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 Nuclear electric quadrupole interaction in single crystals
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Nuclear electric quadrupole interaction in single crystals Petch, Howard Earl
Abstract
The nuclear magnetic resonance absorption technique has been applied to the study of the interaction between atomic nuclei, possessing electric quadrupole moments, and the crystalline electric field gradient existing at the nuclear sites in single crystals. The theory of the dependence of electric quadrupole splitting of nuclear magnetic resonance absorption lines in a single crystal on the orientation of the crystal in an external magnetic field was originally developed by Pound for crystals in which the electric field gradient is axially symmetric. The theoretical section of this thesis presents Dr. Volkoff’s extension of this theory to cover the case of a crystal with nonaxially symmetric electric field gradient at the site of the nuclei being investigated. It is shown that if the interaction is weak, so that only first order perturbation theory is needed, an experimental study of the angular dependence of this splitting for three independent rotations of the crystal about any three mutually perpendicular axes will yield complete information about the orientation of the principal axes and the degree of axial asymmetry of the electric field gradient tensor. The absolute value of the quadrupole coupling constant for those nuclei will also be given. Further, if the quadrupole coupling constant is so strong that second order perturbation effects appear then a single rotation about any arbitrary axis will yield the complete information. The author has performed experiments on the splitting of the Li⁷and Al²⁷ absorption lines in a single crystal of LiAl(SiO₃)₂ (spodumene) and has used the above theory to analyse the results. The absolute value of the quadrupole coupling constant for the Li⁷ nuclei in spodumene is found to be [formula omitted]=75.7±0.5 kc. per sec. The axial asymmetry parameter of the field gradient tensor at the site of the Li nuclei is found to be [formula omitted]= 0.79±0.01. One of the principal axes of this tensor (the y axis corresponding to the eigenvalue of intermediate magnitude) is experimentally found to coincide with the b crystallographic axis of monoclinic spodumene as required by the known symmetry of the crystal. The other two principal axes are in the ac plane, the z axis (corresponding to the. Eigenvalue [formula omitted] of greatest magnitude) lying between the a and c axes at an angle of 46.5º±1º with the c axis. It is shown that the four Li atoms per unit cell all exist in equivalent crystal positions as required by the crystal symmetry. The absolute value of the quadrupole coupling constant for the Al²⁷ nuclei in spodumene is found to be [formula omitted]=2960±10 kc. per sec. The axial asymmetry parameter of the field gradient tensor at the site of the Li nuclei is found to be [formula omitted]=0.95±0.01. One of the principal axes of this tensor (the x axis corresponding to the eigenvalue of smallest magnitude) is experimentally found to coincide with the b crystallographic axis of monoclinic spodumene as required by the known symmetry of the crystal. The other two principal axes are in the ac plane, the z axis lying between the a and c axes at an angle of 55.5º±1º with the c axis.. It is shown that the four Al atoms per unit cell exist in equivalent crystal positions.
Item Metadata
Title 
Nuclear electric quadrupole interaction in single crystals

Creator  
Publisher 
University of British Columbia

Date Issued 
1952

Description 
The nuclear magnetic resonance absorption technique has been applied to the study of the interaction between atomic nuclei, possessing electric quadrupole moments, and the crystalline electric field gradient existing at the nuclear sites in single crystals.
The theory of the dependence of electric quadrupole splitting of nuclear magnetic resonance absorption lines in a single crystal on the orientation of the crystal in an external magnetic field was originally developed by Pound for crystals in which the electric field gradient is axially symmetric. The theoretical section of this thesis presents Dr. Volkoff’s extension of this theory to cover the case of a crystal with nonaxially symmetric electric field gradient at the site of the nuclei being investigated. It is shown that if the interaction is weak, so that only first order perturbation theory is needed, an experimental study of the angular dependence of this splitting for three independent rotations of the crystal about any three mutually perpendicular axes will yield complete information about the orientation of the principal axes and the degree of axial asymmetry of the electric field gradient tensor. The absolute value of the quadrupole coupling constant for those nuclei will also be given. Further, if the quadrupole coupling constant is so strong that second order perturbation effects appear then a single rotation about any arbitrary axis will yield the complete information.
The author has performed experiments on the splitting of the Li⁷and Al²⁷ absorption lines in a single crystal of LiAl(SiO₃)₂ (spodumene) and has used the above theory to analyse the results.
The absolute value of the quadrupole coupling constant for the Li⁷ nuclei in spodumene is found to be [formula omitted]=75.7±0.5 kc. per sec. The axial asymmetry parameter of the field gradient tensor at the site of the Li nuclei is found to be [formula omitted]= 0.79±0.01. One of the principal axes of this tensor (the y axis corresponding to the eigenvalue of intermediate magnitude) is experimentally found to coincide with the b crystallographic axis of monoclinic spodumene as required by the known symmetry of the crystal. The other two principal axes are in the ac plane, the z axis (corresponding to the. Eigenvalue [formula omitted] of greatest magnitude) lying between the a and c axes at an angle of 46.5º±1º with the c axis. It is shown that the four Li atoms per unit cell all exist in equivalent crystal positions as required by the crystal symmetry.
The absolute value of the quadrupole coupling constant for the Al²⁷ nuclei in spodumene is found to be [formula omitted]=2960±10 kc. per sec. The axial asymmetry parameter of the field gradient tensor at the site of the Li nuclei is found to be [formula omitted]=0.95±0.01. One of the principal axes of this tensor (the x axis corresponding to the eigenvalue of smallest magnitude) is experimentally found to coincide with the b crystallographic axis of monoclinic spodumene as required by the known symmetry of the crystal. The other two principal axes are in the ac plane, the z axis lying between the a and c axes at an angle of 55.5º±1º with the c axis.. It is shown that the four Al atoms per unit cell exist in equivalent crystal positions.

Genre  
Type  
Language 
eng

Date Available 
20120229

Provider 
Vancouver : University of British Columbia Library

Rights 
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

DOI 
10.14288/1.0085542

URI  
Degree  
Program  
Affiliation  
Degree Grantor 
University of British Columbia

Campus  
Scholarly Level 
Graduate

Aggregated Source Repository 
DSpace

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Rights
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.