• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.4
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• pp.149-156
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• 2006

For an aspect ratio (transport length-to-width) of 5, Pr = 2.89, Le = 0.018, Pe = 2.29, Cv = 1.11, $P_B$=40 Torr, solutally buoyancy-driven convection $(Gr_s=3.03{\times}10^5)$ due to the disparity in the molecular weights of the component A $(Hg_2Cl_2)$ and B (He) is stronger than thermally buoyancy-driven convection $(Cr_t=1.66{\times}10^4)$. The crystal growth rate is decreased exponentially for $2.5\;{\leq}\;Ar\;{\leq}\;5$, with (1) the linear temperature profile and a fixed temperature difference, (2) the imposed thermal profile, a fixed crystal region and varied temperature difference. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. But, with the imposed thermal profile, a fixed source region and varied temperature difference, the rate is increased far $2\;{\leq}\;Ar\;{\leq}\;3$, and remains nearly unchanged for $3\;{\leq}\;Ar\;{\leq}\;5$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.20 no.3
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• pp.125-132
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• 2010

For typical governing dimensionless parameters of Ar = 5, Pr = 1.16, Le = 0.14, Pe = 3.57, Cv = 1.02, $Gr_s=2.65{\times}10^6$, the effects of thermo physical properties such as a molecular weight, a binary diffusivity coefficient, a partial pressure of component B on solutally buoyancy-driven convection (solutal Grashof number $Gr_s=2.65{\times}10^6$) are theoretically investigated for further understanding and insight into an essence of solutal convection occurring in the vapor phase during the physical vapor transport of a $Hg_2Cl_2-N_2$ system. The solutally buoyancy-driven convection is significantly affected by any significant disparity in the molecular weight of the crystal components and the impurity gas of nitrogen. The solutal convection in a vertical orientation is found to be more suppressed than a tenth reduction of gravitational accelerations in a horizontal orientation. For crystal growth parameters under consideration, the greater uniformity in the growth rate is obtained for either solutal convection mode in a vertical orientation or thermal convection mode in horizontal geometry. The growth rate is also found to be first order exponentially decayed for $10{\leq}P_B{\leq}200$ Torr.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.5
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• pp.203-209
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• 2006

For $P_B=50,\;{\Delta}T=10K$, Ar=5, Pr=2.36, Le=0.015, Pe=1.26, Cv=1.11, the intensity of solutal convection (solutal Grashof number $Grs=3.44x10^4$) is greater than that of thermal convection (thermal Grashof number $Grt=1.81x10^3$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A($Hg_2Cl_2$) and B(He). With increasing the partial pressure of component B from 10 up to 200 Torr, the rate is decreased exponentially. The convective transport decreases with lower g level and is changed to the diffusive mode at 0.1 $g_0$. In other words, for regions in which the g level is 0.1 $g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than 0.1 $g_0$ can be adequate to ensure purely diffusive transport.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.20 no.3
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• pp.117-124
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• 2010

For Ar=5, Pr=1.18, Le=0.15, Pe=2.89, Cv=1.06, $P_B$=20 Torr, the effects of impurity $(N_2)$ on thermally and solutally buoyancy-driven convection ($Gr_t=3.46{\times}10^4$ and $Gr_s=6.02{\times}10^5$, respectively) are theoretically investigated for further understanding and insight into an essence of thermo-solutal convection occurring in the vapor phase during the physical vapor transport. For $10K{\leq}{\Delta}T{\leq}50K$, the crystal growth rates are intimately related and linearly proportional to a temperature difference between the source and crystal region which is a driving force for thermally buoyancy-driven convection. Moreover, both the dimensionless Peclet number (Pe) and dimensional maximum velocity magnitudes are directly and linearly proportional to ${\Delta}T$. The growth rate is second order-exponentially decayed for $2{\leq}Ar{\leq}5$. This is related to a finding that the effects of side walls tend to stabilize the thermo-solutal convection in the growth reactor. Finally, the growth rate is found to be first order exponentially decayed for $10{\leq}P_B{\leq}200$ Torr.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.17 no.6
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• pp.231-237
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• 2007

For an aspect ratio (transport length-to-width) of 5, Pr=3.34, Le=0.078, Pe=4.16, Cv=1.01, $P_B=50$ Torr, only thermally buoyancy-driven convection ($Gr=4.83{\times}10^5$) is considered in this study in spite of the disparity in the molecular weights of the component A ($Hg_2Cl_2$) and B which would cause thermally and/or solutally buoyancy-driven convection. The crystal growth rate and the maximum velocity vector magnitude are decreased exponentially for $3{\le}Ar{\le}5$, for (1) adiabatic walls and (2) the linear temperature profile, with a fixed source temperature. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. The rate for the linear temperature profiles walls is slightly greater than for the adiabatic walls far varied temperature differences and aspect ratios. With the imposed thermal profile, a fixed source region, both the rate and the maximum velocity vector magnitude increase linearly with increasing the temperature difference for $10{\le}{\Delta}T{\le}50K$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.17 no.6
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• pp.256-263
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• 2007

For $P_B=50Torr,\;P_T=5401Torr,\;T_S=450^{\circ}C,\;{\Delta}T=20K$, Ar=5, Pr=3.34, Le=0.01, Pe=4.16, Cv=1.05, adiabatic and linear thermal profiles at walls, the intensity of solutal convection (solutal Grashof number $Grs=7.86{\times}10^6$) is greater than that of thermal convection (thermal Grashof number $Grt=4.83{\times}10^5$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A ($Hg_2Cl_2$) and B (He). With increasing the partial pressure of component B from 20 up to 800 Torr, the rate is decreased exponentially. It is also interesting that as the partial pressure of component B is increased by a factor of 2, the rate is approximately reduced by a half. For systems under consideration, the rate increases linearly and directly with the dimensionless Peclet number which reflects the intensity of condensation and sublimation at the crystal and source region. The convective transport decreases with lower g level and is changed to the diffusive mode at $0.1g_0$. In other words, for regions in which the g level is $0.1g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than $0.1g_0$ can be adequate to ensure purely diffusive transport.