrated cupric ions on the
sulfonic-acid-type cation exchangers.
The g values decreased and the
hyperfine structure intervals increased as the amount of covalent
character in the bond to the adsorbent increased.
For a given adsorbent,
the g values were substantially reduced and the hyperfine structure
interval increased when the coordinated water molecules attached to the
cupric ion were replaced with ammonia molecules.
The spectra of the
samples containing cupric ions adsorbed on the anion exchanger suggest
the formation of bonds to four nitrogen atoms on the adsorbent.
Some
evidence was found for an unresolved hyperfine structure due to inter
action of the electron spin with the nitrogen nuclei in both the anion
exchanger and the ammoniated samples.
The results with the copper
samples seem to support the molecular orbital theory proposed by Stevens
and Owen.
Very narrow lines and g values very close to 2.00 indicate a strongl
non-cubic, axially symmetrical electrostatic field about the vanadyl
ion.
Hyperfine structure interaction constants with absolute magnitudes
of 0.0182 and 0.007L5 cm
for A and B, respectively, were found for
vanadyl ion adsorbed on the sulfonic-acid-type cation exchangers.
These
constants were reduced by covalent bonding in the case of vanadyl ion
_i
adsorbed on the anion exchanger to 0.0158 and 0.00612 cm , respectively.
Assuming that the decrease was due principally to a decrease in an
isotropic contribution to the hyperfine structure, it was shown that
the constants A and B must have the same relative sign.
In general, the spectra obtained from the adsorbed ions were
similar to the spectra of these ions when in solution or in crystals
of known symmetry.
Consequently, it was possible to draw a number of
conclusions concerning the nature of the bonding between the ions and
the adsorbents, and the nature of the adsorbed phase.
TABLE OF CONTENTS
Page
INTRODUCTION.................................................
1
HISTORICAL SUMMARY
2
...................
Introduction
....
General Theoretical Principles..............................
Characteristic Parameters of the Spectra.................
Line Positions...........
Line "Widths.............................................
Specific Transition-metal Ions.......
Manganese...............................................
Copper.................................................
Vanadium...............................................
PARAMAGNETIC RESONANCE SPECTROMETER...........................
1
3
3
7
10
13
13
18
26
28
Introduction..............................................
Apparatus.................................................
The Magnetic Field......................................
The Electromagnet....................................
The Magnet Power Supply...............
Magnetic Field Modulation
......................
Magnetic Field Measurement...........................
The Microwave System....................................
The Signal Detection and Display System
............
The Preamplifier.................................
The Lock-in Amplifier................................
Operating Procedure........
28
29
29
29
32
37
UO
I4.U
50
50
52
59
PREPARATION OF SAMPLES AND EXPERIMENTAL RESULTS................
6U
General Procedure.......................................... 6h
Manganese.................................................
65
Preparation of Samples..................................
65
Analysis of the Spectra.................................
76
Copper....................................................
79
Preparation of Samples........................
79
Analysis of the Spectra.................................
90
Optical Reflectance Spectra.
......................... 98
Vanadium.................................................. 100
Preparation of Samples......
100
Analysis of the Spectra................................. 101
viii
TABLE OF CONTENTS - Continued
Page
DISCUSSION...................................................
108
Manganese.................................................
.......... ..................................
Copper
Vanadium......................
108
112
120
SUMMARY................................
125
REFERENCES.................................................... 128
ix
LIST OF TABLES
TABLE
Page
Covalent Bonding in Manganese-Containing Phosphors......
17
Adsorption of Manganese Sulfate by Various Adsorbents
67
III
Approximate A 1 Values for Manganese Powder Samples......
78
IV
Adsorption of Cupric Ion by Various Adsorbents..........
80
V
Analysis of Copper Spectra............................
96
VI
Summary of Results for Copper Powder Samples............
97
I
II
VII
VIII
Revised Estimates of Hj_ and gx For Ammoniated Copper
Samples...................
Adsorption of V0S04 by Various Adsorbents..............
97
101
IX
Analysis of VO*"*" Powder Spectra........................ 106
X
Summary of Results for V0^"+ Samples.......... ........... 107
XI
XII
Hyperfine Structure Constants and Configurational Inter
action Constants for the Copper Samples.................
llU
Covalent Bonding Parameters in Molecular Orbital Theory... 116
x
LIST OF FIGURES
FIGURE
Page
1. Diagram of L, S 5 I, and H based on the vector model of
the atom..............................................
5
2 . Energy levels of Cu^+
..........................
6
........................
3 . Electron spin levels of Mn'
■
4"P
5* Cu
absorption line for random orientation of symmetry
axes..................................................
15
5- Orbital levels of V + 4 ..................................
27
6 . The electromagnet
.................................
30
7. 3-Phase bridge rectifier for magnetpower supply.........
33
8 . Screen-voltage regulator for magnetpower supply.........
33
9. Magnet current control circuit.........................
35
10. 25-Watt audio amplifier................................
36
11. Multivibrator and power supply.........................
39
12. Proton resonance magnetic fieldstrength meter............
52
13. Schematic diagram of microwave and signal detection
systems...............................................
53
15 ■ Klystron power supply......
56
15. The spectrometer.......................................
57
16. Standing wave pattern for rectangular cavity oscillating
in the TE102 mode......................................
59
17 . Preamplifier...........................................
5l
18. Twin-tee filter for lock-in amplifier...................
51
+-
\
25
19. Lock-in amplifier..................................... 53~55
20. Audio signal derived from paramagnetic resonance line by
field modulation..................................
xi
55
LIST OF FIGURES - Continued
FIGURE
Page
.21. Power supply for preamplifier and lock-in amplifier......
60
22. Spectra
of manganous ion adsorbed
on Dowex-50.......
68
23. Spectra
of manganous ion adsorbed
on Dowex-50.......
69
25. Spectra of manganous ion adsorbed
on Dowex-50 and on
Amber lit e IR-100.......................................
70
25* Spectra
of manganous ion adsorbed
on Amberlite XR-100.
71
26. Spectra
of manganous ion adsorbed
on zeolite........
72
27. Spectra of manganous ion adsorbed
gel....................
on charcoal and silica
73
28. Spectra of manganous ion adsorbed on Amberlite IR-100 and
subsequently dehydrated................................
77
29. Spectra
of cupric ion adsorbed on
Amberlite IR-100..
81
30. Spectra
of cupric ion adsorbed on
Amberlite IR-100..
82
31. Spectra of cupric ion adsorbed on
Dowex-50 ......
Amberlite IR-100 and
32. Spectra
Dowex-50........
of cupric ion adsorbed on
33• Spectra of cupric ion adsorbed on
IR-5B.........
83
85
charcoal and Amberlite
85
35. Spectra of cupric ion adsorbed on Amberlite IR-5B.......
86
35. Spectra of ammoniated cupric ion adsorbed on Amberlite
IR-100................................................
91
36. Spectrum of ammoniated cupric ion adsorbed oncharcoal..,.
37* H versus concentration for copper samples..............
P
3 8 . Reflectance spectra of copper-zeolite samples...........
39* Spectrum of vanadyl ion adsorbed on Dowex-50, showing
intense central portion of the spectrum.................
92
95
99
102
50. Spectrum of vanadyl ion adsorbed on Dowex-50, showing the
weak outer portions of the spectrum..................... 103
51. Spectra of vanadyl ion adsorbed on charcoal and Amberlite
IR-5B...................................................105
xii
INTRODUCTION
Despite the work which has been done by means of various physical
methods on the nature and state of adsorbed substances, some points
remain unsettled; for example, the actual way in which ions are bound
to adsorbents is not completely clear.
Since paramagnetic resonance
absorption provides a new tool for studying paramagnetic ions, it was
thought that this technique might provide additional information about
the environment of the adsorbed ions.
Hence, a group of paramagnetic
ions were selected for study, the spectra of which are obtainable at
room temperatures and show nuclear hyperfine structure.
Spectra were
obtained for these ions adsorbed on a number of typical adsorbents.
HISTORICAL SUMMARY
Introduction
When a substance containing unpaired electron spins is placed in
a magnetic field, the magnetic moments associated with the spinning
electronic charges assume quantized orientations with respect to the
direction of the applied magnetic field. The energies associated with
the possible orientations are different, being greater for those orien
tations which oppose the applied field.
These energy levels are the
Zeeman levels, and the differences between them appear as a fine
structure in the optical spectra of paramagnetic substances.
Paramagnetic resonance absorption is a means of observing directly
transitions between the various spin states. The experimental procedure
involves varying the strength of an applied magnetic field until the
energy separation between the Zeeman levels is equal to the fixed energy
of quanta of radiation incident upon the sample.
A plot of energy trans
mitted by the sample against magnetic field strength shows a peak or
peaks corresponding to these transitions. Investigation of paramagnetic
ions is usually performed with the electromagnetic radiation in the
microwave region and field strengths in the neighborhood
of 3000 gauss.
The paramagnetic resonance absorption phenomenon was first observed
by Zavoisky (l) in Russia in 1955 a-nd slightly later by Cummerow and
Halliday (2) in the United States and by Bagguley and Griffiths (3) in
England.
Since then a large number of publications have appeared,
mainly from British and American workers, reporting both theoretical
and experimental investigations.
Wertz (5), Ingram (5)9 and Gordy, Smith,
and Trambarulo (6 ) have produced brief general reviews of the field.
Detailed summaries of the theoretical and experimental work on crystals
have been made by Bleaney and Stevens (7) and Bowers and Owen (8 ).
General Theoretical Principles
Characteristic Parameters of the Spectra
The energy separation between successive spin states of a paramagnetic
substance is given by
AE
-
g ? H
(1)
where H is the applied external magnetic field; p is the Bohr magneton,
and g is the spectroscopic splitting factor.
The g factor is one of
the important parameters of paramagnetic resonance absorption spectra,
for the position of any line in such spectra can be specified by
expressing the g factor associated with it.
E and H are variables
depending upon the experimental conditions; g is characteristic of a
given line.
The number of different spin levels in a paramagnetic ion is equal
to the spin multiplicity, 2S +- 1.
Each level corresponds to a different
value of the spin quantum number, M, which in the vector model is the
component of the spin vector, S, in the direction of the axis of
quantization, as shown in Figure 1.
are allowed, with the selection rule
Transitions between these levels
A M = ± 1.
Depending on the
symmetry of the crystalline electrostatic field in which the ion is
located, these 2S allowed transitions will occur at different values
u
1M
Figure 1. Diagram of L, S, I, and H based on the vector model
of the atom. At the field strengths used in paramagnetic
resonance experiments, the orbital magnetic moment vector, L,
and the electron spin magnetic moment vector, S, precess inde
pendently about the direction of the applied magnetic field, H.
The nuclear spin magnetic moment vector, I, precesses about
the direction of S. Ml , Mg (= M), and m are the projections
of L, S, and I, respectively, on the appropriate axes of
quantization.
of the applied magnetic field.
This multiplicity of lines in the para
magnetic resonance absorption spectrum is termed fine structure.
The line corresponding to a given spin transition in the para
magnetic resonance absorption spectrum may be further split if the
nucleus of the paramagnetic ion possesses a spin, I, and an associated
magnetic moment.
Interaction between the nuclear and electronic spins
splits each electronic level into a number of components corresponding
to the various nuclear spin levels.
There are 2 1 + 1 such levels, one
for each of the values taken by the nuclear spin quantum number, m.
The latter is the component of the nuclear spin vector, I, on the axis
of quantization ■which in this case is the direction of the magnetic
field produced by the unpaired electrons.
presence of nuclear spin is
The selection rule in the
A m = 0 ; that is, the nuclear orientation
does not change during an electronic spin transition.
A splitting of
the spectral lines still occurs, however, for the order of the 2 1 + 1
component levels is inverted for spin states of opposite sign, with the
l
result that each electronic transition is split into 2 1 + 1 lines.
This splitting of lines in the paramagnetic resonance absorption spectrum
due to Interaction with the nuclear spin magnetic moment is termed
hyp erfine strue tur e .
For a free ion (in the absence of any fields) there is one orbital
energy level which is (2L +1) - fold degenerate.
In the presence of
an electrostatic field produced by ions and dipoles in the vicinity of
the paramagnetic ion, some or all of this degeneracy may be lifted,
^-This effect is illustrated by the behavior of the energy levels of the
cupric ion as shown in Figure 2.
6
2n
D3/ 2
^
/
FREE ION
CUBIC FIELD
A.
TETRAGONAL
FIELD
ELECTRONIC
L-S COUPLING
S P LITTIN G
m
\\i>
B.
NUCLEAR
FIGURE 2 .
SP LITTIN G
EN ER GY
LEVELS
OF
Gu + +
MAG. FIELD
7
depending on the strength and symmetry of the field.
Each of the
orbital levels is (2S + 1)- fold degenerate in spin.
This spin
degeneracy may also be partially or completely lifted by second order
effects in which the electrostatic field interacts with the electron
spins by means of the spin- orbit coupling, which even in strong fields
is not completely absent.
The spin levels may then be further
separated by the external magnetic field. The influence of these two
interactions with the crystalline field will become evident later when
particular paramagnetic ions will be discussed in more detail.
Line Positions
The totality of the interactions of a paramagnetic ion has been
expressed by Abragam and Pryce (9) thus:
W= %
tV
* WSS ‘ P S' (L +
+ WN - YP nS 1
(2)
In this equation, the various symbols havethe following meanings:
W
is the total energy of the ion.
Up
isthat part of the energy whichdepends only on the
configur
ational variables of the electrons and not on their spin.
V
is the electrostatic energy due to the crystalline field.
W ls is the energy due to coupling of the spin and orbital motions,
commonly called spin-orbit coupling.
Wgg is the spin-spin coupling energy.
pH-(L *- 2S) describes the interaction of the external magnetic
field with the orbital and spin magnetic moments.
Ifijflj includes two interactions involving the nuclear spin, 13 namely
the interaction of the nuclear moment with the orbital and spin
magnetic moments and, if I
1, the interaction of the nuclear
quadrupole moment with the gradient of the crystalline electric
field.
8
TP^H*_E
is the energy of interaction of the external magnetic
field with the nuclear spin magnetic moment.
(3 is the Bohr magneton
is the nuclear magneton
On the basis of this analysis of the interaction energies, a
general Hamiltonian expression for an ion in a crystalline field of
axial (tetragonal or trigonal) symmetry was constructed.
> t = p [g„ Hz Sz * g± (H* Sx + Hy Sy )]
*" A Sz Iz + B(SX Ix
Sy Iy)
+■ D[SZ - 1/3 S(S * 1)]
Qflf - 1/3 1(1 + 1)] - T P jU ’I
In this equation the various symbols have the following meanings:
H^., H , and Hz are the components of the magnetic field vector
Xiong the coordinate axes.
Sx , Sy, and Sz are the corresponding components of the electron
spin vector.
Ixj» lyj
Ig are
spin vector.
corresponding components of the nuclear
gtt and g
are the two principal values assumed by a tensor, g,
when directed respectively parallel and perpendicular to
the symmetry axis.
D is a constant associated with the fine structure separation in
the spectrum.
A and B are similar constants associated with the hyperfine
structure intervals.
Q is related to the degree of interaction of the nuclear quadrupole
moment with the gradient of the electrostatic field .
S is defined by setting the multiplicity of the electrostatic
energy levels equal to 2S +■ I .
Bleaney (10) has used this Hamiltonian to derive an expression for
the allowed transitions in strong magnetic fields, using perturbation
theory carried to the second order.
His calculations were carried out
■with two limitations imposed on the problem, namely tha.t the electro
static field must have axial symmetry and that Q must be much less than
A and B.
He obtained equations describing the separation, hv
, between
energy levels, as a function of the angle, 0 , between the external
magnetic field and the symmetry axis. The selection rules were
A M = ± 1,
A m = 0.
Since paramagnetic resonance absorption experi
ments are commonly performed at constant frequency and variable field,
it is more convenient to adopt the custom of defining HQ as hzS / g p,
and dividing through by g p to obtain equations for the values of the
magnetic field strength, H, at which allowed transitions occur.
When
this is done, Bleaney'3 equations assume the following forms.
For fine structure only, ignoring nuclear spin interactions,
H = H° -
(M - 1/ 2 ) [3 {g* (cos*
■n
- (— 2—
g P
D
-
6 ) / g2} - 1 ]
gir g, COs 0 sin 0 2
(--- i-- -------- ) . [US(S.l)-2l4M(M-l)-9]
g2
1
g± sin 6
4
)S 'BEEJp (
i
}
[2s(s+i)-6m (m -i )-3]
(U)
2
-1
)
— L.
2H 0
In the presence of hyperfine structure, the following terms must be
added to the right hand side of equation U.
Km
B2
2Hq
lair- (-Tr1 ’)
£K
[ m ( 2 M - l) ] - •—
l
'
' J
2H0 v
)
£skm( m - i ) ’
I
■
^
Z
'
s in 2 0 co s2 0
K
[ k X l- D - B m Z - l]
m s in 2 0 c o s 2 0
Kg'" ^ ‘ [ 2 I ( I + 1 ) - 2 m a- l ] ra sin4 0
(5 )
10
In these equations, g2 = g§ cos2 © *- gj sin2 ©, K 2g 2 = A 2g 2 cos2 © +
B 2g 2 sin2 0 and the other symbols have the same meanings as before.
M is the higher quantum number in the transition M —
M-l.
The various parameters, gM, g , H q , A, B, D, and Q may be
determined empirically from measurements of the positions of the
spectral lines, provided that the interactions associated with them
contribute noticeably to the spectrum.
It is the aim of theoretical
studies in electron spin paramagnetism to account for and predict the
observed values.
Line Widths
The widths of paramagnetic
resonance absorption lines are important,
both theoretically and practically.
Practically, observation of very
broad lines is difficult or impossible^ narrow lines are more easily
detectable and permit more precise measurement of the spectral para
meters.
The theoretical implications of line width may be indicated by
a brief survey of the factors influencing line width.
A given paramagnetic ion experiences not only the steady magnetic
field produced by the external magnet, but also a small, random field
produced by neighboring magnetic dipoles . The result is that resonance
occurs throughout a range of field strengths and the absorption line Is
broadened.
This effect involves a direct interaction between electron
spins (spin-spin interaction) and the resulting broadening of the
absorption line is called dipolar broadening.
Since the spin-spin
interaction decreases as the inverse cube of the distance between
11
interacting dipoles, only near neighbqurs contribute to the line width.
Consequently, line widths may be greatly reduced by diluting a para
magnetic substance with a diamagnetic one, thereby increasing the
separation between paramagnetic centers.
This technique, which has
been widely used, is known as magnetic dilution.
According to the uncertainty principle, the uncertainty in the
energy of an excited state increases as the lifetime in that state
decreases.
Hence, any relaxation process, which provides a mechanism
for the unpaired electron spins to return from a higher spin level to
a lower one, reduces the lifetime in the higher state and broadens the
absorption line corresponding to that transition.
The process which
provides this mechanism is the indirect interaction between the electron
spin and the thermal vibrations of the crystalline lattice by means of
the spin-orbit coupling and spin-spin coupling.
The lattice vibrations
affect the orientation of the orbital magnetic moment because of
electrical interactions with the non-spherical electron cloud.
The
orbital magnetic moment is, in turn, magnetically coupled to the
electron spin.
Likewise, the lattice vibrations produce periodic
variations in the distance between neighboring magnetic spin dipoles.
Both of these effects provide means whereby the excess energy of the
electron spin in an excited state may be transferred to the lattice
and the spin may return to alignment with the magnetic field. The life
time of the excited spin state is directly proportional to the amount
of splitting of the orbital levels by the crystalline electrostatic
field and inversely proportional to the spin-orbit coupling constant, A ,
12
and to the temperature.
As a result, when spin-lattice interaction
contributes significantly to the line width, the width may be decreased
by reducing the temperature.
The third major factor influencing line width is electron exchange
interaction between neighboring paramagnetic centers.
The effect is
analogous to the valence bond treatment of the single bond, in which
the two bonding electrons resonate between orbitals associated with
each of the nuclei because of the indistinguishability of electrons.
When a pair of paramagnetic ions between which exchange occurs are
oriented identically with respect to the magnetic field and therefore
have identical resonance frequencies, the effect of exchange is to
smooth out the random magnetic fields experienced by the two and sharpen
the absorption lines.
Van Vleck (11) has calculated the effect of
exchange interaction on the various moments of the absorption line and
finds that no contribution to the second moment occurs, but that the
fourth moment is greatly increased. The effect on line shape is that
the line is much more sharply peaked at the center than is the typical
Gaussian curve.
When the two ions between which exchange occurs are
differently oriented in the magnetic field and therefore tend to resonate
at different field strengths, the effect of exchange is to produce a
single resonance line at the arithmetic mean of the two individual lines,
and line broadening occurs.
This contribution to line width also depends
on the distance between paramagnetic centers and may be reduced by
magnetic dilution.
13
Specific Transition-metal Ions
It is now possible to consider the application of the general
principles outlined above to the special cases of the three iron-group
transition elements which were the subject of this investigation.
Manganese
The doubly charged manganous ion occupies the middle position in
the series of iron-group transition elements, because here the 3 d shell
is exactly half filled (S = 5/2) and there is no orbital degeneracy of
energy levels (L = 0) . Under the proper conditions, a fine structure
consisting of five lines may be expected in the paramagnetic resonance
absorption pattern and, since the Mn55 nucleus possesses a spin of 5/2,
each of the spin levels is resolved into six components and a six-line
hyperfine structure pattern is also to be expected.
Hence, with all
the degeneracy removed, the absorption pattern of manganous ion should
1
consist of thirty lines.
An energy level diagram is shown in Figure 3.
Resonance absorption has been detected at room temperature for
most of the compounds involving manganous ion, since, with L = 0 for
the ground state, there is almost no spin-orbit coupling and the spinlattice relaxation time is very long.
However, narrow lines have been
obtained only at high dilution, for the large value of the spin makes
dipolar broadening an important factor at higher magnetic concentrations.
In cubic fields, the hyperfine structure only is observed; the fine
structure becomes evident in fields of lower symmetry.
^-Under certain conditions more have been observed (12) .
The effect of
Hi
M
+ 5/2
+ 3/2
+ 1/2
5/2
FREE ION
EL ECT RO N
CLOUD
DIST OR TION
MAGNETIC
FIELD
-5 /2
FIGURE 3.
ELE CT RO N SPIN LE V E L S
OF M h + +
CFROM INGRAM5 }
15
crystalline field symmetry upon the paramagnetic resonance absorption
pattern is illustrated by the results of Hershberger and Leifer (13)*
who investigated various phosphor crystals containing small amounts of
manganese.
These workers found a simple six line spectrum due to hyper
fine structure in three crystals possessing cubic symmetry, a thirty
line spectrum in hexagonal zinc sulfide, and a single, broad resonance
750 to 1000 gauss wide in seven crystals of tetragonal, rhombohedral and
rhombic symmetry.
The observed value of the hyperfine structure constant, A, is
.
anomalously high (ca. 0.01 cm
_i.
) if the only electron configuration
6
contributing to the ground state is 3s2 3d5,
S.
Abragam and Pryce (9)
postulated the promotion of inner electrons in order to explain this
large interaction with the nuclear spin.
Although the energy involved
in promoting 3 s electrons is very large, their contribution to the
hyperfine structure is also very large, because of the large value of
the s-type wave function at the nucleus. Consequently, a small
admixture of the configuration 3 s 3 d5 Us,
S
was postulated, so that
6
the actual state of the ion could be represented by
6
where
S stands for the main term and
S
6
+ a
S T,
6
S' for some normalized linear
combination of these two terms, and a is a small coefficient.
With
this treatment, A is proportional to a and to the values of the 3s and
Us wave functions at the origin.
Van Wieringen (lU) investigated paramagnetic resonance absorption
in powdered samples containing manganous ion diluted in various dia
magnetic compounds of cubic symmetry.
The observed six line spectra
16
conformed to the equation
H = HQ - A Tm - A t2/2Hq
This equation
[ I (I f 1)
is derived fromequations
-m 2 ]
(6 )
h and 5by setting D = 0, A = B,
and taking only the first two terms of equation 5-
Here, for con
venience, A T is defined as
A'
= A/g p,
(7)
where A has dimensions of energy and A ’ of field strength.
A progressive
decrease in the magnitude of A 1 was observed as the extent of covalent
bonding between the manganous ion and its neighbors increased.
On the basis of the promoted s-electron hypothesis of Abragam and
Pryce, Van Wieringen concluded that the contribution to the hyperfine
splitting from the covalent bond is less by a factor of ten than the
contribution from the ionic bond.
In the first approximation the
covalent contribution can be neglected.
Thus, the amount of hyperfine
splitting is directly proportional to the amount of ionic bonding.
With the further assumption that the bonding is completely ionic when
the neighbors
are fluoride ions or water dipoles, it is possible to
state the percent of covalent bonding on the basis of measured values
of A ’. The results for a few phosphors are collected in Table I.
The effect of exchange interactions on the manganous ion spectrum
has been observed in powered zinc sulfide phosphor containing varying
amounts of manganous ion (lU)* and in aqueous solutions of manganous
ion (lj?) . In both cases, as the magnetic concentration increases the
hyperfine structure first disappears because of dipolar broadening, and
exchange interaction then narrows this single broad resonance.
17
TABLE I
COVALENT BONDING IN MANGANESE-CONTAINING PHOSPHORS
(From Van Wieringen (1U))
Neighbour
-2
-2
_2
_2
_2
H20
F~
C03
98
98
9h
80 - 90
69
65
59
Percent co
valent bonding 0
0
5
10 - 20
30
35
U0
Approx. A ’
0
s
Te
Se
A disappearance of the paramagnetic resonance absorption spectrum
was observed in aqueous solution by Cohn and Townsend (16) when a complexing agent was added.
This effect was attributed to line broadening
due to decreasing symmetry about the ion.
The dissociation constants
of several biochemically important complexes involving manganese were
measured using the fact that only the uncomplexed ion contributed to
the resonance absorption.
McGarvey (17) investigated aqueous solutions of a number of iron
group ions, including manganous, cupric, and vanadyl.
The observed
widths were accounted for by assuming that the ion is present in a small
micro-crystal formed from solvent molecules or complexing groups and
that this micro-crystal possesses a spin Hamiltonian similar to that
observed in solid crystals.
The widths depended on the symmetry of the
electric field created by the complexing groups.
18
Copper
The ground state of the cupric ion is
2
. The free ion has
fivefold orbital degeneracy which is lifted in cubic and tetragonal
crystalline fields in the manner shown in Figure 2.
In the hydrated
salts the separation between the two lowest orbital levels is so great
that only the lowest level is inhabited at room temperature.
Since the
3d shell lacks one electron of being completely filled, the net spin is
S - l/2 .
The behaviour in paramagnetic resonance absorption experiments
is similar to that of an ion having only one electron in the 3 d shell.
No fine structure is to be expected for S = l/2. In most compounds
owing to the wide separation of the orbital levels, the spin-lattice
relaxation time of the cupric ion is sufficiently long to allow room
63
temperature observation of absorption. Both copper isotopes, Cu
and
65
,
Cu , possess nuclear spins of I = 3/2. The resulting four-line hyper63
fine structure in the spectrum is due mainly to the Cu
isotope, which
is much more abundant.
In tetragonal fields, when the line widths are too great for
nuclear quadrupole interactions to be observed, the angular variation
of the spectrum is described by the following equation:
H = Ho - Km - r s y
- — ~ h~
( A 1k" ~
(
) [ 1 (I + x) - ra8 ]
’ m
sin2 6 cos2 0
This equation is obtained from equations U and 3 dy setting D and Q
equal to zero.
^
19
The positions of the lines in the copper spectrum change consider
ably- as the angle 0 between the symmetry axis and the magnetic field is
varied.
Typical values for the various parameters are as follows:
gTt = 2.U3 g±
= 2.1; A = 0.010 cm'1; B - 0.003 cm’1.
On the assumption that the only electronic configuration contribut2
2
6
9
ing to the D ground state of the hydrated cupric ion is 3s 3p 3d ,
Polder (18) calculated g values as follows:
g„
=
2( 1 - h A / A 3 )
(8)
gj.
=
2(1-
(9)
A/ A
4 )
In these equations, A is the spin-orbit coupling constant in the crystal,
and A 3 , and
are the orbital energy separations indicated in Figure 2.
Because the 3b shell is more than half filled, /\ is negative and the
g values are greater than 2.00.
A simplified presentation of Polder’s
treatment and its application to cupric sulfate has been made by Kikuchi
and Spence (19)• More
than
recent experimental valuesforcupric sulfate
thosequoted inthe latter paper were reported
byBagguley
and
Griffiths (20).
Although Polder’s theory accounts fairly well for observed g values,
it fails to explain the hyperfine structure. Specifically, this theory
predicts that B should be greater'than A, whereas the reverse is invari
ably true.
Abragam and Pryce (21,22) have invoked the promoted s
electron hypothesis which was used to explain the hyperfine structure of
the manganese spectrum, to account for this anomaly, too.
Polder's
theory, with no s electron promotion, leads to the following relations
between the hyperfine structure parameters and the g values1
.
20
A = [(g„ ~ 2)
3/7 ( gx -
B = [(g± - 2 )
3/1 U
(gx -
2)
- U/7] P
2)
(10)
2/7] P
(1 1 )
P is estimated by comparison with the optical hyperfine spectrum of the
free copper atom in the configuration 3d9 Us2, or by calculating the
mean value of 1// r3 from known Hartree wave functions for the configuration 3d
10
of the cuprous ion.
Both methods lead to approximately the
same result:
P ^
0.035 cm
(12)
The assumption of a promoted s electron leads to an isotropic correction,
k, on the hyperfine structure parameters so that with typical values
of 2 .i| and 2.1 inserted for glf and g^ , A and B become,
A = ( - k - 0 .13)
P
(13)
B = ( -k + 0.365)
P
(lU)
If k is arbitrarily taken to be 0.25* A and B become -0.013 cm
O.OOJ4 cm
, respectively, in good agreement with observation.
_i
and
Here,
k is proportional to the degree of admixture of excited configurations
and to the values of the 3 s and Us wave functions at the origin.
Sands (23) reported the application of this theory to the cupric
ion resonance spectrum in glass.
= 2.06; A = -0.0157 cm
13 and
The observed quantities were g„ = 2.32;
o
-1
;B - 0.00228cm . By means of equations
lU avalue of k = 0.26 was obtained.
The question of the formation of covalent bonds involving the
paramagnetic cupric ion is a difficult one.
The coordination number of
copper is four, and the ligands are commonly arranged in a square about
the central ion.
These facts lead naturally to the supposition that
21
dsp2 hybridization of the orbitals belonging to the cupric ion occurs.
This possibility has been considered by Abragam and Pryce (9*21) and
repeated by Abragam (22), who reported that, although a satisfactory
anisotropy can be obtained for the hyperfine structure, the presence
of the unpaired electron in the state Up2 leads to gtt = 2.
Moreover,
this covalent structure has different symmetry properties from Polder’s
ionic structure, and no resonance can exist between them.
Stevens (2U) and Owen (25*26) have proposed a molecular orbital
theory of covalent bonding in octahedral cupric complexes which does not
involve the change in electron configuration.
The complex is treated
by the method of molecular orbitals with the assumption that the unpaired
spin is partly in the central d orbits and partly in
the outer nuclei.
orbits around
This leads to a reduction in the orbital g factor
and to the possibility of observing hyperfine structure from the outer
nuclei.
The resulting equations for the g values are:
g„
=
gj_ =
where
ion.
2 - 8( A'/A3)a2 b2
2 -
( x'/A 4 )a2 ( 1 . b 2)
(15)
(16 )
is nearly equal to the spin-orbit coupling factor in the free
The parameters a and b may assume values between zero and one.
Howard (27) proposed an explanation of the magnetic properties of
the covalent ferricyanide complex based on the assumption of a strong
electrostatic field which removes the coupling of spin to orbit and of
spin to spin.
Here, the results were the same as if the molecular orbital
or the Slater-Pauling theory had been applied. The theory of Howard
was later used by Kotani (28) to calculate the magnetic moment of the
22
ferricyanide complex.
Again the results were qualitatively the same as
Pauling’s covalent theory.
Orgel (29) has given a simple electrostatic interpretation of the
extra stability of the non-octahedral complexes of the cupric ion.
If
the four ligands in one plane move closer and the other two move away
from the central ion, a plane of higher electron density is formed.
Then, the copper orbital containing the unpaired electron moves into
this plane, giving stabilization.
The predictions concerning the g values and hyperfine structure
intervals made by the various theories may be compared with some experi
mental results in a number of cupric compounds possessing tetragonal
symmetry.
Polder’s theory predicts gT, = 2.5, g± =
2.1 for ionic bonds
between the central cupric ion and its neighbour. The promoted s
electron hypothesis of Abragam and Pryce further predicts A = 0.013 cm
_i
and B = 0.00U cm . Bagguley and Griffiths (20) found gn = 2.57,
g± = 2.08 for cupric sulfate pentahydrate. Bleaney, Bowers and Ingram
(30) found gf? = 2.55, g± = 2.15, A = 0.0103 cm
, and B = 0.0035 cm
for cupric potassium sulfate.
Spence and Carlson (31) reported g„ = 2.22, g± = 2.05 in copper
tetrammine sulfate.
These workers discussed the covalent bonding in
this crystal in terms of the ratio, /V / A o*
the spin-orbit coupling
constant in the crystal to that of the free ion.
In the hydrated
complexes this ratio is 0 .8 , whereas in the tetrammine complex it is
0.55.
23
McGarvey (32) found g„ = 2.25U, g± = 2.075 in single crystals of
cupric acetylacetonate. A nuclear hyperfine structure was observed in
solutions of cupric acetylacetonate in mixtures of various solvents.
Because of the averaging effect of the random motion in liquids, the
observed splitting should be due only to the isotropic term, kP, in
equations 13 and lH. Also observed -was a solvation effect amounting
to a ten percent variation in the splitting as the composition of the
solvent was changed. The magnitude of the splitting decreased as the
complexing action of the solvent increased.
Perhaps the smallest g values were observed by Bennett and Ingram
(33) in cupric phthalocyanine. They found gIt = 2.165, gx = 2.055-
In
a crystal in which the copper ions were diluted with zinc, a hyperfine
_i
structure appeared with A = 0.021 cm
and B = 0,003 cm
"When the orientation of the various cupric ions in a bulk sample
is completely random, and the local field about each ion has axial
symmetry, it is also possible to measure the spectral parameters.
The absorption spectrum, which is the sum of the absorptions over all
possible orientations of the symmetry axis, possesses sharp upper and
lower boundaries.
tion.
Sands (23) has calculated the shape of this absorp
In the absence of nuclear hyperfine structure, the absorption
intensity is related to the magnetic field thus:
N ( Hn V
(
2
H3 )
(17)
2
( (gtr - g± ) [( Hc/H )2 ' gf]
)
Here, I is the intensity of absorption; N is a proportionality factor
related to the number of paramagnetic centers in the sample;
= h V /p .
2h
The shape of this curve is shown in Figure U.
In the presence of hyper
fine structure, there would be 21 + 1 such absorption curves, corres
ponding to the various orientations of the nuclear spin, I.
In this
case the positions of the upper and lower edges of the spectrum are
given by the following equations:
Hu = H0/gx
= H0/g„
where
and
- m B '/ p Si
(18 )
-
(19)
m'A
MAG. FIELD
CNOT TO SCALE !)
28
PARAMAGNETIC RESONANCE SPECTROMETER
Introduction
The apparatus required in order to observe the paramagnetic resonance
absorption phenomenon consists of three rather distinct systems.
First,
there is required a magnetic field, which is homogeneous throughout the
volume of the sample, steady over a period of time up to one-half hour
long and capable of variation between zero and several thousand gauss.
This magnetic field removes the degeneracy between the various magnetic
spin states of the paramagnetic material.
Second, there must be a
source of radiation to provide the energy needed to effect transitions
between these spin states.
The energy of the quanta absorbed and there
fore the wavelength of the absorbed radiation at resonance depends upon
the strength of the magnetic field which separates the magnetic energy
levels. With field strengths of about 3000 gauss the wavelength of
absorbed radiation is about three cm. corresponding to a frequency of
about 9300 megacycles.
Third, since the power absorbed in paramagnetic
resonance absorption is frequently only a minute fraction of the total
power incident on the sample, devious means must be employed to detect
the absorption, to increase the signal-to-noise ratio, and to display
the resulting signal as a function of the magnetic field strength.
29
Apparatus
The Magnetic Field
1
The Electromagnet,
The magnet was designed for a high voltage
power supply since 'electronic regulation of high voltage supplies is
somewhat simpler than the regulation of low voltage supplies.
.A rectangular yoke was used to provide the necessary mechanical strength
and improve uniformity of field.
Pole pieces 7 l/2 inches in diameter
provide a uniform field over a relatively large area.
Water cooling
was employed to minimize change of the resistance of the coils through
heating.
A mechanical means of varying the pole gap was considered
desirable since it is occasionally necessary to accommodate larger
apparatus.
Since pole caps of different materials are useful under
various circumstances a means should be provided for replacing these.
The yoke must have a large enough cross section to provide a low
reJ/-^tance magnetic path and also mechanical strength.
With these
considerations in mind the design outlined below was adopted.
The dimensions and method of assembly of yoke and pole pieces are
shown in Figure 6 and the mechanical means of varying the pole gap is
indicated.
These parts were constructed from cold-rolled steel and
were machined to close tolerances in the Mechanical Engineering Depart
ment.
The yoke was assembled first, using l/2" x 13" cap screws, and
the holes for the pole pieces bored together in one operation.
xMany of the details of the construction of the magnet and some of its
associated electronic circuitry have been previously described by
Rogers, Thompson, and Faber (38)-
30
YOKE
POLE PIECE SUPPORT
SUPPORT FOR BOLT D
THREADED l" STEEL ROD
HANDW HEEL
COLLARS LOCKED TO BOLT
THREADED l" HOLE
H
J
K
L
M
N
FIGURE 6 .
POLE PIECE, 7 1/2" DIA.
POLE CAP
STUD TO HOLD CAP
ALUM INUM END PLATES
MAGNET COILS
COOLING COILS
THE ELEC TR O M A G N ET
31
The pole pieces were then inserted and hand-lapped for a smooth sliding
fit.
The parts for moving the pole pieces in and out were added and
the entire assembly placed on a welded angle-iron base.
The energizing coils are wound in six sections.
Each section is
wound on a copper spool as shown in Figure 6 . The copper spool was
built from sheet copper cut to size and soldered.
The cooling coils
consist of one turn of l/U'T o.d. copper tubing soldered to each side
of the spool and shaped so that adjacent
copper coils of one spool
spools fit together with the
contacting the sheet copper side of thenext.
In this way heat transfer is maximized and, since the coils are all in
parallel, resistance to flow of cooling water is minimized.
About 1200
turns of Formvar-insulated No . IJ4. copper magnet wire are wound on each
spool in 60 layers of 20 turns each.
The inner lead is brought out
through a hole in the side of the coil and is protected by a fluorothene
sleeve.
Three coils are placed on each pole piece with a
aluminum sheet on each side and the whole sandwich bolted
bolts through the aluminum.
piece of l/U"
together by
This is done to bring the cooling coils
into close contact with the spools.
The electrical leads are carried
out to a terminal board and the copper tubing leads were connected to
water inlet and outlet manifolds.
The six coils taken together have about 7200 turns of No. iJLj. wire
with a length of about 23,000 feet and resistance of about 50 ohms.
With a maximum current of
9 amperes from the power supply the maximum
number of ampere-turns is about 63 ,000 .
32
The uniformity of the magnetic field at the sample depends upon
the homogeneity of the metal in the pole caps and the smoothness of
their surfaces.
The faces of the machined pole caps were first made
reasonably flat by grinding on a centerless grinder.
annealed to remove internal strain.
Next they were
Finally the faces were ground by
hand lapping with Pyrex discs and Carborundum powder in a vehicle of
turpentine and polished with jewellers*rouge suspended in turpentine
on a cloth lap.
The technique employed was the standard three-disc
method of making optical flats as described by Ingalls (39).
The polished
pole faces were compared with a quartz optical flat by observing the
interference fringes formed between the two surfaces in the monochromatic
light of a sodium lamp. Grinding and polishing were stopped when both
pole faces were within two or three fringes of true optical flatness.
The surfaces thus formed were washed with turpentine, then with acetone
and wiped free of dust with lens tissue.
The entire face and sides of
both caps were then covered with several coats of a clear plastic spray
of the sort used to protect automobile chrome against corrosion.
The Magnet Power Supply. Power for the magnet is produced from
the local 220 volt three-phase supply, which is converted to direct
current by selenium rectifiers in a three-phase bridge as shown in
Figure 7 . This bridge is capable of delivering 250-300 volts at up to
25 amperes.
The rectifiers are forced-air cooled by means of a fan
which is automatically turned on with the input to the rectifiers.
The rectifiers may also be connected to a UUO volt supply; as yet the
current control circuitry for the magnet is not adapted for this
voltage although the necessary changes are minor.
"HI... iH
^
o— il
TT-o^o-
°— H
TV-o^a-
4 4 0 V.
/V
^
-CH—
i—
1|
-o+
s 3“
°— H
HE
HI
inf°-
H
t j - r —
1»
Cl—
ft
i—
-o—
nnX.
2 2 0 V.
I
s2
Q|
CD,
CM
CM
MAGNET CURRENT CONTROL CIRCUIT
rio
O
OJ
in
ll_
FIGURE 9.
CM
>
lO
Q
Is-
LjlI
I 9 — cc (D
CM
* 2 p 2 -1
CO
X
>
U_
UJ
X
in
CM
in
I—
CO
U-
CO
O
CM
UJ
„ o
"T^VWV
u_
o o
a: LU
u_ or
UJ
CD
u_
o
CO
<
CD
ZD
O
QC
O
36
0.1
6 L6
INPUT
OUTPUT
C“^ ° 5 0 0
fc-o 250
0.56 M
6SL7
0 .2 7 M
20
12K
0.25-vi 0.5 M
COMMON
0.25M
0.1M
4.7 K
4.7 K
0.3
6 L6
6.2 V.FIL.
40
5U 4
FIGURE 10.
2 5 W A TT AUDIO
I2.5K
20 W
A M P L IF IE R
40
37
potential provided by an independent voltage supply and the two 0B3
voltage regulator tubes.
Thus, any positive excursion of the positive
terminal of the magnet coils produces a positive excursion of the 6AU6
grid bias which increases the current through the one megohm dropping
resistor, resulting in a negative excursion of the 6L 6 grids and a
decrease in the magnet current which cancels the original fluctuation.
Although this type of circuit would operate satisfactorily with
the 6L 6 screen grid voltage obtained from the positive supply via another
dropping resistor, it was found convenient to obtain this grid voltage
from the separate fixed voltage regulator circuit shown in Figure 8
which had been installed in a previous modification of the power supply
unit.
The output current of the voltage regulator is determined by the
grid potential of the 6AU6 . Hence coarse control of the magnet current
is provided by the two ganged 32K potentiometers and fine control by the
fifteen-turn 10K Model B Helipot potentiometer. The latter is driven
by an a.c. motor and gear train for automatic sweeping through an
absorption signal. Control of the sweep rate is obtained by varying
the voltage across the motor coils by means of a Variac autotransformer.
Magnetic Field Modulation. Modulation of the magnetic field is
obtained with an auxiliary pair of "wobbling" coils which are wound on
two separate forms and mounted coaxially with the main coils, one on
each pole piece as shown in Figure 6 . Rings of felt separate them from
the aluminum retaining plates of the main coils, and they are held in
place by four aluminum rods which bridge the gap between them.
38
The coils are connected in series, with their external leads connected
to the same terminal board as the main coils.
From here a connection
is made by means of* the overhead conduit to the output terminals of the
twenty-five watt audio amplifier shown in Figure 10. Thus a voltage
signal of any desired shape may be impressed across the input terminals
of the audio amplifier and be converted into a fairly large current
through the wobbling coils. At 100 cycles/second the impedance of the
coils is about eight ohms and a current of about three amperes can be
obtained from the amplifier. This gives a modulation of the magnetic
field whose amplitude is about ten gauss.
Because the modulation signal obtained from the multivibrator is
very strong and no voltage amplification is necessary, the audio amplifier
consists only of power supply, volume, treble and bass attenuators and
a power stage involving a 6SL? twin triode which divides the signal
between two 6L 6 tetrodes arranged for push-pull operation.
The circuit of the multivibrator and its power supply is shown in
Figure 11.
Such a circuit acts essentially as a non-sinusoidal oscillator.
Although the two halves of the 63N7 twin triode are nearly equivalent,
the condition of equal plate currents is unstable; i.e. the tendency is
for the grid of one triode section (say the one on the left) to be
driven below cutoff and the other to full conduction.
Any random
tendency in this direction is supported by positive feedback:
a negative
excursion of the left-hand grid produces an increase in the left-hand
plate voltage and, since the voltage across the capacitor C cannot change
suddenly, a positive excursion of the right-hand grid occurs, producing
39
AB
40 K
40K
-a
0.2 M
■o-
0.22 M
1/2 6S N 7
0.22M
1/2 6S N 7
0.12M
0.12M
6S J7
4 0 0 -fL
1/2 6S N 7
500
5K
22K
1/2 6S N 7
22K
2.2K
A/WV
20
20
6K
5Y3
VR 150
1.5K
AM/V
20
FIGURE
II.
M ULTIVIBRATOR AND POWER SUPPLY
5K
VR 150
—o
46K
1*0
a decrease in the plate potential which sends the left-hand grid further
toward cutoff, With complete cutoff attained the charges on the
capacitors C, C ’ slowly leak off through the 0.12M resistors at a rate
determined by the time constants of the resistance-capacitance circuits,
The left-hand grid potential rises above cutoff causing current to flow
in that section and the right-hand grid potential falls, reducing the
current in that section.
When the currents reach equality, the circuit
again triggers and the right-hand triode becomes non-conducting.
This
oscillation continues at a rate determined by the values of the
capacitors C and C 1.
A pentode amplifying stage employing a 6SJ7 is direct-coupled to a
cathode in the multivibrator and the output of the amplifier is in turn
direct-coupled to two cathode follower output stages.
Since capacitative
coupling is avoided, the amplifier and output stages operate at any
frequency at which the multivibrator will oscillate.
The capacitors in
the first stage are plugged into a receptacle on the front panel and
the frequency is changed by plug-in units.
The output of the modulator
is an approximately square wave of about 130 volts height.
Magnetic Field Measurement. The nuclear magnetic resonance frequency
of the proton as a function of magnetic field strength is well known
and is given by the formula:
3
V p = U-2577 H x 10
Consequently, a measurement of
-1
cm.
(20)
by a conventional nuclear magnetic
resonance technique is a simple, convenient and highly accurate method
of measuring the field strength.
1*1
A sample containing a dilute solution of manganous sulfate in
distilled water is placed within the probe coil of a Pound—Knight
marginal oscillator and the coil is placed as closely as possible to
the waveguide absorption cavity with its axis perpendicular to the
direction of the steady magnetic field, as shown in Figure 13.
The
oscillator output is impressed across the vertical plates of an
oscilloscope whose horizontal sweep is synchronized with the modulation
frequency.
Then as the magnetic field is swept back and forth through
the proton resonance frequency which the oscillator is tuned to receive,
a peak will appear on the oscilloscope trace which represents the proton
resonance line shape.
The frequency to which the oscillator is tuned
may be measured accurately to five significant figures by means of a
type BC-221-0 United States Army Signal Corps frequency meter.
In the marginal oscillator, whose circuit diagram is shown in
Figure 12, the sample coil and the two variable capacitors form a
parallel tuned combination in the grid circuit of a cathode-coupled
oscillator employing a 12AT7 twin triode.
This oscillator is simply
an amplifier with sufficient positive feedback between the right-hand
plate and the tuned grid to supply its own input and thus to maintain
continuous oscillation.
Both the oscillation amplitude and the amount
of radio-frequency current in the sample coil can be controlled by the
two 2000 -ohm potentiometers in the cathode and second grid circuits.
When the nuclear magnetic resonance condition is reached, an absorption
of energy occurs in the sample coil causing a decrease in the oscillation
amplitude.
The radio frequency voltage developed by the 12AT7 is
B*
4 7 Q /1
33 K
AV\Ar-—--V\Mr
a. =
001
0.001
0.01
RFC.
2K
PROBE
COIL
A/VW
-6 V
O.lM
0.1 M
12AT 7
0.01
4V
RF.C,
I2AX7,
0.01
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filtered by the choke and resistance-capacitance filter network in the
plate circuit so that only the audio—frequency modulation produced by
the absorption signal passes.
This audio-frequency signal is then
amplified by a conventional two-stage audio amplifier consisting of a
12AX7 twin triode.
The power supply for this circuity shown in Figure 12, is mounted ,
along with the dry cells used to provide the grid bias, on a panel rack
attached to the angle-iron frame of the magnet,
A power cable leads
from the power supply chassis and terminates in a plug which fits a
four-hole socket in the chassis of the oscillator.
The output of the
oscillator is brought via a shielded cable to a phono jack in the magnet
terminal box and thence through the overhead conduit to the oscilloscope.
*
The Microwave System
The microwave system has but few components.
In the order of their
appearance there is a type 2K25 reflex klystron which generates the
microwave radiation, a directional attenuator, a variable attenuator
which controls the amount of microwave power incident on the sample,
followed by a length of hollow rectangular waveguide which confines
the radiation and conducts it to the absorption cavity.
From the cavity
the radiation is conducted through another length of waveguide to a
1N2I|E silicon crystal diode which detects the incident radiation.
A stable variable-voltage power supply is required to operate the
klystron; the schematic diagram of this circuit is shown in Figure ll*.
It was constructed from a model PS-3 Heathkit to which a regulated
auxiliary supply for the repeller was added.
The unit is mounted in
U5
the central control panel and the cathode, repeller, and filament
voltages are brought out to an octal socket on the front of the panel.
Connection is made to the terminal box mounted on the side of the
magnet by means of a power cable which passes through the overhead
conduit shown in Figure 13 9 and ends in another octal socket in the
terminal box.
The principles governing the operation of voltage-
regulated power supplies have been discussed in connection with the
magnet power supply and are applicable also to this circuit.
The shell
of the klystron is commonly operated at ground potential, the cathode
at -300 volts, and the repeller at about 180 volts negative with
respect to the cathode.
The klystron is mounted in a socket which forms one end of the
waveguide train and is enclosed in a metal box.
Because the reflector
potential must always be negative with respect to the cathode to prevent
drawing reflector current and burning out the tube, a 6H6 diode is
mounted in the box with its plate connected to the klystron repeller and
its cathode connected to the klystron cathode.
The 6H6 acts as a safety
valve to prevent positive excursions of the repeller with respect to
the cathode.
The power for the klystron and the filament voltages for
klystron and diode are obtained via a power cable which terminates in a
plug which fits the above mentioned octal socket in the magnet terminal
box.
In order to isolate the klystron from the rest of the system a unidirectional transmission line
1
is placed next in line.
This isolator
Aniline Microwave Gyrator Model 88 ~?6B, Cascade Research Corp.,
Los Gatos, Calif.
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-A/WV-
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U8
allows radiation to pass in the forward direction virtually undiminished
but attenuates reflected radiation passing in the reverse direction.
This component is necessary to prevent "pulling” of the klystron fre
quency by the reflected waves.
The sample cavity shown schematically in Figure 13 is a rectangular
box with 0.25 inch holes coupling it to the waveguide line at both ends.
Its dimensions are such that it will resonate at 92^0 megacycles. It is
a full-wavelength cavity 1.88 inches long, the other two outside
dimensions being those of the one by one-half inch waveguide.
With this
type of coupling and these cavity dimensions the cavity resonates in the
TE102 mode as shown in Figure 16.
There is a node in the plane a-a,
the magnetic lines of force being most intense there.
A hole 5/l6 inches
in diameter was made in the top of the cavity at the plane a-a and was
used for insertion of the samples into the cavity.
The electric node
at this plane allows insertion of samples with a minimum of dielectric
loss in a region of maximum magnetic field intensity.
This node of
oscillation is important in paramagnetic resonance absorption experi
ments, since it is the magnetic component of the radiation which will
induce the necessary magnetic dipole transitions in the inserted samples,
and such a cavity produces polarization of the radio-frequency field
normal to the external magnetic field when the sample is placed on the
axis of the cavity.
The ”Q” of a resonant cavity is defined as the
ratio of the power stored in the cavity to the power dissipated in the
cavity per cycle.
When the sample absorbs energy from the cavity, the
Q decreases and, as a result, the power transmitted through the cavity
decreases .
k9
HOLE, 5/16" DIA.
CENTERED
13/4
COUPLING
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TOP VIEW
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SIDE VIEW
F IG U R E 16.
STANDING WAVE PATTERN FOR RECTANGULAR
OSCILLATING
CAVITY
IN THE T E |0 2 MODE
CAFTER HUTCH IS O N 470
50
The transmission line consists of type RG'52/U waveguide.
The
various sections are coupled by flanges, type UG-39/tf, and chokes, type
UG-UO/U, soldered to each section.
The attenuator is a Waveline type 611
variable attenuator, The tunable crystal mount which forms the end of
the line is a Hewlett-Packard Model X-U85B.
The entire system, including the klystron housing, is supported by
rubber shock absorbers fastened to the magnet frame. Pickup of
vibrations transmitted by the floor of the building and the vibrations
caused by the wobbling coils is thereby reduced.
The Signal Detection and Display System
The Preamplifier. Alternating current variations in the voltage
across the crystal detector are amplified by a wide-band preamplifier
mounted in a small box on the end of the waveguide train, as shown in
Figure 15>, to minimize signal attenuation and noise introduced by the
transmission cable.
in Figure 17.
The circuit diagram for this preamplifier is shown
The only special feature of this circuit is a cathode
feedback loop between the 12AU7 and the first half of the 12AX7 tube.
This connection furnishes noise reduction and gain stability.
Power for this unit is obtained from the supply for the lock-in
anplifier, which is mounted in the panel rack as shown in Figure 15.
The power cable terminates in a Magnal four-prong plug which fits a fourhole socket in the magnet terminal box.
This socket, in turn, is
connected to the power supply by means of a cable which is passed
through the overhead conduit.
51
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FIGURE 17.
P R E A M P L IF IE R
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FIGURE 18.
T W I N - T E E FILTER FOR
L O C K -IN
A M PLIFIER
52
The voltage gain of this amplifier -was determined as a function of
frequency by connecting the input to a variable-frequency signal
generator and comparing the output and input voltages by displaying
them on the calibrated screen of an oscilloscope.
At 20 cycles/second
the gain was found to be 320; at 20,000 cycles/second it was 620.
The
gain was fairly constant between 820 and 850 in the frequency range
200 to 6000 cycles/second. At 100 cycles/second, the modulation
frequency used in all the experimental work here described, the gain
was 7 10 .
The Lock-in Amplifier. The output of the preamplifier is connected
via a shielded cable, the magnet terminal board, and the overhead con
duit to the lock-in amplifier circuit shown in Figure 19.
In order to appreciate the operation of this circuit one must first
consider the nature of the signal which it receives.
The amplitude of
the modulation of the magnetic field is chosen so that only a fraction
of the total width of the paramagnetic resonance absorption line is
swept through.
Under these conditions, the power incident on the
crystal detector and therefore the voltage output of the preamplifier
will be modulated at a frequency equal to the modulation frequency of
the magnetic field; in this case 100 cycles/second.
The magnitude and
phase of this voltage modulation are determined by the magnitude and
sign, respectively, of the first derivative of the absorption line.
How this occurs can readily be seen in Figure 20.
The input to the lock-in amplifier then, consists of random voltage
fluctuations (noise) of a wide range of frequencies, superimposed on
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56
which is the signal, at 100 cycles/second. The function of the lock-in
amplifier is to separate the signal from as much noise as possible and
measure both the amplitude and phase of the signal.
The first section of this circuit is a frequency—selective amplifier
which is tuned to amplify the signal frequency at the expense of all
other frequencies, thereby increasing the signal-to-noise ratio.
Frequency selection is accomplished by employing two twin—T bridge
circuits (see Figure 18).
The impedance of a twin-T bridge varies with
frequency in such a way that it has a low impedance at all frequencies
except one, at which the plot of impedance versus frequency has a sharp
peak.
The first tube, a 6AU6, provides additional amplification of the
signal, and a certain amount of frequency selection, since the signal
is negatively fed back to its grid via a twin-T bridge.
The amount of
gain in this stage is varied by the potentiometer tap on its plate
resistor.
The signal is then impressed on the grid of the first half
of a 12AU7j which simply serves as an impedance matching device to
couple the signal Into the twin-T amplifier, consisting of the second
6AU6 and the second half of the 12AU7 . Here a positive excursion of the
6AU6 cathode results in an amplified positive excursion of its plate.
This plate is connected through a capacitor to the grid of the 12AU7.
Thus, a positive excursion of the 12AU7 grid occurs, producing two
results.
An amplified negative excursion of its plate is produced, and
this signal is sent to the next stage of the circuit.
Also resulting,
however, is a positive excursion of the 12AU7 cathode as it ''follows''
57
the grid, and this signal is fed back through the twin—T bridge to the
6AU6 grid, cancelling the original signal except at the selected
frequency (100 cycles/second), where the impedance of the twin—T bridge
is high.
Consequently, the only strong signal passing through this
stage is found in a narrow band of frequencies centered upon 100 cycles/
second.
The next stage consists of the two halves of a 12AU7 twin triode
arranged to provide two stages of variable phase-shift in series.
In
each stage, the output signal is taken from the .junction of the capacitor
and resistor which connect the plate and cathode.
The phase of the
output signal, relative to the input signal at the grid, is determined
by the values of the resistor and capacitor.
Coarse, step-wise control
of phase-shift is accomplished by switching capacitors of various
values into the circuit, and fine control is furnished by the variable
25>K resistors.
The third stage is a phase-selective detector.
Here the signal
is compared with a reference signal derived from the multivibrator
which drives the magnetic field modulation coils.
Hence, the reference
signal and the absorption signal have identical frequency and the phase
angle between them is made to be zero or an integral multiple of pi by
the phase-shift stage.
The reference signal is a square wave whose
fundamental frequency is 100 cycles/second.
It is first amplified and
then divided into two parts of equal magnitude but opposite phase by
the successive action of the two halves of a 6SL7 twin triode.
The
two equal and opposite signals thus produced are applied to the grids of
another 6SL7 tube in such a way that one—half of this tube conducts
during the first half—cycle and the second half conducts only
during the second half—cycle.
The absorption signal, after leaving the
phase-shift stage, is applied to the grid of a 6SJ7 whose plate is con
nected directly to the combined cathodes of the last-mentioned 6SL7.
Under these conditions, with zero absorption signal, the two plates
of the 6SL7 will be at the same potential.
(Exact balance between the
two halves is achieved by adjusting the 0.5M variable resistor in the
plate circuit.)
However, if an absorption signal is present which pro
duces a positive excursion of the 6SJ7 grid during the first half of th
reference cycle, there will result a negative excursion of the 6SL7
cathodes and, for the half-tube which conducts, a positive excursion
of its plate relative to the zero-signal level.
Hence a positive
absorption signal during the first half cycle causes a potential dif
ference between the plates of the 6SL7* with the half-tube which donducts during the first half cycle being positive with respect to the
other. An absorption signal which is negative during the first half
cycle, accordingly, produces a potential difference of opposite sign
between the two plates.
The 6SL7 plates are connected via a resistance-capacitance filter
network to a 6SN7 dual triode which acts as a vacuum-tube voltmeter to
drive a meter and provide a signal for a recording potentiometer.
The
resistance-capacitance network filters out additional noise; the larger
the time constant of this circuit, as determined by the values of the
capacitors which are switched into the circuit, the lower the noise
59
level in the recorded signal.
The penalty one must pay for a long time
constant is a slow sweep rate through the absorption line.
With broad
lines this is not much of a problem but with the narrow lines found in
free radicals, for example, one must exercise caution lest the recorded
line shape be distorted by failure of this circuit to follow the change
in the signal.
Power for the lock—in amplifier is obtained from the separate power
supply chassis which is mounted on the same panel rack.
The circuit
diagram of this power supply, which also serves the preamplifier, is
shown in Figure 21.
Operating Procedure
The resonance frequency of the sample cavity may be determined by
placing a tuned cavity wavemeter in the microwave line, separated from
the sample cavity by a directional coupler, and measuring the frequency
at which maximum power is transmitted through the sample cavity.
Although a calibrated wavemeter was available, a simpler, though in
direct, procedure was adopted. The g value of solid diphenylpicrylhydrazyl is known to be 2.0037.
This is more precise by an order of
magnitude than the most precisely known g value for the broad lines
encountered in the spectra of paramagnetic ions.
The Helipot dial
reading in the magnet control circuit was noted at points where the
proton resonance frequency was exactly equal to an harmonic of the 100
kc crystal oscillator in the frequency meter; namely at nJ
= 16,000,
b
15,000, 1U,000 and 13,000 kc. These correspond to intervals of 235 gauss.
60
POWER
■ T O ftn r
A
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21.
LfcjOjUULttfiJ
FIGURE
J
I0 t OQ O D PO OJ
AMPLIFIER
LOCK-IN
|l
AND
AAAA/
SUPPLY
—W W
FOR PREAMPLIFIER
K
61
The Helipot dial reading was also noted at the point where the magnetic
f*T®ld strength was exactly equal to the resonance value for diphenyl—
picrylhydrazyl, as determined by displaying the output of the preamplifier
directly on the oscilloscope screen, and centering the diphenylpicryl—
hydrazyl absorption line on the screen.
A change of 0.1814 ± .002 gauss per division of the Helipot dial was
obtained, and the diphenylpicrylhydrazyl resonance occurred only 25
divisions (U.6 gauss) above the 1U,000 kc. check point.
This check
point corresponds to a value of the magnetic field strength of 3288.2
gaussj hence the value of H at the diphenylpicrylhydrazyl resonance
point was determined as H — 3292.8 gauss.
Consequently, the ratio
hi)/p, a constant characteristic of the sample cavity, can be found
since
hV/£ = gH = 6597.8 gauss.
(21)
This procedure was performed three times, at intervals separated by
several days, and no variation in the fifth significant figure was
observed .
The spectra were obtained by the following procedure:
a warm-up
period of at least two hours was allowed the klystron and its power
supply, since even slight changes in the resistors of the power supply
or in the internal cavity of the klystron tube might seriously change
the output frequency.
Provision was made for switching the input
terminals of a Dumont type 30 J4A oscilloscope to any one of four
positions:
the preamplifier output, position 2; the plate of one-half
of the phase-sensing twin triode in the lock-in amplifier, position 3>
62
or the output of the Pound—Knight oscillator, position U . Position one
involved no connection.
With the oscilloscope input selector switch on
position 2, powdered cupric sulfate or any other concentrated paramagnetic
material was placed in the sample cavity and the klystron frequency was
adjusted by means of the repeller voltage until the resonant frequency
of the cavity was reached . This point was determined by the fact that
the 60 cycles/second ripple in the klystron power supply produces a
60 cycles/second modulation of the pre-amplifier output which is very
large on either side of the cavity frequency and passes through zero
with a phase reversal at that frequency.
With the klystron frequency adjusted to the cavity resonant
frequency, the 25 watt amplifier was adjusted to send a current of
about 3 amperes through the wobbling coils, and the magnetic field was
brought to the proper value for absorption of microwave energy by the
sample by manual adjustment of the potentiometer in the current control
circuit.
The oscilloscope input selector was then set to position 3,
displaying the 100 cycles/second sine wave signal superimposed upon the
100 cycles/second square-wave reference signal.
The phase difference
between them was reduced to zero by adjusting the phase-shift capacitors
and resistors in the lock-in amplifier circuit.
The copper sulfate
sample was then removed, and the sample whose spectrum was to be
obtained was inserted. Dry powdered samples were placed in a fluorothene
tube 2 l/2 inches long, with an outside diameter of about 3/l6 inches
and an inside diameter of about l/8 inch.
This tube rested on the
bottom of the cavity and projected up out of the hole in the top.
63
Single crystal samples were fastened to the end of a fluorothene rod
with Duco cement and positioned at the geometrical center of the cavity.
Since the resonant frequency of the cavity changed slightly with each
new sample in place, the oscilloscope input selector was again switched
to position 2 and the klystron tuning procedure was repeated, With the
oscilloscope connected to position 3* the magnet current was caused to
pass through the absorption band and the gain and sensitivity controls
of the lock-in amplifier were adjusted to give a signal of convenient
strength at the output.
When no signal was visible on the oscilloscope
screen, these controls were simply set to give a maximum deflection of
the output meter.
The Pound-Knight oscillator was then tuned to receive
a signal at 16,000 kc . by reducing to zero the beat frequency produced
with an harmonic of the crystal oscillator, the magnet current was
brought to a value well above that at which absorption occurred, and
the automatic motor drive was connected to the control circuit Helipot.
The Leeds, and Northrup recorder was turned on and the oscilloscope input
selector was switched to position k . When the proton signal crossed
the center of the oscilloscope screen, a pip was placed on the recorder
trace by momentarily breaking the input connections to the recorder with
a key in the circuit.
The oscillator was then tuned to the next lower
harmonic (1^,000 kc.) and this procedure was repeated until the
complete absorption pattern had been traced out by the recorder.
6U
PREPARATION OF SAMPLES AND EXPERIMENTAL RESULTS
General Procedure
The general procedure for the production of samples of paramagnetic
ions adsorbed on various substrates, was as follows.
The adsorbent
materials were dried at 110°C for four hours, and approximately threegram samples were weighed accurately into separate flasks.
Various
known quantities of standardized 0.1 molar solutions of the paramagnetic
salts were added and the flasks stoppered.
The solutions were allowed
to equilibrate with the adsorbents at room temperature with occasional
shaking of the flasks.
No attempt was made to ensure complete equilibra
tion or to standardize the length of time of contact between adsorbent
and solution, since the amount of paramagnetic material adsorbed was
to be determined later.
After standing in contact with the solutions,
the adsorbent was removed on a paper filter and washed several times.
The filtrate and washings were collected and analyzed for the cation
they contained. The quantity of paramagnetic cation adsorbed was calcu
lated as the difference between the amount present in the filtrate and
the amount added originally.
were as follows:
The adsorbents used in the experiments
Dowex -5>0, an extremely fine-mesh sulfonic acid-type
cation ion exchange resins Amberlite IR-100, the prototype of sulfonic
acid—type cation exchange resinss and Amberlite IR—I4B which holds a
similar position with respect to the anion exchange resins. Amberlite
IRC-^OH is a weakly acidic, carboxylic acid-type exchange resin.
1
Also used were a commercial form of powdered zeolite, activated silica
1E. H. Sargent and Co., Chicago, 111.
65
gel,
1
and activated charcoal.
2
Attempts were made to observe the spectrum of manganese adsorbed
by single crystals of the natural zeolites,
natrolite and analcite,
which were obtained from the Geology department collection.
Preparation of Samples
The method of analysis used was that developed by Lingane and
Karplus (lj.0) . To the manganese sample to be analyzed was added 200 ml.
of saturated sodium pyrophosphate buffer solution.
Bromthymol blue
indicator was added and enough hydrochloric acid to give a pH of six,
as matched against a standard buffer solution containing the same con
centration of indicator. This solution was then titrated with standard
potassium permanganate solution.
The equivalence point was detected
with the Fisher Titrimeter.
The standard permanganate solution was prepared and analyzed accord
ing to the procedure of Pierce and Haenisch(Ul). Weighed samples of
analytical grade arsenious oxide were dissolved in sodium hydroxide
solution and aliquot portions of the diluted solutions were titrated
with potassium permanganate solution, which proved to be 0.01206 ±
0.00006 normal.
Commercial grade, mesh-size 60-200$ sold by Davison Chemical Co.,
Baltimore, Md.
2Acid washed, prepared by R. E. VanderVennen
66
Five—ml. samples of 0,1 M manganese (II) sulfate solution were
titrated with the standard permanganate solution according to the pro
cedure outlined above.
Five ml. of manganese (II) sulfate solution was
equivalent to 5 0 .U2 ± .08 ml. of permanganate solution, indicating a
_molarity of 0.1316 for the manganese (II) sulfate solution.
Samples of manganese sulfate adsorbed on charcoal, Dowex —50, Amberlites IR-100 and IR-1|B, zeolite, and silica gel were prepared.
The
charcoal sample was one previously prepared by R. E. Vander Vennen (U2).
Table II contains the pertinent data for the others.
Column three of
this table lists the number of ml, of 0.1316 M manganese (II) sulfate
solution added to the dried sample of adsorbent, and column four lists
the number of ml. of 0.01306 normal potassium permanganate solution
required to titrate the combined filtrate and washings.
An approximately 0.1 M solution of hexacyanomanganate (II) complex
anion was prepared by adding sodium cyanide to the standard manganese
(II) sulfate solution until further addition did not deepen the yellow
color of the solution.
Ten ml. of this solution and approximately three
grams of Amberlite IR-hB were placed In a stoppered flask and allowed
to remain in contact, with occasional shaking, for four hours.
The
resin was then treated in the usual manner, but subsequent examination
revealed no detectable paramagnetic resonance absorption.
No absorption
could be detected in a sample of the solution either.
The spectra obtained from the samples of Table II are shown in
Figures 22-27.
Some of the spectra are not reproduced in order to avoid
unnecessary repetition.
The complete series of five samples containing
67
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68
100 G
A M u , D —5 0 I
Figure 22. Spectra of manganous
ion adsorbed on Dowex-fjO. The
concentration of Mn is (A) 0.367,
(B) 0.i170 m.moles/g. In this and
succeeding spectra, gauss is
abbreviated by the symbol G.
100 G
B
M h t D - 5 0 II
69
1 00 G
Figure 23. Spectra of manganous ion
adsorbed on Dowex—90. The concen
tration of Mn is: (A) 0.061
(B) 0.023 m. moles/g.
I0 Q G
B M h, D -5 0
IV
70
100 G
A
M h tD-50 V
100 G
B
Mh, IR 100 I
Figure 2U- Spectra of manganous ion adsorbed on
Dowex-^O and on Amberlite IR-100. The concentration
of Mn is: (A) 0.010, (B) 0.7U0 m. moles/g.
71
100 G
A M n , IR - 1 0 0
II
Figure 25. Spectra of manganous
ion adsorbed on Amberlite IR-100.
The concentration of Mn is:
(A) 0.373, (B) 0.031 m. moles/g.
100 G
B
M n, I R - I O O
IV
72
G
i100
__ i
A Mn, ZEOLITE II
Figure 26. Spectra of manganous ion
adsorbed on zeolite
The concentration of Mn is: (A) 0.612, (B) 0.306
m. moles/g.
I00G
B Mn, ZEOLITE III
00 G
A M n , CHARCOAL
100 G
i_i
B Mn, SILICA GEL
Figure 27. Spectra of manganous ion adsorbed
on charcoal and silica gel. The concentration
of Mn on silica gel is 0.012 m. moles/g.
7U
manganese on Dowex—50 illustrate the effect of dipolar broadening on
the paramagnetic resonance absorption.
As the quantity of manganese
adsorbed decreases, the line width decreases and the resolution of
the pattern improves. As samples IV and V clearly show, the asymmetry
in the pattern, which is noticeable in all the spectra, is due to the
presence of fine structure.
The series of spectra obtained from IR-100
is identical to that from Dowex-50, except that for equal quantities
of manganese adsorbed per gram, the IR-100 spectrum is less completely
resolved than the Dowex-5>0 spectrum.
Samples I and II are reproduced
here, because they provide an extension of the Dowex-50 series in the
direction of less complete resolution, and sample IV is included for
later reference.
The spectrum of manganese-Zeolite I was completely
unresolved and resolution was only incipient in samples II and III.
The spectra of manganese-char coal and manganese-silica 'gel I both
represent the maximum amount of manganese able to be adsorbed on these
substances.
No resolution at all was visible in any manganese-IR-UB
samples, which therefore are not reproduced here.
Single broad line
widths of 236, 2U2, and 277 gauss, respectively, were observed in
samples I, II and IV.
The resonance from sample III was too weak to be
useful.
Samples containing paramagnetic ion adsorbed on charcoal, silica
gel, and ion exchange resins are of necessity powder samples, with
completely random orientation of the symmetry axes of the ions.
Single
crystals of various natural zeolite minerals do occur, however, and
attempts were made to substitute manganous and cupric Ions for part of
75
the cations naturally present in the minerals. Single crystals of
analcite were placed In thick-walled combustion tubes in contact with
saturated aqueous solutions of cupric sulfate and manganese sulfate
and enough excess paramagnetic salt was added to maintain saturation
even at elevated temperatures and pressures.
The tubes were sealed at
room temperature and maintained at a temperature of 250°C in a tube
oven for three days.
When the tubes were opened, the crystal of analcite
which had been in contact with the cupric sulfate solution had disinte
grated, but the crystal in contact with the manganese solution appeared
slightly pink and showed a paramagnetic resonance absorption spectrum
characteristic of manganese; the spectrum was nearly identical with
that obtained from the powder sample manganese-zeolite III.
"When a small amount of the surface of the crystal had been removed
by scraping with the point of a knife, it was found that most of the
manganese was contained in the powder thus produced.
The intensity of
the absorption signal from the powder was greater than the intensity
of the signal due to the manganese left in the crystal.
In an attempt to determine the influence of water of hydration on
the electrostatic field symmetry about the manganese atom, samples of
manganese-Dowex-50 IV and manganese—IR—100 IV were placed in Teflon
tubes similar to the standard fluorothene sample holders, and kept in
a drying oven at 175°C for 18 hours. Upon removal from the oven the
tubes were stoppered and the spectra were obtained.
The Dowex-50 sample
was noticeably blackened by charring at this temperature and a strong
free radical resonance was added at the center of the manganese pattern.
76
No change was noticed In the latter.
showed a considerable change, however.
The manganese-IR-100 IV sample
The spectrum obtained Immediately
after removal from the oven is reproduced in Figure 28—A.
Besides an
enhancement of the free radical resonance normally present in the resin,
two changes were apparent in the manganese pattern:
a reduction of the
signal-to-noise ratio which indicates a decrease in the signal strength,
and a reduction of the degree of resolution of the six hyperfine
structure lines.
After this spectrum had been obtained, the sample was
exposed to the moist air of the laboratory for three days and another
spectrum was taken at the end of this time.
shown in Figure 28-B.
This second spectrum is
The free radical line remained strong, but the
manganese resonance pattern had almost regained its original strength
and degree of resolution.
Analysis of the Spectra
Because of the presence of fine structure in these spectra, it was
impossible to obtain an accurate value for the hyperfine structure
constant, A 1, in Equation 6.
It was possible, however, to obtain a
fairly good approximation to A 1, since the fine structure interaction
was not excessively strong. An examination of the spectra of manganese—
Dowex-5>0 IV and manganese-Dowex-50 V revealed that each of the four
inner lines of the overall six-line spectrum appeared to be resolving
into three.
Taking the midpoints of these broad, poorly-resolved
triplets as the positions of the simple lines described by Equation 6,
it was found that the separation between lines two and five (=3AT) was
77
Mh, IR-100 I
DEHYDRATED
B Mn, IR-100 I
PARTIALLY RESTORED
Figure 28. Spectra of manganous ion adsorbed on
Amberlite IR-100 and subsequently dehydrated.
The concentration of Mn is 0.7U0 m. moles/g.
78
288 gauss, and the separation between lines three and four (=A') was
96 gauss.
The two outside lines in the spectrum were very narrow and
appeared to be unresolved.
U75 gauss.
The separation between them (==5at) was
Thus one obtained values of A' of 95, 96 and 96 gauss
respectively, by measuring the separation between the pairs of lines
one and six, two and five, and three and four.
It was not possible to
locate precisely the midpoints of the four inner lines in the less
completely resolved spectra, but the outer lines remained rather sharp
up to the limit of resolution.
The separation between these outer lines
was measured for all the spectra of manganese-Dowex-50 and the results
were A» = 96 , 96 , 97, 97, 98 gauss for samples V, IV, III, II, I, in
that order.
Thus it would appear that the values of A 1 obtained from
the separation of the outer lines are fairly accurate (± 3 gauss) even
for poorly resolved spectra.
Using this result, values of A T were
obtained for all the manganese spectra which showed any resolution.
The results are listed in Table III.
TABLE III
APPROXIMATE A' VALUES FOR MANGANESE PONDER SAMPLES
Adsorbent
Dowex ~5>0
IR-100
Zeolite
Charcoal
Silica gel
A 1 (±3 gauss)
96
95
96
96
96
Samples Used
I, II, III, IV, V
III, IV, V
III
I
I
79
Copper
P r e p a r a t io n o f S am ples
The m ethod o f a n a ly s is u s e d f o r c u p r ic
io n -was th e io d o m e tr ic
m ethod a s d e s c r ib e d b y P ie r c e and H a e n is h (J4I ) .
A n a p p r o x im a te ly 0 .0 1
N s o l u t i o n o f s o d iu m t h i o s u l f a t e "was made up and s ta n d a r d iz e d a g a in s t
m e ta llic
copper in
A p p r o x im a te ly 0 .1 3
n it r ic
th e m anner a ls o d e s c r ib e d b y P ie r c e and H a e n is h ( U l ) .
gram s a m p le s o f m e t a l l i c
a c id and d i l u t e d
to
c o p p e r w ere d is s o lv e d
250 m l. i n a v o lu m e t r ic
fla s k .
a l i q u o t s o f th e s e s o lu t io n s w e re ta k e n f o r t i t r a t i o n
s o lu t io n .
It
in
F i f t y m l.
b y th e t h i o s u l f a t e
was fo u n d t h a t 0 .1 3 0 0 gram s o f c o p p e r was e q u iv a le n t t o
5 x ( UU. 6U± 0 .0 1 ) m l. o f t h i o s u l f a t e s o l u t i o n , g iv i n g a n o r m a lit y o f
0 .00916U f o r th e t h i o s u l f a t e s o l u t i o n .
I n o rd e r to
s ta n d a r d iz e t h e a p p r o x im a t e ly 0 .1 M c u p r ic s u l f a t e
s to c k s o l u t i o n , 1 0 .0 0 m l.
s a m p le s t h e r e o f w e re d i l u t e d
to
250 m l. i n a
v o lu m e t r ic f l a s k and 50 m l. a l i q u o t s ta k e n f o r t i t r a t i o n .
t h a t 1 0 .0 0 m l. o f c u p r ic
± 0 . 0 1 ) m l.
th e c u p r ic
s u lf a te
o f th e t h i o s u l f a t e
s u lf a te
s o l u t i o n was e q u iv a le n t t o
s o lu t io n ,
5 x ( 2 1 . 6?
i n d i c a t i n g a c o n c e n t r a t io n i n
s o l u t i o n o f 0 .0 9 9 2 6 m o le s p e r l i t e r .
S am ples o f h y d r a te d
c u p r ic
i o n a d s o rb e d on Dowex- 5 0 , A m b e r lit e s
IR - 1 0 0 , IR C -5 0 H , and IR -U B , z e o l i t e ,
p r e p a r e d and a n a ly z e d a c c o r d in g t o
T a b le IV c o n t a in s
I t was fo u n d
c h a r c o a l, and s i l i c a
g e l w ere
th e g e n e r a l p r o c e d u r e g iv e n a b o v e .
th e p e r t i n e n t a n a l y t i c a l d a ta f o r th e s e s a m p le s .
The s p e c tr a o b ta in e d fr o m th e sa m p le s o f T a b le IV a r e re p ro d u c e d
in
F ig u r e s 2 9 -3 l± .
Some s p e c tr a a r e n o t re p ro d u c e d h e re i n o r d e r t o
80
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81
100 G
100 G
B
F ig u r e 29 . S p e c tr a o f c u p r ic i e n a d s o rb e d on A m b e r lit e
IR-100. The c o n c e n t r a t io n o f Cu i s :
(A ) 0.779, (B) 0.^26
m. m o le s / g .
82
100 G
A
Cu, I R - 1 0 0
III
100 G
i____ i
B CU, IR-100 IV
Figure 30. Spectra of cupric
ion adsorbed on Amberlite
IR-100. The concentration
of Cu is: (A) 0.297, (B)
0.169 m. moles/g.
83
100 6
A
C u, I R — 1 0 0 V
100 G
Figure 31 • Spectra of cupric ion
adsorbed on Amberlite IR-100 and Dowex-50.
The concentration of Gu is: (A) 0.032,
(B) 0.U7U in* moles/g.
81;
1006
A
Cu, D - 5 0
II
100 G
i
B
t
C u , D - 5 0 III
Figure 32. Spectra of cupric ion adsorbed on Dowex-50.
The concentration of Cu is: (A) 0,171;, (B) 0.031
m. moles/g.
85
100 6)
t____
A
C u , CH A R C O A L
1006
B Cu, 1 R -4 B I
Figure 33 . Spectra of cupric ion adsorbed on charcoal
and Amberlite IR-I4B. The concentration Cu is: (A) 0.01+0,
(B) 0.1+78 m. moles/g.______
86
100 G
Co, IR - 4 B
II
IO O G
B
Cu, I R - 4 B
111
Figure 3U* Spectra of cupric ion adsorbed on Aniberlite
TR—)|T3. The concentration of Cu is: (A) 0.161, (B) 0.030
m. moles/g.
87
avoid needless repetition of nearly identical patterns.
The complete
series of five copper-IR-100 spectra is included as an illustration of
the effect of dipolar broadening on the resolution of the pattern.
A free radical resonance is noticeable in these spectra and also in
the spectrum of copper — charcoal. The three copper-Dowex—$0 spectra are
also included despite their similarity to the copper-IR-100 spectra,
because they are somewhat clearer and better resolved owing to a better
signal-to-noise ratio.
The five copper-zeolite spectra are not included,
being scarcely distinguishable from the copper-Dowex-50 and copper-IR-100
series.
An attempt was made to prepare a series of samples of cupric ion
adsorbed on Amberlite IRC-50H, but owing to the fact that the adsorbing
power of this resin is low in acidic solution, only a minute quantity
of cupric ion was adsorbed.
The spectra obtained from the copper-IRC-
50H samples were like the spectrum of copper — IR-100 V and are not
reproduced here.
Although the analytical data of Table IV indicate a minute amount
of adsorption of cupric ion by the silica gel, no paramagnetic resonance
absorption signal was found.
Approximately 0.1 M solutions of tetrachloro, tetrabromo , and
tetratartrato cuprate (II) complex anions were prepared by adding solid
sodium chloride, sodium bromide, and sodium tartrate, respectively, to
100 ml. portions of the 0.09926 molar stock solution of cupric sulfate
until the color due to the complex ion did not deepen wuth further
addition.
These colors were:
tetrachlorocuprate (II) ion, greenj
88
tetrahromocuprate (II) ion, intense brown; tetratartratocuprate (II)
ion, deep blue.
Then, 10,
auid 2 ml. samples of these solutions were
placed in contact with approximately 3 g. portions of Amberlite IR-UB
in stoppered flasks • At the end of four hours the resin was removed
on a paper filter and washed several times with distilled water. The
clear filtrates obtained from the chloride and bromide complexes were
slightly green-blue after adsorption.
The intense color of the tartrate
complex filtrate was not noticeably diminished by adsorption.
The
spectra of the first two series of samples were obtained and proved to
be indistinguishable from the spectra of copper — IR-UB; hence they are
not reproduced here.
No paramagnetic resonance absorption signal could
be detected in the resin which had been in contact with the solution
of the tartrate complex, which fact confirmed the evidence that no
adsorption of the tetratartratocuprate (II) ion by IR-UB occurs.
Samples of tetramminocopper (II) complex cation, adsorbed on
Dowex-50, Amberlites IR-100 and IRC-50H, zeolite, and charcoal were
prepared by taking the existing samples of Table IV and letting them
stand in 10 ml. of a 1:U solution of ammonium hydroxide in distilled
water for at least four hours. The zeolite samples turned from a light
to a dark blue within a few minutes.
Where this color change was not
detectable, as in charcoal and IR-100 samples, the adsorbent was allowed
to remain in contact with the ammonium hydroxide solution for eight
hours.
The filtrates obtained upon removal of the adsorbents were
colorless, indicating within the nended accuracy that the quantity of
orup-pic j_on remained about the same as before the exchange of ammonia
89
for the water of hydration occurred. The samples were treated in the
usual manner and their spectra obtained. An examination of these
spectra showed that their parameters were in every case different from
those of the spectra of the corresponding hydrated cupric ion samples,
3*1'though the two sets of spectra were similar in form.
However, an
anomalous variation in the parameters from sample to sample seemed to
indicate that the tetramminocopper (II) ionic complex had partially
decomposed.
This effect was especially noticeable in the copper-
IRC-50H spectra.
In fact, the blue color in these samples had reverted
to the light blue of the hydrated copper ion after dehydration at 110°C.
Only the copper — TR-100 samples seemed unaffected, presumably because
the large size of the resin particles hindered the effusion of ammonia.
In an attempt to preserve the complex, the samples were again treated
with ammonium hydroxide solution as before and washed after filtration,
not with distilled water, but with more ammonium hydroxide solution.
They were then placed In an ordinary calcium chloride drying tube
which was stoppered and fitted with inlet and outlet rubber tubing.
This assembly was placed in the drying oven at 100°G and the rubber
tubes were passed out through a hole in the top of the oven.
The inlet
tube was connected to the nozzle of a cylinder of compressed ammonia,
and a stream of dry ammonia was passed over the sample throughout the
drying process. Visual confirmation of the fact that this new treatment
improved matters was afforded by a comparison of the cuprammonium —
zeolite samples produced in this way with a portion saved from the
previous treatment.
The blue color in the normally colorless zeolite
90
was considerably darkened. The spectra of these samples which were
dried in a stream of ammonia gas were obtained immediately upon removal
of the samples from the oven in order to minimize the replacing of
coordinated ammonia molecules by water molecules from the atmosphere.
Of the spectra obtained in this manner, only 3 are reproduced in
Figures 35 and 36.
Two samples of the five in the cuprammonium-IR-100
series-samples I and II (the numbering corresponds to the numbering of
the hydrated cupric ion series from which they were derived)— are
included to indicate both the slight change in the spectra and the trend
of the series as the line width decreases with decreasing concentration
of paramagnetic species.
The cuprammonium-charcoal spectrum, reproduced
in Figure 36, presents a problem because the copper resonance overlaps
the resonance due to the free radicals in the charcoal.
As is indicated
in the figure, an attempt was made to separate the two resonances by
assuming that the free radical resonance was symmetrical about its
center and subtracting the postulated free radical absorption from the
total absorption to leave a ,fcorrected” spectrum for the copper absorp
tion .
Analysis of the Spectra
It has been shown (23) that as the line width decreases, the center
of the strong very asymmetrical peak in the copper powder spectrum tends
toward a value of the field strength given by the equation:
Hj.
A E /p
gx
(22)
91
1 00 G
C o C N H O ., IR -1 0 0 I
100 G
6
Cu CNHOa ,
I R - 1 0 0 III
Figure 35* Spectra of ammoniated cupric ion
adsorbed on Amberlite TR-100. The concen
tration of Cu is: (A) 0.779, (B) 0.297
m. moles/g.
C u C N H J , , CHARCOAL
92
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93
It has also besn shown that the center of the weak, partially obscured
four—peak pattern occurs at a field strength of
H„
=
A E/p g„
(23)
and that the separation between these peaks, in gauss, is equal to the
hyperfine structure constant, A * , in equation 1 9 .
"Wherever possible, an effort was made to reduce the error in the
determination of Hx , due to the finite line width, by plotting as a
function of copper concentration a measurable parameter of the para
magnetic resonance absorption spectrum, which in the limit of zero
concentration would approach
. A number of quantities might be
chosen, including the point of intersection of the first-derivative
plot with the base line, or the point of maximum slope in the firstderivative plot.
Because of the nature of the spectra at high concen
tration another closely related parameter was chosen, namely the point
of intersection with the base line of a straight line tangent to the
first-derivative plot at the point of maximum slope.
The use of this
parameter, designated H , which was identical with the two mentioned
P
above at low concentrations of copper, resulted in a fairly straight
line of smaller slope than would have been given by the use of either
of the other parameters.
This straight line was extrapolated to zero
concentration of copper, and the extrapolated value of H
was taken as
Jr
Hj_ for that series of spectra.
The positions of the lines in the
weak four-line spectrum were taken to be the points of half-intensity
of the peaks appearing in the first derivative plot, on the high-field
9h
side of the peaks. Table V lists the parameters of these spectra, and
Figure 37 shows the graphs and extrapolations used to obtain Hx
the copper series.
for
Table VI contains a summary of these results•
Values of the quantities gtl, gx, and A for these spectra were
computed in the following manner, Where all four of the quantities
H3/ 2 *
H^3^/2 were known, HT, was taken as the average of the
two midpoints l/2(H3//2
H_3/2) and l / ^ H ^ / g + HX//2). Values g„ and gx
were then computed from Equation 19 . A 1 was taken as the average of
the two quantities 1/3(H 3//2 - H3//2) and (H -jy2 — H-jy2).
Where the
positions of only two or three of these four lines were known, the
positions of the remaining obscured lines were postulated on the basis
of the observed lines and the above procedure was then followed. The
»
hyperfine structure interaction constant, A, was computed by means of
the relationship,
A
The observed values of
g„ A'
(7)
for the ammoniated copper samples are
also plotted in Figure 37 and the lines (not shown in the figure) with
slopes equal to the slope of the plot for the copper-zeolite samples
were drawn through the points obtained from the most concentrated
samples, where the contribution of dipolar broadening to the line
width is probably greatest^ the intercepts of these postulated plots
yield values of Hj_ and gj_ for the ammoniated samples as listed in
Table VII.
95
to
z
X
Q
Q
>-
UJ
K
UJ
in
QD
cr
m
00
SAMPLES
Z
3200
CM
o
CM
CO
ro
ro
S S 0 V 9 td H
rO
ro
rO
Figure 37.
H p VERSUS
o
CONCENTRATION
FOR
COPPER
cr>
Q
96
TABLE V
ANALYSIS OF COPPER SPECTRA
Sample
H
P
^3/2
^ 1/ 2
ft-1/2
H-3/2
Hydrated Copper Samples
Cu-IR-100
Cu-Dowex-5>0
Cu-Zeolite
I
II
III
IV
V
3092
3106
3130
3136
I
II
III
3111
3139
311+1
2583
-
I
II
III
IV
3138
2606
—
2735
261U
-
2796
311+5
3151+
3159
3163
-
-
2592
-
—
-
-
270h
-
-
2692
-
-
-
-
I
II
III
3169
2923
27U8
3163
3168
3170
Ammoniated Copper Samples
I
II
III
IV
3190
3189
3192
3187
-
2928
Cu-Zeolite
Cu-Charcoal
I
II
III
3180
3187
III
IV
V
3170
3185
-
-
-
—
—
3078
289U
3087
3188
3187
—
-
2701
-
2702
-
-
3278
2888
2711
-
3102
2705
—
-
-
-
—
~
Cu-Dowex-^O
-
3053
-
2720
-
-
—
Cu-IRC-50H
Cu-IR-100
-
3162
-
2818
-
-
Cu-Charcoal
Cu-IR-hB
2808
-
2878
—
-
2877
-
3055
~
-
3050
—
2863
3053
—
3270
3267
97
TABLE VI
SUMMARY OF RESULTS FOR COPPER POWDER SAMPLES
Sample
Sit
^ 5 gauss
Cu-IR-100
.2.096
2.39
Cu-Dowex-50
2.U0
2.099
Cu-Charcoal
2.086
2.32
Cu-Zeolite
2 .083
2.35
CU-IRG-50H
2.080
Cu-IR-UB
2.079
2.19
Cu (NH3)4-IR-100
2.068
2.21
Cu(NH3)4-Dowex-50
2 .078
2.22
Cu (NH3)4-Charcoal
2.22
2 .07
2.22
Cu(NH3)4-Zeolite
2 .072
not stable
Cu(NH3)4-XRC-50H
Cu (NH3)4, CuCl^ CuBr, IR-UB same as Cu-IR-UB
A5cm
110
115
1U0
0.0122
130
0.01U2
0.0128
0.0152
—
—
180
188
172
177
175
0.018U
0 .019U
0.0178
0.018U
0.0182
TABLE VII
REVISED ESTIMATES OF Hj_ AND gj_ FOR AMMONIATED COPPER SAMPLES
Sample
Cu (NH3)4-IR-100
Cu(NH3)4-Dowex-50
Cu (NH3)4-Zeolite
Hj_, gauss
3216
3208
3208
gj_
2 .052
2.057
2.057
Optical Reflectance Spectra
The colorless zeolite allows the determination of the optical
absorption spectrum of the cupric ions contained on it.
Since the
sample was in the form of an opaque powder, it was necessary to obtain
the spectrum of the light reflected from it.
An amount of colorless
zeolite crystals roughly equal to the amount of available copper—contain
ing sample was spread in a thin layer on the horizontal bed of an opaque
projector.
The powder was illuminated by a 1000 watt tungsten-filament
electric lamp and the reflected light was focused and projected by the
mirror and lens system of the projector.
The beam of light emitted by
the projector was focused by a condensing lens on the entrance slit of
a Beckman Model DU Spectrophotometer, from which the lamp housing had
been removed.
1
A reference curve was then obtained with the colorless
zeolite by noting the slit opening required to give a 100$ transmittance
reading at twenty-m^JL
microns.
intervals throughout the range of U00 to 1000 mill
Then the colorless reference sample was replaced by the copper-
containing sample and, using the slit widths indicated by the reference
sample, percent transmittance was read from the spectrophotometer scale.
The actual quantity being measured was, of course, not transmittance
but reflectance.
The results of this experiment for hydrated copper-
zeolite samples and for an ammoniated copper-zeolite sample are shown
in Figure 36.
xThis method of obtaining the reflectance spectrum was suggested by
Professor J, C. Sternberg.
Figure
38.
REFLECTANCE
SPECTRA
OF COPPER-2E0LITE
SAMPLES
HYDRATED
99
39ISIV103U3M %
100
Vanadium
Preparation of Samples
An approximately 0.1 M solution of vanadyl sulfate "was prepared by
dissolving twenty grams of vanadyl sulfate dihydrate in 100 ml. of
distilled water and boiling the mixture. A dark blue murky solution
was formed. This solution was cooled to room temperature and filtered
and the clear blue filtrate was diluted to 1000 ml. with distilled
water. The brown colored precipitate was collected on the filter paper
and discarded.
The 0.01 N potassium permanganate solution was restandardized against
arsenious oxide as described above.
It was found that 1.000 ml. of
permanganate solution was equivalent to 0.00796 ± 0.00002 g. of arsenious
oxide.
Thus, the normality of the permanganate solution was N = 0.01288
± 0.00003.
The concentration of the vanadyl sulfate solution was determined
by adding to 5-000 ml. samples of the solution 25 ml. of distilled
water and 5 mlL. of concentrated sulfuric acid.
The solution was heated
to boiling at the beginning of the titration with potassium permanganate
solution, and again at the end point.
A sharp end point was obtained,
and it was found that 5.000 ml. of vanadyl sulfate solution was equiva
lent to Ul.00 ± 0.01 ml. of permanganate solution.
Hence, the concen
tration of the vanadyl sulfate was 0.1056 moles per liter.
Samples of vanadyl ion adsorbed on Amberlites IR-100 and IR-UB,
Dowex-50, silica gel, and charcoal were prepared and analyzed in the
usual manner.
The analyses were not successful.
With the exception
101
of the silica gel sample, no sharp end points could he obtained and
with the IR-I4B samples, no end point whatsoever was detected.
These
erratic results were probably caused by small quantities of organic
matter leached out of the resins by the water.
However, since an
examination of the spectra obtained from these samples revealed no
dependence upon concentration, no attempt was made to improve the
doubtful analytical data.
These data are collected in Table VIII.
TABLE VIII
ADSORPTION OF V0S04 BY VARIOUS ADSORBENTS
Sample
VO-IR-100
W t . of Adsorbent g.
m
. voso4
Ml. Permanganate
I
II
3-777U
2.9258
9.000
28.3
1.000
17.2
I
II
III
U.6113
3.8923
3.3015
1.000
0.500
5.000
2.3
I
II
2.9663
2.7167
10.00
5.000
12 .3
VO-Charcoal
0.5769
5.000
VO-Silica gel
3 .2U 82
V0-Dowex-50
VO-Zeolite
VO-IR-UB
I
II
2 .U900
3.3183
10.00
5.000
1.000
2.1
-
—
80.37
-
Analysis of the Spectra
The typical spectra obtained from these samples are reproduced in
Figures 39 > U0 and I4.I.
Figure 39 shows the strong pattern of eight
cn
gauss. Consequently,
B f is less than twenty-five gauss, and B is less than 0.0026 cm”1.
This result is comparable to Sands'(23) observed value of O.OO2I4 cm”1.
Calculation of B by means of Equation 11 leads to the result B = 0.0030
«i
cm , in fairly good agreement with the approximate upper limit set by
the line width.
The situation is somewhat more complicated in the copper-IR-UB and
the ammoniated copper samples, since the line width may be due to un
resolved hyperfine structure involving interaction with nitrogen nuclei.
A calculation using Equation 11 and based on the average observed g
factors and hyperfine structure intervals leads to B = O.OO32 cm
for
-i
copper-XR-ljB and B = 0.0019 cm
for the ammoniated samples. These
quantities are both too small to account for the width of the line
centered at H in these samples. This fact also suggests that an unu
resolved hyperfine structure is the principal contribution to the line
width.
Sussman and Nachod (l_jf>) reported preliminary and somewhat incon
clusive results on the adsorption of copper by an anion exchange resin.
Copper was removed from a copper sulfate solution upon passage through
a bed of a salt of an anion exchange resin, and also was removed from
119
ammoniacal copper sulfate solution upon passage through a bed of alkali
regenerated anion exchange resin.
The suggested overall stoichiometry
is:
Gu++ 4- 2(RNH)C1
=
(Cu(RN)2)C12 4- 2H*"
(27)
for the first reaction, and
Cu(NH3)4++
for the second reaction.
. k RN = (Cu(RW)4)++ + 1* NH3
(28)
In these equations, RN represents the alkali
regenerated anion exchanger base.
These authors claimed to have found
experimental evidence for the diammine in Equation 27, but were un
certain whether the tetrammine or diammine was found in the reaction
represented by Equation 28.
The paramagnetic resonance absorption spectra obtained in this
investigation from the copper — IR-UB samples prepared from copper
sulfate solution and from ammoniacal copper sulfate solution were
indistinguishable.
Hence, it seems probable that the copper complexes
formed in the two reactions represented by Equations 27 and 28, are
the same.
Furthermore, since the observed spectra indicate tetragonal
symmetry, with g factors and hyperfine structure constants very nearly
equal to those of the ammoniated copper spectra on cation exchangers,
the tetrammine structure of Equation 28 seems to be a more probable
product in both reactions.
The spectra of the samples prepared from the tetrachloro and
tetrabromocuprate (IX) anions and Amberlite IR-I4B are also indis
tinguishable from the spectrum of copper-IR-UB (Figure 35)•
The copper
was probably adsorbed not in the form of a complex anion, but rather
120
as the same complex as that formed from aqueous solution of cupric ion.
This mechanism appears the more probable because of the loss of color
of the complex anion in the solution in contact with the resin.
No
color change was observed when a solution of tetratartratocuprate (II)
anion was placed in contact with the resin, and no copper spectrum
appeared in the subsequently dried sample of resin.
Apparently the
tartrate corrplex was too stable to release free copper ions to the
resin.
Kozyrev (35) reported that the spectrum of cupric ion supercooled
in organic solvents at 90°K consisted of an "exchange peak" at g = 2.091
and also four hyperfine-structure peaks separated by an interval of 130
gauss and centered at g = 2.369.
It now seems probable that this spectrum
was actually a random powder spectrum of the sort observed in this
investigation, produced by the reduction of the random molecular motions
at low temperature.
Interpreted in this manner, the results lead to
_i
gtt = 2.369, g^ = 2.091, and A = 0.011+6 cm
which are in good agreement
with the values obtained by Sands (23) and those obtained in this
investigation.
Vanadium
No theoretical investigation of the paramagnetic resonance absorp
tion of quadrivalent vanadium has appeared to date.
systems have been treated, however.
Two analogous
Bleaney (1+6) considered the case
of trivalent titanium, which is isoelectronic with quadrivalent vanadium,
in a trigonal field.
Polderrs (18) treatment of the cupric ion in a
121
tetragonal field considers the electron configuration to be equivalent
to a single positive electron in the d orbitals, that is, an electron
''hole" . Neither of these analogous systems is completely equivalent
to the case of quadrivalent vanadium, however, for Bleaney’s treatment
is based on trigonal symmetry, and Polder’s treatment results in an
inversion of the orbital energy levels.
Both theories predict g values
approaching 2.00 when the energy separation between orbital levels
becomes very large, that is, when the symmetry of the axial field departs
strongly from cubic symmetry.
Since the vanadium in the samples used
in this investigation was in the form of the vanadyl ion, V0<”t’, the
presence of oxygen would produce a strongly non-cubic, axially symmetrical
field. The electrostatic field symmetry accounts, then, both for the
proximity of the g factors to the free-spin value, 2 .00 , and for the
very weak spin-lattice interaction as shown by the narrow line width.
All of the spectra of vanadyl ion on various adsorbents conform to
the equation developed by Sands (23) for random orientation of symmetry
axes.
The striking differences in appearance between these spectra
and those obtained from the copper samples arise from the fact that the
g values of the vanadium spectra are nearly isotropic; the ma.jor contri
bution to the anisotropy comes from a highly anisotropic hyperfine
structure. For a given value of the nuclear magnetic quantum number,
m, the integrated line shape is given by Equation 17.
Since the g
factor is nearly isotropic, the upper boundary corresponds sometimes
to the parallel orientation and sometimes to the perpendicular orien
tation of the symmetry axis.
122
Table IX shows clearly that the separation, in gauss, between the
upper and lower boundaries of the broad integrated line corresponding
to a given orientation of the nuclear spin, varies with m.
The separa
tion is greater for the extreme values of m than for intermediate
values, and is a minimum for some intermediate value.
The apparent
intensity or sharpness of the peaks which mark the upper and lower
boundaries is dependent upon the separation between the boundaries,
being greatest for the lines whose boundaries are closest together.
The spectrum of vanadyl ion on Arriberlite IR-ljB, Figure Ul-B,
provides a striking example of this effect.
One line in this spectrum
is much more pronounced than the others; in fact, the maximum and minimum
values of the slope lie outside the scope of the figure.
This line
corresponds to the transition for m - l/2, and the separation between
its upper and lower boundaries is probably of approximately the same
magnitude as the line width.
From the g factors and hyperfine structure constants collected
in Table X, a trend similar to the one observed in the copper samples
may be discerned.
The g factors remain constant, probably within the
limits of experimental error.
This fact indicates that the strongly
non-cubic electrostatic field produced by the oxygen of the vanadyl
radical overshadows any minor changes in spin-orbit interaction produced
by the adsorbent.
The hyperfine structure intervals, however, do vary
from one adsorbent to another. The interval is largest in the two
sulfonic acid—type cation exchangers, slightly smaller on charcoal, and
much smaller when bonding to nitrogens on the anion exchanger occurs.
123
The magnitude of the hyperfine structure interaction
(about 0.018
-l
cm
for A) indicates that the promoted s—electron hypothesis of Abragam
and Pryce may be required for the vanadyl ion* too.
The decrease in
splitting "with increase of covalent character in the bonding suggests
a shift of the magnetic electron toward the ligand in accordance with
the molecular orbital theory of Stevens and Owen.
The relative signs of the two hyperfine structure constants, A and
B, are predicted by theory but cannot be measured directly, since the
hyperfine structure interval is a measure only of their absolute values.
Indirect means must be employed to evaluate the relative signs of the
i
constants.
When an isotropic contribution to the splitting is present,
as predicted for the copper spectrum, an examination of the way the
absolute values of A and B change with variation of this isotropic
term reveals their relative sign.
For the copper spectrum, decreasing
k causes the absolute value of A to decrease and the absolute value of
B to increase, according to Equation lU , when the constants have
opposite sign.
The observations by Pake and Sands (37 ) of an eight line
spectrum for vanadyl ion in aqueous solution, where any anisotropic
contributions would be averaged out, confirms the presence of such an
isotropic contribution also to the vanadyl spectrum.
Hence, the fact
that the absolute values of A and B both decrease with increasing
covalent bonding indicates that A and B probably have the same sign.
iBleaney (10) suggested one method of doing so for the case where
S 4 1/2.
12U
The thirteen line spectrum observed by Kozyrev (35) Tor vanadyl
salts in non-aqueous solutions at 90°K is undoubtedly a random pattern
of the sort observed in this investigation.
The reduction of molecular
motion at the low temperature would produce a random orientation of
the symmetry axes such as occurred in the powder spectra reported here.
Interpretation of Kozyrev’s results in this manner leads to glt = 1.92$
_i
g± = 1,960$ A = O.OI78 cm
_i
$ B = 0.0070 cm
ment with the results of this investigation.
$ which are in good agree
125
SUMMARY
Paramagnetic resonance absorption spectra were obtained for samples
containing manganous, cupric, and vanadyl ions adsorbed on various
adsorbents. The adsorbents included two forms of commercial sulfonicacid -type cation exchange resins, a carboxylic-acid-type cation exchange
resin, an anion exchange resin, silica gel, commercial zeolite, and
sugar charcoal activated at I4OO0 centigrade.
The spectra were obtained by means of a paramagnetic resonance
spectrometer employing a transmission cavity which resonated at 9 ,2^0
megacycles.
The microwave radiation was generated by a klystron,
detected by a silicon diode crystal, and the resulting signal was
analyzed by a lock-in amplifier and displayed on a strip-chart recorder.
Magnetic field strengths were measured by means of the magnetic resonance
frequency of the proton.
The g values and hyperfine structure inter
vals were computed on the basis of measured line positions.
A study of the spectra of manganese adsorbed on various resins
enables a number of conclusions to be drawn concerning the properties
of the adsorbed ions. All the spectra of the manganese samples had g
values of 2.00.
All but the spectra obtained from the anion exchange
resin showed nuclear hyperfine structure with intervals of 96 gauss
between the various lines . The presence of a weak fine structure in
the charcoal and cation exchange resin spectra indicated electrostatic
fields of less than cubic symmetry, probably tetragonal.
A lower
symmetry, which left the hyperfine structure barely detectable, was
126
present in the zeolite samples.
The electrostatic field symmetry about
the manganous ions bound to the anion exchange resin "was even lowers no
hyperfine structure was resolved.
The hyperfine structure interval
indicated essentially ionic bonding about the manganous ion in all the
spectra where resolution was obtained . The line width of the unresolved
spectrum of manganese on an anion exchange resin suggested approximately
fifty percent covalent bonding between the manganese and the resin.
The most useful information was obtained from the study of adsorbed
cupric ion because variations in the g values and hyperfine structure
constants were observed in the copper samples.
These quantities depended
upon both the nature of the adsorbent and upon the coordinated ligands
about the cupric ion.
Higher g values and smaller hyperfine structure
intervals were present in the spectra of hydrated cupric ions on the
sulfonic-acid-type cation exchangers,
The g values decreased and the
hyperfine structure Intervals increased as the amount of covalent
character in the bond to the adsorbent increased.
For a given adsorbent,
the g values were substantially reduced and the hyperfine structure
interval increased when the coordinated water molecules attached to the
cupric ion were replaced with ammonia molecules, The spectra of the
samples containing cupric ions adsorbed on the anion exchanger suggest
the formation of bonds to four nitrogen atoms on the adsorbent.
Some
evidence was found for an unresolved hyperfine structure due to inter
action of the electron spin with the nitrogen nuclei in both the anion
exchanger and the ammoniated samples. The results with the copper
samples seem to support the molecular orbital theory proposed by Stevens
and Owen.
12?
Very narrow lines and g values very close to 2.00 indicate a
strongly non-cubic, axially symmetrical electrostatic field about the
vanadyl ion.
Hyperfine structure interaction constants with absolute
magnitudes of 0.0182 and 0.007i*5 cm'1 for A and B, respectively, were
found for vanadyl ion adsorbed on the sulfonic-acid-type cation
exchangers.
These constants were reduced by covalent bonding in the
case of vanadyl ion adsorbed on the anion exchanger to 0.0158 and
0.00612 cm
, respectively.
Assuming that the decrease was due
principally to a decrease in an isotropic contribution to the hyperfine
structure, it was shown that the constants A and B must have the same
relative sign.
In general, the spectra obtained from the adsorbed ions were
similar to the spectra of these ions when in solution or in crystals of
known symmetry.
Consequently, it was possible to draw a number of
conclusions concerning the nature of the bonding between the ions and
the adsorbents, and the nature of the adsorbed phase.
128
REFERENCES
1. E. K. Zavoisky, j. Phys. (U.S.S.R.) 9, 21*5 (19l*5)j C. A., 1*0. 1072
(19U6).
"
—
2. R.
L. Cummerow and D. Halliday, Phys. Rev., ]0, 1*33 (191*6).
3. D.
M. S. Bagguley andJ. H. E. Griffiths, Nature, 160, 532 (191*7).
1*. J. E. Wertz, Chem. Rev., 55* 829 (1955).
5. D. J. E. Ingram, "Spectroscopy at Radio and Microwave Frequencies,"
Butterworths Scientific Publications, London, England, 1955*
6 . W. Gordy, W. V. Smith and R. F. Trambarulo, "Microwave Spectroscopy,"
John Wiley and Sons, New York, N. Y., 1953.
7. B. Bleaney and K. W. H. Stevens, Repts. Progr. in Phys., 16, 108
(1953).
8 . K. D. Bowers and J. Owen, ibid., 18, 30l* (1955).
9. A. Abragam and M. H. L. Pryce, Proc. Roy Soc. (London), A205, 135
(195D .
10. B. Bleaney, Phil. Mag., 1*2, 1*1*1 (1951).
11. J. H. Van Vleck, Phys. Rev., 7l*, 1168 (191*8).
12. H. M. McConnell, J. Chem. Phys., 2U, 90l* (1956).
13. W. D. Hershberger and H. N. Leifer, Phys. Rev., 88 , 7lU (1952).
ll*. J. S. Van Wieringen, Discussions Faraday Soc., 19., 118 (1955).
15. M. A. Garstens and S. H. Liebson, J. Chem. Phys., 20, 161*7 (1952) .
16. M. Cohn and J. Townsend, Nature, 173, 1090 (195U) 17. B. R. McGarvey, J. Phys. Chem., 61, 1232 (1957).
18. D. Polder, Physica, 9,, 709 (19l*2) .
19. C. Kikuchi and R. D. Spence, Am. J. Phys., 18, 167 (1950) .
20. D. M. S. Bagguley and J. H. E. Griffiths, Proc. Roy. Soc. (London),
A201, 366 (1950).
129
21. A. Abragam and M. H. L. Pryce, ibid., A 206, 161* (1951).
22. A. Abragam, Physica, 1£, 209 (1951).
23. R. H. Sands, Phys. Rev., £9, 1222 (1955).
21*. K. W. H. Stevens, Proc. Roy. Soc. (London), A219, 51*2 (1953).
25. J. Owen, ibid., A227, 183 (1955).
26. J. Owen, Discussions Faraday Soc., 19, 127 (1955).
27. J. B. Howard, J. Chem. Phys., 3_, 813 (1935).
28. M. Kotani, J. Phys. Soc. Japan, 1*, 293 (191*9).
29. L. E. Or gel, J. Chem. Soc., 1*756 (1952).
30. B. Bleaney, K. D. Bowers and D. J. E. Ingram. Proc. Phys. Soc.,
A 61*% 758 (1951).
31. R. D. Spence and E. H. Carlson, J. Chem. Phys., 21*, 1*71 (1956).
32. B. R. McGarvey, J. Phys. Chem., 60, 71 (1956).
33. D. J. E. Ingram and J. E. Bennett, Discussions Faraday Soc., 19
11*0 (1955).
3l*. D. J. E. Ingram, J. E. Bennett, P. George and J. M. Goldstein,
J. Am. Chem. Soc., ?8, 35U5 (1956) .
35* B. M. Kozyrev, Discussions Faraday Soc., L9, 135 (1955).
36. F. W. Lancaster and H. Gordy, J. Chem. Phys., 19, 1181 (1951).
37. G. E. Pake and R. H. Sands, Bull. Am. Phys. Soc., 2£, 18 (1951*).
38. M. T. Rogers, et a l ., Final Technical Report, Contract Nonr 02300,
NR 358-232,
39. A. G. Ingalls (ed.), "Amateur Telescope Making, Advanced," Scientific
American Publishing Co., New York, N. Y., (1952).
1*0. J. J. Lingane and R. Karplus, Ind. Eng. Chem., Anal. Ed., 18, 191
(191*6 ).
1*1. W. C.Pierce and E. L. Haenisch, "Quantitative Analysis," John
Wiley and Sons, New York, N. Y., (191*8).
1*2. R. E.VanderVennen, Unpublished Ph. D. Thesis, Michigan State
University, (195U)•
130
h3. J> E. Guessic and D. Williams, Phys, Rev., 99* 612 (1955).
UU. M. Tinkham, R. Weinstein and A. F. Kip, Phys. Rev., 8U, 8U8 (1951).
U5. F. C. Nachod (ed.), "Ion Exchange: Theory and Application,"
Academic Press Inc., New York, N. Y., 19U9 •
U6. B. Bleaney, Proc. Phys. Soc., A63, U07 (1950).
U7. C. A. Hutchison, Jr., Technical Report No. 1, Contract N6ori-20,
Institute for Nuclear Studies, University of Chicago, Spring, 1951.