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A germanium bent-crystal monochromator for nuclear spectroscopy
NUCLEAR
INSTRUMENTS
AND
METHODS
16 (1962)
17-28;
NORTH-HOLLAND
PUBLISHIN(;
CO.
A GERMANIUM BENT-CRYSTAL MONOCHROMATOR FOR NUCLEAR SPECTROSCOPY E. J. S E P P I ,
II. H E N R I I , ; . S O N , F. B O E H M a n d J. vv'..M. D U M O N D
Cali iornia Institute o.t Tech~ ology, Paxadena, Cali/ornia Received 24 F e b r u a r y 1962
4, precision b e n t c r y s t a l g a m m a - r a y m n n o c h r o m a t o r w i t h s t a t i o n a r y source has been built. T h e i t l s t r u m e n t c o n s i s t s of t h r e e p h y s i c a l l y i n d e p e n d e n t u n i t s : T h e line source (a r a d i o a c t i v e source or t h e anode of a n X - r a y tube), t h e 2 m e t e r - r a d i u s b e n t d i f f r a c t i o n - c r y s t a l w i t h its p i v o t a n d sine-lnotion m e c h a n i s m , a n d t h e h e a v y - d u t y c u r v e d t r a c k f r a m e w o r k which s u p p o r t s t h e collimator, d e t e c t o r a n d shielding. T h e m o t i o n s of tile c r y s t a l p i v o t unit a n d of t h e d e t e c t o r - c a r r i a g e u n i t a r e linked t o g e t h e r in such a w a y t h a t T;he reflection condition is satisfied. R e s u l t s a r e p r e s e n t e d s h o w i n g t h a t t h e precision of t h e
m o n o c h r o m a t o r Ior m e a s u r e m e n t of v - r a y w a v e l e n g t h s is 0.003 x - u n i t s . T h e line w i d t h a t half m a x i m u m , /12, o b s e r v e d w h e n t h e (800) planes of a b e n t g e r m a n i u m c r y s t a l a r e used is 0 0 8 x-units. T h e resolution wlfich has been a t t a i n e d w i t h t h e g e r m a n i u m c r y s t a l is illustrated b y a m e a s u r e m e n t of t h e 244.264keY, 246.056keY, a n d t h e p r e v i o u s l y u n o b s e r v e d 245.237 keV g a m m a line in t h e d e c a y of x,VZaa. Finally, exp e r i t n e n t a l results o b t a i n e d u s i n g t h e m o n o c h r o m a ~ o r to obs e r v e nuclear resonance e x c i t a t i o n in F :9 a n d Mn ~ a r e described.
1. Introduction Curved-crystal diffraction monochromators and spectrometers have been described by several authors. A review article including a complete list of references has been written by DuMondt). The instruments make use of the focusing Bragg-reflection property of a curved c r y s t J , such as quartz. In the monochromator arrangement the line shaped source is situated on the focal circle through ttle curved crystal. Gamma-rays scattered at the Bragg angle are detected by a large NaI counter after having passed through a collimator. The monochromator has considerably bigher luminosity, per unit wavelength interval, as compared to the spectrometer arrangement in which the role of the source and counter is interchanged. It is, therefore, well suited for experiments where gamma-ray or X-ray lines are scanned in a point by point manner over a certain wavelength interval. The CMtech monochromator (3lark I) built by DuMond 1'2'3) uses a stationary collimator and detector system. Both source and crystal move in a fashion that the Bragg condition is maintained at all times. For m a n y applications, however, it is
desirable to have a stationary source, for example if the source is connected to a reactor, an accelerator, or an X-ray tube. The instrument described in this paper is a monochromator with stationary source. It has been primarily designed for nuclear resonance scattering experiments using a powerful X-ray tube. It also is being used as a precision wavelength measuringdevice. It has an accuracysomewhat superior to Mark I. 2. Design of the Monochromator 2.1. D E S C R I P T I O N
OF TIIE CRYSTAl, PIVOT AND THE
DETECTOR CARRIAGE
The monochromator consists of three physically independent units: (a) the crystal pivot, (b) the detector carriage, and (c) the line source. Units (a) and (b) are illustrated in the line drawing, fig. 1. A photograph of the crystal pivot is shown in fig. 2. In this section we ~dll pre~sent a brief description of these two units and refer the reader to the appendix for a detailed description of the mechanical design. The crystal-pivot unit (fig. 1) contains the bent diffraction crystal, the pivot bearing, and the precision sine-screw mechanism. The precision lead screw moves the lever arm which turns the diffraction crystal about an axis provided by the pivot bearing. The sine of the Bragg angle is determined
x) j . W. M. l)uMond, Ann. R e v . Nucl. Sci. $ (1958) 163. l) D. E. Muller, H . C. H o y t , D. J. K l e i n a n d J . \ v . M. DuMond, P h y s . R e v . 88 (1957) 775. z) j . W . M. DuMond, R e v . Sci. I n s t r . 15 (1947) 626. 17
18
E.J.
SE P P I
through the sine-screw mechanism and can be read off directly on a dial. This reading is, of course, direct!y proportional to the wavelength. The design is such that on the monochromator dim the screw SHIELDED DETECTOR
et el.
dixdsion (s.d.), corresponds to one x-unit when the diffraction is from the (310) planes of quartz. Included in the sine-screw mechanism is a calibration cam which is used to correct for small
COLLIMATOR
C U R V E DCRYSTAL
CLAMRNG BLOCKS
\ SINE SCREW MECHANISM
,.. %.
.... ... "" ~
TRACK
~--7
l
. . . . . .
!!'
DETECTOR
[--
i
PIVOT ', ". ",
2___.__~7~7....... ,
.~
-
BEARING
/
/'
-
~
CARRIAGE
CRYSTAL
PIVOT
Fig. 1. L i n e d r a w i n g of t h e bent--crystal m o n o c h r o m a t o r i l l u s t r a t i n g t h e c r y s t a l - p i v o t unit and t h e d e t e c t o r - c a r r i a g e u n i t .
non-linearities in the pitch of the lead screw. The detector-carriage unit (fig. 1) provides for the motion of the heavily shielded detector and collimator system, in such a way that the Bragg reflection condition is satisfied. The shMded detector and collimator are carried on a platform which is constrained by circular tracks to rotate about an axis through the pivot bearing. The motion of the platform is electrically linked to that of the crystal pivot. The design of the detector carriage as a unit mechanically separate from the crystal pivot has the advantage that mechanical strains resulting from tl-e motion of the heavy shielding have no effect on the precise crystal setting which is determined by the sine-screw mechanism. 2.2. DI';SCV. I P T I O N O F Tl-i!'." D I F F R A C T I O N AND CRYSTAI. IIOLi)ER
Fig. 2. A p h o t o g r a p h of t h e monochrormtt,~r c r y s t a ! - p i v o t unit .showing t h e c u r v e d - c r y s t a l clanlping blocks, t h e p i v o t bearing, t h e lever a r m , allll thlt sine-screw lliechauisrll.
CH.YSTALS
The Bragg reflectiou is provided by a thin ooticaliy ground lamina of quartz or germanium clamped between stainless steel blocks which have been profiled to a two-meter radius of curvature. The single crystals are oriented so that the quartz (310) and germanium (400) planes arc' used in the
A GERMANIU3I
BENT-CRYSTAL
MONOCHROMATOR
reflection. The q u a r t z crystal is a square l a m i n a 7.5 cm b y 7.5 cm a n d 2 m m thick. Excellent results h a v e been achieved in the energy resolution a n d reflection power o b t a i n e d using the g e r m a n i u m crystal. The g e r m a n i u m crystal is a r e c t a n g u l a r l a m i n a 7.5 cm b y 3.8 cm a n d 1.3 m m thick. The crystal slab was cut from a n oriented cylindrical single crystal ingot of g e r m a n i u m t . Before bending, the dislocation d e n s i t y of the crystal was less t h a n 5 000 pits/cm 2. T h e slab was optically polished on b o t h sides to a flatness of a b o u t l 0 fringes of sodium light a n d then m o u n t e d in the crystal clampingblocks described below. This crystal is smaller t h a n t h e o p t i m u m size a n d will be replaced ~dth a larger one as soon as larger ingots become available. T h e m e t h o d developed b y DuMond, Lind, a n d Cohen 4) is used to grind the concave a n d convex cylindrical surfaces of the clamping blocks. The blocks h a v e a 5.5 x 4.5 cm aperture. The convex block a p e r t u r e has two ribs r u n n i n g n o r m a l to the generators of the cylinder. The surface of this block is lapped against the m a t i n g concave surface of a cast iron block which has been checked b y t h e F o u c a u l t knife-edge test a n d corrected to b e t t e r t h a n one q u a r t e r of a fringe of sodium light. The microscopic scratches in the surface a n d edges of t h e q u a r t z l a m i n a present a d a n g e r when the crystal is being bent. To minimize the possibility of fracture the q u a r t z is e t c h e d ~ t h conc e n t r a t e d hydrofluoric acid. The scratches are etched preferentially eliminating the s h a r p V c h a r a c t e r of the grooves. The crystal b e n d i n g is done in a dust free box. T h e optical contact is checked b y obseI~ing the interference fringes in the interface as the q u a r t z l a m i n a is rocked across the convex surface of the c l a m p i n g block. A t h i n neoprene gasket (0.5 mm) is placed on the crystal; t h e n the concave block is slowly clamped in place w i t h four spring loaded screws. W h e n b e n d i n g a g e r m a n i u m crystal lamina, interference fringes cannot, of course, be observed; therefore great caution must be exercised to insure a dust free interface. W h e n finally clamped in place tile concave surface of the g e r m a n i u m can be t T h e c r y s t a l slab was p r e p a r e d b y Mono Silicon, inc.. G a r d e n a , California, u n d e r t h e d i r e c t i o n of Dr . Simon A, Prussin.
FOR NUCLE.,kR SPECTROSCOPY
19
checked with the Foucault knife-edge test to verify t h a t it conforms to the convex crystal clamping block.
3. Monochromator Wavelength Calibration 3.1. G A G E B L O C K C A L I B R A T I O N
In the initial wavelength calibration of the monoc h r o m a t o r precision gage blocks were used to d e t e r m i n e the linearity of the m o n o c h r o m a t o r screw. The calibration cam described in the section on the crystal pivot in the a p p e n d i x is used to correct for sma]l dexdations in the l i n e a r i t y of the precision ground a n d lapped screw. The calibration curve A s h o w n in fig. 3 was o b t a i n e d w h e n a linear cam is used. The curve shows the deviation in the screw position from t h a t m e a s u r e d b y gage blocks as a function of the position on the screw. Scales on the figure show t h e m e a s u r e d dimensions in inches a n d also in screw divisions. Curve B of fig. 3 shows POSITION ON SCREW (INCHES) 0.0
2.0
4.0
6.0
8.0
IO.O
CURVE A
m o
_z *i.O
+0.01 ~
~o 0.0
0.00 to
~ -I .0
-0.01
>-
w z
CURVE B
J
÷0.01 ~
~ ÷1.0 u.
:wlii'-'{-':z--i;.-l;l~[~i.-llli!II-
z 0.0 o • -I.0 ~
0 . 0 0 u.
g
-0.01 ti
i
i
/
r
+ 400 ÷2 O0 0 -200 - 400 MONOCHROMATOR POSITION (SCREW DIV.) Fig. 3. C a l i b r a t i o n c u r v e s g i v i n g t h e d e v i a t i o n of t h e s c r e w position from l i n e a r i t y versus t h e m o n o c h r o m a t o r position. Cu r v e A w a s o b t a i n e d w i t h a l i n e a r c a l i b r a t i o n cam. C u r v e B was o b t a i n e d u s in g a c a m profiled to c o r r e c t for t i l e d e v i a t i o n s s h o w n in c u r v e A.
a calibration m e a s u r e m e n t using a cam profiled to correct for the deviations sho,~m on curve A. F o r the curve B the RMS deviation of the points from linearity is 0.002 s.d. D a t a points are not s h o w n in tile region + 2 0 0 t o + 400s.d. I n this region an error 4) j . ~,V. M. D u M o n d , D. A. L i n d a n d E. R. Cohen, R e v . Sei. I n s t r . 18 (1947) 617.
20
E.J.
SEPPI
was discovered which required a change in the shape of the calibration cam. 2\ new cam was installed which now results in a n overall linear monoc h r o m a t o r setting to within the accuracy shown on the curve B. 3.2. G . \ M M A - L I N F X V A V E L E N G T I I C : k L I B H A T I O N
A check on the final calibration h a s been m a d e b y m e a s u r e m e n t s of several g a m m a lines using germanium and q u a r t z diffraction crystals. Consistency checks h a v e been made in two ways : (i) by c o m p a r i n g the measured waveiengths of a single g a m m a l i n e in various orders, n, of reflection from the g e r m a n i u m crystal a n d in first order from the q u a r t z (ii) b y m a k i n g use of c e r t a i n well-established g a m m a - r a y energy c o m b i n a t i o n - e q u a t i o n s k n o w n from the decay schemes. W i t h these two m e t h o d s i n t e r r e l a t e d measurem e n t s are possible covering the entire range of the m o n o c h r o m a t o r and a n overall l i n e a r i t y check h a s been established. In this c h a p t e r the results of the consistency check (i) are analyzed to d e t e r m i n e a formtlla for e s t i m a t i n g the error of the wavelength measurements. Errors calcttlated using the derived formula are t h e n c o m p a r e d with the deviations observed in the consistency check (ii) Finally possible sources of m o n o c h r o m a t o r error are examined. For the calibration investigation g a m m a lines from the well-known decay of T a 18= a n d T a 18a were used. The g a m m a decay-schemes of these isotopes have been established b y Murray, Boehm, Marmier, a n d DuMondS). These two isotopes supply intense g a m m a lines over a considerable portion of the useful energy range of the m o n o c h r o m a t o r . Using s t a n d a r d techniques =) a 0.005 inch d i a m e t e r t a n t a l u m wire was irradiated at the Material Testing Reactor in Arco, Idaho. W i t h this source the w a v e l e n g t h results listed in table 1 were obobtained. Also listed in the table are the results of Murray, et al. s) which were o b t a i n e d with the Mark I i n s t r u m e n t . The errors e listed in table 1 were o b t a i n e d from the formulas: =
/ ~-2 ~,'*:, + e~,
e~ = 0.003 s.d.
(1)
s) j . j . M u r r a y , F. Boehm, P. M a r m i e r a n d J. V¢. M. DuMond, Phys. R e v . 97 (1955) 1007.
el al.
where t h e s t a n d a r d deviation e¢ is the error in t h e position of the g a m m a line resulting from t h e statistical c o u n t i n g error in the d a t a . T h e monoc h r o m a t o r error ~,. represents the non-statistical part of t h e error a n d gives a n indication of the overall reproducibility a n d self-consistency of the i n s t r u m e n t . T h e m o n o c h r o m a t o r error is a measured q u a n t i t y which was d e t e r m i n e d from the d a t a in table 1 t h r o u g h t h e formula Y ~ Y . 2(). 'j ~m =
-
-~
~.~,o),~-N
--
1
-~
-
i.~f~
•
~
(2)
where n is the order of the reflection a n d ).,J is t h e average w a v e l e n g t h found for the group of measu r e m e n t s of the g a m m a line j. T h e symbols ,;fl a n d r.~J represent respectively the observed wavelength a n d statistica[ c o u n t i n g error of the ith measurem e a t of the line j. In the sum three or more ind e p e n d e n t m e a s u r e m e n t s labelled i were t a k e n from columns I to VI of table 1 of the following g a m m a rays; FD, BA, KG, in W 1s2 and DC, EB, GC, IE, ID, IC in W 183. The t o t a l n u m b e r N of p o i n t s s u m m e d was 32. F r o m this procedure the value of ~m was found to be equal to 0.003 s.d. Making use of t h e g a m m a - r a y energy combination-equations k n o w n from the decay schemes of W t 8, a n d W 18a a check has been m a d e on the magnit u d e of cmin e q u a t i o n (1). The c o m b i n a t i o n equations are given in column I a n d II of table 2. A list of the observed values of the left (column I) a n d right (column II) sides of the c o m b i n a t i o n equations is p r e s e n t e d in colunms I I I a n d IV respectively. The statistical consistency of the deviations between the values in columns I I I a n d IV and the errors listed represents a check on the m a g n i t u d e of e=. Based on t h e results of the two m e t h o d s of checking the w a v e l e n g t h calibration we conclude t h a t the error in the m o n o c h r o m a t o r is given b y equation (I) with the value of E,, equal to 0.003 s.d. M o n o c h r o m a t o r errors which c o n t r i b u t e to the overall error e~ result from (i) screw non-linearity, (ii) lack of complete reproducibility of settings, a n d (iii) deviations caused b y t e m p e r a t u r e variations. The contrilmtion from screw non-linearity is found to be less t h a n 0.002 s.d. as measured with gage blocks. No deviations h a v e been measured which
62. 376 ± 0.0015 55.705
62. 3~0 * 0 . 0 0 ~ 5
$5 7 0 1 a 0 . 0 ~ 1
* The errors
given by Murray 5.
limit|.
34 949 • 0,001!
to q 0 % c o n f i d e n c e
is taken from reference
et al 5 correspond
J'@ T h e i d e n t l f i ¢ a t i o , l o f t h e l e v e l ,
* 0.0016
50. 451 • 0,0016 50.281 ~0 0011
Olher
errors
listed are computed
fl0. Z83 • 0 . 0 0 0 8
from
formula
* 0 0010
50. Z82 • 0 . 0 0 1 5 34.950 • 0,0016
50. ZB3 • 0 . 0 0 3 Z 34.951 • 0.0031
50.284
50.b51
50 6 5 4 ± 0 . 0 0 1 7
flO. 649 • 0.0034
50.651,0.0050
59.Z51 ± 0.0020 58
58.953*0.0042
58.954,0.0016
* 0.0012
( I ) In t h e t c x t
50. 2 8 3 ~, 0 . 0 0 0 5 34.950 • 0 . 0 0 1 0
5 0 . 4 5 1 • 0. 0 0 1 6
50.652
954 = 0 . 0 0 1 5
± 0.0008
59 L54 ffi O.OOZI
76.221
58.95Z * 0.0140
76 ZZI • 0.0011
5 9 . 2 3 4 • 0, 0 1 5 0
± 0.0015
* 0 . 0 0 $1
• 0 0009
76.2L1 i 0 0016
46.852
53.951
55.703
6Z. 375 • 0 . 0 0 1 4
76.2L0 i 0,00~0
7 6 . 2 7 . 2 • 0. 0 0 0 9
• 0.0016
• 0. 0 0 1 5
68.968 i 0.0015
79.115
01.162
106.273 ~ 0.0026
100 841 ± 0.0015
IZ3.59Z • O.O01L
146.085 * 0.0015
102.615 • 0 0oil
188.251 ± 0.0024
Average Vll
W,:ighted
ll4. 630 * 0.0008
183
102
J
1
Gamma Average
• 0.001
• 0 001 • 0.001
t 0.003
0.00l ± 0.007
354.004 • 0.010
Z45.Z~7 • 0,008 246 056 ± 0 . 0 0 L
~ 4 4 L64 • 0. 0 0 6
2 0 9 . 8 6 0 * 0. 0 0 5
208.814
16L. $ L ) • 0 . 0 0 2
101 9 3 1 ±
52.59~ • 0.001
Z64.075 • 0+009
• 0 013
I14 ± 0.004
229.32/
ZZ2
198. 356 * 0. 0 0 5
17q. 394 • 0.004
156. ~g6 * 0 . 0 0 ~
102,44| • 0 . 0 0 3
IIb.4ZI
11~.674 • 0.00Z
100.107 t 0.00i
84.69)
67.7~I
65.?L3
VII1
this Exl~,rim.mt
r a y l i n e s u s e d i:t t h c c a l i b r a t i o n
235. 226 ± 0.00~0
in
Tungsten
5th Order VI
gamma
118.630 i 0.0015
Transitions
Tra1~eitions in
4th Order V
183
Tungsten
a;td tungsten
1 1 4 . 6 2 5 a 0. 0 0 3 0
114.630 • 0,0010
5 5 . 7 0 3 t 0,0010
3rd Order IV
~L
X-Units
u~gs en
Crysh~l
Wavelength
T a b l d a ~ i o ; : o[
Germanium
Ray
I.
* 0.003O
~ 0.0016
53.952 • 0.0060 46.852
* 0.00~4
5 5 . 9 5 1 a 0. 0 0 5 4
• 0.00Z0
* 0.0016
46.853
235.226
60.968
68.966 * 0 . 0 0 ~ Z
5 5 . 7 0 2 ~r 0 . 0 0 5 3
79.117
* 0.0017
81161
• 0.0016
108 841 • 0.0016
± 0.0O34
106 2~3 • 0.00~4
0 0031
79.111 • 0.0030
81.16/
106. Z7Z • 0 . 0 0 4 2
ILL593,
12~ 59L ± 0 . 0 0 1 6
108 8 3 7 • 0 . 0 0 3 4
589 • 0.00~1
igl
• 0 0016
146.084 • 0.0021
182614
Znd O r d e r lll
Gamma
146.007 • 0.0053
188.2~4 ± 0.0O~L
18z.618 • 0.0031
l~t Or,h-r II
182 6 1 4 • 0 . o o ~ 1
t
188.248 * 0 00~3
1
1a1 O r c h . r
Gu.trtz CrystaL
TABI.E
1
Energy Mark
k0.0~
i 0.0L
~,6 t 0 , 0 5
04
• 0.00
0l
• 0.07
354 04 • 0.20
2 4 6 05 t 0 . 0 9
Z 4 4 Z6 • 0 . 0 9
Zo9 87 ± 0.07
208.81
162 3J • 0 . 0 4
107.93 • 0.0L
52.59 ~ 0
Z 6 4 + 0 9 • 0. 10
2z9.~7
2LL. 0 5 1 0 . O l
1 9 8 . II ± 0 . 0 6
1i9
156.37 i0
15Z.41 i0.03
I16.40
113.66 t0.02
100.09 * 0.0L
84.67
67.'/4 * 0.01
65.71 • 0.01
IX
.Spectrometer*
Ray
FB ID IC
IE
GC
EA
EB
DC
CB
KF
CB
KG
JF
KH
JG
HD
KI
J}l
BA
[iF
FD
KJ
X
Identaficatlon**
keV
22
E.J.
S E I ' P I el
can be a t t r i b u t e d to a lack of reproducibility of m o n o c h r o m a t o r settings. Deviations due to temp e r a t u r e variations can c o n t r i b u t e significantly to the error of the m o n o c h r o m a t o r reading. The temp e r a t u r e coefficient due to the t h e r m a l expansion of the mechanical p a r t s of the m o n o c h r o m a t o r is e s t i m a t e d to be - (5 to 13) x 10 - 6 2 s . d . per °C
al.
m a x i m u m of the g a m m a lines in W ~s2 a n d W ts3 is 0.16
A2 = - - - - x - u n i t s , n
-E2 o r A E = 1.3 x 1 0 - ' - - - k e V
(3)
where E is the energy in keV a n d n is the order of reflection. Some results obtained with this source are p r e s e n t e d in section 5.
TABLE 2 E n e r g y c o m b i n a t i o n e q u a t i o n s for t u n g s t e n 182 and t u n g s t e n 183 C o m b i n a t i o n F.quation
I
KJ + K J -iJ H -JlI :HF-:-
O b s e r v e d Values for Column I1
II
III T u n g s t e n 182 264.079:1:0.005 222.109 ± 0.003 198.367 ± 0.002 179.397 ~ 0.002 152.444 ~ 0.001
264.075 ± 0.009 222.114--0.004 198.356 : 0.005 179.394 = 0.004 152.441 : 0.003
T u n g s t e n 183 353.989 = 0.002 406.587 ~ 0.002
354.004 : 0.010 406.587 ~ 0.006
JF JG IIF KJ
-~ = ~
KF KG JF KII
FD
=
HD
D C .:- I D CB ~ DC + I D
O b s e r v e d Values for Column I
~ IC = E B . ~ - 1F.
where I is the m o n o c h r o m a t o r setting in screw divisions. The t e m p e r a t u r e coefficient ~) due to the e x p a n s i o n of tile diffraction crystal is 10.4 x 10 -6 Jl s.d. per °C for the q u a r t z crystal a n d 6.9 × l0 -6 ). s.d. per °C for the g e r m a n i u m crystal. The variation of room t e m p e r a t u r e d u r i n g the a c c u m u l a t i o n of d a t a in table 1 was less t h a n 3 °C. The error due to t e m p e r a t u r e v a r i a t i o n s is thus comparable to the error from screw non-linearity. 4. Monochromator Resolution and Reflection Power Use of the g e r m a n i u m diffraction crystal in place of the q u a r t z crystal gives considerable improvem e n t in the resolution a n d i n t e n s i t y o b t a i n e d w i t h the m o n o c h r o m a t o r . The higher order reflections of the g e r m a n i u m (400)n planes provide sufficient i n t e n s i t y to be useful for high resolution measurements. The best resolution we h a v e o b t a i n e d was achieved with a 0.002 inch d i a m e t e r t a n t a l u m wire source. For this source the full w i d t h at one-half
IV
In a n a t t e m p t to b e t t e r u n d e r s t a n d the reflect i v i t y laws of tile g e r m a n i u m crystal, measurem e n t s of g a m m a lines were m a d e in various orders of refection. Tile results h a v e been analyzed b y a least-square fit to a n e q u a t i o n based on the ass u m p t i o n v) of a mosaic crystal. W i t h this assumption it can be s h o w n s) t h a t neglecting the atomic absorption the reflectivity R ( E , n) is a p p r o x i m a t e l y given b y +~ dO R(E, n) = [I -- e-2WC°)RH] (4)
f
where W(0) is a Gaussian with a half-width given b y the crystal mosaic. The range of the integration, e) M. E. S t r a n m a n i s artd E. Z. A "ka., J. Appl. P h y s . 23 (1952) 330; A. l-I. C o m p t o n a n d S. K. Allison, X - R a y in T h e o r y a n d E x p e r i m e n t (D. V a n N o s t r a n d C o m p a n y , Inc., N.Y., 1947). 7) D. A. Lind, W. W. VCest and J. W. M. DuMond, Phys. R e v . 77 (1950) 475. n) J. \V. Ktlowles, Can. J. P h y s . 37 (1959) 203; ~V. H. Zacharia.sen, T h e o r y of X - R a y Diffraction in Crystals ( J o h n \Viley & Sons, N.Y., 1946).
A GERMANIUM
BEN'r-CRYSTAL
MONOCnROMATOR
2,t, is the angle projected at the crystal b y the source. The function R H is given b y
Ru = d~22
t e - 2~(°)
(5)
where d H is the lattice spacing, V is the volume of the unit cell, t is the thickness of the c r y s t a l , f is the atomic scattering powerg), F H is the lattice structure factor, and e -2u(°) is the Debye factor which is a function of the Debye temperature O. In the limit of a thin crystal the energy dependence of the reflectivity (equation (4)) approaches the wellknown E - 2 law v, to). Experimentally we have determined the ratio of the reflectivity for an energy E in the nth order to that for energy E o in the noth order. The experiment furnishes this ratio in the following way: R(E, n)
I(E, n)
T(Eo)
I.flEo)
a(Eo)
R(E o, no) -- l(Eo, no) T(E) 7~(E~" e(-Ei-
(6)
where I(E, n)/l(Eo, no) is the observed ratio of counts in the detector, T(E) is the transmission through the crystal derived from the atomic absorption coefficient, I~(E) is the iutensity of the g a m m a line as measured by EdwardQ 1), and r.(E) is the efficiency of the detector (including air and source absorption). The values of I(E, n) \\,ere measured for several tungsten lines. Ratios were then determined from equation (6) with n o equal to one and with E o equal to 100.107 keV and 107.933 keV, resl)ectively , for gamlna lines in \~.,1~2 and \\:183. These ratios have been plotted in fig. 4. A least-sqnare fit was made of the observed ratios to those calculated through eq. (4) with the crystal mosaic width and the Debye temperature as the variable parameters, and the results are also shown in fig. 4. The curves were calcu!ated based on the vahles 7.5 sec for the mosaic width and 275:'K for the Debye temperature. The crystal thickness was 1.3 ram. The calculated curves and observed Y) J. B e r g h u i s , 1. M. l{aanappel, M . P o t t e r s , B. O. L,oopstra, C. li. MacGillarry a n d A. L. Veenendaal, Acta, C r y s t . $ (1955) 2.78. 10) ~V. F. F d w a r d s , J. w . . M . Du31ond and F. l:k>ehm, N u c I . P h y s . 26 (1961) 670. n) W. F. E d w a r d s , I.;xperimenta! Studies of Conversion Coefficients in Some D e f o r m e d Nuclei (Doctoral Thesis, Calif o r n i a I n s t i t u t e of Technology, P a s a d e n a , Calif., 1960).
FOR NUCI, EAR
SPECTROSCOPY
23
data points are in agreement to udthin the estimated accuracy of the data. It is interesting to conclude from this that the cq. (4) based on a mosaic crystal seems to account for the experimental findings. ........ ~--
\\\ X \
-..
.
i
......
~
i
.......
~
I
,
10 -2
\
\
10-3
\I
~
IO
".
\
'..
i
QUARTZ
'
"
'
\
~.~,
'.o
IO0
.,
IO00
ENERGY
--
k eV
Fig. 4. R e l a t i v e r e f l e c t i v i t y of tile g e r m a n i u m and q u a r t z c r y s t a l s v e r s u s g a m m a - r a y e n e r g y . Based on eq. (6), d a t a points g i v i n g tile observed r e l a t i v e reflectivity lrom t h e g e r m a n i u m (400) planes in v a r i o u s orders are s h o w n as circular and t r i a n g u l a r points for g a m m a lines in KVI~2 a n d \\:l~.~, respectively. T h e d a t a p o i n t s a r e normalized to 1.0 for the tirst-order reflection of t h e g a m m a lines a t 100.107 keV and 107.933keV (hollow points). Tile c u r v e s show resulis o b t a i n e d using eq. (4) in a le,'L~t-square fit to t h e g e r m a n i u m r e i l e c t i v i t y - d a t a . The solid s q u a r e points represent t h e r e t t e c t i v i t y of t h e q u a r t z c r y s t a l r e l a t i v e to t h e gernlaniunl crystal.
\Ve have also coml)ared the reflectivity of our germanium crystal (400) planes to that of our quartz (310) planes. The ratio of the monochromator counting rate with the germanilnn crystal to TABLE 3 C o m p a r i s o n of reflection f r o m g e r m a n i u m a n d frorn q u a r t z "~ L
Gamma Ray E n e r g y (keV) 67,751 100.!07 222.1!4
.
1G , 'l S o, " 0.6 .:_ 0.1 2.4 .:z 0.6 II.1 x_ 2.3
! i
RC;e. RSiO~
1.4 ± 0.2 3.1 ~= 0.8 11.5 t 2.4
IGe/ISiO= is t h e observed ratio of counts multiplied by 1.5 to a c c o u n t for tile differences in a r e a s of tile crystals, /~Ge.RSiO: is t h e r a t i o of t h e reflectivities.
24
E.J.
energy of 245.23 keV. This transition has not previously been obsela, ed because of the existence of the transitions with energy 246.056 a n d 244.264 in T a ~s3 both of which are considerably more interise t h a n the 245.23 keV transition. We h a v e looked for this line with the present i n s t r u m e n t . The source used in the m e a s u r e m e n t was a 0.002 inch t a n t a l u m x~dre. Fig. 5 shows the resrAts which were obtained. T h e 245.23 keV transition is well resolved between the lines at 246.056 and 244.264 keV. Shown in fig. 6, for comparison, are results which were obt a i n e d with the q u a r t z crystal w i t h a s t a n d a r d 0.008 inch d i a m e t e r source. F r o m a least-square
the counting rate with the q u a r t z crystal was observed for several g a m m a lines of W ~s2. The observed ratio wa~s multiplied b y 1.5 to account for the differences in the areas of the crystals. These ratios IG'/I si°~ are given in table 3. (The thickness of the two crystals is given in section 2.) The ratio of the reflectivities Rc'*/R s~°'- presented in table 2 is equal to the product of IC"/I s~°~ a n d the ratio of t h e crystal transmissions TSi°*(E)/TC"(E). F o r a g r a p h ic comparison of the reflectivities the value of the quantities (RSi°:/R G') x (R(E, n)lR(lO0,1) for the three g a m m a e n e r ~ e s are s h o w n as solid squares in fig. 4. WAVE 50.2
et al.
SEPPI
LENGTH - X.U. 50.4
50.6
50,8 9
o -
6.0 i
~
i SCALE ~
i
4.o
//
'
?.0
/\,
oo[.....
2~i.o
2~;.o ENERGY-
°°
a,4.o
key
Fig. 5. T h e 246.056, 245.237, a n d 244.264 keV g a m m a - r a y lines in Vv"i~a o b s e r v e d in t h i r d - o r d e r reflection f r o m g e r m a n i u m .
5. P e r f o r m a n c e o f t h e M o n o c h r o m a t o r 5.1. N E W L I N E O B S E R V E D
IN DECAY OF Ta t~
I n t h e d e c a y scheme of T a ls3 M u r r a y et al:), p r e d i c t e d t h e t r a n s i t i o n F B (see table l) ~ i t h a n
analysis of the d a t a the ratio of the intensity of the 245.24 keV line to t h a t of the 246.056 keV line was found to be (1.15 + 0.03) x 10 -2 a n d the energy of the transition was d e t e r m i n e d to be 245.237 + 0.008 keV. 5.2. N U C L E A R R E S O N A N C E E X C I T A T I O N
A series of e x p e r i m e n t s on nuclear resonance excitation in which the m o n o c h r o m a t o r is used to provide a monoenergetic b e a m of X - r a y s has been performed a n d is described in a separate paper12). F o r t h e purpose of illustration we shall present a brief description of these experiments a n d t h e i r
9 6.o
o 4.a
z
.~ zc
/ WAVE
,
247~0
5o.2
"
,
LENGTH -- X.U.
~,
246;0 ENERGY-
5o6 24.~0
, '~'4:0
5o8 "
keY
Fig. 6. T h e 246.{256 a n d 244.264 keV g a m m a - r a y lines in W t6a o b s e r v e d w i t h t h e q u a r t z (310) plane.
ti) E. I . Seppi a n d F. Boehm, Bull. A m . P h y s . SCc. [II] 6. (1961) 503; F. B o e h m , J. W. M. DuMond, H. E. tlenrikson, a n d E. J . Seppi, Gotlinburg Conference on E l e c t r o m a g n e t i c L i f e t i m e s a n d lh-operties of Nuclear States, 1961; Publication 974, N a t i o n a l A c a d e m y of Science, N a t i o n a l Research Council, W a s h i n g t o n , D.C. (1962).
A (;ERMANIU.'~! BENT-CRYSTAI.
MONOCHROMATOR
results. The arrangement for the experiment is shown in fig. 7. In the experiment a powerful X-ray tube is placed at the source position and the monochromator is used to select a nearly monoenergetic
FOR NUCLEAR
SPECTROSCOPY
25
radius curved-crystal clamping-blocks, length, pitch and precision of lead screws available, the optimum lever arm length to allow large angular magnification with a minimum of bending, deter-
N0I - DETECTOR/ 1.20
. . . . . .
RESONANCE EXCITATION iN F [9 E= 109.894 -+0005 key Ge SO0 PLANES
_
BEN'~TG~IMAN IUM-IRY~TAI - ~ ¢ ~ C L COLL, M ~ I : I TERER
°o
iio
Fig. 7. S c h e m a t i c a r r a n g e m e n t for t h e nuclear resonancee x c i t a t i o n e x p e r i m e n t . T h e b e n t g e r m a n i u m c r y s t a l is used to d i f f r a c t a n e a r l y m o n o e n e r g e t i c b e a m of X - r a y s f r o m t h e b r e m s s t r a h l u n g s p e c t r u m of t h e X - r a y t a r g e t (anode of a n X - r a y tube). T h e diffracted b e a m passes t h r o u g h t h e c o l l i m a t o r a n d is incident on t h e s c a t t e r e r . "file r a d i a t i o n s c a t t e r e d t h r o u g h 135 d e g r e e s is observed w i t h a N a I detector.
beam of X-rays from the bremsstrahlung spectrum incident on the diffraction crystal. A sample of L i F or Mn is placed in the diffracted X-ray beam and scattered radiation is measured with a NaI scintillation detector. A resonance peak is observed as the wavelength of the incident beam passes through the nuclear resonant energy. Figs. 8 and 9 show results which have been obtained for nuclear excitation of the first excited levels in F t9 and Mn 5~. Least-squares analysis of the data gives 109.894 + 0.005 keV for the fluorine resonance position and from the yield a width of (5.7 4- 0.8) x 10 -7 eV was deduced. Analysis of the Mn SS data gives 125.95 4- 0.01 keV for the position and (1.1 4- 0.3) x 10 -6 eV for the width of the resonance. Acknowledgements We wish to thank C. H. Holland and D. Agresti for their assistance in collection and analysis of the data. Appendix MECtIANICAL DESIGN OF THE MONOCHROMATOR
Many considerations leading to the design of the present monochromator are similar to considerations discussed in references 1) and 13). Practical requirements such as the availability of two meter 1~) j . V¢. M. D u M o n d , E r g e b . e x a k t . N a t u r w .
28
(1955) 232.
-/
~
o/ t
-
'\ k
, ~ - 0J6 ~ . , .
) ,
,
,
112.40
,',
,
~1260 112.80 WAVE LENGTH (X - UNfTSI
,
11300
Fig. 8. N u c l e a r resonance e x c i t a t i o n of t h e first e x c i t e d level in F 19.
w o 1.04 _z
RESONANCE
EXCITATION
Mn55
IN
=r= 125.95'- 0.01key Ge 800 PLANES
o I.O2 L~ N J
Q: 1.00 o z I
I
t
I
98.0 WAVE LENGTH
I
I
A
i
98.5 (X- UNITSI
I
Fig. 9. N u c l e a r resonance e x c i t a t i o n of t h e first e x c i t e d level in .Mn~.
mined the over-all dimensions of the instrument. With these proportions established an analysis of all calculable mechanical errors was made. Each error was to be limited to + 0.001 s.d. which corresponds to 0.001 x-units in wavelength resolution for the quartz (310) planes. The design we have finally adopted is illustrated in fig. 1. 1. Design o! Crystal-Pivot Unit
The crystal-pivot bearing, lever arm, and sinescrew assembly is mounted on an octa_hedron constructed of welded square steel tubing, provided with three leveling screws. The pivot shaft, shown in fig. 10, is ground and lapped and rotates in two
26
E.J.
S E P P I et a./.
"'Oilite" bearings. The inside diameter of each bearing is first fitted accurately to the pivot slmft then milled out leaving two narrow strips, 90 ° apart, as shown in tile insert in fig. 10. A wedge
of four parts. The convex crystal clamping-block is screwed to tile upper plate shown in fig. 10. The upper plate is provided with a large hole which clears the conical portion of the centering button.
CENTERINGBUTTON
CRYSTAL CLAMPING
SCREW DIFFERENTIAL SCREW
PLATFORM ./~LEVER ARM
PUSH-PULL LEVELING$
OILITEBEARINGS i SPRINGS
PIVOT
:
,.~
ADJUSTING SCREW
i
:
T
SLOT
~ W E D G E ~ BOTTOM GROOVE --,
o
STRIPS BALL \ADJUSTINGSCREW Fig. 10. lane drawing of the pivot-bearing assembly showing the pivot shaft with the crystal clamping-block and lever arm. The insert gives the details of the "Oilite" bearings designed to provide a uniform bearing pressure on the pivot shaft.
bottom groove is machined opposite the two strips. A bronze spring ~ i t h a mating wedge projection is inserted in the groove. The spring has two strips that are machined to a slightly larger radius than the pivot shaft. A " T " slot in the top of the spring is engaged by a button on tile adjusting screw which raises or lowers the spring thus decreasing or increasing the bearing pressure on the pivot shaft. The two bearings are mounted 180 ° from each other so that tile moment, due to the weight of the lever arm, is taken up by the solid strips of both " O i l i t e " bearings. The axial thrust of the pivot shaft is carried by a ring of ball bearings. The whole pivot assembly is enclosed in ,an oil filled housing with a felt dust seal at the top. The crystal-block mounting assembly consists
Four radial set screws in tile upper plate clamp the centering button allowing small adjustments in the horizontal plane. The cylindrical end of the centering button pivots in a bored hole in tile crystal platform. A differential screw, mounted on the platform, provides small rotational adiustment of the upper plate. The lower part of the platform is fitted to a taper on the main pivot shaft and clamped ~ i t h a cap screw. The lever arm is clamped rigidly to the main pivot shaft. In the horizontal plane the lever is parabolic in shape, to achieve m a x i m u m rigidity ~ , t h minim u m weight. Tile sine-screw mechanism is shown in fig. I I with one bearing plate and cheek plate removed for clarity. Fig. 12 shows a photograph of the sine-
A GER31ANIU.M BENT-CRYSTAL
2,IONOCII.RO~IATOR FOIl N U C L E A R
screw unit. Tile precision ground a n d lapped lead screw engages a bronze split nut. E n d t h r u s t on the lead screw is borne b y a h a r d e n e d a n d polished spherical b u t t o n bearing against a flat h a r d e n e d
SPECTI,~OSCOPY
27
contact. P a r t of the split nut projects radially a n d is fitted with a small roller which rides on the calibration cam. W h e n the lead screw is r o t a t e d clock-wise tile calibration cam constrains the split UPPER ~
MEEHANITE SPACER BLOCK ~ --
GUIDE BAR
PRECISION LEAD SCREW CALIBRATION CAM
BRONZE SPLIT
MAIN GUIDE BAR
PIVOT LEVER ARM
SPLIT BRONZE BEARING PLATE
/ '
,/ HARDENED STEEL DISC
~
HARDENED STEEL CREEK PLATE
i HAROENEO STEEL BUTTON
Fig. I 1. Line d r a w i n g i l l u s t r a t i n g the sine-screw mechanism.
plate (not shown in the figure). The bronze siflit n u t has an a d j u s t i n g screw to achieve proper t h r e a d
Fig. 12. Photograph of the sine-scre~ mechanism with the cover p l a t e removed. The upper guide bar, precision lead screw and main guide bar can be seen. Also seen is the radial projection from the bronze s p l i t nut held to ride on the calibration cam by t h e spring.
n u t in the t a n g e n t i a l direction. If the contact surface of tile cam were straight the axial motion of the split n u t would be d e t e r m i n e d only b y the pitch of the lead screw. However, as shown in fig. I 1, the cam is profiled to correct for nonlinearities in the pitch of the lead screw. As the split nut projection rides along the cam the profiled surface i m p a r t s additional r o t a t i o n to the split uut t h a t appropriately adds to or s u b t r a c t s from the pitch of the lead screw. The total correction range of the cam is equivalent to 0.1 x-units of ?'-ray wavelength. Straddling the split nut is the sliding assembly provided with two split, bronze bearing plates t h a t slide on the main guide bar. A projection on the " 3 I e e h a n i t e " spacer block is held against the upper guide bar b y a fiat spring. The sliding assembly clears the lead screw and is constrained to move in a s t r a i g h t line b y the two guide bars. Tile ends of the bronze split nut arc polished flat a n d contact two h a r d e n e d and polished cheek plates. These plates e x t e n d down to contact a h a r d e n e d a n d polished steel disc which is clamped in the end of the pivot lever arm. Tim pressure on the main pivot bearings, seen in
28
E.J.
SEPPI
fig. 10 is partially relieved b y p r o v i d i n g a h a r d e n e d a n d polished b u t t o n , a t the end of the lever, w h i c h rides on the m a i n guide bar. The pitch of tile lead screw is such t h a t the crystal pivots t h r o u g h 3 m i n u t e s of arc per turn. One-half t u r n is denoted as one screw division (s.d.). W h e n using the (310) planes of q u a r t z as the diffraction crystal one screw division is exactly equal to one x-unit of wave-length. A revolution counter a n d a vernier dial on t h e lead screw give direct readings to 0.001 s.d. Precision step,~dse m o t i o n of 0.02 s.d. per step is o b t a i n e d b y using a solenoid a c t u a t e d pall to drive a 100 t o o t h rachet wheel a t t a c h e d directly to the lead screw. A direct c u r r e n t m o t o r provides rapid m o t i o n from one s e t t i n g to another. This m o t o r is a u t o m a t i c a l l y disengaged w h e n n o t running.
2. Design o/Detector Carriage The collimator a n d d e t e c t o r are m o u n t e d on a p l a t f o r m which rides on a circular t r a c k assembly shown in fig. I. T h e p l a t f o r m m u s t r o t a t e a b o u t a center which coincides w i t h t h e crystal-pivot b e a r i n g t h r o u g h twice the angle of r o t a t i o n of t h e crystal. T h e t o p of t h e outer t r a c k is m a c h i n e d to form a 90 ° t r i a n g u l a r cross-section. T h e p l a t f o r m is fitted w i t h two pairs of bali bearings t h a t ride on t h e two 90 ° faces of the outer t r a c k c o n s t r a i n i n g t h e p l a t f o r m to rotate in a circle. The two i n n e r bearings, close to the pivot, are conical a n d ride on a conical rail whose apexes coincide at the crystal pivot. This is to allow t h e p l a t f o r m to roll w i t h a
et al.
m i n i m u m of sliding friction. The unit is designed to c a r r y a 6000 lb. load. The position of the co!limator a n d detector relative to the crystal is not, of course, related to the precision of the i n s t r u m e n t b u t affects only the int e n s i t y of the t r a n s m i t t e d ";-ray beam. The collim a t o r presently used is 18 inches long consisting of 29 stainless steel strips, 0.016 inches thick a n d 2 inches high. Each sheet is clad on b o t h sides ~dth 0.002 inch thick lead foil. The tapered openings measure 0.050 inches a t tile e n t r a n c e end a n d 0.06! inches at t h e exit. W i t h this collimator an error in the position of the collimator and detector p l a t f o r m at the outer rail of 0.010 inches results in a 3 % decrease in the i n t e n s i t y of the t r a n s m i t t e d beam. W i t h this in m i n d the following simple tracking solution was used. A square groove was m a c h i n e d in the outer track to a c c o m m o d a t e a curved rack which meshes with a spur gear driven b y a selsyn m o t o r a t t a c h e d to tile carriage. The m o t o r is coupled to a selsyn generator whose r o t o r is connected to t h e lead screw of the sine m e c h a n i s m . Since the r o t a t i o n of the lead screw is proportional to sin e a n d the spur gear a n d rack m e c h a n i s m is proportional to e a linear rack would i n t r o d u c e a n error of 0.1 inches a t each end of the travel. A special rack was cut w i t h a gradual increase i n tooth spacing to correspond to t h e difference 12etween e a n d sin ~ as a increased from 0 to '_- 18 °. The greatest deviation of t o o t h spacing from n o r m a l p i t c h was 0.002 inch, which is less t h a n the n o r m a l allowance for b a c k !ash (0.003 inch) of commercial gears.
INSTRUMENTS
AND
METHODS
16 (1962)
17-28;
NORTH-HOLLAND
PUBLISHIN(;
CO.
A GERMANIUM BENT-CRYSTAL MONOCHROMATOR FOR NUCLEAR SPECTROSCOPY E. J. S E P P I ,
II. H E N R I I , ; . S O N , F. B O E H M a n d J. vv'..M. D U M O N D
Cali iornia Institute o.t Tech~ ology, Paxadena, Cali/ornia Received 24 F e b r u a r y 1962
4, precision b e n t c r y s t a l g a m m a - r a y m n n o c h r o m a t o r w i t h s t a t i o n a r y source has been built. T h e i t l s t r u m e n t c o n s i s t s of t h r e e p h y s i c a l l y i n d e p e n d e n t u n i t s : T h e line source (a r a d i o a c t i v e source or t h e anode of a n X - r a y tube), t h e 2 m e t e r - r a d i u s b e n t d i f f r a c t i o n - c r y s t a l w i t h its p i v o t a n d sine-lnotion m e c h a n i s m , a n d t h e h e a v y - d u t y c u r v e d t r a c k f r a m e w o r k which s u p p o r t s t h e collimator, d e t e c t o r a n d shielding. T h e m o t i o n s of tile c r y s t a l p i v o t unit a n d of t h e d e t e c t o r - c a r r i a g e u n i t a r e linked t o g e t h e r in such a w a y t h a t T;he reflection condition is satisfied. R e s u l t s a r e p r e s e n t e d s h o w i n g t h a t t h e precision of t h e
m o n o c h r o m a t o r Ior m e a s u r e m e n t of v - r a y w a v e l e n g t h s is 0.003 x - u n i t s . T h e line w i d t h a t half m a x i m u m , /12, o b s e r v e d w h e n t h e (800) planes of a b e n t g e r m a n i u m c r y s t a l a r e used is 0 0 8 x-units. T h e resolution wlfich has been a t t a i n e d w i t h t h e g e r m a n i u m c r y s t a l is illustrated b y a m e a s u r e m e n t of t h e 244.264keY, 246.056keY, a n d t h e p r e v i o u s l y u n o b s e r v e d 245.237 keV g a m m a line in t h e d e c a y of x,VZaa. Finally, exp e r i t n e n t a l results o b t a i n e d u s i n g t h e m o n o c h r o m a ~ o r to obs e r v e nuclear resonance e x c i t a t i o n in F :9 a n d Mn ~ a r e described.
1. Introduction Curved-crystal diffraction monochromators and spectrometers have been described by several authors. A review article including a complete list of references has been written by DuMondt). The instruments make use of the focusing Bragg-reflection property of a curved c r y s t J , such as quartz. In the monochromator arrangement the line shaped source is situated on the focal circle through ttle curved crystal. Gamma-rays scattered at the Bragg angle are detected by a large NaI counter after having passed through a collimator. The monochromator has considerably bigher luminosity, per unit wavelength interval, as compared to the spectrometer arrangement in which the role of the source and counter is interchanged. It is, therefore, well suited for experiments where gamma-ray or X-ray lines are scanned in a point by point manner over a certain wavelength interval. The CMtech monochromator (3lark I) built by DuMond 1'2'3) uses a stationary collimator and detector system. Both source and crystal move in a fashion that the Bragg condition is maintained at all times. For m a n y applications, however, it is
desirable to have a stationary source, for example if the source is connected to a reactor, an accelerator, or an X-ray tube. The instrument described in this paper is a monochromator with stationary source. It has been primarily designed for nuclear resonance scattering experiments using a powerful X-ray tube. It also is being used as a precision wavelength measuringdevice. It has an accuracysomewhat superior to Mark I. 2. Design of the Monochromator 2.1. D E S C R I P T I O N
OF TIIE CRYSTAl, PIVOT AND THE
DETECTOR CARRIAGE
The monochromator consists of three physically independent units: (a) the crystal pivot, (b) the detector carriage, and (c) the line source. Units (a) and (b) are illustrated in the line drawing, fig. 1. A photograph of the crystal pivot is shown in fig. 2. In this section we ~dll pre~sent a brief description of these two units and refer the reader to the appendix for a detailed description of the mechanical design. The crystal-pivot unit (fig. 1) contains the bent diffraction crystal, the pivot bearing, and the precision sine-screw mechanism. The precision lead screw moves the lever arm which turns the diffraction crystal about an axis provided by the pivot bearing. The sine of the Bragg angle is determined
x) j . W. M. l)uMond, Ann. R e v . Nucl. Sci. $ (1958) 163. l) D. E. Muller, H . C. H o y t , D. J. K l e i n a n d J . \ v . M. DuMond, P h y s . R e v . 88 (1957) 775. z) j . W . M. DuMond, R e v . Sci. I n s t r . 15 (1947) 626. 17
18
E.J.
SE P P I
through the sine-screw mechanism and can be read off directly on a dial. This reading is, of course, direct!y proportional to the wavelength. The design is such that on the monochromator dim the screw SHIELDED DETECTOR
et el.
dixdsion (s.d.), corresponds to one x-unit when the diffraction is from the (310) planes of quartz. Included in the sine-screw mechanism is a calibration cam which is used to correct for small
COLLIMATOR
C U R V E DCRYSTAL
CLAMRNG BLOCKS
\ SINE SCREW MECHANISM
,.. %.
.... ... "" ~
TRACK
~--7
l
. . . . . .
!!'
DETECTOR
[--
i
PIVOT ', ". ",
2___.__~7~7....... ,
.~
-
BEARING
/
/'
-
~
CARRIAGE
CRYSTAL
PIVOT
Fig. 1. L i n e d r a w i n g of t h e bent--crystal m o n o c h r o m a t o r i l l u s t r a t i n g t h e c r y s t a l - p i v o t unit and t h e d e t e c t o r - c a r r i a g e u n i t .
non-linearities in the pitch of the lead screw. The detector-carriage unit (fig. 1) provides for the motion of the heavily shielded detector and collimator system, in such a way that the Bragg reflection condition is satisfied. The shMded detector and collimator are carried on a platform which is constrained by circular tracks to rotate about an axis through the pivot bearing. The motion of the platform is electrically linked to that of the crystal pivot. The design of the detector carriage as a unit mechanically separate from the crystal pivot has the advantage that mechanical strains resulting from tl-e motion of the heavy shielding have no effect on the precise crystal setting which is determined by the sine-screw mechanism. 2.2. DI';SCV. I P T I O N O F Tl-i!'." D I F F R A C T I O N AND CRYSTAI. IIOLi)ER
Fig. 2. A p h o t o g r a p h of t h e monochrormtt,~r c r y s t a ! - p i v o t unit .showing t h e c u r v e d - c r y s t a l clanlping blocks, t h e p i v o t bearing, t h e lever a r m , allll thlt sine-screw lliechauisrll.
CH.YSTALS
The Bragg reflectiou is provided by a thin ooticaliy ground lamina of quartz or germanium clamped between stainless steel blocks which have been profiled to a two-meter radius of curvature. The single crystals are oriented so that the quartz (310) and germanium (400) planes arc' used in the
A GERMANIU3I
BENT-CRYSTAL
MONOCHROMATOR
reflection. The q u a r t z crystal is a square l a m i n a 7.5 cm b y 7.5 cm a n d 2 m m thick. Excellent results h a v e been achieved in the energy resolution a n d reflection power o b t a i n e d using the g e r m a n i u m crystal. The g e r m a n i u m crystal is a r e c t a n g u l a r l a m i n a 7.5 cm b y 3.8 cm a n d 1.3 m m thick. The crystal slab was cut from a n oriented cylindrical single crystal ingot of g e r m a n i u m t . Before bending, the dislocation d e n s i t y of the crystal was less t h a n 5 000 pits/cm 2. T h e slab was optically polished on b o t h sides to a flatness of a b o u t l 0 fringes of sodium light a n d then m o u n t e d in the crystal clampingblocks described below. This crystal is smaller t h a n t h e o p t i m u m size a n d will be replaced ~dth a larger one as soon as larger ingots become available. T h e m e t h o d developed b y DuMond, Lind, a n d Cohen 4) is used to grind the concave a n d convex cylindrical surfaces of the clamping blocks. The blocks h a v e a 5.5 x 4.5 cm aperture. The convex block a p e r t u r e has two ribs r u n n i n g n o r m a l to the generators of the cylinder. The surface of this block is lapped against the m a t i n g concave surface of a cast iron block which has been checked b y t h e F o u c a u l t knife-edge test a n d corrected to b e t t e r t h a n one q u a r t e r of a fringe of sodium light. The microscopic scratches in the surface a n d edges of t h e q u a r t z l a m i n a present a d a n g e r when the crystal is being bent. To minimize the possibility of fracture the q u a r t z is e t c h e d ~ t h conc e n t r a t e d hydrofluoric acid. The scratches are etched preferentially eliminating the s h a r p V c h a r a c t e r of the grooves. The crystal b e n d i n g is done in a dust free box. T h e optical contact is checked b y obseI~ing the interference fringes in the interface as the q u a r t z l a m i n a is rocked across the convex surface of the c l a m p i n g block. A t h i n neoprene gasket (0.5 mm) is placed on the crystal; t h e n the concave block is slowly clamped in place w i t h four spring loaded screws. W h e n b e n d i n g a g e r m a n i u m crystal lamina, interference fringes cannot, of course, be observed; therefore great caution must be exercised to insure a dust free interface. W h e n finally clamped in place tile concave surface of the g e r m a n i u m can be t T h e c r y s t a l slab was p r e p a r e d b y Mono Silicon, inc.. G a r d e n a , California, u n d e r t h e d i r e c t i o n of Dr . Simon A, Prussin.
FOR NUCLE.,kR SPECTROSCOPY
19
checked with the Foucault knife-edge test to verify t h a t it conforms to the convex crystal clamping block.
3. Monochromator Wavelength Calibration 3.1. G A G E B L O C K C A L I B R A T I O N
In the initial wavelength calibration of the monoc h r o m a t o r precision gage blocks were used to d e t e r m i n e the linearity of the m o n o c h r o m a t o r screw. The calibration cam described in the section on the crystal pivot in the a p p e n d i x is used to correct for sma]l dexdations in the l i n e a r i t y of the precision ground a n d lapped screw. The calibration curve A s h o w n in fig. 3 was o b t a i n e d w h e n a linear cam is used. The curve shows the deviation in the screw position from t h a t m e a s u r e d b y gage blocks as a function of the position on the screw. Scales on the figure show t h e m e a s u r e d dimensions in inches a n d also in screw divisions. Curve B of fig. 3 shows POSITION ON SCREW (INCHES) 0.0
2.0
4.0
6.0
8.0
IO.O
CURVE A
m o
_z *i.O
+0.01 ~
~o 0.0
0.00 to
~ -I .0
-0.01
>-
w z
CURVE B
J
÷0.01 ~
~ ÷1.0 u.
:wlii'-'{-':z--i;.-l;l~[~i.-llli!II-
z 0.0 o • -I.0 ~
0 . 0 0 u.
g
-0.01 ti
i
i
/
r
+ 400 ÷2 O0 0 -200 - 400 MONOCHROMATOR POSITION (SCREW DIV.) Fig. 3. C a l i b r a t i o n c u r v e s g i v i n g t h e d e v i a t i o n of t h e s c r e w position from l i n e a r i t y versus t h e m o n o c h r o m a t o r position. Cu r v e A w a s o b t a i n e d w i t h a l i n e a r c a l i b r a t i o n cam. C u r v e B was o b t a i n e d u s in g a c a m profiled to c o r r e c t for t i l e d e v i a t i o n s s h o w n in c u r v e A.
a calibration m e a s u r e m e n t using a cam profiled to correct for the deviations sho,~m on curve A. F o r the curve B the RMS deviation of the points from linearity is 0.002 s.d. D a t a points are not s h o w n in tile region + 2 0 0 t o + 400s.d. I n this region an error 4) j . ~,V. M. D u M o n d , D. A. L i n d a n d E. R. Cohen, R e v . Sei. I n s t r . 18 (1947) 617.
20
E.J.
SEPPI
was discovered which required a change in the shape of the calibration cam. 2\ new cam was installed which now results in a n overall linear monoc h r o m a t o r setting to within the accuracy shown on the curve B. 3.2. G . \ M M A - L I N F X V A V E L E N G T I I C : k L I B H A T I O N
A check on the final calibration h a s been m a d e b y m e a s u r e m e n t s of several g a m m a lines using germanium and q u a r t z diffraction crystals. Consistency checks h a v e been made in two ways : (i) by c o m p a r i n g the measured waveiengths of a single g a m m a l i n e in various orders, n, of reflection from the g e r m a n i u m crystal a n d in first order from the q u a r t z (ii) b y m a k i n g use of c e r t a i n well-established g a m m a - r a y energy c o m b i n a t i o n - e q u a t i o n s k n o w n from the decay schemes. W i t h these two m e t h o d s i n t e r r e l a t e d measurem e n t s are possible covering the entire range of the m o n o c h r o m a t o r and a n overall l i n e a r i t y check h a s been established. In this c h a p t e r the results of the consistency check (i) are analyzed to d e t e r m i n e a formtlla for e s t i m a t i n g the error of the wavelength measurements. Errors calcttlated using the derived formula are t h e n c o m p a r e d with the deviations observed in the consistency check (ii) Finally possible sources of m o n o c h r o m a t o r error are examined. For the calibration investigation g a m m a lines from the well-known decay of T a 18= a n d T a 18a were used. The g a m m a decay-schemes of these isotopes have been established b y Murray, Boehm, Marmier, a n d DuMondS). These two isotopes supply intense g a m m a lines over a considerable portion of the useful energy range of the m o n o c h r o m a t o r . Using s t a n d a r d techniques =) a 0.005 inch d i a m e t e r t a n t a l u m wire was irradiated at the Material Testing Reactor in Arco, Idaho. W i t h this source the w a v e l e n g t h results listed in table 1 were obobtained. Also listed in the table are the results of Murray, et al. s) which were o b t a i n e d with the Mark I i n s t r u m e n t . The errors e listed in table 1 were o b t a i n e d from the formulas: =
/ ~-2 ~,'*:, + e~,
e~ = 0.003 s.d.
(1)
s) j . j . M u r r a y , F. Boehm, P. M a r m i e r a n d J. V¢. M. DuMond, Phys. R e v . 97 (1955) 1007.
el al.
where t h e s t a n d a r d deviation e¢ is the error in t h e position of the g a m m a line resulting from t h e statistical c o u n t i n g error in the d a t a . T h e monoc h r o m a t o r error ~,. represents the non-statistical part of t h e error a n d gives a n indication of the overall reproducibility a n d self-consistency of the i n s t r u m e n t . T h e m o n o c h r o m a t o r error is a measured q u a n t i t y which was d e t e r m i n e d from the d a t a in table 1 t h r o u g h t h e formula Y ~ Y . 2(). 'j ~m =
-
-~
~.~,o),~-N
--
1
-~
-
i.~f~
•
~
(2)
where n is the order of the reflection a n d ).,J is t h e average w a v e l e n g t h found for the group of measu r e m e n t s of the g a m m a line j. T h e symbols ,;fl a n d r.~J represent respectively the observed wavelength a n d statistica[ c o u n t i n g error of the ith measurem e a t of the line j. In the sum three or more ind e p e n d e n t m e a s u r e m e n t s labelled i were t a k e n from columns I to VI of table 1 of the following g a m m a rays; FD, BA, KG, in W 1s2 and DC, EB, GC, IE, ID, IC in W 183. The t o t a l n u m b e r N of p o i n t s s u m m e d was 32. F r o m this procedure the value of ~m was found to be equal to 0.003 s.d. Making use of t h e g a m m a - r a y energy combination-equations k n o w n from the decay schemes of W t 8, a n d W 18a a check has been m a d e on the magnit u d e of cmin e q u a t i o n (1). The c o m b i n a t i o n equations are given in column I a n d II of table 2. A list of the observed values of the left (column I) a n d right (column II) sides of the c o m b i n a t i o n equations is p r e s e n t e d in colunms I I I a n d IV respectively. The statistical consistency of the deviations between the values in columns I I I a n d IV and the errors listed represents a check on the m a g n i t u d e of e=. Based on t h e results of the two m e t h o d s of checking the w a v e l e n g t h calibration we conclude t h a t the error in the m o n o c h r o m a t o r is given b y equation (I) with the value of E,, equal to 0.003 s.d. M o n o c h r o m a t o r errors which c o n t r i b u t e to the overall error e~ result from (i) screw non-linearity, (ii) lack of complete reproducibility of settings, a n d (iii) deviations caused b y t e m p e r a t u r e variations. The contrilmtion from screw non-linearity is found to be less t h a n 0.002 s.d. as measured with gage blocks. No deviations h a v e been measured which
62. 376 ± 0.0015 55.705
62. 3~0 * 0 . 0 0 ~ 5
$5 7 0 1 a 0 . 0 ~ 1
* The errors
given by Murray 5.
limit|.
34 949 • 0,001!
to q 0 % c o n f i d e n c e
is taken from reference
et al 5 correspond
J'@ T h e i d e n t l f i ¢ a t i o , l o f t h e l e v e l ,
* 0.0016
50. 451 • 0,0016 50.281 ~0 0011
Olher
errors
listed are computed
fl0. Z83 • 0 . 0 0 0 8
from
formula
* 0 0010
50. Z82 • 0 . 0 0 1 5 34.950 • 0,0016
50. ZB3 • 0 . 0 0 3 Z 34.951 • 0.0031
50.284
50.b51
50 6 5 4 ± 0 . 0 0 1 7
flO. 649 • 0.0034
50.651,0.0050
59.Z51 ± 0.0020 58
58.953*0.0042
58.954,0.0016
* 0.0012
( I ) In t h e t c x t
50. 2 8 3 ~, 0 . 0 0 0 5 34.950 • 0 . 0 0 1 0
5 0 . 4 5 1 • 0. 0 0 1 6
50.652
954 = 0 . 0 0 1 5
± 0.0008
59 L54 ffi O.OOZI
76.221
58.95Z * 0.0140
76 ZZI • 0.0011
5 9 . 2 3 4 • 0, 0 1 5 0
± 0.0015
* 0 . 0 0 $1
• 0 0009
76.2L1 i 0 0016
46.852
53.951
55.703
6Z. 375 • 0 . 0 0 1 4
76.2L0 i 0,00~0
7 6 . 2 7 . 2 • 0. 0 0 0 9
• 0.0016
• 0. 0 0 1 5
68.968 i 0.0015
79.115
01.162
106.273 ~ 0.0026
100 841 ± 0.0015
IZ3.59Z • O.O01L
146.085 * 0.0015
102.615 • 0 0oil
188.251 ± 0.0024
Average Vll
W,:ighted
ll4. 630 * 0.0008
183
102
J
1
Gamma Average
• 0.001
• 0 001 • 0.001
t 0.003
0.00l ± 0.007
354.004 • 0.010
Z45.Z~7 • 0,008 246 056 ± 0 . 0 0 L
~ 4 4 L64 • 0. 0 0 6
2 0 9 . 8 6 0 * 0. 0 0 5
208.814
16L. $ L ) • 0 . 0 0 2
101 9 3 1 ±
52.59~ • 0.001
Z64.075 • 0+009
• 0 013
I14 ± 0.004
229.32/
ZZ2
198. 356 * 0. 0 0 5
17q. 394 • 0.004
156. ~g6 * 0 . 0 0 ~
102,44| • 0 . 0 0 3
IIb.4ZI
11~.674 • 0.00Z
100.107 t 0.00i
84.69)
67.7~I
65.?L3
VII1
this Exl~,rim.mt
r a y l i n e s u s e d i:t t h c c a l i b r a t i o n
235. 226 ± 0.00~0
in
Tungsten
5th Order VI
gamma
118.630 i 0.0015
Transitions
Tra1~eitions in
4th Order V
183
Tungsten
a;td tungsten
1 1 4 . 6 2 5 a 0. 0 0 3 0
114.630 • 0,0010
5 5 . 7 0 3 t 0,0010
3rd Order IV
~L
X-Units
u~gs en
Crysh~l
Wavelength
T a b l d a ~ i o ; : o[
Germanium
Ray
I.
* 0.003O
~ 0.0016
53.952 • 0.0060 46.852
* 0.00~4
5 5 . 9 5 1 a 0. 0 0 5 4
• 0.00Z0
* 0.0016
46.853
235.226
60.968
68.966 * 0 . 0 0 ~ Z
5 5 . 7 0 2 ~r 0 . 0 0 5 3
79.117
* 0.0017
81161
• 0.0016
108 841 • 0.0016
± 0.0O34
106 2~3 • 0.00~4
0 0031
79.111 • 0.0030
81.16/
106. Z7Z • 0 . 0 0 4 2
ILL593,
12~ 59L ± 0 . 0 0 1 6
108 8 3 7 • 0 . 0 0 3 4
589 • 0.00~1
igl
• 0 0016
146.084 • 0.0021
182614
Znd O r d e r lll
Gamma
146.007 • 0.0053
188.2~4 ± 0.0O~L
18z.618 • 0.0031
l~t Or,h-r II
182 6 1 4 • 0 . o o ~ 1
t
188.248 * 0 00~3
1
1a1 O r c h . r
Gu.trtz CrystaL
TABI.E
1
Energy Mark
k0.0~
i 0.0L
~,6 t 0 , 0 5
04
• 0.00
0l
• 0.07
354 04 • 0.20
2 4 6 05 t 0 . 0 9
Z 4 4 Z6 • 0 . 0 9
Zo9 87 ± 0.07
208.81
162 3J • 0 . 0 4
107.93 • 0.0L
52.59 ~ 0
Z 6 4 + 0 9 • 0. 10
2z9.~7
2LL. 0 5 1 0 . O l
1 9 8 . II ± 0 . 0 6
1i9
156.37 i0
15Z.41 i0.03
I16.40
113.66 t0.02
100.09 * 0.0L
84.67
67.'/4 * 0.01
65.71 • 0.01
IX
.Spectrometer*
Ray
FB ID IC
IE
GC
EA
EB
DC
CB
KF
CB
KG
JF
KH
JG
HD
KI
J}l
BA
[iF
FD
KJ
X
Identaficatlon**
keV
22
E.J.
S E I ' P I el
can be a t t r i b u t e d to a lack of reproducibility of m o n o c h r o m a t o r settings. Deviations due to temp e r a t u r e variations can c o n t r i b u t e significantly to the error of the m o n o c h r o m a t o r reading. The temp e r a t u r e coefficient due to the t h e r m a l expansion of the mechanical p a r t s of the m o n o c h r o m a t o r is e s t i m a t e d to be - (5 to 13) x 10 - 6 2 s . d . per °C
al.
m a x i m u m of the g a m m a lines in W ~s2 a n d W ts3 is 0.16
A2 = - - - - x - u n i t s , n
-E2 o r A E = 1.3 x 1 0 - ' - - - k e V
(3)
where E is the energy in keV a n d n is the order of reflection. Some results obtained with this source are p r e s e n t e d in section 5.
TABLE 2 E n e r g y c o m b i n a t i o n e q u a t i o n s for t u n g s t e n 182 and t u n g s t e n 183 C o m b i n a t i o n F.quation
I
KJ + K J -iJ H -JlI :HF-:-
O b s e r v e d Values for Column I1
II
III T u n g s t e n 182 264.079:1:0.005 222.109 ± 0.003 198.367 ± 0.002 179.397 ~ 0.002 152.444 ~ 0.001
264.075 ± 0.009 222.114--0.004 198.356 : 0.005 179.394 = 0.004 152.441 : 0.003
T u n g s t e n 183 353.989 = 0.002 406.587 ~ 0.002
354.004 : 0.010 406.587 ~ 0.006
JF JG IIF KJ
-~ = ~
KF KG JF KII
FD
=
HD
D C .:- I D CB ~ DC + I D
O b s e r v e d Values for Column I
~ IC = E B . ~ - 1F.
where I is the m o n o c h r o m a t o r setting in screw divisions. The t e m p e r a t u r e coefficient ~) due to the e x p a n s i o n of tile diffraction crystal is 10.4 x 10 -6 Jl s.d. per °C for the q u a r t z crystal a n d 6.9 × l0 -6 ). s.d. per °C for the g e r m a n i u m crystal. The variation of room t e m p e r a t u r e d u r i n g the a c c u m u l a t i o n of d a t a in table 1 was less t h a n 3 °C. The error due to t e m p e r a t u r e v a r i a t i o n s is thus comparable to the error from screw non-linearity. 4. Monochromator Resolution and Reflection Power Use of the g e r m a n i u m diffraction crystal in place of the q u a r t z crystal gives considerable improvem e n t in the resolution a n d i n t e n s i t y o b t a i n e d w i t h the m o n o c h r o m a t o r . The higher order reflections of the g e r m a n i u m (400)n planes provide sufficient i n t e n s i t y to be useful for high resolution measurements. The best resolution we h a v e o b t a i n e d was achieved with a 0.002 inch d i a m e t e r t a n t a l u m wire source. For this source the full w i d t h at one-half
IV
In a n a t t e m p t to b e t t e r u n d e r s t a n d the reflect i v i t y laws of tile g e r m a n i u m crystal, measurem e n t s of g a m m a lines were m a d e in various orders of refection. Tile results h a v e been analyzed b y a least-square fit to a n e q u a t i o n based on the ass u m p t i o n v) of a mosaic crystal. W i t h this assumption it can be s h o w n s) t h a t neglecting the atomic absorption the reflectivity R ( E , n) is a p p r o x i m a t e l y given b y +~ dO R(E, n) = [I -- e-2WC°)RH] (4)
f
where W(0) is a Gaussian with a half-width given b y the crystal mosaic. The range of the integration, e) M. E. S t r a n m a n i s artd E. Z. A "ka., J. Appl. P h y s . 23 (1952) 330; A. l-I. C o m p t o n a n d S. K. Allison, X - R a y in T h e o r y a n d E x p e r i m e n t (D. V a n N o s t r a n d C o m p a n y , Inc., N.Y., 1947). 7) D. A. Lind, W. W. VCest and J. W. M. DuMond, Phys. R e v . 77 (1950) 475. n) J. \V. Ktlowles, Can. J. P h y s . 37 (1959) 203; ~V. H. Zacharia.sen, T h e o r y of X - R a y Diffraction in Crystals ( J o h n \Viley & Sons, N.Y., 1946).
A GERMANIUM
BEN'r-CRYSTAL
MONOCnROMATOR
2,t, is the angle projected at the crystal b y the source. The function R H is given b y
Ru = d~22
t e - 2~(°)
(5)
where d H is the lattice spacing, V is the volume of the unit cell, t is the thickness of the c r y s t a l , f is the atomic scattering powerg), F H is the lattice structure factor, and e -2u(°) is the Debye factor which is a function of the Debye temperature O. In the limit of a thin crystal the energy dependence of the reflectivity (equation (4)) approaches the wellknown E - 2 law v, to). Experimentally we have determined the ratio of the reflectivity for an energy E in the nth order to that for energy E o in the noth order. The experiment furnishes this ratio in the following way: R(E, n)
I(E, n)
T(Eo)
I.flEo)
a(Eo)
R(E o, no) -- l(Eo, no) T(E) 7~(E~" e(-Ei-
(6)
where I(E, n)/l(Eo, no) is the observed ratio of counts in the detector, T(E) is the transmission through the crystal derived from the atomic absorption coefficient, I~(E) is the iutensity of the g a m m a line as measured by EdwardQ 1), and r.(E) is the efficiency of the detector (including air and source absorption). The values of I(E, n) \\,ere measured for several tungsten lines. Ratios were then determined from equation (6) with n o equal to one and with E o equal to 100.107 keV and 107.933 keV, resl)ectively , for gamlna lines in \~.,1~2 and \\:183. These ratios have been plotted in fig. 4. A least-sqnare fit was made of the observed ratios to those calculated through eq. (4) with the crystal mosaic width and the Debye temperature as the variable parameters, and the results are also shown in fig. 4. The curves were calcu!ated based on the vahles 7.5 sec for the mosaic width and 275:'K for the Debye temperature. The crystal thickness was 1.3 ram. The calculated curves and observed Y) J. B e r g h u i s , 1. M. l{aanappel, M . P o t t e r s , B. O. L,oopstra, C. li. MacGillarry a n d A. L. Veenendaal, Acta, C r y s t . $ (1955) 2.78. 10) ~V. F. F d w a r d s , J. w . . M . Du31ond and F. l:k>ehm, N u c I . P h y s . 26 (1961) 670. n) W. F. E d w a r d s , I.;xperimenta! Studies of Conversion Coefficients in Some D e f o r m e d Nuclei (Doctoral Thesis, Calif o r n i a I n s t i t u t e of Technology, P a s a d e n a , Calif., 1960).
FOR NUCI, EAR
SPECTROSCOPY
23
data points are in agreement to udthin the estimated accuracy of the data. It is interesting to conclude from this that the cq. (4) based on a mosaic crystal seems to account for the experimental findings. ........ ~--
\\\ X \
-..
.
i
......
~
i
.......
~
I
,
10 -2
\
\
10-3
\I
~
IO
".
\
'..
i
QUARTZ
'
"
'
\
~.~,
'.o
IO0
.,
IO00
ENERGY
--
k eV
Fig. 4. R e l a t i v e r e f l e c t i v i t y of tile g e r m a n i u m and q u a r t z c r y s t a l s v e r s u s g a m m a - r a y e n e r g y . Based on eq. (6), d a t a points g i v i n g tile observed r e l a t i v e reflectivity lrom t h e g e r m a n i u m (400) planes in v a r i o u s orders are s h o w n as circular and t r i a n g u l a r points for g a m m a lines in KVI~2 a n d \\:l~.~, respectively. T h e d a t a p o i n t s a r e normalized to 1.0 for the tirst-order reflection of t h e g a m m a lines a t 100.107 keV and 107.933keV (hollow points). Tile c u r v e s show resulis o b t a i n e d using eq. (4) in a le,'L~t-square fit to t h e g e r m a n i u m r e i l e c t i v i t y - d a t a . The solid s q u a r e points represent t h e r e t t e c t i v i t y of t h e q u a r t z c r y s t a l r e l a t i v e to t h e gernlaniunl crystal.
\Ve have also coml)ared the reflectivity of our germanium crystal (400) planes to that of our quartz (310) planes. The ratio of the monochromator counting rate with the germanilnn crystal to TABLE 3 C o m p a r i s o n of reflection f r o m g e r m a n i u m a n d frorn q u a r t z "~ L
Gamma Ray E n e r g y (keV) 67,751 100.!07 222.1!4
.
1G , 'l S o, " 0.6 .:_ 0.1 2.4 .:z 0.6 II.1 x_ 2.3
! i
RC;e. RSiO~
1.4 ± 0.2 3.1 ~= 0.8 11.5 t 2.4
IGe/ISiO= is t h e observed ratio of counts multiplied by 1.5 to a c c o u n t for tile differences in a r e a s of tile crystals, /~Ge.RSiO: is t h e r a t i o of t h e reflectivities.
24
E.J.
energy of 245.23 keV. This transition has not previously been obsela, ed because of the existence of the transitions with energy 246.056 a n d 244.264 in T a ~s3 both of which are considerably more interise t h a n the 245.23 keV transition. We h a v e looked for this line with the present i n s t r u m e n t . The source used in the m e a s u r e m e n t was a 0.002 inch t a n t a l u m x~dre. Fig. 5 shows the resrAts which were obtained. T h e 245.23 keV transition is well resolved between the lines at 246.056 and 244.264 keV. Shown in fig. 6, for comparison, are results which were obt a i n e d with the q u a r t z crystal w i t h a s t a n d a r d 0.008 inch d i a m e t e r source. F r o m a least-square
the counting rate with the q u a r t z crystal was observed for several g a m m a lines of W ~s2. The observed ratio wa~s multiplied b y 1.5 to account for the differences in the areas of the crystals. These ratios IG'/I si°~ are given in table 3. (The thickness of the two crystals is given in section 2.) The ratio of the reflectivities Rc'*/R s~°'- presented in table 2 is equal to the product of IC"/I s~°~ a n d the ratio of t h e crystal transmissions TSi°*(E)/TC"(E). F o r a g r a p h ic comparison of the reflectivities the value of the quantities (RSi°:/R G') x (R(E, n)lR(lO0,1) for the three g a m m a e n e r ~ e s are s h o w n as solid squares in fig. 4. WAVE 50.2
et al.
SEPPI
LENGTH - X.U. 50.4
50.6
50,8 9
o -
6.0 i
~
i SCALE ~
i
4.o
//
'
?.0
/\,
oo[.....
2~i.o
2~;.o ENERGY-
°°
a,4.o
key
Fig. 5. T h e 246.056, 245.237, a n d 244.264 keV g a m m a - r a y lines in Vv"i~a o b s e r v e d in t h i r d - o r d e r reflection f r o m g e r m a n i u m .
5. P e r f o r m a n c e o f t h e M o n o c h r o m a t o r 5.1. N E W L I N E O B S E R V E D
IN DECAY OF Ta t~
I n t h e d e c a y scheme of T a ls3 M u r r a y et al:), p r e d i c t e d t h e t r a n s i t i o n F B (see table l) ~ i t h a n
analysis of the d a t a the ratio of the intensity of the 245.24 keV line to t h a t of the 246.056 keV line was found to be (1.15 + 0.03) x 10 -2 a n d the energy of the transition was d e t e r m i n e d to be 245.237 + 0.008 keV. 5.2. N U C L E A R R E S O N A N C E E X C I T A T I O N
A series of e x p e r i m e n t s on nuclear resonance excitation in which the m o n o c h r o m a t o r is used to provide a monoenergetic b e a m of X - r a y s has been performed a n d is described in a separate paper12). F o r t h e purpose of illustration we shall present a brief description of these experiments a n d t h e i r
9 6.o
o 4.a
z
.~ zc
/ WAVE
,
247~0
5o.2
"
,
LENGTH -- X.U.
~,
246;0 ENERGY-
5o6 24.~0
, '~'4:0
5o8 "
keY
Fig. 6. T h e 246.{256 a n d 244.264 keV g a m m a - r a y lines in W t6a o b s e r v e d w i t h t h e q u a r t z (310) plane.
ti) E. I . Seppi a n d F. Boehm, Bull. A m . P h y s . SCc. [II] 6. (1961) 503; F. B o e h m , J. W. M. DuMond, H. E. tlenrikson, a n d E. J . Seppi, Gotlinburg Conference on E l e c t r o m a g n e t i c L i f e t i m e s a n d lh-operties of Nuclear States, 1961; Publication 974, N a t i o n a l A c a d e m y of Science, N a t i o n a l Research Council, W a s h i n g t o n , D.C. (1962).
A (;ERMANIU.'~! BENT-CRYSTAI.
MONOCHROMATOR
results. The arrangement for the experiment is shown in fig. 7. In the experiment a powerful X-ray tube is placed at the source position and the monochromator is used to select a nearly monoenergetic
FOR NUCLEAR
SPECTROSCOPY
25
radius curved-crystal clamping-blocks, length, pitch and precision of lead screws available, the optimum lever arm length to allow large angular magnification with a minimum of bending, deter-
N0I - DETECTOR/ 1.20
. . . . . .
RESONANCE EXCITATION iN F [9 E= 109.894 -+0005 key Ge SO0 PLANES
_
BEN'~TG~IMAN IUM-IRY~TAI - ~ ¢ ~ C L COLL, M ~ I : I TERER
°o
iio
Fig. 7. S c h e m a t i c a r r a n g e m e n t for t h e nuclear resonancee x c i t a t i o n e x p e r i m e n t . T h e b e n t g e r m a n i u m c r y s t a l is used to d i f f r a c t a n e a r l y m o n o e n e r g e t i c b e a m of X - r a y s f r o m t h e b r e m s s t r a h l u n g s p e c t r u m of t h e X - r a y t a r g e t (anode of a n X - r a y tube). T h e diffracted b e a m passes t h r o u g h t h e c o l l i m a t o r a n d is incident on t h e s c a t t e r e r . "file r a d i a t i o n s c a t t e r e d t h r o u g h 135 d e g r e e s is observed w i t h a N a I detector.
beam of X-rays from the bremsstrahlung spectrum incident on the diffraction crystal. A sample of L i F or Mn is placed in the diffracted X-ray beam and scattered radiation is measured with a NaI scintillation detector. A resonance peak is observed as the wavelength of the incident beam passes through the nuclear resonant energy. Figs. 8 and 9 show results which have been obtained for nuclear excitation of the first excited levels in F t9 and Mn 5~. Least-squares analysis of the data gives 109.894 + 0.005 keV for the fluorine resonance position and from the yield a width of (5.7 4- 0.8) x 10 -7 eV was deduced. Analysis of the Mn SS data gives 125.95 4- 0.01 keV for the position and (1.1 4- 0.3) x 10 -6 eV for the width of the resonance. Acknowledgements We wish to thank C. H. Holland and D. Agresti for their assistance in collection and analysis of the data. Appendix MECtIANICAL DESIGN OF THE MONOCHROMATOR
Many considerations leading to the design of the present monochromator are similar to considerations discussed in references 1) and 13). Practical requirements such as the availability of two meter 1~) j . V¢. M. D u M o n d , E r g e b . e x a k t . N a t u r w .
28
(1955) 232.
-/
~
o/ t
-
'\ k
, ~ - 0J6 ~ . , .
) ,
,
,
112.40
,',
,
~1260 112.80 WAVE LENGTH (X - UNfTSI
,
11300
Fig. 8. N u c l e a r resonance e x c i t a t i o n of t h e first e x c i t e d level in F 19.
w o 1.04 _z
RESONANCE
EXCITATION
Mn55
IN
=r= 125.95'- 0.01key Ge 800 PLANES
o I.O2 L~ N J
Q: 1.00 o z I
I
t
I
98.0 WAVE LENGTH
I
I
A
i
98.5 (X- UNITSI
I
Fig. 9. N u c l e a r resonance e x c i t a t i o n of t h e first e x c i t e d level in .Mn~.
mined the over-all dimensions of the instrument. With these proportions established an analysis of all calculable mechanical errors was made. Each error was to be limited to + 0.001 s.d. which corresponds to 0.001 x-units in wavelength resolution for the quartz (310) planes. The design we have finally adopted is illustrated in fig. 1. 1. Design o! Crystal-Pivot Unit
The crystal-pivot bearing, lever arm, and sinescrew assembly is mounted on an octa_hedron constructed of welded square steel tubing, provided with three leveling screws. The pivot shaft, shown in fig. 10, is ground and lapped and rotates in two
26
E.J.
S E P P I et a./.
"'Oilite" bearings. The inside diameter of each bearing is first fitted accurately to the pivot slmft then milled out leaving two narrow strips, 90 ° apart, as shown in tile insert in fig. 10. A wedge
of four parts. The convex crystal clamping-block is screwed to tile upper plate shown in fig. 10. The upper plate is provided with a large hole which clears the conical portion of the centering button.
CENTERINGBUTTON
CRYSTAL CLAMPING
SCREW DIFFERENTIAL SCREW
PLATFORM ./~LEVER ARM
PUSH-PULL LEVELING$
OILITEBEARINGS i SPRINGS
PIVOT
:
,.~
ADJUSTING SCREW
i
:
T
SLOT
~ W E D G E ~ BOTTOM GROOVE --,
o
STRIPS BALL \ADJUSTINGSCREW Fig. 10. lane drawing of the pivot-bearing assembly showing the pivot shaft with the crystal clamping-block and lever arm. The insert gives the details of the "Oilite" bearings designed to provide a uniform bearing pressure on the pivot shaft.
bottom groove is machined opposite the two strips. A bronze spring ~ i t h a mating wedge projection is inserted in the groove. The spring has two strips that are machined to a slightly larger radius than the pivot shaft. A " T " slot in the top of the spring is engaged by a button on tile adjusting screw which raises or lowers the spring thus decreasing or increasing the bearing pressure on the pivot shaft. The two bearings are mounted 180 ° from each other so that tile moment, due to the weight of the lever arm, is taken up by the solid strips of both " O i l i t e " bearings. The axial thrust of the pivot shaft is carried by a ring of ball bearings. The whole pivot assembly is enclosed in ,an oil filled housing with a felt dust seal at the top. The crystal-block mounting assembly consists
Four radial set screws in tile upper plate clamp the centering button allowing small adjustments in the horizontal plane. The cylindrical end of the centering button pivots in a bored hole in tile crystal platform. A differential screw, mounted on the platform, provides small rotational adiustment of the upper plate. The lower part of the platform is fitted to a taper on the main pivot shaft and clamped ~ i t h a cap screw. The lever arm is clamped rigidly to the main pivot shaft. In the horizontal plane the lever is parabolic in shape, to achieve m a x i m u m rigidity ~ , t h minim u m weight. Tile sine-screw mechanism is shown in fig. I I with one bearing plate and cheek plate removed for clarity. Fig. 12 shows a photograph of the sine-
A GER31ANIU.M BENT-CRYSTAL
2,IONOCII.RO~IATOR FOIl N U C L E A R
screw unit. Tile precision ground a n d lapped lead screw engages a bronze split nut. E n d t h r u s t on the lead screw is borne b y a h a r d e n e d a n d polished spherical b u t t o n bearing against a flat h a r d e n e d
SPECTI,~OSCOPY
27
contact. P a r t of the split nut projects radially a n d is fitted with a small roller which rides on the calibration cam. W h e n the lead screw is r o t a t e d clock-wise tile calibration cam constrains the split UPPER ~
MEEHANITE SPACER BLOCK ~ --
GUIDE BAR
PRECISION LEAD SCREW CALIBRATION CAM
BRONZE SPLIT
MAIN GUIDE BAR
PIVOT LEVER ARM
SPLIT BRONZE BEARING PLATE
/ '
,/ HARDENED STEEL DISC
~
HARDENED STEEL CREEK PLATE
i HAROENEO STEEL BUTTON
Fig. I 1. Line d r a w i n g i l l u s t r a t i n g the sine-screw mechanism.
plate (not shown in the figure). The bronze siflit n u t has an a d j u s t i n g screw to achieve proper t h r e a d
Fig. 12. Photograph of the sine-scre~ mechanism with the cover p l a t e removed. The upper guide bar, precision lead screw and main guide bar can be seen. Also seen is the radial projection from the bronze s p l i t nut held to ride on the calibration cam by t h e spring.
n u t in the t a n g e n t i a l direction. If the contact surface of tile cam were straight the axial motion of the split n u t would be d e t e r m i n e d only b y the pitch of the lead screw. However, as shown in fig. I 1, the cam is profiled to correct for nonlinearities in the pitch of the lead screw. As the split nut projection rides along the cam the profiled surface i m p a r t s additional r o t a t i o n to the split uut t h a t appropriately adds to or s u b t r a c t s from the pitch of the lead screw. The total correction range of the cam is equivalent to 0.1 x-units of ?'-ray wavelength. Straddling the split nut is the sliding assembly provided with two split, bronze bearing plates t h a t slide on the main guide bar. A projection on the " 3 I e e h a n i t e " spacer block is held against the upper guide bar b y a fiat spring. The sliding assembly clears the lead screw and is constrained to move in a s t r a i g h t line b y the two guide bars. Tile ends of the bronze split nut arc polished flat a n d contact two h a r d e n e d and polished cheek plates. These plates e x t e n d down to contact a h a r d e n e d a n d polished steel disc which is clamped in the end of the pivot lever arm. Tim pressure on the main pivot bearings, seen in
28
E.J.
SEPPI
fig. 10 is partially relieved b y p r o v i d i n g a h a r d e n e d a n d polished b u t t o n , a t the end of the lever, w h i c h rides on the m a i n guide bar. The pitch of tile lead screw is such t h a t the crystal pivots t h r o u g h 3 m i n u t e s of arc per turn. One-half t u r n is denoted as one screw division (s.d.). W h e n using the (310) planes of q u a r t z as the diffraction crystal one screw division is exactly equal to one x-unit of wave-length. A revolution counter a n d a vernier dial on t h e lead screw give direct readings to 0.001 s.d. Precision step,~dse m o t i o n of 0.02 s.d. per step is o b t a i n e d b y using a solenoid a c t u a t e d pall to drive a 100 t o o t h rachet wheel a t t a c h e d directly to the lead screw. A direct c u r r e n t m o t o r provides rapid m o t i o n from one s e t t i n g to another. This m o t o r is a u t o m a t i c a l l y disengaged w h e n n o t running.
2. Design o/Detector Carriage The collimator a n d d e t e c t o r are m o u n t e d on a p l a t f o r m which rides on a circular t r a c k assembly shown in fig. I. T h e p l a t f o r m m u s t r o t a t e a b o u t a center which coincides w i t h t h e crystal-pivot b e a r i n g t h r o u g h twice the angle of r o t a t i o n of t h e crystal. T h e t o p of t h e outer t r a c k is m a c h i n e d to form a 90 ° t r i a n g u l a r cross-section. T h e p l a t f o r m is fitted w i t h two pairs of bali bearings t h a t ride on t h e two 90 ° faces of the outer t r a c k c o n s t r a i n i n g t h e p l a t f o r m to rotate in a circle. The two i n n e r bearings, close to the pivot, are conical a n d ride on a conical rail whose apexes coincide at the crystal pivot. This is to allow t h e p l a t f o r m to roll w i t h a
et al.
m i n i m u m of sliding friction. The unit is designed to c a r r y a 6000 lb. load. The position of the co!limator a n d detector relative to the crystal is not, of course, related to the precision of the i n s t r u m e n t b u t affects only the int e n s i t y of the t r a n s m i t t e d ";-ray beam. The collim a t o r presently used is 18 inches long consisting of 29 stainless steel strips, 0.016 inches thick a n d 2 inches high. Each sheet is clad on b o t h sides ~dth 0.002 inch thick lead foil. The tapered openings measure 0.050 inches a t tile e n t r a n c e end a n d 0.06! inches at t h e exit. W i t h this collimator an error in the position of the collimator and detector p l a t f o r m at the outer rail of 0.010 inches results in a 3 % decrease in the i n t e n s i t y of the t r a n s m i t t e d beam. W i t h this in m i n d the following simple tracking solution was used. A square groove was m a c h i n e d in the outer track to a c c o m m o d a t e a curved rack which meshes with a spur gear driven b y a selsyn m o t o r a t t a c h e d to tile carriage. The m o t o r is coupled to a selsyn generator whose r o t o r is connected to t h e lead screw of the sine m e c h a n i s m . Since the r o t a t i o n of the lead screw is proportional to sin e a n d the spur gear a n d rack m e c h a n i s m is proportional to e a linear rack would i n t r o d u c e a n error of 0.1 inches a t each end of the travel. A special rack was cut w i t h a gradual increase i n tooth spacing to correspond to t h e difference 12etween e a n d sin ~ as a increased from 0 to '_- 18 °. The greatest deviation of t o o t h spacing from n o r m a l p i t c h was 0.002 inch, which is less t h a n the n o r m a l allowance for b a c k !ash (0.003 inch) of commercial gears.