• 대한수학회보
• /
• 제57권4호
• /
• pp.909-919
• /
• 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.

• 대한수학회지
• /
• 제44권5호
• /
• pp.1121-1137
• /
• 2007

There are 7 types of 4-dimensional solvable Lie groups of the form ${\mathbb{R}^3}\;{\times}_{\varphi}\;{\mathbb{R}}$ which are unimodular and of type (R). They will have left. invariant Riemannian metrics with maximal symmetries. Among them, three nilpotent groups $({\mathbb{R}^4},\;Nil^3\;{\times}\;{\mathbb{R}\;and\;Nil^4)$ are well known to have lattices. All the compact forms modeled on the remaining four solvable groups $Sol^3\;{\times}\;{\mathbb{R}},\;Sol_0^4,\;Sol_0^'4\;and\;Sol_{\lambda}^4$ are characterized: (1) $Sol^3\;{\times}\;{\mathbb{R}}$ has lattices. For each lattice, there are infra-solvmanifolds with holonomy groups 1, ${\mathbb{Z}}_2\;or\;{\mathbb{Z}}_4$. (2) Only some of $Sol_{\lambda}^4$, called $Sol_{m,n}^4$, have lattices with no non-trivial infra-solvmanifolds. (3) $Sol_0^{'4}$ does not have a lattice nor a compact form. (4) $Sol_0^4$ does not have a lattice, but has infinitely many compact forms. Thus the first Bieberbach theorem fails on $Sol_0^4$. This is the lowest dimensional such example. None of these compact forms has non-trivial infra-solvmanifolds.

• 한국세라믹학회지
• /
• 제31권9호
• /
• pp.1060-1068
• /
• 1994

Stable zirconia sol was prepared from zirconium butoxide Zr(OC4O9)4 as a precursor and ethylacetoacetate(EAcAc) or diethylene glycol(DEG) as a chelating agent under ambient agent under ambient atmosphere by Sol-Gel process. The sythesized sol was coated on 304 stainless steel substrate by dip coating, thereafter zirconia film could be obtained by heat-treatment at $600^{\circ}C$. The characteristics of coating film were determined by FT-IR, XRD, and ellipsometion peak represented Zr-O-Zr bonding of tetragonal phase was shown at 470cm-1. Crystallization of zirconia gel and film from amorphous state to tetragonal phase started at 40$0^{\circ}C$, and then transformed into monoclinic phase around $700^{\circ}C$. Zirconia film coated on 304 stainless steel substrate showed relatively low porosity of 16% when it was coated with 0.4M zirconia sol and thereafter heat-treated at 80$0^{\circ}C$ and the film was densified continuously up to 90$0^{\circ}C$. The zirconia film of 10 nm thick acted as a protective layer against oxidation up to $700^{\circ}C$.

• 한국세라믹학회지
• /
• 제28권1호
• /
• pp.60-66
• /
• 1991

The polymeric alumina sol was prepared by partial hydrolysis of aluminum sec-butoxide reacted with acetylacetone and its characteristics was investigated. The effects of alcohol solvent, acetylacetone, and acid concentration to the sol were investigated. FT-IR and Al27-MASNMR were used to study hydrolysis and polymerization reaction of aluminum complex. Synthesized sol showed the characteristics of polymeric alumina sol. To make a clear polymeric alumina sol, the optimum contents of acetylacetone, H2O and alcohol solvent were 0.4-0.6 mole, 0.25-1.25 mole, 3-5 mole per one mole alkoxide respectively. As a result of the Al27-MASNMR analysis, it was noted that hexa-penta-coordinated Al were main structure.

• 한국전기전자재료학회논문지
• /
• 제17권8호
• /
• pp.852-858
• /
• 2004

An alkoxide-based sol-gel method was used to fabricate $Ba_{0.6}Sr_{0.4}TiO_{3}$thin films doped by Bi from 5 to 20 mol% on a Pt/Ti/$SiO_2$/Sisubstrate. The structural and dielectric properties of BST thin films were investigated as a function of Bi dopant concentration. The dielectric properties of the Bi doped BST films were strongly dependent on the Bi contents. The dielectric constant and dielectric loss of the films decreased with increasing Bi content. However, the leakage current density of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_{3}$ thin film showed the lowest value of 5.13$\times 10^{-7} A/{cm}^2$ at 5 V. The figure of merit (FOM) reached a maximum value of 32.42 at a 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_{3}$thin films. The dielectric constant, loss factor, and tunability of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}Tio_{3}$ thin films were 333, 0.0095, and 31.1%, respectively.

• 한국전기전자재료학회:학술대회논문집
• /
• 한국전기전자재료학회 2004년도 하계학술대회 논문집 Vol.5 No.2
• /
• pp.565-568
• /
• 2004

An alkoxide-based sol-gel method was used to fabricate $Ba_{0.6}Sr_{0.4}TiO_3$ thin films doped by Bi from 5 to 20 mol% on a Pt/Ti/SiO2/Si substrate. The structural and dielectric properties of BST thin films were investigated as a function of Bi dopant concentration. The dielectric properties of the Bi doped BST films were strongly dependent on the Bi contents. The dielectric constant and dielectric loss of the films decreased with increasing Bi content. However, the leakage current density of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_3$ thin film showed the lowest value of 5.13 10-7 at 5 V. The figure of merit (FOM) reached a maximum value of 32.42 at a 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_3$ thin films. The dielectric constant, loss factor, and tunability of the 10 mol% Bi doped $BBa_{0.6}Sr_{0.4}TiO_3$ thin films were 333,0.0095, and 31.1%, respectively.

• 한국전기전자재료학회:학술대회논문집
• /
• 한국전기전자재료학회 2004년도 춘계학술대회 논문집 반도체 재료 센서 박막재료 전자세라믹스
• /
• pp.18-21
• /
• 2004

An alkoxide-based sol-gel method was used to fabricate $Ba_{0.6}Sr_{0.4}TiO_3$ thin films doped by Bi from 5 to 20 mol% on a $Pt/Ti/SiO_2/Si$ substrate. The structural and dielectric properties of BST thin films were investigated as a function of Bi dopant concentration. The dielectric properties of the Bi doped BST films were strongly dependent on the Bi contents. The dielectric constant and dielectric loss of the films decreased with increasing Bi content. However, the leakage current density of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_3$ thin film showed the lowest value of $5.13{\times}10^{-7}\;A/cm^2$ at 5 V. The figure of merit (FOM) reached a maximum value of 32.42 at a 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_3$ thin films. The dielectric constant, loss factor, and tunability of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_3$ thin films were 333, 0.0095, and 31.1%, respectively.

• 한국결정성장학회지
• /
• 제9권1호
• /
• pp.101-106
• /
• 1999

Pb$(Zr_{0.5},Ti_{0.5})O_3$ 박막을 $Pt/Ti/SiO_2/Si$ 기판 위에 spin-coating법으로 제조하였다. 제조된 sol을 초음파 bath 내에서 초음파 처리하여 균일화를 촉진시킨 다음, 박막을 제조하여 초음파 처리되지 않은 sol로 제조된 박막과의 비교를 통해 초음파의 영향을 고찰하였다. 초음파 처리된 sol로 제조된 박막의 경우, $550^{\circ}C$에서 perovskite 단일상을 얻을 수 있었고, "rosette" 구조가 사라졌음을 관찰할 수 있엇따. 초음파 처리되지 않은 sol로 제조된 박막의 유전상수(10kHz), 잔류분극(Pr) 및 항전계(Ec) 값은 335, 12.3$\mu$C/$\textrm{cm}^2$, 168.4 kV/cm 였고, 초음파 처리된 sol로 제조된 박막은 각각 443, 172$\mu$C/$\textrm{cm}^2$, 153,5kVcm 로 전기적 특성이 개선되어 졌음을 알 수 있었다.

• 한국세라믹학회지
• /
• 제32권1호
• /
• pp.95-105
• /
• 1995

Ceria(CeO2) stabilized zirconia(CeSZ) sol was synthesized with zirconium n-butoxide Zr(OC4H9)4 and cerium nitrate hexahydrate Ce(NO3)3.6H2O as precursors and ethylacetoacetate(EAcAc) as a chelating agent under atmosphere. CeSZ films were deposited on AISI 304 stainless steel using the prepared polymeric sol by dipcoating and the coating characteristics were investigated by XRD, ellipsometry, scratch test and SEM. The CeSZ film began to crystallize from amorphous to tetragonal phase at 40$0^{\circ}C$ and it was not converted into monoclinic phase up to 100$0^{\circ}C$ by the addition of 16mol% CeO2 as a stabilizer which could suppress phase transformation of zirconia. The CeSZ films were prepared by varying the EAcAc contents and the cncentration of CeSZ sol and measured the thickness and refractive index. From these results, it was found that the EAcAc contents and concentration of CeSZ coating sol evidently affect the densification of CeSZ film. The CeSZ film coated with 0.4M CeSZ sol and heat-treated at $600^{\circ}C$ for 10min had thickness of 50nm and 17% porosity. The CeSZ film on 304 stainless steel effectively acted as a protective layer against oxidation up to 80$0^{\circ}C$ and had superior corrosion resistance in 25% H2SO4 solution for 4.5 hrs.

• 한국표면공학회지
• /
• 제38권4호
• /
• pp.167-173
• /
• 2005

Surface characteristics of HA(hydroxyapatite) coated dental implant alloy by Sol-Gel method were investigated using potentiostat, ICP, SEM, EDX, EPMA and surface roughness tester. Surface roughness of HA coated specimen by Sol-Gel showed higher than that of PVD coated specimen. Corrosion resistance increased in the order of $1\%$ lactic acid, artificial saliva, $0.5\%$ HCI and $0.9\%$ NaCl solution. Amount of Ca element release was higher than that of V and P in the $0.5\%$ HCI and $0.9\%$ NaCl solution.