Memo: To SANS Staff
From: J.G. Barker
Date: 3/20/2007
File: det_eff_cor2.doc
Correction to Detector at Large Scattering Angles
The previous memo on this topic, sent out on 2/7/2007, did not include the effect of
aluminum attenuation or 'wall effect' on detector efficiency. For the Ordela 2660N
detectors that are currently used on both 30m SANS instruments, there is 4.8 mm thick
spherically formed 6061 aluminum sheet for the dome that holds the 4He gas reservoir,
and 3.2 mm 6061thick flat sheet separating the 4He reservoir from the 3He + CF4
detection gas.
Typical Al-6061 composition, obtained from ASM Metals Handbook, in wt % is:
Al 96.67% Si 0.6% Fe 0.7%, Cu 0.28%, Mn 0.15%, Mg 1.0 %, Cr 0.2 %, Zn 0.25 %, Ti
0.15%.
The phonon cross-section is estimated from the total cross-section for aluminum found in
Brookhaven's Barn Book, after subtracting the absorption cross-section. Since the solid
angle of detection viewed from aluminum phonon scattering site is ≈ 2π, only half of
phonon scattered neutrons are scattered at significantly large angles to avoid the detection
gas volume. The total effective attenuation cross-section for 6061 aluminum is than the
sum of half of phonon and all of absorption terms.
Source
al (cm-1Å-1)
Absorption from aluminum
0.00773
Absorption from alloying elements
0.00089
Phonon scattering from Al (Barn book)
0.0021
Total
0.00967

Also, not all absorbed neutrons are counted by the detector. In particular, the
discriminator preferentially discriminates 'wall affected' neutrons. These neutrons are
absorbed near the front or back aluminum plates of active gas volume, where the total
charge induced by charge particle collisions with the gas is reduced due to one of the
charge particles (triton or proton) penetrating aluminum wall.
The detector efficiency including corrections for aluminum attenuation and 'wall affect'
can be calculated by
 d ( )  W( )e  Alt Al 1  e   HetHe 
where for Ordela 2660N detectors tAl = 0.8 cm, tHe = 2.5 cm, and He = 0.146 cm-1Å-1 x 
for 2.0 bar 3He detection gas, and W() is the fraction of 3He absorption events that are
counted by the electronics. The fraction is expected to decline somewhat at longer  due
to higher fraction of events occuring closer to gas separation sheet , thus greater
likelihood that one charge particle dissapates some energy into the sheet (wall effect),
thus lowering amount of charge collected below electronics discriminator setting.
The wall effect term is estimated by dividing the measured detector efficiency by the
efficiency calculated from 3He absorption attenuated by aluminum structure:
 (Å)
D / W() (calc.)
D (measured)
W() (estimated..)
5Å
0.8036
0.70
0.87
6Å
0.8436
0.74
0.88
8Å
0.8835
0.76
0.86
10 Å
0.8941
-
-
12 Å
0.8911
0.76
0.85
15 Å
0.8758
0.71
0.81
20 Å
0.8421
0.68
0.81

As originally reported By Lindner (2000), and most recently by Brulet (2007), the
detector efficiency will vary with scattering angle. The longer path through detecting gas
will increase fraction absorbed, but only after being attenuated by longer path length
through aluminum. Higher scattering angles will also reduce the average distance of 3He
absorption from aluminum wall, thus causing wall effect W() to be reduced. Since
wall effect's scattering angle dependence is both expected to be weak and is difficult to
model, we ignore it's effect by approximating W(,) ≈ W(). For simplicity, we also
model the curved dome as being flat. A simplified expression for the detector efficiency
from flat gas detectors oriented perpendicular to the beam is

 d ( ,  )  W (  )e   Al tAl / cos( ) 1 e
 He tHe / cos( )

where  is the neutron wavelength, tHe is the thickness of active gas volume, tAl is the
thickness of aluminum in front detection gas,  is the scattering angle and W0 is constant
used to approximate the wall effect. The cross-section for absorption in 3He is
 He /   N A A P / RT
where NA = 6.02e23 is Avogrado's number of atoms per mole, R = 8.314 J/mole/K is the
gas constant, T is the absolute temperature, P is the pressure of the absorbing gas
molecule and A is the absorption cross-section for molecule normalized by wavelength.
For 3He, A = 5333 barns / 1.8Å = 2.963e-25 m2 / Å. For all four Ordela 2660N
detectors, The active thickness t = 2.5 cm, 3He fill pressure is 2.0 bar = 202 KN/m2
yielding He/ = 0.146 cm-1Å-1.
To correct for the increase in detector efficiency at large scattering angles, the data
should be multiplied by the factor:
 D ( ,  ) e
f ( ) 

 D ( , 0)
  Al tAl / cos( )
1  e
 He tHe / cos( )

e   Al tAl 1  e   HetHe


The plot shows the correction as a function of scattering angle for  = 5 Å and 10 Å.
The detector sensitivity correction made by dividing the 2D data with the DIV file
corrects for pixel by pixel variations in the detector efficiency. The DIV file is currently
created by measuring the scattering from plexiglass at 4.0 m sample to detector distance
and  = 6 Å. The maximum scattering angle is 6.5˚ in the corners of the detector. The
large angle detector efficiency correction under these conditions never exceeds 0.15%.
Conclusion
I suggest that we incorporate this correction into the IGOR SANS data reduction macro.
The correction can be made at the same time as the cos3() Jacobian is made.
1.05
det_ef_cor3.qpc
5A
10 A
1.03
d
d
 () /  (0)
1.04
1.02
1.01
1
0.99
0
5
10
15
 (degrees)
20
25
30
Plot of the correction factor f() versus scattering angle for the Ordela 2660N detector.
The correction approaches 5% for  = 5 Å at the maximum scattering angle of  = 30˚
(NG7 at SDD = 1.0 m with 20 cm offset). 

References:
A. Brulet, D. Lairez, A. Lapp, J-P. Cotton (2007) J. Appl. Cryst. 40 p165-177.
P. Lindner, F. Leclercq, P. Damay (2000) Physica B 291 p152-.