We have measured the proton longitudinal spin relaxation rate in dilute gaseous silane (SiH4) between 10−2 and 1 amagats and are able to observe the influence of rotational Q branch centrifugal distortion transitions

Beckmann, Peter A.

Burnell, E. E.

English

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Bryn Mawr CollegeScholarship, Research, and Creative Work at Bryn MawrCollegePhysics Faculty Research and Scholarship Physics1977Nuclear spin relaxation and centrifugal distortioneffects in dilute silane gasPeter A. BeckmannBryn Mawr College, pbeckman@brynmawr.eduE. E. BurnellLet us know how access to this document benefits you.Follow this and additional works at: https://repository.brynmawr.edu/physics_pubsPart of the Physics CommonsThis paper is posted at Scholarship, Research, and Creative Work at Bryn Mawr College. https://repository.brynmawr.edu/physics_pubs/119For more information, please contact repository@brynmawr.edu.Custom CitationBeckmann, Peter A. and E. E. Burnell. 1977. "Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas." CanadianJournal of Physics 55.15: 1354-1355.Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas  Peter Beckmann and E Elliott Burnell  Canadian Journal of Physics, 1976, 54.22: 2209-2212. https://doi.org/10.1139/p76-264   Abstract: We have measured the proton ioiigitudinal spin relaxation rate in dilute gaseous silane (SiH4 between 10−2 and I amagats and are able to observe the influence of rotational Q  branch centrifugal distortion transitions.  In order to interpret nuclear spin relaxation measurements in dilute methane (CH4) gas, the effects of Q branch rotational centrifugal distortion transitions had to be taken into account. This was first done phenomenologically (Beckmann et al. (1972), henceforth referred to as BBB) and, subsequently, in terms of a detailed relaxation theory in which the rotational structure of the methane molecule was explicitly taken into account (Beckmann et al. (1976), henceforth referred to as BBO). In this paper we wish to report measurements of the longitudinal relaxation rate T1−1 as a function of density in dilute silane (SiH4) gas at room temperature. The results are shown in Fig. 1 and the reader is referred to BBB and BBO for a discussion of the nuclear magnetic resonance background, the details of the experimental apparatus and technique, and the role of centrifugal distortion. The major drawback to the measurements in Fig. 1 is that we have not gone to sufficiently low density to properly characterize the T1−1 maximum. Since these measurements were performed, however, the rotational structure of the silane molecule has been investigated in detail by Ozier et al (1976), and we feel it important to note that this structure manifests itself in the relaxation experiments. The expression for T1−1 which incorporates the effects of centrifugal distortion in a phenomenological way is given by BBB (see BBO also),    where B0 is the rotation constant (Ozier et al. 1976) and Ca and Cb are the scalar and tensor spin rotation coupling constants (Ozier et al. 1968). The nuclear Larmor frequency is ω0/2π = 30 MHz and Ω/2π is an 'average' centrifugal distortion frequency (BBB). The correlation time τ for molecular reorientation is related to the density ρ by τ−1= <συ>ρ (BBO). The parameter b can be taken to be 4/45 (BBO).  At the density where τ−1 = τMAX−1 = ω0, the second term in [1] can be neglected if ω0 « Ω. Under these conditions, (T1−1)MAX can be calculated with no adjustable parameters since B0 and Ca are well known. This value is (T1−1)MAX = 115 s−1 and agrees very well with the experimental value in the vicinity of 0.02 amagats. At high densities where ω02τ2and Ω2τ2 « 1, (T1τ) −1 is constant (i.e., T1−1 ρ is constant) and the value of <συ> = 1.1 x 1010 (amagats s) −1 is obtained from the measurements using the known values of B0, Ca, and Cd. In turn, the procedure for determining an effective cross section for molecular reorientation can be found in BBO. The contribution to the Ca term is, then, completely specified and is shown in curve {a) in Fig. 1. The only remaining parameter is Ω and Ω/2π = 200 MHz was used to generate curve (b) in Fig. 1. Curve (c) is (a) plus (b). The fact that Cd is only known to ±40% (Ozier et al. 1968) coupled with the incompleteness, of the present results means that the values <συ> and Ω are only known to about ±25%. It is interesting to compare the value obtained for Ω. with that used to fit the methane experiments (150 < Ω /2 π < 240 MHz) (BBB). The relaxation experiments are clearly not sensitive enough to determine if Ω is different for the two gases. The important feature, and indeed, the purpose of this paper, is to show that Ω » ω0: i.e., the  centrifugal distortion transitions must be taken into account in interpreting the nuclear spin relaxation experiments. The phenomenological treatment of the problem given here is the same as that which has been used in methane (BBB); the detailed theoretical treatment of centrifugal distortion effects in methane (BBO) could now be applied to silane since the rotational structure is now known (Ozier et al. 1976). We note that at lower temperatures, the concept of an average distortion frequency becomes meaningless since individual transitions in low-lying rotational J states become important (BBO). The same is true when the nuclear Larmor frequency is coincident with a distortion frequency (BBO). In fact, it may be that the proposals for doing 'relaxation rate spectroscopy' in methane (BBB, BBO) might be better suited to silane since there are several important distortion transitions in the tens of megahertz region (Ozier et at. 1976). We note that to measure T1 at densities lower than those reported here is difficult, but well within present technology (BBO).  Acknowledgments: We thank Myer Bloom for many fruitful discussions. This work was supported by the National Research Council of Canada.  BECKMANN, P. A., BLOOM, M., and BURNELL, E. E. 1972. Can. J.Phys.50, 251. BECKMANN.P. A., BLOOM, M., and OZIER, I. 1976. Can. J. Phys.54, 1712. OZIER, I., CRAPO, L. M., and LEE, S. S. 1968. Phys. Rev. 172,63. OZIER, I., LEES, R. M., and GERRY, M. C. L. 1976. Can. J, Phys.54, 1094.   Figures:   

Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas

Scholarship;  Research;  and Creative Work at Bryn Mawr College

Bryn Mawr College
Scholarship, Research, and Creative Work at Bryn Mawr
College
Physics Faculty Research and Scholarship Physics
1977
Nuclear spin relaxation and centrifugal distortion
effects in dilute silane gas
Peter A. Beckmann
Bryn Mawr College, pbeckman@brynmawr.edu
E. E. Burnell
Let us know how access to this document benefits you.
Follow this and additional works at: https://repository.brynmawr.edu/physics_pubs
Part of the Physics Commons
This paper is posted at Scholarship, Research, and Creative Work at Bryn Mawr College. https://repository.brynmawr.edu/physics_pubs/119
For more information, please contact repository@brynmawr.edu.
Custom Citation
Beckmann, Peter A. and E. E. Burnell. 1977. "Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas." Canadian
Journal of Physics 55.15: 1354-1355.
Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas 
 
Peter Beckmann and E Elliott Burnell 
 
Canadian Journal of Physics, 1976, 54.22: 2209-2212. https://doi.org/10.1139/p76-264  
 
Abstract: We have measured the proton ioiigitudinal spin relaxation rate in dilute gaseous silane 
(SiH4 between 10
−2 and I amagats and are able to observe the influence of rotational Q  branch 
centrifugal distortion transitions. 
 
In order to interpret nuclear spin relaxation measurements in dilute methane (CH4) gas, 
the effects of Q branch rotational centrifugal distortion transitions had to be taken into account. 
This was first done phenomenologically (Beckmann et al. (1972), henceforth referred to as BBB) 
and, subsequently, in terms of a detailed relaxation theory in which the rotational structure of the 
methane molecule was explicitly taken into account (Beckmann et al. (1976), henceforth referred 
to as BBO). In this paper we wish to report measurements of the longitudinal relaxation rate T1
−1 
as a function of density in dilute silane (SiH4) gas at room temperature. The results are shown in 
Fig. 1 and the reader is referred to BBB and BBO for a discussion of the nuclear magnetic 
resonance background, the details of the experimental apparatus and technique, and the role of 
centrifugal distortion. The major drawback to the measurements in Fig. 1 is that we have not 
gone to sufficiently low density to properly characterize the T1
−1 maximum. Since these 
measurements were performed, however, the rotational structure of the silane molecule has been 
investigated in detail by Ozier et al (1976), and we feel it important to note that this structure 
manifests itself in the relaxation experiments. 
The expression for T1
−1 which incorporates the effects of centrifugal distortion in a 
phenomenological way is given by BBB (see BBO also), 
 
 
 
where B0 is the rotation constant (Ozier et al. 1976) and Ca and Cb are the scalar and tensor 
spin rotation coupling constants (Ozier et al. 1968). The nuclear Larmor frequency is ω0/2π = 30 
MHz and Ω/2π is an 'average' centrifugal distortion frequency (BBB). The correlation time τ for 
molecular reorientation is related to the density ρ by τ−1= <συ>ρ (BBO). The parameter b can be 
taken to be 4/45 (BBO). 
 At the density where τ−1 = τMAX−1 = ω0, the second term in [1] can be neglected if ω0 « Ω. 
Under these conditions, (T1
−1)MAX can be calculated with no adjustable parameters since B0 
and Ca are well known. This value is (T1
−1)MAX = 115 s
−1 and agrees very well with the 
experimental value in the vicinity of 0.02 amagats. At high densities where ω02τ2and Ω2τ2 « 1, 
(T1τ) −1 is constant (i.e., T1−1 ρ is constant) and the value of <συ> = 1.1 x 1010 (amagats s) −1 is 
obtained from the measurements using the known values of B0, Ca, and Cd. In turn, the procedure 
for determining an effective cross section for molecular reorientation can be found in 
BBO. The contribution to the Ca term is, then, completely specified and is shown in curve {a) 
in Fig. 1. The only remaining parameter is Ω and Ω/2π = 200 MHz was used to generate curve 
(b) in Fig. 1. Curve (c) is (a) plus (b). The fact that Cd is only known to ±40% (Ozier et al. 1968) 
coupled with the incompleteness, of the present results means that the values <συ> and Ω are 
only known to about ±25%. It is interesting to compare the value obtained for Ω. with that used 
to fit the methane experiments (150 < Ω /2 π < 240 MHz) (BBB). The relaxation experiments are 
clearly not sensitive enough to determine if Ω is different for the two gases. The important 
feature, and indeed, the purpose of this paper, is to show that Ω » ω0: i.e., the  centrifugal 
distortion transitions must be taken into account in interpreting the nuclear spin relaxation 
experiments. The phenomenological treatment of the problem given here is the same as that 
which has been used in methane (BBB); the detailed theoretical treatment of centrifugal 
distortion effects in methane (BBO) could now be applied to silane since the rotational structure 
is now known (Ozier et al. 1976). We note that at lower temperatures, the concept of an average 
distortion frequency becomes meaningless since individual transitions in low-lying rotational J 
states become important (BBO). The same is true when the nuclear Larmor frequency is 
coincident with a distortion frequency (BBO). In fact, it may be that the proposals for doing 
'relaxation rate spectroscopy' in methane (BBB, BBO) might be better suited to silane since there 
are several important distortion transitions in the tens of megahertz region (Ozier et at. 1976). 
We note that to measure T1 at densities lower than those reported here is difficult, but well within 
present technology (BBO). 
 
Acknowledgments: We thank Myer Bloom for many fruitful discussions. This work was 
supported by the National Research Council of Canada. 
 
BECKMANN, P. A., BLOOM, M., and BURNELL, E. E. 1972. Can. J.Phys.50, 251. 
BECKMANN.P. A., BLOOM, M., and OZIER, I. 1976. Can. J. Phys.54, 1712. 
OZIER, I., CRAPO, L. M., and LEE, S. S. 1968. Phys. Rev. 172,63. 
OZIER, I., LEES, R. M., and GERRY, M. C. L. 1976. Can. J, Phys.54, 1094. 
  
Figures: 
 
 


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Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas

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