X-RAY STUDIES OF THE

ELECTRONIC BAND STRUCTURE OF METALS

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State U n iv e r s ity

By

NATHAN SPIELBERG, B .A ., M .Sc.

The Ohio State University

1952

Approved by*

----- A d v iser ACKNOWLEDGEMENTS

This work was done under the supervision of Professor

C. H. Shaw of the Department of Physics and Astrononiy of The Ohio

State University. It is a pleasure to acknowledge indebtedness to

Dr. Shaw for guidance, encouragement and tutelage.

Thanks are due to Mr. J. A. Soules for his fine work and aid

in construction and maintenance of equipment and to Mr. Carl McWhirt

and his capable machinists in the Physics Shop. I am deeply

grateful to Mrs. Alice B. Spielberg for her constant encouragement

and for her excellent typing of this dissertation.

Gratitude is due to the Office of Naval Research for the

granting of a fellowship through the Ohio State University Research

Foundation, 19Jj9-.!?0, to E, I. du Pont de Nemours and Company for

their grant of a fellowship for 19!?0-5l, and to the Atomic Energy

Commission for supplying funds for a Research Associateship through

the 0. S. U. Research Foundation. Funds for equipment were obtained

from the Graduate School of The Ohio State University, from the

0. S. U. Research Fotmdation, and from the Development Fund of The

Ohio State University.

i

4 £00487 TABLE OF CONTENTS

Page

I. Introduction . 1

II. Theory li

A. Bands for metals U 1 * Orxgxn • « ...... 2. Brillouin zones. »••••• 5 3. N(E) curves ...... 8 iu Calculation of N(E) curves .... 9

B. Spectra 12 1. Widths of inner levels . • • • .12 2. Shapes and widths of band spectra • 0 . 1 3 3. Perturbations to shapes of band spectra . .1 6 U. Suitable spectral regions. • • • .17

I l l * A pparatus

A. Spectrometer 19 1. Design requirements ...... 19 2. The spectrometer shell . . . , .20 3. The crystal axes ...... 26 U. Alignment procedure ...... 36

B. X-ray tube I4.0 1. Design requirements . . . . . • UO 2. The tube ...... UO 3. The power supply . . • • . . U8 Evaluation of x-ray tube and auxiliary equipment ...... 32

C. Detector 53 1. Requirements ...... 53 2. The Allen type multiplier. . . • . 5U 3. Auxiliary equipment ...... 59 h» Operating data ...... 60 5. Evaluation of multiplier . . • . .69

D. The crystals 70 1. Requirements • ...... 70 2. Possible crystals ...... 71 3. Preparation of beryl crystals . • . .7 2 U. ( 1,- 1 ) rocking curves and percent reflection • 78 5. The (1010) grating space of beryl . . . 8 U

i i Page

IV , Data 87

A. Molybdenum ..,..*•.87

B • Copper • «.».«.». 9^

C• Zinc .«..»*.«•« 97

D. Longer wavelengths ...... 102

V. Discussion of Data 103

A. Molybdenum ...... 103

B. Copper . , ...... loU

C. Zinc ...... 109

VI. Conclusions 112

Autobiography 13.Ii

i i i 1

X-RAY STUDIES OF THE ELECTRONIC BAND STRUCTURE OF METALS

I . INTRODUCTION

Many of the properties of solids can be explained in terms of an energy band picture. In an isolated atom, the orbital electrons may be found at certain discrete energy levels, the levels of lowest energy being associated with the innermost orbits. "When this atom is found in a solid, the innermost orbits, and hence the lowest levels, are practically unchanged from the free casej however, the outer orbits are greatly disturbed by the presence of neighboring atoms and the levels are broadened into bands of allowed energy.

These bands, the degree to which they are filled and the forbidden energy ranges between bands, account for and correlate electrical and thermal conductivities, magnetic properties, radiation properties, mechanical properties, alloying properties, e t c .

One of the standard techniques for studying energy levels of atomic systems is the interpretation of emission and absorption spectra. For free atoms, transitions between levels are observed as relatively sharp spectral lin es. As the atoms become more complicated, or as atoms join to form molecules, the resulting more complex network of energy levels introduces fine structure into the spectral lines, requiring more resolving power from instruments. However, so long as levels remain discrete, one can always find, in some region of the spectrum, a line corresponding to a transition between levels. This has led to the development,

for example, of infrared and microwave spectroscopy. On the other

hand, when there are whole bands of levels, as in solids, the

line spectra become band spectra, extending over considerable energy

r a n g e s .

If a transition takes place between two energy bands, or within

a band, any photon energy between values corresponding to the lines

F and G (figure 1) may be involved. Moreover, radiation of a given wavelength may correspond to any one of the transitions A, B, C, D

since the energies involved are the same, and it is quite difficult

to determine what portions of the bands are involved in a given

transition. Transitions between bands usually involve optical and

infrared spectra.

On the other hand, if a transition takes place between one of

the sharp inner levels and the outer band, each energy photon can be correlate': th a definite location in the band, as shown at A,

B, C, I in figure 2. The only ultimate uncertainty in the determi­ n a t i o n ■ energy of the band state is that due to the natural

•! inner level. In this case, the intensity of the ou- spectrum reflects rather directly the statistical weights of the various energy states making up the energy band. The wave­ lengths involved here fa ll in the ultraviolet and x-ray regions,the shorter wavelengths becoming more important with increasing atomic number of the material being studied.

X-ray spectroscopy, therefore, is a useful tool for the study of electronic band structures. 3

A If6 Wed b o n d

ABC

b o n d

A B CD F &

F igu re 1 . Optical transitions between bands

Aff owed v b o n d & £

A ! t o w e e / b o n d & £ .

JL i du rrer /c**<=d AB C D

Figure 2. X-ray transitions from inner level to band h

I I . THEORY

A. Bands for metals

1. Origin. The existence of energy bands in metals has been derived from a particular type of one-electron solution to the

Schrodinger equation, known as the Hund-Mulliken-Bloch scheme.'*'

When applied to solids, this is called the Bloch scheme. It states that the "Jfunction for an individual electron in the solid shall be considered as extending throughout the volume of material, being largest in the neighborhood of individual atoms and rather flat and like plane waves at large distances from the atoms. For a valence electron, in particular, this is equivalent to saying that the electron belongs to the crystals as a whole rather than to an individual atom.

The Schrodinger equation, in one dimension, for example, for valence electrons is written therefore as

For a one-dimensional crystal with lattice constant equal to a, V (x+a) sr V (x). It may be shown^*^ -that there are three types of solutions, one of which increases without lim it as x approaches e it h e r + 0 0 o r - 0 0 . When dealing with an infinite crystal these must be discarded. The eigenvalues of energy, E, corresponding to

•^-Seitz, Frederick, The Modern Theory of Solids, Mew York: McGraw-Hill Book Company, 19lt0, p. 2^1 ^Seitz, op. cit., p. 278 ^Mott, N. F. and Jones, H., The Theory of the Properties of Metals and Alloys, London: Oxford University Press, p. 57 5 to these solutions are forbiddenj there are no electrons allowed in these energy states. The allowed solutions are of the form

where k is real and Cfg(x) has th e l a t t i c e p e r io d ic it y a . The sub­ script k represents the momentum of the electron.

2. Brillouin zones. More detailed assumptions about the nature of the potential function V (x) lead to more information about the allowed and unallowed energy bands. If V (x) is small enough to be treated as a perturbation, then the energy is given by^ A £ / n-=£o E=o — to the second order approximation, except when f~ f l , .

c„ - —-—— and represents the energy for the free electron 2,/n approximation. a ^jfC „ x /^ Vn f VCc) e d x 'd- £r„ ,

kn - k ~ 2JTJ2- H /f)f&qrci{ ex. f Except when /£. —£v, / is small, E follows very closely the free electron formula and is approximately equal to £&, / S0 —£ n ( i s small whenever k is close to *2J£ , and the perturbation formula ex. above for E no longer holds, but rather

£ ^ -k + En */(£*-£„)*• K,* ] the negative sign holding for k <.HIT and the positive for k >!2Zf . Q CL Therefore, at there is a discontinuity in E, the energy jump

^Mott and Jones, op. cit., p. 6 being given by A E ~ ~Z IV* t •

A plot of E vs, k is given in figure 3»

In three dimensions, for a simple cubic lattice, the results are exactly analagous, with k and n now being treated as vectors.

= h U A T * m

' _*£2m I " k — " cx I 1 Again there is a discontinuity in the energy when E = Bn , w hich occurs whenever / Ac j^~ — } k — z — J which reduces to n - k — ~~ ~

Within each zone the energy changes continuously with varying k; however, whenever k crosses a zone boundary, there is a discon­ tinuity in the energy. Figure U shows a two-dimensional zone pattern. The curve of figure 3 shows how the energy varies along a particular axis in k-space.

For the simple cubic lattice the surfaces of constant energy in k—space are spheres so long as they do not approach too close to the zone boundaries, because E varies practically with k ; however as various parts of the spherical surface get closer and closer to the zone boundaries they become misshapen. At those places where the energy surface contacts the zone boundary, holes appear in the surface because of the fact that the particular energy

^Mott and Jones, o£. c it., p. 65 Seitz, ojp. c it., p. 287 Figure 3- E vs. k, showing forbidden ranges of E.

Figure h. Two-dimensional zone pattern, showing energy contours. (After Slater, J. C., Physical Review, i^, 79U ( 1 9 3 * 0 ). 8 value in question is not allowed for those values of k lying on the zone boundary.

3» N(E) curves. From the Brillouin zones and the constant energy surfaces in k—space the nature and extent of the allowed energy bands may be derived. Each zone can be divided into N cells, where N is the number of atoms in the crystal, which represent the allowed states for that particular zone. According to the Fermi statistics, these cells may contain two electrons each (allowing for two orientations of electron spin), and they are filled in the order of increasing energy. The number of these cells between E and E + dE may be calcu­ lated to obtain the degeneracy for a given energy, N(E). 2 N(E) dE is the number of allowed energy states between E and E + dE. This calculation is carried out over all the zones under considerationj each zone then giving rise to an N(E) curve, or density of states curve, which tells how the energy band associated with that zone is to be filled .

It does not always follow that because the zone boundaries represent surfaces of energy discontinuity that every energy in the second zone, for example, is greater than every energy in the first zone. Only at each point on the boundary is the second zone energy greater than the first.^

The energy just inside the second zone at point A on the boundary is greater than the energy just inside the first zone at point A;

6S e it z M ott 9

and the same holds for point Bj but the energy at point B just

inside the second zone may be less than the energy at point A

inside the first zone. Such a case leads to the situation that the range of energies covered by the N(E) curve of the first zone over­ laps somewhat the range of energies covered by the N(E) curve of

the second zone. The corresponding energy bands are said to overlap.

This is considered to be the case for divalent metals. For over­

lapping bands, the two individual N(E) curves may be added to give a new N(E) curve for the entire range. Examples of possible N(E)

curves are given in figures 5 and 6 .

iu Calculation of N(E) curves. Except in certain simple cases, where the assumption of almost free electrons is valid, the calcu­ lation of N(E) curves for various energy bands and metals is rather d i f f i c u l t .

Much of the calculations have been based on the method of the y 8 cellular potential. 9 Copper, in particular, has received much attention from Slater and co-workers.^1^ * ^ 5-^ The total N(E)

curve for copper is shown in figure 7-11 The hatched r e g io n r e p re­

sents the occupied portion of the density of states curve. Figure 8

shows the two parts of the N(E) curvej the high narrow portion being due to the band derived from the 3d atom ic s t a t e s arid th e low broad p o r tio n coming from th e Us s t a t e s . The work o f Chodorow took

^Wigner, E. and Seitz, F., Physical Review, h3, 80U (1933) ^Slater, J. C., Physical Review, U5, 79^. (193U) ^Krutter, H., Physical Review, U8 , 66h (1935) l°Slater, J. C., Physical Review, U9, 537 (1936) URudberg, E. and Slater, J. C., Physical Review, 50, 150 (1936) l^chodorow, M., Physical Review, 55, 675A (1939) 10

f\(&?) Co rye* -(Cor Nor* — Ovr r S c trtc l 5

F ig u re 5 .

f\l(£) C~o ry e -(-or Qy&K/ctppfrvj JEZctnefs

F ig u r e 6 . £ A/(£} curve -/o C o p p (After Rudberg and Slater, Physical Review, 5o, 150 (1 9 3 6 )) F igu re 7 .

3 d

- 0.7 0 . S 04 0.3 - 0,2 0,0 fafo»?i< units) F igu re 8 , Overlapping A/&J Curuea ~£»r Copper (After Slater, Physical Review, U9, £37 (1 9 3 6 )) 12 partially into account exchange effects and also varied details of the 12 calculational method. Much narrower 3d bands were obtained (1.7 e.v.) than in the earlier work, and a sp lit conduction band was formed.

No details other than a brief note have been published.

B . S p e c tr a

1. Widths of inner levels. A s stated in the introduction, the density of states curve should be rather directly reflected in the x-ray spectrum of a particular solid, the ultimate lim itation

(aside from instrumental difficulties) being the width of the inner level involved in a transition.

The width of the inner level is determined by three factors: the heat motion of the emitting atom, the perturbations due to neighboring atoms, and the natural width due to the uncertainty principle. Heat motion can be neglected for x-ray levels, since kT is less than .1 volt for temperatures under 1000° A. Parratt^ has found a change in widths of lines for the first transition group elements in various alloys, which one would most logically attribute to changes in width of the L levels. The maximum change reported was 23$ for Mn K=-< , in a 50-5>0 Mn-Ni alloy. The 3d band of Mn is only half filled so that the greatest change would be expected there. Ni, on the other hand, shows a change of 7$ in a

6O-I1O Mn-Ni alloy, whereas Mn shows a 19$ change in the same alloy.

Surely, then, for the last few elements in the transition group

^ P a r r a t t , Lyman G ., P h y s ic a l R eview , b £ , 36h (193U) 13 and for succeeding elements, the effect of neighboring atoms may be n e g le c te d .

This leaves the uncertainty principle as the main cause of the widths of inner levels. Since At= rr > those states having A t: 9 short lifetim es, A t, should have large natural widths, AE. It

should be expected then that L series spectra should reveal more of

the inherent fine structure than K series spectra, because the K

states are usually more shortlived than the L states.

The occurrence of radiationless transitions may broaden an

inner level by decreasing its lifetim e. Of interest here is the

fact that wavelength measurements indicate that Auger transitions

from Lj to Lm M are e n e r g e t ic a lly p o s s ib le below atom ic number 31

for a ll M "levels" and from Lj j to LjjjMjy^ y below atom ic number

3 0 This would make the Lji level wider than the L j j j . The

K<=^2 lines are broader than the lines for the elements Ti 22 17 to Ge 3 2 .

2. Shapes and widths of band spectra. The study of the x-ray

spectra arising from transitions to and from the bands is, in a sense,

a method for generalized Fourier analysis of the N(E) curve. If the

wave functions associated with the density of states curve are

are expanded in terms of the atomic wave functions ^ for an isolated 10 atom, then one can make use of isolated atom selection rules to

^Cooper, John N., Physical Review, 65>, 155 (19UU) ^Coster, D., and Bril, A., Physica, IX, 8h-96 (19U2) l^Bril, A., Physica, XIII, U61-U89 (19%7) ^Bearden, J. A., and Shaw, C. H., Physical Review, I48, 18 (1935) l^Skinner, H. W. B., Philosophical Transactions of the Royal Society of London, A239, p. 10U (l9Uo) 1U determine the shape of the x-ray spectrum, or from the shape of the x-ray spectrum make an estimate of the Fourier components of the

N(E) curve. The transition probability for an electric dipole radiative transition between the band and the inner state cjg i i s proportional to pte) * //§* n. Jv J2- = jz. (£) f f e I

The integral now represents the transition probability for the isolated atom case, the selection rules for which are well known: AL = *1 j Aj^^±/,

For a transition from the 3d level to the K shell, p(E) is . 2- proportional to (O ^ ^ l because the selection rules for L permit only the transition s to p. In emission, then, the intensity of radiation in the range E to E + dE is Z (£)<*&■ ^ v * /

Skinner18 d e fin e s ) ( £ ) I ^ / V ( £ ) = N p ( £ )

. . JT (A) ^ V'-Npf*) JEr

For a transition to the Lj j j s h e ll

= ja y (£ )f4 > L2_ C? < f> 3 ctV + a ji (£)f

- /« V , ^5 (£) + (£) I *■

'• T ( £ ) c /B l^s as (£) + ^ d .O < d (£-) 1^ A /( £ ) d B o^and have been introduced to take into account the

fact that the isolated atom transition probabilities in the two

cases have different values. It is not possible to define a

meaningful NS(E) or N(j(E) in this case because of the cross-product

term ^ *=* j <=f, ( £ ) ( £ ) but Ns+d(E) = j ^ s Q s (£■) + ^ a d ( £ ) J * N(E) may be defined without making definite the manner in which the s and

d factors are put together.

For Ljj spectra, similarly Ng+d(E) can be defined, which w ill

differ slightly from Ns+d(E) in so far as <=>c^ is concerned, but which

would change ° - j i , and presumably , quite a bit because the

transition between J = 1/2 and J = 5/2 is forbidden.

It should be noted that a reference to the 3d band, for example,

does not mean that the wave functions for the band in question have

d symmetry; but rather at increasing separation of the atoms the

band collapses in width and approaches the position of the atomic 3d

level as a lim it. The wave functions for the band have a symmetry

of their own which is determined by the values of ( e ) There

may well be a certain amount of d symmetry, but there is also s, p,

and other symmetry. This is quite often referred to as admixture of

s, p, etc., function.

Emission spectra, of course, give information about the filled

portion of a band, since the intensity of a transition from an

outer band to an inner level depends upon the actual population of

the outer states. In particular, the high frequency end of the

band should fa ll off very sharply for a metal at the energy corres­

ponding to the Fermi level. This high frequency cut-off is called 18 19 an "emission edge", and has been observed for the light metals. ’

■^Kingston, R. H., Physical Review, 8 i|, 9hh (1951) 16

Absorption spectra, on the other hand, give information about the unfilled portion of the band, again since the intensity of absorption depends upon the capacity of the band to receive inner electrons, i.e ., upon the density of allowed states. Presumably a sharp edge corresponding to the Fermi level should be observed at the beginning of absorption. This has been found for the j j j 20 edge of aluminum.

It should be noted that the V ^ factor is absent in the inten­

sity expression for absorption.

3. Perturbations to shapes of band spectra. There are certain

features of the observed spectra which are attributed to the per­

turbations of the energy level and band system induced by the

excitation of the x-ray states.

Satellite lines are known throughout x-ray spectra and are

found to the short wavelength side of ordinary x-ray lines. These

satellite lines do not correspond to differences between term values

in. the ordinary x-ray level diagram, but are attributed rather to

transitions in doubly ionized atoms. It is presently believed that

these states of double ionization arise from Auger transitions from 21 an excited x-ray state. These have already been mentioned in

connection with widths of inner levels. The effect of double ioni­

zation is to raise the atomic number of the emitting atom to i?-t~X ,

the transitions of which have higher energies than for atomic

^°Tomboulian, D. H. and Pell, E. M., Physical Review, 83, p . 1196-1201 (1951) ^Coster, D. and Kronig, R. deL., Physica, 2, 13 (1935) 17 number Z . 1 O Skinner has accounted for certain features in the i l l emission bands of Na, A1 and Mg in this fashion; and certain features in the K/3 2 £ spectra of the transition metals are said to be due to this.^2 Attempts have been made to explain deviations from the theoretical shape of the long wavelength end of certain emission bands in terms of Auger broadening of the levels in the l 8 23 continuum at the bottom of the conduction band. 3

In insulating crystals, certain lines have been observed in absorption measurements, which are attributed to the creation of

"exciton" levels in the atom ionized by the absorption process. ^ * 2 5

This ionized atom acts like an impurity atom in the solid and has certain discrete, levels below and in the energy range of the contin- uous band. Seitz and Landsberg J have considered this in connec­

tion with the previously mentioned shapes of the long wavelength

ends of the emission bands.

iu Suitable spectral regions. It is desirable to investigate

spectroscopic fine structure at any and all wavelengths. A compari­

son of the transitions involving different inner levels (K, L, M)

presents information which may be used in conjunction with the

^Beeman, w. W. and Friedman, H., Physical Review, 56, 392 (1939) ^^Landsberg, P. T., Proceedings of the Physical Society of London, A62, 806-816 (19U9) ^Uparratt, L. G. and Jossem, E. L., Physical Review, 8 U, 362 (1951) 25cauchois, Y. and Mott, N. F., Philosophical Magazine, Uo, 1260-1269 (19U9) ^Seitz, op. cit., p. U39 18 known selection rules to gain more complete information about the valence bands.

At the long wavelengths a much higher energy resolution can be had than at short wavelengths. An energy separation of one o volt requires a wavelength separation of 0.2 x.u. at 1.5U A, as compared to 2 x .u . a t 5>.U0 £ and lU x.u. at 13.3 w h ile a t 3>0 2 wavelength separation is 200 x.u. Moreover the L series spectra, which are at longer wavelengths than the K spectra, should have narrower inner levels, as indicated in section II Bl.

The short wavelengths, up to about 5> X, have been extensively 13 17 22 studied previously * at high resolution, and the same is true of the spectral region above $0 R 18 * 19, 20^ ,^e present work was undertaken to study with high resolution those spectral features in the region from $ to 20 £. (References to previous work in this region are given in the following text.) 19

I I I . APPARATUS

A. Spectrometer

1° Peslgn requirements. The experimental investigations to be described were carried out on a new, high-vacuura, two-crystal x-ray 27 spectrometer recently completed at the Ohio State University.

This instrument was designed to be used in the wavelength region from five to twenty angstrom units.

Although a higher energy resolution can be had in this spectral range, certain problems which are of less consequence at the short wavelengths become very important. Air absorbs so strongly that for a 100 centimeter path length at 9*9 angstroms the x-ray beam is attenuated by a factor of e~^^ in atmospheric air. The answer to

this particular .problem is to evacuate the spectrometer to a

pressure of fifty microns or less.

The x-ray tube, however, is operated at a vacuum of about

10~*^ mm. Hg. Unless the entire spectrometer is evacuated to this

same pressure, a window must be placed over the x-ray tube to

separate its vacuum from that of the spectrometer. This window must

be thin enough to pass a reasonable percentage of the x-ray beam,

but must be vacuum tight. It is rather difficult to meet both of

these requirements at the longer wavelengths; and in view of the

fact that the window problem arises again with respect to the

detector, the spectrometer was designed so as to dispense with

2?Shaw, C. H., Spielberg, N. and Soules, J., Report No. £3 on C o n tra ct N6 onr-22521 NR 017 606, Columbus: The Ohio State University Research Foundation, May, 1951 20 windows entirely by pumping the entire instrument down to the x-ray tube vacuum*

Requirements for the x-ray source, the detector, and crystals are discussed in sections III B, C, and D respectively.

2. The spectrometer shell. Figure 9 shows the spectrometer exterior and associated vacuum plumbing. The spectrometer shell consists of a hot-rolled steel base plate (figure 10) upon w hich rests a steel bell, which may be raised and lowered by a chain h o i s t .

The base plate, which rests on a welded steel tripod, carries the crystal axes. The center of the base plate bows up 1/6U inch

When the spectrometer is evacuated, but this is compensated by proper alignment of the crystal axes. There are holes in the plate for connection to the vacuum system, for mounting entrance plates for electrical connections and for an external control for the i second crystal axis. The last two are shown in figure 12. Figure

13 is a scale drawing of the base plate.

The b e l l (fig u r e s 11 and llj.) i s made from sea m less s t e e l tu bin g to which a steel top plate and a steel ring are welded* The ring is provided with two gasket grooves with provision for pumping out in between in case of leaks. Actually only one gasket, of l/h in ch molded neoprene with lapped ends, uncemented, has been used, without

any difficulty. Holes are provided in the top of the bell for mount­

ing a liquid air trap, an ionization gauge, and auxiliary apparatus.

The x-ray tube is bolted over the hole in the side of the bell. 21

F igu re 9 . Spectrometer exterior and associated vacuum plum bing. The x -ra y tube is on the left.

F igu re 1 0 . Spectrometer base plate, showing m u ltip lie r housing, crystal axes and microme­ t e r arm. 22

Figure 11. Interior of bell showing liquid air trap and x-ray entrance port.

Figure X2. Micrometer and lever arm for controlling position of first crystal through sylphon seal in base plate. The preamplifier for the photomultiplier is also shown. 23

SwrAce 7e»jj Dew \w trn Fwsd\$y / i ^ppstai

—!

L-i.J

'-D/ffvs/m P vmp :^s

jj- Dmu t I j Ditp J4l -/onc-a ‘X 4 dhp \ 3 Huts Eomir Spagid OHIO STATE UNIVERSITY Smnofvrtu Basc Pun

Dats : 6 -1 1 -4 8

Ha t \ 1020 CP. S rm

.060

Figure 13 2b

x — inninnnii

Surma Finish ' v

17 Dmu » ji D t"-A't3K-g \

Flu Crack * 4- DttK; i H°itt Cqiuiur I BtTMi/t Puns \mr*Wtu>4/n>PtAM

Figure lij 25

Y/ithout the gasket, the bell and base plate bearing surfaces match to within *001 inch. Both have been cadmium plated to make for easier cleaning and to prevent rust.

The pumping system consists of a National Research Corporation diffusion pump, type 10U, six-inch O ctoil, 12^0 CFM at one micron and blank-off at 0,001 micron, backed by a Kinney CVD 556 mechanical pump of l5«2 CFM displacem ent. Forevacuum may be read on a thermo­ couple gauge and a McLeod gauge. The high vacuum inside the spec­ trometer is measured with an ionization gauge. The diffusion pump is run at about one-fourth rated power and has a cold baffle immediately above the umbrellas. Just above this latter baffle is a large liquid air trap, to the bottom of which is soldered another baffle, A short six-inch diameter tube leads from the pump and trap to the spectrometer base plate. Another liquid air trap is provided inside the spectrometer, Just opposite the x-ray tube port

(see figure 11), This elaborate pumping and trapping arrangement is used to minimize back-streaming of diffusion pump o il into the spectrometer and thence to the x-ray tube, where the presence of organic vapors is most undesirable, as w ill be brought out in the description of the x-ray tube.

Gasket seals for a ll auxiliary apparatus are made with Linear

0-rings, Blanking plates may be put over all holes in the spec­

trometer to facilitate leak-hunting.

An ultimate vacuum of 2 or 3 x 10“? j_s obtained with both liquid air traps filled , while the best vacuum with the x—ray

tube in operation is 10- 6 mm, Hg, 26

3. The crystal axes. The crystal axes were machined from

stainless steel. The first axis is mounted at the center of the base plate and can be turned from outside the spectrometer by means of a lever arm and micrometer assembly as shown in figures 10 and

12. This is the only external control. The retaining plate, figure l£, is fastened to the bottom of the spindle bearing, figure 16, The micrometer arm, figure 17, is inserted in the access

hole, A, of figure l6 j and the spindle, figure 18, is passed through

the spindle bearing from above, through the clamp of the micrometer

arm, and bears on a stainless steel ball, which rests on the retain­

ing plate. Play in the bearings is ,0001 inch by measurement, and

corresp o n d s to a maximum t i l t o f th e s p in d le o f te n s e c o n d s. The

platform, figure 19, screws onto the spindle. The fulcrum arm,

f ig u r e 20, passes through the base plate by means of the sylphon

bellows arrangement, figure12 , and is actuated by the micrometer.

The dimensions are so chosen that advancing the micrometer ,001 mm,

rotates the first crystal one second of arc, .

The second axis is mounted eight inches from the first axis.

The spindle, figure 21, mounts in the main body, figure 22, resting

on a ball bearing and retaining plate, as for the first axis. A

set screw, not shown, which bears against the lower bearing, is

provided in the main body, to clamp the spindle. The detector arm

bearing, figure 23, fits over the main body and the detector is

attached on the flat provided. The platform is the same as in

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Figure 23. A 360 degree scale is laid off on the rims of the platforms and on the upper rim of the detector arm bearing, and verniers are used to measure angles to 0 . 1 degree on the platform s.

No grease or lubricant is used in the entire arrangement, and there are no rotating vacuum seals.

A schematic of the crystal holders, which mount on top of the platforms, is shown in figure 2U. Three screws are used to align the crystal surface, and three spring-loaded plungers hold the crystal in place*

hm_ Alignment procedure. The spectrometer is aligned in accordance with the outline below.

a. Zero level. Starrett level with scale divisions — .0005"

per foot = .OOOU radians = 9 seconds. Doubled error

less than one scale division.

b. Level spectrometer base plate by means of adjusting

screws on tripod.

c. Level first axis. Shims underneath base of axis so that

doubled error less than one scale division. The first

axis platform is accurately perpendicular (within 9”)

to the spindle *

d. Level second axis, tilted inward toward first axis

enough to compensate for bowing of base plate under

vacuum* The second axis platform is far enough out

of perpendicularity with spindle to prevent reading

level as spindle rotates. Can level within two or 37

Figure 2lw three scale divisions in direction perpendicular to

line joining the two axes. Tilting along line joining

axes is best done optically (see f*.).

Mount crystal holders and in stall Michelson inter­

ferometer flats. Set these on the axis of rotation,

using the adjusting screws and viewing from above

with microscope; and make surfaces parallel with

rotation axis with aid of telescope and Gauss eyepiece.

Optical leveling and compensation of second axis.

Estimate axis tilts 3' as result of 1/61+ inch deflec­

tion of base plate under vacuum. Using level as

monitor to prevent tilt along direction perpen­

dicular to line of centers of axes, shim approximately

enough to tilt second axis. Turning Michelson plates

parallel to each other, then can see two sets of re­

flected cross hairs with telescope and Gauss eyepiece*

Place a glass plate over x-ray port on bell, set bell

in place on base plate so that can still get reflected

beam of light to and from telescope. Pump out spec­

trometer with forepump, and observe relative motion

of reflected cross hairs. If the second axis is pro­

perly shimmed, the reflected cross hairs w ill move

into coincidence with each other. If not, further

adjustment of second axis shims is necessary. The

axes can be made parallel within ten seconds of arc in the plane containing them and their line of centers. g. Line of centers of axes and "zero" position of x-ray tube.

(l) set .0015 inch slits on axes of rotation in crystal

mounts and render parallel to rotation axis by use of

cross hairs. (2) Set .0015 inch slit over Cu target

Machlett x-ray tube and find zero position for x-rays on

circumference by passing x-ray beam through s lit system

and into Geiger counter. (3) Insert two more .0015 inch

slits between axes and position these to pass the zero

position x-rays through all four slits. h. Measure 2© for Cu K cs^on spectrometer circumference from

"zero" position. Set Cu target x-ray tube in position,

replace slit on first axis by a crystal. Turn first

axis until Cu K-**' radiation is reflected, i. Replace second axis slit by the second crystal and turn

to (1,-1) position for Cu Do not move first axis.

Note and record readings of divided circles and verniers.

These Cu K-*' angles are primary reference angles, k. Check by turning second axis to calculated (1,-tl) position

and record Cu K o S spectrum burning first axis. Note

that extremely narrow slits jnay distort spectrum line

o b ta in e d .

1. A s lit over the Geiger tube can be used to determine

position of detector on peak of (1,-1) curve with

narrow slits. Uo

m* Check positioning of fulcrum arm between micrometer and

first axis lever arm, by using traveling microscope to

measure motion of lever as micrometer is advanced.

B. X-ray tube

1. Design requirements. For high dispersion non-photographic spectroscopy at long wavelengths the x-ray tube must give high intensity radiation, at a constant level for long periods of time, from an uncontaminated target. Contamination, of course, is very serious for any fine structure measurements, since these depend quite often upon the state of chemical combination of the target m a t e r ia l.

Generally speaking, it is not desirable to use too high an accelerating voltage on the x-ray tube, since this would excite higher orders of radiation, so that it becomes necessary to go to high currents to get the desired intensities.

2. The tube. A typical tube^’^ used in this work is shown in figures 25 and 26. The electron gun (at the left) is mounted several inches away from the target to reduce the deposition of cathode decomposition products on the target. An axial magnetic field (center) is used to focus the electron beam on the target

(right). Both electron gun and target are watercooled. They are carried on ground joints which are sealed with Apiezon W wax to the glass envelope. The tube itself is waxed to a brass plate which

^®Shaw, C. H. and Soules, Jack A., Physical Review,83, 233 A (1 9 5 1 ) ia

y / j p m w u x * n

OHIO STATE U M E fiS M Y-Ray Tube Assembly P roject No, 14; Dujy.No'l

D a U : J - e - f l

Figure 25. U2

Figure 26. X-ray tube. From left to right: electron gun assembly, focusing coil and target. U3 bolts onto the side of the spectrometer* The focusing coil is gimbal mounted on the brass plate and it may thus be turned through a small angular range* The long glass tube shown in figure 26 is a liquid air trap, which has since been eliminated. Vacuum is achieved through the spectrometer vacuum system. The overall length of the tube is about 15> inches• In figure 3 can be seen a discarded earlier 27 model tube which carried its own pumping system.

Figures 27 and 28 show the electron gun assembly, the latter with the gun proper removed from the iron holder• The Heil gun has been described in detail elsewhere.^*It consists of an indirectly heated large, hem i-elliptical, oxide coated cathode mounted axially with a specially shaped nozzle plate* The heater draws about 1.33 amperes at 19 volts. The gun operates in the space charge lim ited condition so that the current is determined by

the cathode to nozzle voltage according to the 3/2 power law.

Geometry of the gun is shown in figure 29* There are three major parts of the gun: (1) the cathode, (2) the cold cathode, at cathode

potential, and used for purposes of electrostatic field geometry

and (3) the nozzle plate, insulated by a mica sheet from the cold

cathode. The nozzle plate is made of iron, as is the gun-holder,

to reduce the penetration into the gun by the focusing coil magne­

tic field. These parts may be seen in figure 28: the cathode, which looks like a section of stovepipe, rests on a light-colored

2^Heil, 0. and Ebers, J. J., Proceedings of the Institute of Radio Engineers, 38> 6 h $ (195>0) Figure 27. Electron gun assembly.

Figure 28. Gun proper removed from iron holder j A ^ r / A»e>o ^ /wo A»e>o (£> /*$& 0 .^ 2 /« /.3 : /.o mxcs 2~-rre?S*&s /?ar-f3 A' /«ier«a«r ^3o * * « r / a c * vS ,-f £ < » ) % « < /# ^//»7 /o/7^ //7 C •*» < s * / *» « *» / * s < C•*» ^ o f ^PV//y?so/rf

Figure 2?. U6 disk, the cold cathode, which in turn rests on the larger, darker disk, the nozzle plate.

A fine copper gauze, not shown, rolled into a cylinder and fastened to the edge of the nozzle plate, extends almost to the target and serves to better define the electric fields in the tube.

Without this screen, the glass envelope picks up surface charges which seriously disturb the electron beam.

The copper target assembly is clearly shown in figure 2£. The entire assembly was hydrogen fired to remove any organic matter which might have worked into the surface. This apparently is a very necessary precaution. Prior to firing some difficulty with target staining was encountered despite a ll other precautions*

To put the x—ray tube into operation a rather definite procedure must be followed.

F irst a cover, made of molybdenum and with an O.j? mil tantalum liner, is slipped over the end of the target. The purpose of the cover is two-fold: (1) to protect the target from decomposition products from the cathode and from carbon deposits accumulated during the preliminary outgassing of the tube; and (2) to serve as a means of outgassing the target. The second purpose is accomplished by heating the cover to a bright red color by electron bombardment from the cathode, and thus by radiation and conduction heating the

end of the target* During this process no cooling water is circu­ lated in the target, although a special water coil, not shown in

the figures, keeps the ground joint cool enough that the wax joint h i does not soften, A small piece of iron is wired to -the cover, so that when the outgassing process is completed, the cover can be lifted off with a magnet and deposited out of the way of the electron beam and the x-rays.

The spectrometer is pumped out with the forepump to about ten microns pressure, liquid air is poured into the diffusion pump trap, and the diffusion pump is turned on. When a vacuum of 5 x 10“^ mm.

Hg. or better is obtained, liquid air is poured into the trap mounted on the bell, and very shortly, when the pressure is

1 x 10 ^ mm. Hg., or better, the activation of the x—ray cathode can be begun. It is necessary to follow the above procedure in evacuating the spectrometer in order to reduce as much as possible the amount of diffusion pump vapor in the spectrometer and the x—ray tube. An excessive amount of o il poisons the x-ray cathode and also deposits on the target where it is turned into undesirable carbon by the electron beam bombardment.

To activate the cathode, the target lead is removed and the target connected to the cathode. This serves to prevent target bombardment during activation. The heater voltage is raised in small steps at one minute intervals to 35 volts, where it remains for two minutes before being reduced to the operating potential,

19 volts. The cathode is now activated and may be tested for emission by applying nozzle potential. When the pressure returns to less than 5 x 10 ^ mm. Hg., nozzle voltage is gradually increased to draw more and more current from the cathode, always keeping the 1*8 pressure under 5 x 10“^ mm. Hg. As current is drawn and as pressure improves, the cathode "cures*1 and the emission increases. With a new cathode a current of 1*0 milliamperes at £00 volts should be o b t a in e d .

When the activation procedure is completed, the target is dis­ connected from the cathode and connected to the high voltage. The outgassing of the target is then carried out as described above.

It is important during operation of the tube that good vacuum be maintained, always better than $ x 10""^ mm. Hg. Table I shows the results of two tests on the tube.

T a b le I

Topical Operation Data for X-Ray Tube

T e s t A T e s t B

P r e ss u r e 1.0 x 10~6 mm. Hg. £ . 0 x 1 0 “ ^ mm. Hg. Cathode emission 1 3 0 ma. 200 ma. Nozzle voltage 1 1 0 0 v . 1^ 00 v . Nozzle current 26 m a. 1*2 ma. Target voltage I* 6 0 0 v . 2800 v . Target current 100 m a. 11*0 ma.

The tube has not been pushed to the current capacity of the electron gun because of vacuum conditions* There is considerable electron bombardment of glass and other surfaces, and a long out-

gassing procedure is required, at least with the present pumping

arrangement, before very high currents can be drawn*

3* The power supply* The three electrode x-ray tube lends

itself very readily to the use of electronically regulated power supplies. Block diagrams of the arrangement used are shown in 27 30 figures 30 and 31. 5 Both cathode and target supplies are voltage regulated, the cathode supply monitoring the target current while the target supply monitors the cathode to target potential; thus any changes in cathode to nozzle voltage in the course of current regulation are compensated by adjustments of the nozzle to target voltage, so that the overall accelerating voltage remains

c o n s t a n t •

With this arrangement it is possible to stabilize the electron beam in the target against fluctuations in the operating condition of the x-ray tube and against fluctuations in the power mains to

the laboratory.

The supplies w ill deliver up to $00 ma. and up to 10 kilovolts,

the maximum power being lim ited by the plate dissipation of the

voltage regulator tubes, which must not exceed 1000 watts. Measure­

ments show that at 10 kilovolts a 1C$ power supply change causes

only a 0.1$ target voltage change; while the load regulation is

•02$ for target voltage. It should be noted that the voltage regu­

lator is of the series degenerative type, while the current regula­

tor is of the shunt degenerative type.

The shunt type regulator is used in the cathode supply because

either there would be too large a voltage drop across a series tube,

^Slusher, William Earl, master's thesis, Electronic Voltage and Current Stabilizer for High Voltage Supplies, Columbusl The Ohio State University, 1950 O v -r\ X-/?<+ y X-/?<+ 7~troe la st's: M at!: R ate: ; OHIO STATE UNIVERSITY STATE OHIO Project No. ; Dwg. No. Scale: ; No. Req^ k 7 >^

Figure 30. 51

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Figure 31. 52 leading to an excessively complicated compensating arrangement or the tube would have to operate with a positive control grid.

A noteworthy feature of both supplies is the use of inductive coupling to the regulator tube,^ which sim plifies voltage insulation problems. The error signal drives a radio frequency oscillator which by means of a simple r . f . transformer and a rectifier-filter circuit applies the correcting voltage to the regulator tube grid, which is at high potential.

Safety circuits are included which shut off the high voltage in case of water, vacuum or power failure. These can also be used to turn off the diffusion pump and the detecting instruments.

U* Evaluation of x-ray tube and auxiliary equipment. The anticipated performance of the x-ray source has yet to be attained.

It has not been possible to achieve the large currents desired in the x-ray tube because an excessive amount of gas is evolved, pre- sumably due to bombardment of the walls of the x—ray tube and/or the gun parts. The nozzle current is excessive, due either to penetration of the gun by the focusing coil magnetic field, despite the iron shielding, or to misalignment of the gun parts.

On the other hand, one of the most serious problems in soft x-ray spectroscopy, target contamination, has apparently been over­ come. The size and location of the target spot is rather easily

controlled.

3-^Pepinsky, R. and Jarmotz, P., Review of Scientific Instruments, 19, 2h7 (19U 8) 53

The voltage regulator works very w ell, although the current regulator does not and has therefore not been used. One of the difficulties with the current regulator is that as presently arranged it regulates not only the electron current to the target, but also the current from target to ground through the water cooling system.

As a result the operating characteristics of the regulator tube are shifted unfavorably. In addition, there is an interaction between the x-ray tube and the photomultiplier detection system whenever the current regulator attempts to lock into control. The cause of this interaction has not been found.

It should also be noted that the current regulator does not monitor the current to the focal spot, but rather the total target c u r r e n t .

C. Detector

1. Requirements. An x-ray detector must obviously be sensitive to the desired radiation. It must be stable; it should be as free as possible from spurious effects. It should, if possible, not have an entrance window, which would absorb a large part of the incident radiation. If it has no entrance window, then it should be sensi­

tive only to the desired radiation; in the present case, it should be insensitive to visible light, ultraviolet radiation, electrons,

and ions. The detector should be linear over a wide range of

intensities and relatively free of fatiguing effects. It must be

convenient and easy to use.

Ionization type detectors, such as the Geiger counter, present a serious window problem. The window must be thin yet capable of supporting the chamber pressure when the spectrometer is evacuated and atmospheric pressure when the spectrometer is open. The use of a simultaneous pumping arrangement leads to complications. Photo­ graphic methods are not usable with two-crystal spectrometers, and

crystal counters are not yet sufficiently developed to be practi­ cable. Scintillation counting is difficult because of the low

energy of the x-rays being studied. Ordinary commercially available

photomultipliers have far too thick a window for direct detection of

soft x-rays, and are extremely sensitive to visible light.

2. The Allen type m ultiplier. J. S. Allen has designed and

built a 13-stage electrostatic m ultiplier tube, using dynodes made 32 from a beryllium-copper alloy. Although used originally for

electron counting, it has also been used and tested as an ion counter,

for ultraviolet radiation and for extremely soft x-rays of wave­

length greater than 50 angstroms and for hard x-rays up to three

a n g s t r o m s No previous tests have been reported in the region

from 3 to $0 angstroms.

A number of m ultipliers have been built according to Allen's

specifications. Figure 32 shows a photograph of one while figure 33

shows the electrode arrangement. Before assembly the electrodes

^A llen, J* S., Review of Scientific Instruments, 18, 739 (19h7) ^ M o o r i s h , fj., Williams, G. W., and Darby, E. K., Review of Scientific Instruments, 21, 88U (19!?0) ^Piore, E. R., Kingston, R. H., Gyorgy, E. M., and Harvey, G. G., Review of Scientific Instruments, 22, $ b 3 (19!?1) -^Eisenstein, A., and Gingrich, N. S., Review of Scientific Instruments, 12, 582 (19U1) Figure 32. Allen multiplier. Scale in centimeters. 5 6

Figure 3 3 . e l e c t r o d e arrangement /V ALLBA/ MULT/PUZR ■were cleaned with pumice and water, followed by rinsing in distilled / water and absolute alcohol.

It is necessary that the multiplier be activated by heating in vacuum, between 10"*^ and 10“^ mm. Hg. pressure, for about 10 or 20 minutes with the electrodes at a dull red color. Allen reports that an unactivated beryllium-copper surface has a maximum multiplication of about 1.9, while an activated surface has a maximum multiplication * * v 32 of 3o* Upon exposure to air the surfaces lose their activation slowly, the overall multiplication falling to half after about six hours exposure. The nature of the activation process is not very well understood. The m ultiplier can be reactivated whenever necessary. The activation apparatus used is shown schematically in figure 3iu The D istillation Products GF-25W pump has an approximate speed of 25 liters per second. It can be seen that with the present arrangement the pumping speed is very greatly reduced. It has been found necessary to bake the m ultiplier for some time at low tempera­ ture, using a resistance furnace, in order to outgas the lavite supports. Power for the induction furnace is supplied by an Ajax-

Northrup spark gap converter. Usually, the multiplier is exposed to air for some thirty minutes when it is transferred from the activation apparatus to the spectrometer* Another th irty minutes exposure occurs whenever the spectrometer is opened up to change crystal se ttin g s. Because of the extreme sensitivity of the multiplier to ultra­ violet radiation from the target, which is specularly reflected from the crystals and from m etallic surfaces, i t was found necessary Gfass phfe- w t j U A p t e r o n W m *

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A c t i M t ' ° m A p p a r a t u s 5 9 to place a window over the entrance slit to the multiplier. The only requirement upon the window is th at i t be lig h t tig h t; a short open- ended length of copper tubing soldered to the bottom of the multi­ plier housing insures that the multiplier is under the same vacuum conditions as the spectrometer itself.

3» Auxiliary equipment. The m ultiplier operates at 375 or more volts per stage; therefore a power supply capable of delivering five kilovolts or more, at fairly small currents, is needed. Originally a DuMont type 308-A radio frequency supply, modified to give negative output and fitted with a two section R—C filter, was used. Thus the first electrode was at high negative potential and the collector

near ground. Considerable difficulty was experienced with drifting

output voltage. The r-f supply was put aside in favor of a conven­

t i o n a l 60-cycle negative output circuit. Subsequently it was found that at these voltages a considerable amount of corona’ and surface leakage occurred; and this, although attenuated by the voltage divider at the multiplier, was picked up by the amplification system and resulted in a number of slow irregular pulses which were larger than the actual multiplier counts. These originated in the power supply, in the connecting circuit to the spectrometer and in the Kovar-glass terminal used

to carry high voltage into the spectrometer. The latter was particu­ larly troublesome and was finally replaced by a piece of plate glass with a metal stud through the center, appropriately sealed by O-ring gaskets. The stud at high voltage is at least one inch away from other low voltage surfaces. 60 The corona problem was finally lessened greatly by discarding the negative output supply and returning to the DuMont supply, which had been reconverted to positive output and to which a regulating circuit had been added. A further filter consisting of a 1.8 megohm r e siste r , an r - f choke and a transm itting mica capacitor was inserted between the power supply output and the spectrometer entrance plate. A schematic diagram of the power supply arrangement and the electrical connections to the multiplier is shown in figure 35*

The pulses from the collector grid of the multiplier, which is at high positive potential, pass through a high voltage ceramic condenser, down a shielded, glass bead insulated lead to a shielded

Kovar terminal in the entrance plate. This is connected by a fle x ib le lead to a male connector, to which is attached an Atomic

Instrument Co. model 205>-B preamplifier. The input circuit of the preamplifier was changed to that indicated in figure 3£. The out­ put of the preamplifier is connected to an Atomic Instrument Co. model 20U-B linear am plifier. As used in most of th is work, the overall gain of the preamplifier and linear amplifier combination is 200,000 with a rise time of 0.8 microseconds and a decay time of U.O microseconds for step-function pulses. The pulses are counted on an Atomic Instrument Co. M ultiscaler, model 106, which can be set to count for definite time intervals or for a definite number of counts.

lu Operating data. Initial tests on the multiplier indicated it could detect radiation at 1.5>U angstroms. A copper target Machlett tube was attached to the side of the bell, calcite crystals 61 i

SO/u/uf M o d e le d 6 5 0 0 V. Ci»flcj*hK Art'oniic PWotMp /*«*>/ 2or-&

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TtPi t B p Pt-BCTR/CAL COA/A/pFTtO/VS 62 installed on the axes and the Cu K<^ (1,-1) rocking curve was obtained. The numerical data are of no value because they were

taken at a time when many of the problems associated with the use of the m ultiplier were not solved.

Subsequently an attempt was made to detect copper L radiation using a sheet of mica cemented to a glass plate. Unfortunately

enough ultraviolet radiation from the target was specularly reflected

into the m ultiplier to completely overwhelm any counts due to the x-rays. There was no sensitivity of the multiplier to the visible

light from a flashlight.

The only way to eliminate this ultraviolet radiation is to put

into the radiated beam a window which w ill be opaque to ultraviolet, yet transparent to x-rays of the wavelength under study. The

Machlett tube used for the Cu K

in. For the longer wavelengths a window is placed over the detector

entrance slit, as mentioned in section 2 above.

At hO angstroms, Molybdenum radiation, a one mil beryl­

lium window-^ which gives 76% transmission at that wavelength was

used. With U.8 kilovolts and 20 ma. on the x-ray tube, h7U8 counts

per minute were recorded on the peak of the (1,-1) rocking curve

with beryl crystals. The actual voltage applied to the m ultiplier

was U.6 kilovolts, and the amplifier and scaling system were

arranged so that all pulses greater than 0.1 m illivolts at the pre­

am plifier input were counted.

3&Kindly supplied by Professor L. G. Parratt of Cornell U n iv e r s it y 63

As viewed with the oscilloscope the pulses were as sharp as the amplifier characteristics allowed. Even when the am plifier input was switched to the 0.2 microsecond rise time (the fastest setting available), the leading edges of the pulses were as sharp as the amplifier allowed. This made it possible to distinguish between the pulses from the m ultiplier and those spurious pulses due to surface leakage and corona. The latter as seen on the oscilloscope had a much longer rise time, the fastest ones (which were rare) being as much as two or three microseconds.

Figure 36 shows a plot of the counting rate as a function of. m ultiplier voltage for input pulses greater than 0.1 m illivolt.

Higher voltages were not used because the background, presumably due to greater corona and/or leakage currents increased too rapidly.

The counting rate at the highest voltage may be too low because of statistical losses in the scaler.

Figure 37 displays discriminator bias curves at varying x-ray intensities with 6.0 kilovolts on the m ultiplier.

These data were taken with only the second crystal in place.

They do not constitute a test of linearity with varying intensity because it was impossible to measure the actual current to the focal spot alone of the x-ray target or to be sure it remained constant as the voltage changed. However an indication of linearity may be had from the fact that the (1,-1) rocking curves (which were obtained by counting a ll pulses greater than 0.1 m illivolt) maintained their shapes pretty w ell for varying intensities of 6k

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to *-Zr o,Sd t~{fecfiv& hio$ at" preom ph -fter- /n p u t F ig u r e 3 7 . 66 radiation (see section III D U below)*

It was also not possible to check linearity over wavelength intervals using the continuous spectrum because this would have required a one crystal type arrangement with the detector rotating around^ the crystal* Such an arrangement is not available on the present spectrometer.

At 13*3 angstroms, copper Radiation, a double thickness of 36 0.027 mil aluminum fo ilJ was used for the counter window. This arrangement gives 61$ transmission of the incident radiation. With

3.0 kilovolts and 10 ma. beam current in the x-ray tube, 6522 counts per minute were obtained on the peak of the (1,-1) rocking curve when 5 »3 kilovolts were applied to the m ultiplier and all pulses greater than 0.1 m illivolt were registered.

Figure 38 shows the discriminator bias curves at varying intensities for 13 angstroms. These data were taken for three conditions, namely, near the peak of the (l,**l) rocking curve, completely off the rocking curve, and with the x-rays and multi­ plier power supply turned off* Again the linearity must be inferred from the shapes of the (1,-1) rocking curves.

It is interesting to attempt comparison of the counting rates at the peak of the (1,-1) rocking curves for the two wavelengths,

and 13.3 angstroms.

Adjusting the counting rates for the different m ultiplier voltages (using figure 36), the x-ray tube currents, the percent reflection (see Table II in section III D U below) of the two beryl crystals in series, and the transmission of the windows, the INTEGRAL BtAS CURVES A - /S. 3 A S. 3 kV on t/fu/f ip/ter-

/ OoO

On peak *£■ / t o e * ■ F a r aFf- ///w - x - r a y s o £ f - X-rays f muitip/ier V o/-htae> o~f~P~

to o.x$ o.Sb 0 .7 F . /.oo mi/Ivofte E f-fecttve b / a $ a+ preamp. input F ig u r e 3 8 . V' 68 m ultiplier is an order of magnitude more sensitive at 13.3 angstroms when compared with angstroms. It is rather difficult to decide how to adjust for the differing excitation potentials of the two lines in question, although it should he noted the excitation poten­ tials were exceeded by the same amount for both lin es.

Actually, it is generally assumed that the radiation is more intense from the heavier elements than the lighter ones; if such be the case here, then the m ultiplier is even more sensitive relatively at 13.3 angstroms than is indicated.

The m ultiplier apparently loses some few percent of its sensi­ tivity each time it is exposed to air during the course of operation of the spectrometer. An indication of the durability of the multi­ plier may be had from the following:

A freshly activated m ultiplier was installed about b5 m in u te s after removal from the activation apparatus. Because of a vacuum leak, it was opened to air three or four times for periods ranging from ^ to 20 minutes. It was finally pumped down to forevacuum

pressure and so maintained for two days while the leak in the x-ray

tube was being found and repaired. It was opened to air again for reinstallation of the x-ray tube and then pumped down to operating

pressure. At the end of two weeks, during which period it was

exposed to air five times for half-hour intervals, its sensitivity was 60$ of what it had been when first tested. The m ultiplier was

used four more days, during which it suffered four more half-hour

air exposures and one period of three hours at forevaquum* 6 9

£* Evaluation of m ultiplier. The experience just cited indi­ cates that the durability of the m ultiplier, despite repeated air exposures, is much greater than had been expected* It also seems possible to preserve the m ultiplier simply by keeping it under fore­ vacuum pressure.

On the other hand, at least as presently used, elaborate pre­ cautions are necessary to sxtppress spurious counts due to leakage and corona currents in the power supply* Moreover, rather high gain wide band am plifiers must be used. The spurious counts are particularly troublesome here because of the small size of the pulses recorded.

From the 13*3 angstrom data, over half the pulses recorded were less than 0.2£ m illivolt high at the preamplifier input* This is to be compared with an average pulse height of 0.1 volts reported 3 2 by Allen for electrons and something like one or two m illivolts

estimated from the work of Moorish, W illiams and Darby at 25>00 33 angstroms.-'-'' When detecting electrons, even the first electrode of

the tube serves as a m ultiplication stagej however for photons, the

first electrode serves only to convert the photon into one electron.

It is also true that photoelectrons ejected with considerable energy

have a much lower m ultiplication factor when striking a secondary

emission surface; but it would seem that if such were the case the

pulse heights would increase as the wavelength of the incident

radiation approached the copper L absorption edge.

There is also the possibility that in the case at hand the 70 fifteen inch lead between the m ultiplier output terminal and the pre­ amplifier input caused considerable attenuation of the signal.

The effect of the small pulse size is to increase the serious­ ness of the spurious count problem already mentioned. If the pulses were considerably larger, it would be possible to discriminate against these spurious counts.

One way of solving the problem might be to add two more multi­ plication stages to the m ultiplier, which should give at least an order of magnitude increase to the pulse heights. There would have

to be some assurance, however, that the higher power supply voltage

thus required would not cause more trouble. Should such a step be

successful, it would probably also have the effect of increasing

the counting rate at the present discrimination level, as many pulses too small to be counted would then be registered.

Another possible means of increasing the counting rate might be the use of a heavy metal, such as platinum, as photoelectrode.

The photoelectric processes would then take place much closer to

the surface because of the greater absorption coefficient, and the

photoelectrons would have a better probability of escaping.

D. The crystals

1* Requirements. There are a number of desirable qualities

required of crystals to be used in x-ray spectrometry. They must t be stable and must have a long enough grating space for the spectral

region of Interest. They must be as nearly perfect as possible—

a perfect crystal is one which gives the line shape demanded by 71 theory, This usually requires that there be no faults in the crystal which would disturb the parallelism of the successive reflecting planes. In two-crystal work the reflecting planes should bear a constant planar relationship (preferably, but not necessarily, parallel) to the crystal surface, so that the pair of crystal reflecting planes may be aligned properly and conveniently with each other. They should be large enough and uniform enough over their dimension to allow the x-ray beam to nwalku over the crystal sur­ face without too much variation in the percent of reflected radia­ tion, else thi§ variation w ill introduce spurious observational data. The percent reflection should be high enough to pass as much of the desired radiation as is needed,

2, Possible crystals. The need for a long grating space rules out crystals such as calcite and quartz which have been found satis­ factory at short wavelengths. The stability requirement rules out gypsum because it gives off its water of crystallization and

deteriorates before a high operating vacuum can be obtained in a 37 windowless spectrometer. An unsuccessful attempt was made to

obtain a (1,-1) rocking curve for Cu Kc*, 1,5U angstroms, from mica

sheets cemented to glass plates* A number of unsuccessful attempts

have been made by Stephenson and Martin-^ to obtain rocking curves

from mica in various forms. Failure is attributed to micro-

irregularities in the crystal surface which prevent parallelism

^Stephenson, S. T, and Martin, D, L., Review of Scientific Instruments, 21, 1023 (1950) 72 of the two sets of crystal planes over any but the smallest areas.

There has been little , if any, study of the suitability of organic crystals for two crystal work. Certain techniques are avail­ able for their preparation^a but further investigation of their spectrometric qualities is needed.

Beryl, Be^Alg^iO^)^ which has been used previously with fair r e s u l t s ,38 selected for these studies. The (1010) planes were determined by Stenstrom to have a grating space d = 8.06 As w ill be discussed below, it seems that this figure is incorrect.

3. Preparation of beryl crystals. A large beryl crystal about two inches long and 1 l/U inches in diameter was sawed into 1/h" thick slabs parallel to the (1010) planes (figure 39) on a diamond saw. The slabs were ground and polished and mounted in the crystal holders, figure 2U, which had been previously adjusted with optical flats to insure that the crystal face was parallel with and on the axis rotation of the spindle. When the (1,-1) rocking curve for

Cu radiation (1.5U X) was recorded, it seemed that the full width at half maximum was greater than 75" and was not improved by etching in HP. Adjusting the positioning screws of figure2k to increase the recorded intensity on the peak of the rocking curve, which is a

37aMuller, A., Transactions of the Chemical Society, 123, 20li3 (1923) Shearer, G., Transactions of the Chemical Society, 123, 3152 (1923) Shearer, G. and Muller, A., Transactions of the Chemical Society, 123, 3156 (1923) T rillat, M., Annales de Physique, 6, 5 (1926) 38jyfunier, J. H., Bearden, J. A., and Shaw, C. H., Physical Review, £8, 537 (19U0) 39stenstrom, W., Annalen der Fhysik, Uth Series, 57, 3U7 (1918) a ExBr^Kj / La f h r e F ig u r e 3 9 -

~G

/? e-f fe>cf'ton (zretonre^fry F ig u r e kO, 73 means of bringing the Bragg planes into parallelism , led to the con­ clusion that the reflecting planes and the sawed face made an angle of at least five degrees with each other. This result was checked by- using a good calcite crystal on the first axis and adjusting the tilt of the beryl on the second axis for maximum intensity.

Accordingly, because of the alignment procedure used, it was decided to determine accurately the location of the Bragg planes by means of x-rays and then grind the crystal face to parallelism with these planes.

It is a necessary condition for reflection that the normal, N, to the crystal planes, the incident beam of wavelength 7{ and th e reflected beam all lie in the same plane. If the crystal is rotated about N as an axis, the situation is not changed; and the reflected beam intensity w ill be independent of such angular rotation. If, however, the crystal is rotated about the axis 00’ (figure hO), w hich

is not parallel to N, then for monochromatic radiation there w ill be

only two positions of rotation about 00* for which the incident beam, A, and M w ill form the complement to the Bragg angle, 0, (see

f ig u r e Ho). (In the lim iting case where 00fN lies in the horizon­

tal plane when G is formed, there is only one position of rotation

about 001 to give Bragg reflection.) If now the crystal, and hence

N, is tilted with respect to 00’, then it is possible to bring the

positions of N for Bragg reflection into coincidence with 00'. As

this condition is approached, it w ill be observed that the two

rotational positions about 00' for Bragg reflection w ill broaden 7U into greater and greater angular ranges, until finally uniform reflec­ tion is obtained. It is now possible to grind the crystal face so that it w ill be perpendicular to 00' and thus parallel with the crystal planes.

The above procedure requires, of course, that 00’ make the com­ plement of the Bragg angle with the incident beam. In practice, one has to adjust 001 and the direction of A along with N. These adjust­ ments are most easily made using the two—crystal spectrometer, a conventional sealed x-ray tube, and a Geiger counter. The base plate of the spectrometer was taken as a reference plane, a good calcite was mounted on the first axis, and a copper target Machlett tube clamped onto the edge of the base plate. The beryl crystal was mounted on the fixture shown schematically in figure Ul. The steel shaft, A, takes the place of 00*, while the crystal was cemented to the adjustable brass plate, B. The crystal could then be tilted by means of the adjusting screws, C. The ball-pointed leveling screws,

D, were set in a plane perpendicular to A, by indicator, within

.0002 inch. Yfhen the alignment was done, the brass spindle, E, holding the axis was removed from the clamp, F, and set on a glass plate on the leveling screws, so that the crystal face could be ground off parallel to the atomic planes.

The microscope stand was set on the base plate in place of the second axis and adjusted so that 00’ made approximately the correct angle with the monochromatic beam from the calcite crystal. (Note

001 was made to be in a plane parallel to the base plate.) The 75

Figure Ul. /\hg*nih<£ ana ( 3 rr-tnc/t»nq F ** ^ &- ■for C rystals A, steel shaft; B, adjustable crystal mounting plate; C, adjusting screws; D, ball pointed leveling screws; E, brass spindle; F, clamp. 76 crystal was rotated about 00' and the two reflection positions noted.

The position of the calcite crystal was adjusted by means of the micrometer screw in such a manner that the angular separation of the reflection positions increased until they were 180° apart and in the vertical plane. It was not always possible to make this adjustment by rotation of the calcite alone; and in such a case it was necessary to shift 00' slightly to bring it into a better position, and then adjustment with the calcite continued.

When the two reflection positions were 180° apart, it was necessary to tilt the beryl normal in the vertical plane only. An optical fla t was mounted with "tacky wax" alongside the beryl, and a telescope and Gauss eyepiece set up to monitor the tiltin g process to make sure it was in the normal plane only. After each change of the crystal adjustment screws, the crystal was rotated about 00' to observe the increase in the angular range for reflection.

This procedure was followed for each beryl crystal until it was aligned within half a minute of arc vertically and horizontally.

The crystal faces were then ground, as indicated above, to bring them into parallelism with the reflecting planes. Several different grades of grinding compound were used, ranging down to finer than

3F. It was necessary to remove almost l/l6 inch from one end of each crystal. It is not known whether the original sawing was done that inaccurately or whether there is some significant difference between the reflecting planes and the natural face of the crystal.

After grinding and before removing the crystal from the alignment 77 fixture, it was again checked to be sure that it had not shifted or

tilted during the grinding process.

The ground crystals were then hand polished with a standard opticians compound on fe lt. A rotary lap was not used because there

seemed to be a tendency to polish and round the ends of the crystal

first, which yras most undesirable.

The beryl crystals were finally checked over their surfaces for

parallelism of the atomic planes by mounting them in the (2,-2)

position for Cu K

eter slide across the x-ray beam. A similar fixed slit was placed

over the x-ray tube. So long as the planes bore the same relation­

ship to the ground faces, the positions relative to each other of the

two crystals did not have to be changed to maintain the maximum

intensity of the (2,-2) rocking curve. It was occasionally necessary

to change the position of the x-ray tube and the Geiger counter to

maintain the intensity; but this is of no consequence since the

important factor in two-crystal spectrometry is the relative posi­

tions of the two crystals.

It was found that at one end of each crystal there was a

fault, corresponding to the location of a visible fault line, where

the reflecting planes were bent back by a slight angle from the

original position. After adjusting the first crystal position, the

two bent planes were then brought into parallelism with each other.

The faulty ends of the crystals were sawed off, so that the final

dimensions of the crystals were 2 l/8 x 1 1/8 inches and 2 x 1 inches. 78

The crystals were finally etched in a 10$ HF solution for 50

seconds each.

U. (1,-1) rocking curves and percent reflection. Table IX

displays values of the fu ll width at half maximum of the (1,-1)

rocking curves and of the percent reflection at various wavelengths,

the spectrometer having previously been aligned in accordance with

the procedure outlined in section III A I4 a b o v e .

T ab le I I

(1,-1) Widths and Percent Reflection

for Be (10T0) Planes

W avelen gth (1,-1) widths % (angstroms) crystal rotation x units v o l t s r e f l e c t i o n se c o n d s

0 .7 1 1.9 0 .1 9 U .6 514 1.5U 8.5 0.33 1.71 52 (l.£!i, polished, before etching) 13 0 .5 1 2.52 2 .2 8 1 1 .5 o.U 5 1.08 U6 5 •ItO h2 1 .3 •65 13 1 3 .3 1 230 lu 8 •3U 6

The percent reflection was measured by taking the ratio of the

intensity at the peak of the (1,-1) curve to that at the peak of the

line with one crystal removed. For wavelengths up to 2.28 angstroms,

the second crystal was removed and the detector swung around to

receive the radiation from the first crystal. For greater wavelengths,

with the spectrometer operating in vacuum, it was not possible to do

this because the detector would not clear the wall of the bell. In 1 9 these cases the first crystal was removed after the (1,-1) curve was taken and the x-ray tube (meaning the entire bell) rotated so that the beam would be incident on the second crystal at the Bragg angle.

Since the sensitivity of the photomultiplier detector used decreases somewhat with each exposure to air, the first crystal was inserted again and the (1,-1) peak intensity again determined and averaged with the first determination so that the ratio would not be made falsely high. The values found under vacuum are not as accurate as the other values, but it does not seem they can be in error more than ten or fifteen percent. All measurements except the one noted were taken after etching.

The data at jp.hO angstroms were taken at a target potential of

U.8 kilovolts, which excites second order radiation, but it is not believed this introduced an appreciable error because data at 6.8 kilovolts gave an average width of ill seconds. It was necessary to use this higher voltage to get sufficient intensity for the desired counting rate. At 13.31 angstroms the voltage used, 3.0 kilovolts, would excite second and third order radiation, but going to ii.8 kilovolts had no effect on the width, while going to 8 kilovolts raised the width to 2lj.O seconds. Figures U2, i*3, and UU are typical rocking curves.

A graph of (1,-1) widths in volts against wavelength is shown in f ig u r e U5 for the present beryl crystals and for sim ilarly cut quartz.^ ^he crosses represent data on beryl taken by Munier,

UOparratt, L. G., Review of Scientific Instruments, 6, 113 (193$) 80

CM -3- <1)

o 0o £

J3 E F Z Y L . (fo/o) f* L A tV E $ O r * )R o c k i n g C u f? j/E C u /-*=V/ S3. 3 / A 3 ,0 /O met x-m ys

X jL ± ... I .k a A*j. A * Jk //•4-6o m ftp. A fftrom ** Zap a- 5 ^ / ^ / / y

F ig u r e UU* Figure b$,

3 - ( ( ,- ! ) WiDTHS O P B F P / i L AND QUARTZ AT VARY//VG WAVElF/VGlHS 2 - o Present work (f*5Z) X M u rtr / 5ha*f 094o) /.S’ - A Ste-pAenson / Mhrfrn 0 ?S oY • Purrvft' //93s)

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a. 3 - a s . o.7 - 0.6 -

(/,-!)* * ' Width tn aA - Vo l-h QUARTZ (toa s e a l)0'3 ■

o, H ■ ■ ■ » ■ ■ » i «■ * » . ■ O z 4 6 8 to OL H WAVELENGrU '* AA/G^STROMS 8U Bearden and Shaw, and the triangles represent data taken from a plot of results given by Stephenson and Martin. ^ The percent reflection is plotted in figure h6, along with one value determined by Munier, Bearden and Shaw, again compared with quartz.

Further etching of the beryls to improve rocking curve widths has not been attempted for fear of ruining the present very valuable set of crystals. The decrease in percent reflection at long wave­ lengths is most unfortunate because this means that the two crystals together transmit less than 0*1$ of the desired radiation. The value of careful grinding and polishing and of etching may be seen to be very high upon examining the data of Table II and the results of previous work on beryl as shown in figures U5 and U6.

5* The (lOXO) grating space of beryl* During the course of the measurements described above, some doubt was cast upon the value of the grating space of the (1010) planes of beryl, which had been OQ given as 8.06 angstromsFurther suspicion was aroused upon con­

sideration of the unit cell parameters quoted by Bragg,^ who gives

a_L O Q a - 9*21 A and c = 9*17 A. From figure 39 it can be seen that for this hexagonal crystal d-^Q^Q = a cos 30° = 7*97

By measuring the angular setting of the second crystal, using very narrow slits, for the (l,+8) and (1,-8) positions for l*f>U angstrom radiation, and taking the difference between these two

settings to get twice the Bragg angle, it was found that

^-Bragg, Sir William Lawrence, The Crystalline State, London: G. Bell and Sons, Ltd., 19^9, p* 10U 8f> Figure 1;6. U/A VEl£A/0 U/A TM TROM /i/VGS S

$ 8 6 o dioio = 7 *96 A. It was necessary to use eighth order reflection because the vernier on the second axis permitted readings only to within 0*1 degree.

The error, 0.1 jS!, introduced using Stenstrom’s d is most serious

for a large spectrometer such as the one used in these investigations,

and would lead to a mistake of 3/U inch in positioning the x-ray tube

at 13.31 angstroms, which would be intolerable.

It seems certain that the error in the present measurement can

be no more than .01 which is of no consequence in the present

work, but it would be desirable, of course, to have the grating

space measured on a spectrometer more suited to absolute wavelength

measurements• IV . DATA

A. Molybdenum

To test the apparatus at intermediate wavelengths, the first spectra attempted were taken from the molybdenum L series. A piece of nickel-clad molybdenum^ was silver-soldered to the copper target face and the nickel surface milled off. The target was then fired in hydrogen. The target cover described in section III B 2 was used until the x-ray tube was outgassed. The focal spot was still quite clean after the data were taken.

F ig u r e h i was obtained by averaging two complete and one partial (l,-*l) rocking curves over the g lines. Figure U8 shows the rocking curves. Figure h9 shows an average of four LyS-j^

(1,+1) rocking curves, which may be seen in figure E>0.

The averages were obtained by so adjusting the ordinates of the individual rocking curves that they each enclosed the same area.

Only an indication of the presence of the L/»2 line was obtained.

Tabulated below are data pertinent to the molybdenum rocking c u r v e s .

In connection with curve I for the ^ ^ line, it should be remarked that the x-ray intensity depends on the current to the focal spot, rather than the target current. Curve I for the ex'-j_ g line is too heavily weighted in the final average because of the averaging method used.

^Obtained through the courtesy of Dr. Robert I. Jaffe of Battelle Memorial Institute, Columbus, Ohio. 88 r 9 }

51'

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$ 4-hH-f-minute -4-

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M icrometer setting 92

TABLE I I I

Molybdenum L Series

L ine A T r a n sitio n R ocking x -r a y Counts/min. ( x . u . ) Curve voltage current a t peak No. (kv) (ma) 5 3 9 5 .0 I 6 .8 20 U0U2 ** 1 LI I I “ MV \ <=* 2 5U 01. Li t t -M jy j II 8 .0 35 III 8 .0 20 70U0

a 1 5 1 6 6 .5 LI I " MIV I 8 .0 20 1923 P II 8 .0 35 2062 III 8 .0 35 2059 IV 8 .0 37 2207

/*2 1:910.0 LI I I ~ NIV ,V 8 .0 U5 115

B . Copper

The copper L

the L^]_ in figures 53 and 5U. The target was prepared by unsolder­

ing the molybdenum face previously used,•taking off all remains of

the solder on a sanding wheel, followed by vigorous scrubbing with

pumice and water. The target cover arrangement was again used

successfully. It was not possible to attempt the L>| and spectra • , because at the angular settings required, the detector housing

obstructed the path of the x-ray beam from the target.

Pertinent data are in table XV below.

Because of the averaging method used, curve I of the copper

Lc* l , 2 received twice its proper weight. This is the broadest of

^Siegbahn, Manne, Spektroskopie der Rontgenstrahlen, second edition, Berlin: Julius Springer, 1931, P. 231 93

* 1

I

* —*—■■— I— r -

a, 9 . /ytCrotrHrt&r ^ Figure 53. OOO'H 000

WX I,

I-U-

i 97 the three complete rocking curves recorded and hence it tends to smear the structure recorded in the other curves.

TABLE XV

Copper L Series

L in e ^ T r a n s itio n R ocking X— ray Counts/min. ( x . u . ) Curve v o lta g e cu r r e n t a t peak No. (k v ) (ma)

^ 2 1 3 3 0 7 o Lh i -MIV j v I 8.0 10 681|0 l a 8 .0 22 II 8 .0 22 lltl6 8 I l a 8*0 — l i b 8 .0 — III 8 .0 — 190U6

/ S 1 1 3 0 2 7 . LI I “ MIV I 8 .0 22 3111 II 8 .0 22 2923

C. Zinc

The L<=k-^ 2 and zinc lines are displayed in figures 99

through $80 The target was cleaned in nitric acid and the zinc

electroplated from a solution of zinc chloride in water. The

coating was at least one mil thick. The target was then lightly

scrubbed with pumice. The target cover arrangement was again used, but this time cooling water was allowed to flow into the target so

that the zinc would not get hot enough to evaporate. At the

completion of the data, the target still seemed to be fairly clean.

An a ttem p t to r e c o r d Zn L y j was unsuccessful, apparently

^Siegbahn, 0£. cit., P. 239 98

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I 100 I :

M/rro/rrefer 5etf/r7g Figure S i Ltii± because of weak excitation. The Zn h could not be tried because the detector would have obstructed the x-ray beam.

TABLE V

Zinc L Series

L in e Transition Rocking ray Counts/min. ( x .u .) C urve v o l t a g e c u r r e n t a t p ea k N o . (k v ) (m a)

^ 2 1 2 2 2 9 . LI I I “ MIV ,V I 8 . 0 3 3875 II 8 . 0 h U357

P 1 1 1 9 6 0 . l i i - mi v I 7 186U II 1 0 2527 III 20 2692 00 OO CD CO CD OO 00 OOOO IV • • • # 19 2885

>2 1 3 6 1 0 . LI I ~ MI 8 .0 12 1 2 2

D. Longer wavelengths

It wouW have been interesting to record the nickel Lc^i^2 an(^

L ^ i lines, but again the present geometry of the spectrometer prevented th is. Longer wavelengths, of course, were ruled out be­ cause of the beryl grating space. V. DISCUSSION OP DATA

A. Molybdenum

The molybdenum spectra were undertaken because it seemed the line intensities would be higher in this intermediate wavelength region than at the smaller energies. The fact that the Ly32 l i n e , which involves a transition from the incomplete Ud-shell, was so weak that a worthwhile (1,-tl) rocking curve could not be obtained

indicates that the multiplier sensitivity is quite low at five

angstroms or le ss.

The 2 V i lines represent for molybdenum transitions between inner levels, and hence little band structure is expected.

Examination of figures U7 and U8 shows that the Lot 2 line on the

long wavelength side and the satellite lines on the short wave­

length side of Le*3_ appear rather weak and washed out. This, pre- / sumably, is due to the rather low voltage on the x-ray tube.

Siegbahn^ exhibits curves for MoL«<]_j2 taken at 10, 20, and UO

kilovolts which seem to indicate that the intensity of satellites,

and even the L«*2 line, is greatest at 20 kilovolts, and weakest

at 10. Randall and Parratt^ have also studied the MoLof^

s a t e l l i t e s f apparently at about 1 2 kilovolts and U5 or 50

milliamperes, and with greater resolving power than available here.

It is possible that the satellite lines observed in the present

^Siegbahn, op. cit. p. 198 ^Randall, Charles A. and Parratt, Lyman G., Physical Review, £7, 786 (19U0) ioU data would be as well delineated as in the above references if similar x-ray intensities were used*

The line seems to be free of structure and fairly symmetri­ cal. The index of asymmetry, defined as the ratio of the half width at half maximum on the long wavelength side of the line to the half width on the short wavelength side, is 0*97•

B . Copper

The and lines of copper shown in figures U9 through

52 exhibit similar structure to each other and to the k/ 3 2 ,5 l i n e 17 studied by Bearden and Shaw. However, when the three lines are

plotted on a voltage scale (figure 59) with the positions of peak

intensities coincident, then it may be seen that the structures do

not coincide. If the shapes observed truly represented structure

in t h e N(E) curve, then it would be expected that there would be

better correspondence between the structures of the different lines

when plotted on a voltage scale*

Moreover, no sharp emission edges are visible. Judging from

calculations by Slater and coworkers, as illustrated in figures 7

and 8, one might expect to observe a shape similar to that indi­

cated by the dashed line in figure 59, with a low lying emission

edge due to the broad Us band.

The most obvious explanation of the observed shapes is that

they are distorted by a close-lying satellite line or lines which

arise from states of double ionization. These satellites, then,

mask entirely the underlying structure determined by the uppermost I Figure £9 electron h'oMj electron 1 0 6 parts of the filled portion of the density of states curve.

Figure 60 compares the copper Lo*^ ,2 shape observed here with those reported by Farineau and by Saur.

Farineau’s results were obtained by applying a blackening curve, determined by him with A1 K radiation, to his photometer

curves with background apparently subtracted.^ Saur’s curve is

the actual photometer trace which, judging from his paper, does ■*t not have a linear wavelength scale, although he marks the positions ) ft of a number of features.u As a result the reproduction of the long wavelength side of Saurts curve may be distorted. It should be

noted that in Farineau’s curve the background has been subtracted, but not in the other two. It seems that the present work has the

highest resolution reported so far, although the measurements do

not extend over as large an interval because of the very low

intensities.

Farineau also states that his copper LyQ-j. results differ from

the L«=<3_j2 on^7 in that the relative intensities of the satellites

when compared to the parent line are smaller for the than for

th e L«x-^ 2 . fTJ’ie present results indicate that the positions as well

as the intensities of the satellites depend upon the inner level

in v o lv e d , li9 Skinner and Johnston, in a brief note, ' report measurements

of transitions between the lower M levels and the Mjy^y band in fair

^Farineau, J., Annales de Physique, 10, 20 (1938) ^®Saur, E., Z eitschrift fur Fhysik, 103, h25> (1936) ^Skinner, H. W. B. and Johnston, J. E., Nature, lUO, 508 (1937) P re se n t Work

e l e c t r o n y/oft"s 107 Figure 60. 1 0 8 agreement "with Farineau’s resu lts. Measurements have also been made by Karlsson and by Siegbahn and Thoraeus, who do not give sufficient information to permit comparison of line shapes, and by S^rum, whose paper is not available here.'^*51*52,53

To return to the observed shapes, if they were ascribed to satellites arising from states of -double ionization due to Auger transitions from the Lj state, then it might be argued that the relative probability of such transitions to the Lj j and L-j-j j s t a t e s would be different, thus accounting for the different intensities of the satellites. Such an hypothesis could be verified by observing the lines as the excitation potentials were decreased beneath the

Lj excitation voltage. This would require a much more sensitive detector than is at present available because the Lj voltage is pro­ bably only about a hundred or so volts more than the Lj j j (a b o u t

95>0 v .), which wolild mean that the p line would be very weak* y The present data were taken at eight kilovolts, Farineau's between three and ten kilovolts, and the M line of Skinner and Johnston at three kilovolts•

In view of the doubtful interpretation of the observed shapes, it seems pointless to attempt to estimate from the shapes the width

^^Karlsson, A«, Arkiv for Matematik, Astronomi och Fysik (A), 22, No. 9 (1 9 3 0 ) _ -^Siegbahn, M. and Thoraeus, R., Arkiv for Matematik, Astronomi och pysik, 18, 2U-6 (192U) ^Thoraeus, R., Philosophical Magazine (seventh series) 2, 1007 (1 9 2 6 ) -^Sjz(rum, H., Pet Kongelige Norske Videnskabers Selskabs For hand1in ger, 19> No. 13, UU—7 (19U6) 109 of the filled portions of the overlapping 3d and Us bands,

C. Zinc

Figure 6l compares the observed Lcx^., 2 anc* ¥ 1 shapes for zinc •with the corresponding K ^ 2 shape, 17 while figure 62 compares the hi 5U L*=*i ^2 shape with those observed by Farineau and Gwinner.

Earlier work was done by Friman,^ Hjalmar,^ Siegbahn and

Thoraeus, 5 and Karlsson. The corresponding M line has been 1.0 studied by Skinner and Johnston.

The curves of figure 61 match more closely than was true for

the corresponding copper lines, although the shape differs markedly from the Lcx-^2* A similar result is reported by Farineau

and may a ls o be see n in G w inner's w ork. The comments made in th e

preceding section on the copper curves seem applicable here also:

the missing emission edge may be masked by a satellite line or lines.

^^Gwinner, E., Zeitschrift fur Physik, 108, 523 (1938) 55-prxma.n, E., Untersuchungen uber die Hochfrequenzspektra (L-reihe) der Blemente, .Dissertation, Lund, 1916 ^Hjalmar, e ., Zeitschrift fur Fhysik, 7, 3Ul (1921) 110 I l l

N

>w . so CM

^ s

V

r

t

\- * *o t 1 1 2

VI. CONCLUSIONS

It seems that the work described above has been done with greater resolution than heretofore; and although there are a number of problems which must be solved before the true shapes of the spectral lines are known, it is to be hoped that sufficient improvements can be made on the apparatus to overcome the difficulties.

The central problems to be faced in spectroscopy are those of resolving power and registration. Considerable progress has been made with respect to resolution; however the registration problem has not been so well disposed of. On the present apparatus the registration problem breaks down into individual problems of increasing x-ray tube current, increasing the percent reflection of the crystals, and increasing the detector sensitivity*

The x—ray tube current is at present limited by the low pumping speed through the glass envelope opening, but such a difficulty is certainly surmountable•

The crystal reflectivity is a more difficult problem, and may be solved only by finding other crystals. The beryl used seems to be the best yet found for two-crystal spectroscopy above six or seven angstroms.

Only a start has been made with the multiplier. The present data are apparently the first successful non-photographic charac­ teristic spectra recorded above seven or eight angstroms. The effects of changing the photoelectrode from beryllium-copper alloy 113 to a heavy metal, and of adding a couple of stages to the m ultiplier, need to be investigated. It would seem that as presently used the multiplier is just beginning to come into its own at thirteen a n g stro m s.

Very little reliance can be placed on x-ray line shapes measured

in this region until the effects of satellite lines, if any, are known. It would seem that the most obvious way of studying these

effects would be by experiments on their excitation potentials. Such

experiments must await the solution of the problems outlined above. AUTOBIOGRAPHY

Nathan Spielberg was born in Philadelphia, Pennsylvania,

February 2, 1926, His secondary school education was obtained in

Atla.nta, Georgia. He received the degree of Bachelor of Arts from

Emory University in 19U7 and the degree Master of Science from The

Ohio State University in 19U8. At The Ohio State University he has held the following positions: Graduate Assistant in the

Department of Physics and Astronomy, 1 9 h 7 -1 9 h 9 } Research Fellovf,

19U9-50, E. I. du Pont de Nemours and Company Postgraduate Fellow in Physics, 1950-51, Research Associate, 1951 to date*