• Korean Journal of Mathematics
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• 제18권4호
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• pp.335-342
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• 2010

Let D be an integral domain with quotient field K,$\mathcal{I}(D)$ be the set of nonzero ideals of D, and $w$ be the star-operation on D defined by $I_w=\{x{\in}K{\mid}xJ{\subseteq}I$ for some $J{\in}\mathcal{I}(D)$ such that J is finitely generated and $J^{-1}=D\}$. The D is called a Pr$\ddot{u}$fer $v$-multiplication domain if $(II^{-1})_w=D$ for all nonzero finitely generated ideals I of D. In this paper, we show that D is a Pr$\ddot{u}$fer $v$-multiplication domain if and only if $(A{\cap}(B+C))_w=((A{\cap}B)+(A{\cap}C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $(A(B{\cap}C))_w=(AB{\cap}AC)_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $((A+B)(A{\cap}B))_w=(AB)_w$ for all $A,B{\in}\mathcal{I}(D)$, if and only if $((A+B):C)_w=((A:C)+(B:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with C finitely generated, if and only if $((a:b)+(b:a))_w=D$ for all nonzero $a,b{\in}D$, if and only if $(A:(B{\cap}C))_w=((A:B)+(A:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with B, C finitely generated.

• 전기학회논문지
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• 제58권9호
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• pp.1757-1763
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• 2009

The composites were fabricated by adding 0, 15, 20, 25[vol.%] Zirconium Diboride(hereafter, $ZrB_2$) powders as a second phase to Silicon Carbide(hereafter, SiC) matrix. The physical, mechanical and electrical properties of electroconductive SiC ceramic composites by Spark Plasma Sintering(hereafter, SPS) were examined. Reactions between ${\beta}-SiC$ and $ZrB_2$ were not observed in the XRD analysis. The relative density of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 90.93[%], 74.62[%], 74.99[%] and 72.61[%], respectively. The XRD phase analysis of the electroconductive SiC ceramic composites reveals high of SiC and $ZrB_2$ and low of $ZrO_2$ phase. The lowest flexural strength, 108.79[MPa], shown in SiC+15[vol.%] $ZrB_2$ composite and the highest - 220.15[MPa] - in SiC+20[vol.%] $ZrB_2$composite at room temperature. The trend of the mechanical properties of the electroconductive SiC ceramic composites moves in accord with that of the relative density. The electrical resistivities of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 4.57${\times}10^{-1}$, 2.13${\times}10^{-1}$, 1.53${\times}10^{-1}$ and 6.37${\times}10^{-2}$[${\Omega}$ cm] at room temperature, respectively. The electrical resistivity of mono SiC, SiC+15[vol.%]$ZrB_2$. SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ are Negative Temperature Coefficient Resistance(hereafter, NTCR) in temperature ranges from 25[$^{\circ}C$] to 100[$^{\circ}C$]. The declination of V-I characteristics of SiC+20[vol.%]$ZrB_2$ composite is 3.72${\times}10^{-1}$. It is convinced that SiC+20[vol.%]$ZrB_2$ composite by SPS can be applied for heater or electrode above 1000[$^{\circ}C$]

• 한국세라믹학회지
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• 제47권6호
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• pp.578-582
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• 2010

$ZrB_2$ has a melting point of $3245^{\circ}C$ and a relatively low density of $6.1\;g/cm^3$, which makes this a candidate for application to ultrahigh temperature environments over $2000^{\circ}C$. Beside these properties, $ZrB_2$ is known to have excellent resistance to thermal shock and oxidation compared with other non-oxide engineering ceramics. In order to enhance such oxidation resistance, SiC was frequently added to $ZrB_2$-based systems. Due to nonsinterability of $ZrB_2$-based ceramics, research on the sintering aids such as $B_4C$ or $MoSi_2$ becomes popular recently. In this study, densification and high-temperature properties of $ZrB_2$-SiC ceramics especially with $B_4C$ are investigated. $ZrB_2$-20 vol% SiC system was selected as a basic composition and $B_4C$ or C was added to this system in some extents. Mixed powders were sintered using hot pressing (HP). With sintered bodies, densification behavior and high-temperature (up to $1400^{\circ}C$) properties such as flexural strength, hardness, and so on were examined.

• Bulletin of the Korean Chemical Society
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• 제26권1호
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• pp.63-71
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• 2005

Equilibrium geometries, electronic structures, and energies of borocarbon clusters (binary compounds of carbon and boron), an unexplored class of molecules with highly unusual characteristics and potential for further development, have been investigated by means of B3LYP/6-311+G$^*$ density functional theory computations. A large number of B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ clusters with planar and non-planar monocyclic and polycyclic rings, as well as cage structures, have been systematically studied. Unexpectedly, planar forms are predicted not only to be the most stable structures, but also, in many cases, to have unprecedented planar heptacoordinate boron (p-heptaB) and planar heptacoordinate carbon (p-heptaC) arrangements. All these pheptaB and p-heptaC have 6π electrons and are aromatic according to the nucleus independent chemical shift (NICS). This novel bonding pattern is analyzed in terms of natural bond orbital (NBO) analysis. For virtually all possible B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ combinations, the p-heptaB arrangements are the more stable than other type structures.

• 한국세라믹학회지
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• 제31권7호
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• pp.739-744
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• 1994

The B4C-C system was investigated to gain an understanding of the sintering behaviors of B4C. In order to get sintered density of 97% TD, sintering temperature of 225$0^{\circ}C$ was necessary. Since such a high temperature operation is actually difficult on a commercial basis, our objective was to examine the possibility of decreasing the sintering temperature by adding SiC. The addition of SiC in B4C increases the sintering rate about at 210$0^{\circ}C$ and results in a fine microstructure with more than 98% relative density on 55 wt% B4C-40wt% SiC-5 wt% C composition. The probability of liquid phase sintering was investigated, but the evidences of liquid phase formation were not observed with XRD and TEM observation. It was proposed that the addition of SiC and carbon to B4C reduce interface energy during sintering, which results in enhanced grain-boundary diffusion. Thus, the enhanced grain-boundary diffusion and retarded grain growth by SiC improve densification.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 추계학술대회 논문집 전기물성,응용부문
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• pp.191-193
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• 2004

The composites were fabricated, respectively, using 61vol.% SiC-39vol.% $TiB_2$ and using 61vol.% SiC-39vol.% $ZrB_2$ powders with the liquid forming additives of 12wt% $Al_2O_3+Y_2O_3$ by hot pressing annealing at $1650^{\circ}C$ for 4 hours. Reactions between SiC and transition metal $TiB_2$, $ZrB_2$ were not observed in this microstructure. The result of phase analysis of composites by XRD revealed SiC(6H, 3C), $TiB_2$, $ZrB_2$ and $YAG(Al_5Y_3O_{12})$ crystal phase on the SiC-$TiB_2$, and SiC-$ZrB_2$ composites. The ${\beta}\;{\alpha}$-SiC phase transformation was occurred on the $SiC-TiB_2$, $SiC-ZrB_2$ composites. The relative density, the flexural strength and Young's modulus showed respectively value of 98.57%, 226.06Mpa and $86.37{\times}10^3Mpa$ in SiC-$ZrB_2$ composites.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1997년도 춘계학술대회 논문집
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• pp.135-140
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• 1997

The influences of ZrB$_2$ additions to SiC on microstructural, DDM(Electrical Discharge Machining), mechanical and electrical properties were investigated. composites were prepared by adding 15, 30, 45 vol.% ZrB$_2$particles as a second phase to SiC matrix. SiC-ZrB$_2$ composites obtained by hot pressing for high temperature structural application were fully dense with the relative densities over 99%. The fracture toughness of the composites were increased with the ZrB$_2$contents. In case of composite containing 30vol.% ZrB$_2$, the flexural strength and fracture toughness showed 45% and 60% increase, respectively compared to that of monolithic SiC sample. The electrical resistivities of SiC-ZrB$_2$ composites decreased significantly with the ZrB$_2$ contents. The electrical resistivity of SiC-30vol.% ZrB$_2$ composite showed 6.50$\times$10$^{-4}$ $\Omega$.cm. Cutting velocity of EDM of SiC-ZrB$_2$ composites are directly proportional to duty factor of pulse width. Surface roughness, however, are not all proportional to pulse width. Higher-flexural strength composites show a trend toward smaller crater volumes, leaving a smoother surface; the average surface roughness of the SiC-ZrB$_2$ 15 vol.% composite with the flexural strengthe of 375㎫ was 3.2${\mu}{\textrm}{m}$, whereas the SiC-ZrB$_2$ 30.vol% composite of 457㎫ was 1.35${\mu}{\textrm}{m}$. In the SEM micrographs of the fracture surface of SiC-ZrB$_2$ composites, the SiC-ZrB$_2$ two phases are distinct; the white phase is the ZrB$_2$and the gray phase is the SiC matrix. In the SEM micrographs of the EDM surface, however, these phases are no longer distinct because of thicker recast layer of resolidified-melt-formation droplets present. It is shown that SiC-ZrB$_2$ composites are able to be machined without surface cracking.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 제38회 하계학술대회
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• pp.1303-1304
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• 2007

The composites were fabricated, respectively, using 61[vol.%]SiC-39[vol.%]$TiB_2$ and using 61[vol.%]SiC-39[vol.%]$ZrB_2$ powders with the liquid forming additives of 12[wt%] $Al_{2}O_{3}+Y_{2}O_{3}$ by hot pressing annealing at $1650[^{\circ}C]$ for 4 hours. Reactions between SiC and transition metal $TiB_2$, $ZrB_2$ were not observed in this microstructure. ${\beta}{\rightarrow}{\alpha}$-SiC phase transformation was occurred on the SiC-$TiB_2$ and SiC-$ZrB_2$ composite. The relative density, the flexural strength and Young's modulus showed the highest value of 98.57[%], 226.06[Mpa] and 86.38[Gpa] in SiC-$ZrB_2$ composite at room temperature respectively. The electrical resistivity showed the lowest value of $7.96{\times}10^{-4}[{\Omega}{\cdot}cm]$ for SiC-$ZrB_2$ composite at $25[^{\circ}C]$. The electrical resistivity of the SiC-$TiB_2$ and SiC-$ZrB_2$ composite was all positive temperature coefficient resistance (PTCR) in the temperature ranges from $25[^{\circ}C]$ to $700[^{\circ}C]$. The resistance temperature coefficient of composite showed the value of $6.88{\times}10^{-3}/[^{\circ}C]$ and $3.57{\times}10^{-3}/[^{\circ}C]$ for SiC-$ZrB_2$ and SiC-$TiB_2$ composite in the temperature ranges from $25[^{\circ}C]$ to $700[^{\circ}C]$.

• 한국분말재료학회지
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• 제1권1호
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• pp.15-20
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• 1994

The effect of SiC addition on sintering behaviors and microstructures of TiB2 ceramics were studied. The sintering of TiB2 was limited due to the surface diffusion and rapid grain growth at high temperature. However the addition of SiC to TiB2 ceramics improved the densification to above 99% of the theoretical density. The sintering of TiB2-SiC composite starts at 120$0^{\circ}C$ with the melting of the oxides in particle surface as impurities. After the reduction of the oxide by additional cabon at above 140$0^{\circ}C$, the grain boundary diffusion through the interface of TiB2-SiC play an important role. TEM observation showed neither chemical reactions nor other phases formed at the TiB2-SiC interfaces but the microcracks were observed due to the mismatch of thermal expansion between TiB2-SiC.

• Applied Biological Chemistry
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• 제43권1호
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• pp.39-45
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• 2000

본 연구에서는 종합비타민 액제중의 비타민 A, $B_1,\;B_2,\;B_6$, C의 안정성을 규명하기 위하여 경시함량 변화 및 분해속도를 동력학적으로 검토하였다 종합 비타민 액제의 제조에 있어서 지용성 비타민의 가용화를 위하여 계면활성제인 polysorbate 80과 용해보조제인 프로필렌글리콜을 병용하므로써 첨가제의 양을 최소화시킬 수 있었다. 종합 비타민 액제의 안정성 평가를 위한 가속시험에서 heterogenous solution system에서의 반응 기작이 그대로 나타나는 것은 아니겠지만 비타민 A는 zero-order, 비타민 $B_1$과 C는 first-order kinetics에 따르는 분해 양상을 나타내었으며 Arrhenius식을 이용하여 구한 비타민 A, $B_1$, 및 C의 활성화 에너지는 각각 26.27, 21.67 및 23.50 kcal/mol이고 상온$(25^{\circ}C)$에서의 유효기간은 각각 1493, 449 및 639일 이었다. 그리고 비타민 $B_2$ 광퇴색 속도식은 first-order kinetics의 분해양상을 나타내었으나 광희색 반응에 미치는 비타민 $B_2$ 초기농도$(C_0)$ $0.544{\times}10^2{\sim}1.632{\times}10^{-2}M$의 영향을 고려하여 비타민 $B_2$의 광퇴색 반응은 다음과 같은 속도식으로 진행되는 것으로 판명되었다. $-{\frac {dc}{dt}}=K_{c}\;{\frac C{C_0}}$ $K_c\;:\;C_0$에 따르는 상수 비타민 $B_6$의 안정성은 인공광원보다 태양광선에 의한 비타민 $B_6$의 광분해가 촉진되었고 그리고 태양광선에 의한 계절에 따른 분해는 모두 비슷하였다. 한편 용기에 의한 비타민 $B_6$의 광분해는 폴리에틸렌용기>갈색유리병>투명유리병 순으로 안정함을 나타내었다 이상의 실험결과로 종합비타민 액제 설계의 안정성의 기초적 실험에 기여되리라고 사료된다.