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Explicit expressions for displacement parameters are derived based on power series expansions of displacement components.
For the three-node triangular elements, the displacement parameters are linear variation within one element, so that the second and the third derivatives of displacement parameters are close to zero.
However, in the elimination process, care has to be exercised as to which displacement parameters are to be retained.
And then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force deformatin relationships.
Then explicit expressions for displacement parameters are derived and the exact dynamic stiffness matrix is determined using force displacement relationships.
The corresponding crystal and structure refinement data are summarized in Table 1 and all atomic coordinates and equivalent isotropic displacement parameters are given in Table 2.
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Anisotropic displacement parameters were modelled using the TLS formalism [23,24].
Anisotropic displacement parameters were modelled using TLS rigid-body constraints [23,24].
Unsurprisingly, free refinement of this model was unstable, so the occupancies and isotropic displacement parameters were fixed to sensible values and the positions, declinations and azimuth parameters of the carbon and hydrogen tori were constrained to be equal.
Anisotropic displacement parameters were used and no restraints were introduced on the framework atoms.
Anisotropic displacement parameters were used for all atoms, including the H atoms.
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