• Journal of Integrative Natural Science
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• v.10 no.2
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• pp.110-114
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• 2017

The connected and simply connected four-dimensional matrix solvable Lie group $Sol^4_1$ is the four-dimensional geometry. A crystallographic group of $Sol^4_1$ is a discrete cocompact subgroup of $Sol^4_1{\rtimes}D(4)$. In this paper, we geometrically describe the crystallographic groups of $Sol^4_1$.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1209-1251
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• 2015

The purpose of this paper is to classify all compact manifolds modeled on the 4-dimensional solvable Lie group $Sol_1^4$, and more generally, the crystallographic groups of $Sol_1^4$. The maximal compact subgroup of Isom($Sol_1^4$) is $D_4={\mathbb{Z}}_4{\rtimes}{\mathbb{Z}}_2$. We shall exhibit an infra-solvmanifold of $Sol_1^4$ whose holonomy is $D_4$. This implies that all possible holonomy groups do occur; the trivial group, ${\mathbb{Z}}_2$ (5 families), ${\mathbb{Z}}_4$, ${\mathbb{Z}}_2{\times}{\mathbb{Z}}_2$ (5 families), and ${\mathbb{Z}}_4{\rtimes}{\mathbb{Z}}_2$ (2 families).

• Korean Journal of Crystallography
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• v.13 no.3_4
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• pp.109-147
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• 2002

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.909-919
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• 2020

The 4-dimensional solvable Lie group Sol₀⁴ does not admit a lattice. The purpose of this paper is two-fold. We study poly-crystallographic groups of Sol₀⁴, and then we study Nielsen fixed point theory on the spaces modeled on Sol₀⁴.

• Korean Journal of Crystallography
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• v.12 no.4
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• pp.227-232
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• 2001

Structure-physical properties relationships for Aurivillius ceramics are discussed, with empha-sis in symmetry considerations. Single-crystal materials and polycrystal ceramics are analysed. Electric and magnetic coupling properties are considered. Colour Symmetry Groups and Texture Analysis tool are emploed. Symmetry conditions for polarisation vectors and inverse pole figures related to Aurivillius phases are given. The influence of crystallographic texture of the physical properties of polycrystalline Aurivillius ceramics is evaluated.

• Journal of Integrative Natural Science
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• v.14 no.3
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• pp.139-146
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• 2021

The purpose of this paper is to classify the torsion-free extensions 1→ℤ³→𝛱→ℤ_𝜱→1 with injective abstract kernel 𝜙 : ℤ_𝜱→Aut(ℤ³). From this classification, we handle the sufficient conditions so as to classify the crystallographic groups of Sol⁴_m,n.

• Korean Journal of Crystallography
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• v.6 no.1
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• pp.56-62
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• 1995

The thirty two point groups consist of eleven Laue groups (centrosymmetric point groups) and twenty one noncentrosymmteric point groups. In this paper, the reciprocal lattice points equivalent under the operations of 21 noncentrosymmetric point groups are derived.

• Korean Journal of Crystallography
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• v.7 no.1
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• pp.88-93
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• 1996

The multiplicity factor, which is defined as the number of different planes in a form having identical interplanar spacing and identical intensity, is tabulated here for the 21 noncentrosymmetric point groups on the basis of their symmetries.

• Korean Journal of Crystallography
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• v.7 no.2
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• pp.196-200
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• 1996

The transformation processes from unit cell data, Miller indices and atomic coordinates of non-standard space groups to the ones of the standard space groups in monoclinic system and the calculation processes of their standard deviations have been shown and computerized. The computer programs can be applied to all the seven crystal systems.

• Transactions of the Korean hydrogen and new energy society
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• v.17 no.1
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• pp.109-116
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• 2006

The heat treatment characteristics of natural talc sample was investigated in diverse analytical view point. The mass decrease comes to heat treatment was resulted by the continuous and the discontinuous process and the obtained result show very similar two step profiles with 8.9 % mass decrease. The dehydroxylation of -OH groups contained talc crystal was analyzed by spectroscopic method and the crystallographic variations was also observed after heat treatment. According to XPS result, the magnesium hydroxide($Mg(OH)_2$) of untreated talc powder changed to magnesium oxides(MgO) after heat treatment.