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A nuclear quadrupole resonance spectrometer Fulton, Beverley Joan 1956

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A NUCLEAR QUADRUPOLE RESONANCE SPECTBOHETER  by BEVERLEY JOAN FULTON 1  B.A., University of British Columbia  A Thesis submitted l a partial fulfilment of the requirements for the degree of Master of Arts i n 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 alignment and nuclear specific heat, a spectrometer has been developed i n order to investigate the hyperfine structure of compounds with suitably large quadrupole coupling by the technique of Nuclear Quadrupole Resonance.  The auxil-  iary equipment which was built i n addition to an externally quenched superre- • generative oscillator provided-for frequency modulation and oscilloscopic display as well as Zeeman modulation and chart recorder display. The superregenerative oscillator has a frequency range of 1!?0 - 600 Mc./sec., which i s the range required for investigation of the compounds concerned 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*^ i n Snl^, I2, Sbfirj and BaCBrO^g. Using the spectrometer, a search was made for resonances i n 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 s u l phonate since we knew from theoretical investigations the approximate frequency 127 at which the I  1  resonance occurs. A possible explanation i s given for the  failure to detect any such resonance.  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the requirements f o r an advanced degree a t the  University  of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may of my  be granted by  Department or by h i s r e p r e s e n t a t i v e .  stood that  Head  I t i s under-  copying or p u b l i c a t i o n of t h i s t h e s i s f o r  f i n a n c i a l gain  s h a l l not be  allowed without my  permission.  Department of  EH2SICS..  The U n i v e r s i t y of B r i t i s h Vancouver Canada. D a t e  the  riF.OFMBfifi, 1956.  Columbia,  written  ACKNOWLEDGBfflJTS  I f i r s t expressrayappreciation 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 i n 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 i n 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 i n this research.  I acknowledge the receipt of  (195U-55) and a Studentship (1955(1955 and 1956). The research has been  a National Research Council Bursary  56) and summer  supplements  supported by a research grant to the Low Temperature Laboratory for the study of hyperfine structure.  iii.  TABLE OF CONTENTS page INTRODUCTION CHAPTER I  •  1  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 i n theory 2. The superregenerative oscillator i n our quadrupole spectrometer  19 22  s  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  ••••  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  F i l t e r 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  2 2  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  (a) Photograph of the Auxiliary Equipment  30  (b) Photograph of the Tuning System  30  (a) The I  1 2 7  32  (b) The I  1 2 7  Plate II  Plate III  Plate 3V  Plate V  3ignal i n I  2  signal i n Snl^  32  (a) The B r  7 9  signal i n SbB^  32  (b) The B r  7 9  signal i n BafBrt^)?  32  Photograph of crystallographic data on the benzene sulphonates  33  INTRODUCTION  Electrostatic interaction between the nucleus and i t s surroundings can occur through the electric 2^-pole moments of the nucleus  U  a  2,U)j the ;  interaction of the quadrupole moment with internal electric fields i s called the nuclear quadrupole coupling.  The quadrupole moment i s a characteristic  of the particular nucleus and i s 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 various orientations of the nucleus with respect to the axis of the molecular electric field.. The work on nuclear quadrupole resonance reported i n this thesis i s a contribution to the problem of nuclear alignment by the mechanism f i 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 f i e l d 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 w i l l f a l l into the lowest hyperfine level. A nuclear orientation relative to the crystal axes w i l l result, depending i n degree on the temperature reached and the size of the quadrupole coupling. As a consequence of this hyperfine splitting, a Schottky type anomaly i n the specific heat appears at temperatures approximating h^/k  y  where V i s the frequency of transition between two hyperfine levels, and k i s Boltzman s constant. At these temperatures, a rearrangement of the populations 1  of the..levels' takes place according to the Boltzman distribution producing a specific heat whjich i s 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 i n  the magnesium salt of para-iodo benzene sulphonate i s being investigated at low -temperatures by the group which i s interested i n the Pound method of nuclear alignment,  "  "' '  In the study of nuclear alignment and nuclear specific he^at, i t i s important to have a method cf investigating directly the hyper fine structure of the compounds concerned.  The technique used i s 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 be ;supplied to the system at the frequency corresponding to 1  the splitting between them. In pure quadrupole. resonance, the lines are detected and recorded by use of an absorption spectrometer.  The sample i s  placed i n a c o i l which i s carrying radio frequency current. This c o i l forms the tank circuit of the oscillator supplying the radio frequency power. The magnetic dipole moment of the nucleus interacts with the alternating magnetic f i e l d produced i n the c o i l , inducing a reorientation of the nuclei against the electrostatic f i e l d of the molecule.  The transitions which occur between energy  levels are accompanied by the macroscopic phenomena of absorption and dispersion.  Since the resonant frequencies involved are usually i n 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 f i e l d gradient tensor with the nuclear quadrupole moment. "When the quadrupole system i s subjected to a static magnetic f i e l d , a Zeeman splitting of the absorption lines occurs i n single crystals.  In a polycrystalline sample, the Zeeman splitting for each crystal  i s different, and an external magnetic f i e l d 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 f i e l d relative to the crystal axes i n 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 f i e l d  orientation w i l l be calculated i n 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 i n 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.  (19U9)  Townes and Dailey  have found approximate methods for the determination of the electric  field gradient from a consideration of the valence electrons i n the molecule. The thesis deals mainly with the construction of the superregenerative spectrometer which was used to observe nuclear quadrupole resonances. The tange covered i s 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 i n 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 i n the region of 280 megacycles, where the resonance i s expected from theoretical calculations.  A discussion i s given concerning the  failure to detect the resonance along with a description of the other,investigations which were made i n 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 o f potential V produced by the charges exterior to the nucleus. The potential V can be expanded i n a series around the origin and the energy then takes the form:  the summation signs applying to cartesian coordinates x,y,z, i n the following discussion.  The f i r s t term i s independent of the orientation of the nucleus  and the second term i s 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 gradient are We can write  of the tensor which represents the electric f i e l d where i , j stand for the cartesian coordinates x,y,z. 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 i s independent of orientation, and therefore w i l l be considered no further. &  • £*  t  The trace of  i s then zero:  - 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/dz ±  principal components of the tensor.  2  i s the largest of the  Then i t follows from condition (3) that:  *v  *V  2  2  2  therefore,  and  (U)  Si  Ji5J  }V 3153"  (5)  whenever i f j  0  The distribution of charge i n the nucleus i s also axially symmetric, with respect to the z' axis of the nuclear coordinate system x'y'z'. Therefore, pOx' dX * f py' 2  2  d U * B, while we put f />z' d r = A. If the x and x» axes 2  are allowed to f a l l together and i f © i s the angle between the z and z axes, 1  Diagram 1  p>a ' d t - f/>(z*coa 6 - y«sin 6 ) d t - A cos © +,B sin ©  then  2  2  j'pj - dT -  A sin © + B cos ©  Jpz  B  2  2  6X. -  2  2  2  , (,6)  2  ;  (7) (8)8  We can now obtain from equation (2) a new expression for the energy: EQ = I  £ (B) - i (A sin © + B cos ©) + q (A cos © • B sin ©) 2  2  2  2  (9)  (A - B)(3/2 cos © - 1/2) 2  In this equation (A - B) can be expressed i n 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'  * yt  2  2 +  x' )} dL 2  = %ff Oz* ~ r ) d L  2  2  2  (10)  The integral, denoted by eQ , defines an inherent property of the nucleus called the quadrupole moment. It has the dimensions of area and i s usua^y expressed i n barns do- * cm. ). It i s positive when the nuclear charge is a 21  6. prolate spheroid and negative when the nuclear charge i s an oblate spheriod. For.a spherical charge distribution, eQ vanishes. We can write down the equation for the classical quadrupole interaction energy:  %, EQ - 4 «Q <l (3/2 cos © - 1/2)  (11)  2  In order to derive the quantum-mechanical energy eigenvalues of the quadrupole system from the classical expression, we most replace cos © with the operator 2  ^  E - V 8 e Q q U3I, - 1(1 • 1)1 2  Q  ( 1 2 )  1(14-1) It i s 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 ' i n equation (12) i s replaced by the normalized value Q, then EQ should have the value which would be obtained by putting cos 9 - 1 i n the classical expression (11). The value  Q - <f (21 - 1) 2  (13),  (I • 1)  is the normalized quadrupole moment; this Q i s used i n the literature. The energy eigenvalues are now: Em " [3*a " 1(1 + D] • \ 1*1(21-1)  tthf  2  The coefficient eQq i s called the quadrupole coupling constant and i s f r e quently expressed i n megacycles (eQq/h). We notice that for I •  '  „i  [3m - 1(1*1)3 " 0, and so the application 2  of nuclear quadrupole resonance i s restricted to nuclei of spin greater than \* The quadrupole moment i s 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 i s integral, there are I doubly degenerate, levels and one nondegenerate level i n an axially symmetric f i e l d ; i f the f i e l d i s not axially symmetric, the levels are i n 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  i s 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 i s not axially symmetric, the parameter T\~ (V^g-VyyO/q i s used to describe the asymmetry.  If  i s 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} - 0.55 2  3/10 eQq (1 - 0.2037 Yl + 0.18^) 2  For I = 7/2,  >j = / y 3 (1 • 3.7331 >£= 2/3 y  2  - 6.86^)  (1 - O.U667n • 1.82n ) 2  3  (20)  11  ^= 3/lU eQq (1 - 0.1000 V} - 0.019 q *) 2  1  (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 : m~m.  W  -  8  l H ^ l ' ) | /y m  2  ( ) 22  yrtiere M i s the magnetic moment operator a n d ^ S v i s the energy density of the  1 I radiation f i e l d i n a range of frequency 5X centred on the transition frequency V,  For the quadrupole system the nuclear magnetic moment i s parallel to the  angular momentum ?, and so  v  |(m |li | mi) | -  |(m|t|m»)|  2  Then |(m j ? | m')|  2  v  ,  2  (23)  can be expressed as the sum of the squares of the matrix 1  elements of the vector components  I , I .  X)  y  2  Since the matrix elements for  and ly are equal, while those for I vanish, we obtain, remembering that z  |* - a |- 1,  ^  ^ ^ ^  2  _ ^ 2 / j 2 J ^ k j 4. 2.) 2  - mmTJ  (2U)  Combining equations (2U) and (22), we f i n a l l y obtain  m~m«  W  ° (kTr jJ/3h I ){I{I+ 3  2  2  1) - WL*)f  y  (25)  2. Electronic structure of molecules and nuclear quadrupole coupling constants In order to calculate i^y/dz , the distribution of charges i n the 2  molecule must be known. An accurate calculation requires a determination of wave functions for the electrons; an approximate calculation i s made from structural considerations because 4pV/&z = q depends on a few simple para2  meters of bond structure.  If q i s calculated or estimated, and the nuclear  quadrupole coupling i s found experimentally, the value of the nuclear quadrupole moment can be determined from Q (cm. ) = 13.8 x l C T 2  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 i n the remainder of the molecule i s negligible. (One electronic charge at one angstrom contributes 1 0 ^ e.s.u.). An s-type orbit or any closed shell of electrons around the nucleus i 3 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 i s from the p-orbitals i n the valence shell; the value of q at the nucleus depends mainly on the way i n 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 i n character, the electron shell of each atom i s partly closed and the coupling reduced because q from the other ion i s much less than that of a p-electron i n the shell i t s e l f .  Electrons i n different atomic orbitals have  widely different couplings. For this reason, hybridization of a p-state bond with an s-state bond w i l l increase the value of q, while hybridization with a d-state bond w i l l decrease the value of q.  Resonance between different  10 covalent.structures, which occurs i n the aromatic carbon compounds, may result in an increase i n q and the quadrupole coupling constant. The wave function \£ for one valence electron outside a closed shell can be expanded i n terms of the atomic wave functions Ynlm* ^ - Snlm a ^ Y o l m  <27,)J.-  where a ^ i s largest for lowest allowed values of n and jt, and the axis of p  m  the molecular bond i s chosen as a reference direction for the magnetic quantum ; -'a  numbers.  '  |J  Since .  » (e/r) =  (3 cos © - 1) e/r3 ,  2  (28)  2  where © is. the azimuthal angle with respect to the bond axis, i t follows that £? *z  = e /  2  cos © - l)\j> dX j3  (29)  2  J  Inserting the series expansion for \^ , gathering terms, and using the simplifying notation  r  <tolm,n'l«m»  (3 cos © - 1) V n f , dT,  "With*  (30)  2  n  m  we have: ifl ^ 2'  =  B  lajQjul qnim n3^i * 2  +  ,2. Snlm ^'I'm* ^nln.n'l'm' nlm,n l m' ' ,  < ) 31  ,  where the quantities ^ni^nim are the values of d V/dz for each of the atomic 2  2  states and are multiplied by I l | > " ^ coefficients of the respective a  2  n  f  ie  m  atomic states i n the molecular wave function.  Except that for 1-C, q Q = 0, n  i s a rapidly decreasing function of n and J?. only those terms for which n f n and 1  either  £ 0 or  m  The second sum includes  and for which m =ra ,and 1  -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) i s neglected. Then the value of q due to a single valence electron i s regarded as a sum of contributions I n l a l a  2  Silm ^  r  o  m  the various atomic states.  Moreover, i f the lowest  energy atomic state i s 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) i s %10 "  2>2U x Z  1  1(1+1)  e.s.u.  (32)  (2/+l)(2^-1)(2^+3)  The fine structure splitting h\* which arises from -c. s coupling i s known for most elements.  Values of AV , expressed i n cm."-'-, have been compiled by  Moore (19U9). In the approximation i n which only p—electrons are considered, q**fv» where 1^, Ny, and N respectively.  z  -C(Nx + ^ ) ( i < l n , l , l ^ ^ % , l , - l )  are the numbers of electrons i n the p^, Py, and p  Since q ^ i ^ i " ^,1,-1 q « t x + %)/2" (N  • N, q ^ o ]  =  (33)  z  orbits  ~ 9*1,1,0 > then  N ] qmo  s  a  Up qmo  C3U)  where Up i s the number of unbalanced p-electrons and q^Q per unbalanced p-electron given by 2.98 x 1 0 ^  i s the contribution  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 w i l l 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 i t 3 octet, N and U » + 1. P  = 1, Njj. - N l  a  S •  y  •» 2',  32. 3. Theory behind the method of detection  , ..  i,  The expression for the classical quadrupole interaction energy derived i n section 1 i s Eq * £ eQq (3/2 cos © - l/2). 2  The dependence; on the  angle © causes a torque which tends to align the nuclear and molecular, axes. The -nuclear spin I w i l l respond to this torque by a precession around the z4-«xxs The diagram demonstrates how the components of the magnetic dipole }*- and the  c  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 i s 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 f i e l d .  The coupling  of the elegtric quadrupole moment with the radiation f i e l d i s 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 i s equal to the precession frequency of the magnetic dipole, the quadrupole system absorbs radio frequency energy frcm the f i e l d .  Near resonance the nuclei precess with phase coherent  with that of the radio frequency f i e l d . I  z  Half of the nuclei of one energy have  reversed with respect to the I of the other half. z  These two sets of nuclei  precess i n opposite directions, and therefore near resonance a pulsating mag-  netie moment i s induced parallel to the radio frequency f i e l d .  There i s no  moment perpendicular to the field because the contributions of theytwo 'sets of nuclei cancel.  The pulsating magnetic moment M = (M' - jM'^eJ**^ i s not 1  necessarily i n phase with the radio frequency f i e l d K •  . !•< Its macro-;  scopic effect can be described by the complex magnetic susceptibility i V X - K - jC-  ;  v  H  ,.  ' '(35i  ' .  1  where fa i s the susceptibility related to absorption and /U the suscept1  i b i l i t y for dispersion*  When the energy of the radiation f i e l d ' i s removed,  the pulsating magnetic moment decays exponentially with the spin-^spin relaxation time T2.  "'  The pulsating magnetic moment absorbs radio frequency energy from the sample c o i l , and can induce a radio frequency voltage i n the same c o i l ; 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 c o i l becomes jLcoQL + h7T( id- j/lCOj + r = and i t s quality factor  jL (1 • liir^)U> + (r + lifr^Lu)) '  (36)  Q «» Lu)/r becomes such that  (l/Q*)  -  (1/Q) + hT)L"*  UfT(X'/Q)  (37)  •If Q i s sufficiently great (from 100 to 200) the expression simplifies to a term in  :  .. d(i/»  -  kvrxf  —>  dQ.^TrxV  (38)  The voltage which i s induced by the residual magnetic moment i s proportional to M and therefore to ( X. -¥J^)  5  ; the inductive effect produces, i n  passing through the resonance, a curve resulting from the combination of absorption and dispersion terms. The energy absorbed per cycle of the radio frequency f i e l d  is  <$>U.d$ where and  -  X-H/sin <p  (39)  2  £ = f i l l i n g factor of the sample c o i l (j) = (H^^z), the angle between the f i e l d direction and the bond axis. .  The total energy absorbed for a line i s proportional to /  XiF).dF,  the area under the absorption curve •  (UO) X^(F).  Thus i t i s seen that the amount •'. i  of radio frequency energy absorbed by the system of spins i s measured by tile .. .. J variation dQ of the coefficient Q of the sample c o i l , : ' i S  1  15. U. Theoretical aspects of the Zeeman effect The quadrupole transitions take place in general between two degenand t (m  erate energy states corresponding to i .  2  •»• 1).  The energy of  interaction of the nuclear magnetic moment with a static magnetic f i e l d i s dependent on the sign of the quantum number m ; z  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 i s  (UD  EI  where  H • magnetic field vector of magnitude H. I = spin vector of the nucleus  The Larmour frequency  i s the frequency of nuclear precession in the f i e l d  H, and i s related by:  (U2)  Using equation (U2), we obtain E =  - K (I.H) H  (U3)  The pattern of the Zeeman effect depends upon the relative orienta-r tion of the electric f i e l d axis and the magnetic f i e l d .  For a f i e l d in the  xz plane, the perturbation operator is H* -M^)  • -Jb& I  (Ix sine • I  z  cosG) - - y j l x sine + I  z  cos©)  where e « (H,z) i s the anrle between the magnetic f i e l d and the z-axis.  (hh) For  the case of spin 5/2, the perturbation matrix i s given below, where a » - y sin© L  and b = - y'-^cos©.  11' = 2  5b  JTa  JTa  3b  J8"a  0  J(3 a  0  0  0  0  0  C  0  b  3a  0  0 0  0  0  3a  -b  J8 a  0  0  0  JIT a  -3b  J5"a  0  0  0  JTa  -5b  0  (U5)  16. The perturbed energies to second order i n H* are  *m = \  • "mm' •  <W  2* n Em " En •  . \  where the prime on S denotes the omission of the term n » m from the summation, and the unperturbed energies ^ E  ±5/2 =  eQq , •  are:  *3/g- ~ "  E  '  e Q q  E  +l/2 = ~  (U7)  eQq  When the unperturbed state m i s degenerate with state k, equation (li6). w i l l hold only i f Hj^ i s zero and the degeneracy between the states k 1  and m i s removed i n f i r s t order. k » - 3/2.  This i s so for m = 5/2, k = - 5/2  However, for m » l/2, k « - l/2, % ' 1 - HJi 1 jfrO.  1  and m = 3/2,  In this  case i t i s only necessary to diagonalize the submatrix Hjnm  ^ak  Hkm  H,•kk  (U8)  "before calculating the perturbed energies. The diagonalized submatrix i s + 1?  0  o - n 9a  £  and the perturbation operator i s /5b  J^a  0  0  0  0  0  0  /8~a J9a +b 0  0  0  JTa H' ="K 2  0  3b  0 J3" a 2  2  0  0  0 -JlJa^+b J T a  0  0  0  0  (8"a  -3b  JTa  \0  0  0  0  /Ta  -5b/  2  (1*9)  j  Using equation (U6), i t i s now possible to obtain the perturbed energies from the above matrix (k?) s  1  17? W  t5/2  =  ^  h  e  Q  "  q  5  /  2  fe  c  o  s 0  +  2  *  / 7  ^  s i  "  2 e  eQq f3/2  S  "  =  " ^ * 3  2  c  o  *  s 6  n  ^/  ?  n y 2  sin 6  2  2  L  eQq W ^- « - ]/5 eQq - V +1  V ^ l J c o s © t 9sin ©  2  - 20 n  2  2  2  V  2  sin ©  2  2  L  eQq -l/2 "  W  w  V S eQq + fc/ Vj, J c o s © -t- 9sin © 2  2  -  2  20 n  V  2  sin ©  2  2  L  eQq -3/2 " " V l O eQq + 3/2 t V  W  L  eos©  •  115/7 n V 2  sin ©  2  2  L  eQq >^/ - =  w  2  1/U eQq -f 5/2 n ) ^ cos ©  + 25/7 n V 2  sin ©  2  (50).  2  L  eQq For the (J3/2|<—*fl/20 transition we obtain the frequencies of transition: VV3/2«->l/ )  " V l O eQ^ - 3/2 y . * •  2  K jcos 9 4 9sin ©  cos e +  L  2  2  + 255/ l^sin © 7 2  (  e  Q  q  A  )  (51) y(_3/2«-*-L/2)  " 3/  =  2  c  o  s e  • >^-|cos ©^9sin © 2  *  2  2  + 255 >j sin Q 2  7  2  (eQq/h) (52)  The four lines which separate i n pairs from the unperturbed resonance line V  0  are symmetrical with respect to this line and separated from i t by ±A)^= i ^ i f e for both & - ©  and © - ?T-©.  cos©  -  (cos © + 9sin ©)^] 2  2  (53)  The last term i n 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 f i e l d axis and H perpendicular to the electric f i e l d axis. Case 1. H parallel to the f i e l d axis:  © • 0, cos © - 1, sin © - 0  For the (3/2 *—*• 2/2) transition, there w i l l 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 separated by Ay's V^. 2  In general they are separated by A V . 2'^ cos ©.  Case 2. H perpendicular to the f i e l d axis:  0 aTT/2,  cos 9 - 0 , sin © • 1.  Only the state |ra^.| - \ i s s p l i t and the (3/2  l/2) line  becomes two lines separated by A V _ 3 V^. In a polycrystalline sample, the line i s smeared out when the Zeeman splitting i s greater than the line width. • For I width i s approximately I4O kc. angle i s 2 V . L  1 2  ? i n Ig, the line  The least splitting which occurs for any  S i n c e / ^ j / l for the iodine nucleus i s 0.8565 kc., the f i e l d  necessary to cause this line to disappear completely i s about 25 gauss.  CHAPTER II  The superregenerative oscillator  1. The superregenerative oscillator i n theory when oscillation conditions are established for the vacuum tube oscillator, the envelope of the oscillations rises exponentially u n t i l i t i s limited by non-linearities i n the c i r c u i t . 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 i n the circuit decay exponentially.  The period length of the "quench" voltage, as i t i s called,  is about 10 times as long as the decay time constant of the tank circuit so that the voltage across the tank circuit w i l l be reduced to the order of thermal noise voltages before the tube i 3 switched on again.  The tube i s  l e f t on long enough for the oscillations to level off at the saturation amplitude Ujaax*  ^  n e  time which i s necessary for the oscillations to build  up to this value depends sensitively on the minimum amplitude Uj^in.  ' •  If any signal i s present i n the tank circuit at the moment the oscillator i s 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 w i l l appear as \, a change i n 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 i s a greatly amplified reproduction of the amplitudes present i n 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 i s placed i n the tank c o i l of the superregenerative  oscillator, the nuclei absorb energy from the tank circuit at the resonant frequency, lowering i t s 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 i s turned off, the processing nuclei continue precessing and induce a voltage i n the tank circuit which i s additional to the minimum amplitude Djoin that i s reached during the cut-off interval.  This voltage  f a l l s 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 i n the tank circuit during the low oscillation interval of the previous quench cycle.  This  radio frequency voltage i s given by  ,  AU = - UrXQ«*Unax  ,(5U) ]  where Q i s the quality factor of the tank circuit and  '  I  r  '  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 . AU and U ^ .  .  ;  .  1  '  It i s 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 '." i s comparable to the period of the quench voltage.  If T for a substance i s 2  too short, the quench frequency cannot be chosen to satisfy both these conditt  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 i n the superregenerative oscillator circuit: G  = * Umax 2I/Rt ^ q  (V + V )/V n  s  n  (55)  where  f  = quench frequency  L  a  "  j  tank c o i l inductance  Rp = net series tank resistance = R + Rj^ R  « series loss resistance of tank circuit  Rjj = negative series resistance representing the regenerator tube V V  n  = noise voltage, at instant that oscillations start = signal voltage at instant that oscillations start  The gain i n this case can be as high as lO^j for a sine wave quenching voltag i t i s higher. However, i t i s d i f f i c u l t to apply the gain law i n 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 i s important i n the region 100U00 mc./sec. where radio techniques are d i f f i c u l t . ( i i ) It develops a high radio frequency power with relatively l i t t l e noise. In the substances to be investigated there i s almost no chance of saturating the resonance, so that the large output i s very useful. Its principal disadvantages are: (i) It i s sometimes tempermental and erratic and adjustment i s c r i t i c a l . (ii) The detection i s dependent on Tg; therefore the spectrometer i s limited in the substances which i t can be used to investigate.  < ' ;' 2. The superregenerative oscillator i n our quadrupole spectrometer  2?.  •  In our spectrometer, the superregenerative oscillator uses two acorn triodes  i n a tuned anode, tuned cathode, grounded grid push-pull  circuit (see figures 1 and 2). The oscillation frequency i s essentially determined by the resonant frequency of a lecher wire system i n the anode circuit; the lecher wire system i n the cathode circuit has a smaller effect on the frequency. However, for oscillation to take place, i t i s necessary that the cathode c i r c u i t be inductive at the frequency of oscillation. Proper adjustment of the oscillator i s 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 i s 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 i n the anode- circuit gives the oscillator It can resonate to the frequency f vtiien i t s effec-  i t s wide frequency range.  tive length i s equal to (n/2 - l/h) A where A. i s the wave length corresponding to frequency f. As the length of the line i s increased, sustained o s c i l l a tions are obtained i n successive ranges.  The cathcde line can usually be  adjusted so that i t i s indiictive for only one mode of oscillation.  When  conditions are such that two modes of oscillation are possible, usually only the lower mode i s produced because the circuit losses are lowest i n 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 i n developing a satisfactory oscillator.  ,  In the final circuit of the oscillator, the frequency range from 15>G to 600 mc./sec. was covered i n 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 J  c  (the lengths of the .anode line and ithe cajbhode  OSC. WAVE  2: O U T - •=•  FORM SIGNAL  47 K  OUT—2  V  v  v  05  X  \  E  ]  N  A  \/  BRASS  PLATE  COPPER  WIRE  < IO K FREQUENCY  ]  — W  MODULATION  •05  r.f.  lOO K  choke •01  1.  ^  " /! /  \  1 a NODE 4  C  v  \  3 . 5 v  S  10 K  •Ol  22 K K 5K  .33 K  H T - -_ Ov-  H  6v  SCREEN 3 1 GRID  ^  i  QUENCH  IN  TUBING  05  20 K  o  BRASS  -2:  IO K W V W  o  <a n  ro FIGURE  I  JUNCTION  BOX  FIGURE  2  SUPER - REGENERATIVE  OSCILLATOR  2.  EXTERNAL  FIGURE  OSCILLATOR  3  QUENCH  OSCILLATOR  RFC  PLATE I to follow page 22  line), and drawing the contours for each mode. The anode lecher wire system i s made of 0.120" diameter copper wires with centres spaced l/2* apart.  The sample c o i l , made of the same  copper wire, was attached to the anode stub at the tube end of the lecher system.  The c o i l , 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 i s shown  in the appendix that the magnetic field generated in the c o i l i s a maximum in a A/8 c o i l .  The cathode line i s 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 conductor i n 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 i s effected by running a phosphor-bronze shorting bar along the • lecher system.  /  The signal i s , i n principle, independent of the quantity of sample, provided the f i l l i n g factor of the sample c o i l i s 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 c o i l .  In  practice, for a c o i l 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 i n 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 frequency and amplitude, and the various potentials applied to the electrodes of the oscillator tubes. The adjustment which i s obtained i n 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 i s easily recognized because i t i s 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 f i r s t oscillator was the original design of the f i n a l 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 satisfied with the oscillator because we considered the signal-to-noise ratio obtained for known signals to be inadequate i n the .search for unknown signals.  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, f i 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.  I t i s 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 i n 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 i n the circuit due to the greater r i g i d i t y of larger diameter wires, and ( i i ) 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 i n an equilateral triangle i n the mount for the relay coil.  The test signals were improved i n 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 i s given i n figure k.  Frequency modulation was used for Yri.de band detection and o s c i l l o -  scopic display; Zeeman modulation was used for narrow band detection with the phase sensitive detector and automatic recording.  The various parts of the  spectrometer w i l l be described individually in this section. 1. Modulation In nuclear magnetic resonance the magnetic field can be modulated around i t s value Hq at the resonancej i n nuclear quadrupole resonance, i t i s impossible to modulate the electrostatic field gradient. culty can be avoided by using the Zeeman effect.  However, this d i f f i -  If i t i s preferred to operate  i n the absence of any magnetic f i e l d , the radio frequency excitation can be modulated i n 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 i s necessary i n nuclear quadrupole resonance i n view of the line widths involved.  The amplitude'of i  the frequency modulation must be variable and about 10 mc./sec. maximum. I t should be about ]$> of the oscillator frequency and many times the line width. A vibrating condenser operated by a relay c o i l at 60 c.p.s. has a maximum amplitude of vibration which provides a spread i n frequency of 10 mc./sec. The vibrating condenser, shown i n side view i n figure 7, i s connected i n parallel to the tank circuit, on the anode lecher wire system.  The same unit  which drives the relay c o i l (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 i s required.  While the field i s on, the resonance i s  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  FREQUENCY  QUENCH  MODULATOR  SUPER  OSCILLOSCOPE  OSCILLATOR  REGENERATIVE  OSCILLATOR  SAMPLE  LOW  PASS  AMPLIFIER 9  DB.  FILTER 60  cps 1 2 0 cps  AMPLIFIER 20/4-0 DB.  \/  COIL  A  POWER AMPLIFIER  HELMHOLTZ  COILS  SQUARING  AUDIO  SENSITIVE  CIRCUIT  OSCILLATOR  DETECTOR  A RECORDING  POWER PACK  FIGURE  4  BLOCK  PHASE  DIAGRAM  Ml LLI A M M E T E R  OF  NUCLEAR  QUADRUPOLE  SPECTROMETER  27 of course not work for a single crystal.  A field le3S than 5>0 gauss i s 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 f i r s t used to provide the square wave fieldj a battery and rheostat served to bias the f i e l d 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 f i e l d but i t i s ex-  pected to be less than this.  The axis of centres was placed perpendicular to  the direction of the axis of the sample c o 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, another method had to be found. A power amplifier (figure 10), i n 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 f i e l d 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 simplified version of the squaring circuit, shown i n figure 11. pack was designed to provide grid bias of the power tube.  A special power  2^0 volts for the plate and - 70 volts for the 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 i s the minimum frequency l e f t unattenuated by the low frequency f i l t e r and i t i s not a simple multiple of the mains frequency.  A square wave f i e l d would be more easily produced at lower frequen-  cies because of the time constant of the c o i l s .  Because of the large induct-  ance of the coils (~S henries), the f i e l d was measured to be only 13 gauss. The advantages i n the Zeeman method of modulation are: (i) No previous knowledge of the line width i s necessary to obtain optimum  modulation efficiency. ( i i ) Response to spurious signals i s greatly reduced. There i s , however, one d i f f i c u l t y : "pick up" of the modulation frequency i s enhanced. The signal can be observed on the oscilloscope as well as on the pen recorder.  The picture w i l l 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 frequency i s swept over should be determined by: (i) the line width of the resonant absorption ( i i ) the time constant used i n the detecting apparatus.  .  For automatic recording of signals a sweep linear with time i s , required.  The lucite sector illustrated i n 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. arrangement gave a sweep very close to linear.  This  However, i t was. useful only i  1  until the length of the anode line became too short at the higher frequencies of the oscillator. The length of the anode line could be varied at a constant speed using a D. C. motor. The speed of a l/lO H. P. motor was varied with'a  j t  '  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.  GLASS  o o" LECHER  FIGURE  7  RELAY  COIL  8.  WIRES  VIBRATOR  O  LUCITE  110 v  DC FAST  IOOO 100 W FIGURE OF  8  1/10  H P  MOTOR  SLOW  SHAPE  LUCITE  1A  SECTOR  SPEED REDUCTOR  300". I  WORM  WORM  GEAR  m GLASS  ROD  RUBBER  TUBING  LUCITE STEEL  ROD  BRASS  CYLINDER  THREADED  FIGURE  9  FREQUENCY APPARATUS  SPACER-  SHAFT  SWEEP  NUT  to  follow  page  28  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 i n the c i r c u i t .  <  $  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 where t i s the duration of the signal as the t  oscillator sweeps through i t , usually the higher harmonics.  Therefore, the  unimportant lower harmonics can be removed before the last stage of amplification.  A slight amplitude modulation occurs as a consequence of the 60  c.p.s. frequency modulation, which i s 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 frequencies 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 i s taken from the oscillator across the tank circuit i s fed into a low pass amplifier having a gain of 9 decibels and f a l l i n g 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 amplification, 20 and hO decibels.  The signal which i s directed to the phase  sensitive detector i s 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) i s basically the Schuster  circuit described in Review of Scientific Instruments (1951). signal at the grid of the pentode produces a plate current  The input  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 w i l l travel. I t 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 e o f f period.. The "lock i n " effect is obtained at high reference v o l t 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 ) « l , the "direct voltage output U is of the form 2  »  U - 2 k.e.cosif where  (56)  i s the phase difference between the two voltages and k i s the gain  of the detector. The direct voltage output U from the plates of the 6SN7 tubes i s 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 i s recorded on an Esterline-Angus recording milliammeter. An overall sensitivity of lOO^a./mv. was achieved for the detector. The effective noise band width i s 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 i s slow.  0-5  5 0  ,  47K  K  4-IK RELAY  115 v AC  FIGURE  TUNED FIGURE 6  FILTER  FOR  COIL  3  10 6 3v  h>250v  E.,H.T.X- S W E E P  •1-5  >3-3K l-5K> 5  1 0 0  K  T PHASE  FREQUENCY  TO VERY  120 cps LOW  ON  CONTROL  MODULATOR  TUNED FREQUENCIES  TO  6 0 cps  ( < 4 0 0 cps)  CR  50  2.  POWER  henries  AMPLIFIER  POWER  PACK  5 •o •a O  FIGURE  10  POWER  AMPLIFIER  DRIVING  THE  HELMHOLTZ  COILS  FIGURE  II  SQUARING  CIRCUIT  FIGURE  12  AUXILIARY  OSCILLATOR  IN  50 K  •09 H  -09H  500 K  -vWv-  50C  500  IOOO  P<  500 pf  > 100 K -z= 500  250v  OUT  ! /  2  6 S L 7 GT  '/2  NULL  FREQ.  FIGURE  18-6  13  6 S L 7 GT  '/2  6SL7  GT NULL  Kc.  LOW  PASS  AMPLIFIER  '/2 FREQ.  6SL7  7-75  Kc.  GT  -300 v 25 K lO K  50 K  X  IN  20 K  <50K  (M  220 K  680 w  4>  K  IOK  S  SIOK  -r-  UJ  •5  X O  Q  1  3  1>.  -  O UJ  SECONDS  <—<;  •01  J  5 M  5 M  O  REFERENCE  ADJUSTMENT  20 K  16  HAMMOND 933  ZERO  BALANCE  6SN7  6SN7  3 9 0 i< 6C4  332  t 250  380 K K 500  PHASE  '740  40  O  69 SIGNAL IN  G  if!  TIME ' CONSTANT  40  6SJ7  o  OJ  40  SHIFT 20  T3 O (O  330 K  Ol II— 1  4  , 0  K°  DC-  AMPLIFIER  AMPLIFIER  K'  1  4 7 0 K< . Q 5  6AC7  ~~1 , 160 >  ^  T '  25  FIGURE  14  PHASE  SENSITIVE  DETECTOR  The Auxiliary Equipment  The Tuning System  PLATE I I  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 c o i l i n a liquid a i r bath. A stronger signal should be expected since, by cooling the sample, we are i n creasing the difference i n the populations of the different levels. Contrary to what was expected, we found that the signal was either decreased i n strength or else could not be relocated after the cooling.  It i s most l i k e l y that dew  or frost on the lines causes a large dielectric loss, a situation which i s d i f f i c u l t to remedy. About twenty different samples were prepared and tried, but resonance lines from only four of these were recorded on the Esterline-Angus. Searching for resonances i n the samples which had melting points at liquid a i r temperatures was abandoned because of the trouble encountered whenever the oscillator c o i l i s immersed in liquid air.  The five signals i n the four sam-  ples ranged in frequency from 16U.5 to 332.h Mc./sec.  The data collected on  each signal for c r i t i c a l conditions with Zeeman modulation i s displayed i n the table below.  The signal-to-ncise ratio for the same signal with fre-  quency modulation i s also given, although the conditions for resonance sometimes change slightly from one method of modulation to the other. The lucite sector was used i n sweeping the frequency for the f i r s t three samples, while the tuning system shown in plate II was used i n order to sweep through the 127 l-  LCi  signal i n Ig-.  and IV.  Photographs of the recordings are given i n plates III ,  32.  Sample  SbBr  3  Ba(Br0 ) 3  Snl  '*2-  u  2  Nucleus  Resonant freq. mc.  Br  7 9  l6h.5  Br  7 9  17b. 6  J127  207.6 209.1  ll27  332. U  Quench amplitude  Signal-to-noise  119  39$ Eico 80^ internal  300:1  U48  hZ% Eico 50% internal  150:1  lUS  $1% Eico $0% internal  150:1 200:1  20:1  129  8l£ Eico 60% internal  500:1  6:1  Quench freq. kc.  3:1  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 i n connection with Pound's method of nuclear alignment, and i n which no quadrupole resonances have yet been reported. The iodine atom covalently bonded to aromatic carbon atoms in iodo benzene sulphonate salts was of particular interest. the resonant frequency of I  Rollin and Hatton (195U) have estimated  i n this compound to be 280 Mc./sec.j i f the  quadrupole coupling were this large, then the compound would be suitable i n this respect for nuclear alignment, A sample of the magnesium salt of p-iodo benzene sulphonate was obtained from the low temperature laboratory and carefully studied from about 250 to 3U0 Mc./sec. making adjustments i n 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 analysis, 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 i n 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 i n the other "Cwo compounds,  a sample of sodium meta-iodo benzene sulphonate was prepared i n 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, i n which the bonds are expected to be covalent, were prepared: K^Hgl^, K ^ g l ^ , Kgfinl^, I^Snl^. reactions were: HgCl  2  + 2KI -> Hgl 2  2  followed by  Hgl  2  • 2KI  The  KgHgl^.  Group theory shows that a dp s combination i s possible for the tetragonal bonding in these compounds. By a consideration of the bonding orbitals and a com127 parison to those in the covalent I about 350 l.ic./see.  2  bond, we estimated the I  resonance to be  An investigation was made i n this region and also around  175 Mc./sec, but without results.  The failure to observe an iodine resonance  in these compounds i s at least consistent with the fact that the chlorine resonance i n K PtCl£ cannot be seen. 2  into K", Pt^ , and CI 4  +  KgPtCl^ i n solution i s known to break up  ions, which suggests that the molecular complex i s dis-  torted rather than moved bodily.  The resulting crystal strains may cause a  spread i n the values of the f i e l d gradient at the site of the iodine nucleus and broaden the lino to the extent that i t i s unobservable.  H. E. Petch and  N. G. Cranna, Investigating a milky sample of spodumene i n this laboratory, have seen a similar effect.  The quadrupole satellites of the H. M. R. line  could not be found, although easily oisSiErved i n other samples.  Probably crystal  imperfections cause a broadening of the lines as described above.  ^n «n  3  C  /.  *  ?i  *• P I  PLATE V  r,  ?.  •* s  Photograph of crystallographic data on the benzene sulphonates  to follow page 33  APPENDIX  Design of the sample c o l l for maximum f i e l d intensity The energy stored i n the magnetic f i e l d of the c o i l i s d i s t r i buted throughout the field with a density  U  a  ^yitH joules/meter. 2  The  energy density of the magnetic f i e l d can also be derived by calculating the work done i n forcing the electrons of the current against the opposing electromotive force  e «• L i / t .  D - q.e - £ i . t x L i / t - § L i joules  {$!)  2  Diagram 3 illustrates (a) the transmission line and (b) the equivalent circuit with a c o i l of inductance L.  1 <g  4> I  V  o L  >  (a)  (b) Diagram 3  For the equivalent circuit we have: V = E sin 27ll \ and  i « E cos  (£8)  2ffl  (£o)  The impedance of the c o i l of inductance L i s  X - U)L - Zq tan  2T&  A  (6o)  L = Z\  Therefore,  tan 27TX  0  277c" Then  X  ' 'i  L i - Z g \ tan 2/7j^ . e£ cos ZTtt 2  (62)  2  277c"  A  Z  2  *  >  !'•  1  *  •  Simplifying, we find  L i oC A s i n kTlt \ 2  Equation (63)' shows:  ' '  '  ' "  '  •  ' • ' i (63)' » J.  5'  j,  .  ' I  '  (i) that more energy i s stored i n the magnetic f i e l d at the lower frequencies of oscillation. ( i i ) that the quantity L i i s a maximum •when sin klfi. - 1, i.e. when £• = ^/8. 2  It i s thus seen that the inductance of the sample c o i l should be equivalent to a length A./8 of the transmission line i f the f i e l d and energy density i n the c o i l are to be maximum.  BIBLIOGRAPHY t  i  (1) Bloembergen, N., Purcell, E. M., Pound, R. V., Phys. Rev., t|, 679 (19UB): 1  (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, Cambridge, 1950. (23) Wyckoff, R. W. G., Crystal Structures, vol. I, II, III, Interscience Publishers, Inc., New York, 1953.  ;' ' ''  

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