محاسبه نمودارهاي فازي با استفاده از الگوريتم "جارويس"

Calculation of phase diagrams using "Jarvis" algorithm

ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﯾﮑﯽ از اﺑﺰارﻫﺎي اﺻﻠﯽ در ﻃﺮاﺣﯽ آﻟﯿﺎژﻫﺎي ﻣﻬﻨﺪﺳﯽ ﻫﺴﺘﻨﺪ. ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﺑﺎ اﺳﺘﻔﺎده از ﺗﺮﻣﻮدﯾﻨﺎﻣﯿﮏ ﻣﺤﺎﺳﺒﺎﺗﯽ در دﻫﻪﻫﺎي ﮔﺬﺷﺘﻪ ﻣﻮرد ﺗﻮﺟﻪ وﯾﮋه داﻧﺸﻤﻨﺪان ﺣﻮزه ﻣﻮاد ﺑﻮده اﺳﺖ. ﺗﻼشﻫﺎي اﻧﺠﺎم ﺷﺪه در ﭼﻨﺪ دﻫﻪ ﮔﺬﺷﺘﻪ، ﻣﻨﺠﺮ ﺑﻪ ﺗﻮﺳﻌﻪ اﻟﮕﻮرﯾﺘﻢﻫﺎي ﻣﺨﺘﻠﻔﯽ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﺷﺪه اﺳﺖ. ﺑﺎ اﯾﻦ ﺣﺎل ﺑﺴﯿﺎري از اﻟﮕﻮرﯾﺘﻢﻫﺎي اراﺋﻪ ﺷﺪه ﯾﺎ ﺑﺴﯿﺎر ﭘﯿﭽﯿﺪه ﻫﺴﺘﻨﺪ و ﯾﺎ در ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﻣﺤﺪودﯾﺖ ﻫﺎﯾﯽ دارﻧﺪ. ﻫﺰﯾﻨﻪ ﻣﺤﺎﺳﺒﺎﺗﯽ ﺑﺎﻻ، ﺧﻄﺎ در ﻣﺤﺎﺳﺒﻪ ﻧﻮاﺣﯽ ﺷﺎﻣﻞ ﺷﮑﺎف ﺣﻼﻟﯿﺖ و ﻋﺪم ﺗﻮاﻧﺎﯾﯽ در ﺗﻔﮑﯿﮏ ﺗﻌﺎدل ﺷﺒﯿﻪ ﭘﺎﯾﺪار از ﺗﻌﺎدل ﭘﺎﯾﺪار ﺗﻨﻬﺎ ﺑﺨﺸﯽ از ﻣﺤﺪودﯾﺖﻫﺎي اﻟﮕﻮرﯾﺘﻢﻫﺎي ﻣﻮﺟﻮد ﺑﺮاي ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﻫﺴﺘﻨﺪ. از اﯾﻦ رو ﺑﻬﯿﻨﻪ ﺳﺎزي اﻟﮕﻮرﯾﺘﻢﻫﺎي ﻣﻮﺟﻮد و ﯾﺎ ﺗﻮﺳﻌﻪ اﻟﮕﻮرﯾﺘﻢﻫﺎي ﺟﺪﯾﺪ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﻫﻤﻮاره ﻣﻮرد ﺗﻮﺟﻪ داﻧﺸﻤﻨﺪان ﺑﻮده اﺳﺖ. در ﺗﺤﻘﯿﻖ ﺣﺎﺿﺮ اﻣﮑﺎن اﺳﺘﻔﺎده از اﻟﮕﻮرﯾﺘﻢ ﺟﺎروﯾﺲ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ. اﻟﮕﻮرﯾﺘﻢ ﺟﺎروﯾﺲ ﯾﮏ اﻟﮕﻮرﯾﺘﻢ ﺷﻨﺎﺧﺘﻪ ﺷﺪه در ﻫﻨﺪﺳﻪ ﻣﺤﺎﺳﺒﺎﺗﯽ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﭘﻮش ﻣﺤﺪب اﺳﺖ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن داد ﮐﻪ اﻟﮕﻮرﯾﺘﻢ ﭘﯿﺸﻨﻬﺎدي ﻣﯽﺗﻮاﻧﺪ ﺑﻪ ﺧﻮﺑﯽ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮدارﻫﺎي ﻓﺎزي ﻣﻮرد اﺳﺘﻔﺎده ﻗﺮار ﮔﯿﺮد. ﺳﺎدﮔﯽ ﭘﯿﺎده ﺳﺎزي و ﻫﺰﯾﻨﻪ ﻣﺤﺎﺳﺒﺎﺗﯽ ﭘﺎﯾﯿﻦ از وﯾﮋﮔﯽﻫﺎي اﻟﮕﻮرﯾﺘﻢ ﭘﯿﺸﻨﻬﺎدي اﺳﺖ.

Phase diagrams are one of the main tools in designing engineering alloys. The calculation of phase diagrams using computational thermodynamics has been of great interest to materials scientists in recent decades. Efforts in the last decades have led to the development of various algorithms for calculating phase diagrams. However, many of the proposed algorithms are either very complex or have limitations in calculating phase diagrams. High computational cost, errors in calculating miscibility gap areas, and inability to distinguish meta-stable equilibrium from stable equilibrium are just some of the limitations of existing algorithms for calculating phase diagrams. Therefore, optimization of existing algorithms or development of new algorithms for calculating phase diagrams has always been of interest to scientists. In the present study, the possibility of using the Jarvis March algorithm to calculate phase diagrams has been investigated. The Jarvis March algorithm is a well-known algorithm in computational geometry for calculating convex hulls. The results show that the proposed algorithm can be successfully used to calculate phase diagrams. The Simplicity of implementation and low computational cost are the main features of the proposed algorithm.