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## Inżynieria Materiałowa

2011 | Vol. 32, nr 2 | 132-134
Tytuł artykułu

### Sedymentacja w ciałach stałych i cieczach

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Wybrane pełne teksty z tego czasopisma
Warianty tytułu
EN
Sedimentation in solids and liquids
Języki publikacji
PL
Abstrakty
PL
EN
The sedimentation process is wildly known as the transport of macroscopic solutes induced by gravitational or centrifugal field in a gas, liquid and solid solvent. Nowadays, the sedimentation is being applied in technique in order to separate isotopes (in gas mixtures) and produce gradient materials. In this work we present the existing models of sedimentation and propose the new method. The complete theoretical framework to derive consistent set of equations describing sedimentation in multi component system is shown, i.e. the interdiffusion induced by the gravity (centrifugal) field. The model combines the mass conservation law, the equation of motion and the volume continuity equation with the Nernst-Planck flux formulae. The method known as bi-velocity or Darken model is based on the postulate of the unique transport mechanism of the volume and of the mass. Using the model, it is possible to predict the evolution of concentration, drift velocity and pressure generated during the sedimentation in solids. The described mathematical model has a numerical solution. The concentration profile in equilibrium state is found by solving the nonlinear set of equations. An applications of this theory to Bi-Sb system (Fig. 1) is an evidence of sedimentation of substitutional atoms in condensed matter via interdiffusion mechanisms. Comparison of the simulation results with experimental data shows good agreement. An applications of this theory in a case of arbitrary ternary alloy (presented in Fig. 2) is an evidence of its correctness for modelling diffusion processes induced by the gravity (centrifugal) field in multicomponent system. Presented examples show the potential of the method, especially volume continuity equation in describing the transport processes, i.e. sedimentation process by the evolutionary method. The unique aspects of the method are: 1) the diffusion fluxes are defined in the lattice fixed (material) frame of reference, and 2) the different partial molar volumes of components are considered.
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Czasopismo
Rocznik
Strony
132-134
Opis fizyczny
Bibliogr. 17 poz., rys., tab.
Twórcy
autor
autor
autor
• Wydział Inżynierii Materiałowej i Ceramiki, Akademia Górniczo-Hutnicza, Kraków, bwierzba@agh.edu.pl
Bibliografia
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• [2] Planck M.: Ber die potentialdierenz zwischen zwei verdnnten lsungen binrer elektrolyte. Ann. Phys. Chem. 40 (1890) 561.
• [3] Svedberg S.: The ultra-centrifuge and the study of high-molecular compounds. Nature 139 (1937) 1051.
• [4] Beams J. W.: High speed centrifuging. Rev. Mod. Phys. 10 (1938) 245.
• [5] Mashimo T.: Self-consistent approach to the diffusion induced by a centrifugal field in condensed matter: sedimentation. Phys. Rev. A 38 (1988) 4149.
• [6] Ono M., Mashimo T.: Sedimentation process for atoms in Bi-Sb system alloy under the strong gravitational field: a new type of diffusion of substitutional solutes. Phil. Mag. A 82 (2002) 591.
• [7] Barr L. W., Smith F. A.: Observations on the equilibrium distribution of gold diffusing in solid potassium in a centrifugal field. Phil. Mag. 20 (1969) 1293.
• [8] Anthony T. R.: Sedimentation in the solid state, sedimentation a l'etat solide sedimentation in festkörpern. Acta. Metall. 18 (1970) 877.
• [9] Mashimo T., Okazaki S., Shibazaki S.: Ultracentrifuge apparatus to generate a strong acceleration field of over 1,000,000 g at high temperature in condensed matter. Rev. Scient. Instrum. 67 (1996) 3170.
• [10] Mashimo T., Okazaki S., Tashiro S.: Sedimentation of atoms in solid under a strong acceleration field of around 1 million g. Jap. J. appl. Phys. 36 (1997) 498.
• [11] Mashimo T., Ikeda T., Minato I.: Atomic-scale graded structure formed by sedimentation of substitutional atoms in a Bi-Sb alloy. J. appl. Phys. 90 (2001) 741.
• [12] Mashimo T., Ono M., Huang X., Iguchi Y., Okayasu S., Kobayashi K. and Nakamura E.: Sedimentation of isotope atoms in monatomic liquid Se. App. Phys. Lett. 91 (2007) 231917.
• [13] Mashimo T., Ichikawa M., Omurzak E., Nishihara M. and Ihara H.: Graded oxide glasses in binary systems (Si-Ti, Si-V, and Si-Zr) prepared by the sol-gel and centrifugal process. Chem. Mater. 21 (2009) 2339.
• [14] Lamm O.: Die differentialgleichung der ultrazentrifugierung. Ark. Mat. Astron. Fys. 21B (1929) 1.
• [15] Danielewski M., Wierzba B.: Thermodynamically consistent Bi velocity mass transport phenomenology. Acta Mat. 58 (2010) 6717.
• [16] Kattner U.: The thermodynamic modeling of multicomponent phase equilibria. JOM 49 (12) (1997) 14.
• [17] Kaufman L., Bernstein B.: Computer calculations of phase diagrams with special reference to refractory materials. Academic Press, New York (1970).
Typ dokumentu
Bibliografia
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