Investigation on the double reflection neutron crystal monochromator

NUCLEAR

INSTRUMENTS

INVESTIGATION

ON

AND

THE

60(1968)

METHODS

DOUBLE

182-188;

REFLECTION

0 NORTH-HOLLAND

NEUTRON

CRYSTAL

Arsenal,

N.J.,

PUBLISHING

co.

MONOCHROMATOR*

C. S. CHOI Explosives

Laboratory,

FRL, Picatinny

Received 20 November

Dover,

U.S.A.

1967

A small neutron monochromator was built to operate inside the reactor beam port. The device provides for consecutive reflection from two identical crystals, and so gives a beam in the same direction and position independently of the neutron wavelength. Factors affecting the instrumental resolution are discussed. The intensity is necessarily much less than in the single reflection method, but the unwanted second order neutron contaminations

are reduced to less than 10% of what they would be with single reflection. Large fluctuations due to simultaneous Bragg reflection were observed in the primary beam intensity. The effect is much more noticeable with this device than with a single reflection crystal monochromator, and the orientations of the various contributing planes are discussed.

1. Introduction

80 cm and 100 cm respectively. The coarse collimator aperture is 4 cm high and 6 cm wide at the outer end, and diverging inward with 30 min angular divergence. The collimator is surrounded by heavy concrete. The monochromator assembly consists of a Soller collimator, a crystal mount, and an outlet beam path, as shown in fig. 1, and can be disassembled into two parts for easy access to the crystal. The Soller collimator aperture is 4 cm high, 6 cm wide, and 40 cm long, and the width is divided into 15 equal spaces by 14 sheets of 0.4 mm thick steel plate, giving 30 min horizontal angular divergence in fwhm. The surrounding space is filled with a borax and paraffin mixture to reduce neutron leakage. The outlet beam path, 4 cm wide, 4 cm high, and 40 cm long, is oriented parallel to the axis of the Soller collimator and positioned to avoid the direct beam radiation from the Soller collimator by 1” separation. The inner wall of the housing of the crystal mount and the outlet beam path are covered with 1 mm thick cadmium sheet to reduce the background due to scattering from the wall. The surrounding space of the beam path is filled with a paraffin and borax mixture, and 20 cm of lead. Fig. 2 is a schematic diagram of the crystal mount of the parallel reflection double crystal monochromator. Two identical Pb single crystals are mounted on the two sides of the parallelogram, the first crystal on the front frame and the second crystal on the rear frame. The parallelogram is supported by a rotation axis 0 at the center of the second crystal frame, and linked to an angle divider consisting of two equal length levers, AC and BC, which meet at a sliding joint Con the extension arm of the second crystal frame. The joints B and A are the same distance from the axis 0, and BO direction is

A monochromatic neutron beam has been obtained by consecutive transmission through two identical Pbsingle crystals, oriented parallel inside of the beam port of the TRlGA Mark-2 Reactor of the Atomic Energy Research Institute, Republic of Korea. The double reflection method has the inherent disadvantage of weakening intensity, compared with the single reflection method. However, there are also some advantages. Since the direction of a singly reflected beam changes with the neutron wave length according to Bragg’s law, it must be installed outside of the reactor shielding, and requires a large rotatable shield to stop the direct beam from the reactor core. In the case of parallel reflection by two identical crystals, the twice reflected beam is always parallel to the incident beam, which makes it possible to build a monochromator inside of the reactor shielding or beam port, so that the reactor itself acts as a part of the shielding. In the present parallel reflection monochromator, the two crystals are kept parallel with the rotation axis of the second crystal fixed, as illustrated later, to keep the direction of the twicereflected beam fixed. Consequently, the sample table (or detector) is fixed in position which simplifies installation of associated apparatus and shielding regardless of weight. The instrumental resolution of the monochromator and the orientation of simultaneous Bragg reflections were discussed. The neutron beam obtained by the monochromator was analyzed by means of a neutron diffraction unit to examine higher order neutron contaminations. 2. Apparatus The double reflection neutron monochromator constructed in this work consists of two cylindrical tubes with 20 cm dia., namely, a coarse collimator plug and the monochromator assembly, with a length of

* This work was done under the auspices of the Atomic Energy Research Institute, there.

182

Republic of Korea, while the author was

183

THE DOUBLE R E F L E C T I O N N E U T R O N CRYSTAL M O N O C H R O M A T O R

/Y/Y/Y/A:.."......". 100 crn Pb

@

Paraffin

*

1

Borax

Fig. 1. Schematic diagram of double reflection crystal monochromator.

parallel to the side frames of the parallelogram. The axis O and joint A are fixed on the monochromator housing, provided that the OA direction is parallel to the Soller collimator axis. Under these conditions, the shape of the parallelogram is constrained in such a way that the second crystal frame bisects the angle BOA, or the first crystal frame bisects the angle between the side frame of the parallelogram and the direct beam from the Soller collimator. If the reflection plane of the first and second crystals is set to be perpendicular to the frame where they are mounted, the direct beam from the Soller collimator is reflected by the first crystal with an angle 0, propagated parallel to the side frame, intercepted by the second crystal with the same glancing angle 0, and reflected toward the direction parallel to the

original direct beam. Consequently, the emerging beam is always in the same direction and positioned independent of neutron wavelength. The changes of the glancing angle are performed by a worm wheel, which is attached to the second crystal frame and which rotates along the common axis O. A small worm gear is linked to the worm wheel, and its shaft is extended to the outer end of the monochromator through the shielding for remote control. It is designed to cause 2 ° of angle change of the crystals by one revolution of the micrometer. Professor T. Watanabe, University of Osaka, Japan, kindly donated to us the lead crystal, 2" dia. × 10" long, which is grown along the (110) axis at his laboratory. The crystal was machined carefully to two square plates, 5 cm × 5 cm × 1 cm, with identical shape and orientation. The major surface of the crystal plate, 5 cm x 5 cm, is parallel to the (111) plane and the other two side surfaces, 5 crux 1 cm, are parallel to (110) and(ll2) plane respectively. These crystals were mounted on the frame of the parallelogram, so that the (110) plane of each crystal was roughly perpendicular to the frame upon which they were mounted. Parallel positioning was achieved by rotating the first crystal through approximately a 2 rain interval by means of a microscrew which was attached to the frame, until the counting rate of the monochromatic beam reached its maximum value. 3. Instrumental resolution

Fig. 2. Diagram to illustrate the structure of the crystal mount.

The instrumental resolution of the single reflection crystal monochromator has been investigated extensively by Sailor et al.1). Later, Willis 2) and Caglioti et al. 3) extended the investigation to the double axis spectrometer. In accordance with Sailor et al.l), it is assumed that the transmission functions of neutrons

184

c . s . CHOI

....

nl

_. d2

",

. . . .

Fig. 3. Solid line indicates a central ray (¢1 = 0 and *l~= ~12= 0) and dotted line any individual ray. If the plane distances, dt and d2 are the same, then tit = -r~2. through a collimator, and the mosaic spread of the crystal is Gaussian in form. Then the transmission of the incident neutrons at an angle 4 from the axis of the Soller collimator is e x p ( - ~ b 2 / 0 ~ 2 ) , and the reflection probability of a mosaic block oriented at an angle t/ from the mean direction is (K///) exp (-tt2///2). ~ is a measure of the horizontal angular divergence of the Soller collimator and // is that of the crystal mosaic spread. The full width at half maximum (fwhm) of each function is resp. 2(1n2)*-~ and 2(ln2)~'//. K is a constant related to the crystal reflectivity. Let us consider a neutron transmitted through the Soller collimator at angle 41, reflected in the first crystal by a mosaic block at angle r/a, reflected in the second crystal by a mosaic block with orientation t/2, and finally coming to the detector at an angle 4~3 from the central ray, as shown in fig. 3. Denoting the angular divergence of the collimator as cq, mosiac spread of the first and the second crystal as/11 and//2 respectively, the intensity distribution function with respect to 43 becomes

J(4'3) = { / < / ( / / , & ) } " •

f

oe -

2

2

2

exp { - ( 4 x / ~ +ql///x +qz///~)}d6, oc

= (6-4,3,

Then, the intensity distribution

41 =

J(43) becomes;

j(~b3) = {K a/(f12 + f12)~} exp { - (~b2/e2)}. Therefore, the intensity distribution after consecutive parallel reflection by two identical crystals remains the same as that of an incident neutron beam from the Soller collimator, and the direction of the twice reflected beam is parallel to that of the incident beam.

exp [ - {q~2/~2 + (4x - (3)2///2 +

J(6) = {K/(//x//z)} -oc

= =

+

.exp[_62/{cd+

2 2 (//x//.)/(//,

z

For two identical crystals it is assumed that their mosaic spreads are the same so that//1 =//2 - / / a n d the fwhm of the resolution function becomes 2(In 2)~(e 2 +½//2)½. It is interesting to compare these two functions which describe the present system and those of a conventional single reflection m o n o c h r o m a t o r in fwhm.

Double reflection

Single reflection

R1

(~12+ 4//2) "~

J(43) 46)

2

where 6 is the deviation of the glancing angle of an individual ray for a mosaic block from the mean Bragg angle. For the consecutive reflection by two identical planes, 6 = 4x + r h = (~2 "t-/'/2" Using (~2 = ~DI +2~/1 and q53 = ~b2+2q2, the relations between the parameters are conveniently rearranged as; = -,2

To investigate the instrumental resolution, it is desired to express the intensity distribution as a function of 6. Using above relations between the parameters, the resolution function J(6) has the form;

-

+//,b

It is well known that the neutron beam obtained by single reflection is diverged by the crystal mosaic spread. In the double reflection, however, the angular divergence of the twice reflected beam is not affected by the mosaic spread because the second crystal restores the divergence caused by the first crystal. Consequently there is no need of using a second collimator in the double crystal monochromator. 4. The thermal neutron spectrum measured by the monochromator The monochromator was placed in the tangential beam port of the reactor to avoid the direct beam of fast neutrons and g a m m a rays• The absolute energy was calibrated by using the P b ( l l 1) reflection of another diffraction unit. Subsequently, the thermal neutron spectrum from the reactor was investigated, and the intensity distribution as shown in fig. 4 was obtained.

THE D O U B L E R E F L E C T I O N N E U T R O N CRYSTAL M O N O C H R O M A T O R

185

10

/\ rt

j

1

t

i

ID

2 3 4 5

o

I 0.01

\/', % 10

6 7

11

"\

12

"",.,..~, I

I

I

I

I

I

I

0.05

I

I

I

,

I

i

,i

0.1 eV

Fig. 4. The pile neutron spectrum measured.by the double reflection crystal monochromator. The calculated orientations of simultaneous Bragg reflection are indicated by position numbers which are referred "to in table 1.

The intensity peak was hard to find because of a strong parasitic effect due to simultaneous Bragg reflection. The first crystal was immersed fully in the incident beam in the lower energy region but was only partially immersed at 0.07 eV and slipped away completely from the beam near 0.1 eV. As a result, the observed diffraction intensity shows a rapid decrease from 0.07 eV and only a constant background beyond 0.1 eV. The high neutron background is not surprising because the distance between the incident and the twice-reflected beam path is only one inch. The observed thermal neutron spectrum was unlike the original smooth maxwellian distribution because of fluctuations due to simultaneous Bragg reflection. It has long been known that the primary diffraction intensity is modified by simultaneous reflections in a way to increase or to decrease intensity when two or more lattice points lie on the sphere of reflection simultaneously. There are many investigators who observed the simultaneous reflection effect when analyzing the thermal neutron spectrum from a reactor when using a crystal monochromator. Recently, Moon and Shull 4)

have discussed the effect of simultaneous reflections on primary diffraction intensity both theoretically and experimentally. In the present work, the orientation of the simultaneous reflection planes was investigated but the quantitative treatment of the primary intensity changes was not discussed because of improper geometric conditions. In the present double crystal monochromator, the primary reflection planes are (220) and the crystal rotation axis is parallel to the (112) direction. A cartesian coordinate system is conveniently defined in the crystal with the (111), (110) and (112) planes of the reciprocal lattice, with their unit vectors denoted as X, Y,Z, respectively. These coordinates are represented with subscript zero when the crystals take the special positions at which the Bragg angle of the primary reflection plane (220) becomes zero. The X0 represents the direction from which the incident beam came, as shown in fig. 5. The Xo, Yo,Zo coordinates are fixed in the sphere of reflection and X,Y,Z are fixed in the reciprocal lattice space of the crystal. Denoting the unit vector toward the (hkl) reciprocal lattice point by N,

186

c. $. CHOI

the Bragg relation may be expressed as follows, for (220) reflection, 2 = 2dy(Xo Y), for (hkl) reflection, 2 = 2d,.(XoN). Here, (XoY) and (XoN) are positive since the lattice vector on the sphere of reflection makes an acute angle with Xo. The condition of simultaneous reflection by two lattice planes is that their diffraction wavelengths are equal,

d,(Xor) = d.(X0N). Since X o is the unit vector obtained by rotating X by an amount 0 around the Z-axis, it is readily expressed in X,Y,Z coordinates. Rearranging the above equation, cot 0 = {(dy/d,) - (YN) } I (XN). In the cubic lattice, the unit vector of a reciprocal lattice point (hkl) is represented conveniently by the Miller indices in the crystallographic unit cell coordinates. The xyz components are h/r, k/r, l/r, respectively and the plane distance is a/r, where r=(hZ+k2+12) ~. The above equation then becomes, cot 0 = x/3 {(h 2 + k z +/2)_ 2(h - k)} / {(2x/2) (h + k + 1)}. The orientation for simultaneous reflection was calculated for reflection planes with low Miller indices and are listed in table 1. Comparison of the calculated position of the dips with that observed is shown in fig. 4. The agreement is quite crude because the azimuthal angles of the crystals are not accurately determined. 5. Higher order neutron eontamination The monochromatized neutron beam obtained by means of diffraction techniques is always accompanied

•

Xo

(00

kl)

o

(2~m

Fig. 5. Diagram to illustrate simultaneous Bragg reflection.

TABLE 1 Calculated orientations o f simultaneous Bragg reflection for low Miller index planes. No.

Energy

Angle

Simultaneous Bragg

(eV)

(27.0)

reflection planes

1 2 3

0.0117 0.0169 0.0184

49°24 ' 39o14 , 37020 '

311, 002, 222, 222,220,402, 400, 313,

4

0.0190

36034 '

113,313,

5 6 7

0.0206 0.0247 0.0255

34°58 ' 31o29 " 31o00 '

113, 31i, 420, 204, 331, 511,

8 9 10 11

0.0295 0.0433 0.0473 0.0619

28034 ' 23°15 ' 22013 ' 17017 ,

111, 022, 131, 333,404, 5 i l , 331, 511, 020, 420, 240, 024, 004,440, 042,

12

0.0700

18o05 '

i13, 131, 044,151,

by higher order neutrons. Since the thermal neutrons from the reactor have a Gaussian spectral distribution with peak intensity near 1 A, the percentage of the highe order contamination increases rapidly with increasing neutron wavelength in the lower energy region. The reflectivity of a crystal is governed primarily by the crystallographic quantity Q and by the Debye-Waller temperature factor exp ( - 2 M ) , where

Q = K23N2F2/sin(20); M = {6h/(mkO)} (½n/d) 2 {¼+ (T/O)(a(O/T)}, where

@(O/T) =

f

OlT

xl(e x - 1)}dx;

"10

K: Polarization factor (unity for neutron); N: Number of unit cells in a unit volume; F: Crystal structure factor; n: Order of reflection; O : Debye temperature; 2: Neutron wavelength; 0: Bragg angle; T: Absolute temperature. Let us compare the reflectivity of the second order reflection (4740) to the first order (220) for a lead crystal, where the two reflections have the same structure factor. The Q of the second order reflection is ~ that of the first order since the Q is proportional to ;~3. Assuming that O = 88 ° K and T = 300 ° K for the Pb(220) reflection, the ratio of attenuation by the temperature factor in the second to that in the first order reflection is exp ( - 6M) = 0.34. The combined effect of the Q and the tempera-

THE DOUBLE REFLECTION

NEUTRON

187

CRYSTAL MONOCHROMATOR

(A)

(440)

A

I

,x,

• , ~ , ~ e J ° , ° o e • , ° , . • • . ° °

0.011 eV

/i

• . . . . . . . . . .

°.•°

•°.•

. . . . .

. . . . . . . . . . .

, . . . . .

, . . ° ° ° . , , . .

°

0.013 eV

(A)

.(4~o)

(x)

....................

t

A

.. . . . . . . . . . .

(B)

.~ ". . . . . . . . . . . . . . . . . . . . . . .

I T°' /i

l'\ ........................................

(A)

• °•e•*lo°

•

•

,

•

•

*•

J

•

° ....

J

•

(B)

• ....

•.....

.

• .....

° .....

•°...••

?

,o .....

---"•°..*..,°......•..o. i

I

I

I

l0 o

20 °

30 °

I

d

I

40 °

5 o

60 °

2e [PL,(lnl] Fig. 6. Investigation of the second order neutron contamination in the monochromator beam by means of a Pb (111) diffraction unit. A collimator was not inserted between the two crystals of the double reflection crystal monochromator. ture factor reduces the second order reflection to 0.04 times the first order intensity. This estimated discrimination ratio may tend to give a smaller value than that in the real crystal, because the reftectivity with small absorption varies as Q", with n between 1 and 1, as discussed by Bacon and LowdeS). The value n = 1 gives correct reflectivity only when the crystal is thin enough to warrant neglect of both primary and secondary extinction effects. When the crystal is thick and the reflectivity becomes proportional to Q~, the discrimination ratio of the second order reflection becomes 0.12. Therefore, we may assume that the discrimination ratio of the second order reflection is in the order of 10% for Pb (220) reflection. In consecutive reflection by two crystals, the second crystal also discriminates the second order reflection with the same ratio. The overall discrimination ratio is of the order of 1% in the double reflection crystal monochromator. The twice reflected beam from the m o n o c h r o m a t o r was analyzed by Pb (111) diffraction unit to observe the second order neutrons in the lower energy region, with the results shown in fig. 6. The peak marked (A) represents the primary reflection beam by (220) plane of the analyzing crystal. The position of the second order neutron peak is marked (440). No second order contamination was observed (i.e. less than neutron

background). Instead, some other neutrons marked as (X) and (Y) were mixed in the beam. It appears that some other lattice plane which has similar orientation to the (220) plane is also participating in the reflection, because the two crystals are close together. The Bragg reflection written as a function of lattice vectors in the previous section is rearranged as,

2 = 2d(XN) = [2a{2(h + k + 1) 2+ 3(h - k) 2 }~" • {(h 2 + k 2 + l/)x/6}- 13 sin (q~ + 0), tanq~ = ((h + k+/)x/Z}/{(h - k)x/3). Since the wavelengths of the contaminated neutrons were known from the observed data, corresponding (hkl) planes are readily obtained by trial and error methods from above relations. It was found that the peak (X) was caused by (331) reflection and (Y) was the same peak, but observed by (222) reflection of the analyzing crystal. To eliminate the (331) contamination, a very coarse collimator was inserted between the two crystals. The contamination peaks then completely disappeared• 6. Summary

The double reflection crystal monochromator is a simple device for producing monochromatic thermal

188

c.s. cHol

neutron beams. The intensity is not comparable to the single reflection method but the second order contaminations are much less, in the order of 10% or less, than that of the single reflection method. Consequently this device is suitable for obtaining low energy neutrons. The neutron background was high but it could be reduced by improving the mechanical parts. In principle the double reflection m e t h o d should produce less backg r o u n d t h a n the single reflection method, because the second crystal is n o t exposed to the direct beam from the reactor core. Perhaps the m o s t important feature of this device is that the m o n o c h r o m a t i c beam is fixed in position independently of the neutron wavelength.

The a u t h o r is grateful to Mr. S. U. Oh and Y. P. Lee for their help t h r o u g h o u t the course of this work. T h a n k s are also due to Dr. W. U. Whittemore for valuable discussions.

References 1) V. L. Sailor, H. L. Foote, H. H. Landon and R. E. Wood, Rev. Sci. Instr. 27 (1956) 26. 2) B. T. M. Willis, Acta Cryst. 13 (1960) 763. a) G. Caglioti, A. Paoletti and F. P. Ricci, Nucl. Instr. 3 (1958) 223 and Nucl. Instr. and Meth. 9 (1960) 195; G. Caglioti and F. P. Ricci, Nucl. Instr. and Meth. 15 (1962) 155. 4) R. M. Moon and C. G. Shull, Acta Cryst. 17 (1964) 805. 5) G. E. Bacon and R. D. Lowde, Acta Cryst. 1 (1948) 303.