بررسی انجماد برخی فلزات مایع با استفاده از نظریة تابعی چگالی وزنی اصلاح شده

نوع مقاله : مقاله پژوهشی کامل

نویسنده

ریاست پیام نور استان خوزستان

چکیده

در این مقاله گذار فاز مایع–جامد بصورت عددی و با استفاده از تقریب (MWDA)، مدل پتانسیل کره‌سخت ( HS) و بستار پرکس یویک (PY )، با محاسبه‌ی انرژی آزاد کل فلزات مایع مانند سدیم، منیزیم و آلومینیم مورد مطالعه قرار گرفته شده است. سپس با رسم نمودارهای انرژی آزاد برحسب چگالی، برای مایع کره‌سخت و جامدهای fcc ،bcc وhcp مقادیر چگالی جامد و مایع همزیست را محاسبه نمودیم که این نتایج با نتایج شبیه سازی مونت کارلو و سایر کارهای پیش از این در توافق خوبی بود. در آخر پایداری شبکه‌های fcc ،bcc وhcp با توجه به انرژی‌های آنها مورد بررسی قرار گرفت.

کلیدواژه‌ها


عنوان مقاله [English]

Study of MWDA functional theory: freezing of simple liquids

نویسنده [English]

  • alireza razeghizadeh
چکیده [English]

In this paper fusion liquid-solid phase by numerical method using weighted density functional theory (MWDA) , hard-sphere potential model (HS) and function (PY) by calculating total free energy of liquid metals such as sodium, magnesium and aluminum has been studid.
Then we calculated the amount of density of the solid and liquid coexist using free energy graph according to density of hard-sphere fluid and solids fcc, bcc and hcp wich these results good agreement with Mont Carllo simulation results and other Previous works. Finally we study stability lattices fcc, bcc and hcp, according to their energy.

Finally we study stability lattices fcc, bcc and hcp, according to their energy.

کلیدواژه‌ها [English]

  • : Modified weighted density approximation
  • Helmholtz free energy
  • hard sphere potential model
  • freezing
 
[1]. J.P. Hansen, I.R. McDonald, Theory of Simple Liquids, 2nd. Academic, London (1986).
[2]. R. Evans, D. Henderson, Fundamentals of inhomogeneous fluids, New York: Marcel Dekker (1992).
[3]. R.G. Parr, W. Yang, Density-functional theory of atoms and molecules, Oxford University Press )1989(.
[4]. G. Rickayzen, P. Kalpaxis, E. Chacon, A self consistent approach to a density functional for homogeneous fluids, The Journal of Chemical Physics 101 (1994) 7963-7970.
[5]. C.F. Tejero, J.A. Cuesta, Hard-sphere and hard-disk freezing from the differential formulation of the generalized effective liquid approximation, Physical Review E 47 (1993) 490.
[6]. A. González, J.A. White, Generating function density functional theory: free-energy functionals and direct correlation functions for hard-spheres, Physica A: Statistical Mechanics and its Applications 296 (2001) 347-363.
[7]. G. Rickayzen, A. Augousti, Integral equations and the pressure at the liquid-solid interface, Molecular Physics 52 (1984) 1355-1366.
[8]. M. Moradi, M.K. Tehrani, Weighted density functional theory of spherically inhomogeneous hard spheres, Physical Review E 63(2001) 021202.
[9]. P. Tarazona, Free-energy density functional for hard spheres, Physical Review A 31(1985) 2672.
[10]. S.F. Taghizadeh, S. Ghanbar, Z. Sazeshi, The study of the structural and  thermodynamic properties of two-dimensional fluid with disc-shape molecules by Lenard-jonard potential model, Journal of Research on Many-Body Systems 2 (2012) 1-7.
[11]. I.G. Tóth, L. Gránásy, G. Tegze, Nonlinear hydrodynamic theory of crystallization, Journal of Physics: Condensed Matter 26 (2014) 055001.
[12]. C. Rascón, L. Mederos, G. Navascués, Solid to solid isostructural transition in the hard sphere/attractive Yukawa system, The Journal of Chemical Physics 103(1995) 9795-9799.
[13]. M. Baus,The present status of the density-functional theory of the liquid-solid transition, Journal of Physics. Condensed Matter 2 (1990) 2111-2126.
[14]. W. Yang, Gradient correction in Thomas-Fermi theory, Physical Review A 34(1986): 4575.
[15]. A.R. Yasemina, H. Akbarzadeh, M.R. Mohammadizadeh, Iranian Annual Physics Conference (1997) 415.
[16]. C. Ebner, H.R. Krishnamurthy, Rahul Pandit, Density-functional theory for classical fluids and solids, Physical Review A 43 (1991) 4355.
[17]. T.V. Ramakrishnan, M. Yussouff. Theory of the liquid-solid transition, Solid State Communications 21 4 (1977) 389-392.
[18]. A.D.J. Haymet, D.W. Oxtoby, A molecular theory for the solid–liquid interface, The Journal of Chemical Physics 74 (1981) 2559-2565.
[19]. J.L. Barrat, J.P. Hansen, G. Pastore, E. M. Waisman, Density functional theory of soft sphere freezing, The Journal of Chemical Physics 86 (1987) 6360-6365
[20]. W.A. Curtin, Freezing in the density functional approach: Effect of third order contributions, The Journal of Chemical Physics 88 (1988) 7050-7058
[21]. P. Tarazona, A density functional theory of melting, Molecular physics 52 (1984) 81-96.
[22]. M. Moradi, H. Shahri, Equation of state and freezing of gmsa hard spheres, International Journal of Modern Physics B 17 (2003) 6057-6065.
[23]. V.B. Warshavsky, X. Song, Calculations of free energies in liquid and solid phases: Fundamental measure density-functional approach, Physical Review E 69 (2004) 061113.
[24]. V.B. Warshavsky, X. Song, Fundamental-measure density functional theory study of the crystal-melt interface of the hard sphere system, Physical Review E 73(2006) 031110.
[25]. W.A. Curtin, N.W. Ashcroft, Weighted-density-functional theory of inhomogeneous liquids and the freezing transition, Physical Review A 32 (1985) 2909.
[26]. W.A Curtin, N.W. Ashcroft, Density-functional theory and freezing of simple liquids, Physical Review Letters 56 (1986) 2775.
[27]. W.A. Curtin,Density-functional theory of the solid-liquid interface, Physical Review Letters 59(1987) 1228.
[28]. W.A. Curtin, K. Runge, Weighted-density-functional and simulation studies of the bcc hard-sphere solid, Physical Review A 35 (1987) 4755.
[29]. A.R. Denton, N.W. Ashcroft, Modified weighted-density-functional theory of nonuniform classical liquids, Physical Review A 39 (1989) 4701.
[30]. D.W. Marr, A.P. Gast, Planar density-functional approach to the solid-fluid interface of simple liquids, Physical Review E 47 (1993) 1212.
[31]. A. Suematsu, A. Yoshimori, M. Saiki, J. Matsui, T. Odagaki, Solid phase stability of a double-minimum interaction potential system, The Journal of chemical physics 140n (2014) 244501.
[32]. M. Oettel, S. Dorosz, M. Berghoff, B. Nestler, T. Schilling, Description of hard-sphere crystals and crystal-fluid interfaces: A comparison between density functional approaches and a phase-field crystal model, Physical Review E 86 (2012) 021404.
[33]. V. Ogarko, N. Rivas, S. Luding, Communication: Structure characterization of hard sphere packings in amorphous and crystalline states, The Journal of Chemical Physics 140 (2014) 211102.
[34]. E. Thiele, Equation of state for hard spheres, The Journal of Chemical Physics 39 (1963) 474-479.
[35]. M.S. Wertheim, Exact solution of the Percus-Yevick integral equation for hard spheres, Physical Review Letters 10, (1963) 321-323.
[36]. R. Roth, R. Evans, A. Lang, G. Kahl, Fundamental measure theory for hard-sphere mixtures revisited: the White Bear version, Journal of Physics: Condensed Matter 14 (2002) 12063.
[37]. Z. Tang, L.E. Scriven, H.T. Davis, Density functional perturbation theory of inhomogeneous simple fluids, The Journal of chemical physics 95 (1991) 2659-2668.
[38]. A.R. Denton, N.W. Ashcroft, Weighted-density-functional theory of nonuniform fluid mixtures: Application to the structure of binary hard-sphere mixtures near a hard wall, Physical Review A 44(1991) 8242.
[39].W.G. Hoover, F.H. Ree, Melting transition and communal entropy for hard spheres, The Journal of Chemical Physics 49 (1968) 3609-3617.
[40]. P. Tarazona, Free-energy density functional for hard spheres, Physical Review A 31 4 (1985) 2672.
[41]. F. Igloi, J. Hafner, Density functional theory of freezing with reference liquid, Journal of Physics C: Solid State Physics 19 (1986) 5799.
[42]. G.L. Jones, U. Mohanty, A density functional-variational treatment of the hard sphere transition, Molecular Physics 54 (1985) 1241-1252.
[43] A.D.J. Haymet, A molecular theory for the freezing of hard spheres, The Journal of Chemical Physics 78 (1983) 4641-4648.
[44] J.L. Colot, M. Baus, The freezing of hard spheres: II. A search for structural (fcc-hcp) phase transitions, Molecular Physics 56 (1985) 807-824.