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A nuclear quadrupole resonance spectrometer Fulton, Beverley Joan 1956

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A NUCLEAR QUADRUPOLE RESONANCE SPECTBOHETER by BEVERLEY1 JOAN FULTON B.A., University of British Columbia A Thesis submitted la partial fulfilment of the requirements for the degree of Master of Arts in the Department of Physics We accept this thesis as conforming to the standard required for the degree of Master of Arts The University of British Columbia December^ lo£6 ABSTRACT In conjunction v/ith low temperature experiments on nuclear align-ment and nuclear specific heat, a spectrometer has been developed in order to investigate the hyperfine structure of compounds with suitably large quad-rupole coupling by the technique of Nuclear Quadrupole Resonance. The auxil-iary equipment which was built in addition to an externally quenched superre- • generative oscillator provided-for frequency modulation and oscilloscopic dis-play as well as Zeeman modulation and chart recorder display. The superregenerative oscillator has a frequency range of 1!?0 - 600 Mc./sec., which is the range required for investigation of the compounds con-cerned j the spectrometer has reproduced satisfactorily test signals over the range l61i.3> to 332.U Mc./sec. The test signals were obtained from the known quadrupole resonances of 1^7 and Br*^ in Snl^, I2, Sbfirj and BaCBrO^g. Using the spectrometer, a search was made for resonances in a number of substances which were of interest for the nuclear alignment programme, and in which no resonances had yet been reported. In particular, we were able to make a careful investigation of the magnesium -salt of para-iodo benzene sul-phonate since we knew from theoretical investigations the approximate frequency 127 at which the I 1 resonance occurs. A possible explanation is given for the failure to detect any such resonance. In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representative. I t i s under-stood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of EH2SICS.. The University of B r i t i s h Columbia, Vancouver Canada. D a t e riF.OFMBfifi, 1956. ACKNOWLEDGBfflJTS I first express ray appreciation to Dr. J. M. Daniels, my research director. I am indebted to him for the preliminary desig the spectrometer, and for his constant assistance and instruction. I thank also Dr. Gilles Lamarche for his interest in the experiments,! his many' suggestions, and for much of the work which was done before I took over the project. ! I have been greatly helped in my work by the staff of the workshop, headed by Mr. Alec Fraser, and the department glassblovrer, Mr. John Lees. The financial assistance of the National Research Council has enabled me to take part in this research. I acknowledge the receipt of a National Research Council Bursary (195U-55) and a Studentship (1955-56) and summer supplements (1955 and 1956). The research has been supported by a research grant to the Low Temperature Laboratory for the study of hyperfine structure. i i i . TABLE OF CONTENTS page INTRODUCTION • 1 CHAPTER I THEORY h 1. Energy of nuclear orientation and transition frequencies *..........*. h 2. Electronic structure of molecules and nuclear quadrupole coupling constants 9 3. Theory behind the method of detection 12 ii . Theoretical aspects of the Zeeman effect ............ 15 CHAPTER II THE SuPERRECENERATIVE OSCILLATOR 19 1. The superregenerative oscillator in theory 19 2. The superregenerative oscillator in our quadrupole spectrometer s 22 3. A review of the various oscillators used 21* CHAPTER III THE VARIOUS PARTS OF THE SPECTROMETER 26 1. ISodulation 26 2. Frequency sweep apparatus 28 3. Filtering and Amplification 29 lu Phase sensitive detector, noise limiter, and d.c. amplifier 29 CHAPTER IV 'RESULTS AND DISCUSSION '.. 1 3!Lj, 1. Performance of the spectrometer on known signals .... 31 2. Performance of the spectrometer on unknown signals ». 32 APPENDIX "• DESIGN OF THE SAMPLE COIL FOR MAXIMUM FIELD STRENGTH ... 3k BIBUJOGRAPHI .' 36 LIST OF ILLUSTRATIONS following page Figure 1 Junction Box • • • • 2 2 Figure 2 Superregenerativ© Oscillator 22 Figure 3 Quench Oscillator 22 Figure h Block Diagram of the Nuclear Quadrupole Spectrometer ... 26 Figure 5 Frequency Modulator 30 Figure 6 Filter for Very Low Frequencies 30 Figure 7 Relay Coil and Vibrator 28 Figure 8 Shape of Lucite Sector 28 Figure 9 Frequency Sweep Apparatus 28 Figure 10 Fewer Amplifier Driving 12ie HelLmholta Coils 30 Figure 11 Squaring Circuit 30 Figure 12' Auxiliary Oscillator 30 Figure 13 Low Pass Amplifier 30 Figure lli Phase Sensitive Detector 30 Plate I (a) Photograph of the Superregenerative Oscillator 22 (b) Full View of the Superregenerative Oscillator 22 Plate II (a) Photograph of the Auxiliary Equipment 30 (b) Photograph of the Tuning System 30 Plate III (a) The I 1 2 7 3ignal in I2 32 (b) The I 1 2 7 signal in Snl^ 32 Plate 3V (a) The Br 7 9 signal in SbB^ 32 (b) The Br 7 9 signal in BafBrt^)? 32 Plate V Photograph of crystallographic data on the benzene sulphonates 33 INTRODUCTION Electrostatic interaction between the nucleus and its surroundings can occur through the electric 2^-pole moments of the nucleus Ua 2,;U)j the interaction of the quadrupole moment with internal electric fields is called the nuclear quadrupole coupling. The quadrupole moment is a characteristic of the particular nucleus and is a measure of the deviation of the nuclear charge distribution from spherical symmetry. The various energy levels of the nucleus which result from this quadrupole interaction correspond to var-ious orientations of the nucleus with respect to the axis of the molecular electric field.. The work on nuclear quadrupole resonance reported in this thesis is a contribution to the problem of nuclear alignment by the mechanism fi r s t proposed by Pound (1°U°)« The alignment takes place as a result of the hyper-fine splitting produced by the interaction of the nuclear electric quadrupole moment with the internal electric field of the molecule. A crystal containing covalently bonded nuclei which have sufficiently high quadrupole coupling need only be brought into thermal equilibrium with a substance that has been cooled by adjabatic demagnetization to a temperature of a few hundredths of a degree and the majority of the nuclei will f a l l into the lowest hyperfine level. A nuclear orientation relative to the crystal axes wil l result, depending in degree on the temperature reached and the size of the quadrupole coupling. As a consequence of this hyperfine splitting, a Schottky type an-omaly in the specific heat appears at temperatures approximating h^/ky where V is the frequency of transition between two hyperfine levels, and k is Boltzman1s constant. At these temperatures, a rearrangement of the populations of the..levels' takes place according to the Boltzman distribution producing a specific heat whjich is additional to the other contributions to the specific heat of the crystal. Thus, the hyperfine structure might be detected calpri-metrically at very low temperatures* The nuclear specific heat of iodine in the magnesium salt of para-iodo benzene sulphonate is being investigated at low -temperatures by the group which i s interested in the Pound method of nuclear alignment, " "' ' In the study of nuclear alignment and nuclear specific he^ at, i t is important to have a method cf investigating directly the hyper fine structure of the compounds concerned. The technique used is Nuclear Quadrupole Resonance. Transitions between the allowed orientations of the nucleus,. I, 1-1, -I, produce a spectrum of frequencies V=» (ElmI - E|m*| )/h. In order to excite these transitions between energy levels and,make the spectrum observ- 1 able, energy must be1;supplied to the system at the frequency corresponding to the splitting between them. In pure quadrupole. resonance, the lines are detected and recorded by use of an absorption spectrometer. The sample is placed in a coil which is carrying radio frequency current. This coil forms the tank circuit of the oscillator supplying the radio frequency power. The mag-netic dipole moment of the nucleus interacts with the alternating magnetic field produced in the coil, inducing a reorientation of the nuclei against the elec-trostatic field of the molecule. The transitions which occur between energy levels are accompanied by the macroscopic phenomena of absorption and dis-persion. Since the resonant frequencies involved are usually in the hundreds of megacycles, the spectrometer was designed to have this frequency range and the absorption and dispersion are detected by radio frequency methods. The spectrum obtained in pure quadrupole resonance yields the product of the principal components of the electric field gradient tensor with the nuclear quadrupole moment. "When the quadrupole system is subjected to a static magnetic field, a Zeeman splitting of the absorption lines occurs in single crystals. In a polycrystalline sample, the Zeeman splitting for each crystal is different, and an external magnetic field causes the line to be smeared out" and disappear. The Zeemaa splitting of the lines can be studied as a function of the orientation of ;the magnetic field relative to the crystal axes in order 3. to determine the orientation in the crystal of the principal axes of the field gradient. The splitting of the energy levels as a function of field orientation will be calculated in the theoretical discussion for the case of spin 5/2 usirfg second order perturbation theory. A comprehensive review of nuclear quadrupole resonance has been given by Dehmelt (195U). Many pure quadrupole resonances have been determined theoretically and experimentally by Dehmelt and Kruger; the nuclei which have been investigated and found to have quadrupole couplings in various molecules of the order of hundreds of megacycles are: iodine, bromine, arsenic, antimony, bismuth, and mercury. Kruger (l$>j?l) and Dean {19$h) have developed the theory of the Zeeraan effect on pure quadrupole resonance lines. Townes and Dailey (19U9) have found approximate methods for the determination of the electric field gradient from a consideration of the valence electrons in the molecule. The thesis deals mainly with the construction of the superregener-ative spectrometer which was used to observe nuclear quadrupole resonances. The tange covered is l£0 Mc./sec. to 600 Mc./sec. Apparatus was constructed to provide either wide band oscilloscopic display or narrow band pen recorder display of the resonances. As we expected from a spectrometer of this type, there was a great deal of trouble in obtaining satisfactory performance. However, several known signals with satisfactory signal-to-noise ratio were found with the spectrometer, and a few examples are given. A sample of the magnesium salt of para-iodo benzene sulphonate was obtained from the low temperature group and was investigated to find the !l27 resonance. The sodium salt of meta-iodo benzene sulphonate was prepared iii the laboratory and investigated for the same iodine resonance. The search was made over a wide range of frequen-cy and more carefully in the region of 280 megacycles, where the resonance is expected from theoretical calculations. A discussion is given concerning the failure to detect the resonance along with a description of the other,investi-gations which were made in the last chapter. CHAPTER I THEORY 1, Energy of nuclear orientation and transition frequencies If we take as origin the centre of the nucleus we can calculate the electrostatic energy E •» J^pv d"C of an element of charge p»6.X> placed at a point of potential V produced by the charges exterior to the nucleus. The potential V can be expanded in a series around the origin and the energy then takes the form: the summation signs applying to cartesian coordinates x,y,z, in the following discussion. The f i r s t term is independent of the orientation of the nucleus and the second term is zero because a nucleus dees not possess an electric : dipole moment. Then that part of the energy of electrostatic interaction which depends on the orientation of the nucleus iss where we have a scalar product of two tensors which represent the distribution of potential and the distribution of nuclear charge around the origin. The elements of the tensor which represents the electric field gradient are where i , j stand for the cartesian coordinates x,y,z. We can write as the sum of two tensors, one with V^V^ *» 0 and the other a multiple of the unit tensor. The latter causes a shift of the centre of gravity of the energy spectrum which is independent of orientation, and therefore will be considered no further. The trace of is then zero: & • £ * t - 0 (3) In the case of a potential axially symmetric about the z-axis, tine xyz axes are principal axes of the 7±^ tensor and d^V/dz2 is the largest of the principal components of the tensor. Then i t follows from condition (3) that: and Ji5J *2V * 2v therefore, } V 3153" Si 2 0 whenever i f j (U) (5) The distribution of charge in the nucleus is also axially symmetric, with respect to the z' axis of the nuclear coordinate system x'y'z'. Therefore, pOx'2 dX * f py' 2 dU * B, while we put f />z'2 d r = A. If the x and x» axes are allowed to f a l l together and i f © is the angle between the z and z 1 axes, Diagram 1 then p>a2' d t - f/>(z*coa 6 - y«sin 6) 2 dt - A cos2© +,B sin2© j'pj2- dT - A sin2© + B cos2© Jpz2 6X. - B We can now obtain from equation (2) a new expression for the energy: , (,6) ; (7) (8)8 EQ = I £ (B) - i (A sin2© + B cos2©) + q (A cos2© • B sin2©) (9) (A - B)(3/2 cos2© - 1/2) In this equation (A - B) can be expressed in z' and r, the distance from the origin to the element of volume dT. A - B - fjK**2 - y | 2 + x' 2 ) dt. - \f />{3z , 2~(z' 2 * y t 2 + x'2)} dL 2 = %ff Oz*2 ~ r 2) dL (10) The integral, denoted by eQ , defines an inherent property of the nucleus called the quadrupole moment. It has the dimensions of area and is usua^y expressed in barns do-21* cm. ). It is positive when the nuclear charge is a 6. prolate spheroid and negative when the nuclear charge is an oblate spheriod. For.a spherical charge distribution, eQ vanishes. We can write down the equation for the classical quadrupole inter-action energy: %, EQ - 4 «Q <l (3/2 cos2© - 1/2) (11) In order to derive the quantum-mechanical energy eigenvalues of the quadrupole system from the classical expression, we most replace cos2© with the operator ^ E Q - V 8 e Q q U3I,2 - 1(1 • 1)1 ( 1 2 ) 1(14-1) It is conventional to define eQ* with respect to the molecular axis z rather than the nuclear axis z', and for the state I » I^. Ihen Q ' in equa-tion (12) is replaced by the normalized value Q, then EQ should have the value which would be obtained by putting cos 9 - 1 in the classical expression (11). The value Q - <f (21 - 1) (13), 2 (I • 1) is the normalized quadrupole moment; this Q is used in the literature. The energy eigenvalues are now: Em " [3*a2 " 1(1 + D] tthf • \ 1*1(21-1) The coefficient eQq is called the quadrupole coupling constant and is fre-quently expressed in megacycles (eQq/h). ' „i We notice that for I • [3m2 - 1(1*1)3 " 0, and so the application of nuclear quadrupole resonance is restricted to nuclei of spin greater than \* The quadrupole moment is also zero for a nucleus of spin ]r. The allowed values of m are m = I, 1-1, -I. When I is half integral, the energy levels are each doubly degenerate, corresponding toim. IShen the spin is integral, there are I doubly degenerate, levels and one non-degenerate level in an axially symmetric field; i f the field is not axially symmetric, the levels are in general a l l non-degenerate. Since transitions induced by an alternating magnetic field are magnetic dipole transitions, the selection rule Am « £1 applies. If m takes on the larger value of spin com-ponent for the two states considered, the frequency of transition between the states i s : y - 3 eQq (2|m)-l) (1?) Ul(2I - 1) The quadrupole spectrum consists of equally spaced lines. For I = 3/2, there is a single line of frequency y=|eQq (16) For I - 5/2, there are two lines >{» 3/20 eQq and >£- 3/l0 eQq (17) For I » 7/2, three lines >J* eQq, 1/7 eQq, )>- 3/Hi eQq (18) V/hen the field is not axially symmetric, the parameter T\~ (V^g-VyyO/q is used to describe the asymmetry. If is small, the quadrupole resonance frequencies can be derived using perturbation theory: For 1-3/2, / - \ eQq (1 (19) For 1 = 5/2, >> = Y2/2 (1 + 1.296IT}2 - 0.55 3/10 eQq (1 - 0.2037 Yl 2 + 0.18^) (20) For I = 7/2, >j = /y3 (1 • 3.73312 - 6.86^) >£= 2/3 y3 (1 - O.U667n2 • 1.82n11) ^= 3/lU eQq (1 - 0.1000 V}2 - 0.019 q1*) (21) The relative intensity of the quadrupole transition lines depends on the probabilities of transition between the different states involved. The probability of a dipole transition per unit time from a state m into a state m' or vice versa i s : Wm~m. - 8 l H ^ l m ' ) | 2 / y ( 2 2) yrtiere M is the magnetic moment operator and^Svis the energy density of the 1 I radiation field in a range of frequency 5X centred on the transition frequency V, For the quadrupole system the nuclear magnetic moment is parallel to thev angular momentum ?, and so v |(m |li | mi) | 2 - |(m|t|m»)| 2 , (23) Then |(m j ? | m')| 2 can be expressed as the sum of the squares of the matrix elements of the vector components 1X) I y , I 2 . Since the matrix elements for and ly are equal, while those for I z vanish, we obtain, remembering that |* - a |- 1, ^ ^ ^  ^ 2 _ ^ 2/ 2j2 J^kj 4. 2.) - mmTJ (2U) Combining equations (2U) and (22), we finally obtain Wm~m« ° (kTr3jJ/3h2I2){I{I+ 1) - WL*)fy (25) 2. Electronic structure of molecules and nuclear quadrupole coupling constants In order to calculate i^y/dz 2, the distribution of charges in the molecule must be known. An accurate calculation requires a determination of wave functions for the electrons; an approximate calculation is made from structural considerations because 4pV/&z2 = q depends on a few simple para-meters of bond structure. If q is calculated or estimated, and the nuclear quadrupole coupling is found experimentally, the value of the nuclear quadru-pole moment can be determined from Q (cm.2) = 13.8 x lCT 1 2 eQq (no.) (26) <j(e.s.u.) In any calculation of q, only the contribution of the valence shell need be considered. The effect of nuclear and electronic charges outside the valence shell in the remainder of the molecule is negligible. (One electronic charge at one angstrom contributes 10^ e.s.u.). An s-type orbit or any closed shell of electrons around the nucleus i3 spherically symmetric and hence gives no contribution to q at the nucleus or to the variation of energy with nuclear orientation. Polarization and distortion of this closed spherical shell of electrons can occur without an appreciable effect on the value of q. / The largest contribution to q is from the p-orbitals in the valence shell; the value of q at the nucleus depends mainly on the way in which these orbitals are f i l l e d . The shared electronic charge of a pure covalent bond can be divided equally between two atoms and q can be calculated as though one electron of the shared pair existed in the atomic orbital of each atom. Vihen bonds are partially ionic in character, the electron shell of each atom is partly closed and the coupling reduced because q from the other ion is much less than that of a p-electron in the shell itself. Electrons in different atomic orbitals have widely different couplings. For this reason, hybridization of a p-state bond with an s-state bond will increase the value of q, while hybridization with a d-state bond will decrease the value of q. Resonance between different 10 covalent.structures, which occurs in the aromatic carbon compounds, may result in an increase in q and the quadrupole coupling constant. The wave function \£ for one valence electron outside a closed shell can be expanded in terms of the atomic wave functions Ynlm* ^ - S a ^ Y o l m <27)J.-nlm , where a p^ m is largest for lowest allowed values of n and jt, and the axis of the molecular bond is chosen as a reference direction for the magnetic quantum ; -'a numbers. |J' Since . »2(e/r) = (3 cos2© - 1) e/r3 , (28) where © is. the azimuthal angle with respect to the bond axis, i t follows that £ ? = e / cos2© - l)\j> dX (29) *z 2 J j3 Inserting the series expansion for \^ , gathering terms, and using the simpli-fying notation r <tolm,n'l«m» "With* (3 cos2© - 1) V n n f m , dT, (30) we have: i f l = lajQjul2 qnim + , 2 . Snlm ^ 'I'm* ^nln.n'l'm' <31) ^B2' n3^ i * nlm,n,l,m' ' where the quantities ^ni^nim are the values of d2V/dz2 for each of the atomic states and are multiplied by I a n l m | 2 > "f^ie coefficients of the respective atomic states in the molecular wave function. Except that for 1-C, qnQm= 0, is a rapidly decreasing function of n and J?. The second sum includes only those terms for which n f n 1 and and for which m = ra1, and either £ 0 or -l* 22 (otherwise q^m ti'I»m' w o u l d 0 6 zero). The calculations of Townes and Dailey (19U9) show that an accuracy of 10? can be obtained when the second sum of equation (31) is neglected. Then the value of q due to a single valence electron is regarded as a sum of contri-butions I anlal 2 Silm ^ r o m the various atomic states. Moreover, i f the lowest energy atomic state is a p-state, contributions from other states may be neglected. When hydrogen-like wave functions are substituted for the Vnln* the value of q^^ for the case of -I perpendicular to a (m = 0) is %10 " 2>2U x 1(1+1) e.s.u. (32) Z1 (2/+l)(2^-1)(2^+3) The fine structure splitting h\* which arises from -c. s coupling is known for most elements. Values of AV , expressed in cm."-'-, have been compiled by Moore (19U9). In the approximation in which only p—electrons are considered, q * * f v » -C(Nx + ^ ) ( i < l n , l , l ^ ^ % , l , - l ) • N, q ^ o ] (33) where 1^, Ny, and N z are the numbers of electrons in the p^, Py, and p z orbits respectively. Since q ^ i ^ i " ^ ,1,-1 = ~ 9*1,1,0 > then q « t ( Nx + %)/2" - Na] qmo s Up qmo C3U) where Up is the number of unbalanced p-electrons and q^Q is the contribution per unbalanced p-electron given by 2.98 x 10^ e.s .u. from equation (32). • Z» The evaluation of Up depends upon the nature of the chemical bond formed by the atom considered; this can be determined from such data as dipole moments, bond energies, bond angles, and the electronegativities of the ,atomsj v The sign of q will be negative for an excess of electrons along the z-axis .and positive for a deficit along this axis. As an example, for a halogen atom forming a single covalent bond to complete it3 octet, Na = 1, Njj. l- N y •» 2', and U » + 1. S • P 32. 3. Theory behind the method of detection , .  i, The expression for the classical quadrupole interaction energy derived in section 1 is Eq * £ eQq (3/2 cos2© - l/2). The dependence; on the angle © causes a torque which tends to align the nuclear and molecular, axes. The -nuclear spin I will respond to this torque by a precession around the z4-«xxs cThe diagram demonstrates how the components of the magnetic dipole }*- and the electric ,quadrupole moment eQ of the nucleus accompany the precession, of the spin Diagram 2 One half of the nuclei precess as illustrated, the other half with I_ reversed. Z Although the orientation energy is determined by the nuclear quad- \' rupole interaction with the electric field gradient, the observed transitions between energy levels are induced by the interaction of the magnetic dipole moment of the nucleus with the alternating electromagnetic field. The coupling of the elegtric quadrupole moment with the radiation field is too weak to induce observable transitions. The transitions are therefore magnetic dipolar and the dipole selection rule Am » ±1 applies. When the frequency of the radiation field is equal to the precession frequency of the magnetic dipole, the quadrupole system absorbs radio frequency energy frcm the field. Near resonance the nuclei precess with phase coherent with that of the radio frequency field. Half of the nuclei of one energy have I z reversed with respect to the I z of the other half. These two sets of nuclei precess in opposite directions, and therefore near resonance a pulsating mag-netie moment is induced parallel to the radio frequency field. There is no moment perpendicular to the field because the contributions of theytwo 'sets of nuclei cancel. The pulsating magnetic moment M = (M' - jM'^eJ**^1 is not necessarily in phase with the radio frequency field K • . !•< Its macro-; scopic effect can be described by the complex magnetic susceptibility ' i V X-K - jC- ; , . '(35i H v 1 ' . where fa is the susceptibility related to absorption and /U1 the suscept-i b i l i t y for dispersion* When the energy of the radiation field'is removed, the pulsating magnetic moment decays exponentially with the spin-^spin relax-ation time T2. "' The pulsating magnetic moment absorbs radio frequency energy from the sample c o i l , and can induce a radio frequency voltage in the same coil; the absorption effect i s sometimes seen alone, sometimes accompanied by the inductive effect. When absorption occurs, the impedance jl</0+ r of the sample coil becomes jLcoQL + h7T( id- j/lCOj + r = jL (1 • liir^)U> + (r + lifr^Lu)) ' (36) and its quality factor Q «» Lu)/r becomes such that (l/Q*) - (1/Q) + hT)L"* UfT(X'/Q) (37) •If Q is sufficiently great (from 100 to 200) the expression simplifies to a term in : .. d(i/» - kvrxf —> d Q . ^ T r x V (38) The voltage which is induced by the residual magnetic moment is proportional to M and therefore to ( X. -¥J^) 5 ; the inductive effect produces, in passing through the resonance, a curve resulting from the combination of absorption and dispersion terms. The energy absorbed per cycle of the radio frequency field is <$>U.d$ - X-H/sin2<p (39) where £ = f i l l i n g factor of the sample coil and (j) = (H^^z), the angle between the field direction and the bond axis. . The total energy absorbed for a line is proportional to / XiF).dF, (UO) the area under the absorption curve X^(F). Thus i t is seen that the amount • •'. i of radio frequency energy absorbed by the system of spins is measured by tile S .. . J variation dQ of the coefficient Q of the sample coil, : 1 ' i 15. U. Theoretical aspects of the Zeeman effect The quadrupole transitions take place in general between two degen-erate energy states corresponding to i . and t (m2 •»• 1). The energy of interaction of the nuclear magnetic moment with a static magnetic field is dependent on the sign of the quantum number mz; such a perturbing interaction has the effect of l i f t i n g the degeneracy of the unperturbed energy states. The energy term is E -I (UD where H • magnetic field vector of magnitude H. I = spin vector of the nucleus The Larmour frequency is the frequency of nuclear precession in the field H, and is related by: Using equation (U2), we obtain E = - K (I.H) H (U2) (U3) The pattern of the Zeeman effect depends upon the relative orienta-r tion of the electric field axis and the magnetic field. For a field in the xz plane, the perturbation operator is H* -M^) • -Jb& (Ix sine • I z cosG) - - y j l x sine + I z cos©) I where e « (H,z) is the anrle between the magnetic field and the z-axis. the case of spin 5/2, the perturbation matrix is given below, where a » (hh) For - yLsin© and b = - y'-^ cos©. 5b JTa 0 0 0 0 11 ' = 2 JTa 3b J8"a 0 C 0 0 J(3 a b 3a 0 0 0 0 3a -b J8 a 0 0 0 0 JIT a -3b J5"a 0 0 0 0 J T a -5b (U5) 16. The perturbed energies to second order in H* are *m = \ • "mm' • 2 * <W n Em " En • . \ where the prime on S denotes the omission of the term n » m from the summat-ion, and the unperturbed energies ^ are: E±5/2 = eQq , • E*3/g- ~ " e Q q ' E+l/2 = ~ eQq (U7) When the unperturbed state m is degenerate with state k, equation (li6). w i l l hold only i f Hj^ 1 is zero and the degeneracy between the states k 1 and m is removed in fi r s t order. This is so for m = 5/2, k = - 5/2 and m = 3/2, k » - 3/2. However, for m » l/2, k « - l/2, % ' 1 - HJi 1 jfrO. In this case i t is only necessary to diagonalize the submatrix Hjnm ^ak Hkm H, (U8) •kk "before calculating the perturbed energies. The diagonalized submatrix is + 1? 0 o - n 9a£ and the perturbation operator is /5b J ^ a 0 H' ="K 2 0 0 0 0 0 0 0 0 JTa 3b J3" a 0 0 /8~a J9a2+b2 0 0 0 0 -JlJa^+b2 JTa 0 0 0 (8"a -3b J T a j \0 0 0 0 /Ta -5b/ Using equation (U6), i t is now possible to obtain the perturbed energies from the above matrix (k?) s (1*9) 1 Wt5/2 = ^ h e Q q " 5 / 2 fe c o s 0 + 2 * / 7 ^  s i " 2 e eQq Sf3/2 = " " 3 ^ 2 * c o s 6 * n ^ / ? n 2 y L 2 sin 26 eQq W+1^ 2- « - ]/5 eQq - V 2 V ^ l J c o s 2 © t 9sin2© - 20 n 2 V L 2 sin2© eQq W-l/2 " w VS eQq + fc/2 Vj, J c o s 2 © -t- 9sin2© - 20 n 2 V L 2 sin2© eQq W-3/2 " " VlO eQq + 3/2 t V L eos© • 115/7 n 2 V L 2 sin2© eQq w>^/2- = 1/U eQq -f 5/2 n ) ^ cos © + 25/7 n 2 V L 2 sin2© eQq For the (J3/2|<—*fl/20 transition we obtain the frequencies of transition: 17? (50). VV3/2«->l/2) " VlO eQ^ - 3/2 y L cos e + K jcos29 4 9sin2© + 255/ l^sin 2© . * • 7 ( e Q q A ) (51) y(_3/2«-*-L/2) = " 3/2 c o s e • >^-|cos2©^9sin2© + 255 >j 2sin 2Q * 2 7 (eQq/h) (52) The four lines which separate in pairs from the unperturbed resonance line V0 are symmetrical with respect to this line and separated from i t by ±A)^= i ^ i f e cos© - (cos2© + 9sin2©)^] (53) for both & - © and © - ?T-©. The last term in equations (5l) and (52) can be neglected for fields of about 100 gauss. There are two special cases which can be treated, for H parallel to * the electric field axis and H perpendicular to the electric field axis. Case 1. H parallel to the field axis: © • 0, cos © - 1, sin © - 0 For the (3/2 *—*• 2/2) transition, there will be only two lines instead of four separated by Ay>» 2V^. For the (5/2 3/2) transition, the two perturbed lines which always appear for this transition are separ-ated by Ay's 2 V^. In general they are separated by AV. 2'^ cos ©. Case 2. H perpendicular to the field axis: 0 aTT/2, cos 9-0, sin © • 1. Only the state | ra^. | - \ is split and the (3/2 l/2) line becomes two lines separated by AV _ 3 V^. In a polycrystalline sample, the line is smeared out when the Zeeman splitting is greater than the line width. • For I 1 2? in Ig, the line width is approximately I4O kc. The least splitting which occurs for any angle is 2V L. Since/^j/l for the iodine nucleus is 0.8565 kc., the field necessary to cause this line to disappear completely i s about 25 gauss. CHAPTER II The superregenerative oscillator 1. The superregenerative oscillator in theory when oscillation conditions are established for the vacuum tube oscillator, the envelope of the oscillations rises exponentially until i t is limited by non-linearities in the circuit. In a superregenerative oscillator, the vacuum tubes are switched on and off by applying a periodically varying bias to the gridj during the off period.the oscillations in the circuit decay exponentially. The period length of the "quench" voltage, as i t is called, is about 10 times as long as the decay time constant of the tank circuit so that the voltage across the tank circuit will be reduced to the order of thermal noise voltages before the tube i3 switched on again. The tube is left on long enough for the oscillations to level off at the saturation amplitude Ujaax* ^ n e time which is necessary for the oscillations to build up to this value depends sensitively on the minimum amplitude Uj^in. ' • If any signal is present in the tank circuit at the moment the oscillator is switched on, the oscillations build up from this rather than noise, and' reach the limiting amplitude sooner than i f this signal were ' •absent. Thus the additional e.m.f. at the oscillation frequency ZiU which the signal represents can cause the time average of the oscillation amplitude to change. Any modulation of this small additional potential will appear as \, a change in this time average, which can be detected. The superregenerative oscillator circuit functions also as a very high gain amplifier; The smoothed output from the osoillator is a greatly amplified reproduction of the ampli-tudes present in the tank circuit at the start of oscillations. The three operations, oscillation, quenching, and detection, can be .performed by three separate vacuum tube circuitsj or by using a class C o s c i l l -ator, the same tubes can oscillate and detect. In the "self-quenching" o s c i l l -ator a l l three functions can be performed by the same tubes. When a sample is placed in the tank coil of the superregenerative oscillator, the nuclei absorb energy from the tank circuit at the resonant frequency, lowering its Q, and causing the build up time for oscillations to be lengthened. During the period of strong oscillation following the bnild up, the nuclear spins precess coherently with the applied oscillations. When the oscillator is turned off, the processing nuclei continue precessing and induce a voltage in the tank circuit which is additional to the minimum amplitude Djoin that is reached during the cut-off interval. This voltage falls off exponentially with the characteristic spin-spin relaxation time T2 of the substance. The oscillations of the next quench period can start up from the voltage which the precessing nuclei induce in the tank circuit during the low oscillation interval of the previous quench cycle. This radio frequency voltage is given by , AU = - UrXQ«*Unax ,(5U) ] where Q is the quality factor of the tank circuit ' ' I r and oCis a factor less than unity to account for the pulsating(character of the radio frequency field exciting the nuclei. , * ' The line shape of the abscrotion lines depends upon the phase relation between 1 1 . AU and U ^ . . ; . ' It is thus seen that the quench period must be long compared with the build up time of the oscillations and the decay time constant of the tank circuit, but not so long compared with the spin-spin relaxation time. The \ relaxation time must be such that the duration of the signal from the sample '." is comparable to the period of the quench voltage. If T 2 for a substance is too short, thetquench frequency cannot be chosen to satisfy both these condit-ions, and the resonance can not be detected on the superregenerative spectrometer. By assuming a perfect square-wave quenching voltage, Van Voorhis (19U8) obtained an expression for the'gain in the superregenerative oscillator circuit: G = * q Umax 2I/Rt ^  (V n + V s)/V n (55) where f = quench frequency " j L a tank coil inductance Rp = net series tank resistance = R + Rj^  R « series loss resistance of tank circuit Rjj = negative series resistance representing the regenerator tube V n = noise voltage, at instant that oscillations start V = signal voltage at instant that oscillations start The gain in this case can be as high as lO^j for a sine wave quenching voltag i t is higher. However, i t is difficult to apply the gain law in the case of sine wave because cannot be assumed constant. The advantages of the superregenerative oscillator are: (i) It has a high gain with few tubes. This is important in the region 100-U00 mc./sec. where radio techniques are difficult. (ii) It develops a high radio frequency power with relatively l i t t l e noise. In the substances to be investigated there is almost no chance of saturating the resonance, so that the large output is very useful. Its principal disadvantages are: (i) It is sometimes tempermental and erratic and adjustment is cr i t i c a l . (ii) The detection is dependent on Tg; therefore the spectrometer is limited in the substances which i t can be used to investigate. < ' ;' 2?. 2. The superregenerative oscillator in our quadrupole spectrometer • In our spectrometer, the superregenerative oscillator uses two acorn triodes in a tuned anode, tuned cathode, grounded grid push-pull circuit (see figures 1 and 2). The oscillation frequency is essentially determined by the resonant frequency of a lecher wire system in the anode circuit; the lecher wire system in the cathode circuit has a smaller effect on the frequency. However, for oscillation to take place, i t is necessary that the cathode circuit be inductive at the frequency of oscillation. Proper adjustment of the oscillator is attained by proper selection of potentials applied to the electrodes of the tubes and of the quench voltage and frequency. A sinusoidal wave form was chosen for the quench. The quench oscillator is an electron coupled oscillator with frequency range lf>0 - 2000 kc. when lower frequencies are desired, i t can be used as an amplifier and matching device for an external audio oscillator. The lecher wire system in the anode- circuit gives the oscillator its wide frequency range. It can resonate to the frequency f vtiien its effec-tive length is equal to (n/2 - l/h) A where A. is the wave length corresponding to frequency f. As the length of the line is increased, sustained oscilla-tions are obtained in successive ranges. The cathcde line can usually be adjusted so that i t is indiictive for only one mode of oscillation. When conditions are such that two modes of oscillation are possible, usually only the lower mode is produced because the circuit losses are lowest in this situation. In some cases, however, the circuit may oscillate in both modes alternately by switching modes rapidly, slowly or irregularly. We found this effect to be a major obstacle in developing a satisfactory oscillator. , In the final circuit of the oscillator, the frequency range from 15>G to 600 mc./sec. was covered in the three modes A/U, 3^ -A,\ and 5A./U. The oscillator was calibrated by locating measured frequencies of oscillation on coordinate axes £ a and Jc (the lengths of the .anode line and ithe cajbhode O S C . WAVE F O R M O U T •=• 47 K X - 2 : S IGNAL O U T — 2 V v v v \ 0 5 S C ^ E N 1. A 1 a N O D E \ " /! \ / \ / < IO K 3 . 5 v 4 — W r.f. choke ] •05 l O O K •01 H T - -_ O v -•Ol 10 K 2 2 K 5K K 6 v 3 1 GRID ^ .33 K H 0 5 S C R E E N o i o <a n ro 2 0 K Q U E N C H IN - 2 : IO K W V W F I G U R E I J U N C T I O N B O X F IGURE 2 ] B R A S S P L A T E C O P P E R WIRE F R E Q U E N C Y M O D U L A T I O N B R A S S T U B I N G SUPER - R E G E N E R A T I V E O S C I L L A T O R 2. R F C E X T E R N A L O S C I L L A T O R F I G U R E 3 Q U E N C H O S C I L L A T O R PLATE I to follow page 22 line), and drawing the contours for each mode. The anode lecher wire system is made of 0.120" diameter copper wires with centres spaced l/2* apart. The sample coil, made of the same copper wire, was attached to the anode stub at the tube end of the lecher system. The coil, which had li$> turns of diameter 3/8", was equivalent to about A/8 of the line at the central frequency of the system. It is shown in the appendix that the magnetic field generated in the coil is a maximum in a A/8 coil. The cathode line is of l/8" diameter brass tubes which are spaced 1/2**. The heater wires are passed through the tub©3 to keep the heaters at the same radio frequency potential as the cathodes. A third con-ductor in the neutral plane of each lecher system connects the shorted end of the anode line to high tension and that of the cathode line to ground. Tuning is effected by running a phosphor-bronze shorting bar along the • lecher system. / The signal is, in principle, independent of the quantity of sample, provided the f i l l i n g factor of the sample coil is maximum. The f i l l i n g factor 4 measures the ratio between the magnetic energy contained in the volume of the sample and the total magnetic energy contained in the sample coil. In practice, for a coil solenoidal in form: 5 = volume of sample volume of solenoid An auxiliary oscillator using a 955 tube and a lecher wire system (see figure 12) aided in the adjustment of the oscillator. The lecher wire is loosely coupled to the superregenerative oscillator to provide signals on the oscilloscope which can be improved through selection of the quench fre-quency and amplitude, and the various potentials applied to the electrodes of the oscillator tubes. The adjustment which is obtained in this manner should then be optimum for observation of a resonance at that particular frequency. The side bands of the spectrum have a separation equal to the quench frequency fq. The line corresponding to the centre of the spectrum is easily recognized because i t is not displaced by a slight varia^fcion of f , while the-side bands/are displaced on the oscilloscope screen pattern. 3. A review of the various oscillators used The fi r s t oscillator was the original design of the final circuit and used the 955 tubes. It had three modes of oscillation -tyU, 3A/I4, and 5/Vk and a wide frequency range, from 166 to 700 mc./sec. We were not sat-isfied with the oscillator because we considered the signal-to-noise ratio obtained for known signals to be inadequate in the .search for unknown sig-nals. Minor alterations such as taking the audio frequency signal from the plates of the tubes instead of from the grids had no effect. The tubes were replaced, fi r s t with 6JI4 tubes and then with 9002 tubes. The circuit with 6jlt tubes oscillated on many more modes than the previous circuit, but unfortunately these modes overlapped. It is supposed that resonances could not be observed because of the switching from one mode to another. The only objection to the circuit using 9002 tubes was that fre-quencies as high as UOO mc./sec. and higher could not be obtained. The next oscillator was an experiment in adapting the lighthouse ' tube to a lecher wire oscillator. The lecher wire system was of larger over-a l l dimensions than the system of the previous oscillator. The advantages .were (i) reduction of noise in the circuit due to the greater rigidity of larger diameter wires, and (ii) separation of the plate and cathode circuits due to the construction of the lighthouse tube. The main disadvantage was' that, for a given length of anode stub, only a small frequency range could be covered with the lecher system. " » The original.circuit was reconstructed with-some modifications.. The third conductor was added to the lecher systems to return the direct current 25. from the shorted ends to the remainder of the circuit. The condenser plates for frequency modulation were placed horizontally rather than vertically as they were before. The movable plate of the condenser can be positioned using three screws placed in an equilateral triangle in the mount for the relay coil. The test signals were improved in signal-to-noise ratio. The perform-ance of the oscillator seemed satisfactory for the search for unknown signals. 26 CHAPTER III The various parts of the spectrometer The block diagram of the superregenerative spectrometer is given in figure k. Frequency modulation was used for Yri.de band detection and oscillo-scopic display; Zeeman modulation was used for narrow band detection with the phase sensitive detector and automatic recording. The various parts of the spectrometer will be described individually in this section. 1. Modulation In nuclear magnetic resonance the magnetic field can be modulated around its value Hq at the resonancej in nuclear quadrupole resonance, i t is impossible to modulate the electrostatic field gradient. However, this d i f f i -culty can be avoided by using the Zeeman effect. If i t is preferred to operate in the absence of any magnetic field, the radio frequency excitation can be modulated in frequency. Then a single parameter, the frequency, determines at \ the samfe time the position and shape of the quadrupole resonance lines. > Some mechanical method of frequency modulation is necessary in nuclear quadrupole resonance in view of the line widths involved. The amplitude'of i the frequency modulation must be variable and about 10 mc./sec. maximum. It should be about ]$> of the oscillator frequency and many times the line width. A vibrating condenser operated by a relay coil at 60 c.p.s. has a maximum amplitude of vibration which provides a spread in frequency of 10 mc./sec. The vibrating condenser, shown in side view in figure 7, is connected in parallel to the tank circuit, on the anode lecher wire system. The same unit which drives the relay coil (see figure 5) provides phase control and 60 c.p.s. sweep for the oscilloscope. For Zeeman modulation, a square wave zero—based magnetic field of about f>0 gauss maximum is required. While the field is on, the resonance is smeared out by the Zeeman splitting of the levels and modulation of the signals results. It is important to use a polycrystalline sample; the method would F R E Q U E N C Y M O D U L A T O R Q U E N C H OSC I L LATOR O S C I L L O S C O P E S U P E R R E G E N E R A T I V E O S C I L L A T O R S A M P L E COIL H E L M H O L T Z CO ILS LOW PASS AMPL IF IER 9 DB . F I L T E R 6 0 cps 120 cps AMPL I F I ER 2 0 / 4 - 0 D B . P O W E R A M P L I F I E R A S Q U A R I N G C I R C U I T AUDIO OSC I L LATOR P O W E R P A C K \/ A P H A S E S E N S I T I V E D E T E C T O R R E C O R D I N G Ml LLI A M M E T E R F I G U R E 4 B L O C K D I A G R A M O F N U C L E A R Q U A D R U P O L E S P E C T R O M E T E R 27 of course not work for a single crystal. A field le3S than 5>0 gauss is ade-quate for narrow lines. A circuit to square the output of a Hewlett-Packard audio oscillator and Helmholtz coils driven frora a 10 watt Hi F i Bell amplifier were fi r s t used to provide the square wave fieldj a battery and rheostat served to bias the field at zero. The coils were each 92 turns of No. 26 wire wound on a lucite former to a diameter of 5 cm. and separated by the distance r - 2.5 cm. The total reactance was k ohms which matched the output transformer of the power amplifier. A calculation gives 50 gauss as the maximum field but i t is ex-pected to be less than this. The axis of centres was placed perpendicular to the direction of the axis of the sample co i l . It was soon found that we required & larger separation between coils, and since the design already made the best use of the 10 watt amplifier, an-other method had to be found. A power amplifier (figure 10), in which the Helmholtz coils take the place of the plate resistance of the power tube, was designed and built to replace the commercial amplifier. An automatically biased square wave field was obtained from the coils by applying to the grid of the power tube a square wave input voltage of the frequency desired for modulation. A square wave of 105 volts amplitude was obtained from a simpli-fied version of the squaring circuit, shown in figure 11. A special power pack was designed to provide 2^ 0 volts for the plate and - 70 volts for the grid bias of the power tube. Coils of 3U00 turns of No.'33 enamelled copper wire-each were wound on a lucite former with a separation of 5 cm. A frequency of U07 c.p.s. was chosen because this is the minimum frequency left unattenu-ated by the low frequency f i l t e r and i t is not a simple multiple of the mains frequency. A square wave field would be more easily produced at lower frequen-cies because of the time constant of the coils. Because of the large induct-ance of the coils (~S henries), the field was measured to be only 13 gauss. The advantages in the Zeeman method of modulation are: (i) No previous knowledge of the line width is necessary to obtain optimum modulation efficiency. (ii) Response to spurious signals is greatly reduced. There i s , however, one difficulty: "pick up" of the modulation frequency is enhanced. The signal can be observed on the oscilloscope as well as on the pen recorder. The picture will show one half of the noise appearing higher on the oscilloscope than the other half. 2. Frequency sweep apparatus In wide band search for known signals, manual variation of the frequency was used. Fine adjustment was obtained from a rotating condenser in parallel with the anode line. During automatic recording, the speed at which the resonant fre-quency is swept over should be determined by: (i) the line width of the resonant absorption (ii) the time constant used in the detecting apparatus. . For automatic recording of signals a sweep linear with time is , required. The lucite sector illustrated in figure 8, which has a radius of 6.3 cm. and an angle of 75°, was inserted between the anode lecher wires and was driven by a clock motor having a speed of 3 revolutions per hour. This arrangement gave a sweep very close to linear. However, i t was. useful only i1 until the length of the anode line became too short at the higher frequencies of the oscillator. j The length of the anode line could be varied at a constant speed t using a D. C. motor. The speed of a l/lO H. P. motor was varied with'a ' rheostat and reduced by a factor of 300 with a gear reductor (see figure 9). The worm gear and worm arrangement had a drive of 0.12 cm./min. minimum and 3. U3 cm./min. maximum. Alternatively, at a right angle to this drive, a 3 foot threaded shaft produced a drive of 0.016 cm./rain. minimum and 0,k$7 cm./min. maximum. G L A S S o o" L E C H E R WIRES F I G U R E 7 R E L A Y CO I L 8. V I B R A T O R L U C I T E O 110 v D C F A S T I O O O 1 0 0 W 1A 1/10 H P M O T O R F I G U R E 8 S H A P E O F L U C I T E S E C T O R SLOW S P E E D R E D U C T O R W O R M 3 0 0 " . I G L A S S R O D R U B B E R T U B I N G m W O R M G E A R LUC ITE SPACER-S T E E L R O D BRASS CYL INDER T H R E A D E D S H A F T F I G U R E 9 F R E Q U E N C Y S W E E P A P P A R A T U S N U T to follow page 2 8 The lucite rod attached to the shorting bar was replaced by glass when these drives were used because the flexible lucite buckled and caused abrupt frequency changes. Connections were made from the motor shaft to the glass rod with rubber tubing. Then the drive was smooth and did not add < appreciably to the noise in the circuit. $ 3» Filtering and Amplification • Essentially only the higher harmonics of the modulation frequency are necessary to produce a strong line on the oscilloscope. Fourier analysis of the wave form of the signal shows that the important harmonics are those whose frequencies are about l / t t where t is the duration of the signal as the oscillator sweeps through i t , usually the higher harmonics. Therefore, the unimportant lower harmonics can be removed before the last stage of amplifi-cation. A slight amplitude modulation occurs as a consequence of the 60 c.p.s. frequency modulation, which is carried by the 60 c.p.s. and 120 c.p.s. components. For these reasons, a f i l t e r was designed to attenuate frequen-cies below hOO c.p.s. and present infinite attenuation to the 60 c.p.s. and 120 c.p.s. components (see figure 6). The amplitude modulated radio frequency voltage which is taken from the oscillator across the tank circuit is fed into a low pass amplifier having a gain of 9 decibels and falling off sharply at 3000 cyles-. The quench frequencies used are thus removed completely. The amplifier output passes through the f i l t e r to another amplifier which has two levels of ampli-fication, 20 and hO decibels. The signal which is directed to the phase sensitive detector is again amplified before i t reaches the Schuster circuit. h. Phase sensitive detector, noise liaiiter, and d.c. amplifier The phase sensitive detector (figure lit) is basically the Schuster circuit described in Review of Scientific Instruments (1951). The input signal at the grid of the pentode produces a plate current i » g^ eg ; the reference voltage applied to the grids of the switching tube 6SN7 determines through which of the two 50K plate resistors the current will travel. It alternately cuts off one half and causes the other half to conduct. The grid resistors limit the grid current and maintain the grid to cathode potential at a small positive val-ue during the "on" period of the tube. The 2yM.fd. condensers prevent the plates of the 6SN7 from returning to H. T. • during the eoff period.. The "lock in" effect is obtained at high reference volt-ages; that i s , a threshold effect is added to the intrinsic antiparasitic quality. If e, the signal voltage, and E, the reference voltage, are such that (e/E) 2«l, the "direct voltage output U is of the form » U - 2 k.e.cosif (56) where is the phase difference between the two voltages and k is the gain of the detector. The direct voltage output U from the plates of the 6SN7 tubes is fed to a d.c. amplifier through appropriate R. C. elements which limit the band pass for noise. The direct current between the plates of the 6SN7 amplifier tubes is recorded on an Esterline-Angus recording milliammeter. An overall sensitivity of lOO^a./mv. was achieved for the detector. The effective noise band width is approximately the reciprocal of the time constants of the R. C. elements, which were 0.5, 1.0, and 3.0 seconds. The noise band limiter does not attenuate the signal since the signal has essentially a very small frequency band width centred on f - 0, provided the frequency sweep is slow. 115 v AC 0-5 5 0 , K 4 7 K 4-IK h> 2 5 0 v 10 6 3v >3-3K •1-5 RELAY COIL 3 E.,H.T.-X- S W E E P ON C R l-5K> 1 0 0 K T PHASE CONTROL FIGURE 5 FREQUENCY MODULATOR TUNED TO 120 cps TUNED TO 6 0 cps FIGURE 6 F ILTER FOR VERY LOW FREQUENCIES ( < 4 0 0 cps) 5 0 henries 2. P O W E R A M P L I F I E R P O W E R P A C K 5 •o •a F I G U R E 10 P O W E R AMPL I F I ER DRIVING T H E H E L M H O L T Z COILS O FIGURE II SQUAR ING C IRCU IT F IGURE 12 AUXIL IARY O S C I L L A T O R IN 5 0 K •09 H - 0 9 H 5 0 0 K -vWv-50C P< 5 0 0 IOOO > 100 K -z= 5 0 0 pf 5 0 0 2 5 0 v OUT ! / 2 6 S L 7 GT '/2 6 S L 7 GT N U L L F R E Q . 18-6 Kc. '/2 6 S L 7 GT '/2 6 S L 7 GT N U L L F R E Q . 7-75 Kc. F I G U R E 13 LOW PASS A M P L I F I E R X lO K HAMMOND 9 3 3 2 5 K 16 B A L A N C E 2 0 K Z E R O A D J U S T M E N T - 3 0 0 v R E F E R E N C E IN •01 3 3 2 t 6 8 0 K w <—<; 2 2 0 K 5 0 K < 5 0 K 5 M 2 0 K IOK S S I O K 2 5 0 K 4> 1>. 6 C 4 5 0 0 ' 7 4 0 4 0 3 9 0 i< O (M 6 S N 7 J 5 M -r-4 0 3 3 0 K •5 1 3 S E C O N D S UJ Q -X O O UJ i f ! 4 0 6 S N 7 3 8 0 K T I M E ' C O N S T A N T P H A S E SHIFT 2 0 4 , 0 K ° 6 S J 7 AMPL I F I ER D C - AMPLIF IER o T3 O (O OJ O 6 9 K' O l S IGNAL G II— IN 1 1 4 7 0 K< .Q5 6 A C 7 ~~1 , 160 > ^ 2 5 T ' FIGURE 14 PHASE SENS IT IVE D E T E C T O R The Auxiliary Equipment The Tuning System PLATE II to follow page 30 CHAPTER IV RESULTS. AND DISCUSSION 1. Performance of the spectrometer on known signals The behavior of the oscillator was studied by testing i t with samples which gave previously known resonance lines. By using various sam-ples, we hoped to ascertain the .frequency range over which the oscillator gives satisfactory performance. We also studied the effect of lowering the temperature by immersing the sample and th^ e sample coil in a liquid air bath. A stronger signal should be expected since, by cooling the sample, we are in-creasing the difference in the populations of the different levels. Contrary to what was expected, we found that the signal was either decreased in strength or else could not be relocated after the cooling. It is most likely that dew or frost on the lines causes a large dielectric loss, a situation which is difficult to remedy. About twenty different samples were prepared and tried, but reson-ance lines from only four of these were recorded on the Esterline-Angus. Searching for resonances in the samples which had melting points at liquid air temperatures was abandoned because of the trouble encountered whenever the oscillator coil is immersed in liquid air. The five signals in the four sam-ples ranged in frequency from 16U.5 to 332.h Mc./sec. The data collected on each signal for critical conditions with Zeeman modulation is displayed in the table below. The signal-to-ncise ratio for the same signal with fre-quency modulation is also given, although the conditions for resonance some-times change slightly from one method of modulation to the other. The lucite sector was used in sweeping the frequency for the f i r s t three samples, while the tuning system shown in plate II was used in order to sweep through the 127 l-LCi signal in Ig-. Photographs of the recordings are given in plates III and IV. , 32. Sample Nucleus Resonant freq. mc. Quench freq. kc. Quench amplitude Signal-to-noise SbBr3 Br 7 9 l6h.5 119 39$ Eico 80^ internal 300:1 3:1 Ba(Br0 3) 2 Br 7 9 17b. 6 U48 hZ% Eico 50% internal 150:1 Snl u J127 207.6 209.1 lUS $1% Eico $0% internal 150:1 200:1 20:1 '*2- ll27 332. U 129 8l£ Eico 60% internal 500:1 6:1 These signal-to-noise ratios are as good as any which have been reported by other workers, e.g. Dehmelt (195U). 2* Performance of the spectrometer on unknown signals' When the performance of the spectrometer on the test signals was found satisfactory, we decided to investigate some compounds which were of interest to the low temperature studies in connection with Pound's method of nuclear alignment, and in which no quadrupole resonances have yet been reported. The iodine atom covalently bonded to aromatic carbon atoms in iodo benzene sulphon-ate salts was of particular interest. Rollin and Hatton (195U) have estimated the resonant frequency of I in this compound to be 280 Mc./sec.j i f the quadrupole coupling were this large, then the compound would be suitable in this respect for nuclear alignment, A sample of the magnesium salt of p-iodo benzene sulphonate was ob-tained from the low temperature laboratory and carefully studied from about 250 to 3U0 Mc./sec. making adjustments in the circuit at every few megacycles. to follow page 32 PLATE I? to follow page 32 33. In order to purify the sample, which was found to be 10% pure by chemical anal-ysis, i t was recrystallized from water. Neither the polycrystalline sample nor the small single crystals gave a resonance line with either method of modulation. Eollin investigated this substance in 1953 and did not see a line (unpublished). This result can be attributed to ionic interaction with impurities which could decrease the spin-spin relaxation time, and make the detection impossible. Plate V shows the benzene sulphonate structure; meta-, ortho-, and para-iodo denote different substitutions of the iodine atom on the benzene ring in this structure. Since the above result with the para compound does 127 not eliminate the possibility of an I resonance in the other "Cwo compounds, a sample of sodium meta-iodo benzene sulphonate was prepared in the laboratory from metanilic acid by Sandmeyer's reaction. It was investigated for a reson-ance over the same frequency range and again no signal was detected. A set of complex compounds containing iodine, in which the bonds are expected to be covalent, were prepared: K^Hgl^, K^gl^, Kgfinl^, I^Snl^. The reactions were: HgCl2 + 2KI -> Hgl 2 followed by Hgl 2 • 2KI KgHgl^. 2 Group theory shows that a dp s combination is possible for the tetragonal bond-ing in these compounds. By a consideration of the bonding orbitals and a com-127 parison to those in the covalent I 2 bond, we estimated the I resonance to be about 350 l.ic./see. An investigation was made in this region and also around 175 Mc./sec, but without results. The failure to observe an iodine resonance in these compounds is at least consistent with the fact that the chlorine res-onance in K2PtCl£ cannot be seen. KgPtCl^ in solution is known to break up into K4", Pt^ +, and CI ions, which suggests that the molecular complex is dis-torted rather than moved bodily. The resulting crystal strains may cause a spread in the values of the field gradient at the site of the iodine nucleus and broaden the lino to the extent that i t is unobservable. H. E. Petch and N. G. Cranna, Investigating a milky sample of spodumene in this laboratory, have seen a similar effect. The quadrupole satellites of the H. M. R. line could not be found, although easily oisSiErved in other samples. Probably crystal imperfections cause a broadening of the lines as described above. ^ n « n 3 C / . * ? i r , ? . *• P I •* s PLATE V Photograph of crystallographic data on the benzene sulphonates to follow page 33 APPENDIX Design of the sample coll for maximum field intensity The energy stored in the magnetic field of the coil is distri-buted throughout the field with a density U a ^yitH2 joules/meter. The energy density of the magnetic field can also be derived by calculating the work done in forcing the electrons of the current against the opposing electromotive force e «• Li/t. D - q.e - £ i . t x Li/t - § L i 2 joules {$!) Diagram 3 illustrates (a) the transmission line and (b) the equivalent circuit with a coil of inductance L. 4> 1 <g V o L I > (a) (b) Diagram 3 For the equivalent circuit we have: V = E sin 27ll (£8) \ and i « E cos 2ffl (£o) The impedance of the coil of inductance L is X - U)L - Zq tan 2T& (6o) A Therefore, L = Z0\ tan 27TX 277c" X ' 'i Then L i 2 - Zg\ tan 2/7j^ . e£ cos 2 ZTtt (62) 277c" A Z 2 * > !'• 1 * ' • ' ' ' " ' ' I ' Simplifying, we find L i 2 oC Asin kTlt . ' • ' i (63)' \ • » J . Equation (63)' shows: 5' j, (i) that more energy is stored in the magnetic field at the lower frequencies of oscillation. (ii) that the quantity L i 2 is a maximum •when sin klfi. - 1, i.e. when £• = ^ /8. It is thus seen that the inductance of the sample coil should be equivalent to a length A./8 of the transmission line i f the field and energy density in the coil are to be maximum. BIBLIOGRAPHY i t (1) Bloembergen, N., Purcell, E. M., Pound, R. V., Phys. Rev.,1 t|, 679 (19UB): (2) Buyle-Bodin, M., Ann. de Phys., 10, 53b (1955) « (3) pean, C, Phys. Rev., 96, 1053 (195b) (h) Dehmelt, H. G., Zeits. f. Phys., 130, 356 (195l) (5) Dehmelt, H. G., Zeits. f. Phys., 130, U80 (195l) (6) Dehmelt, H. G., Phys. Rev., 92, 12U0 (1953) .(7) Dehmelt, H. G., Am. Jour. Phys., 22, 110 (195b) (8) Dehmelt, H. G., and Kruger, H., Zeits. f. Phys., 130, 385 (195l) (9) Dehmelt, H.,G., Robinson, C. W., Gordy, W., Phys. Rev.', 93, b30 (195U) ; (10) Gordy, W., Smith, W. V., Trambarulo, R. F., Microwave Spectroscopy, John Wiley and Sons, Inc., New York, 1953. (11) Haissinsky, M., J. Phys. Radium, 7, 7 (19b6) '(12) Kruger, H., Zeits. f. Phys., 130, 371 (1951) (13) Kruger, H., and Meyer-3erkhout, U., Zeits. f. Phys., 132, 221 (1952)-(lb) Pound, R. V., Phys. Rev., 76, lblO (19U9) . (15) Ramsay, N. F., Nuclear Moments, John Wiley and Sons, New York, 1953. (16) Robinson, C. W., Dehmelt, H. G., Gordy, W., Phys. Rev., 89, 1305 (1953) (17) Rollin, B. V., and Hatton, J., Trans. Faraday Soc., 50, 358 (195b) (18) Schuster, N. A., Rev. Sci. Instrum., 22, 25b (1951) (19) Shimomura, K., Kushida, T., Inoue, N., Imaeda, Y., J. Ghem. Phys., 22, 19bb (195b) (20) Townes, C. H., and Dailey, B. P., J. Chem. Phys., 17, 782 (19b9) (21) Van Voorhis, S. N., Microwave Receivers, vol. 18, M. I. T. Radiation Laboratory Series, McGraw-Hill, New York, 19b8. (22) Whitehead, J. R., Superregenerative Receivers, University Press, Cam-bridge, 1950. (23) Wyckoff, R. W. G., Crystal Structures, vol. I, II, III, Interscience Publishers, Inc., New York, 1953. ;' ' '' 


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