Zeeman Effect on the Quadrupole Spectrum of Iodic AcidRalph Livingston and Henry Zeldes Citation: The Journal of Chemical Physics 26, 351 (1957); doi: 10.1063/1.1743297 View online: http://dx.doi.org/10.1063/1.1743297 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/26/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nonlinear polarizability of alphaiodic acid J. Chem. Phys. 62, 3571 (1975); 10.1063/1.430950 Nuclear Quadrupole Resonance Zeeman Study of 2,4Dichlorophenoxyacetic Acid J. Chem. Phys. 47, 2262 (1967); 10.1063/1.1703303 Zeeman Effect of the Nuclear Quadrupole Resonance Spectrum in Crystalline Powder J. Chem. Phys. 35, 1289 (1961); 10.1063/1.1732041 Analysis of the Absorption Spectrum and Zeeman Effect of Thulium Ethylsulphate J. Chem. Phys. 34, 1182 (1961); 10.1063/1.1731717 Zeeman Quadrupole Spectrum of Cyanuric Chloride J. Chem. Phys. 29, 1381 (1958); 10.1063/1.1744727

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EQUIVALENT ORBITAL BOND MOMENTS 351

B2H6: The parameters are those of Hamilton.18 The unprimed orbitals are on B I , the primed orbitals on B2. h denotes the 1s orbital on hydrogen. x is the dipole moment operator in the direction of the hydrogen atom, measured from the center of symmetry of the molecule.

18 W. C. Hamilton, Svensk Kern. Tidskr. 67, 395 (1955).

THE JOURNAL OF CHEMICAL PHYSICS

(sl xl '11') = 1.1100

(O'lx I '11') =0.0000

(hlxlh)=1.8810

(0' I x I h) = 0.2842

(s I x I '11") = 0.3886

(0' I x I '11") = 0.3691

(slxlh)=0.5152 ('II'I x I h) =0.8106

CH4 : The parameters are those of Coulson 6 Cr 28 = 2.98 ; t2p= 1.62).

(2se I z 12pO' e) = 0.4989.

VOLUME 26. NUMBER 2 FEBRUARY. 1957

Zeeman Effect on the Quadrupole Spectrum of Iodic Acid*

RALPH LIVINGSTON AND HENRY ZELDES

Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee (Received April 16, 1956)

The pure quadrupole spectrum of J127 in iodic acid has been observed at several temperatures. At 22°C the z component of the quadrupole coupling is 1126.9 Mc and '7, the asymmetry parameter is 0.4505. Zeeman studies on the low frequency transition (±1/2-t±3/2) showed an intensity effect that depended on the orientation of the crystal in the rf coil. Extra Zeeman components were present that resulted from a proton interaction, and the study of these essentially located the hydrogen in the crystal lattice. Zeeman studies on the high frequency transition (±3/2-t±5/2) showed four components for each type of iodine atom, the two not normally present unless '7 is large were weak. The splittings of the levels were uniquely assigned and the directions of the principal axes computed.

INTRODUCTION

T HE pure quadrupole spectrum for iodine in alpha iodic acid, HIOa, has been studied with and

without externally applied magnetic fields. The original purpose was to determine the directions of the principal axes of the field gradient tensor in a single crystal of iodic acid and to compare these directions with the known features of the crystal structure. In the course of the Zeeman work a number of unusual and for the most part unexpected phenomena were observed and studied. These are reported here along with the loca­tions of the principal axes.

The quadrupole interaction, without applied mag­netic fields, for J127 (spin 5/2) gives rise to three twofold degenerate energy levels as indicated in the left portion of Fig. 1. A measurement of the two indicated transi­tions allows calculation of the magnitude of the z component of the quadrupole coupling, eQ( i)2V / az2

) or eQc/Jzz and the magnitude of the field gradient tensor asymmetry parameter, 71= (c/Jxx-c/Jyy)/c/Jzz. Expressions for the energy levels for the case of an axially symmetric field gradient tensor (71=0) have been given by Pound! and by Dehmelt and Krtiger.2 In this case the upper transition frequency of Fig. 1 is exactly twice that of the lower. A more general theoretical treatment for 7J~0 has been given by Krtiger,3 Pound,! and Bersohn.4

* This work was performed for the U. S. Atomic Energy Commission.

1 R. V. Pound, Phys. Rev. 79, 685 (1950). 2 H. G. Dehmelt and H. Kruger, Z. Physik 129, 401 (1950). 3 H. Kruger, Z. Physik 130, 371 (1951). 4 R. Bersohn, J. Chern. Phys. 20, 1505 (1952).

In cases without axial symmetry the frequency ratio is less than two.

Figure 1 also indicates the manner in which the levels are split by applying a magnetic field to the crystalline substance. The zero field line splits into components that are always symmetric about the zero field line. In the work considered here the magnetic splitting of the levels is very small compared with the quadrupole splitting and the Zeeman component separations are

+3 -'2

+1.. - 2

"-

No Field

l'

rr I I I I I I I I 11 II I I I I I I

I ~ I I

j,

With Field

FIG. 1. Energy levels and transitions for the pure quadrupole spectrum of J127 (I = 5/2) with and without an externally applied magnetic field.

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352 R. LIVINGSTON AND H. ZELDES

linear with field strength H. The level splittings depend on the orientation of the magnetic field relative to the principal axes of the field gradient tensor. For this reason single crystals are needed for experiments. Theoretical results for the Zeeman effect in the case of an axially symmetric field gradient tensor have been given by Krliger. 3 For 1]rOO Bersohn4 has derived ex­pressions for the linear Zeeman effect by perturbation calculations using terms out to 1]2 whereas Cohen5 has given a treatment for arbitrary 1].

Several Zeeman studies on pure quadrupole spectra have been reported. The first of these was Dehmelt's6 observations on iodine in tin tetraiodide. Dean7 made a particularly significant study of the chlorine (1=3/2) resonance in p-dichlorobenzene. In this case 1] cannot be determined directly from the zero field transition, but the Zeeman study allowed both 1] and the directions of the principal axes to be determined.

The structure of iodic acid has been determined by Rogers and Helmholtz8 using x-ray diffraction. It was found to be orthorhombic with four molecules in the unit cell and all iodine atoms crystallographically equivalent. The hydrogen atoms were not located experimentally. The iodine and oxygen parameters showed the 103 groupings to be pyramidal and to be considerably distorted. An assignment was made as to which was the hydroxyl oxygen in the structure, and evidence was given for intermolecular hydrogen bond­ing. These factors suggested at once that the field gradient tensor would probably have considerable asymmetry, and this proved to be the case.

Garrett and Levy9 paralleled the present study with a neutron diffraction investigation on iodic acid with the determination of the hydrogen atom parameters as one of their objectives. They made available oriented single crystals of iodic acid which were used for much of the quadrupole work.

EXPERIMENTAL METHODS

The radio-frequency portion of the pure quadrupole spectrometer was a simple regenerative oscillator­detector circuit using an ultra high-frequency triode (6T4) and a transmission line tuned circuit. The ap­paratus was arranged like that previously described for the lower frequencies. lO As before, the oscillator was frequency modulated with a vibrating condenser, and when visual oscilloscope display was used the detector output was filtered to remove undesirable amplitude modulation components, amplified and presented on an

5 M. H. Cohen, Phys. Rev. 96, 1278 (1954). 6 H. G. Dehmelt, Z. Physik 130, 356 (1951). 7 C. Dean, Phys. Rev. 86, 607 (1952). 8 M. T. Rogers and L. Helmholtz, J. Am. Chern. Soc. 63, 278

(1941). 9 B. S. Garrett, The Crystal Structure of Oxalic Acid Dihydrate

and Alpha Iodic Acid as Determined by Neutron Diffraction, Report ORNL-1745, Oak Ridge National Laboratory, July 29, 1954.

10 R. Livingston, Ann. N. Y. Acad. Sci. 55, 800 (1952).

oscilloscope. Frequency measurements were made with a Gertsch FM-1B frequency meter. In the few cases where absolute frequencies, rather than frequency shifts, were needed the meter was calibrated at the settings used in the measurements.

The magnetic field for Zeeman studies was produced by a pair of air-cooled coils each having a mean di­ameter of 13 inches and a 2 X 2 inch window area wound with about 6000 turns of No. 23 enameled copper wire. They were rigidly clamped in the Helmholtz arrangement (6.5 inch mean separation). The coils were powered from an electronically regulated supply and the current could be set at any value up to 500 ma although 350 ma was not exceeded for continuous operation. Magnet currents were obtained by measuring the voltage drop across a 1 ohm standard resistor with a type K potentiometer. The Helmholtz coils were calibrated with the proton magnetic resonance method at a field of about 170 gauss and were found to give 0.3826 gauss/mao The homogeneity of the central portion of the field far exceeded the needs of the present experiments.

In early portions of the work a smaller set of Helm­holtz coils was used, and these were initially calibrated (to about 1%) by Zeeman measurements on a single crystal of sodium chlorate. These coils were later com­pared with the larger coils in the course of the work on iodic acid, and all fields were eventually referred to the proton resonance calibration.

It was necessary to change the orientation of the magnetic field relative to the axes of the crystal under study. This was accomplished by mounting the Helm­holtz coils in a large goniometer. A complete 360 0

azimuthal traverse (axis of the coils in a plane parallel to the worktable) was available, and although the complete circle for the elevation traverse was also available only about ± 100 could be used before the coils touched the vertical transmission line from the spectrometer. This restriction was not serious since it was usually desirable to traverse the magnetic field in a particular plane of the crystal. This could be ac­complished by carefully mounting the crystal in the spectrometer so that the desired crystallographic plane was parallel to the table top (within a few degrees). Adjustment screws on the goniometer base plate were then turned until the plane of the goniometer base was precisely parallel to the crystallographic plane as evidenced by the Zeeman patterns. The azimuthal traverse would then carry the field through the different orientations in the plane while the elevation adjustment would give several degrees of rocking in and out of the crystallographic plane. Both the azimuthal and ele­vation scales were read with verniers having a least count of 0.1 0

, and 0.05 0 could easily be read because of the large scale size.

A portion of the study was made with a chart recording spectrometer in order to obtain a greater signal to noise ratio. The radio-frequency portion of

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IODIC ACID SPECTRUM 353

the spectrometer was the same for both oscilloscope and chart presentation, and conversion could be made from one to the other without disturbing the crystal orientation. The detected output of the oscillator was amplified with a narrow band twin-T amplifier (100 cps center frequency) and analyzed with a phase sensitive detector. One major departure from the con­ventional method was made, however, in order to avoid difficulty from the large amplitude modulation signal component in the detected oscillator output that would be present if 100 cps frequency modulation were used. In the present case the oscillator was frequency modulated at 50 cps and the 100 cps component of the absorption line was passed through the narrow band amplifier and was analyzed in the phase sensitive detector. The 100 cps reference signal for the phase sensitive detector was derived from the 50 cps modu­lation signal by frequency doubling with a very stable multiplier.!1 This method of chart recording gives the second derivative rather than the usual first derivative of the absorption line with some loss in sensitivity, but, nevertheless, adequate signal to noise ratios were obtained. Rather than tune the oscillator frequency over the absorption lines, the lines were scanned by varying the Zeeman magnetic field. This was ac­complished by a motor drive on the control for the magnet power supply.

Iodic acid obtained from two sources of supply was found not to contain much iodic acid but to be mostly the anhydride. Suitable iodic acid was obtained by crystallizing the material from nitric acid, and addi­tional single crystals were grown from such a solution.

THE SPECTRUM WITHOUT APPLIED FIELDS

Since the structure of iodic acid has four crystallo­graphically equivalent molecules in the unit cell, there is only a single high- and low-frequency transition present for the pure quadrupole spectrum. These transitions were measured at several temperatures, and the results are summarized in Table I.

In view of the large magnitude of 1/ it was most convenient to factor the spin 5/2 secular equation4 to the desired accuracy rather than use the perturbation treatments given in the literature. Actually a complete set of tables was constructed on a high-speed digital computer which gave the roots of the secular equation for all preset values of 1/ in increments of 0.001. The 1/

and eQcpzz values were derived from these tables.12 It is interesting to note that the magnitude of eQcpzz increases as the temperature is lowered, as normally expected, but the magnitude of 1/ decreases. As a consequence there is the somewhat unusual behavior of the low­frequency transition dropping to a shallow minimum and then increasing as the temperature is lowered.

11 P. G. Sulzer, Proc. Inst. Radio Engrs. 39, 1535 (1951). 12 R. Livingston and H. Zeldes, Table of Eigenvalues for Pure

Quadrupole Spectra, Report ORNL-1913, Oak Ridge National Laboratory, July 13, 1955.

TABLE I. Summary of pure quadrupole spectrum measurements on iodic acid.

Frequency, Me Toe ±1/2-->±3/2 ±3/2-->±S/2 leQq,,, I I~I

",,22° 202.87 325.95 1126.9 0.4505 0 202.85 326.63 1128.8 0.4479

-78 202.89 328.62 1134.5 0.4406 -196 203.12 330.84 1141.0 0.4337

THE RELATION OF THE ZEEMAN EFFECT TO CRYSTAL STRUCTURE

In general, a quadrupole line for the lower frequency transition in iodine (± 1/2~±3/2) will split into four Zeeman components symmetric about the frequency of the unsplit line. The magnitude of the splitting and relative spacings of the components depend, in part, on the angles made by the applied magnetic field with the principal axes of the field gradient system. The iodic acid crystal has four molecules in the unit cell and each iodine atom has its own field gradient system, equivalent except for orientation. Thus an externally applied magnetic field will not necessarily make the same angles with the principal axes for each iodine atom, and, in general, 16 Zeeman components will be present, four for each iodine atom. A simplification is obtained if the magnetic field is applied along special directions depending on crystal symmetry properties. In these special cases some of the sets of four lines will be superimposed to give fewer than the general 16 line spectrum. It is also possible for the basic four line pattern to consist of fewer lines. For example, at a given angle the innermost pair of lines might merge at the unsplit line frequency to give a basic three line pattern for this special orientation.

Iodic acid has been assigned8 the orthorhombic space group D24- P2 12121• This space group has twofold screw axes normal to each face of the unit cell from which the pertinent symmetry properties can be de­rived. Any vector defined by crystal parameters (such as a bond direction or the directions of the principal axes of the field gradient tensor) with direction cosines a, (3, 'Y referred to the crystallographic a, b, c axes will be transformed to crystallographically equivalent directions by the operations of the twofold screw axis symmetry elements. Thus rotation about the screw axis with direction cosines 0, 0, 1 transforms a, (3, 'Y to the new direction -a, -(3, 'Y while rotation about the screw axes normal to the remaining two faces generates a, -(3, -'Y and -a, {3, -'Y. This completes the set of four crystallographically equivalent directions. The screw axes will also translate a vector, but this is not of concern here.

The Zeeman pattern for an iodine atom is determined by the angles made between the applied field and the principal axis system for the given atom. The direction cosines for the principal axes of one iodine atom in the crystal system may be designated (ai,{3i,'Yi) where i

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354 R. LIVINGSTON AND H. ZELDES

, ~ , w I

(646 Gfl.USS FIELD)

w I

~ -,,-AXIS \I \!K/ \/ ~ 0 .e:\------',,·W·''''----r----~- ~~ n //i\ \ {I\ ~ 30 i j V i'~ \ ~ :~ i / /\: /\ \\ ~ 60 II 1 .\:/. 1 .~ ~ 70 , \: I , f-w- 80 j \ /:\ j \

,,-AXIS I \I : \I i ~9°Ci"" ,/>~ 1-

-160 -120 -80 -40 0 40 80 120 160

DISPLACEMENT FROM ZERO FIELD LINE. Kc

FIG. 2. Zeeman components measured for various orientations of the applied magnetic field in the a c plane of HIOa•

refers to the x, y, or z principal axis. The orientations of the remaining three principal axis systems are given by the symmetry operations described above. If a magnetic field is applied normal to a face of the crystal, say, along the a axis, the cosines of the angles between the field and the principal axes for the one iodine are ai. The remaining three iodines, at most, only involve a change in sign of ai. This is equivalent to a reversal in direction of the magnetic field to which the Zeeman effect is invariant. Thus all four sets of principal axes experience an equivalent field and only the basic four line Zeeman pattern should be observed. The situation is similar for the field along either of the other crystal axes.

It may also be shown that if the field is confined to one of the basal planes the four sets of field gradient directions behave as two pairs, and, in general, no more than 8 Zeeman components should be observed. If the iodine atoms could be labeled, the pairing for the field in each of the three planes' would be found to follow the three ways in which four iodine atoms can be combined two at a time. A method that essentially

~ -40 \ \Yj i ~ ~~~ ... , j /\i/\ i

\"'/ [fi,'\ I \ ~-10 c-AXIS : ____ :.1,\:. ___ ---,\/ ~ 0 /\ r;::,i /\------j

~ ~~ /1) }6~, ( \ g 40 (J i ,/;\\\ \, \~ ~ :~ ~,i/ l i i\ \.), ti 70 :/ Ii . : '\'" '\"'\"""" . Z 80 /,' !: \ ~ )J.-AXIS .:',/ :,' :e 90 • I. ",J', --

-160 -120 -80 -40 0 40 80 120 160

DISPLACEMENT FROM ZERO FIELD LINE. Kc

FIG. 3. Zeeman components measured for various orientations of the applied magnetic field in the b c plane of HIOa•

labels the iodine atoms (with respect to an external preferred direction) will be described later.

THE ZEEMAN EFFECT ON THE LOW-FREQUENCY TRANSITION (± 1 /2--7 ±3 /2)

Figure 2 shows the Zeeman splittings at room tem­perature observed with a constant magnetic field of 64.6 gauss restricted to the a c crystallographic plane. Just the expected four lines are seen along the a and c directions and no more than eight appear for inter­mediate angles. These observations were made with the visual, oscilloscope spectrometer. Figures 3 and 4 show the similar patterns observed with the field in the a band b c planes. In these cases, however, some of the components, at and near the direction of the b axis, appear as close spaced doublets in seeming con­tradiction to the assigned crystal symmetry. Such is not the case, however, and these doublets that arise from a proton interaction will be treated in detail later.

I ~ I {646 GAUSS FIELD} W I ~ 1

~ "-AXIS\/ ____ '\~ ~/ \/

~- 1~ /\ /",j/\ ;/\\. //i\.\ / \ >=0 20 f \ / /i\. \

; l~ I /.1 ( { iJ il ! 70 ~ \ \1/ .i \\ A

g .. / / \\ //::''''~// \\·X/· w 80 Q-AXIS\XI i3 90 '---~ ~ fI.\ /'" i /'\ /"/\

"160 -120 -80 -40 0 40 80 120 160

DISPLACEMENT FROM ZERO FIELD LINE, Kc

FIG. 4. Zeeman components measured for various orientations of the applied magnetic field in the a b plane of HIO,.

If the magnetic field is traversed through the entire azimuthal circle, the Zeeman patterns should have mirror symmetry about each crystal axis. This is indi­cated in Fig. 3 where the experimental data are ex­tended for about 40° into a second quadrant. The solid curves indicate the components originating from one pair of iodine atoms while the dotted curves are for the other pair. Note, however, that the pairs of atoms exchange places as the axis is crossed. This is in the sense that the outermost components on one side of the c axis belong to one pair of iodine atoms, but the lines showing the same splitting on the opposite side of the c axis belong to the other pair of iodine a toms. Although the positions of the components appear to mirror exactly the intensities do not. This was generally true whenever observations were made with the mag­netic field in any of the three crystallographic planes and with the particular orientation of the crystal in the rf coil used for most of the work. Although it was difficult to make accurate intensity measurements,

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IODIC ACID SPECTRUM 355

striking comparisons could be made. For example, consider the central group of four components in Fig. 3. The first experimental points off the c axis lie at ±8.5°. The approximate relative intensities of the group (from one side to the other) at +8.5° were 3, 2, 2,3, while for -8.5° they were 3, 4, 4, 3; i.e., the outer two were strongest on one side while the situation was reversed for the mirror angle. The intensity effect was found to be due to the manner in which the single crystal was mounted in the spectrometer radio-fre­quency coil. In the above case the axis of the coil was along a skew direction through the crystal. The in­tensities mirrored exactly with a second crystal that was cylindrically shaped with the b axis along the cylinder axis, the coil wrapped around the crystal, and the field traversed in the a c plane. In this case the oscillating magnetic field was along the b axis and hence made the same angles with each of the four sets of field gradient directions. In the case of the first crystal different angles were made between the oscillating magnetic field and each of the four sets of field gradient directions. This intensity effect essentially labels the iodine atoms as weak or strong absorbers as a result of their orientation in the oscillator coil. Hence in a traverse from one quadrant to another the strong lines from one pair of iodine atoms exchange places with the weak lines from the other pair and there is the resulting reversal in intensities. In Fig. 3 the intensity effect was used in assigning which four lines went with each pair of atoms. Otherwise there would have been an ambi­guity in assigning which outermost component went with a given centrally located component. Cohen" has given a theoretical treatment for the line intensity when the angle to the oscillating field is varied for the case of the pure quadrupole spectrum (no applied magnetic field). He has also indicated that in the presence of an applied field the intensity formulas are extremely complicated for arbitrary orientations, but in the majority of cases orientation of the oscillating field along the x axis of the field gradient gives maximum intensity.

Figures 2, 3, and 4 also show that Tf must be quite different from zero. For Tf= 0 and when the magnetic field makes an angle of 90° to cf>zz the outermost com­ponents coincide with the inner ones to reduce the basic four line pattern to a two line one. The 90° angle must have been passed at least once in traversing each of the three planes; yet in no case does the outer grouping of lines meet the inner lines.

A study has been made of the close spaced doublets (Figs. 3 and 4) that appear for the outermost com­ponents when the magnetic field is oriented in the general direction of the crystallographic b axis. These doublets are caused by a magnetic dipole-dipole inter­action of the iodine nucleus with a near neighbor proton. One can consider the doublet to be caused by the small adding or subtracting field contributions at an iodine nucleus caused by the proton being in one

or the other of its two states in the externally applied field. The expected angular dependence for the sepa­ration would be (3 cos20-1) where 0 is the angle made between the applied field and the line joining I and H. By comparison to similar effects in nuclear magnetic resonance13 it was presumed that the angular part would be multiplied by 2p,I,3 where p, is the proton magnet moment and , is the I to H distance. The doublet separation should not vary with changes in strength of the externally applied field if the field is large compared to p,lr. All Zeeman components moved linearly with field over the range 21 to 164 gauss, and the doublet separation remained constant. The meas­urements could not be extended to weaker fields because the line widths were such that the doublets began to merge with the inner Zeeman components. A doublet should be seen for all angles except 0=54°44', and, indeed, for all of the Zeeman components. However, the finite line widths did not allow resolved proton doublets excepting for the outermost components near the b direction.

A study of the manner in which the doublet sepa­ration varies with the orientation of the applied mag­netic field should fix the orientations of the I-H vectors in the crystal. The angular function is at a maximum for 0=0°. The doublet separation in Figs. 3 and 4 appears to approach a maximum as the b axis direction is approached and hence the I-H vectors all point roughly in the direction of the b axis.

Several methods for quantitatively locating the I-H directions were tried, but only one gave good results. The first method tried was to single out one of the doublets and follow the separation as the field orien­tation was varied to seek out the maximum separation (0=0°). This required moving out of the crystal planes so that the simple patterns of Figs. 2, 3, and 4 were split into many more components giving very weak lines to follow. The outermost lines which show the doublets, unfortunately, are very much weaker than the centrally located components. Also, the angular function is least sensitive to changes in 0 at 0= 0° so that very small changes in separation would have to be measured accurately to find 0=0°. This approach merely confirmed that the I-H directions grouped to favor the b axis direction.

Other methods tried included the following: (a) measuring the doublet separation for angular traverses in a crystallographic plane and fitting the variation to (3 cos20-1) where the measured angle is 0 projected into the plane, (b) locating 0=54°44' (chart recording) in two different planes by measuring the angle where the doublets merged into a single line (the criterion for line coincidence being maximum intensity of the merged lines), and (c) locating 0=90° in two different planes where the doublets form a subsidiary maximum in separation. In this latter case, 0= 90°, the separation

13 G. E. Pake, J. Chern. Phys. 16,327 (1948).

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356 R. LIVINGSTON AND H. ZELDES

FIG. 5. Measurements showing the angular lag for the separation in one set of proton doublets compared to that in the other. The externally applied field is traversed in the b c plane, and the indicated angles are measured from the b axis. The second derivatives of the absorption lines are recorded.

is not quite enough to resolve the doublet, but a rather sharp minimum in line intensity, as chart recorded, is found. These methods did little more than indicate that the J-H directions were within several degrees of the b axis. It was later found that one major difficulty was associated with a variation in line width with orien­tation of the applied field presumably arising from next to nearest proton neighbors.

The final method used to locate the J-H vector directions does not depend on the exact form of the angular dependence of the doublet separation. It may be developed from the following observation. In Fig. 3, the mapping of the b c plane, two sets of doublets originating from the two pairs of iodine atoms are present. As one maps away from the b direction both sets of doublets decrease in separation, but one set has an angular lag behind the other. This lag angle should be constant throughout the plane. Consider, for the moment, that the J-H vectors lie in the b c plane of the crystal (or in planes parallel to the b c plane), one pair inclined at +4> from b and the other, by crystal symmetry, at -4>. These sets of J-H directions are now separated by an angle of 24>, and as a magnetic field sweep is made in the plane one doublet separation will always lag the other by 24>. Hence, one half the lag angle gives the inclination of the J-H vectors away from the b axis. In general it is necessary to measure lag angles in two planes for a unique solution. If ct, {3, l'

are the direction cosines for an J-H direction it can be

shown that a mapping of the b c plane gives i'Y/{3i = tan! i ~4> i where ~4> is the lag angle. Similar expres­sions hold for the other planes. Lag angle measurements were made in the a band b c planes. The general pro­cedure was to advance the setting of the goniometer in small angular increments and to chart record the doublets at each setting. The lag angle was evaluated from a comparison of the recordings. Figure 5 shows recordings made in the b c plane for 5 ° angular incre­ments. One doublet is obviously lagging the other, and a large number of recordings showed this lag angle to be 8±2°. Similar recordings in the a b plane gave a lag angle of 0±3°. These comparisons, for the most part, were made where the doublet separation is small and the components are starting to merge. This gave excellent angular sensitivity. It was necessary to record data in two (mirror) quadrants for each plane. The criterion for having the goniometer precisely aligned so that the magnetic field was in the crystallographic plane was to make goniometer tilt adjustments until the lag angle for each quadrant was about the same. Slight misalignment would alter the values, but the average for the two quadrants was not changed. A misalignment of 0.1° out of the crystal plane could easily be detected. This method of aligning the goni­ometer largely compensates for the earth's magnetic field. The above lag angle measurements show directly that the four J-H directions are parallel to vectors in the b c plane (within ± 1.5°) inclined, in pairs, towards

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lODIC ACID SPECTRUM 357

the c axis making angles of ± (4± 1) 0 with the b axis. The error limits are based only on the lag angle measure­ments and not on other sources of error to be mentioned later.

The doublet separation was measured with the field along the b direction, which is 40 from the orientation that would give maximum separation. The measure­ments were made in magnetic field units by observing the doublets on the oscilloscope and measuring the change in magnetic field needed to move one doublet over to the previous location of the other. Many sets of measurements were made at nominal fields from 21 to 164 gauss and with different spectrometer frequency sweep widths. These measurements are summarized in Table II. The average of these values is 4.41 gauss separation. A chart recording of the doublet with the field along the b direction is shown in Fig. 6.

The above results along with Rogers and Helmholtz's8 structure data should fix the hydrogen locations. Actually the solution is not unique since there are four molecules in the unit cell, and the decision would have to be made as to which one of the determined directions went with a given iodine atom. Moreover, there would be the choice of taking the distance in a positive or negative sense. Features of the structure would clearly eliminate some of the possibilities. Since some of the errors in the quadrupole method used here have not been completely appraised, and since in addition the H parameters are now known from a neutron diffraction study,S it appears more appropriate to compare results with the neutron diffraction study rather than deduce the lattice parameters. If 2J.1./r3 is taken as the correct radial function the above doublet separation with 0=4 0 gives 2.33±0.02 A for the J-H distance. The estimated error is based only on the accuracy of the doublet separation measurement. The value from the neutron diffraction study is 2.407±0.013 A. The effect of thermal motion of the hydrogen would make the quadrupole value appear smaller since in this case the value is derived from the average of 1/r3• However, it is not known that the entire difference is caused by this effect since the use of (2J.1./r3) (3 cos20-1) for the doublet separation has not been justified theoretically.

The preceding angle measurements show that the J-H direction (from which the complete set may be deduced) makes an angle of 90° with the a axis (lies in the b c plane) and an angle of 4° with the b axis. The

TABLE II. Doublet separation with field along the b axis.

Nominal field. gauss

21 50 92

102 106 106 164

Separation, gauss

4.45 4.43 4.42 4.31 4.50 4.40 4.38

FIG. 6. The doublet arising from the proton interaction where the externally applied field is along the b axis. The second deriva­tives of the absorption lines are recorded.

values computed from the neutron diffraction parame­ters9 give 86.0° from a and 5.7° from b. A source of error that has not been evaluated is the effect of changing line width with orientation of the field on lag angle measurements. In view of the manner in which lag angles were measured, this effect could explain the small discrepancy between the values above.

THE ZEEMAN EFFECT ON THE HIGH-FREQUENCY TRANSITION (±3/2->±5/2)

Zeeman components were observed and measured for the high frequency transition (326 Mc) with a field of 64.6 gauss applied along the band c axes and for a few intermediate angles in the b c plane. Figure 1 indicates two allowed transitions (solid lines). However, all of the four possible transitions were seen, although the ones indicated by dotted lines were very weak.

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358 R. LIVINGSTON AND H. ZELDES

TABLE III. Zeeman splittings for a field of 64.6 gauss.

Unsplit Field Spacing from center, ±kc transition direction Outer components Inner components

±3/2->±5/2 C 130.2 21.3 ±3/2->±5/2 b 103.2 10.2 ±1/2->±3/2 a 134.8 20.0 ±1/2->±3/2 b "133.5 38.8 ±1/2->±3/2 c 94.9 11.0

• Measured to the midpoint of the doublet.

The doublets caused by the proton interaction were not resolved. The appearance of the extra transitions allowed the level splittings to be uniquely assigned to the proper levels, which helped greatly in the subsequent computation of parameters fixing the principal axes.

The Zeeman splittings of the observed lines with the field along the axis directions for the one set of measure­ments made on the high frequency transition are given in Table III. The averages for several sets of measure­ments are also given for the low frequency transition (± 1/2---t±3/2). The level splittings calculated from the b axis data for the ±3/2---t±5/2 transition are ±56.7 kc and ±46.5 kc. One of these is the splitting of the ±5/2 level and the other is for the ±3/2 level, but the level assignment is ambiguous. The correspond­ing data for the ±1/2---t±3/2 transition gives level splittings of ±86.2 kc and ±47.4 kc for the same orientation and field. The common level splitting (going with ±3/2) is then determined to be ±46.5 kc from the high-frequency transition and ±47.4 kc from the low; hence 56.7 kc must go with the 5/2 level and 86.2 kc with the 1/2 level. Similarly for the c-axis orientation the splitting of the ±5/2 level is ±75.8 kc and the ±1/2 level is ±42.0 kc. The ±3/2 common level is ±54.5 kc from the high-frequency transition and ±53.0 kc from the low. The agreement for the splittings of the common level is considered to be satisfactory.

The weak components seen for the ±3/2---t±5/2 transition would not have been observable for cases where 1]=0. As a consequence of the relatively large value of 1] the zero field "forbidden" transition, ± 1/2---t±5/2, in powdered iodic acid should also be strong enough to be observed. It should appear at 528.8 Mc at room temperature. Cohen" has discussed the probabilities of such transitions.

THE PRINCIPAL AXES

The directions of the principal axes were determined using the treatment given by Cohen" for arbitrary 1]

but to first degree in field strength. The calculations were made using the level splittings deduced from experiments made with the field along crystal axes. No attempt was made for a best fit to data taken in crystallographic planes away from these axes, which would have been a formidable computational task. The direction cosines for one set of the principal axes are given in Table IV. The remaining three sets may be deduced from the symmetry properties discussed earlier. The angles defined by the direction cosines in Table IV are estimated to have probable errors of 2° and each principal axis is estimated known with a probable error of 3°.

The choice must be made as to which of the four iodine atoms has the axes assigned as written in Table

TABLE IV. Direction cosines of the principal axes referred to the a, b, c crystal axes.

Principal Crystal axis axis a b

X 0.310 0.536 -0.785 y -0.654 0.720 0.234 z 0.691 0.441 0.573

IV. Only one choice appears reasonable, and this is the one in which the z component is approximately normal to the plane of the three oxygens of an iodate group. If the three oxygens were equivalent the z component would be in this direction. The crystal structure parameters9 and direction cosines given in Table IV show the z component of the field gradient to be tilted 13.2° from the normal to the plane of the oxygens. The three oxygen atoms are nonequivalent, the first being a hydroxyl oxygen and a second having an intermolecular hydrogen bond. In this order, the angles made between the 1-0 bond directions and the normal to the plane are 61.4°, 60.0°, and 59.2°. The corresponding angles made between the z component of the field gradient tensor and the 1-0 bond directions are 73.1°, 60.6°, and 49.3°.

ACKNOWLEDGMENTS

We have derived much benefit from many helpful discussions with H. A. Levy and B. S. Garrett who also kindly supplied oriented crystals of iodic acid. We also wish to thank B. M. Benjamin for synthesizing pure iodic acid and additional single crystals needed for the work.

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