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An 8mm solid state spectometer 1962

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AN 8mm SOLID STATE SPECTROMETER by KER PING LEE B.Sc, Chung Chi College, 1960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1962 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia, Vancouver 8, Canada. Date - i i - ABSTRACT A sensitive, wide or narrow band, sol id state spectrometer operating at a wavelength of 0.85 cm has been b u i l t which i s described in deta i l . The spectrometer i s of the crystal detector reflection-cavity-in-magic-Tee-bridge type and can operate from room down to l i q u i d helium temperatures. The cavity Is excited In the TE-JJJL mode and the magnetic f i e l d modulated at 140 cps. Both large and small f i e l d modulations are incorporated for scope presentation of linewidth varying from about 0.5 to 500 gauss. Signals from single crystals of copper sulphate pentahydrate and polycrystal l ine l - l -d ipheny l -2 -p icry l hydrazyl (DPPH) have been obtained. From the l a t t e r , a sensit ivity l imi t of about 10 gram i s obtained at room temperature for a bandwidth of 1 cps Indicating a sensit ivi ty of the order of 10~^ gram at 4 . 2 ° K. Various methods of improvement were discussed in order to reach the ultimate sens i t iv i ty . - i i i - ACKNOWLEDGMENT The research described in this thesis was supported.by the National Research Council of Canada through the research grant to Dr. J . Veit and the award of two summer assistantships (1961,62) to the author. I am indebted to Dr. J . Veit who f i r s t introduced me to the present f i e l d . To Dr. I F i r t h , I am grateful for his valuable assistance without which the thesis could not have been completed. I wish to akcnowledge the generosity of Dr. G. Voss of the E l e c t r i c a l Engineering Department for lending me the EMI klystron osc i l la tor used in the experiment. I am much thankful to Mr. J . Banner whose incessant aid throughout the construction of the apparatus as well as the experi- ment has been greatly appreciated. The members of the Physics Work Shop have been very cooperative. I would l ike to thank, especially, Mr. A. Fraser for making a l l the microwave cavities used in the experiment and Mr. J . Lees for building the vacuum system. I wish also to thank Mr. J . Felton and Mr. R. Weissbach for supplying the l iqu id nitrogen and l i q u i d helium and Mr. D. Y. Chung for assisting in transferring l i q u i d helium. F i n a l l y , acknowledgment i s made to Dr. R. Howard and Dr. J . B. Brown for their kindness in reading the manuscript. - i v - TABLE OF CONTENTS Page ABSTRACT . . i i ACKNOWLEDGMENT i i i LIST OF TABLES v i LIST OF ILLUSTRATIONS vi. • LIST OF PLATES v i i CHAPTER I INTRODUCTION . . , 1 II QUANTUM THEORY OF PARAMAGNETISM 3 2.1 The Magnetic Resonance Phenomenon 3 2.1.1 Resonance Condition 3 2.1.2 Fine Structure 4 2.1.3 Hyperfine Structure i 5 2.2 Theory of Line Width 6 2.2.1 Spin-Lattice Interaction 6 2.2.2 Spin-Spin Interaction 7 2.2.3 Exchange Interaction 8 2.3 Effect of Crystall ine F ie ld 9 2.4 The Theoretical Hamiltonian .10 III DESCRIPTION OF APPARATUS 15 3.1 Introduction 15 3.2 The Microwave System 15 3.2.1 The Microwave Power Source .15 3.2.2 Waveguide Components .16 3.2.3 Crystal Detectors 16 3.2.4 The Cavity Resonator 17 3.2.5 Wavelength Measurement 17 3.3 Magnetic Fie ld Equipment 17 3.3.1 The Magnet 17 3.3.2 The Magnet Power Supply 18 3.3.3 Low Frequency Modulation 19 3.4 The Detection System 19 3.5 The Vacuum System 20 IV EXPERIMENTAL PROCEDURE 22 - V - CHAPTER Page V EXPERIMENTAL RESULTS 26 5.1 Introduction . . . 26 5.2 General Information . . . . . . , : 27 5.3 Results 28 VI CONCLUSION AND DISCUSSION 32 Appendix 34 Bibliography 40 - v i - LIST OF TABLES TABLE Page 1 Sensit ivity of Q-band Spectrometer Obtained . 30 2 Comparison of Sensit ivity of Different Spectrometers . . . 31 LIST OF ILLUSTRATIONS To Follow FIGURE Page 1 Energy Level Diagram for S = 3/2 ion with Magnetic F ie ld H para l l e l to the Axis of Crystall ine F ie ld 4 2 Electronic Splitt ings of C u 2 + 4 3 Block Diagram for 8 mm Microwave Circui t 15 4 Cross-Section of" the Cavity 17 5 Block Diagram of a Single Modulation Spectrometer 25 6 A Schematic Diagram of the Vacuum System ., 20 7 The Cryostat 20 8 Signals from 2 mg of CuS04:'5H20 Single Crystal .28 9 Signal from 0.2 mg of Powder DPPH 28 - v i i - LIST OF PLATES To Follow PLATE Page I View of the Main Microwave Arrangement . . . . . . . . . 15 II View of the Magnet and the Cryostat .15 III General View of the Apparatus ...... 42 - I - CHAPTER I INTRODUCTION Magnetic resonance i s a branch of radio-frequency spectroscopy invaluable to the study of the sol id state. It can be c lass i f ied into nuclear, ferromagnetic, antiferromagnetic and paramagnetic resonance. Nuclear resonance i s concerned with nuclear dipoles, the others with electronic dipoles. In ferromagnetic and antiferromagnetic substances, the electronic dipoles are strongly coupled together by exchange forces while in paramagnetic materials, the electronic dipoles form a loosely coupled system; each paramagnetic ion may be treated individual ly . The phenomenon of paramagnetism occurs whenever a system of charges has a resultant angular momentum. If this momentum is of electronic or ig in , one speaks of electronic paramagnetism. For instance, paramagnetism can be found in atoms and molecules having an odd number of electrons, in molecules with an even number of electrons but having a resultant angular momentum, in the so-called colour centres, in metals and semiconductors (caused by conduction electrons). The properties of-the paramagnetic ion can be obtained from measure- ments of the suscept ibi l i ty , specific heat, gyromagnetic ra t io , Faraday effect, paramagnetic relaxation and paramagnetic resonance. However only the las t method enables studies to be made from the microscopic -2- point of view. It i s also more sensitive than any of the other methods. Consequently, i t can deal with very small quantities of paramagnetic substance. This i s very convenient and often advantageous. A considerable amount of research has been carried out on microwave absorption in sol id state compounds and most attention has been given to paramagnetic resonance absorption. The results obtained from an analysis of these spectra give considerable information on forces and interactions existing in the sol id state. Paramagnetic resonance gives the most direct and accurate description of the ground state and of the effect of crystal l ine f i e l d on the energy levels of the paramagnetic ion. Its high sensit ivity also permits the perturbations of the nuclear spin and nuclear e lectr ic quadrupole moment to be detected. In this thesis, we shall be concerned with the design of a spectrometer suitable for such studies. A short account of the theory of paramagnetic resonance w i l l be given in Chapter II . Chapters III and IV give the descriptions of the apparatus and the experimental procedure in deta i l . Following are the experimental results obtained from the testing of the spectrometer. - 3 - CHAPTER II QUANTUM THEORY OF PARAMAGNETISM Excellent summaries of the experimental and theoretical aspects of paramagnetic resonance can be found in the review art ic le by Bleaney and Stevens (B4) and in a complementary review by Bowers and Owen (B5). In this chapter, the theory w i l l be br ie f ly discussed. For more deta i l , the reader i s referred>to the above-mentioned art ic les together with the texts by Low (L2) and Ingram (II). 2.1 The Magnetic Resonance Phenomenon 2.1.1 Resonance Condition If a free ion of a resultant angular momentum J i s placed in a uniform magnetic f i e l d H, the energy levels corresponding to the various spatial orientation of J. are given by W = g ^HM (2.1) , eh g i s the Lande g factor and i3 = ^-^ I s "the Bohr magneton; e, m are the charge and mass of the electron, c i s the velocity of l i g h t , h is Planck's constant, M i s the component of J along the f i e l d acting on the ion. If an alternating field"of frequency V i s applied at right -4- angles to H, magnetic dipole transitions are produced when h V = g £ H (2.2) according to the selection rule A M = 1 1. In a system of ions in thermal equilibrium with their surroundings, the lowest state has the greatest population. Since transitions up and down have the same a p r i o r i probabi l i ty , the net result i s a greater . absorption than emission of energy causing a damping of the tuned c i rcu i t with which the paramagnetic substance i s coupled. 2.1.2 Fine Structure The degeneracy of the ground state of a paramagnetic ion in a crystal i s often l i f t e d by the crystal l ine e lectr ic f i e l d and other interactions. Consider an ion of spin 3/2 with an i n i t i a l sp l i t t ing between the doublets M = 1 \ and M = - 3/2 due to an axial crystal l ine f i e l d : ( F i g . l ) . The energy levels diverge l inear ly when a magnetic f i e l d i s applied along the axis which i s taken as the axis of quanti- zation. An osc i l la t ing magnetic f i e l d component perpendicular to the £ axis induces transitions A M s = ± 1 and the p a r a l l e l component induces transitions i Mg =0 . In A M s = - 1 transit ions, a t r i p l e t structure results when the frequency is kept constant as indicated by the arrows in F i g . 1 and the magnetic f i e ld is varied. This forms the 'fine structure' of the spectrum. 2+ • In Cu ion shown in F i g . 2 (11), most of the to ta l degeneracy•of (2L+1)(2S+I) = 10 i s removed by the cubic and tetragonal f ie lds of the To fol low page 4 M s Initial splitting by crystalline • field H increasing F i g . 1 Energy Level Diagram for S=3/2 ion with Magnetic F ie ld H Parallel to the Axis of the Crystalline F i e l d . 2 , Ground State D f \ i i » i ~ i i mt \ « » / » / » / • / % \ » \ / / \ E l £ h » = g^H Free Cubic Tetragonal Spin-orbit Magnetic Ion F i e l d Fie ld Coupling Fie ld + 2 F i g . 2 Electron Splittings of Cu -5- crystal l ine l a t t i c e , the whole of the degeneracy being removed by the addition of the spin-orbit interaction. According to Kramers theorem.(K2) an ion having an odd number of electrons must have i t s energy levels remain two-fold degenerate and the degeneracy can be raised only by an applied magnetic f i e l d . Since the orbi ta l spl i t t ings are very large a l l the copper ions w i l l be in the lowest state Ej_, and we have a paramag- netic resonance absorption spectrum without fine structure. 2.1.3. Hyperfine Structure When the nucleus of a paramagnetic ion also possesses a resultant angular momentum I and hence a magnetic moment, there w i l l be an inter- action with the electronic motion.. In-a strong external magnetic f i e l d , each electronic leve l i s s p l i t into (21+1) levels due to the (21+1) different orientations of the nucleus. The osc i l la t ing f i e l d exerts a negligible effect on the nuclear moment (about 10 times smaller than that of the electron) so that the allowed transitions become A. Mj = 0. • This together with A M g = i l selection rule gives (21+1) hyperfine l ines . Since at normal temperatures a l l nuclear orientations are equally probable, the l ines w i l l have equal intensity. Also in a strong f i e l d , the energy levels vary l inearly with the f i e l d . The l ines are therefore equally spaced. If the external f i e l d is comparable to that produced by the nucleus, the component hyperfine levels w i l l contain an admixture of different Mj states giving rise to unequal sp l i t t ing of the levels . When two states contain the same value of Mj, a transit ion i s allowed which appears to be "forbidden" when the states are labelled by their strong f i e l d quantum numbers. - 6 - Another cause of unequal spacing is due to the interaction of the nuclear e lectr ic quadrupole moment with the gradient of the e lectr ic f i e l d produced at the nucleus. If the applied f i e l d i s para l l e l to the gradient of the e lectr ic f i e l d , this interaction w i l l shift the energy 2 levels by an amount proportional to Mj . If the two directions are not p a r a l l e l , the various nuclear states are admixed and forbidden t rans i - tions result as before. 2.2 Theory of Line Width Very often, the resolution of the fine structure and hyperfine structure i s l imited, not by instrumental effects, but by the l ine widths of the absorption l ines . This width i s dependent upon the intei?- action between the paramagnetic ions and their surroundings and on the interaction among the ions themselves. The natural l ine width arises from the f in i t e l ifetime of a given state and i s completely negligible compared with the other factors ( l l ) . It w i l l not be discussed here. The other more important sources of broadening w i l l be br ie f ly treated below.. 2.2.1 Spin-Lattice Interaction The spin- latt ice interaction may be characterized by a spin-latt ice relaxation time T-̂  which is a measure of the rate at which a spin system approaches equilibrium with the la t t i ce after having been disturbed by the absorption of energy. The mechanisms have been discussed by many authors (L2). There i s the indirect process or Raman process in which the spins - 7 - transfer energy with the la t t i ce by means of inelast ic scattering of 2 7 phonons. For the case of S = 1/2, Tj_ cC ^ 6 / \ T for T < Debye temperature @ ^ and proportional to for T > ® n . A i s the height of the next orbi ta l above the ground state and A. i s the spin-orbit coupling coefficient. I f the spins exchange a quantum of energy direct ly with a la t t i ce vibration of the appropriate frequency, we have the direct process. —2 —1 Then T^ 0 0 H T for non-Kramers salts (even number of electrons) and Tj_ °c H-^T"~^ for Kramers salts . The Orbach process (01), aris ing from phonon resonance effects, gives T-j_ oC. exp ( ^ / k T ) . Spin-lattice relaxation i s the predominant l ine broadening mechanism at high temperatures. In practice the temperature at which measurements are made i s always reduced u n t i l the l ine width Is due to spin-spin rather than spin-latt ice interaction. 2.2.2 Spin-Spin Interaction The second broadening effect arises from the interaction between the dipoles which can be regarded as rather l ike bar magnets precessing about the external f i e l d . The component in the f i e l d direction sets up a steady f i e l d at the neighbours altering the to ta l f i e l d value s l ight ly . This process of broadening is similar to that produced by an inhomo- geneous magnetic f i e l d . Also the rotating component sets up a rotating f i e l d which may induce transitions in the neighbouring ions and thus decreasing the normal lifetime of the energy state. A broadening results as a consequence of the Uncertainty Principle . The theory of spin-spin interaction has been developed by Van Vleck (V2) and Pryce and Stevens (P4). For free spins, the mean- square width as given by Van Vleck i s \2 = i sCS+ne2 A 2 51 l-Scos^Q 2 > 2 I 2 3* (2 .3 ) where 0 i s the angle between the l ines joining the dipoles and the direction of the applied f i e ld r being the distance between the j and kth ion. The second term refers to interaction between dissimilar ions. This dipolar interaction can also be described by a relaxation time T2 as defined by T2 = \ T g C V ) ] (2.4) ^ L. Jmax where g ( V ) i s the normalised l ine shape function. 2.2.3 Exchange Interaction If the paramagnetic ions are close enough together exchange inter- action may occur between them, which can alter the l ine width consider- ably. When the spins are identical and S = 1/2, Van Vleck (V2) shows that the exchange interaction contributes to the fourth moment but not to the second moment of an absorption l ine . Since the tota l area of -9- the l ine cannot change, the l ine w i l l be. peaked and the extra area d i s - tributed in the wings. This i s exchange narrowing. For dissimilar ions, such as ions precessing about different axes., the exchange interaction tends to bring the two different transitions together and hence produce one wider l ine . In other words, the exchange interaction contributes to the second moment and we have exchange broad- ening. In general, both exchange broadening and exchange narrowing are present and the resultant l ine width depends on the relative contribution of each. The effect of exchange interaction is well exemplified in the test samples. Copper sulphate shows exchange broadening as a result of the coalescence of the two l ines due to the two dissimilar Cu ions in the unit c e l l (Bl) . For DPPH free radicals , considerable exchange narrowing resul t s ' in a very narrow l ine width even in a polycrystal l ine sample (H2). 2.3 Effect of Crystal l ine Fie ld As indicated in section 2.1.2, a paramagnetic ion in a crystal is subjected to a strong inhomogeneous e lectr ic f i e l d called the crystal l ine e lectr ic f i e l d . This f i e ld originates in the environment of the para- magnetic ion and consists of (a) static and (b) fluctuating components. The latter, i s due to the thermal vibration of the la t t i ce and contr i - butes only to the l ine width (see section 2.2.1). The static component, to the f i r s t approximation, w i l l have the same symmetry as the crystal structure. Its effect i s to cause a Stark sp l i t t ing of the energy levels of the Ions thereby removing some of the (2J+1) degeneracy; -10- (J=L+S). The degree to which this degeneracy is l i f t e d depends on the symmetry of the f i e l d . Experimental data reveals that the strength of the various crystal l ine f ie lds f a l l into three groups. ( i) In the weak f i e l d case, L and S are not uncoupled but s t i l l precess around the resultant J which- in turn precesses about the direc- tion of the applied e lectr ic f i e l d . Good examples are the rare earth salts where the unpaired 4f electrons are somewhat shielded from the direct influence of the crystal l ine f i e l d . ( i i ) Medium Fie lds . The coupling between L and S Is broken so that they precess about the f i e l d separately and J i s no longer a good quantum number. It i s found that the orbi ta l motions are usually quenched. For example the iron group hydrated salts . ( i i i ) The f i e l d may be so strong as to destroy both the LS coupling and the coupling between the angular momenta and spins of the individual electrons. Again the orbi ta l motion i s quenched. This i s typif ied by the iron group cyanides. 2.4 The Theoretical Hamiltonian The Hamiltonian of an ion in a crystal l a t t i ce can be written as the sum of a ..number of interaction terms. The exact solution i s usually obtained for the largest term and the contributions of the remaining terms taken into account by perturbation calculations. The various terms' are: (a) The Coulomb interaction of the electrons with the nuclear charge Ze and the mutual repulsion of the electrons. In the -11- n o n - r e l a t i v i s t i c approximation, i t i s given by. N N W F = 21 ( P k / 2 m ~ Z e / r k ) + Yl 6 /r kj k=l k > j=l where P k = l i n e a r momentum r k = radius vector from nucleus to electron. (b) The magnetic interaction between the electron spin ŝ . with the o r b i t a l momentum l k . . W-LS 3k where a j k ' ̂ jk» c j k a r e constants. (c) The mutual interaction between the electronic spins V *j • sk 3 ( r - k • S - P O ^ • ^ Woo - L 3 k r 3k 3k (d) The interaction energy due to the nuclear spin I and nuclear quadrupole moment Q. 2 % 4- i 3 - — + ~ 5" ~ + — ^ O k H ' 1 w e 2Q Q 21(21 - 1 ) k I I 1(1 + 1) 3 ( r k . I)- Here >̂ ̂  and "Y refer to the nuclear magneton and nuclear - 1 2 - gyromagnetic ra t io . ..(e) The effect of the external magnetic f i e l d H which produces the sp l i t t ing of the electronic levels between which the transitions are observed. (f) The direct interaction of the nucleus with the external f i e l d . \ • - t e N H • 1 (g) The interaction of the crystal l ine e lectr ic f i e l d . Wy = eV(x k 5 y k , z k ) where V^x^, y^., z-̂ ) i s the potential . The general Hamiltonian is therefore given by ^ = WF + Wy + W L S + W s s + WH + WN 4- WQ + Wh ( 2 . 5 ) The order of magnitude of these interactions are Wp ̂  10^ cm ~̂, 3 4 -1 2 3 - 1 ' -1 - 1 Wy 'n- 10 - 10 cm , W-̂ g ^ 1 0 - 10 cm , Wgg ̂  cm , Ŵ  ̂  cm , WN ~» 1 0 - 1 - 1 0 ~ 3 c m - 1 , W Q ^ - 1 0 ~ 3 c m - 1 , and Ŵ . ~ 1 0 ~ 3 cm" 1. If we confine our discussion only to states which are eigenstates of L and S, eon. ( 2 . 5 ) can be written as a sum involving terms represent- ing electronic interactions and terms representing nuclear interactions. -13- A perturbation method of calculation has been given by Pryce (P3) in which the operators referring to spin and nuclear variables are treated as non-commuting algebraic quantities. An expression involving the components of S and I i s obtained. This i s called the 'Spin Hamiltonian' whose f i r s t order approximation gives 3 f = S - . - D ' S + p H ' g - . S + S ' T ' I + I ' P ' I - T^ N H • I - p2 H • A • H (2.6) If the crystal l ine f i e l d has axial symmetry about the z-axis, s z 2 - \ S(S + 1) I y ) + p [ l / - | 1(1 + l ) j + A S z I z + B(S X I X + S y g N p N H • I - £ H ' A ' H (2.7) S here i s the effective electronic spin and i s determined by equating the mult ip l ic i ty of the l ine observed to 2S. The term in D describes how the levels behave in zero magnetic f i e l d in the absence of nuclear interaction. -gf and g x are the g values when the f i e l d is applied para l l e l and perpendicular to the crystal l ine e lectr ic f i e l d axis respectively. A and B measure the sp l i t t ing of the hyperfine structure. P refers t© the quadrupole sp l i t t ing and i s related to Q through p = 3eQ ^3^X^/41(21 - 1). The f i n a l term - a? H • i\ • *H representing -14- a constant interaction independent of S or I i s normally very small and can be neglected. The actual energies are then given by the eigenvalues of the new operator in the equation l^'ty- E 0 l | ^ where represents the wave functions of the effective spin states. -15- CHAPTER III DESCRIPTIONS; OF APPARATUS 3.1 Introduction The essential elements of a microwave sol id state spectrometer are (a) a monochromatic source, preferably of variable frequency, (b) a cavity (absorption or reflection type), (c) a variable magnetic f i e l d , and (d) a detector. In this chapter, the components of the narrow band, single modula- tion spectrometer are described in deta i l . Block diagrams w i l l be employed to i l lus tra te the design principles and the actual c i rcu i t diagrams are collected together in the appendix. The spectrometer can function from room to helium temperatures. 3.2 The Microwave System The Block diagram for the microwave setup Is shown in F i g . 3. The photograph in Plate I shows the general arrangement of the microwave components. 3.2.1 The Microwave Power Source Besides having a variable frequency source, a good spectrometer further requires that To follow page 15 K L Y S T R O N rlSOLATOl ? A T T N D I R E C C Q U p i . F . R H M A T C H E P L O A D STUB T U N E R M A G I C TEE C A V I T Y F X R SUPPLY . A T T N A T T N 1 W A V E - M E T E R 1 IN53 X T A L < • STUB T U N E R IN53 X T A L F i g . 3 Block Diagram for 8mm Microwave Circuit . To follow page i5 PLATE II VIEW OF THE MAGNET AND THE CRYOSTAT -16- (a) the frequency and power be suff ic iently stable, (b) there must be enough power output (usually of the order of milliwatts),and (c) a low noise level is desirable for good resolution and sensi t iv i ty . In the present experiment an EMI valve type reflex klystron (VX5023T) capable of generating about 50 mW of power i s used. This klystron i s tunable from 34.6 to 36.4 Gc/s and i s forced air-cooled. In order to satisfy (a), i t i s necessary to have a stable low ripple power supply. We have chosen an FXR Model Z815B Universal Klystron Power Supply Unit with a regulation of better than 0.3%. The rms ripple voltage i s less than 3 mV for the beam voltage and less than 1 mV on the ref lector. Saw-tooth, square-wave,sine wave and pulse modulations are available at various voltage levels and frequencies. In the experiment, only saw-tooth modulation was used to sweep through the klystron reflector mode. 3.2.2 Wave-Guide Components A l l of the wave-guide components are commercial units manufactured by the DeMornay Bonardi Corporation except for the circulator which is a Cascade Research product. This unit i s used to isolate the microwave source from the rest of the system (G2). 3.2.3 Crystal Detectors For the detection and monitoring of the microwave power 1N53 s i l i con diodes are used. These are designed for a centre frequency of 35.0 Gc/s and are mounted on broad-band crystal mounts. -17- 3.2.4 The Cavity Resonator A c ircular cy l indr ica l cavity resonator operating in the H-^-^ mode has been designed from data given by Wilson (W2). It i s made -of brass. The choice of the fundamental mode of excitation has the advantage of concentrating the microwave energy at the bottom of the cavity where the sample can be conveniently placed. Care has been taken to choose a size as large as possible within the l imitat ion of the magnet gap such, that no interference modes nor crossing modes can exist. This la t ter precaution reduces the trouble of determining the mode of excita- tion in the cavity which i s very troublesome at 8 mm and below. The cavity used i s a fixed size one. However, i t i s re lat ive ly simple to convert to a'tunable cavity by incorporating a choke plunger as the termination. The Q of the cavity i s of the order of 2000 at room temperature and the diameter and thickness of the coupling hole are respectively 1.5 and 0.2 mm. 3.2.5 Wavelength Measurement A broadband absorption type low Q cavity frequency meter i s employed as an estimate of the klystron frequency by monitoring the power from a-directional coupler (Fig. 3). It i s a Sperry product and i s suitable for operation in the range of 26.5 - 39.0 Gc/s. The abso- lute accuracy is about 0.1%. This low Q wavemeter i s convenient for a rapid estimate of the frequency of the klystron. For more precise work, a high Q wavemeter should be included. 3.3 Magnetic Fie ld Equipment 3.3.1 The Magnet A magnetic f i e ld intensity of over 10 kilogauss i s produced by To follow page 17 Supporting Brass Block Tuning Screws Solder Flux Coupling Flange 7.6 Rectangular German Silver Guide Screw(No. 000-120) ] ~ A l Coupling Disc Brass Cavity Sample 9.2 F i g . 4 Cross-section of the Cavity . ( A l l Dimensions in m m . ) -18- a small electromagnet designed by Buckmaster and partly constructed in the departmental machine shop. For fu l l er detai ls , reference should be made to H. A. Buckmaster1s thesis (B6). Br ie f ly , the main features are (a) adjustable gap up to 3" (b) rotatable magnet yoke (360° with 0 . 5 ° calibration) (c) ver t ica l l eve l adjustment (d) water cooled (e) good homogeneity of the order of 0.5% (f) tro l ley mounting for ease of moving. Plate II shows the view of the magnet with the cryostat. 3.3.2 The Magnet Power Supply The magnet current of up to 15 amperes i s supplied by 51 twin-triode tubes (6AS7G) connected in p a r a l l e l . The grids are biased to near cut-off with a regulated power supply (see Appendix). The normal plate voltage used i s 220 volts . This i s obtained by connecting two generators in series since each generator in the Physics Building can give only 150 volts maximum. The s tabi l i ty thus produced has been measured to be of the order of < 0.5%. This was done by comparing the voltage developed across a standard manganin resistor (0.124 ohm) with a standard mercury c e l l and the difference detected by a Honeywell n u l l indicator. The f i e l d s tab i l i ty should be much higher since the magnet i s working near saturation. Signal from DPPH have been recorded indicating that the 4 s tabi l i ty approximates to 1 in 10 . Such s tabi l i ty i s sufficient for most applications. However, i t must be emphasized that higher s tab i l i ty i s required for narrower l ines than that of DPPH ( ~ 4 gauss). With the use of transistors, i t becomes re lat ive ly -19- inexpensive to bui ld a supply having s tabi l i ty of the order of 1 in 10 or better (Gl) . 3.3.3 Low Frequency-Modulation A sinusoidal current source i s used to drive a pair of Helmholtz coi ls for low frequency f i e l d modulation. The modulator consists of a 6AU6A driver tube whose grid input i s fed from an audio-oscil lator (Beckman/Shasta Model 301A) and the output i s used to control the current flowing through 14 6AS7-tubes a l l connected in para l l e l (Appendix). By this means, a large modulation can be obtained. For the study of narrow l ines such as DPPH signals some di f f i cu l ty arises in the production of small modulation because of the great number of turns of wire (350 turns) in the Helmholtz co i l s . A convenient solution i s to shunt the coi ls with a variable load. In our case, a 3.2 ohm rheostat i s used which can be disconnected whenever a large modulation i s needed. 3.4 The Detection System "A three stage, low noise, variable gain amplifier (2.10^ maximum) of standard design i s used to amplify signals from the crystal detector. The design data has been taken from an RCA Receiving Tube Manual (Tech. Series RC-19, 1959). A typical noise leve l i s about 2y V input. The filaments are d.c. heated to reduce hum and the plate voltage is obtained from a regulated Lambda-power supply. It i s found that 60 c/s pickup exists despite the precautions taken including the use of coaxial '• cables between stages. Following the high gain amplifier i s a f i l t er -ampl i f i er to reduce -20- noise. This i s a low gain device and employs a twin-f i l ter with a bandwidth of 20 c/s and centre frequency 135 c/s (Vl ) . In this way i t is possible to eliminate 60 cps pickup completely. ' Before passing on to a pen-recorder for a permanent record, the amplified signal i s fed into a phase sensitive detector. The design follows very closely the one due to Schuster (S i ) . Normally a band- width of 1 or 2 c/s is employed and the recorded signal is the d i f f er - ential of the absorption l i n e . Detailed c ircui ts of a l l the electronic Instruments can be found in the Appendix. 3.5 The Vacuum System Experimental techniques at low temperatures are well known (Wl). In this section, only a br ie f description w i l l be given. A schematic representation of the vacuum insta l lat ion i s shown in , F i g . 6. and M2 are the mercury and o i l manometers for measuring pressure in the dewar. The Cenco Supervac o i l diffusion pump used i s for high speed evacuation down to about a micron of mercury pressure. This i s preceded by a backing pump (Cenco Pressovac) capable of producing about 10 microns of pressure. The backing pump, besides pumping down one arm of the manometer, i s also used to evacuate the jackets of the trans- fer syphon and that of the helium dewar. F i g . 7 depicts a double dewar cryostat arranged concentrically so that the outer forms a l i q u i d nitrogen space, surrounding the inner dewar which contains- l iqu id helium. The dewars are made of pyrex glass and silvered by Brashear's chemical method (S2) such that two narrow strips To follow page 20 PIRANI G A U G E T O J A C K E T - O F SIPHON 4 4 0 1 Trap DIFFUSION PUMP 4 BACKING ;PUMP 4 T O J A C K E T O F H E L I U M D E W A R Mj : Mercury Manometer Mo : Oi l Manometer F i g . 6. A Schematic Diagram of the Vacuum System. To follow page 20 To Kinney Pump Brass Cap Rubber Sleeve To Backing pump' Outer Dewar Resonator I Transfer Siphon inlet Mica Window {fcs-«» To Waveguide System 2^ I To Manometer" Helium Gas Return Inner Dewar German Silver Guide Toluene Soaked Cotton F ig . 7 The Cryostat ( Cap Diam. 2.56" ) -21- are l e f t for l iqu id leve l observation. The helium dewar encloses the german-silver waveguide terminated by a Q-band resonator. It i s topped with a brass cap (2.56" O.D.) that carries also outlets for the helium transfer syphon, the manometers, the helium gas return l ine and the Kinney pump for pumping over the l i q u i d helium to obtain temperatures below 4 . 2 ° K. The big control valve V]_ i s bypassed by two progressively smaller valves and Vg to allow fine control of the pumping speed. The lowest temperature normally obtained in this laboratory i s about 1 . 5 ° K. A rubber sleeve over the cap and the dewar completes the vacuum tight compartment. The whole assembly of cap and vacuum system is mounted•rigidly on a Dexion stand. As a result of the small magnet gap available for experiments, i t has been necessary to make an open-bottomed outer dewar. Cooling of the lower parts of the helium dewar is then achieved by a continuous stream of l i q u i d nitrogen flowing over i t s surface. This method of cooling was later found to be insufficient and wasteful. A normal helium run lasted only 2 to 3 hours. In the experiment to be described in chapter 4, the Kinney pump is not employed as i t is uneconomical to lower the temperature below 4 . 2 ° K. V -22- CHAPTER IV EXPERIMENTAL PROCEDURE An outline of a typical paramagnetic resonance experiment at 4 . 2 ° K w i l l be given. The procedure for room temperature performance is the same except for the low temperature technique which is then of no concern. A known amount of the sample under investigation is mounted on the bottom of the cavity with n a i l varnish (colourless type). Care must be taken to use an amount that w i l l not overload the cavity. The cavity resonator i s then properly tightened to the german-silver guide and the klystron power supply switched on together with the fan which cools the klystron valve. Saw-tooth modulation i s applied on the reflector so that a whole mode can be swept through and displayed on a Tektronix scope 545A whose sweep is synchronized with the modulating frequency. With the reflected power from the cavity displayed on the scope, the klystron i s mechanically tuned u n t i l a pip appears on the mode. To distringuish a true cavity resonance peak from peaks caused by ref lect ions, the following tests have been found useful and convenient. By squeezing the german-silver waveguide, the guide wavelength i s increased without causing changes in the frequency of the electro- magnetic radiation. Consequently, peaks caused by reflection which i s -23- a function of the guide wavelength w i l l be shifted in position as seen on the screen while the resonant pip i s not affected. As the german- si lver guide protrudes above the brass cap, this method i s applicable at helium temperatures when other means of cross-checking i s d i f f i c u l t to achieve. The other test makes use of the effect of temperature, e.g. cooling down the cavity with l iqu id nitrogen. As the cavity shrinks i t s resonant frequency increases causing the pip to move across the screen without affecting the peaks from other ref lect ion. Once the resonance has been found, the tuning screws in front of the coupling hole are adjusted to give a desired coupling condition. In a l l the experiments performed, the cavity i s s l ight ly undercoupled (YD- • Now the double dewar cryostat i s ready for mounting. After having evacuated the inner dewar-, clean helium gas from a cylinder i s in tro- duced into the dewar at a few centimeters above atmospheric pressure. The over-pressure i s maintained throughout the precooling to ensure that the helium gas i s not d ir t ied when i t returns to the helium l iquef ier in the event of a s l ight leakage in the vacuum system. As mentioned before (3.5) the outer dewar is different from the conventional one. In order to decrease the flow rate, cotton soaked with toluene is used to block part of the flow (see F i g . 7). However this i s not very sat is- factory because the adjustment is almost impossible once the toluene has so l id i f i ed . Subsequently, the open end i s completely blocked off and. l i q u i d nitrogen is allowed to flow down only through three small tubings which can be seen in Plate (II). They may also be par t ia l ly blocked i f necessary. -24- When the helium gas inside the inner dewar has cooled down to the lowest temperature attainable, the l i q u i d helium transfer can start . The transferring i s achieved by applying an over pressure of 4 cm mercury to the helium in the can. The return l ine must be opened during the transfer and after to allow the evaporated helium gas to return to the gas holder and the jacket of the transfer syphon i s evacuated to 50yU before the transfer. As soon as enough l iqu id helium has been syphoned over, the pressure on both sides of the syphon i s equalized. The helium can i s then removed and the syphon blocked. Since the dielec- t r i c helium w i l l get into the cavity, i t i s necessary to retune the cavity- as the resonant frequency w i l l be lowered by about 2.4%. At this stage the magnet is slowly rol led in place and the experi- ment is ready to begin. It should be mentioned that for maximum stabi l i ty of operation, the magnet current i s l e f t at about 6 amperes for about 2. hours previous to the experiment to allow the magnet and the power supply to reach thermal equilibrium. The high intensity magnetic f i e l d is applied at right angle to the microwave magnetic f i e l d . To observe paramagnetic resonance, the klystron modulation i s slowly turned down and the reflector voltage adjusted so that the klystron osci l lates at the resonant frequency of the cavity at zero modulation. Then a large f i e l d modulation is superimposed on the main f i e l d and the signal displayed on the screen. The power input to the cavity may be increased to allow visual observation without additional amplification. The stub tuner in arm 2 of the magic Tee (Fig. 3) i s carefully adjusted by varying i t s penetration and position along the guide u n t i l a pure absorption mode appears. The depth of penetration -25- of the tuner has been intentionally increased to cause some microwave bucking. However, no attempt has been made to find the optimum amount necessary for high sensit ivi ty performance. F ina l ly the signal is recorded with a small f i e l d modulation by synchronising the rotation of the motor of the recorder with the magnet current control d i a l . The detection scheme is shown in F i g . 5.: K L Y S T R O N M O D U L A T I O N C O I L M A T C H E D L O A D STUB T U N E R MAGIC T C A V I T Y © L-Y X PHASE S H I F T E R E . STUB T U N E R IN 53 X T A L a.f . A M P F I L T E R A M P a..f. L O C K - I N M O D P E N R E C O H O S H F i g . 5 Block Diagram of a Single Modulation Spectrometer. -26- CHAPTER V EXPERIMENTAL RESULTS 5.1 Introduction Electron Spin Resonance (ESR) can be observed with any substance that has a structure with an unpaired electron (Chapter I ) . Such sub- stances are paramagnetic and they include atoms, free radicals , b iradica ls , crystals containing paramagnetic ions, crystals with la t t i ce defects and several other species. However, the phenomenon of microwave absorption in paramagnetic salts was only f i r s t discovered in 1945 by Zavoisky (Zl) , while the paramagnetic resonance of free radicals was f i r s t reported by Holden and others in 1950 (H2, T2). The experimental technique was greatly advanced by Penrose (P2) in 1949 when he discovered the method of magnetic di lut ion in order to resolve the hyperfine structures so often masked by spin-spin interaction. In this chapter, copper sulphate pentahydrate and DPPH (diphenyl p i c r y l hydrazyl) are used to test the operation of the spectrometer. These two substances have often been employed as standards in many ESR experiments for various reasons. DPPH i s a stable free radical that gives a very strong signal of narrow l ine width. The copper salt has been f u l l y studied and analysed both theoretically and experimentally. -27- 5.2 General Information COPPER SULPHATE PENTAHYDRATE CuS0 4'5H 20 The crystal i s tri-clihiC', of Space Group C^ and contains two molecules per unit c e l l (B2). Unit Ce l l Dimensions a Q = 6.12 1 oC = 82° 16' b = 10.7 6 = 107° 26' o r c Q = 5.97 Y = 102° 40' The axial rat io i s a : b : c = 0.5715 = 1 = 0.5575. Measurements made by Krishnan and Mookherji (K3, K4) showed that i t i s magnetically anisotropic. As pointed out by them, the asymmetry of the crystal l ine f i e l d acting on the paramagnetic ion i s the ultimate cause. The most complete paramagnetic resonance work was due to Bagguley and Griff i ths (Bl) who found that the l ine width varies greatly for different orientations of the crystal and at different wavelengths used. At " 0.85 cm, the l ine width at room temperature may vary from 25 to 450 gauss. According to our measurement, the l ine width also seems to increase at low temperature. l,l-DIPHENYL-2-PICRYL HYDRAZYL (DPPH) The stable crystal l ine DPPH was the f i r s t free radical studied by ESR (H2, T2). Its structural formula i s -28- Subsequently, more detai l studies have been done by Hutchison et a l (H3) and Kikuchi et a l (Kl) . Since each molecule has one unpaired election associated with i t , a very intense signal i s obtained. The g-value is s l ight ly anisotropic being in the range of 2.0035 to ,2.0041 depending on orientation. For a polycrystal l ine sample, a half-width of 3.7 Oe is observed at 3 cm wavelength (H3). However, the-half-width is only 1.8 gauss when the external f i e l d i s 3 gauss. Although no special attention has been paid to the measurement of l ine width, our value i s about 5 gauss indicating a poss ib i l i ty of further broadening under higher f i e l d intensity. 5.3 Results 1 The signals obtained from 2.0 mg of CuSO^'S^O crystal are shown in F ig . 8. The crystal was mounted on i t s a* face with the b-axis approximately at right angle to the static magnetic f i e l d . The experiment was carried out at room temperature as well as at 4 . 2 ° K To follow page 28 (a) At 3 0 0 ° K (b) At 4 . 2 ° K F i g . 8 Signals From 2mg of C u S 0 4 .5H O Single Crystal F i g . 9 Signal From 0.2mg of Powder DPPH -29- and the modulating f i e l d used in each case i s about one-fifth of the l ine width value. Figure 9 shows the signal from 0.2 mg of DPPH in polycrystal l ine form. In this case the modulating f i e l d i s about 0.7 gauss as measured by the voltage induced in a c o i l located at the centre of the magnet gap. The sensit ivi ty deduced from these measurements is shown in Table 1. The relevant data for calculation being power input P Q 1 mW, bandwidth A v> = 1 cps, unloaded cavity QQ = 3000, noise figure F = 1, f i l l i n g factor ^ = 1, l ine width A H = 150, 400, and 4 gauss. Theoretical sensi t iv i t ies have been calculated using the equation (2.8) ( F l ) . Mass sensit ivi ty (2.8) where F tota l noise factor of the detector system molecular weight of the sample electronic magnetic moment Avogadro's number k Boltzmann's constant T temperature in K. -30- TABLE 1 SENSITIVITY. OF Q-BAND SPECTROMETER OBTAINED Sample Temperature Ultimate Sensit ivity Experimental Sensit ivity CuS0 4'5H 20 300° K 7 • lo--10 gm 2 •10" -4 gm 4 . 2 ° K 3 •10" -13 gm 4 •10--6 gm DPPH 300° K 2 10" -11 gm 4 •10" -6 gm It seems that the experimental sensit ivi ty i s far from satisfying. However, i t must be mentioned that the actual f i l l i n g factor was calculated to be 0.004, 250 times less than the ideal one. Also, the noise figure that can be normally achieved i s not 1, but of the order 10. Therefore, the present sensit iv i ty could be easily improved by a hundred fold by increasing the f i l l i n g factor alone. Further improve- ment could be achieved by reducing the noise leve l of the system which i s reckoned to be a b i t high although the true value was not determined. For comparison, we give the sensit ivi ty of various spectrometers that have been specially designed for high sensit iv i ty operation. These are shown in Table 2 for the testing sample DPPH only. -31- TABLE 2 COMPARISON OF SENSITIVITY OF DIFFERENT SPECTROMETERS AT 290° K •Type . Operating Band Sensitivity Reference Single f i e ld _ g modulation X band 3x10 gm PI Super heterodyne detection X " 8xl0 _ : 7 gm HI 9 9 Single f i e l d ' modulation K " 8x10 ' gm B6 Double f i e l d modulation K " l x l O - 1 1 gm B7 Single f i e l d modulation Q " ~ 10 _ gm -32- CHAPTER VI CONCLUSION AND DISCUSSION An 8 mm sol id state spectrometer has been tested and found satisfactory in most respects. Although the sensit iv i ty s t i l l f a l l s short of the theoretically predicted value, i t i s comparable to the most sensitive spectrometers reported. The discrepancy probably l i e s in the fact that the external interferences have not been tota l ly eliminated. The external interferences may be e l ec tr i ca l or mechanical in nature. They cause ins tab i l i t i e s of about five to ten times the leve l of random noise (HI). Frequency ins tab i l i ty is not a l imit ing factor as the Q of the cavity is only a few thousand. E l e c t r i c a l interference has been eliminated. Mechanical interference coming from building vibrations has not been taken care of although rather straight- forward shock mounting should eliminate them. The sensit iv i ty can be increased by improved methods of detection. Using.double f i e l d modulation, an improvement of about 1000 should be possible as has been demonstrated by Buckmaster (B7). However i t may not be an easy task to overcome the problems involved in high'frequency modulation since we are now working at a shorter wavelength.. The method of superheterodyne detection applied to the present setup should theoretically give 10^ times better sensit ivi ty than a -33- crystal or bolometer detector (Ml). This is mainly because of the greatly reduced crystal noise which i s inversely proportional to frequency (T l ) . Under pract ica l conditions, only 5-10 times improve- ment has been achieved (F l ) . Moreover, the need for an auxil iary osc i l la tor and an automatic frequency control system to keep the frequency difference between the two osci l lators constant makes the superheterodyne more complicated. The auxil iary osc i l la tor may in i t s e l f be a further source of noise. High frequency modulation is not very satisfactory because the increased modulation frequency introduces more pickup originating from the magnetic forces of the static f i e l d interacting with the eddy currents induced in the cavity walls by the a.c. f i e l d component. With sufficient effort,such as the use of nonconducting walls with plated inter ior surfaces, i t may be possible to reduce the eddy currents (LI). The best approach, i f ultimate sensit ivi ty is not absolutely necessary, seems to be the use of bolometer. The only change needed then is to decrease the modulation frequency since bolometer functions better below 100 cps. Also the problem incurred in designing new detecting instruments w i l l be re lat ive ly simple and quickly achieved. -34- APPENDIX The c i rcu i t diagrams used are collected together in this Appendix. Unless otherwise stated the values for the resistors are in ohms and the capacitors in microfarads. Page Circui t 1. Magnet Current Supply 35 Circui t 2. Modulation Supply 36 Circui t 3. High Gain Audio Amplifier 37 Circui t 4. Phase Shifter 38 Circui t 5. F i l t e r Amplifier 38 Circui t 6. Phase Sensitive Detector 39 All Resistors "Ohmite" Circuit 1. Magnet Current Supply ( 3 chassis in series ). A Oscillator at 140cps I0K>* 6AS7G 6AS7G 14*~'fuEes" in" 220K> 3.4> J .05ZZ > < .02 Hammond 263C60 I20V.A.C 1 f3 470K T20 parallel 680 680 ^ ^ l l 6 ^ 3 V . A . C . 6AU6 ^ ) 6A87G 20H I50mA I5(150W) Pilot HE 68) I M J-500 I T M F D 46 MOD Coil 5 ohms D . C . u T 220VDC + Circuit 2. Modulation Supply. 5693 5693 5693 To filter amplifier Circuit 3. High Gain Audio Amplifier. -38- 250V + + Circuit 4 . Phase Shifter. Values for Twin-Filter are 1% Al l Others 10% and |W Circuits . Filter-Amplifier. 12AU7 ' + 2 5 0 V ,Balance -VSA* 2 0 K W W u u u u Hammond T 2 0 D 80 6AU6 + 2 5 0 V 4 OK 1 2 A T 7 1 r^-V M 4 . 7 M ^ _ _ ,7 Recorder 4 -05 .11 .22 .5 1 <*± JL J . ± 1 1 T T T T T T Circuit 6. Phase Sensitive Detector. -40- BIBLIOGRAPHY Bl Bagguley, D.M.S. and Gr i f f i ths , J . H . E . , Proc. Roy. Soc. A201 (1950) 366. B2 Beevers, C A . and Lipson, H. , Proc. Roy. Soc. A146 (1934) 570. B3 Bethe, H . A . , Ann. Phys., Lpz. 3 (1929) 133. B4 Bleaney, B. and Stevens, K.W.H. , Rept. Prog. Phys. 16 (1953) 108. B5 Bowers, K.D. and Owen, J . , Rept. Prog. Phys. 18 (1955) 304. B6 Buckmaster, H . A . , Ph.D. Thesis, University of Br i t i sh Columbia (1955). B7 Buckmaster, H.A. and Scovi l , H . E . D . , Can. J . Phys. 34 (1956) 711. F l Feher, G . , Be l l Syst. Tech. J . 36 (1957) 449. Gl Garwin, R . L . , Rev. Sc i . Instr. 29 (1958) 223. G2 Ginzton, E . L . , "Microwave Measurements" (McGraw-Hill, New York, Toronto and London, 1957). HI Hirshow, J . M . and Fraenkel, G . K . , Rev. Sc i . Instr. 26 (1955) 34. H2 Holden, A . , K i t t e l , C . , Merri t t , F.R. and Yager, W.A., Phys. Rev. 77 (1950) 147L. H3 Hutchison, C A . J r . , Pastor, R . C and Kowalsky, A . G . , J . Chem. Phys. 20 (1952) 534L. II Ingram, D . J . E . "Spectroscopy at Radio and Microwave Frequencies" (Butterworths, London, 1955). Kl Kikuchi, C. and Cohen, V.W., Phys. Rev. 93 (1954) 394. K2 Kramers, H . A . , Proc. Acad. Sc i . Amst. 33 (1930) 959. K3 Krishnan, K.S. and Mookherji, A . , Phys. Rev. 50 (1936) 860. K4 Krishnan, K.S. and Mookherji, A . , Phys. Rev. 54 (1938) 533. L l Lambe, J . , Ager, R . , Rev. Sc i . Instr. 30 (1959) 599N. L2 Low, W., "Paramagnetic Resonance in Solids" Supp. 2, Solid State Physics Series (Academic Press, New York and London, 1960). Ml Misra, H . , Rev. Sc i . Instr. 29 (1958) 590. 01 Orbach, R. , Proc. Roy. Soc. 264A (1961) 458. PI Pake, G.E. , Weissman, S.I. and Townsend, J . , Disc. Faraday Soc. 19 (1955) 147. P2 Penrose, R . P . , Nature Lond. 163 (1949) 992. P3 Pryce, M . H . L . , Proc. Phys. Soc. A63 (1950) 25. P4 Pryce, M . H . L . , and Stevens, K.W.H. , Proc. Phys. Soc. A63 (1950) 36. 51 Schuster, N .A . , Rev. Sc i . Instr. 22 (1951) 254. 52 Strong, J . , Neher, H.V. , Whitford, A . E . , Cartwright, C H . and Hayward, R . , "Procedures in Experimental Physics" 22nd printing (Prentice H a l l , New Jersey, 1961). T l ' Torrey, H.C. and Whitmer, C . A . , "Crystal Rectifiers" (McGraw-Hill, MIT Radiation Lab. Series, Vol . 15, p. 187, 1948). T2 Townes, C H . and Turkevich, J . , Phys. Rev. 77 (1950) 148. VI Valley, G.E. and Wallman, H . , "Vacuum Tube Amplifiers", MIT'Radiation Lab. Series, Vol . 18 (McGraw-Hill, New York, Toronto and London, 1948). V2 Van Vleck, Phys. Rev. 74 (1948) 1168. Wl White, G . K . , "Experimental Techniques in Low-Temperature Physics", (Clarendon Press, Oxford, 1959). W2 Wilson, I . C , Schramm, C'.W. and Kinzer, J . P . , Be l l Syst. Tech. J . 25 (1946) 408. -42- Y l Yariv , A. and Clapp, F . , Rev. Sc i . Instr. 30 (1959) 684. Z l Zavoisky, E . , J . Phys. USSR 9 (211) 1945. T o follow page PLATE III GENERAL VIEW OF THE APPARATUS


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