Transcript Document
Прямое наблюдение эффекта Бормана при дифракции нейтронов по Лауэ в кристаллах кремния
Е.О.Вежлев 1,2 , В.В. Воронин 1,2 , И.А. Кузнецов 1 , С.Ю. Семенихин 1 , В.В. Федоров 1,2 1 Петербургский институт ядерной физики 2 Санкт-Петербургский государственный политехнический университет
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
Outline
• Motivation • “Kato” theory of diffraction for deformed (bent) crystal Influence of external force on diffracting neutrons • Two-crystal scheme introduction • Borrmann effect • Experimental observation of theory effectiveness for proposed scheme • m i / m G experiment with neutron • Summary
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
Motivation
• For Laue diffraction with Bragg angles close to the right one there is a significant diffraction enhancment factor of an external affect on the neutron*:
K d Si
87 0
B
10 7 10 8 • This factor can be used for observation of small external forces affecting the diffracting neutrons • But, we must be sure that all of the dynamical diffraction predictions work well in thin (up to the 220 mm) crystals *V.V. Fedorov et.al. JETP Lett. 85, 82 (2007)
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
Laue neutron diffraction in weakly deformed crystal
B
z
k g
(hkl)
y
(1)
Neutron difraction in weakly deformed crystal can be described by imposing “Kato forces”*:
f k
(
y z
2(
k
0
k
0 2
k
0 4 cos
B
z
1
g
) (
y z
Deviation from exact Bragg condition
“Kato trajectories” are determined by the equation:
k g
(2)
*N.Kato , J. Phys. Soc. Japan (1963)
19
, 971
Вежлев Егор (ПИЯФ)
2
z
y
2 tan(
B
)
m
0
f k
(1) or
(2)
2F g V/d
ИТЭФ, 11/22/2011
Influence of an external force
Parameter of deviation from exact Bragg condition: 2(
k
0
g
) /
k
0 2 ,
k
0
k
0
g
/ 2 Deformation changes the reciprocal lattice vector External force changes the incident neutron wave vector
k
0
k
0
g
k
0
k
0
g
/ 2
In fact, F ext ||g is equivalent to the gradient of interplanar distances with the value F ext /2E n Вежлев Егор (ПИЯФ)
f K
The “Kato force” for the neutron in this case:
tan(
B
)
d F ext
2
E n
ИТЭФ, 11/22/2011
Influence of an external force
B
z
k k g g
y
Force affecting the neutron
F n ||Z
Neutron trajectory equation (Laue diffraction case): 2
z
y
2 2 tan (
m
0
B d F n
2
E n
Equation for freely flighting neutron: We obtain a gain factor for the diffracting neutron
K d
2
z
y
2
F n
2
E n
2 tan (
B
)
m
0
d
For silicon (220) planes
Вежлев Егор (ПИЯФ)
K d
2 tan (
B
5
B
(84 0 87 ) (10 7 10 8 )
ИТЭФ, 11/22/2011
Two-crystal scheme of the experiment
S
1
F
Where
2 2
x
1
F
tanh
2 cos
L
B
g
External force shifts the spot of the neutron beam at the exit surface:
1
F
tan 2
B L
2
m dE
0
n F n
1
F
Due to well known Borrman effect* amplitudes will be different for two Bloch waves ψ(1) and ψ(2). In fact, we got different values of absorption for this two types of waves:
a
1,2 ~ exp
L eff
1
2
0
g
Zero-harmonic of absroption g-harmonic of absorption *H. Rauch, D. Petrachek, in Neutron Diffraction (Springer, Berlin, 1978) 303-351
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
Two-crystal scheme of the experiment
In case of strong Borrmann effect (strong absorbing crystal):
2
L
g
/ cos
1
S F
tan 2
n L
2
F n
For (220) plane of Silicon:
L
10
cm
,
S
1
mm
,
B
80
So, only one Bloch wave comes to the exit surface of the crystal.
The resolution for this setup is:
W F
S
tan 2
n
L
2
slit size
S
,
W F
10
12
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
Experimental observation of Laue diffraction in the large silicon crystal (L=220 mm)
220 silicon plane intensity reflex
Effective crystal length can reach few meters for 220 mm silicon crystal
One-crystal scheme Theoretical prediction wtihout taking Borrmann effect into account Вежлев Егор (ПИЯФ) Two-crystal scheme ИТЭФ, 11/22/2011
Experimental observation of Laue diffraction in the large silicon crystal (L=220 mm)
The intensities ratio for one- and two-crystal schemes of the setup
Ratio varies from 3/2 to 1/2 •
Ratio depends on two-crystal scheme setup geometry
•
Experimental results coincide with the theory Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
Sun
m i /m G Possible applications. experiment with neutron (I)
F G
F r
F G = F r
for the Earth ?
m n i m n G
m i
G m
?
Earth neutron
F G
F r
for the neutron
F m
Possible arrearence of the non zero force:
F G
F i m m g n R
2 1
m i n m i
/
m n g
/
m g
m i
/
m g
1 13 1
m n i m n g
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
m i /m G Possible applications. experiment with neutron (II)
0:00
F G
F r
F m
13 1
m i n m n g
F m
g c
F m changes its sign in the laboratory coordinate system
12:00
g c F m
g c
Daily oscillations of the
F m value
The possible sensitivity of the setup:
ext
10
17
Вежлев Егор (ПИЯФ)
(
m i
m G
) /
m G
4 10
5
*Present accuracy 2∙10 -4 (Schmiedmayer, 1989)
ИТЭФ, 11/22/2011
m i /m G Possible applications. experiment with neutron (III)
Large silicon crystal (220 mm)
Layout of the experimental setup (Already mounted on the beamline of WWR-M
)
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011
n
WWR-M reactor (PNPI, Gatchina)
Вежлев Егор (ПИЯФ)
Silicon (220)
ИТЭФ, 11/22/2011
Summary
•
Two-crystal scheme of the Laue diffraction with bragg angles close to the right one is a very sensitive experimental instrument (resolution to the external force reaches 10 -12 eV/cm)
•
The uncertaintity of measuring inertial to gravitational mass ratio for the neutron (in fact, direct test of PoE) can reach magnitude ~10 -5
•
It’s possible the new instrument for measuring e n
Вежлев Егор (ПИЯФ) ИТЭФ, 11/22/2011