Calculate and Plot Activity =========================== Given an existing database for Al-Zn, we would like to calculate the activity of the liquid. Experimental activity results ----------------------------- In order to make sure we are correct, we'll compare the values with experimental results. Experimental activities are digtized from Fig 18 in A. Yazawa, Y.K. Lee, Thermodynamic Studies of the Liquid Aluminum Alloy Systems, Trans. Japan Inst. Met. 11 (1970) 411–418. https://doi.org/10.2320/matertrans1960.11.411. The measurements at at 1073 K and they used a reference state of the pure Zn at that temperature. .. code:: ipython3 exp_x_zn = [0.0482, 0.1990, 0.3550, 0.5045, 0.6549, 0.8070, 0.9569] exp_acr_zn = [0.1154, 0.3765, 0.5411, 0.6433, 0.7352, 0.8384, 0.9531] Set up the database ------------------- Al-Zn database is taken from S. Mey, Reevaluation of the Al-Zn system, Zeitschrift F{ü}r Met. 84 (1993) 451–455. .. code:: ipython3 from pycalphad import Database, equilibrium, variables as v import numpy as np dbf = Database('alzn_mey.tdb') comps = ['AL', 'ZN', 'VA'] phases = list(dbf.phases.keys()) Calculate the reference state ----------------------------- Because all chemical activities must be specified with a reference state, we're going to choose a reference state as the pure element at the same temperature, consistent with the experimental data. .. code:: ipython3 ref_eq = equilibrium(dbf, comps, phases, {v.P: 101325, v.T: 1023, v.X('ZN'): 1}) Calculate the equilibria ------------------------ Do the calculation over the composition range .. code:: ipython3 eq = equilibrium(dbf, comps, phases, {v.P: 1013325, v.T: 1023, v.X('ZN'): (0, 1, 0.005)}) Get the chemical potentials and calculate activity -------------------------------------------------- We need to select the chemical potentials from the xarray Dataset and calculate the activity. .. code:: ipython3 chempot_ref = ref_eq.MU.sel(component='ZN').squeeze() chempot = eq.MU.sel(component='ZN').squeeze() acr_zn = np.exp((chempot - chempot_ref)/(8.315*1023)) Plot the result --------------- .. code:: ipython3 %matplotlib inline import matplotlib.pyplot as plt plt.plot(eq.X.sel(component='ZN', vertex=0).squeeze(), acr_zn, label='Calculated') # add experimental data plt.scatter(exp_x_zn, exp_acr_zn, label='Yazawa 1970') plt.xlim((0, 1)) plt.ylim((0, 1)) plt.gca().set_aspect(1) plt.xlabel('X(ZN)') plt.ylabel('ACR(ZN)') plt.title('Activity of Zn at 1073K') plt.legend(loc=0) .. parsed-literal:: .. image:: PlotActivity_files/PlotActivity_11_1.png