ConstructingPhaseDiagram.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"ConstructingPhaseDiagram.ipynb","provenance":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"Gs1anMv-ysd0","colab_type":"text"},"source":["# Constructing Phase Diagrams\n","\n","Phase diagrams are diagrams having axes as Temperature and Compisition. \n","To construct one, we need the usage of G vs X diagrams. \n","\n","For regular solution with $\\Omega$ > 0 i.e the system is going to phase separate, we are going to construct the G vs X diagram first at a particular temperature, find the x points where the $\\Delta$G becomes minimum and plot them in the T vs X plot. \n","\n","Since the system is going to phase separate, our phase diagram will have a miscibility gap region. \n","\n","Also we are going to use non dimensionalized version of entities involved as its computionally much better."]},{"cell_type":"code","metadata":{"id":"PiDVNNoXz96-","colab_type":"code","colab":{}},"source":["# importing libraries\n","import numpy as np\n","from matplotlib import pyplot as plt\n","%matplotlib inline"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"IwmEimOW0Fq1","colab_type":"text"},"source":["As usual we are going to consider an array named x having composition percentages from 0.001 to 0.999, as that's our range of composition values. "]},{"cell_type":"code","metadata":{"id":"rSP4Q0v80Rm-","colab_type":"code","colab":{}},"source":["x = np.arange(0.001, 1.000, 0.001) # x is considered as composition"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"QiWuz2bg0ol8","colab_type":"text"},"source":["As before the expression for free energy change for a regular solution is \n","\n","$\\Delta$G = $\\alpha$x(1-x) + xlnx + (1-x)ln(1-x) \n","\n","where\n","\n","> $\\alpha$ = non dimensionalized regular solution parameter\n","\n","Each $\\alpha$ corresponds to a temperature as $\\alpha$ is inversely proportional to T. So we need to plot our graph over a range of $\\alpha$ to get the phase diagram."]},{"cell_type":"code","metadata":{"id":"7HBs9gNA1xlZ","colab_type":"code","colab":{}},"source":["a = np.zeros(400) # a is for aplha\n","a[0] = 2.0\n","a_step = 0.1\n","\n","for i in range(0, 399, 1): # considering 400 tempeatures here\n","    a[i+1] = a[i] + a_step"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"9tDN42jd144v","colab_type":"text"},"source":["Since we know that in G vs X curve, the minima wells form at the two extremes, we are going to define two arrays of non dimensionalized G and two arrays to store the value of x at the minimas."]},{"cell_type":"code","metadata":{"id":"S-gN10bA2RtD","colab_type":"code","colab":{}},"source":["DG1 = np.zeros(500) # array to store the free energy change to the left side for different T \n","x_min1 = np.zeros(400) # array to store the x values of left minima in G vs X curve\n","DG2 = np.zeros(500) # array to store the free energy change to the right side for different T \n","x_min2 = np.zeros(400) # # array to store the x values of right minima in G vs X curve"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"fC4plUkt3Fsl","colab_type":"text"},"source":["Now we use two for loops and mathematical formula to calculate free energy values and find the minimas as each temperature."]},{"cell_type":"code","metadata":{"id":"NgpfOGSR3PxM","colab_type":"code","colab":{}},"source":["for i in range(0,400,1) : \n","  # loop for traversing through different temperatures\n","    for j in range(0,500,1) :\n","       # loop for traversing through different composition values\n","        DG1[j] = a[i] * x[j] * (1 - x[j]) + x[j] * np.log(x[j]) + (1 - x[j]) * np.log(1 - x[j])\n","    \n","    x_min1[i] = x[np.argmin(DG1)] # finds the left minima values\n","    \n","    for j in range(500, 999) :\n","        \n","        DG2[j - 500] = a[i] * x[j] * (1 - x[j]) + x[j] * np.log(x[j]) + (1 - x[j]) * np.log(1 - x[j]) \n","    \n","    x_min2[i] = x[np.argmin(DG2)] # finds the right minima values"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"Pa5S8xGs3kor","colab_type":"text"},"source":["Phase Diagram plots are plotted with Temperature vs Composition axes. \n","\n","> Non Dimensionalized Temperature, T = 1 / $\\alpha$"]},{"cell_type":"code","metadata":{"id":"hNL3jjBR4BHP","colab_type":"code","outputId":"3fdca1ce-0b0f-46b4-8cbe-f0a0274b7110","executionInfo":{"status":"ok","timestamp":1591804210153,"user_tz":-330,"elapsed":7927,"user":{"displayName":"Tapashree Pradhan","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14Gghq0gewRaoBSbhn5XTwxV6o8xzUgw5Z-fCRzQQPA=s64","userId":"10194166132523392925"}},"colab":{"base_uri":"https://localhost:8080/","height":312}},"source":["temp = 1 / a \n","x_min2 = x_min2 + 0.5\n","\n","# plotting the results \n","\n","plt.plot(x_min1, temp, color = \"green\")\n","plt.plot(x_min2, temp, color = \"green\")\n","plt.xlabel(\"Composition % of B in A\")\n","plt.ylabel(\"Non-Dimensionalized Temperature\")\n","plt.title(\"Miscibility Gap Phase Diagram\")"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0.5, 1.0, 'Miscibility Gap Phase Diagram')"]},"metadata":{"tags":[]},"execution_count":6},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[],"needs_background":"light"}}]}]}