Metal-containing liquid-crystal phases

Abstract

An iterative perturbation scheme is constructed for LEED calculations. The subplanes comprising an ideal crystal surface are assigned a definite order. and it is shown how to calculate the scattering amplitude to any order in reverse scattering. Each order involves the same computational procedure so that convergence can easily be checked. The method is similar in structure to the Renormalized Forward Scattering (RFS) theory. However. unlike RFS it can be used without supplementation by other methods when there are several inequivalent subplanes in a surface layer, and should therefore be particularly valuable for work on complex surface structures. It has great advantages of speed and low core storage requirements compared with exact methods. The scheme is tested by calculations on a Ni (111) layer, a case for which perturbation theory in the ion-core T matrices diverges, and it is found that the results of calculations to fifth order in reverse scattering are practically identical to the exact results. A convergence study shows that third-order calculations would be sufficient for most purposes.

Structure and Mesomorphism of Neodymium(III) Alkanoates

“…The SmA phase as we describe here, is very comparable to that observed for the alkali metal soaps in the "neat soap" lamellar mesophase. 29 The mesophase behavior in ionic metal alkanoates is discussed in the review articles of Mirnaya et al, 30 Akanni et al, 31 Polishchuk and Timofeeva, 32 and Giroud-Godquin. 33 The M mesophase observed for the neodymium(III) alkanoates up to neodymium(III) undecanoate can be considered as a phase with partially molten alkyl chains, in contrast to the SmA phase with totally molten alkyl chains.…”

On the magnetic anisotropy of lanthanide-containing metallomesogens

“…In particular, when the long molecular axis coincides with the x axis corresponding to the minimum component 1 of the tensor of molecular magnetic susceptibility (cos ␣ϭ1, cos ␤ ϭcos ␥ϭ0) we have ʈ lm ϭ 1 , and ⌬ lm ϭ 1 Ϫ( 2 ϩ 3 )/2 Ͻ0, i.e., the anisotropy is negative. In the other limiting case, in which the long molecular axis is directed along the z axis corresponding to the maximum principal component 3 (cos ␣ϭcos ␤ϭ0, cos ␥ ϭ1), we have ʈ lm ϭ 3 and ⌬ lm ϭ 3 Ϫ( 1 ϩ 2 )/2Ͼ0, i.e., the anisotropy is positive. In the general case, when none of the three principal magnetic axes coincide with the direction of the long molecular axis, the magnetic anisotropy of the liquid crystal is intermediate between the two limiting values 1 Ϫ( 2 ϩ 3 )/2 ͑negative͒ and 3 Ϫ( 1 ϩ 2 )/2 ͑positive͒.…”

“…We come, therefore, to the conclusion that the magnitude and sign of magnetic anisotropy of metallomesogenic complexes in the mesophase depend not only on the molecular magnetic anisotropy of individual metal complexes ͑which is characterized by the difference 3 Ϫ 1 between the maximum 3 and minimum 1 principal components͒, but also on the orientation of the long molecular axis with respect to the principal axes of the tensor of molecular susceptibility. In particular, when the long molecular axis coincides with the x axis corresponding to the minimum component 1 of the tensor of molecular magnetic susceptibility (cos ␣ϭ1, cos ␤ ϭcos ␥ϭ0) we have ʈ lm ϭ 1 , and ⌬ lm ϭ 1 Ϫ( 2 ϩ 3 )/2 Ͻ0, i.e., the anisotropy is negative.…”

“…Note that the trace of the matrix determines the average magnetic susceptibility iso of a powdered sample ( 1 ϩ 2 ϩ 3 ϭ3 iso ), while the anisotropic part of is traceless. Formally, the principal magnetic susceptibilities 1 , 2 , 3 and directions of principal magnetic axes are obtained by diagonalization of the matrix in Eq. ͑2͒.…”

“…[1][2][3][4][5][6][7] In contrast to conventional diamagnetic liquid crystals, which can be oriented only in strong magnetic fields, paramagnetic metallomesogens can be oriented in rather weak magnetic fields. 8,9 For easy alignment of these metallomesogenic molecules in a magnetic field a pronounced magnetic anisotropy is required.…”