[01] Nguyen Cong Toan, Department of Physics, Hanoi University of Science, Hanoi, Vietnam. [02] Nguyen Van Hung, Department of Physics, Hanoi University of Science, Hanoi, Vietnam. [03] Nguyen Ba Duc, Department of Physics, Tan Trao University, Tuyen Quang, Vietnam. [04] Dinh Quoc Vuong, Quang Ninh Education & Training Department, Cam Pha School, Quang Ninh, Vietnam.

In this work, a theory is derived for the calculation and analysis of phase diagram of binary alloys composed of constituent elements having the same structure and any proportion. Analytical expression of phase diagram has been derived using the ratio of root mean square fluctuation in atomic positions on the equilibrium lattice positions and the nearest neighbour distance. The theory is based on Lindemann criterion so that the calculated phase diagram provides information on Lindemann melting temperatures and eutectic point of binary alloys. Numerical results for Cs_1-xRb_x, Cu_1-xAu_x, Cu1_-xNi_x and Cr_1-xCs_x are found to be in good and reasonable agreement with experiment.

Phase Diagram, Lindemann Melting Temperature, Eutectic Point, Binary Alloys

[01] Gillvarry J. J. The Lindemann and Gruneisen laws. Phys. Rev. 1956, 102, 308-316. [02] Ross Marvin. Generalized Lindemann melting law. Phys. Rev. 1969, 184(1), 233. [03] Kittel Charles. Introduction to Solid State Physics. 7th Edition (Wiley&Son, New York, 1996). [04] Massalski T. B. Binary Alloy Phase Diagrams, 2^nd edition (ASM International Materials Parks, OH, 1990). [05] Machon Denis, Toledano Pierre, Krexner Gehard. Phenomenlogical theory of phase diagrams of binary eutectic systems. Phys. Rev. B 2005, 71, 024110. [06] Alfe D., Vocadlo L., Price G. D., Gillan M. J. Melting curve of materials: Theory versus experiments. J. Phys.: Condens. Matter 2004, 16, S973-S982. [07] Kierfeld Jan and Vinokur Valerii. Lindemann criterion and vortex lattice phase transitions in type-II superconductors. Phys. Rev. B 2004, 69, 024501. [08] Zhou Yaoqi, Karplus Martin, Ball Keith D., Berry R. Stephen. The distance fluctuation criterion for melting: Comparison of square-well and Morse potential models for cluster and homopolymers. J. Chem. Phys. 2002, 116, 2323. [09] Chakravarty Charutsita, Debenedetti Pablo G., Stilinger Frank H. Lindemann measures for the solid-liquid phase transition. J. Chem. Phys. 2007, 126, 204508. [10] Ziman J. M. Principles of the Theory of Solids. Cambrige University Press, London, 1972. [11] Hung N. V. and Rehr J. J. Anharmonic correlated Einstein model Debye-Waller factors. Phys. Rev. B 1997, 56, 43. [12] Daniel M., Pease D. M., Hung N. V., Budnick J. D. Local force constants of transition metal dopants in a nickel host: Comparison to Mossbauer studies. Phys. Rev. B 2004, 68, 134414. [13] Hung N. V. and Fornasini P. Anharmonic effective potential, correlation effects, and EXAFS cumulants calculated from a Morse interaction potential for fcc metals. Phys. Soc. Jpn. 2007, 76, 084601. [14] Hung N. V., Tien T. S., Duc N. B., Vuong D. Q. High-order expanded Debye-Waller factors of hcp crystals based on classical correlated Einstein model. Mod. Phys. Lett. B 2014, 28, 1450174. [15] Trung N. B.; Hung N. V.; Khoa H. D. Temperature dependence of high-order expanded anharmonic correlated Debye model Debye-Waller factor of metallic Copper. Int. J. Adv. Mater. Research. 2016, 2(4), 52-58.