_:ga,iE:g._,1,:.5Z:E_:.::_::.::= mm '1. 3.“ ‘ ‘ 9 ‘ I 2*. éeg-yas {2 5 I". Hi; E -‘ ‘3 O . fit - o ... .Ohrav \l' chm: G . a”... flu teul cravnh mg LIBRARY Mlchtgan State University This is to certify that the thesis entitled 2%.. ”aft-.022: 12......“ ,4. 5-74 a7.“ 7.93.4.4... 717%: ataaéu: presented by #7; ya// /4. has been accepted towards fulfillment of the requirements for A. ._ degree in £41; {”2 M Maj r professor Dat%L // /7J'J" 0-169 mmiiiiiiiiigii PHYSICS liBRARt’ PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 1/99 c/CIRC/DateDuepes-ota PttU'i'Ula i-JlGNIfiTIC iihi‘Xil‘JAI‘lJE IN SINGLE CLtKSTAL‘)‘ OF SODIUM THIOSULFATE I‘ifli‘t‘AH‘fI‘i’ATd by Hugh Galt, Jr. A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of PL’XSTiil OF SCIENCE Department of Physics 1955 Ho " b" D r I Tolamn ACI‘LNOJJLEI X}: L #34 re Fr? Li P—3 The atthor wishes to express his thanks and appreciation to Dr. Robert D. Spence for his constant interest and encouragement during the course of first Rex, t. this work. PROTON MAGNETIC RESONANCE IN SINGLE CRYSTALS OF SODIUM T HIOSULF AT E PENT AHY DRAT E by Hugh Galt, Jr. AN ABSTRACT Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics 1955 Approved 2 D 5:3“ fl Hugh Galt, J r. Thesis Abstract This the sis reports an investigation of sodium thiosulfate pentahydrate to determine the positions of the hydrogen atoms of the waters of hydration in the unit cell of the crystal. The crystals were investigated by the proton magnetic resonance method developed by Pakel. The dipole-dipole interaction of the proton pairs produces a doublet whose separation is anisotropic. The cyrstals were grown by slow rotation of a seed crystal in a slowly evaporating aqueous solution. The doublet separations were recorded from the resonance signals as the crystal was rotated in the magnetic field. The angular position of the maximum value of the doublt separation indicates the position of the p-p vector whose dipole-dipole interaction produces the signal. The hydrogen atoms were assumed to lay on the chemical bonds of the atoms of the compound so thatthey would form the bonds 0-H- - - 0, and 0-H- - - S. Crystallographic data indicates that the unit cell is tetramolecular and thus possesses twenty waters of hydration. The angle between each p-p vector and the magnetic field was calculated by trignometry with the assumption that the distances of the two protons from the oxygen atom of the water were equal. These calculations indicated that there are twenty non-equivalent waters of hydration in a unit cell. Comparing the experimental results with the assumed positions indicated that ten of the p-p vectors were located as assumed. Experimental evidence indicat- ed four p-p vectors inpositions that did not agree with any of the assumed Hugh Galt, Jr. Thesis Abstract locations. The maximum value of the inter-proton distance, as calculated from the values of the maximum doublet separations, was 1. 46 A. 1. Fake, G. E., Journal Chem. Phys., _l_6_ 327 (1948). l'l'll'l I 'l II I'llll'l-l“! l TABLE OF CONTENTS I. INTRO DUCTION II. CRYSTALLOGRAPHY OF SODIUM THIOSULFATE‘ PENTAHYDRATE A. Morphology B. X-ray Analysis III. THEORY A. p-p Interaction B. Proton location IV. EXPERIMENTAL PROCEDURE A. Crystal Growth Bo Apparatus C. Method of Recording Signal V. ANALYSIS OF RESULTS A. EXperimental Results B. Discussion C.Sunlnary page 17 20 2h 27 28 I. Il'i'l‘le CU C i l‘ ‘N Recently proton magnetic resonance has been adapted to an investigation of hydrated crystalline compounds in the hope that.more might be learned about the position of the hydrogen atoms of the waters of hydration in the crystal. The ordinary methods of crystallography employing the X-ray and electron diff- raction techniques fail to locate the hydrogens because of their small scatter- ing cross section. The proton resonance technique was first employed by G. E. Pakel. By means of this resonance method he located the hydrogens' positions . 2 h in single crystals of gypsum. Since then other crystals have been studied ’3’ . In these previous studies the number of waters of hydration in a unit cell of the crystal under investigation ranged from two to eight. However, the invest- igators in each instance were fortunate that the total number of non-equivilant p-p orientations, the line joining the two protons of each water'molecule, never exceeded two. This raises the interesting question as to whether the proton resonance tech- nique can be used in an investigation of hydrated crystals with a fairly large number of non-equivilant waters of hydration in a unit cell. There are a great many such compounds and an investigation of one of these might prove helpful in outlining a general.program to be employed in further work. This thesis deals with an investigation of such a crystal. The crystal undertaken for study was that of sodium thiosulfate pentahydrate, or hypo. II. GYRSTAIILOHATHY OF SOJlUH THIOJULFATE PMHTAHIDRATE A. Morphology The morphology of sodium thiosulfate pentahydrate has been studied by Groths. He describes a single crystal as being monoclinic and prismatic with the axial ratio, a : b : c := 0.3508 : l : 0.2716; andp =103° 58' Figure (1) shows a rough sketch of the crystal from Groth's data. B. X-Ray Analysis A crystallographic study of hype, as the compound will be referred to here- after, has been made by Taylor and Beevers6. They substantiate Groth's morph- ological results and assign a class P21/c to tte crystal. They describe a unit cell of the crystal as being tetramolecular. This means a unit cell of the crystal contains twenty molecules of water, their'being five waters per molecule of hype. The complete unit cell, from Taylor and Beevers' paper, is pictured in figure (2). Data from this figure was used to construct a three dimensional model of the unit cell (see figure 3). The tops of tie dowels in the model represent some of the atoms of the unit cell. The sodium atoms were neglected because they do not enter into any consideration of proton positions. The white thread corresponds to the chemical bonds as indicated in Taylor and Beevers' paper. The black thread represents the hypothesized p-p orientations under assumptions to be defined later. r-- - I i 1 W /\t// Figure 1. Sketch of single crystal of sodium thiosulfate pentahydrate. A o 1 r a f sA. .-s ..~.Q.o O-Hp Figure 2. The unit cell of Na2 WSEO W5 0. The heights of the atoms are shown in Angstrom uni 3 above a standard plane perpendicular to the a axis. Figure 3. Photograph of three-dimensional scale model of a unit cell for hypo. ‘D b (I) 09 L.--“ _- __ . ii 0 l I I I P- I 39~ ‘6~ 5‘ Figure h. Diagram defining various angles relating Ho direction to crystal axes and the p-p vector in a water molecule of hypo. III. THEDRY A. p-p Interaction If we assume the proton pair associated with a water molecule is an isolated pair, then at resonance they should yield a doublet whose separation is given byl Ah:(H-HO)=tat(3 c0826 ~1), (l) where H0 is the resonance magnetic field in the absence of the p-p interaction, at = 3/2 h r'3, (2) O is the angle between the p-p vector and the magnetic field vector, and r is tre inter-proton distance. Since we shall always consider the total sep- aration betUeen the doublet, equation (1) may be rewritten Ah= «'(3 c0329 -1), (3) a" 3 3 P r‘3. (’4) The angle 9 may be related to the angle of inclination S and the angle of rotation Q.(see figure 1;) by computing the dot product of the magnetic and p-p vectors so that case =cos$cos(q -Q.). (5) Substitute this into equation (3) and, A11: d’EBcosZS 0052(Q-Q.)-1], (6) <9 is the angular orientation of the magnetic field vector with the p-p vectors' "/ projections in the plane of rotation. S and <9. are constant angles for each p-p vector. A significant change can be made in equation (6) that will greatly assist the investigator. We know, Ah‘ [3 c0323 cosz(

1 and equation (10) gives the solid curve illustrated in figure (5). If (3 = 0, then 1 = 1 and the dotted curve of figure (5) is the result. The inverted section of the curve is a result of only considering the absolute values. If p is negative then % < l and the dashed curve illustrated in the figure is the result. The curve is seen in the positive quadrant since only absolute values are considered. Consider the particular case of @ negative. This means ‘6 I. 1, so that 3/2 0032 8 < 1. (1h) Solve this inequality, restricting the solution to the first quadrant, and it follows that S > 35.30. This means those p-p vectors whose angle with 00. .m. no 333, 5.39:3 com 092 :4 zuuzpuo maimzocjum 0 on. cm a? . n Maser... OAQ LIV the plane of rotation is greater than 35.30 contribute a doublet whose separat- ion is very small. Conversly, any p-p vector with an angle 8 4 35.30 may give a doublet whose separation is large. B. Proton Location To simplify calculations the protons belonging to the waters of hydration were assumed to lie on straight line bonds joining the atoms of the hypo crystal. If we adept this criterion and assume the chemical bonds illustrated in Taylor and Beavers are correct then the protons form the following types of bonds; 0 - H0000, and O - H°°'S. The bonds for the protons of each water molecule were arbitrarily chosen. In some cases the choice of bonds was easy since the oxygen of the water molecule was bound to the sodium atcms and to two other oxygen atoms of the sulfate group. Then the only choice for the proton pos- ition is on the O - 0 bond. However, for other waters the choice was not as restricted. Then the most likely'bond was chosen. There is no certain know- ledge which indicates that the protons must lie on these bonds. Indeed, it is possible that the O - H bond is warped away from the straight line bond. Furthermore we may postulate that the protons undergo a rotation, either free or hindered, and never remain stationary, thus continually changing the p-p orientation for a water molecule. The resonance signal obtained from such molecules will be a single line. This is due to the pdp vector having a ran- dom orientation and so giving a resonance Signal not unlike that of a liquid. If the O - H bonds are warped then maximum line separations will occur at angular orientations that do not coincide with the expected angles. The 0 - H bond distance for each proton was takwn to be the same in calculat- ing the angles 8 and q. . These angles were determined by inserting the values of the space coordinates of the atoms whose bonds contained the protons into equations (15) and (16). _ [(yz - y) A (Y1 - y) Bl (15) °- [(xz -x)A-(x1-x)B], [(xz - x) A - (x1 - X) B3 (16) tanq cotS cosq.- [(z2-z)A-(21-Z)B]’ where A= [kl-302+ (n-y)2+(zl-2)2]%, and B: [(xg-x)2+ (ye-y)2+(22-Z)2]%o Table (l) is a list of the angles calculated in such a manner. The angles are for each p-p vector in regard to crystal rotation about the a axis. To identify each p-p vector the following notation was adopted. Each vector is associated with a water molecule. The unit cell is divided into four molecular sections and each section assigned a Roman numeral. Thus the notation 7II refers to the p-p vector associated with water molecule H207 in the second molecular section. The result of the calculations is that there are twenty non-equivilant p-p directions, or a unique direction for each water of the unit cell. If this is true one should observe twenty pairs of lines in the proton resonance sig- nal. These twenty lines should each be uniquely anisotropic in that they will reach a maximum and minimum in doublet separations at certain angular orientat- ions of the crystal with the magnetic field. Also their separations will not all be the sane, but will depend on the p-p orientations with the plane of rotation. _ _,_-_ -__ __. _ . .~.._ . —.__.-__ _.'--._— w t w t Molzcfile 8 (#0 Molzcile 8 ¢o 0—:— hI -19° L3' 1620 09' hII 69° 35' 36° hl' 51 - 9 06 1u2 20 511 -12 0h 35 20 7 61 to 37 93 06 611 -32 00 99 11 - 71 - u 27 162 27 711 -12 13 8 22 81 -h2 02 177 33 811 58 12 7 S7 h111 -38 26 bl 05 th -69 26 1&3 In 5111 27 31 51 36 SIV hl 53 131 39 .6III 37 M: 93 h? 61V to 111 92 Sh 7111 22 12 22 50 71v u3 17 161 56 8111 -12 08 S 55 81v -h2 32 178 16 - 0—“...--- m— A; ““11? \_ _- Table l. Angles of orientation for the p-g vectors in regard to crystal rotation about the a axis with O = c' axis. 8. Axis r (A) b Axis r (A) c' Axis r (A) 0° 1.h6 0° 1.1m “ I 60° 1.111 100° 1.111; 60° 1.118 130° 1.1.3 150° 1.1m 95° 1.213 125° 1.h6 Table 2. Angular positions of maximum splitting and values of inter- proton distance. 10 1v. EXPERDINTAL mom-hush; A. Crystal Growth The single crystals of hypo were grown by slow rotation of a seed crystal in a slowly evaporating super-saturated aqueous solution of hypo, maintained at room temperature. The time required for growth to the necessary size of approx- imately 2 cm. in length and 1 cm. in diameter was between two and four days. The seed crystal was grown in about two or three hours by pouring a small amount of the super-saturated solution into an evaporating dish to produce rapid evaporation. A close watch was maintained on the solution and when the first crystals began to form the more promising ones were separated from the rest. This was done so that only single crystals would grow rather than twins as was the usual case if the solution were left to its own accord. When the crystals had attained a size convenient for their attachment to ordinary house- hold thread they were removed from the dish. Duco cement was used to glue the seeds to the thread. Duco cement gives a proton resonance signal, a single line, however the small quantity used in the crystal was not expected to affect the hypo signal appreciably. The seeds were lowered into the slowly evaporating bath and when they had grown to the desired size removed and the thread cut. AfteI‘ ascertaining the crystal axes by visual observation and comparison with Groth's data (see figure 1) they were glued, again using Duco cement, to a small section of dowel. Three Crystals were grown in this manner and each was attached to a wood dowel so that. the crystal could be conveniently rotated about one of its crystallo- graphic axes. A separate crystal was used for rach axis; a, b, and c‘ (the I " . . . ‘ c an<13 is the csinp ax15 of Taylor and Beever's data). xfhile mentioning tm signal obtained from Duco cement it should also be noted that wood gives a proton resonance signal. However, here again the signal was not of a large enough magnitude and was neglected. L'Jhen this wood influence was first noted a spare crystal was attached to a piece of foam glass, tha foam glass was first tested for proton resonance with negative results, an.) the resonance signal still contained a strong central line. When the crystals were not being used they were stored in a sealed glass tube containing a small wad of cotton soaked in hypo solution. This was done to maintain an atmosphere that would prevent evaporation of the waters of hydrat- ion. As a precaution to prevent evaporation during prolonged exposure to air the crystals were sprayed with a thin coating of Krylon (duI’ont acrylic spray). It might be remarked in passing that the growth of the hypo crystals was quite irregular in that they would grow in one instance and fail in what was suppos- ed a like instance. Several different methads were tried before the rather standard process of slow evaporation and rotation was used. Some of these methods were; fast evaporation at room temperature of a super-saturated aqueous solution, and controlled temperature decrease with no evaporation. In the latter attenpt the seed crystal was immersed in a super-saturated bath at a temperature of about 112° C. and the temperature slowly lowered about three degrees a day. One crystal was grown in this manner, however further attempts failed . 12 B. Apparatus The radio-frequency bridge method devised by Bloembergen, Purcell, and Pound7 was used to detect the proton resonance signal. The apparatus is essentially the same as that described by Jain8 (see figure 7). A block diagram of the apparatus is shown in figure (8). The lock-in ainplifier was used with a 280 cycle modulating field of low amplitude. In order to provide a slow sweep of the resonance line a separate coil was mounted on one of the pole pieces of the magnet. This coil supplied an additional field parallel to th: original mag- netic field, H0. In order to produce a nearly linear sweep a constant speed motor varied the position of a rheostat contact by means of a gear driven rack an d pinion. The shaft of the crystal holder was turned down from an aluminum rod approx- imately five inches in length and one-half inch in diameter. Mounted on one end of the shaft was a circular plate on which two five inch celluloid pro- tractors were glued so as to make a complete 360 degree scale. On the other end of the shaft a Teflon rod (duPont fluorine-substituted poly-ethylene) was fastened. The rod was notched at the free end so that the dowel holding the crystal might be inserted. The entire holder was held in a vertical position between the pole faces of the magnet (see figure 9). A pointer was fashioned from some brass rods and attached to the magnet supports so that the relative angular positions of the crystal with the magnetic field could be read from the protractors . 13 Figure 7. Photograph of Nuclear Resonance Apparatus. IIJ .zmo .m:...4a¢3m ¢u30a .oo _uaoom cuiuoum 4.00 mam: (m .0 mcnoI .. :3 it A: .WEhou: m "FM zw>.¢o # - make! C macs—m .h. .c .200 awu3m- 304m Ifl .zmo .02 on 15 Figure 9. Photograph shoving sample holder in position batsmen the pole-faces of the magnet. C. Method of Recording the Signal The separate crystals were placed in the coil and rotated in a clockwise dir- ection perpendicular to the magnetic field. In each instance the crystal was oriented in the holder so that one of the crystal axes corresponded to the pre- defined zero degree mark on the holder. The output of the lock-in amplifier is porportional to the 310pe of the res- onance curve. This output was connected to a Millivac Sanborn chart recorder. From the recorder a trace of the derivative of the resonance curve was obtain- ed. This derivative of the signal was taken for every ten degrees as the crystal was rotated through 180 degrees. Four derivative traces were recorded at each angle so that any non-linearity in the sweep might be averaged out. Samples of these traces at various angles appear for rotation about the a, b, and c' axes in figure (10). Photographs of the signal as seen on the oscillo- scepe were made by‘a Polaroid Land camera (see figure 11). The photographs were used as a check on the line width measurements obtained from tre derivative curves o Visual measurements were made of the line separations from the signal as it appeared on the oscilIOSCOpe. These measurements were made for'each axial rotation through a full 360 degrees, at ten degree intervals. This was done for a general check on the shape of the doublet separation curves and to assure the observer that the curves repeated themselves in 180 degrees. The reason for using the derivative trace of the signal was two-fold. First; higher accuracy was attained in the separation measurements. In the visual 17 Figure 10. Samples of the derivative traces of the proton resonance signal from single crystals of hypo. Figure 11. Photographs of the proton resonance signal from single crystals of hypo. 18 Observations very rough estimates had to be made of the positions of the doub- let because of the weakness of the signal and the large amount of noise. Second; the derivative apparatus had a much higher resolving power and there— fore was able to detect more lines than by visual means. In one instance seven lines were detected with the derivative apparatus while only five lines could be seen on the oscilloscope. The line separation is measured in gauss as is customary. The variable rheo- stat was calibrated.by measuring the time required for the rheostat to run through a complete signal. This value was divided into the value of the mod- ulating magnetic field, Hm. Its value was obtained from a previous calibration of the modulating voltage done in the manner described by Jain . The quotient of this division is the number of gauss per second that the rheostat sweeps through as it is varied. The recorder tape is known to move at a constant speed of 2.5 squares per second. 30 by dividing this value into the previous quotient the final result is the number of gauss per square for a particular modulating and rheostat voltage. By multiplying this value by the number of squares between the signal peaks of the derivative the doublet separation in gauss is obtained. 19 V. AI-EALYSIS (‘F iti'ljUL'l'S A. Experimental Results The experimental values of the doublet separations as a function of the angle of rotation about the three crystal axes are shown in figures (12), (13), and (1h). The solid lines through the experimental points represent theoretical curves with shapes corresponding_to equation (10). The dotted lines through the points are hypothetical curves based on experimental evidence. Because of a definite broadening of the doublet components of the signal at particular angles the curves were assumed to intersect as indicated at the several points. The resonance signals that appear may in.scme cases result from the superpos- ition of two or more proton pairs that have very nearly the same orientation. The strong central line that appears in the signals (see figures 10 and 11) is prObably due to a superposition of several narrow doublets and/or a result of rotating proton groups as previously described. Because of the confused situation which exists in the central portion of the line the doublet separation of a given proton pair can be traced only for those angles for which the sep- aration is large. Therefore we will consider only components with large sep- arations, thus the angle 8 for all the p-p orientations listed is less than 35.3°. The angle (9. for the p-p vectors obtained from an investigation of figures (12), (13), and (1b) is listed in table (2). The angles listed under the a axis are for a clockwise rotation about that axis with 0° corresponding to the C EXis. The angles listed under the b and c' axes are for clockwise rotations about these axes with 00 corresponding to the c' and a axis respectively. 20 .m_x< 4 MI... haom< zo_h<._.0¢ “—0 m40z< NI». “.0 20:023.... 4 m4 zo_h<¢<&um buqmaoo .N. Muse... fl m.x<.o 00. cm. 0?. ON. 00. CV ON 0 a! q _ . _ . _ L a \\d\ 10‘ 9"OI/ 0 \O\\ In a 1 o. 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