- Email: [email protected]
The partial conversion of incoherent into coherent neutron scattering from rotating molecules
Physica B 234-236 (1997)59-60
ELSEVIER
The partial conversion of incoherent into coherent neutron scattering from rotating molecules W . P r a n d l a' *, D . H o h l w e i n ~'b, P. S c h i e b e l a, K . S i e m e n s m e y e r b, J. T u a' b, K . W u l f a, T h . Z e i s k e ~'b alnstitutfiir Kristallographie, Universitiit Tiibingen, Charlottenstr. 33, D-72070 Tiibingen, Germany b Hahn-Meitner-Institut, Glienicker Str. 100, D-14109 Berlin, Germany Abstract
The energy-integrated incoherent scattering of coupled pairs of CH3 rotors in lithium acetate is modulated as Ajo(X ) with x = Q T R p r o t o n _ p r o t o n . At T < 4K the amplitude A stays well below saturation indicating that Tspin > Tlattic e. Powder-diffraction-type experiments can be used to analyse the spin conversion process. Keywords: Molecular rotation; Spin conversion
The energy-integrated incoherent scattering S(20) of neutrons by rotating molecules is independent of Q and 2 0 as long as the rotation may be treated by classical continuous or jump diffusion models [1]. S(20) does not give any information about the geometry or the dynamics of such models. We have observed recently that unhindered NH3 quantum rotators in Ni(NH3)6(PF6) a show modulated S(20) from which we have extracted particle-particle distances and thermodynamic data [2]. Energy integration over the elastic and inelastic contributions given in [-3] results in S(20) = Z w l ( T )F(l,1 ,)Jr2 r(Qx(1,1,20)rsin00, , where w z ( T ) is the Boltzmann factor, F(l,l') contains spin matrix elements and the k'/k factor, J,,(x) is a Bessel function, r the distance between the rotation axis and the protons. Qx = Q T O T A L ( I , l', 20) is the momentum transfer which depends on the energy difference A E = Er -- E, between the initial
*Corresponding author.
and the final states l, 1', respectively, sin c~ is the angle between QT and the reotation axis. For powder samples S(20) has to be averaged, and for trigonal molecules we obtain a dominant elastic term in forward direction (S(20))powder Ajo(QTR) + B + C(QT)R) 6 approximately valid for Q x R < 1.5 ft. Here R = rx/3 is the p r o t o n - p r o t o n distance and jo(x) = sinx/x. In Ni(NH3)6(PF6h six rotors surround an empty lattice position in an octahedral arrangement with a separation of ~ 5 A between the planes of rotors located at opposite corners: rotor-rotor coupling is very weak in this case, and we can indeed describe the observed proton densities by a quantum statistical model [4, 5]. We present here first results with coupled rotors (see Ref. [6] and earlier references given there) in LiAc, (CH3COO)2Li. 2HzO. Measurements were made with the F L A T - C O N E diffractometer at the reactor BER I I / H M I Berlin using a curved linear detector with 400 cells in A20 = 80 ° (2 = 2.41 A). After an initial quick cool down of the samples (30 min from 20 to 1.5 K) data were taken during 3.3 h/run, and then the temperature was raised to
0921-4526/97/$17.00 © 1997 ElsevierScienceB.V. All rights reserved PII S0921-4526(96)00878-2
o
60
W. Prandletal./Physica B 234-236 H99~ 59-60
7O0
i
i
6oo~
soo~
"~0 •
i
LITHIUMACETATEDIHYDRATE" (CH3COO)2Li2H20
400
,7-.. ,,,e 3O0
•
~,\
•e
2OO
I.EI 100 ,,Q
~'n=2"411
o
~
0
-100
'
20
4'0
6b
8'0
20[ ° ]
Fig 1. sidual which effects
The difference spectrum AI = I(1.58 K) - I(99.6K). Refeatures at 48 °, 62 ° and 71 ° are due to Bragg reflections have not been completely cancelled out due to thermal (contraction and DWF).
700 600 500
LITHIUMACETATEDIHYDRATE (CH3COO)2Li 2H20
400~
f " Amplitude t
§ a00:
o
200 100~ .
2'0
,
4'0 T[K]
"2
6'0
~
in Fig. 2. At temperatures above 4 K the amplitude behaves very similar to our earlier results [2]. For T < 4 K, however, the amplitude is lower, instead of approaching saturation as expected. This is a clear indication that during the cooling procedure the conversion of the nuclear spin doublet states which contribute to the E-type wave functions with l = 3 m _ 1 have not been completely converted into A states (l = 3m), resulting in a spin temperature of ~ 7 K for the lowest lattice temperature T = 1.5 K given. Indeed we find from an extrapolation of measured conversion times • [6] a z > 3200 h at T = 1.5 K. At 4 K on the other hand the measured z [6] is 1.6 h, comparable with the time scale of the present experiment. At low temperatures the coupled rotors have a staggered configuration, so the autocorrelation function contains three essentially different distances R i and one might therefore expect that three terms Jo ( Q T R j ) are necessary to describe the modulation in S(20). Since the data can be fitted with only one term we conclude that the only well-defined distance is Rproton_proton within the individual CH3 groups: intermolecular proton-proton distances are washed out by the relative quantum mechanical distribution of protons belonging to different molecules of a pair. We acknowledge the financial support by the B M F T (02-PR4-TUE8) and the D F G (PR44/7-2).
References Fig 2. The amplitude A and the background B of a fit AI = A jo(QrR) + B. Connecting lines are guides to the eye.
the next value (Fig. 2) within 5 rain. The data were corrected for sensitivity differences among the different cells. A difference diagram AI = I ( T ) - I (99.6 K) with T = 1.58 K is shown in Fig. 1. Fitting I with the approximation given above results in amplitude A(T ) a n d background B (T) as plotted
[1] M. Bee, Quasielastic Neutron Scattering (Adam Hilger, Bristol, 1988). 12] P. Schiebel et al., Physica B 226 (1996) 234. [3] D.W. Matuschek and A. Htiller, Can. J. Chem. 66 (1988), 495-505. [41 P. Schiebel et al., J. Phys.: Condens. Matter 6 (1994), 10989-11005. [5] P. Schiebel et al., these Proceedings (ECNS '96), Physica B 234-236 (1997). [6] X.Guckelsberger, H. Friedrich and R. Scherm, Z. Phys. B 91 (1992) 209-219.
ELSEVIER
The partial conversion of incoherent into coherent neutron scattering from rotating molecules W . P r a n d l a' *, D . H o h l w e i n ~'b, P. S c h i e b e l a, K . S i e m e n s m e y e r b, J. T u a' b, K . W u l f a, T h . Z e i s k e ~'b alnstitutfiir Kristallographie, Universitiit Tiibingen, Charlottenstr. 33, D-72070 Tiibingen, Germany b Hahn-Meitner-Institut, Glienicker Str. 100, D-14109 Berlin, Germany Abstract
The energy-integrated incoherent scattering of coupled pairs of CH3 rotors in lithium acetate is modulated as Ajo(X ) with x = Q T R p r o t o n _ p r o t o n . At T < 4K the amplitude A stays well below saturation indicating that Tspin > Tlattic e. Powder-diffraction-type experiments can be used to analyse the spin conversion process. Keywords: Molecular rotation; Spin conversion
The energy-integrated incoherent scattering S(20) of neutrons by rotating molecules is independent of Q and 2 0 as long as the rotation may be treated by classical continuous or jump diffusion models [1]. S(20) does not give any information about the geometry or the dynamics of such models. We have observed recently that unhindered NH3 quantum rotators in Ni(NH3)6(PF6) a show modulated S(20) from which we have extracted particle-particle distances and thermodynamic data [2]. Energy integration over the elastic and inelastic contributions given in [-3] results in S(20) = Z w l ( T )F(l,1 ,)Jr2 r(Qx(1,1,20)rsin00, , where w z ( T ) is the Boltzmann factor, F(l,l') contains spin matrix elements and the k'/k factor, J,,(x) is a Bessel function, r the distance between the rotation axis and the protons. Qx = Q T O T A L ( I , l', 20) is the momentum transfer which depends on the energy difference A E = Er -- E, between the initial
*Corresponding author.
and the final states l, 1', respectively, sin c~ is the angle between QT and the reotation axis. For powder samples S(20) has to be averaged, and for trigonal molecules we obtain a dominant elastic term in forward direction (S(20))powder Ajo(QTR) + B + C(QT)R) 6 approximately valid for Q x R < 1.5 ft. Here R = rx/3 is the p r o t o n - p r o t o n distance and jo(x) = sinx/x. In Ni(NH3)6(PF6h six rotors surround an empty lattice position in an octahedral arrangement with a separation of ~ 5 A between the planes of rotors located at opposite corners: rotor-rotor coupling is very weak in this case, and we can indeed describe the observed proton densities by a quantum statistical model [4, 5]. We present here first results with coupled rotors (see Ref. [6] and earlier references given there) in LiAc, (CH3COO)2Li. 2HzO. Measurements were made with the F L A T - C O N E diffractometer at the reactor BER I I / H M I Berlin using a curved linear detector with 400 cells in A20 = 80 ° (2 = 2.41 A). After an initial quick cool down of the samples (30 min from 20 to 1.5 K) data were taken during 3.3 h/run, and then the temperature was raised to
0921-4526/97/$17.00 © 1997 ElsevierScienceB.V. All rights reserved PII S0921-4526(96)00878-2
o
60
W. Prandletal./Physica B 234-236 H99~ 59-60
7O0
i
i
6oo~
soo~
"~0 •
i
LITHIUMACETATEDIHYDRATE" (CH3COO)2Li2H20
400
,7-.. ,,,e 3O0
•
~,\
•e
2OO
I.EI 100 ,,Q
~'n=2"411
o
~
0
-100
'
20
4'0
6b
8'0
20[ ° ]
Fig 1. sidual which effects
The difference spectrum AI = I(1.58 K) - I(99.6K). Refeatures at 48 °, 62 ° and 71 ° are due to Bragg reflections have not been completely cancelled out due to thermal (contraction and DWF).
700 600 500
LITHIUMACETATEDIHYDRATE (CH3COO)2Li 2H20
400~
f " Amplitude t
§ a00:
o
200 100~ .
2'0
,
4'0 T[K]
"2
6'0
~
in Fig. 2. At temperatures above 4 K the amplitude behaves very similar to our earlier results [2]. For T < 4 K, however, the amplitude is lower, instead of approaching saturation as expected. This is a clear indication that during the cooling procedure the conversion of the nuclear spin doublet states which contribute to the E-type wave functions with l = 3 m _ 1 have not been completely converted into A states (l = 3m), resulting in a spin temperature of ~ 7 K for the lowest lattice temperature T = 1.5 K given. Indeed we find from an extrapolation of measured conversion times • [6] a z > 3200 h at T = 1.5 K. At 4 K on the other hand the measured z [6] is 1.6 h, comparable with the time scale of the present experiment. At low temperatures the coupled rotors have a staggered configuration, so the autocorrelation function contains three essentially different distances R i and one might therefore expect that three terms Jo ( Q T R j ) are necessary to describe the modulation in S(20). Since the data can be fitted with only one term we conclude that the only well-defined distance is Rproton_proton within the individual CH3 groups: intermolecular proton-proton distances are washed out by the relative quantum mechanical distribution of protons belonging to different molecules of a pair. We acknowledge the financial support by the B M F T (02-PR4-TUE8) and the D F G (PR44/7-2).
References Fig 2. The amplitude A and the background B of a fit AI = A jo(QrR) + B. Connecting lines are guides to the eye.
the next value (Fig. 2) within 5 rain. The data were corrected for sensitivity differences among the different cells. A difference diagram AI = I ( T ) - I (99.6 K) with T = 1.58 K is shown in Fig. 1. Fitting I with the approximation given above results in amplitude A(T ) a n d background B (T) as plotted
[1] M. Bee, Quasielastic Neutron Scattering (Adam Hilger, Bristol, 1988). 12] P. Schiebel et al., Physica B 226 (1996) 234. [3] D.W. Matuschek and A. Htiller, Can. J. Chem. 66 (1988), 495-505. [41 P. Schiebel et al., J. Phys.: Condens. Matter 6 (1994), 10989-11005. [5] P. Schiebel et al., these Proceedings (ECNS '96), Physica B 234-236 (1997). [6] X.Guckelsberger, H. Friedrich and R. Scherm, Z. Phys. B 91 (1992) 209-219.