‘l 1‘ \ ‘l in * ( NM 1 | I IN l “W 133 305 THS ELECTRON SPEN RESONANCE A? LOW MAGNETIC FEELDS Thesfis for Hm Degree of M. S. MICHIGAN STAEE UNEVERSETY Walter 'Wysoczanski 1957 ' llHlllllllHHlllllllHll‘WlHllllllIIIHHLIULUIIHIIHW 3129301743 ELECTRON SPIN RESONANCE AT LOW MAGNETIC FIELDS B! WALTER WYSOCZANSKI A THESIS Submitted to the College of Science and Arts of the Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics 1957 ‘ {flag/3‘7 ? /c>'L 7‘5. ELECTRON SPIN RESONANCE AT LOW MAGNETIC FIELDS by Walter Wysoczenski AN ABSTRACT submitted to the College of Science and Arts of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree 0! MASTER OF SCIENCE Department of Physics Year 1957 (’5’, - .‘LVA‘L‘ Approved I” (1' ABSTRACT Walter wysoczanski Apparatus has been designed and constructed for observing electron spin resonance at magnetic fields from 0.3 to 30 genes. The radio frequency spectrometer consists of a modified Pound-Knight circuit. A modulated static magnetic field for resonance is provided by a pair of Hemholtz coils, while the stray field of the laboratory (mainly the 0.8 gauss field of the earth) is "bucked out" to within 0.0005 gauss by a second set of coils. The apparatus has been used to study the variation of spectro- scopic splitting factor (g-factor) in the organic free radical diphenyl picryl-hydrazl (DPPH), and in a 0.23 molar solution of sodium in liquid ammonia. The g value in the DPPH was found to vary in a manner similar to that obtained by Garstens*; while in the sodium solution, g was observed to be constant over the range studied, with a value of 2.002 t 0.002. * M.A. Garstens, L.S. Singer, and A.H. Ryan, Phys. Rev. ACKNOWLEDGEMENT I wish to thank Dr. J. A. Cowen, who suggested this problem, for his continued advice, help, and en- couragement throughout the course of this work. I thank Dr. J. L. Dye and Mr. R. Sankuer for the preparation of the sodium-ammonia solution. Also, the financial support of the National Science Foundation was much appreciated. TABLE OF CONTENTS I INTRODUCTION ................... 1 II DISCUSSION - - - - - - - .......... - _ - 3 III DETAILS OF THE EXPERIMENT ............ 6 1. APPARATUS ................... 6 a. THE SAMPLES ................ 6 b. THE MODULATED STATIC FIELD --------- 6 c. THE RADIO FREQUENCY PIELD — - - ...... 9 d. THE BUCKING FIELD - - - - ......... 12 2. PROCEDURE ................... 13 a. DETECTION OF RESONANCE ........... 13 b. ALIGNMENT OF TEE FIELDS - - ........ 15 c. THE EXPERIMENT ...... . ......... 18 3. RESULTS -------------------- 19 REFERENCES .................... 27 I INTRODUCTION The energy absorbed from the rf field in the electron spin resonance experiment is given up to the lattice in the form of thermal energy by means of a spin- orbit coupling mechanism. In the hope of obtaining new information about this process, a program of investigating the effect of ultrasonic energy on the resonance line has been undertaken. This investigation is confined to resonance at low magnetic fields for which it is possible to generate ultrasonic energy at the resonant frequency. This thesis deals with the preliminary stages of this program in that it reports on the design and construction of apparatus for the detection of the resonance, and its application to the study of the variation ix: spectroscopic splitting factor (g-factor) of an organic free radical and an alkali-metal-ammonia solution in the frequency range from .8 to 15 No. In order to study electron spin resonance at low Inagnetic fields, it is desirable that the line width be of "the order of magnitude of the resonance field. There are, 111 general, 2 classes of materials with narrow lines at Inaom temperature: the organic free radicals, and the SOlutions of alkali metals in liquid ammonia. Line widths irl the free radicals lie between 1 and 31 gauss while -1- -2- those in the solutions are less than 0.1 gauss. Recently, Garstens192 investigated the variation of the g-factor at low fields in the free radical diphenyl picryl-hydrazl (DPPH) and was able to fit his data to a gas model of the unpaired electron in the free radical. It appeared worth while to check the electron spin resonance equipment by retaking his data. At the same thme it was felt that an attempt to determine the low frequency behavior of the g-factor in a solution of sodium in liquid ammonia might shed new light on the paramagnetic properties of these very interesting solutions.3’h The line width of the sodium solution is of the order of 0.03 gauss, hence a highly homogeneous static field must be used. Also, at the low fields used (0.3 to 6.0 gauss), the contribution of any stray fields must be considered -- primarily, the earth's magnetic field (about 0.8 gauss here). This problem was most easily solved by bucking out the earth's field in the vicinity of the sample, and, thereby, providing essentially zero stray field over this region. For the accurate detection and observation of the .resonance line, the required high sensitivity is obtained by using a technique in which the static field is sinusoidaly modulated at a low frequency -- this modulation be ing detected by a marginal oscillator supplying the radio frequency field. II DISCUSSION If a static magnetic field is applied to a degenerate ground state in a paramagnetic material, the degeneracy may be removed and transitions between the resulting levels induced by a rf magnetic field.5 The resonance condition is given by: AE=hf=gfiH f=g§§ where AE is the energy splitting; f, is the frequency of the rf field; H, the static magnetic fieldglfi, the Bohr magneton; h, Planck's constant; and g, the spectroscopic splitting factor. The g-factor is thus the proportionality factor which tells how large a splitting occurs for a given applied magnetic field. For a free electron g = 2.0023, but for electrons in crystals g may differ significantly from 2 depending essentially on the contribution of the orbital magnetic moment to the total paramagnetism. In the case of the organic free radicals, the single unpaired electron which participates in the resonance is Iloosely bound and, in most cases, the g value is very close 't0>that for the free electron. Garstens has shown that, 111 DPPH, at low frequencies, g varies inversely as the fourth power of the resonant frequency, and has explained 'tllis theoretically by a model consisting of a gas of -3- 4&- magnetic dipoles. In this case, according to him, it is the exchange interaction which allows the spin moments to simulate the gas of dipoles. He also finds it necessary to assume that the dipoles have a Boltzman distribution during collisions, and this, in turn, gives rise to non- zero absorption at zero field, and the corresponding shift in the g value. The solutions of alkali metals in liquid ammonia exhibit some very interesting properties, one of which is the very narrow electron spin resonance line. Kaplan and Kittel have developed a model of these solutions in which they picture the metal as ionized in the solution, with the released electrons trapped in cavities in the liquid; these cavities having a volume of approximately 2 to h ammonia molecules. The electrons are supposed to be in 2 different states: a low lying singlet state, containing two electrons, and a somewhat higher level single electron state. The lower lying states are diamagnetic while the electrons in the upper states give the solution its paramagnetic properties. By assuming that the electrons are shared by the protons on the ammonia molecules adjacent ‘to»the cavity, and further, that the resonance line is narrowed due to the motion of the molecules, they are able ‘t<3 predict the line width and the g value at high free quencies. On this basis they predict, following the argument of Kahn and Kittel6 as applied to F-centers, that -5- the g value will be smaller than that of the free electron, due to a large admixture of higher orbital (g) states. Although no explicit calculation of the low field variation of the g—factor has been done for these solutions, it was thought to be of sufficient interest to determine, within the ltmits of this experiment, if the g-factor varied at low magnetic fields. From the resonance condition, one can show that g is obtained from the ratio of the radio frequency to the value of the static field for resonance at the given frequency: g = .71uu5 f(No) (gauss) In this experiment the frequency is obtained directly, while the field strength is found by measuring the direct current producing it. III DETAILS OF THE EXPERIMENT 1. Apparatus a. The samples A .23 molar solution of sodium in liquid ammonia was prepared by distillation as described by Hutchison7. This sample occupied a height of 2.9 cm. in its cylindrical container made from 1.35 cm. i.d. pyrex tubing. It was stored in dry ice but used at temperatures in the neighbor- hood of 267° K. A quantity of DPPH powder filling a 0.8 ea. i.d. test tube to a height of 1.5 cm. was used at room temperature. b. The modulated static field A highly homogeneous static magnetic field was provided by a pair of coils 12.1 cm. in radius, totaling 500 turns, and approximating the Helmholtz geometry. Calculation showed that these coils would give an axial field of 37.0h gauss per ampere of current through the coils -- this figure agreed with that obtained by using ‘the known g-factor of DPPH at 15 Me as a standard. A 0.2 to 0.7 gauss, peak to peak, 60 cps modulation (If this field was introduced by series connection of the Secondary winding of a 6.3. volt filament transformer (I’lg. l). A capacitor was used to confine the alternating -6- -7- current to the Helmholtz coils. Direct current was supplied by a 6 v Edison battery; current adjustment being accomplished by a combination of a rheostat and decade resistance box. The current was determined by measuring the potential drop across a one ohm standard resistor with a L & N type K potentiometer. DJmE OZEUDm mom wipu NFJOIZJwI m.:ou NSoIsjm: m5 mod .53qu H .OE 042... 2.535 03.443002 mi. mod m.:OU NHJOIEJMI .. F A w III-ll 4)‘ u I“ 5| ) 3+ .. s .1. ~26 M. mmfimfi @ EL: 17.0 “ |Hr 001 * xomwwm _ _ mo23 .u.<.>o: > U FII'L ITO xom .mmd wo.__H|Ia Shaka H; u % 1...... a . . . .69 r._>_ 3;. E .E i >Om. bx.. u 7 K lllll t 11 .o. I gong; gem moo. _. w :88. .:8 3m: 2 P __ .fi 1 FEFDO _o. v62 :03 hx<~_ v: {on at. w...<~. 924 Huanumo -12.. This oscillator-amplifier was compactly built on a 2" x 3" x 6" aluminum chassis with a 3/8" o.d. x 8" brass tube serving as the outer conductor of a coaxial line to the sample holding inductor. During operation, it was suspended above the Hemholtz coils (Fig. h). The frequency of oscillation was adjusted by a 200 uuF variable capacitor; fixed mica capacitors being added, as required, to cover the lower frequencies. This frequency was measured by a Signal Corps BC-221-C hetero- dyne frequency meter whose crystal calibrator was checked against WWV. At a given frequency, to obtain best signal, RK (see circuit in Fig. 2), was adjusted for maximum signal with R6 at zero; then R0 was adjusted to improve the signal further by giving operation at a point very close to cut- off. For the higher frequencies, with the liquid sample, the best marginal oscillation conditions were achieved by decreasing the feedback, i.e., by increasing the resistance of control RF' d. The bucking field The effect of the earth's magnetic field in the xricinity of the sample was minimized by a pair of Hemholtz (Hails totaling 270 turns on a diameter of hl cm. Current was supplied, through a decade resistance box, by a 6 V Edison battery, and monitored by a O-lSO dc milliameter. -13- A current of 73.5 ma was required to produce best bucking; as determined by a method discussed in section 2 b. 2. Procedure a. Detection of Resonance The Pound Knight type spectrometer detects resonance by its sensitivity to the variations in the Q of its tank circuit (as when the external magnetic fields produce resonance in the sample). Using the a c modulation method, these Q variations follow the modulation of the static field; thus giving an output as shown schematically in Fig. 3. Notice that the output trace is completely symetrical when the static field is exactly at resonance -- this is the principle used here for detection. Although the 90° difference in phase between any two resonance peaks could be judged by inspecting the waveform traced by the oscilloscope set for ordinary sweep, a faster, and perhaps, more accurate technique was used. This was accomplished by using a faster sweep sufficient to display one half cycle of the wave, and adjusting the triggering of the scOpe so as to trigger for each resonance pulse; and, thereby, presenting two resonance traces which indicated exact :resonance when brought into superposition; as in the central figure of the last row in Fig. 3. This method of detection was found to be independent Of' the amplitude of the modulation used. -1h- \m 5:... a 5:0 um<1¢oo 82.4285". 545 .._o 20:35:. at... m. .0: if; T unasa 1uon< mzk m< .nxcmn< 9 l I wuz