Determination of anisotropic magnetic susceptibility of a biaxial crystal via orientational fluctuation of its microcrystalline suspension under magnetic field

Abstract

The ratio of the anisotropic magnetic susceptibility r χ [ ð 2 À 3 Þ=ð 1 À 2 Þ] of a biaxial crystal was determined using a suspension of its microcrystalline powder. The suspension was rotated in a static magnetic field and subjected to in situ X-ray diffraction measurement. Following the theory proposed previously to relate the X-ray half-widths to the orientation fluctuation, the experimentally obtained half-widths were translated to the orientation fluctuation that is relevant to the magnetic anisotropy 2 À 3 , 1 À 3 , and 1 À 2 . L-Alanine and D-mannitol microcrystals were investigated and their r χ values were determined as 1.0 and 1.2, respectively, which were in good agreement with those reported in the literature. By using the determined r χ value of L-alanine, it was demonstrated that this value is a crucial parameter for determining the experimental magnetic condition when preparing a three-dimensional magnetically oriented microcrystal array that produces high-quality X-ray diffractions.

Single-Crystal X-ray Diffraction Analysis of Microcrystalline Powders Using Magnetically Oriented Microcrystal Suspensions

“…For the present experimental condition, the square of the fluctuations is expressed as follows: Here, K = 2μ 0 k B T /( VB 2 ), where μ 0 , k B , T , and V represent the magnetic permeability of vacuum, Boltzmann constant, temperature, and volume of the microcrystal, respectively, and R mag = T int / T rot . Previously, we have reported that χ 1 – χ 2 ≅ χ 2 – χ 3 for l -alanine. Inserting this relation, we obtain ⟨ω 1 2 ⟩ = ( R mag + 1), ⟨ω 2 2 ⟩ = 2 −1 (2 R mag + 1) −1 ( R mag + 1), and ⟨ω 3 2 ⟩ = 2 −1 ( R mag + 1) R mag –1 , where common factors are ignored.…”

“…Here, K = 2μ 0 k B T/(VB 2 ), where μ 0 , k B , T, and V represent the magnetic permeability of vacuum, Boltzmann constant, temperature, and volume of the microcrystal, respectively, and R mag = T int /T rot . Previously, we have reported 17 that χ 1 − χ 2 ≅ χ 2 − χ 3 for L-alanine. Inserting this relation, we obtain ⟨ω 1 2 ⟩ = (R mag + 1), ⟨ω 2 2 ⟩ = 2 −1 (2R mag + 1) −1 (R mag + 1), and…”