A Further Test of the Nishina Theory of X-Ray Absorption Citation Winger, Ralph Edgar (1929) A Further Test of the Nishina Theory of X-Ray Absorption. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pxfj-3z34. https://resolver.caltech.edu/CaltechTHESIS:08122024-220446257 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1929 Record Number: CaltechTHESIS:08122024-220446257 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08122024-220446257 DOI: 10.7907/pxfj-3z34 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16628 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 13 Aug 2024 23:21 Last Modified: 13 Aug 2024 23:21 Thesis Files PDF - Final Version See Usage Policy. 8MB Repository Staff Only: item control page

A FURTHER TEST OF THE NISHINA THEORY OF X-RAY ABSORPTION T HE S I S BY Ralph Edgar Winger In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, Calif ornia 1 9 2 9 SUMMARY Aoya.,."'Tia , ,\Dnura, and Ni shina have give n a theory for the displacement of the x -1·ay I'C1 absorption ede;e in chlorides. The theory is derived by carry ing out a cyclic p rocess in whic h a IC e lectron is removed fr om the c hlo r ine ion in a lattice, follovred by the removal of the resultin g ar gon-like c1- ion. L-ri attempt is made to k eep track of all the ene r gy c hanges while the ion is being brought back to its original state, and after neglecting small terms the conclusion i s reached t hat the change in absorption frequency 1.vith compound, ,vhe re the compounds have similar crystal structure and c hemical bond, should be a linear function of the l attice energy. Four experime n-t,al points are plotted to a strai ght line, but the experimental er r or is too great and the points lie to o close to s ether to justify the conclusion tha t the experiments c heck the theo1-y. For a furt her test of t he t heory, more points have been secuTed by t ak ine; x-ray spectrograms of chlorides in vrhich l arger ab so rpt ion edge s hifts were to be expect ed. Lattic e ener g i es have been calculated, and the r esultinf; data p lotted. The points lie approximate l y on a strai Ght line, but not in such a way as to c he ck the theory. The extrapolat ions of a ll such lines s hou l d conve q:;e to a comn1o n interce pt , and in the present case there is a diver gence. 'ihe Aoyaraa-I<.: i..m ura- Nis h ina wo rk is criticised for the omission f rom the graph of certa in points which lie f a r from t he p lo tted line s.nd which Yrnuld cast muc h doubt on its proper location . In a paper as yet unpublished, Pauling f ind s the o reti ca l object ions to tho theor.y . The conclusion is reached that the theory is not e v en a pproximately correct, that it is probably too simple, a nd that we do not yet know v e ry we ll the me c han ism of the absorbing a ct or the fac t or_s Yrhich enter into it. Page 1 I NT RODUC T I ON Yfuen a beam of x-rays passes through a slit and is let fall on the plane surface of a crystal, it is resolved into a spectrum, the lines of vrhich take positions according to the law, deduced by the Braggs, n:\ = 2d sin e where n is the order of the spectrum, .A . the tvave length, d the lattice constant ·of _the crystal, and 0 the angle made by'~the beam with the crystal face. Such spectra were first obtained by the Braggs 1 • The spectrum so obtained may be thought of as tvrn superposed spectra--one consisting of emission lines, which vrill be characteristic of the elements composing the anti-cathode, the other being a continuous spectrum of "white" radiation, which will be manifest by a general darkening of a photographic plate. If between the x-ray source and the photographic plate a substance is interposed in the path of the x-rays, the rays will be partially absorbed in such a way as to yield another type of spectrum--the absorption spectrum. This type of spectrum was first observed by de Broglie 2 as a sudden change in the blackening of the plate. It is now i'rell knovm that the intensity of the x-rays which pass through the absorbing body is a critical function of the frequency--that when a certain definite frequency is reached the radiation is strongly absorbed, but vri th frequenc y furt her increasing, the absorption falls off until another critical frequency is attained. These discontinuities, or "absorption edges, 11 have definite wave lengths which are characteristic of the absorbing substance. Corresponding to the emission spectra, the absorption spectra may occur in several series, vrith several edges in a given series. For some time it was thought that the position of an edge is a function only of the element to which it is due. Bergengren 3 first Page 2 discovered indications that the spectra vrere influenced also by the chemical combination of the atom, but his investigations were limited in Lindh4 continued the study and scope and his conclusions erroneous. discovered that the positions of the absorption edges may vary considerably with chemical compound. The greatest single determining factor seems to be the chemical valence of the element. With increasing valence of a given element, the x-ray absorption begins at higher frequencies. Stelling5 has explained the effect of valence as being due to the $Creening effect of electrons in external parts of atoms. As an example of the shift in absorption edge we may cite the sulfur compound s . The wave lengths of the principal K edge of a large number of 4-valent inorganic compounds of sulfur are separated on the average by about 8 X.U. from the corre s ponding edge of 6-va lent compounds, and between the 2-val ent and 4-valent compounds there is a wave lene;th separation of about 13 X.U . All the substances thus far investigated show in general a similar behavior. '.L'he re are still othe r factors influencing the edges, but to a lesser degree. In the sulfates of potassium and strontillrn, for example, t he va lence of sulfur is the same, but the edges are about one X. U. apart, due appa rently to the different metals. Icinally, the crystal lattice structure is knovm to produce small changes in t he position of the edce s. In investigating the latter effect it is desirab le to work vri th a single element in several compounds in which it occurs with t he sarrte valence, a nd ,vith s:i.milar crystal structure. In the following pages will be described some new work on these sr.1.all shifts. NATURE 0 F T HE P R OBL E M The present investi gation deals v,ith the shifts in the principal K absorption edge of monovalent chlorine in a serie s o:f Page 3 compounds. These edges are already well knmm for a number of compounds, from the researches of Lindh 6 and Stelling7 Aoyama, Kimura, and Nishina 8 have given a theory which relates the shift in edge to the 11 Gitterer..ergie II or lattice energy of the absorbing substance. The theory as developed is limited in its application to chlorides of similar chemical binding and similar crystal structure. If the position of the K1 edge of some standard substance--say sodium chloride--is taken as a reference, then the other chlorides of the same crystal structure and type of binding will show· edges which are displaced with reference to the Na.Cl edge. According to the theory, this displacement should be a linear function of the lattice energy. The theory is derived by • carrying out a cyclic process in which a I( electron is · removed from the chlorine ion in a lattice, followed by the removal of the resulting argon-like c1- ion. While the ion is being taken through the cyclic process and brought back to its original state through a series of steps, an attempt is made to follow all the energy changes incident to the process. Since the initial and the final states a re the sa.'"ne, an equation may be vrri tten for the energy changes. '.:.'his equation, after dropping two comparatively small terms, which partially cancel each other, takes the form in v,hich KXCl is the energy required to remove a K electron from the chlorine ion in a lattice, Kc 1 - the corresponding energy for the free chlorine ion (which is a constant ) , U1 the lattice energy, and u2 the energy of deformation of the lattice and the electron shells. On the assumption of a proportionality between U1 and Uz the equation becones Page 4 where "a II is a constant. Kxcl is supposed to be the energy absorbed There are good reasons for believing when x-rays fall on the lattice. that u2 = O in the actual absorbing act, as it talces place too quickly for the establish.ment of the equilibrium ·which is assuraed in the cyclic process of Hishina a.nd his colleagues. 'l'his point was not noted by them, but it would have the effect only of giving the constant "a'' the value 1, Md hence the line represented by the equation should have the slope 1. The authors of tho theory have ta.ken data on the chlorides of sodium, potassium, rubidium, and lithium, and on ammonium chloride--substances for which the theory is supposed to hold sufficiently closely. They have used sodium chloride as a reference material, and for the other substances have taken the shift of the edge from the NaCl value, in v/R units . energy, also in Against these values they have plotted the lattice v/R units, and have indeed obtained a straight line. Their curve is shmm in Figure 1, beiow. 0.l?i a:5'' 0 .,. I '' ' ', ' ''' '' ' '2 '' '' Fig. 1 ', '' 0 '1 0 ' ', QJ 02 0.3 Q4 LolFce Ener.9_y 1n v/R "' ~ Q6 0.5 Page 5 The NaCl point necessarily lies on t he line, as it is the reference point. The othel· three points are closely bunc hed, a nd lie not far from the lTaCl point. considering the possibility of exper:L71ental error, a nd the ease with which a l most any sort o f line ca n be dravm near closely grouped points, it seemed to the writer that the exper:L71ental data were far too meager to j ustify any conclusions as to the experimenta l verific a tion of the theory, ani that a greater spread of points was therefore desirable. To obtain more points, under t he r e striction of similar cryst~l structure and chemical binding, it seemed that compounds similar to ammonitun chloride might be used, where the hydrogen atoms are displaced by methyl or ethyl or higher carbon cha in groups. A number of x-ray plates were accordingly made, using the sub stances just metnioned as absorbers, and also with NaCl f or reference, and NH4 Cl as a check. DESCRI PT ION O:F' J\PPAEA'J'U S .i\JJD AD,JUSTI.fZHTS '.:'he photo graphs were all taJ:en with a va cuum x-ra y s pect ro gr aph, simila r to t hat described b y Sie gbahn in his " Spectroscopy of X-rays," pp 62 ff. This appa r atus may be thought of as consisting of two rather distinct parts--a Coolidge x-ray tub e , a nd the spectrograph proper. The main body of the x-ray tube is hollowed out of a piece of brass, a nd has t-wo ground cone s projecting from it, f or t he attachment of glass tubes. These gl a ss tubes serve as supports for t he cat hode a nd the anti-cathode, b oth of which l:lO.Y t hus b e insulated from the rest of t he spect r ogr aph i f desired. For continuous operation vrater coolin g is necessary for both cathode and tar get, and as an added precaution-the 1.1ody of the tube was itself c ha nneled, and wa ter Page 6 circulated continuously. about 60°. 'lhe target was a copper tube, beveled to It was slipped into a loosely fittin g constricted ne ck of the glass tube, and sealed with sealing wax. 'l.'he position of the target could be adjusted by softening the wax, and slipping the target vrithin the glass tube. The fi lament distanc 0 could be adjusted by two supplementary means. The filament mountini:; was carried on a brass tube, similar to the target tube, but instead of a wax seal to the insulating glass tube, a ground cone joint was used, to facilitate rapid removal for change of filaments. The brass cone 1: ras itself a 1 sleeve, fit ti ng closely to the cylindr ical tube, and capable of being sealed at any desired position by sealing wax. adjustment. This served as a rough The fil ame nt holder was attached to the cooling tube by tungsten wires of about 1 mm diameter, which could be slipped ba ck and forth in hol e s drilled in the end of the cooling tube, and fastened by set screws. This served as a convenient fine adjustment. Once a satisfe.ctory fi l ament distance was determined, fil aments could be chanr;ed without d isturbing the adjustment. J:.s the 1 if'e of a fila:u.ent is a matter of hours, a convenient method of making and replacing filaments is desirable. I'ilaraonts were made of 10- rnil tungsten wire, vround first i nto a conica l spiral. grooved spindle form made from The winding was done on a spirally ¼ brass rod, 11 'l'he conic al spiral Yras then fl attened by heating it to vrhitene s s in a Bun sen flmue, and pulling it aga inst sheet asb e stos, be.eked firmly by a metal plate. ',everal such t reat:m.ent s were us ually necessary if the filar,ient was to remain fa irly permanent l y in a flat spirc..l . One ond of the f ilrunent ,vas grounded in the water coolin[:, tube, and the other was insulated and led to the outside through an air ti r;ht seal. 'i'he opt i mum distance of f ilament from taq;et is a characteristic of an individual x-ray tube Page 7 and its electrodes, and had to be detennined experimentally. The x-ray tube was fastened to the spectrograph proper with solder, a free opening communicating betwe en the two. In front of this opening the slit was placed. In the center of the bottom of the spectrograph were tvro coaxial ground cones, mounted vertically. To the internal end of one of these cones was attached an arm the outer extremity of which carried the plate holder, a simple brass frame with spring clamps to hold the plate firmly in ple.ce. • By means of the cone bearing, the plate holder could be rotated to any desired position. '.i.'he external end of this cone was rigidly attached to a precision angle scale, and was divided to. 5 1 of arc over a complete circle. ·;:iith the help of a microscope readings could be made to about 15 11 of arc. The plate holder a nd the slit were placed equidistant from the axis of rotation-which is necessary for g;ood sharp lines, especially if the rotating crystc.l IJ.ethod is to be used. The mounting of the crystal requires great care, and entails some dif ficulty. It is first fastened to a b rass plate by some sort of wax---beeS\1rax-rosin is good. For a particularly valuabl e crystal a slower but safer method was used. Be eswax ,Tas partially dissolved or softened i n carbon bisulfide, and applied to t he ba ck of the crysta l u little at a time and built up in layers until there was enough bD.ck ing to stick the beeswax to t he met a l plat e. This procedure obv i ated the dange r of breaJ::ing the crystal by the heat of the melted be e swax-rosin. After the crystal is stuck to the metal plate, the plate i s faste ne d nit h screws to a mountinr_; wh ich permits adjustments in two directions. The first adjustment is to bring tho face of t he crystal into parallelism with the a:x:is of rotation of its mounting. A screw device pe rmits the tilting of the plane of the crystal until the desil·ed orientation is reached. 'l'o determine when the crynta l has the proper t ilt, a piece of plane-parallel glass ( interferometer p l ate) is cla.Inped to the crystal f a ce, one end of the glass p rojecting above the crystal. This glass plate is used as a mirror, in which may be viewed the image of a scale throui::;h a telescope set about two meters avray, and the position of the cross hair noted. Then the crystal and glass plate are rotated through 180° and the scale again viewed, using the othc1· side of the plate as the r:1irror. '.'!hen this rotation produces no s hi ft in pos ition of the cross hair on the scale, the crystal face is parallel to the It was not possible to ,riew the glass plate axis of rotation. directly with a telescope, as the plate was a few centimeters belmv the top o f the spectro graph . overcome this difficulty. A pair of pr isms was arranged to The se prisms introduc ed other reflecting • surfa ces, and in the multiplicity of images visible it was sometiries hard to locate the right one. The next adj ustment is to move the crysta l parallel to its face until the f a c e wholly conta ins the 'l'his is accomplished by another auxiliary device axis of rotation. which is clamped to the p late holder arm. A fine ivory point is mounted so that it ca n be moved with fine ad,7usting sc1·ews, either a long or perpendicular to its axis. This point is brought into coinc ide nce Yrith the axis o f rotation of the plate holder and crystal. ':!hen the plate holder revolves, the ivory point moves with it about the same axis. 'i'he point is viewed through a :microscope, and by means of a scale in the eyepiece the position of no rotation of the tip can be observed. The point being adjusted to this position, the crystal is moved fonv-ard by a micrometer screw, a straight dovetail Page 9 groove guiding the motion so that the directional orientation of the crystal remains unchanged. The point and its irnage in the crystal can be observed simultaneously, and the two aro brought toward each other until they just meet, thus completing the crystal adjustment. The crystal and plate holder must be capable of independent rotation. This was accomplished by means of the tvro coaxial ground cones of brass previously mentioned. a thin conical sleeve of steel. The cones vrnre sepa1•e,ted by To exclude air most effectively, a grease made by the prolonged boiling of vase line and the addition of finely powdered graphite was found satisf2,ctory. These cones could be turned from the outside, permitting the setting of plate and crystal without the loss of vacuum. A degree scale and vernier sufficed for a rough setting of the crystal, which does not require fine adjustment for angle. The vernier was carried on a rigid arm attached to the same cone which carried the crystal mounting. The large circular cover (40 cm diameter) of the spectrograph rested on a rubber gasket and was fastened with screws. This cover had to be removed for loading plates, ad j usting slit, and chanr;ine; crystal orientation. For slowly rotating the cr;ystal a gear boz was used with a reducing ratio of 125,000:1. motor. This was driven by a small electric The slovr turning of the end gear caused a nut to travel and push the vernier arm, which rotated the crystal through approximately a tenth of a degree per hour. It was necesnary to turn the crystal in order to get homo geneous plates. ··J ith stationary crystal, the plate was covered with streaky marks, due to local irregularities, and these marks were hard to distinguish from lines and edges. 'The pumps were of the usual mercury condensation type, with Hyvac fore pump, and pressure was further reduced by a trap, cooled Pap;e 10 sometimes with liquid air, sometimes with solid carbon dioxide. E XPE H IHEHTAL P R OCE DURE A problem always pre sent in soft x-ra.y technique is to shut out the light inevitably given off by the x-ray tube vrithout cutting off too much of the x-radiation. Soft x-re.ys are strongly absorbed by even the thinnest of paper. Several different devices were tried and discarded. One such was the making of thin celluloid films by dissolving celluloid in amyl acetate, and allowing the solvent to evaporate from the thin surface film which forms when a drop of the solution is put on a water surface. These films could be atta ched to a brass frame, and placed in the path of t he light. But it was more difficult to render them effectively opaque to visible light. Attempts vvere made to use red dye, india ink, and a deposit of soot from burning camphor. 'the dryine; of the liquid usually broke the films, and the la.mp black coatint~ vras hard to control. The films were extremely thin (of the order of a fevr wave lengths of light) and consequently very fra r;ile, and finall y other ,neans were tried. Thoraeus 9 has described a spectro graph in which he interposed n. sheet of almninur.1 foil between the filament and target. 'l'his not only shut out th0 li 6ht, but also prevented the deposit o.i.' tungsten vapor on the target, and yet permitted electrons from the filament to go through to the target with but slight decrease in velocity. This met hod seemed very pronising, and considerable time and effort was spent on it. But it proved to be unsuccessful in our hands, and Thoraeus himself has apparently abandoned it. \'ie finally made use of three diff erent light ab sorbing screens-carbon paper, ciga rette paper coated with india inl<:, and blackened celluloid films. All Page 11 three gave about the sa.."'Ue results. The usual commercial liquid india ink is somewhat gur.uny and has a tendency to crack or "draw·" when it dries. Better to the purpose is Chinese india ink--solid sticks from which a suspension can be prepared by rubbing the sticks on a piece of wetted slate. Also celluloid films (not nearly so thin as those mentioned above) were made by applying a coat of dissolved celluloid to a glass plate, and removinc with a razor blade when dry. One or two such films were successfully coated with india ink and gave good results. 'i'he preparation of absorbing screens vras also the subject T-:ubbing the powdered solid into the of considerable experimenting. pores of tissue paper was tried, but it did not adhere very well. Then the crystals were finely pulverized in an agate mortar and made into a thin paste with celluloid painted onto glass to dry. dissolved in amyl acetate, e.nd Some good screens were made in this way, but it is ha rd to make them homogeneous, and to remove them from the glass without breaking . The paste may also be applied to thin paper, but this increases the thickness of the screen. One of the best methods wc:.s to put a thin coat of the celluloid solution on thin (cigarette) paper, and then gently sift the powder on through a fine meshed screen or cloth. This method gave greater homogeneity, and the thickness of the layer was easier to control. photographs were made with such scre ens. 3ome of the ,'.fith care, one side of the paper could be blackened, and the other side coated with the powder. For an a mnoniurn chloride screen, the salt was heat ed until it sublimed, and by holdine; blackened paper in the pat h of' t he dense cloud ensuing, a deposit of extremely fine particles could be obtained in almost any desired thickness. But the substances we ·were particularly Page 12 interested in---tetramethyl- and tetraethyl ammonium chloride---proved to be entirely too hygroscopic for any such treatment. We finally tried moistening a paper with the concentrated solution, and found that in the evacuating process the salt had dried and left a layer, not of scattered and relatively large crystals, but thin and uniform. The appearance was much liko that of the gum on postage stamps. These salt solutions were placed on the unbl~ckened side of carbon paper, and screens so made gave good results. The best thickness of absorbing material to use for scre ens has to be determined by experiment for a given material. The general tendency is to make the screen too thick. The plates used vrere Eastman ~;peed11Tay. Eastman X-ray were first tried, but the grain seemed coa rser, and no superiority over Speedway could be noticed. photo graphed. On each plate a reference mark was This mark was made by a fine slit in a narrow piece of brass (about 2 mm wide ) which was placed immediately in front of the plate. It wa s found that a small dish containing a few grruns of phosphorous pentoxide spread out to a l a r ge surface and placed in the spectrograph caused the filaments to last nuch longer. Pz05 the life of a filament was about four to ten hours. life was increased to from t hirty to fifty hour s . Yi- ithout the ?Jith it, the This is evide ntly due to the absorption of water vapor which is knovm to have a very destructive effect on tungsten fil ame nts when it is present in even the minutest quantities. It is desirable to have long lived filaments so as not to lose vacuum during the necessarily long exposures. The l ength of exposure varied from about 15 to 35 hours. The time required to obtain a good edr;e seemed to vary according to Page 13 absorbing screens and light screens used , as vrell as with applied voltage and current in the x-ray tube: Usually a preluninary plate was made, and from that was infe1·red the exposure time requisite to t he best results. thousand. device. The voltage used was from fifteen to twenty We used an ordinary x-ray transformer, with no rectifying For further work, by all means a good rectifying and wave smoothing arrangement should be installed. Currents up to fifty With bette r transforme1·s, two or even three millianperes -vrere used. times that current co.n be used, at hi gher voltages, with corr esponding shortening of exposure time. On all the plates we were interested in measuring the position of the principal IC absorption edge of chlorine. Following Aoyama, J~:iJaura, and Nishina, sodium chloride rras used as a reference substance, and we observed the shift in position of the c hlorine edge of the other substances from the lJaCl position. the linear shift on the plate. 'l'o obtain this, we meaaured ,_·;e shall call this shift To fit in with the Aoyama-r i nmra- Hishina scheme, vre 1,rish the corres ponding change in wave number, ·which vre shall call 6tJ. This was calculated directly from measurer2ents of 6 l and the formula 6v= - cote 6l 2r). This formula is based on the Bragg relation, n\ n dA 2d sin e ancl its derivative 2d cos e de, the relation I -x- ]) I dV de crystal to plate. X dA, dl 2r and its derivative and t he £;eometric:·,l relation vrhe re r is the distance from I?or the si:iall s hifts obtained, the i ntrinsic Page 14 error due to the use of this formula was entirely ne gligible. For convenience in calculating sodiura chloride v~ l ue of ,6.( ~) for the shift from the , we may compute the coefficient Cot e 2 Rr.X us i ng the fol l owing constants : = 6058 .08 ~( . u. for calcite) 6 46° 21 1 27 11 (Based on 2d R 109,737 (Eydberg number) 4384 . 0 ::cu. ~ T"° . h 1na ' !.\ ( ...oyan1aAll!1Urt1.- V i'nS. 17. 981 cm ( -. u irec .1'-.' measurement) r - value) The v a lue of the coefficient is 5 . 5125, and we now have the simple formula 5.5 . 25.L l which applies of c ourse only to the special con<li tions of this investigation. The measurer.tent of .6 1 involved the comparison of each plate with a standard NaCl pl ate . The edges leave somet l: in g to be desired in sharpness, a s t hey appear rather fuz zy under t he comparator. The difficulty of determinin g t ho proper location of the edge has • d lJY ,,c•t e 11·ing lO • b een d iscusse 'I'he ordinary comparat or method was used , supplen,ented by a nother method, vrhich v'T ill be briefly des c ribed . The two plates to be cor-:,pared for shift are mounted at rir,; ht a n ,;les to each othe r, one of theu being fixed to a carr iage wh ich ca n be moved by a !:licromet c r screw. Beruns of li s ht, e.fter passing normal l y throu gh the tvro plates, are made parallel by 1:1eans of a half silvered surface between two prisms, and tho two bee.ms before entering the prisms are cut off hy straight edz;es in such a vray that any l ines or edges to be compared are viewed directly end to e nd. The re f erenc e Page 15 lines can be brour;ht easily and accurately into juxtaposition, and the shift in edge can then be measured directly by turning the If the edges are of micrometer screw until the edr;es coincide. about the same degree of fuzziness (and in the present ca se they appeared to be so) it is no longer necessary to speculate on their . proper location. The n ethod suffers from the difficulty usual in compai·ators--lack of contrast--but is rapid and d irect and permitted the d,,plication of readings to within about two hundredths rrun. By taldng a large nur.iber o.f readings the err or was much reduced . The comparator was made by Dr. R . J . Ke nnedy of this In stitute, and has been used by hL":l for measuring s hifts in interfe re nce fr inges. ·:men using either type of comparator it was found to be a dec i ded advanta r;e· to ':1-ork in a dark r o om, shuttin 0 out as much stray li c ht as possible. The use of a gr oon f:i.l ter also s oe·,:·:ed to i mp rove the contrast in some cas es . a.,1.~onium chloride . To Givo an i dea of the degree of uncertainty involve d in settins on an edge and on the referenc e line , the follovring sanple table is introduced: Plate J!.. ·ir 12 NlI4 Cl '.'?.eference iiiark Position of Edge 65 .219 mm .214 .1 99 .233 .201 .229 .210 .223 . 205 .215 .202 .215 . 227 .196 .228 .221 . 224 .220 .228 .211 Hean Value Diffe rence ,,_ .., 59.046 :mrn . 050 ~047 .045 .050 .048 .044 .047 .046 .049 59.047 mm .224 .215 .217 .221 .212 .219 .220 .231 .212 .238 .227 . 222 .2 12 . 224 .227 .209 .210 .207 .215 ___.194 ______ ...______ 65.217 mm ..._. . 6.17 mm Page 16 Of the ab ove values .for edge, 87 % lie within 7 .5 % of the mean value, and 75 %are within 5 % of the mean . A more complete tabulation wil l b e [;iven la t or. For the lattice energy, t he values given by Aoya:ma, Kimura, and Nishina ,v-ere used for NaC l and rrn:4 c1. c al culated from the Dorn formula 11 Some of these ;,•rere , and the others ,irere derived by Born 12 a nd Grii·nm13 from cyclic p rocesses, usin g thermochemical constants. The Born formula was also used for c alculating the latt ice energy of the new substances under consideration. The applicat i on of thi s forTJ.ula to a compound re qu ires a knowl edge of i ts This structure is known f or H( CI·I3 ) Cl, but not 4 cry sta l structure. for I-J ( c H ) cl so far a s the author· coul d a scerta i n . 2 5 4 Howe ver, the structure is Jr.no-vm for both the corres ponding iodides , and we are thereby enabled to infer what it should be for t he ch lo r ide with a probability of very littl e error . Jumnonium c hloride and the tetramethyl n::r.1onium halides 14 have a crystal structu.re very similar to that of ce sium c hloride. The structures are illustrated in Fi e;s . 2 and 3. ~ \ I \ \ \ .""" I ,.,/ :-r Gs l<j ~ I // -\ I \ / ~ I \ I __l_ ·~ \ ~ '7 l_ Fig. 2 cs + 0 Cl - • Fig. 3 Page 17 For cesium chloride 15 the Coulomb ener 0y is u' z' e' s 1.7624 where S represents the smallest distance bet-,veon oppositely charged ions, z is the nunber of unit charges per ion, and e the value of •.t. l uni" c,mrge . Tho tetra.methyl arnmonium chloride structure differs slightly from the cubical cesium chloride structure, as v,rill be noted from the figure . From crystal structure data 1He have, referring to Figure 3, The formula given above for the energy of cesilun chloride may be applied with negligible error to this distorted cesiU;71-chloride-like structure. 'Je shov, this by calculating the energy of eight chlorine ions with respect to a positive ion, both when the chlo!·ine ions are at the corners of a cube, and v,hen they are in the ammonium chloride position. If the Cl - vrere at the corners the energy (for a sinGle cube) would be 8 z'/.. e'- /s,, where S1 = 4. 77 A, or W = 1.677 z" e'/.. . 0 Rut for the actual structure vrn have and on substituting for the S values given above, We therefore see that in our case we may consider the crystal to have the cesi1JJn chloride structure, since the results just calculated If we then take the enerr;y of the for Ware practically identical. methyl ammonium chloride to be U' zt.e?.. -s- 1.7624 Page 18 the error involved vrill be of tho order of 0.1 ;~We infer the structure of tetraethyl ammoniu,-n chloride from that known for the corresponding iodide 16 and the methyl chloride and iodide, by assUJning a proportionality. . . 4.96 A, and for N(c 2n 5 ) 4 I is approximately 5.72 A, then on the foregoing assUt-npt ion, rec a lling tha t (' 0 s1 for the methyl c hloride is - (.572) 4 77 I= 5.50 X 1-\496 • We are now in a position to calculate the energy for the methyl and \ ethyl a1:U11onitun chlorides. The Coulomb energy s hould be modified by multiplying it by the factor (1 - 1/9), in order to ::;et the lattice energy 1 7, the repulsion exponent beine; t aken a s 9. z 1 s1 4.77 x 10-8 cm (4.774) 2 X 10- 20 X 1.767 X 8 8 4.77 X 10- X 9 ergs 8.43 x 10- 12 ergs . ::::;::::::;. 0.351 _ V/R units = 1 s1 = 5.50 x 10- 8 cm z _ (4.774) 2 X 10- 20 X 1.767 X 8 5.50 X 10-8 X 9 = 6 .48 x 10-12 ergs 0.300 We may now smmnarize the experimental data in the following t able: ergs v/R units Par;e 19 6 ) NaCl mm No. of Pl ates No. of Read ings NaCl 2 100 ---- ---- 0 .581 NH4 Cl 2 40 0.102 0 .056 .504 H(CH3 ) 4 Cl 3 130 .17 .094 .351 1'J(C 2H5 ) 4 Cl 2 140 .22 .121 .300 Substance Lattice Energy 6 (-W-) IifaCl JL H '.i.'he above values are plott ed in Fi gure 4 , along with the previously given plot of Aoywna , I{i mura , and Nishina . --- I : : ! I I : 0.5 ' r,.. i ' ' ,;...I~, ' i i II o..,. I i I iI I ~-l ; I ' ' ', .'.J '' ' I I I 0- I I ' 7 -I l I ! -- ---,. __ 0.1 ' '- - '' --◄ ~H,~CI ficH,J,ci' NISHINA 0 WINGER◊ .. ·- 0 ' ' ', - 01 I '' ' ~ i IIH,CI: I- ~ ,n 0.4 v/R !- _J -- oNH c,c,, O.c. 0.3 Le71f1ce Enersry i '- (15 - .. fC'i - -L Q6 Fi g. 4 DI S CUS S I ON 0 F RE S UL T S It will be noticed at once that the new results fall somewhat off the straight line dravm by the former experimenters. their po int for r-n-14 Cl is not checked. Also, that The difference betwe en the two Pa.ge 20 NH,:101 values, however, lies within the experimental error allowed by ± Aoya:ma, Kimura, and Nishina. The shifts in edge measured are so small for the substances they investi gated that there is a very large uncertainty in the location of their points. The new points represent well over twice the range of displacement, and the observational error should be reduced correspondingly. But it would seem unduly optimistic to claim an accuracy in measurement greater than one or two hundredths nun, w-hich is from 10 to 20 %of the quantity measured in the present case, and rather more than that for the other observers, considering their small shifts, and the lower dispersion given by their spectrograph. In Fig. 4 appear two Aoyama-KLnura-Nishina points which did not appear in their published graph of Fig. 1. These points correspond to cesium and lithiwn chloride, tend inasmuch as values were published for those compounds, it is not easy to see why they wore not included in the r..;raph. Cesium chloride is mentioned among a group of other chlorides which were not plotted on the ground that thooo compounds have either a different crystal structure or a different kind of chemical bond from NaCl. But on that basis, there is not even as much justification for their plotting of Ii!H4 Cl, since its crystal structure is slightly further from NaCl than is CsCl-at least in the form at which it crysta llizes at usual temperatures-whereas CsCl has the same kind of bond as NaCl. The CsCl point lies far from the line plotted by Aoyama., Kimura, and Nishina. Still more difficult to understand is why the LiCl point was not plotted. Both in crystal structu1·e and in chemical binding it is a perfectly . orthodox mer:iber of the alkali group, and deserves the same consideration as any of the others. W ben we take this point into account, much Page 21 uncertainty is throvm on the proper slope of the line. The author has plotted his points also on a straight line., which has only about half as steep a slope as the Aoyama-Kimura-IJishina line. Moreover, all these points meet the conditions of the Nishina theory by being all of the same crystal structure and chemical binding, although they differ somewhat from the alkali group. This might be interpreted as a confirmation of the theory, as a somewhat different slope is to be expected, but there is so much similarity in the compounds that the difference should not be any way near the magnitude observed. There is a further serious flaw. the lines to u1 = 'I'he extrapolation of 0 should give for the intercept the difference between the absorption frequency of free Cl- ion and tha:t of NaCl, hence all the possible lines should converge to the s~~e intercept. Instead, the lines seem to diverge. Finally, in an unpublished :re.per, Pauling finds theoretical objections to the theory. In vievr of the results above, it is the opinion of the author that the Aoyama-I{imura-Nishina theory is no longer tenable. It seems to be too simple, and the evidence indicates that at least some very important factors have been left out of consideration. We do not as yet know very well the mechanism of the absorbing act, nor the factors entering into it. depend on more e]cperimental data. A comprehensive theory will Page 22 BIBLIOGRAPHY 1. W. H. and W. L. Bragg, Proc. Roy . Soc., 88 A, p 428, (1913) 89 A, p 246, (1914) 2. M. de Broglie, Comptes ~{endus, 157, p 1413, (1913) 158, p 1493, (1914) 3. J . 4. A. Lindh, Comptes Hendus, 172, p 1175, (1921) 175, p 25, (1922) ZS. f. Phys., 6, p 303, (1921); 31, p 210, (1925) 5. Otto Stelling, ZS. f. Phys., 50, p 506, (1928) 6. A. Lindh, loc. cit. 7. Otto Stelling, lac. cit. 8. Aoyarna, Kimura, and Nishina, ZS . f. Phys., 44, p 810, (1927) 9. n. Thoraeus, Phil. J•fag., 1, 7th Series, p 312, (1926) 10. otto :,telling, lac. cit. 11. LL Born, Problems of Atomic Dynamics (M. I. T ., 1926) p 166 12. H. Born, ibid. pp 168 ff. 13. '! , 14. n. w. G. V{yckoff, ZS. 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