{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Equilibrium Properties and Partial Ordering (Al-Fe and Al-Ni)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Only needed in a Jupyter Notebook\n", "%matplotlib inline\n", "# Optional plot styling\n", "import matplotlib\n", "matplotlib.style.use('bmh')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from pycalphad import equilibrium\n", "from pycalphad import Database, Model\n", "import pycalphad.variables as v\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Al-Fe (Heat Capacity and Degree of Ordering)\n", "Here we compute equilibrium thermodynamic properties in the Al-Fe system. We know that only B2 and liquid are stable in the temperature range of interest, but we just as easily could have included all the phases in the calculation using `my_phases = list(db.phases.keys())`. Notice that the syntax for specifying a range is `(min, max, step)`. We can also directly specify a list of temperatures using the list syntax, e.g., `[300, 400, 500, 1400]`.\n", "\n", "We explicitly indicate that we want to compute equilibrium values of the `heat_capacity` and `degree_of_ordering` properties. These are both defined in the default `Model` class. For a complete list, see the documentation. `equilibrium` will always return the Gibbs energy, chemical potentials, phase fractions and site fractions, regardless of the value of `output`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Dimensions: (P: 1, T: 34, X_AL: 1, component: 2, internal_dof: 5, vertex: 2)\n", "Coordinates:\n", " * P (P) float64 1.013e+05\n", " * T (T) float64 300.0 350.0 400.0 450.0 500.0 550.0 ...\n", " * X_AL (X_AL) float64 0.25\n", " * vertex (vertex) int64 0 1\n", " * component (component) object 'AL' 'FE'\n", " * internal_dof (internal_dof) int64 0 1 2 3 4\n", "Data variables:\n", " MU (P, T, X_AL, component) float64 -7.274e+04 ...\n", " GM (P, T, X_AL) float64 -2.858e+04 -2.994e+04 -3.15e+04 ...\n", " NP (P, T, X_AL, vertex) float64 1.0 nan 1.0 nan 1.0 nan ...\n", " X (P, T, X_AL, vertex, component) float64 0.25 0.75 ...\n", " Y (P, T, X_AL, vertex, internal_dof) float64 0.5 0.5 ...\n", " Phase (P, T, X_AL, vertex) object 'B2_BCC' '' 'B2_BCC' '' ...\n", " degree_of_ordering (P, T, X_AL, vertex) float64 0.6666 nan 0.6665 nan ...\n", " heat_capacity (P, T, X_AL) float64 25.45 26.93 28.47 30.18 32.15 ...\n", "Attributes:\n", " hull_iterations: 5\n", " solve_iterations: 146\n", " engine: pycalphad 0.2.5+63.g4069829.dirty\n", " created: 2016-02-17 16:23:02.404841\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r" ] } ], "source": [ "db = Database('alfe_sei.TDB')\n", "my_phases = ['LIQUID', 'B2_BCC']\n", "eq = equilibrium(db, ['AL', 'FE', 'VA'], my_phases, {v.X('AL'): 0.25, v.T: (300, 2000, 50), v.P: 101325},\n", " output=['heat_capacity', 'degree_of_ordering'])\n", "print(eq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also compute degree of ordering at fixed temperature as a function of composition." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Dimensions: (P: 1, T: 1, X_AL: 100, component: 2, internal_dof: 5, vertex: 2)\n", "Coordinates:\n", " * P (P) float64 1.013e+05\n", " * T (T) float64 700.0\n", " * X_AL (X_AL) float64 1e-09 0.01 0.02 0.03 0.04 0.05 0.06 ...\n", " * vertex (vertex) int64 0 1\n", " * component (component) object 'AL' 'FE'\n", " * internal_dof (internal_dof) int64 0 1 2 3 4\n", "Data variables:\n", " MU (P, T, X_AL, component) float64 -2.312e+05 ...\n", " GM (P, T, X_AL) float64 -2.447e+04 -2.565e+04 ...\n", " NP (P, T, X_AL, vertex) float64 1.0 nan 1.0 nan 1.0 nan ...\n", " X (P, T, X_AL, vertex, component) float64 1e-09 1.0 ...\n", " Y (P, T, X_AL, vertex, internal_dof) float64 1e-09 1.0 ...\n", " Phase (P, T, X_AL, vertex) object 'B2_BCC' '' 'B2_BCC' '' ...\n", " degree_of_ordering (P, T, X_AL, vertex) float64 1.137e-15 nan 2.015e-16 ...\n", "Attributes:\n", " hull_iterations: 5\n", " solve_iterations: 390\n", " engine: pycalphad 0.2.5+63.g4069829.dirty\n", " created: 2016-02-17 16:25:53.860451\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r" ] } ], "source": [ "eq2 = equilibrium(db, ['AL', 'FE', 'VA'], 'B2_BCC', {v.X('AL'): (0,1,0.01), v.T: 700, v.P: 101325},\n", " output='degree_of_ordering')\n", "print(eq2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots\n", "Next we plot the degree of ordering versus temperature. We can see that the decrease in the degree of ordering is relatively steady and continuous. This is indicative of a second-order transition from partially ordered B2 to disordered bcc (A2)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1yV707FDBqk0NPDh5Of/1l+nc/tpClmzY1vyE8pwzLHHICJYzyuwe5sYEtK8o\n4/NDqjnviIN4d0k9T3+0mncWb+SlOXW8MreOUw/pzH8d3Z0e7ffhxinGHECyqnkAiMhY4BLcyX5L\ngYdV9cE8ZsvIah6mkJZv3M5fpq5k4py1JBRKBU4/rAsXD+tuF2k0sVLwmoeI3IS7d8d4dl/b6joR\n6amqt4YRxJio6tGhgu+eUMMFR3bjz1NX8MrcOp6duZYXZ9dx5qAuXHRkd7q0tZqIaVmyrXl8FXex\nwvtU9QVVvQ93LsaV+YuWmdU8wmU5s9OrqoLrTuzDfZ8/nJP6d2RnQnn6ozVc9th07nl7Ceu2NkQi\nZzbikBEsZ5Rle7RVW/x9PALWAq3DjWNM9NV0rOTGU/px0bCtPDxlObULNvC3D1fzz5lrOXdwVw5u\naCx2RGPyLtvzPP4ItAe+DyzC7ba6FdiiqpfkNWEaVvMwUTJ3zRb+OGU5by/aCEDHyjKu/lQvTurf\nyS4PbyIlzJpHtrutrgHqcWd+bwKmApuBb4YRwpg4O6RrG3582gB+ffZAjujWlvXbdvLTVxdyw/Mf\ns2zjPl/Rx5hIy6rxUNWNqnopbjdVD6CNql6qquubeWleWM0jXJYzHIOq2/KLzx7K6W2X076ilClL\n67nyiRn8ZeoKGhqjdbfmqC/LJMsZXTndv1NVE6q6yu5bbkx6JSJ88uAO3P+Fwzn1kE7saFQenLyc\ncX+fxYeB+7IbE3dZn+cRJVbzMHHx3tJ67nxz8a7dV2ce1oWvHNeTDpXZHqtiTHiKUfMwxuyDo3q1\n577zB/Hlo7pTViI8N2stX3l8Bi/PrSOOK27GJGVsPETk54HnpxQmTnas5hEuyxmu1Jytykq49Jge\n3HPeIIZ0b8eGbTu57V8LufH5j1m3pSHDVAqbMaosZ3Q1teURPAHwyXwHMeZAV9Opkl+cdQj/74Qa\n2leU8u7SesY9abUQE08Zax7+FrCrgI+A64Hb0o2nqj/IW7oMrOZh4m7tlgZufWU+H67YTInA14b3\n4vwjDrLzQkxeFarm8QXc+Rw9AAEOTvPoHUYIY1qaLm3KuX3MoXxhSDUJhXv/s5T/fXkBm3fY2ekm\nHjI2Hv6Q3FtU9WvAn1V1bJpHUW4kbjWPcFnOcGWbs6xEuPKTvfjBqf1oU15C7YL1XPPkLObXbc1z\nwgNvWRZbXHKGKduTBMeKSCcRuVREbvB/O+c7nDEtwai+HfntuYfRv3MlSzdu51tPzeLFOWuLHcuY\nJmV7bauJawLlAAAaP0lEQVRPAf8EZuIuyV4DHA6cpapv5TVhGlbzMAeibTsT3PXmYibOqQNgzKAu\njBvRm1ZldkS9CUcxzvO4AxinqiNV9SJV/TRwNfDrMEIYY6CyrIRrT6jhO6MOprxUeHbmWr7zzGyW\n19v1sUz0ZNt4DAQeS+n3OHBIuHGyYzWPcFnOcO1PThHhzEFdueNzA+nevhVz1mzlmidnMXVZfYgJ\nW8ayLKS45AxTto3HHODClH5fBD4ON44xBuDQrm347bmHMaKmA/XbG/nvFz5m0uKNxY5lzC7Z1jxG\nAs8As3E1j77AocBnVfXf+QyYjtU8TEuRUOU3by7mnzPXUl4i3DS6LyP7dCx2LBNTBa95+AZiAHAX\n8C7wG+CQYjQcxrQkJSJ869MHc94nDqIhofzvS/N5fd66YscyJvsLI6rqOlX9k6re7v/W5TNYU6zm\nES7LGa6wc4oIXx/RiwuGVtOo8JNXF/DSnP3792upyzJf4pIzTHYMoDExICJccVxPLjm6OwmFn7+2\nkOdmril2LNOC2f08jImZR95fwe8nLQfgmpG9OXvwQUVOZOIitvfzEJEzRGSmiMwWkeubGO84EWkQ\nkfMLmc+YOLjwyO58fUQvAO769xIe/2BlkROZlijrxkNEykXkeBG5wHe3FZG2Oby+BFdwPx34BHCR\niAzKMN7PgBcyTctqHuGynOEqRM7zj6jmmyPddUnve2cZE95bkdPrbVmGKy45w5RV4yEiQ3CH6f4O\neMD3PhH4fQ7zGg7MUdWFqtoAPAKck2a8b+JOQFyVw7SNaXE+N/ggrj2hBgH+8O5y/jB5md2d0BRM\ntud51AL3qurDIrJOVTv5rY7ZqtorqxmJfB44XVWv9N1fBoar6rcC4/TEXcH3ZBF5EPiHqv4tdVpW\n8zBmt1fm1nH7awtJKHxpaDVfHZ7Vv6RpgYpR8/gE8Cf/XAFUdTPQOowQAXfgbjyVZHfGMaYZpxzS\nmZtO6UepwGMfrGLibLsir8m/sizHWwAcA0xO9hCR4cDcHOa1FHc13qTevl/QscAj4m6n1hU4U0Qa\nVPXp4Eh33nknbdu2pabGTa6qqoohQ4YwatQoYPf+x2J3J/tFJU+m7rvvvjuSy8+WZ/bdAnxr1OH8\n6o1F/Pihf1A3sjcXnnVqxvGnTZvG1VdfHYnl1VR36mdf7DxxW561tbVMmDABgJqaGqqrqxk9ejRh\nyHa31WdxtY57gGuBW4GvA19T1YlZzUikFJgFjAaWA+8AF6nqjAzjZ9xtNX78eL3iiqLchyontbW1\nuz7QKLOc4SpmzjtqF/HszLV0a9eK3557GB0q068f2rIMV1xyhrnbKuvzPETkKOBrQB9gMfA7VX03\np5mJnAHcidtd9oCq/kxErgJUVe9LGff3wDNW8zAmezsaE1z7zBxmrd7C0b3ac+vpAygtsb2/xilK\n4xEl1ngYk9mqTTv4xpOz2LBtJxcd2Y2xx/UsdiQTEQUvmItIhYjcKiLzRGSD73eaiFwTRohc2Xke\n4bKc4Sp2zup2rbjplL6UCPzl/ZW8uWD9XuMUO2O2LGd0ZXu01a+AI4D/wh9tBUzH3U3QGBMxw3q2\n5yt+i+Pnry1k8fptRU5kDjTZFsyX4y7BvllE6lS1s++/XlULfnMB221lTPNUlVtfWcDr89fTp2Ml\nd549kDatSosdyxRRMc7z2EHKYb0ichBgB5QbE1EiwnePr6FPx0oWrt/G+DcW2RnoJjTZNh5/BR4S\nkX4AItIDd52qR/IVrClW8wiX5QxXlHK2aVXKD07tR5vyEt6Yv57Hp7mr/kQpY1MsZ3Rl23jcCMwH\npgEdcfc0Xwb8KE+5jDEhObhjJd87sQ8AD0xaxnvL6oucyBwImq15+KvcngS8qarb/e6qNVrE7V+r\neRiTuwcnLeMv76+kqrKM3557GNXtWhU7kimwgtY8VDUBPKWq23336mI2HMaYfXPpMT04pld7Nmzb\nyf++PJ8djYliRzIxlu1uq9dFZERek+TAah7hspzhimrO0hLhhpP70q1dKya9/W9emBX9412iuixT\nxSVnmLK9MOJC4DkReQp3aZJdWx6q+oN8BDPGhK9DZRlfHFrNT96Hmau38LliBzKxle15Hg9mGqaq\nY0NNlAWreRiz76av3MR3/jGHAV1ac/d5e93M0xzAwqx5ZLXlUYwGwhiTH/06tUaAheu20dCYoLw0\n67tRG7NLtte26p/h0csfjVVQVvMIl+UMV9RztmlVSvny6exMKIsiftmSqC/LpLjkDFO2NY+57K5z\nSOA5QEJEngbGqerKMMMZY/KjZ1UFC4B5dVsZ0KVNseOYGMp2q+FrwARgIFAJHAY8DIwDhuAaod/m\nI2A6w4YNK9Ss9kscbg4DljNscch54vHHA/Dx2q1FTtK0OCxLiE/OMGW75fEj3IURk9u4c0VkHDBb\nVe8VkctxZ50bY2JgQJfWgNvyMGZfZLvlUQL0TelXAyQv0bmZ7Bui/WY1j3BZznDFIeea2VMAt+UR\n5XN+47AsIT45w5TtD/4dwCv+kN3FQG9grO8PMAZ4K/x4xph8qKooo31FKfXbG1m9ucEuVWJylss9\nzM8Avgj0BJYDj6nq83nMlpGd52HM/rvu2TlMXbaJH5/WnxE1VcWOYwqg4Od5APiGoiiNhTEmfAM6\nt2bqsk18vHarNR4mZ3YP8zyKy35QyxmuOOSsra2lvy+aR/mIqzgsS4hPzjDZPcyNaaEGdHbnd9gR\nV2Zf2D3MjWmhGhoTnPPQB+xMKE9eOtTub94C2D3MjTH7rby0hD6dKgGYv862Pkxu7B7meRSX/aCW\nM1xxyJnMOKBztOsecViWEJ+cYbJ7mBvTgsWhaG6iKevzPHa9wO5hbswB4/1l9Xzv2bkcdlAbfnPO\nYcWOY/Ks4Od5iMhg4HigM1AHvAF8FEYAY0zxJLc8FtRtpTGhlJaE8rtiWoAmd1uJ83vc7qobgbOB\nm4APRORBESnKN81qHuGynOGKQ85kxvYVZVS3K2d7o7J04/Yip9pbHJYlxCdnmJqreVwJnASMUNU+\nqvopVa0BPoXbErkql5mJyBkiMlNEZovI9WmGXywi7/tHrYgMyWX6xpjcJc/3sLqHyUWTNQ8RqQV+\npqrPpBn2WeAGVf10VjNydxycDYzGFdsnAReq6szAOCOAGaq6wV9L62ZVHZE6Lat5GBOeh95dzp/f\nW8EFQ6v5yvBexY5j8qiQ53kMBl7LMOw1Pzxbw4E5qrpQVRtwh/meExxBVd9W1Q2+823AvsnG5Nmu\nw3XtTHOTg+Yaj1JVrU83wPfP5f7lvXCXc09aQtONw1eB59INsJpHuCxnuOKQM5hx142hIrjbKg7L\nEuKTM0zNHW1VLiIn4+5bvi+v3yd+nmOBtPd2fO2115g8eTI1NTUAVFVVMWTIkF23gkx+kMXuTopK\nnkzd06ZNi1QeW5757542bdqu7jnvv8OOhfOo6zOUdVsamD7lP0XPF7fu4PKMQp5kd21tLRMmTACg\npqaG6upqRo8eTRiaq3ksYPeFENNS1X5ZzcjVM25W1TN89/fdy/W2lPGGAk8AZ6jqx+mmZTUPY8L1\n3X/M5sOVm/nJGQM4tneHYsc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.gca().set_title('Al-Fe: Degree of bcc ordering vs T [X(AL)=0.25]')\n", "plt.gca().set_xlabel('Temperature (K)')\n", "plt.gca().set_ylabel('Degree of ordering')\n", "plt.gca().set_ylim((-0.1,1.1))\n", "# Generate a list of all indices where B2 is stable\n", "phase_indices = np.nonzero(eq.Phase.values == 'B2_BCC')\n", "# phase_indices[1] refers to all temperature indices\n", "# We know this because pycalphad always returns indices in order like P, T, X's\n", "plt.plot(np.take(eq['T'].values, phase_indices[1]), eq['degree_of_ordering'].values[phase_indices])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the heat capacity curve shown below we notice a sharp increase in the heat capacity around 750 K. This is indicative of a magnetic phase transition and, indeed, the temperature at the peak of the curve coincides with 75% of 1043 K, the Curie temperature of pure Fe. (Pure bcc Al is paramagnetic so it has an effective Curie temperature of 0 K.)\n", "\n", "We also observe a sharp jump in the heat capacity near 1800 K, corresponding to the melting of the bcc phase." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7aslIFaYOSXzxeUrRgcZ3T8mroDFN3ghaU4t/MXR/PzBoXYnGU8BQ1e2qehww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\nPFR1qarOUtWZqnqIqv7C3b5bVU9S1Um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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.gca().set_title('Al-Fe: Heat capacity vs T [X(AL)=0.25]')\n", "plt.gca().set_xlabel('Temperature (K)')\n", "plt.gca().set_ylabel('Heat Capacity (J/mol-atom-K)')\n", "# np.squeeze is used to remove all dimensions of size 1\n", "# For a 1-D/\"step\" calculation, this aligns the temperature and heat capacity arrays\n", "# In 2-D/\"map\" calculations, we'd have to explicitly select the composition of interest\n", "plt.plot(eq['T'].values, np.squeeze(eq['heat_capacity'].values))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To understand more about what's happening around 700 K, we plot the degree of ordering versus composition. Note that this plot excludes all other phases except `B2_BCC`. We observe the presence of disordered bcc (A2) until around 13% Al or Fe, when the phase begins to order." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Il8AsVR0gInOBWTGx0AgsCzeV87t3lrJ+ZxUdW2fxP+OLGNrDGqJBZlSf9jx4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\nsr2ihsdnrgHg54f0tnmiDCM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.gca().set_title('Al-Fe: Degree of bcc ordering vs X(AL) [T=700 K]')\n", "plt.gca().set_xlabel('X(AL)')\n", "plt.gca().set_ylabel('Degree of ordering')\n", "# Generate a list of all indices where B2 is stable\n", "phase_indices = np.nonzero(eq2.Phase.values == 'B2_BCC')\n", "# phase_indices[2] refers to all composition indices\n", "# We know this because pycalphad always returns indices in order like P, T, X's\n", "plt.plot(np.take(eq2['X_AL'].values, phase_indices[2]), eq2['degree_of_ordering'].values[phase_indices])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Al-Ni (Degree of Ordering)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Dimensions: (P: 1, T: 110, X_AL: 1, component: 2, internal_dof: 5, vertex: 2)\n", "Coordinates:\n", " * P (P) float64 1.013e+05\n", " * T (T) float64 300.0 320.0 340.0 360.0 380.0 400.0 ...\n", " * X_AL (X_AL) float64 0.1\n", " * vertex (vertex) int64 0 1\n", " * component (component) object 'AL' 'NI'\n", " * internal_dof (internal_dof) int64 0 1 2 3 4\n", "Data variables:\n", " MU (P, T, X_AL, component) float64 -1.719e+05 ...\n", " GM (P, T, X_AL) float64 -2.526e+04 -2.585e+04 ...\n", " NP (P, T, X_AL, vertex) float64 0.3829 0.6171 0.3543 ...\n", " X (P, T, X_AL, vertex, component) float64 0.25 0.75 ...\n", " Y (P, T, X_AL, vertex, internal_dof) float64 1e-12 1.0 ...\n", " Phase (P, T, X_AL, vertex) object 'FCC_L12' 'FCC_L12' ...\n", " degree_of_ordering (P, T, X_AL, vertex) float64 1.0 7.962e-15 1.0 ...\n", "Attributes:\n", " hull_iterations: 5\n", " solve_iterations: 1047\n", " engine: pycalphad 0.2.5+63.g4069829.dirty\n", " created: 2016-02-17 16:32:02.881604\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r" ] } ], "source": [ "db_alni = Database('NI_AL_DUPIN_2001.TDB')\n", "phases = ['LIQUID', 'FCC_L12']\n", "eq_alni = equilibrium(db_alni, ['AL', 'NI', 'VA'], phases, {v.X('AL'): 0.10, v.T: (300, 2500, 20), v.P: 101325},\n", " output='degree_of_ordering')\n", "print(eq_alni)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots\n", "In the plot below we observe two phases designated `FCC_L12`. This is indicative of a miscibility gap. The ordered gamma-prime phase steadily decreases in amount with increasing temperature until it completely disappears around 750 K, leaving only the disordered gamma phase." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MHz689Qm9ZbRDrumWvELPL2Z69OjRRW/v8cfvo6bmTMaNWwjAww/3p6ICxo6Nrs2cOdHf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\ncxzHcQLF53k4juP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pycalphad.plot.utils import phase_legend\n", "phase_handles, phasemap = phase_legend(phases)\n", "\n", "plt.gca().set_title('Al-Ni: Phase fractions vs T [X(AL)=0.1]')\n", "plt.gca().set_xlabel('Temperature (K)')\n", "plt.gca().set_ylabel('Phase Fraction')\n", "plt.gca().set_ylim((0,1.1))\n", "plt.gca().set_xlim((300, 2000))\n", "\n", "for name in phases:\n", " phase_indices = np.nonzero(eq_alni.Phase.values == name)\n", " plt.scatter(np.take(eq_alni['T'].values, phase_indices[1]), eq_alni.NP.values[phase_indices], color=phasemap[name])\n", "plt.gca().legend(phase_handles, phases, loc='lower right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the plot below we see that the degree of ordering does not change at all in each phase. There is a very abrupt disappearance of the completely ordered gamma-prime phase, leaving the completely disordered gamma phase. This is a first-order phase transition." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GZOS8884rdAQTIbHc87A2j3BZznDFJacxzRHLysMYY0xhxbLysDaPcFnOcMUl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\nY4zJjwbbPESkEpigqn9JMe0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.gca().set_title('Al-Fe: Degree of fcc ordering vs T [X(AL)=0.1]')\n", "plt.gca().set_xlabel('Temperature (K)')\n", "plt.gca().set_ylabel('Degree of ordering')\n", "plt.gca().set_ylim((-0.1,1.1))\n", "# Generate a list of all indices where FCC_L12 is stable and ordered\n", "L12_phase_indices = np.nonzero(np.logical_and((eq_alni.Phase.values == 'FCC_L12'),\n", " (eq_alni.degree_of_ordering.values > 0.01)))\n", "# Generate a list of all indices where FCC_L12 is stable and disordered\n", "fcc_phase_indices = np.nonzero(np.logical_and((eq_alni.Phase.values == 'FCC_L12'),\n", " (eq_alni.degree_of_ordering.values <= 0.01)))\n", "# phase_indices[1] refers to all temperature indices\n", "# We know this because pycalphad always returns indices in order like P, T, X's\n", "plt.plot(np.take(eq_alni['T'].values, L12_phase_indices[1]), eq_alni['degree_of_ordering'].values[L12_phase_indices],\n", " label='$\\gamma\\prime$ (ordered fcc)', color='red')\n", "plt.plot(np.take(eq_alni['T'].values, fcc_phase_indices[1]), eq_alni['degree_of_ordering'].values[fcc_phase_indices],\n", " label='$\\gamma$ (disordered fcc)', color='blue')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }