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The Zeeman splitting of nuclear quadrople resonances in single crystals of zinc bromate hexahydrate and.. 1959

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THE ZEEMAN SPLITTING OF NUCLEAR QUADRUPOLE RESONANCES IN SINGLE CRYSTALS OF ZINC BROMTE HEXAHYDRATE AND COBALT BROMATE IiEXAKYDRATE b y ALAN KENNETH GOODACRE B.A., University of Br i t i s h Columbia, 1957 A THESIS SUBMITTED IN 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 required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1959. i i A B S T R A C T The Zeeman splitting of nuclear quadrupole resonances i s discussed and a formula given for the s p l i t resonance frequencies as a function of the angle between the perturbing magnetic f i e l d and the symmetry axis of the crystalline electric f i e l d . The direction of this axis i n the crystal can be found If the electric f i e l d does not have cylindrical symmetry then for certain angles the spectrum becomes simplified and the directions of the three principal axes of the electric f i e l d gradient tensor can be found as well as the degree of as- ymmetry of the electric f i e l d . These resonances are observed with the aid of a super-regenerative osci- l l a t o r . A brief description of i t s operation i s given as well as some signal to noise ratio considerations for various methods of detection of the resonances. The spectrometer used i s described. The Zeeman spectra of the nuclear quadrupole resonances of i n single crystals of Zn(B r0^)2 .6H2O and CotBrC^^.&^O are observed. The accuracy of the observations i s discussed and the conclusion i s reached that within the error of the experiment the crystalline electric fields have cylindrical symmetry with four different directions of the symmetry axes in the crystal. They are p a r a l l e l to the j l ^ l j > crystal axes. The crystals have cubic structure. In presenting 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 at the U n i v e r s i t y of B r i t i s h Columbia, I agree that 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 f u r t h e r agree that permission f o r extensive 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 be granted by the Head of my Department or by his' r e p r e s e n t a t i v e s . . I t i s understood that 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 w r i t t e n permission. The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada. Date i i i TABIE OF CONTENTS Page Chapter I Zeeman Splitting of Nuclear Quadrupole Resonances. Chapter II Chapter III The Super-regenerative Oscillator. The Nuclear Quadrupole Resonance Spectro- meter. 10 19 Chapter IV Information Obtained about Single Crystals of Zn(Br03)2 .6H2O andCo(Br03)2 .6H2O from their Zeeman Spectra. 23 Bibliography 29 i v LIST OF ILLUSTRATIONS Figure to follow page 1 Plot of ± 3 ess Q ± ( c o s * 0 - ^sin2-9f 6 2 Operation of Super-regenerative Oscillator with No Sample Present a) Envelope of Rectified Oscillations. Coherent Operation. b) Envelope of Rectified Oscillations. Incoherent Operation. c) Rectified Output of Super-regenerative Oscillator. Coherent Operation. d) Rectified Output of Super-regenerative Oscillator. Incoherent Operation. 12 3 Effect of Sample Upon Super-regenerative Oscillator Operation. a) Envelope of Rectified Oscillations. b) Rectified Output of Super-regenerative Oscillator. 13 U Effect of the Quenching Process on the Signal to Noise Ratio of the Separate Detection Method. 16 $ Block Diagrams of the Apparatus a) Separate Detection. b) Phase-Sensitive Detection. 20 6 Wiring Diagrams a) Crystal Controlled Oscillator and Tripler. b) L - C Oscillator. c) Mixer. 20 V Figure to follow page 7 Wiring Diagram. Frequency Modulated 'Quench Oscillator. 20 8 F i e l d Strength vs. Distance Along Axis of One Helmholtz C o i l . 22 9 A Crystal with Cubic Structure. a) Crystal Faces. b) Labelling of the z-symmetry Axes. 2$ 10 . The Zeeman Splitting of the Nuclear Quadrupole Resonance of B ^ 1 i n a Single Crystal of ^.(B^^^H^O. The(|,|j) Face i s Perpendicular to the Axis of Rotation. 2̂ 11 Zeeman Spl i t Resonances of ZnfBj.O-j^^h^O. Crystal Mounted with the(l,i;i) Face Perpendicular to the Axis,of Rotation. a) Self Detection with Phase Sensitive Detection. b) Separate Detection with Phase Sensitive Detection. c) Separate Detection. Rectified Noise. 26 12 Zeeman Split Resonances of CoCBrO-^.SF^O. Separate Detection.Rectified Noise a) Coincidence of an Inner and Outer Line. Crystal Mounted with the(l I \ ) Face Perpendicular to the Axis of Rotation. ' b) Coincidence of Four Inner and Four Outer Lines. Crystal Mounted x*ith the(i \\) and(| i 7) Faces Parallel to the Axis of Rotation. ' 27 v i LIST OF PLATES Plate to follow pag I The Spectrometer 22 II Helmholtz Coils. Crystal Holder. 22 v i i LIST OF TABLES Table to follow page 1 Observations of the Zeeman Spectra of ZnCBpO^.S^O and Calculations of the Crystal F i e l d Parameters. 26 Observations of the Zeeman Spectra of ZnCB-jXi-^.&^O and Calculations of the Crystal F i e l d Parameters. 26 Observations of the Zeeman Spectra of Co(Br03)2.6H20 and Calculations of the Crystal Field Parameters. 2 7 Observations of Second Order Effects of the Zeeman Splitting of the Nuclear Quad- rupole Resonance of CoCBrO-^^^O. 2 7 v i i i • A C K N O W L E D G E M E N T I would especially like to thank Dr. J.M. Daniels for suggesting the topic of this thesis and his subsequent interest and guidance i n a l l phases of the work. Also I appreciate the added discussions with Professor R.E. Burgess about the thesis. Mr. H.M. Zerbst has given me valuable assistance by designing and building the Helmholtz coils and crystal holder. 1. CHAPTER 1, ZEEMAN SPLITTING OF NUCLEAR QUADRUPOLE RESONANCES Nuclear quadrupole resonances may be observed i n a system where there exists a nucleus possessing an electric quadrupole moment located i n an e l - ectric f i e l d which possesses a constant average electric f i e l d gradient. The resulting interaction energy depends on the orientation of the nucleus i n the electric f i e l d . Transitions between adjacent energy levels may be induced by a radio frequency f i e l d which interacts with the nuclear magnetic dipole mom- ent. The nuclear charge distribution has rotational symmetry. Also, the e l - ectric fields found i n crystals, where the requirement of a constant average electric f i e l d gradient may be met, often have cylindrical symmetry to a f i r s t approximation. The effect of higher order derivatives of the electric f i e l d on the interaction energy i s too small to be observed. The observable interaction energy of the svstem i s : u' = </ L W e - i ] v „ u) .̂ i s the quadrupole moment e is the angle between the quadrupole symmetry axis and the electric f i e l d symmetry axis and ^zz ^ s defined by equation For example, consider the energy of orientation of a linear electric quadrupole where V z z constant. If the four charges are i n i t i a l l y at the origin and then moved to the position shown i n the diagram 2. (the quadrupole i s i n the x-z plane and the super- scripts refer to position.) the energy needed to do this i s ~(v--v-) . - ( g \ . . i ~ e - ( ^ s i . e and , 1 therefore If the z-axis i s a symmetry axis then - O and V K=0 (3) CM a) gravity of the energy levels which cannot be observed i n these experiments and w i l l be neglected. Hence the usual formulation of the interaction energy i s The quantum mechanical energy levels- of the system may be found by replacing Cos 0 by 7- (where I i s the spin of the nucleus) and Ĉ i) by ~ "̂ Q since the usual definition of the quadrupole moment i s ^ i s the nuclear charge density A. i s the distance of the volume element from the center of the nucleus 2. i s the projection of A on the axis of symmetry of the nucleus. Also i t i s customary to use the projection of the quadrupole moment on the axis of quantization when this projection i s a maximum. So we replace Q b y Q x X C I * l) U X -1) The energy levels are given by N a Q - i a t l » ( 1 0 ) " H I (XX -1) K where the symmetry axis of the electric f i e l d i s the axis of quantization. Zeeman splitting of the energy levels occurs when a homogenous magnetic f i e l d H i s applied to the system. For our purposes the interaction energy between the nuclear magnetic dipole moment^ and the magnetic f i e l d w i l l be For convenience we set so using equation l^ck. It i s mathematically convenient to use a potential V for the interaction energy such that V „ * V y v * V „ - o fe) Now there i s an electron charge density at the nucleus so we have v., • v;, * v„ . v;; f vy; . v;; c?) where V i s a new potential representing a spherically symmetric f i e l d . That i s |l l ' M V = v . v xx yy We can rewrite equation 7 as v' - v" * V - v" . v - v; . o or where ry = v;> - v ; ; etc . u) Using equations (H b) y and 1$) we find In nuclear quadrupole resonance experiments we are interested i n differences between energy levels. The f i r s t term in equation \̂ \) w i l l give a set of energy levels whose "center of gravity" i s constant, i . e . the arithmetical sum of the energy levels i s zero. The second term represents a shift of the center of 5. where much smaller than the unperturbed interaction energy. In this case the per- turbing energy TJ i s ( j " - ^ ^ cos 0 (11^ where 0 i s the angle between the applied magnetic f i e l d and the nuclear mag- netic dipole moment. The energy levels of the system are given by -- F \ ( W t - I ( u l ) ) + L-b^S c o s Q 0 )̂ In this experiment X' i n fact, the magnetic interaction energy i n the state Hl^ =• i s too large to be considered as a perturbation of the electric interaction energy. The Hamiltonian for the case 1 = ̂ - i s , i n general ̂  A t Where Q and <j> are the polar angles of the magnetic f i e l d with respect to the axis of quantization and i f I Vxxj ̂  |V Yy| ̂  | Vj^j then the asymmetry parameter W i s defined as m - v - in) For /TJj-O and S" « fl the only important off diagonal matrix elements are those connecting the 07} t - t 4^ states and the Hamiltonian i s /3r\*3Stos9, o o o o o o -+3B-3f<.os& 6 The roots of the secular equation are A, 3R + 3£ cos 0 ^ - -3R - J C e o ^ Q ^ s ^ Q ) ^ AH * 3R - 3 J c o s © and for the allowed A'"Hj- - 1 transitions five resonances are expected but th'at with frequency of the order of -=L w i l l not be considered. The four re- sonance frequencies are given by(Figure l ) W - GP\ t 35 C o s 9 t $ U°s l© + <tsi* 4Q^ 05") The curves of the Zeeman s r l i t resonances are symmetrical about the un- s p l i t frequency 6A . The two resonances with the smaller frequency spl i t t i n g are called the "inner lines" and the other two resonances are called the "outer lines". In general the secular equation for the energy eigenvalues i s A" - K{ log* -v K R z + b a y ] + A l^UPlf + 7* 5 u v ^ 0 - 2 7 f l t f % ^ * 0 COSZ^} ^ 7 - 2 S u v , 2 0 C O S Z</> ( K> ) * o A simplification to a quadratic i n A occurs i f the coefficient of A i s made zero. This corresponds to two resonance frequencies being the same, or that  7 the inner and outer lines coincide. This coefficient i s zero when /n C o s X(b - 3 - =̂ If Y[_ - O the inner and outer lines w i l l coincide when then the roots of the secular equation are given by X A , * 3 R A , - A, * \ - 3ft A 1 = si + I B x ± V/cr^^^fl^ 1 If f ̂  A and using the expansion ( I - I \ for small * then the four roots are _ 1 1 and the three resulting resonance frequencies are given by If \ fo the inner and outer lines w i l l coincide i f ^ u>s2< i > = 3 - T^-Q- W O The directions of the three principal axes of the tensor describing the electric f i e l d gradient may be found by f i r s t examining the splitting of the inner lines to find the direction of the z-axis. When the magnetic f i e l d i s along the z-axis the Hamiltonian becomes 3 f t + 3 5 , fJftv. O , O O , o , + 5 v3*H 0 , 0 , v ^ A ^ . , - 3 5 and the roots of the secular equation are given by 8. and Using the expansion ( | t X ) 1 = I + J - £ for small X. the energy levels 2 are , „X\'L r- _ * A* = -3A0 + - j i + i - j _ i l _ _ Cl + V)*'" 3 Ft C I + ̂  } vz 3 and the resulting resonance frequencies are given by t 3 l "I V ^ (1+2^)''* 3 A ( H - ^ H . 3 and ' ' 7 z for any value o f a n d to the second order i n the magnetic f i e l d . VJhen the magnetic f i e l d i s paral l e l to the z-axis the frequency difference between the inner lines i s a maximum (from symmetry considerations of the Zeeman spectra) and i s equal to H ^ . The value of 47 e ^ O X <fc - 3 ~ — — ^ ° o J ) may be determined by observing the angle at which the inner and outer lines coincide. Then rotating the system^- radians about the z-axis, the value of ^ may be determined. Then 9 Using eq\iations(Z0c^{7jL)^and C.2-0 the x and y- principal axes may be found. For example, once the inner lines of the spectra are identified from a general inspection of the s p l i t lines, the crystal can be oriented so that the frequency difference between them i s equal to H $ . This determines the d i r - ection of the z-axis (forrnula^^ t)). In practice this may be d i f f i c u l t , how- ever, the directions of the z-axes i n the crystal can often be determined from symmetry considerations. Once the direction of the z-axis i s found the directions of the x-axis and y-axis can be found as mentioned previously by using formulae (20 cS)} Ĉ -Ow) and . Alternatively, i t i s possible to rotate the crystal about the z-axis and determine the x-axis and y-axis directions, as well as 7£ , from the maxima and minima of the s p l i t t i n g of the inner components."*" 10 CHAPTER II THE SUPER-REGENERATIVE OSCILLATOR Nuclear quadrupole resonances may be observed by placing a suitable crystalline sample i n a solenoid which has an oscillating voltage of the proper frequency applied to i t . The internal f i e l d of the solenoid can be considered as the superposition of two magnetic fields rotating i n opposite directions. The sample w i l l absorb energy from the magnetic f i e l d by means of the coupling between the magnetic f i e l d and the nuclear magnetic dipole moments. Classically, the resonating nuclei can be pictured as precessing around the z-axis of the electric f i e l d . About half of the nuclei w i l l tend to be aligned and rotating in one direction while the others w i l l tend to be aligned and rotating i n the other direction. Energy w i l l continue to be absorbed as thermal motions tend to dephase the precessing nuclei and i f the oscillating voltage i s removed the net magnetization w i l l decay with a time constant characteristic of the sample while i t i s inducing a voltage i n the solenoid. For maximum coupling the axis of the solenoid should be at right angles to the electric f i e l d z-axis. To observe the Zeeman splitting of nuclear quadrupole resonances the sample must be a single crystal because of the frequency dependance of the sp l i t lines with angle between the electric f i e l d z-axis and the applied mag- netic f i e l d . Also, since the magnetic f i e l d removes the 1 W[ degeneracy of the energy levels, only one rotating component of the solenoid f i e l d w i l l cause the nuclei to precess. This i s the same as i n nuclear magnetic resonance. 1 1 . In practice this solenoid forms part of a tuned c i r c u i t tuned at the resonance frequency and the production of the oscillating voltage and the observation of the resonance can be accomplished by a super-regenerative oscillator. A super-regenerative oscillator i s an ordinary oscillator which has a periodic voltage applied to one of i t s electrodes so that the o s c i l l - ations occur i n bursts. This periodic voltage i s called the quench voltage. An idealized super-regenerative oscillator using a square wave quench voltage can be described by the following equivalent c i r c u i t X i L j C ; &̂  represent the tuned c i r c u i t and L i s the sample c o i l . The osci- l l a t o r c i r c u i t may be adjusted so that the conductance supplied by the tube, G"x~G[ i s negative. rp The action of a square wave quench voltage of period ' i s to open and close the switch £ . When the switch i s closed at tj = O the oscillations w i l l be given by where r î JL = c< t > O • ^ = o< < O When the switch i s opened at time the oscillations w i l l be given by If -<£ i s long enough, the oscillator w i l l saturate and the envelope of the 12. oscillations i-d.ll become f l a t with a constant voltage ( J . This mode of operation i s depicted i n Figures 2 and 3. m If at time I rp where "K̂  i s the average amplitude of the noise voltage i n the tuned c i r c u i t the oscillations w i l l start up again from this voltage Ŷ , (1*) and coherent operation w i l l result. (Figure 2a. ). However, i f Y b ( i s much less than ^ then the oscillations w i l l start up from the randomly phased noise volt- age present and incoherent bursts of oscillations vrill result (Figure 2b.). The frequency spectrum of the oscillator energy i s a Fourier transform of the time variation of the energy present in the tuned c i r c u i t . Without a sample, i n the coherent state the frequency spectrum consists of a central line with a number of sidebands separated by the quench frequency. (Figure 2 c ) . As the tuned ci r c u i t i s varied i n frequency the set of lines w i l l shift acc- ordingly i n frequency. In the incoherent state the frequency spectrum i s a continuous noise spectrum with the shape that of the frequency response curve of the tuned c i r - cuit to a f i r s t approximation and the half-power points are separated by the bandwidth Bj t of the tuned c i r c u i t (Figure 2d. ) where ^ % = G - L / 2 T T C corresponding to a noise bandwidth Also as the tuned ci r c u i t i s varied i n frequency the peak of the noise 3pectrum shifts accordingly i n frequency. F I G U R E 2 to follow page.2 E N V E L O P E OF R E C T I F I E D O S C I L L A T I O N S C O H E R E N T OPERATION TIME x UJ o O E + <t >t o > N C O H E R E N T OPERAT ION T I M E R E C T I F I E D O U T P U T O F 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 ^ 1 F C O H E R E N T O P E R A T I O N 0) 27T F R E Q U E N C Y UJ 2 IT F R E Q U E N C Y O P E R A T I O N O F 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 W I T H N O S A M P L E P R E S E N T 13. The behaviour of the super-regenerative oscillator which, without a sample i s operating i n the incoherent state,is somewhat different with a sample present i n the solenoid. When the switch i s closed at t - O the oscillations build up and energy i s absorbed by the sample and the nuclei caused to precess as described previously. When the switch i s opened at "t ~ there i s , i n addition to the voltage given by equation (2.1b) , a vo l t - age induced by the precessing nuclei - Ct - V> where i s the frequency of the nuclear quadrupole resonance. At time rf1 the oscillations w i l l start up from this voltage and coherent oscillations w i l l result with the frequency of oscillation determined by L>JQ . The radiated energy has a frequency spectrum similar to that for coherent oper- ation without a sample except that as the tuned ci r c u i t i s varied i n frequency the center line and sidebands stay constant i n frequency but their amplitudes w i l l change because of the tuned ci r c u i t frequency response. (Figure 3. ). The relaxation tine of the sample must not be too short otherwise the signal Y s w i l l be less than the noise voltage and incoherent operation w i l l result. The most sensitive point of operation would seem to be that where, with- out a sample, the super-regenerative oscillator i s almost entering the coherent state. This point can be reached by adjusting various c i r c u i t parameters such as feedback, quench voltage and frequency, and electrode potentials. The signal to noise ratio of a resonance w i l l be determined by the signal voltage across the resistor^) , as well as the effective noise voltage per unit bandwidth)2 across G, and the effective noise bandwidth BL^of the detection F I G U R E 3 to fo l low page 13 a b R E C T I F I E D O U T P U T O F 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 — N O S A M P L E - S A M P L E : » F R E O U E N C Y E F F E C T O F S A M P L E U P O N 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 O P E R A T I O N lk. system. Since the signal voltage i s X ( t ) = e the mean square signal voltage i s and the mean square noise voltage i s where -fc i s Boltzmann's constant Teff i s the effective temperature of the noise present i n the system. The value of Teff i s given by the temperature of a resistor that w i l l prod- uce the same available noise power per unit bandwidth as the system does since, over a small frequency range, the system noise power per unit bandwidth i s constant. Part of this system noise i s produced by the conductance which usually i s at room temperature. The temperature of the noise produced by the tube de- pends upon i t s operation. A tube when operated as a super-regenerative oscillator i s probably somewhat noisier than when i t i s operated as an amplifier since, as with a mixer, i t i s not operated at i t s least noisy point at a l l times. An external quench oscillator can introduce noise since variations i n the quench frequency (assuming a square wave quench voltage) w i l l cause variations i n the starting up time of the oscillations and hence add a certain incoherence i n them. If the detection process takes place i n the super-regenerative oscillator c i r c u i t and the detected signal passed through an audio amplifier of effective noise bandwidth B~ AF the signal to noise ratio i s 15. (as) In the case where B^AF^-B^ the effective noise bandwidth of the rp system i s . For best results the quench period I i s r p _ co-nstft*t _ VS _ X _K VJhere the constant K i s chosen so that the oscillations i n the tuned c i r c u i t without a sample w i l l just die down below the noise level before the next cycle begins. This expression i s a maxinum for and the signal to noise ratio i s Therefore, for optimum c i r c u i t constants, the signal to noise ratio w i l l be proportional to the decay time ^ of the sample. Alternatively, i t i s possible to amplify the signal radiated by the super-regenerative oscillator, f i l t e r i t through an effective noise bandwidth B.^RF detect i t , and pass i t through an audio f i l t e r of effective noise bandwidth AF . B^RF i s assumed to be less than and B^AF ^ B^RF The signal to noise ratio i s 16. The factor (I-v S) arises i n the denominator because when the super- regenerative oscillator i s operating i n the coherent state with a sample i n the solenoid i t can be considered as an amplitude modulated oscillator where T the modulation i s a complex combination of sine waves of periods n where H i s integral. Therefore, signal voltage w i l l be modulated and poss- ess several sidebands on either side of the signal frequency spaced by the quench frequency (Figure lib. ) The noise can be considered as several (i n f i n i t e l y many) noise voltages with instantaneous frequencies spread through- out the spectrum determined by the tuned c i r c u i t of the Super-regenerative oscillator (Figure Ua.). Hence each noise voltage w i l l have several sidebands on either side of the instantaneous frequency and spaced by the quench f r e - quency. The effect of the modulation i s to place more noise voltages within the noise bandwidth B^RF (Figure lie. ). The noise voltages add incoherently so that the increase i n noise power may be described by & where £ depends upon the complex modulation and the shape of the tuned cir c u i t response curve. I f a large enough bandwidth B^RFx^Bj i s used then a l l the energy radiated by the Super-regenerative oscillator i s accepted and the presence of the quench voltage has no effect on the signal to noise ratio which w i l l then be that given i n equation ( 5 ) • For very weak signals, inaximum sensitivity i s obtained using some form of phase-sensitive detection. Usually i n this method of detection the signal i s modulated at an audio frequency with the modulation being detected and then passed into a phase-sensitive mixer whose local oscillator signal i s taken from the modulation oscillator with a possible phase change. A direct current out- UJ ID < \-_i o > F I G U R E 4 to follow page 16 SIGNAL AND NOISE a FREQUENCY UJ tD <t V- _ l o > MODULATED SIGNAL nRF 2 TT FREQUENCY UJ O _J O > MODULATED SIGNAL AND NOISE B, nRF j s n o n LM 2 7T FREQUENCY E F F E C T O F T H E Q U E N C H I N G P R O C E S S ON T H E S IGNAL TO NOISE RATIO O F THE S E P A R A T E DETECTION M E T H O D 17 put i s obtained and passed through a resistance-capacitance f i l t e r of time constant,^ and then displayed with an ammeter. Because of the large local oscillator voltage present at the phase-sensitive mixer the effective noise bandwidth i s B^ DC = two times the effective noise bandwidth of a single stage R- C f i l t e r The factor two occurs since both the upper and lower noise sidebands resulting from the mixing process contribute to the noise output. Therefore, we have a. ^D.C. &i V 1 In the case where the signal i s frequency modulated and the modulation recovered by passing the signal through a linear frequency discriminator the signal voltage may be represented by > 1 - 1-. -2. Di scriminator Response Curve frequency The factor -| occurs since the undeviated signal i s kept at the mid-point of the discriminator curve. The factor < 1_ allows for the frequency deviation of the signal being less than the width of the frequency discriminator curve. When this voltage is passed through a quadratic detector where V M Ct) = i ) v*w 18 the output voltage i s 4 where ^ means a time average long compared to <_ow but short compared to to • Without modulation the direct current output signal voltage would be V . „ t - D Y L ^ > U ^ With the coefficient of the Cos u)̂ ,tT o u t p u t ^ e q u a l to \ Y°«t given by(xc\Vj)» 1^ t n e spectral density of the noise power i s independent of f r e - quency over the range which the signal i s deviated, then frequency modulation of the noise produces no extra noise output at the modulation frequency after being passed through a frequency discriminator and a quadratic detector. There- fore, this particular type of recovery of frequency modulation reduces the s i g - nal to noise ratio by a factor of two assuming equal effective noise bandwidths i n each case. The maximum signal to noise ratio w i l l be most easily obtained by using a phase-sensitive detection system with a direct current f i l t e r of long time constant while using as high a quench frequency as possible. 19. CHAPTER III THE NUCLEAR QUADRUPOLE RESONANCE SPECTROMETER The basis of the spectrometer i s a push-pull grounded-grid super- regenerative oscillator with cathode quench voltage injection using type 955 acorn triode tubes. The tuned circuits are shorted p a r a l l e l wire trans- mission lines. The cathode line i s adjusted to give the proper feedback and the plate line, which has the sample c o i l i n parallel with i t , determines the frequency of operation of the osc i l l a t o r . The value of Teff i s assumed to be of the order of a few thousand degrees Kelvin *?hen the system i s operated at 150 mc/s. The tuned c i r c u i t bandwidth B 1 i s of the order of ?00 kc/s at this frequency. The quench f r e - quency i s normally 50 kc/s. If the detection process takes place i n the super-regenerative o s c i l l - ator c i r c u i t the signal can be amplified and displayed on an oscilloscope with the oscillator frequency modulated using a vibrating condenser and the o s c i l l - oscope swept i n synchronism with the frequency changes. Since the feedback, which i s controlled by the tuning of the cathode line, does not have to be changed over a f a i r l y wide frequency range of plate line tuning the spectro- meter i s suitable for searching for nuclear quadrupole resonances. For maximum sensitivity i n searching, phase-sensitive detection may be used where the re- sonance i s modulated by using a Zeeman modulation f i e l d supplied by a set of small Helmholtz c o i l s . ^ The disadvantage of the self-detection process i s that the adjustments 20. are much more c r i t i c a l than when the detection i s accomplished separately. It also tends to be unsuitable for observing Zeeman splittings of nuclear quadrupole resonances since the resolution i s essentially determined by the bandwidth B A of the tuned c i r c u i t . Greater resolution can be obtained by amplifying the radiated signal from the super-regenerative oscillator and passing i t through a f i l t e r of bandwidth B R ? which determines the resolution and then detecting the resonance. The radiation of the super-regenerative oscillator i s fed to a bal- anced germanium diode crystal mixer through capacitive coupling consisting of a short length of wire situated near the super-regenerative os c i l l a t o r tuned c i r c u i t . The l o c a l oscillator voltage i s supplied to the mixer by a triode frequency t r i p l e r stage excited by a quartz crystal controlled o s c i l l - ator (Figure 6a.). The difference frequency i s fed into a Haramurlund HQ-129-X communications receiver. The difference frequency i s determined by a BC-221-A frequency meter. The receiver i s equipped with a crystal f i l t e r so that the bandwidth B R F can be varied from a few hundred to a few thousand c/s. B^RF , the noise bandwidth, i s of the same order. The nuclear quadrupole resonance which appears as a series of noisy peaks separated by the quench frequency at the output of the receiver can be heard with earphones or i t may be recti f i e d and displayed with an ammeter (Figure 5a. ). Since the signal from the superwgenerative receiver into the mixer i s large no extra noise i s introduced by the rest of the spectrometer. The r e c t i - fied noise voltage at the output of the receiver was found to vary inversely as the quench frequency over a wide range of quench frequencies. In practice, when observing the Zeeman splitting of the resonances, the F I G U R E 5 SEPARATE D E T E C T I O N t o f o l l o w po ge 2 0 S U P E R REGENERATIVE OSCILLATOR -II- MIXER R E C EIVER 3 Q U E N C H OSCILLATOR HIGH F R E Q . C R Y S T A L C O N T R O L L E D OSCILLATOR P H A S E S E N S I T I V E D E T E C T I O N S U P E R REGENERATIVEH H M I X E R OSCILLATOR R E C E I V E R Q U E N C H OSCILLATOR HIGH FREQ. L ( OSCILLATOR FREQ. MOD. A U D I O OSC. AUDIO F I L T E R P H A S E S E N S I T I V E M I X E R B L O C K DIAGRAMS O F T H E A P P A R A T U S F I G U R E 6 t o f o l l o w p a g e 20 C R Y S T A L C O N T R O L L E D O S C I L L A T O R ft T R I P L E R 4 5 . 5 m c 8. 4 5 . 5 m c s . 1 3 6 . 5 m c s. L - C O S C I L L A T O R WIR ING D I A G R A M S F I G U R E 7 to follow page 20 F R E Q U E N C Y M O D U L A T E D Q U E N C H O S C I L L A T O R + B lOK 0 0 0 0 5 ^ 1 . > . 0 0 0 0 5 ^ f •11- Hh 8 2 K PI H A M M O N D 3 3 3 M O D U L A T I O N W I R I N G D I A G R A M 21. receiver i s set to a given frequency with the aid of the frequency meter, and the super-regenerative oscillator tuned for maximum noise at the receiver output. The crystal i s rotated i n the magnetic f i e l d and, since the local oscillator frequency is known, the frequency of the resonance as a function of crystal orientation i n the magnetic f i e l d may be determined. Since there are several peaks for each resonance the center line can be found by changing the quench frequency since only the central line w i l l remain unchanged i n f r e - quency. If the resonance is f a i r l y strong, a frequency modulated quench osc- i l l a t o r may be used and the resulting unmodulated center line picked out t quickly (Figure 7.). For more sensitivity phase-sensitive detection i s used. Modulation of the signal i s obtained by modulating the high frequency oscillator and i s re- covered by sweeping the resonance back and forth over one side of the receiver response curve. The resulting variations are f i l t e r e d and passed into the phase sensitive mixer, the signal being displayed on an Esterline-Angus graphic meter. A time constant TT-D.C. °f three seconds i s usually used. (Figure £b.) Suitable frequency modulation of the crystal controlled oscillator was not obtained and amplitude modulation of this oscillator has the disadvantage that the noise i s modulated also, introducing a D.C. component when passed into the phase-sensitive detector. The long term D.C. s t a b i l i t y was not good enough for the weak signals encountered. Instead, another local oscillator was used where the frequency was determined by an ordinary tuned c i r c u i t . The plate voltage was modulated slightly causing the resulting local oscillator signal to be almost entirely frequency modulated. The second harmonic was used for mixing. (Figure 6b.). 22. Modulation of the magnetic f i e l d could be used vjhen Zeeman s p l i t reson- ances are observed but the frequency deviation of the resonance i s proportional to the spli t t i n g and i n some cases a resonance would not be observed. The main magnetic f i e l d i s supplied by a set of water cooled Helmholtz c o i l s . Each c o i l has a bobbin with a winding space of 50 mm by 50 mm f i l l e d with #lU B. and S. gauge enamel covered copper wire. This gives 620 turns. The wire i s spaced every two layers by thin strips of card and the bobbin has holes punched i n the sides to allow a free flow of cooling water. The bobbin has a brass ring for the center and another brass ring i s slipped over the outer edge. Circular Tufnol plates with grooves and neoprene washers are placed on either side and held together with long bolts to make a water tight jacket. The inlet and outlet pipes for the water also act as terminals for the c o i l s . The f i e l d strength along the axis of one of the coils was measured using a flux meter and a graph (Figure 8.) drawn to determine the position of most nearly linear variation of f i e l d strength with distance, i . e . the point of i n - flexion of the curve. The graph indicated that the'two coils should be placed as close together as possible. The spacing was actually limited by the pro- jection of the outlet pipes from the inner faces. The crystal holder i s mounted on a rotating shaft and the supporting post which acts as a bearing i s attached to the base of the Helmholtz c o i l s . The crystal holder, shaft, and post are made of lucite to avoid distorting the magnetic f i e l d near the crystal. The system was aligned i n order to have the axis of rotation as nearly normal to the magnetic f i e l d as possible. At a current of 25 amperes through each c o i l the f i e l d at the crystal i s l . U kilogauss and l i t t l e heating of the coils i s noticed.  P L A T E I to follow poge 22 T H E S P E C T R O M E T E R SEP • 59 P L A T E I I to f o l l o w p a g e 22 H E L M H O L T Z C O I L S SEP • 59 CR Y S T A L HOLDER 23. CHAPTER IV BIFORMATION OBTAINED ABOUT SINGLE CRYSTALS OF Z n(B r03) 2 .6H20 AND C o ( B r 0 3 ) 2 .6H20 FROM THEIR ZEEMAN SPECTRA. The Zeeman splitting of the nuclear quadrupole resonances of single crystals of Z ^ B ^ ^ .6H20 and C o ( B R 0 3 ) 2 «^ H2° W E R C observed. The crystals were grown by evaporating an aqueous solution of the salt from a beaker i n which a seed crystal had been placed. The resulting crystals had volumes of about one cubic centimeter. The lucite crystal holders were turned on a lathe so that the face would be normal to the axis of rotation of the shaft. The crystals were usually attached by gluing one crystal face to the holder with a thin layer of polystyrene glue, which had the advantage that the crystal could be pried off easily without damage and could be remounted with a different orientation i n the magnetic f i e l d . If necessary lucite shims could be used to mount the crystal i n any given position. The current for the Helmholtz coils was supplied by a generator and was kept at a constant value of 25.00 - .05 amperes by means of a high-wattage variable carbon compression resistor. Care had to be taken to avoid the mag- netic f i e l d from the Helmholtz coils affecting the reading of the D.C. ammeter used to measure the magnet current. Q-i Since most unsplit resonance frequencies of the B r x isotope i n the metallic bromates l i e i n the 1U0 mc/s to 150 mc/s range a U5.5 mc/s quartz crystal was used so that the resulting frequency of 136.500 - .015 mc/s allowed 2h a convenient difference frequency to be accepted by the receiver. Absolute frequency measurements were estimated to be accurate to within i 20 kc/s. Relative frequency measurements where the receiver was set at a given f r e - quency with the frequency meter and then used to determine the resonance frequencies were estimated to be accurate within t 5 kc/s over periods of an hour or so. In practice the measured unsplit resonance frequency did not show this s t a b i l i t y . Variations i n the quench voltage and frequency and variations of the tuned c i r c u i t frequency of the super-regenerative oscillator i-rauld change the central line frequency by as much as - 20 kc/s. Daily variations i n the central line frequency amounted to as much as - 30 kc/s. Although i t i s assumed i n Chapter II that the super-regenerative osci- l l a t o r does not react- on the sample, by "pulling" the nuclear quadrupole resonance frequency, f o r example, i t may do so to a small extent but the main source of error i s believed to l i e i n the dependence of the resonance frequency on the temperature of the sample. The resonance frequency increases about 5 mc/s. when the temperature of ZnCBpO-^^H^Ois changed from room temperature to l i q u i d air temperature. At room temperature the unsplit resonance frequencies of ^(BrO^^^H^O and Co(B r03) 2.6H 20 are lU8.028t . 0 2 5 mc/s and lkl.926 - . 0 2 5 mc/s respectively for the B r ^ isotope. The line width (the frequency separation between half- power points) i s about U kc/s for both substances. When the perturbing magnetic f i e l d was applied the line width increased to about 1 5 kc/s due to inhomogen- ieties i n the magnetic f i e l d . The axis of rotation of the crystal holder was perpendicular to the magnetic f i e l d within 0 . 1 ° . - Since the secular equation for the energy levels 2$. depends upon s i n 2 © (formula (j 6)) replacing 0 b y - © w i l l not change the o resultant frequencies. When the samples were rotated 180 the difference between the two observed frequencies was less than 3 kc/s or 0.2% of the amount of the frequency s p l i t t i n g . A right angle was assumed in calcul- ations. The d i a l on the shaft could be read to 0.2 . In the case of ZnCBj.O.^.o'H^O the positions of the molecules in the unit c e l l are given by Wyckoff^. H 2 O similar to 0 ^ V\40 U - , vj= . 0 5 - 0 * = . 6 ^ 5 " ) Because of the 3-fold symmetry about the Br-Zn-Br axis, the electric f i e l d Z-axes should have direction cosines > ff, ; fg^and the asymmetry should be zero. The four Z-axes are p a r a l l e l to the £ I, I, 1̂  crystal axes. 7 A crystal of Zn ( 3 ^ 3 ) 2 * 6 ^ 0 was mounted with a face perpendi- cular to the axis of rotation and a plot of the frequencies of the s p l i t lines versus the d i a l reading of the shaft d i a l was made. (Figure 10). Formula ( l 5 ) was used with cos Q replaced by S ^.^n. Cos ^ ( ^ C 3 o ) where f i s the d i a l reading °C i s the angle between the z-axis and the axis of rotation • _ y~5~~ 5vn <\ — : from symmetry considerations. F I G U R E 9 c to fol low page 25 C R Y S T A L F A C E S L A B E L L I N G O F T H E Z - S Y M M E T R Y A X E S C A C R Y S T A L WITH C U B I C S T R U C T U R E F I G U R E 10 to follow page 2.5" T H E Z E E M A N S P L I T T I N G OF THE N U C L E A R Q U A D R U P O L E R E S O N A N C E OF Br 8 1 IN A SINGLE C R Y S T A L OF Z n ( Br CLL • 6H 0 . T H E ( l , l , l ) F A C E I S P E R P E N Dl C U L AR TO THE AXIS OF R O T A T A T ION. R E P R E S E N T S t V f T f e o s r i ((4 - (8/5) c o s 1 / ) * X X R E P R E S E N T E X P E R I M E N T A L R E S U L T S 26. The value of § was obtained by calibrating the magnetic f i e l d using the Co(B r03) 2.6H 20 crystal with two of t h e ^ l l j j type faces perpendicular to the axis of rotation (as mentioned on page 21), and using formula Q % ] . This was j u s t i f i e d because the crystal seemed to be accurately mounted and experi- mentally i t had cubic symmetry with negligible asymmetry. Because of the combination at times of weak signals and several side- bands some of the experimental points (FigureID) may be i n error by — 5>0 kc/s., the quench frequency used. However, the plot shows that formula(3o)[s satisfied closely which indicates that the crystal has a cubic structure and the asymm- etry parameter i s negligible to a f i r s t approximation. The ai gles i n space LS/^ ) W"X^/^^y to^bf the z-axes were found with the aid of \ .c^^nejKi a*is Here5wio^ i s calculated with the aid of formula(31\ Second order frequency changes i n the s p l i t lines to the magnetic f i e l d are subtracted out. Using formulae (^\)and(\7t)Tables 1 and 2 were prepared. An e s t i - mate of the experimental accuracy was obtained from the two values of given by each table. The two values d i f f e r by l°2ki. A l l the values given f a l l within 70° 32 ± hi' where 70° 32' is the value expected from symm- etry considerations. The value of 0^ as indicated by the angles at which the inner and outer lines coincide i s estimated to be less than 0,0$ since the T A B L E 1 to f o l l o w page 26 OBSERVATIONS OF THE ZEEMAN SPECTRA OF Z n(B r0 3) 2.6H 20 AND CALCULATIONS OF THE CRYSTAL FIELD PARAMETERS #1 Z-symmetry axis par a l l e l to axis of rotation H = 1U30 gauss 2 ^ ( 6 ^ 3 ) 2 . 6 ^ 0 Maximum frequency separation Dial reading Y between inner lines #2 2.789 mc/s 2L-.0.0 ° #3 2.7U8 359.1 ° #U 2.79U 119.8 ° SVA\C\ where cX i s the angle between the Z-symmetry axis and the axis of rotation n .9U58 #3 .91*15 #U .9U65 Angles [3^^. between the Z-symmetry axes fth2 = 69° U71 1^23 a 71° 07' - 69°U5' Dial reading Y where inner and outer lines coincide #2 292.U° ; 187.6° #3 306.9 ° , 51.U ° #U 171.8 ° , 67.8 ° Observed angles of coincidence Calculated angles (\*°) #2 52.U ° 52.U & #3 52.3 ° 52.2 ° #U 52.0 a 52.U ° T A B L E 2 to follow page 26 OBSERVATIONS OF THE ZEEMAN SPECTRA OF Z n(B r0 ?) 2.6H 20 AND CALCULATIONS OF THE CRYSTAL FIELD PARAMETERS #3 Z-symmetry axis paralled to axis of rotation H = 1U30 gauss Z n(B rO ?) 2.6H 20 Maximum frequency separation Dial reading ^ between inner lines ftl 2.70U mc/s 2U0.0 ' #2 2.780 359.8 ° #h 2.706 119.U ° 5w\ D{ where °^ i s the angle between the Z-symmetry axis and the axis of rotation #1 .9365 #2 Mo #U .9366 Angles ^^between the Z-symmetry axes f% - 71* n ' Pzx- 71°01' ( 9 ^ , 70- 27' Dial reading K where inner and outer lines coincide #1 292.0 ' , 187.9 #2 307.2 ° ; 52.3 ° #U 171.6 4 , 67.3 ° Observed angles of coincidence Calculated angles C ^ - 0 ) #1 52.1 ° 51.9 #2 52.6 ° 52.3 #3 52.1 ° 51.9 F I G U R E II tolollow page 26 Z E E M A N SPL IT R E S O N A N C E S OF Zn(BrO_) 6 H O S E P A R A T E D E T E C T I O N WITH P H A S E SENSIT IVE DETECTION Ul S I D E B A N D C E N T R A L L I N E > A N G L E / , S E P A R A T E D E T E C T I O N R E C T I F I E D NOISE * < C R Y S T A L M O U N T E D W I T H T H E ( i l l ) F A C E P E R P E N D I C U L A R T O T H E A X I S OF ROTATION 27. 0 determinations seem to be limited by the 0.2 error i n the d i a l reading and the line width of the s p l i t lines. According to Groth^, Co(BR03)2.6H20 as well as Zn^rOi^.&^O has a cubic structure. A crystal of C o(B r0T)2 »^ H 2° w a s mounted so that (I \ ,0 and 0.v,V)faces were parallel to the axis of rotation and the(i ~\ ,v) and (_\̂\ ,\) faces each made an angle of 5U.7 with the scds of rotation. Table 3 was pre- pared using formulae (3o], (̂>\) and(lA). Table 3 gives the angles between the Z-axes of the ei c t r i c f i e l d . Similar considerations of error as for Zn(Br03) 2.6H 20 apply except for the two Z-axes at 5U.7 to the axis of ro- tation. Since the rate of change of frequency with angle Y was slow the lines were harder to position accurately than the others. Table U deals with the observation of second order effects caused by the magnetic f i e l d as given by formula(is) . The unsplit resonance frequency of Ni(Br0^)2.6H20 was found to be 1U8.2U6 "t .030 mc/s at room temperature with a line width of about 10 kc/s. The signal to noise ratio was about one-fourth that of the unsplit resonance from Z n(B r03) 2.6H 20. The determination of the directions of the principal axes of the electric f i e l d gradient tensor as well as the asymmetry parameter i n this salt xrould be of interest since, according to the "Handbook of Chem- ist r y and Physics" this crystal has a monoclinic structure whereas, according to Groth, this crystal has a cubic structure as do the other two crystals studied here. Also, i f Ni(Br03) 2.6H 20 i s monoclinic then the information about the electric f i e l d gradient cannot be deduced from crystal symmetry. Unfortunately the Zeeman s p l i t resonances were not observed. This i s be- lieved to be due to the weaker, broader unsplit resonance produced by this crystal compared to that of Z n(B r03) 2.6H 20. However, the signal to noise ratio might be improved enough to obtain f a i r l y accurate data by increasing T A B L E 3 to follow page 27 OBSERVATIONS OF THE ZEEMAN SPECTRA OF Co(B r0 3) 2.6H 20 AND CALCULATIONS OF THE CRYSTAL FIELD PARAMETER #1 and #3 Z-symmetry axes perpendicular to axis of rotation H = 1U30 gauss Co(Br03)2.6H20 Maximum frequency separation Dial reading Y between inner lines #1 3.296 mc/s 53.2 ° #2 3.299 123.7 S w ^ where °i i s the angle between the Z-symmetry axis and the axis of rotation #1 1.000 #2 1.000 Angle ^^between the Z-symmetry axes /?13 » 70.5 ° Dial reading X" where inner and outer lines coincide //l 358.6 ° , 107.9 ° #3 178.6 ° , 68.9 #2 and 4k 358.2 ° , 178.2 ° Observed angles of coincidence Calculated angles C.^" 0) #1 5U.7& 5U.7 #3 5U.9° 5U.7 ° #2 and #U 90.0 " 90.0 ° Assuming 1^=-o and using formulae (j 7k)and (31) then /?2k * 7 0 ^ " ft 12 =" 70*7 ° = 70aU° T A B L E U to follow p a g e 27 OBSERVATIONS OF SECOND ORDER EFFECTS OF THE ZEEHAN SPLITTING OF THE NUCLEAR QUAD- RUPOLE RESONANCE OF Co(B r 0 3 ) 2 . 6 H 2 0 . Co(B r03) 2 .6H 20 with ?"1 and f'3 Z-symmetry axes perpendicular to axis of rotation H = 1U16 gauss Unsplit resonance frequency Dial reading Y 17.7 " 87.8 * 158.6 197.U 268.0 338.5 f l ~ = 18 kc/s 3A LU7.926 mc/s Frequency difference between unsplit li n e and coincidence of inner aid outer l i n e . 2U kc/s 23 23 a. 22 22 Unsplit resonance frequency V Outer line 87.8 ° 268.0 " Outer line (--) 87.8 268.0 1U7.930 mc/s Observed frequency 150.778 mc/s 150.776 1U5.119 1U5.120 Calculated frequency 150.756 mc/s 150.756 1U5.10U 1U5.10U F I G U R E 12 to follow page 2 7 Z E E M T k N SPLIT R E S O N A N C E S OF C o ( Br oJ BH^O S E P A R A T E D E T E C T I O N R E C T I F I E D NOISE SIDEBAND UJ A o < Y- -I O > C E N T R A L L I N E a A N G L E / — > C O I N C I D E N C E O F AN INNER AND AN O U T E R L I N E C R Y S T A L M O U N T E D W I T H T H E ( i l l ) F A C E P E R P E N D I C U L A R T O T H E AXIS OF R O T A T I O N UJ o <t h- _l o > S I D E B A N D C E N T R A L L I N E \ / x {K C E N T R A L L I N E ( O B S C U R E D ) SIDEBAND . M S I D E B A N D 1 ' b A N G L E Y C O I N C I D E N C E O F FOUR INNER AND F O U R O U T E R L I N E S C R Y S T A L M O U N T E D W I T H T H E ( M l ) A N D ( i l l ] F A C E S P A R A L L E L TO T H E A X I S OF R O T A T I O N 28 the sample size, lowering the sample temperature, and using a more homogen- ous magnetic f i e l d . In conclusion the folia-ring has been achieved, (i) A nuclear quadrupole resonance spectrometer has been b u i l t to work on narrow band operation with sufficient s t a b i l i t y to measure the Zeeman 8l splitting of the nuclear quadrupole resonance lines of B r at 1U8 mc/s. ( i i ) This instrument i s sufficiently stable to detect second order effects i n the Zeeman splitting of these lines but not to measure these quan- t i t a t i v e l y . ( i i i ) Two salts, Z^Bj.O^g.&^O and C o(B r0^)2»6H20 have been examined. Both have been reported to be cubic i n structure, although l i t t l e data i s given for the cobalt salt. The nuclear quadrupole resonance spectrum i s con- sistent with a cubic crystal structure. There are k non-equivalent (B r0^) ions per unit c e l l . To within the accuracy of the experiments, the principal axis of the electric f i e l d gradient at the Bj. site i s along the ̂  I \t \ j crystal axes, and the asymmetry, which farthis cubic structure should be zero, i s measured to be less than 0.05? i n each case. (iv) An unsuccessful attempt was made to determine the crystal f i e l d parameters i n monoclinic Ni(Br0^)2.6H20. In this system these parameters are not determined by symmetry considerations. The reason for lack of success was poor signal to noise ratio for the weak, broad lines i n this s a l t . 29 B I B L I O G R A P H Y 1. C. Dean, "Zeeman Splitting of Nuclear Quadrupole Resonances", The Physical Review, Vol.96, No.U, 1053-1059, November 15, 195U. 2. C. Dean and M. Pollak, "Suppressing Side-band Interference i n Super- regenerative r . f . Spectrometers", The Review of Scientific Instruments, Vol.29, No.7, pp 630-632, July 1958. 3. H.G. Dehmelt, "Nuclear Quadrupole Resonance". American Journal of Physics, Vol.32, No.3, pp 110-120, March 195U. U. Beverley Joan Fulton, "A Nuclear Quadrupole Resonance Spectrometer", M.A. Thesis, University of British Columbia, Vancouver, B.C., 1956. 5. P. Groth, "Chemische Krystallograph!e", Vol .2, pp 112, Wilhelm Engele- mann, Leipzig, 1906. 6. Charles D. Hodgman, Edit. "Handbook of Chemistry and Physics" hDth Edition, Chemical Rubber Publishing Co., Cleveland, 1959. 7. Kenji Shimomura, "Structural Investigation by Means of Nuclear Quad- rupole Resonance I (Determination of Crystal Symmetry)" Journal of the Physical Society of Japan, Vol.12, No.6, pp 652-657, June 1957. 8. S.N. Van Voorhis, Edit. "Microwave Receivers", Vol.18. M.I.T. Radiation Laboratory Series, McGraw-Hill Book Co., New York, 19U8. 9. J.R. Whitehead, "Super-regenerative Receivers", Cambridge University Press, 1950. 10. Ralph W.G. Wyckoff, "Crystal Structures", Vol.11, Chap.X, text page 32, Interscience Publishers Inc., New York, 1951.

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