• Title/Summary/Keyword: Longitudinal diffusion coefficients

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Determination of Diffusion Coefficients of Boron from Borate Rods in Wood Using Boltzmann's Transformation

  • Ra, Jong-Bum
    • Journal of the Korean Wood Science and Technology
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    • v.31 no.3
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    • pp.24-29
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    • 2003
  • This research was performed to investigate the diffusivity of borate rods in radiata pine (Pinus radiata D. Don) conditioned to 40 percent moisture content (MC). The deepest penetration of boron were observed in the longitudinal direction, followed by the radial and the tangential directions. The boron loading on the wood face adjacent to the borate rod tended to increase with diffusion time in all directions. To mathematically quantify boron diffusion, the diffusion coefficient of boron was determined using Boltzmann's transformation by assuming that it was a function of concentration only. The values of the longitudinal diffusion coefficients were between 1.3×10-8 cm2/sec and 9.2×10-8 cm2/sec. The radial diffusion coefficients were between 1.4×10-8 cm2/sec and 9.5×10-8 cm2/sec, and the tangential diffusion coefficients were between 5.2×10-9 cm2/sec and 1.3×10-8 cm2/sec. The differences of diffusion coefficients between the longitudinal direction and the radial direction were slight, although their concentration profiles were markedly different. This indicates that the amount of boron loading on the wood face adjacent the borate rod is one of the most important factor for boron penetration in wood with low MC.

Analysis of Electron Swarm Diffusion Coefficients and Energy Distribution Function in $e^-$-$CF_4$ Scattering ($e^-$-$CF_4$산란중에서 전자군의 확산계수 및 에너지분포함수 연구)

  • 하성철;임상원
    • Electrical & Electronic Materials
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    • v.10 no.4
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    • pp.342-348
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    • 1997
  • In this paper, the behavior of electron swarm parameters and energy distribution function of the discharge under high E/N condition in e$^{-10}$ -CF$_{4}$ gas have been analysed over the E/N range from 1-300(Td) by the MCS and BEq methods using set of electron collision cross section determined by the authors. The swarm parameters and energy distribution function have been calculated for the pulsed Townsend, steady-state Townsend and Time of Flight methods. The results gained that the value of electron swarm parameters such as the electron drift velocity, the electron ionization and attachment coefficients and longitudinal diffusion coefficients in agreement with the experimental and theoretical data for a range of E/N. The electron energy distribution function has been explained and analysed in e$^{-10}$ -CF$_{4}$ at E/N : 5, 10, 100, 200, 300(Td) for a case of the equilibrium region in the mean electron energy and respective set of electron collision cross sections. The validity of the results has been confirmed by TOF and SST methods.

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The Study of Electron Transport coefficients in $SiH_4$-Ar Mixtures by Using Boltzmann Equation Analysis and Monte-Carlo Simulation (볼츠만방정식과 몬테칼로법에 의한 $SiH_4$-Ar 혼합가스의 전자수송계수에 관한 연구)

  • 하성철;전병훈
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.14 no.2
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    • pp.169-174
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    • 2001
  • The electron transport coefficients(the electron drift velocity, W, and the longitudinal and transverse diffusion coefficient, D$_{L}$ and D$_{T}$) in SiH$_4$-Ar mixtures containing 0.5% and 5.0% monosilane were calculated over the E/N range from 0.01 to 300 Td and over the gas pressure range 0.5, 1.0 and 1.5 Torr by the time-of-flight(TOF) method of the Boltzmann equation(BE.) and Monte-Carlo simulation(MCS). The electron energy distribution function in each SiH$_4$-Ar mixtures at E/N=10 Td and L=0.2 cm, which in equilibrium region in the mean electron enregy were compared.red.

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The study of electron transport coefficients in pure $CO_2$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CO_2$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Kim, Ji-Yeon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.164-167
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure $CO_2$ were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of $CO_2$ molecular gas. And for propriety of two-term approximation of Boltzmann equation analysis, the calculated results compared with the electron transport coefficients measured by Nakamura.

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The study of electron transport coefficients in pure $CF_4$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CF_4$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.29-32
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    • 2001
  • We measured the electron transport coefficients(the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_L$) in pure $CF_4$ over the E/N range from 0.04 Td to 250 Td by the double shutter drift tube. And these electron transport coefficients in pure $CF_4$ were calculated over the E/N range from 0.01 to 250 Td at 1 Torr by using the two-term approximation of the Boltzmann equation.

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Diffusion coefficients of electrons in $SF_6$-Ar Mixtures Gas used by MCS-BEq Algorithm ($SF_6$-Ar 혼합기체(混合氣體)의 MCS-BE_q알고리즘에 의한 확산계수)

  • Kim, Sang-Nam;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2004.07b
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    • pp.1150-1153
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    • 2004
  • Diffusion coefficients Of electrons in $SF_6$-Ar mixtures gas used by MCS- BEq algorithm has been analysed over the E/N range $30\sim300$(Td) by a two term Boltzmann equation and by a Monte Carlo Simulation using a set of electron cross sections determined by other authors, experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6$-Ar mixtures were measured by time-of-flight(TOF) method, The results show that the deduced electron drift velocities, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients and mean energy agree reasonably well with theoretical for a rang of E/N values The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

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A Monte-Carlo method and Boltzmann Equation analysis on the electron swarm parameter in SiH$_4$+Ar mixtures gas. ($SiH_4+Ar$ 혼합기체의 전자군 파라미터에 대한 볼츠만 방정식 및 몬테 칼로법 해석)

  • 김대연;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1999.05a
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    • pp.387-390
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    • 1999
  • Electron swarm parameterdthe drift velocity and longitudinal diffusion coefficienthn $SiH_4-Ar$ mixtures containing 0.5% and 5% monosilane were measured using over the range of E/N from 0.01 to 300 Td at room temperature. Electron swarm parameters in argon were drastically changed by adding a small amount of monosilane. The electron drift velocity in both mixtures showed unusual behaviour against E/N. It had negative slope in the medium range of E/N, yet the slope was not smooth but contained a small hump. The longitudinal diffusion coefficient also showed a corresponding feature in its dependence on E/N. A two-tern approximation of the Boltzmann equation analysis and Monte Carlo simulation have been used to study electron transport coefficients.

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A Study on the Electron Transport Coefficients in Hydrogen Molecular ($H_2$의 전자 수송 계수에 관한 연구)

  • Park, Eun-Joo;Jeon, Byung-Hoon
    • Proceedings of the KIEE Conference
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    • 2009.07a
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    • pp.1402_1403
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    • 2009
  • The electron transport coefficients in hydrogen molecular is calculated over the range of E/N values from 0.01 to 300 Td and at temperature state of 77K, 293K and 300K by Boltzmann equation method. The results gained that the values of the electron transport coefficients such as the electron drift velocity, the electron ionization coefficients, longitudinal diffusion coefficients consisted with the results of measured and calculated for a ranage of E/N.

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Determination of the Inelastic cross Sections for $C_{3}F_{8}$ Molecule by electron Swarm Study

  • Jeon, Byung-Hoon;Ha, Sung-Chul;Yang, Jeong-Mo
    • Transactions on Electrical and Electronic Materials
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    • v.2 no.1
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    • pp.7-11
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    • 2001
  • We measured the electron transport coefficients, the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_{L}$, over the E/N range from 0.03 to 100 Td and gas pressure range from 0.133 to 122 kPa in the 0.526% and 5.05% $C_{3}F_{8}$-Ar mixtures by the double shutter drift tube with variable drift distance. And we calculated these electron transport coefficients by using multi-term approximation of Boltzmann equation analysis. We determined the electron collision cross sections set for $C_{3}F_{8}$ molecule by the comparison of measurement and calculation. Our special attention in the present study was focused upon the inelastic collision cross sections of the $C_{3}F_{8}$ molecule.

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The study of electron transport coefficients in pure Xe by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 Xe분자가스의 전자수송계수의 해석)

  • Ma, Su-Young;Jeon, Byung-Hoon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.174-177
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure Xe were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Xe molecular gas.

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