pymatgen.analysis.defects.dilute_solution_model — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.defects.dilute_solution_model

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    Evaluate the defect concentration based on composition, temperature,
    and defect energies using "Dilute Solution Model"
    Reference: Phys Rev B, 63, 094103, 2001,
    "Density of constitutional and thermal point defects in L12 Al3Sc",
    C. Woodward, M. Asta, G. Kresse and J. Hafner.
    Manual and citation for the code, DOI: 10.1016/j.cpc.2015.03.015
    """

    import math
    import copy
    import numpy as np

    from monty.fractions import gcd
    from sympy import Symbol, nsolve, Integer, Float, Matrix, exp, solve

    from monty.dev import deprecated

    __author__ = 'Bharat Medasani'
    __version__ = "0.2"
    __maintainer__ = "Bharat Medasani"
    __email__ = "mbkumar@gmail.com"
    __status__ = "Alpha"
    __date__ = "6/4/14"

    # physical consts
    k_B = 8.6173324e-5  # eV/K

    # Check the inputs
    def _check_input(def_list):
        flag = True
        for defect in def_list:
            if not defect:
                flag = False
                break
        return flag

    @deprecated(message="Refactoring of the defects module will eventualy remove this function")
    def dilute_solution_model(structure, e0, vac_defs, antisite_defs, T, trial_chem_pot=None, generate='plot'):
        """
        Compute the defect densities using dilute solution model.

        Args:
            structure: pymatgen.core.structure.Structure object representing the
                primitive or unitcell of the crystal.
            e0: The total energy of the undefected system.
                This is E0 from VASP calculation.
            vac_defs: List of vacancy defect parameters in the dictionary format.
                The keys of the dict associated with each vacancy defect are
                1) site_index, 2) site_specie, 3) site_multiplicity, and
                4) energy. 1-3 can be obtained from
                pymatgen.analysis.defects.point_defects.Vacancy class.
                Site index is expected to start with 1 (fortran index).
            antisite_defs: List of antisite defect parameters in the dictionary
                format. The keys of the dict associated with each antisite defect
                are 1) site_index, 2) site_specie, 3) site_multiplicity,
                4) substitution_specie, and 5) energy. 1-3 can be obtained
                from pymatgen.analysis.defects.point_defects.Vacancy class.
            T: Temperature in Kelvin
            trial_chem_pot (optional): Trial chemical potentials to speedup
                the plot generation. Format is {el1:mu1,...}
            generate (string): Options are plot or energy
                Chemical potentials are also returned with energy option.
                If energy option is not chosen, plot is generated.

        Returns:
            If generate=plot, the plot data is generated and returned in
            HighCharts format.
            If generate=energy, defect formation enthalpies and chemical
            potentials are returned.
        """

        if not _check_input(vac_defs):
            raise ValueError('Vacancy energy is not defined')
        if not _check_input(antisite_defs):
            raise ValueError('Antisite energy is not defined')

        formation_energies = {}
        formation_energies['vacancies'] = copy.deepcopy(vac_defs)
        formation_energies['antisites'] = copy.deepcopy(antisite_defs)
        for vac in formation_energies['vacancies']:
            del vac['energy']
        for asite in formation_energies['antisites']:
            del asite['energy']
        # Setup the system
        site_species = [vac_def['site_specie'] for vac_def in vac_defs]
        multiplicity = [vac_def['site_multiplicity'] for vac_def in vac_defs]
        m = len(set(site_species))  # distinct species
        n = len(vac_defs)  # inequivalent sites

        # Reduce the system and associated parameters such that only distinctive
        # atoms are retained
        comm_div = gcd(*tuple(multiplicity))
        multiplicity = [val / comm_div for val in multiplicity]
        e0 = e0 / comm_div
        T = Float(T)

        # c0 = np.diag(multiplicity)
        c0 = np.diag(np.ones(n))
        mu = [Symbol('mu' + i.__str__()) for i in range(m)]

        # Generate maps for hashing
        # Generate specie->mu map and use it for site->mu map
        specie_order = []  # Contains hash for site->mu map    Eg: [Al, Ni]
        site_specie_set = set()  # Eg: {Ni, Al}
        for i in range(n):
            site_specie = site_species[i]
            if site_specie not in site_specie_set:
                site_specie_set.add(site_specie)
                specie_order.append(site_specie)
        site_mu_map = []  # Eg: [mu0,mu0,mu0,mu1] where mu0->Al, and mu1->Ni
        for i in range(n):
            site_specie = site_species[i]
            j = specie_order.index(site_specie)
            site_mu_map.append(j)
        specie_site_index_map = []  # Eg: [(0,3),(3,4)] for Al & Ni
        for i in range(m):
            low_ind = site_species.index(specie_order[i])
            if i < m - 1:
                hgh_ind = site_species.index(specie_order[i + 1])
            else:
                hgh_ind = n
            specie_site_index_map.append((low_ind, hgh_ind))
        """
        dC: delta concentration matrix:
        dC[i,j,k]: Concentration change of atom i, due to presence of atom
        j on lattice site k
        Special case is [i,i,i] which is considered as vacancy
        Few cases: dC[i,i,i] = -1 due to being vacancy special case
                    dC[k,k,i] = +1 due to increment in k at i lattice if i
                                   lattice type is of different element
                    dC[i,k,i] = -1 due to decrement of ith type atom due to
                    presence of kth type atom on ith sublattice and kth type
                    atom specie is different from ith sublattice atom specie
                    dC[i,k,k] = 0 due to no effect on ith type atom
                    dC[i,j,k] = 0 if i!=j!=k
        """
        dC = np.zeros((n, n, n), dtype=np.int)
        for i in range(n):
            for j in range(n):
                for k in range(n):
                    if i == j and site_species[j] != site_species[k] and \
                            site_species[i] != site_species[k]:
                        dC[i, j, k] = 1
            for j in range(n):
                for k in range(n):
                    if i == k:
                        dC[i, j, k] = -1
        for k in range(n):
            for j in range(n):
                for i in range(n):
                    if i != j:
                        if site_species[j] == site_species[k]:
                            dC[i, j, k] = 0

        for ind_map in specie_site_index_map:
            if ind_map[1] - ind_map[0] > 1:
                for index1 in range(ind_map[0] + 1, ind_map[1]):
                    for index2 in range(ind_map[0]):
                        for i in range(n):
                            dC[i, index1, index2] = 0
                    for index2 in range(ind_map[1], n):
                        for i in range(n):
                            dC[i, index1, index2] = 0

        # dE matrix: Flip energies (or raw defect energies)
        els = [vac_def['site_specie'] for vac_def in vac_defs]
        dE = []
        for i in range(n):
            dE.append([])
        for i in range(n):
            for j in range(n):
                dE[i].append(0)

        for j in range(n):
            for i in range(n):
                if i == j:
                    dE[i][j] = vac_defs[i]['energy']
                else:
                    sub_specie = vac_defs[i]['site_specie']
                    site_specie = vac_defs[j]['site_specie']
                    if site_specie == sub_specie:
                        dE[i][j] = 0
                    else:
                        for as_def in antisite_defs:
                            if int(as_def['site_index']) == j + 1 and \
                                    sub_specie == as_def['substitution_specie']:
                                dE[i][j] = as_def['energy']
                                break
        dE = np.array(dE)

        # Initialization for concentrations
        # c(i,p) == presence of ith type atom on pth type site
        c = Matrix(n, n, [0] * n ** 2)
        for i in range(n):
            for p in range(n):
                c[i, p] = Integer(c0[i, p])
                site_flip_contribs = []
                for epi in range(n):
                    sum_mu = sum([mu[site_mu_map[j]] * Integer(dC[j, epi, p]) for j in range(n)])
                    flip = Integer(dC[i, epi, p]) * exp(-(dE[epi, p] - sum_mu) / (k_B * T))
                    if flip not in site_flip_contribs:
                        site_flip_contribs.append(flip)
                        c[i, p] += flip

        total_c = []
        for ind in specie_site_index_map:
            val = 0
            for i in range(*ind):
                sum_i = sum([c[i, j] * multiplicity[j] for j in range(n)])
                val += sum_i
            total_c.append(val)

        c_ratio = [total_c[-1] / total_c[i] for i in range(m)]

        # Expression for Omega, the Grand Potential
        omega1 = e0 - sum([mu[site_mu_map[i]] * sum(c0[i, :]) * multiplicity[i] for i in range(n)])
        omega2 = []
        fm_en_eff = []
        used_dEs = []
        for p_r in range(n):
            for epi in range(n):
                sum_mu = sum([mu[site_mu_map[j]] * dC[j, epi, p_r] for j in range(n)])
                if p_r != epi and site_mu_map[p_r] == site_mu_map[epi]:
                    continue
                if dE[epi, p_r] not in used_dEs:
                    omega2.append(k_B * T * multiplicity[p_r] * exp(-(dE[epi, p_r] - sum_mu) / (k_B * T)))
                    fm_en_eff.append(dE[epi, p_r] - sum_mu)
                    used_dEs.append(dE[epi, p_r])
        omega = omega1 - sum(omega2)

        # Compute composition range
        li = specie_site_index_map[0][0]
        hi = specie_site_index_map[0][1]
        comp1_min = sum(multiplicity[li:hi]) / sum(multiplicity) * 100 - 1
        comp1_max = sum(multiplicity[li:hi]) / sum(multiplicity) * 100 + 1
        delta = float(comp1_max - comp1_min) / 120.0
        yvals = []
        for comp1 in np.arange(comp1_min, comp1_max + delta, delta):
            comp2 = 100 - comp1
            y = comp2 / comp1
            yvals.append(y)

        def reduce_mu():
            omega = [e0 - sum([mu[site_mu_map[i]] * sum(c0[i, :]) for i in range(n)])]
            x = solve(omega)
            return x

        def compute_mus_by_search():
            # Compute trial mu
            mu_red = reduce_mu()

            mult = multiplicity
            specie_concen = [sum(mult[ind[0]:ind[1]]) for ind in specie_site_index_map]
            y_vect = [specie_concen[-1] / specie_concen[i] for i in range(m)]
            vector_func = [y_vect[i] - c_ratio[i] for i in range(m - 1)]
            vector_func.append(omega)
            min_diff = 1e10
            mu_vals = None
            c_val = None
            m1_min = -20.0
            if e0 > 0:
                m1_max = 10  # Search space needs to be modified
            else:
                m1_max = 0
            for m1 in np.arange(m1_min, m1_max, 0.01):
                m0 = mu_red[mu[0]].subs(mu[-1], m1)

                try:
                    x = nsolve(vector_func, mu, [m0, m1], module="numpy")
                except Exception:
                    continue

                c_val = c.subs(dict(zip(mu, x)))
                # if all(x >= 0 for x in c_val):
                specie_concen = []
                for ind in specie_site_index_map:
                    specie_concen.append(sum([sum(c_val[i, :]) for i in range(*ind)]))
                y_comp = [specie_concen[-1] / specie_concen[i] for i in range(m)]
                diff = math.sqrt(sum([pow(abs(y_comp[i] - y_vect[i]), 2) for i in range(m)]))
                if diff < min_diff:
                    min_diff = diff
                    mu_vals = x

            if mu_vals:
                mu_vals = [float(mu_val) for mu_val in mu_vals]
            else:
                raise ValueError()
            return mu_vals

        def compute_def_formation_energies():
            i = 0
            for vac_def in vac_defs:
                site_specie = vac_def['site_specie']
                ind = specie_order.index(site_specie)
                uncor_energy = vac_def['energy']
                formation_energy = uncor_energy + mu_vals[ind]
                formation_energies['vacancies'][i]['formation_energy'] = formation_energy
                specie_ind = site_mu_map[i]
                indices = specie_site_index_map[specie_ind]
                specie_ind_del = indices[1] - indices[0]
                cur_ind = i - indices[0] + 1
                if not specie_ind_del - 1:
                    label = '$V_{' + site_specie + '}$'
                else:
                    label = '$V_{' + site_specie + '_' + str(cur_ind) + '}$'
                formation_energies['vacancies'][i]['label'] = label
                i += 1
            i = 0
            for as_def in antisite_defs:
                site_specie = as_def['site_specie']
                sub_specie = as_def['substitution_specie']
                ind1 = specie_order.index(site_specie)
                ind2 = specie_order.index(sub_specie)
                uncor_energy = as_def['energy']
                formation_energy = uncor_energy + mu_vals[ind1] - mu_vals[ind2]
                formation_energies['antisites'][i]['formation_energy'] = formation_energy
                specie_ind = site_mu_map[i]
                indices = specie_site_index_map[specie_ind]
                specie_ind_del = indices[1] - indices[0]
                cur_ind = i - indices[0] + 1
                if not specie_ind_del - 1:
                    label = '$' + sub_specie + '_{' + site_specie + '}$'
                else:
                    label = '$' + sub_specie + '_{' + site_specie + '_' + str(cur_ind) + '}$'
                formation_energies['antisites'][i]['label'] = label
                i += 1
            return formation_energies

        # If generate option is energy compute effective formation energies
        # at ideal stoichiometry and return the formation energies and chem pot.
        if generate == 'energy':
            if not trial_chem_pot:
                mu_vals = compute_mus_by_search()
            else:
                mu_vals = [trial_chem_pot[element] for element in specie_order]

            formation_energies = compute_def_formation_energies()
            mu_dict = dict(zip(specie_order, mu_vals))
            return formation_energies, mu_dict

        if not trial_chem_pot:
            # Try computing mus by assuming one of the defects is dominant at 0.01
            # concen.  First vacancy is tried and then antisite

            # Generate trial mus assuming vacancy as dominant defect
            # for specie-0 at lower yval
            li = specie_site_index_map[0][0]
            hi = specie_site_index_map[0][1]
            li1 = specie_site_index_map[1][0]
            hi1 = specie_site_index_map[1][1]
            spec_mult = [sum(multiplicity[li:hi]), sum(multiplicity[li1:hi1])]
            ln_def_conc = 4.60517
            for i in range(li, hi):
                vac_flip_en = vac_defs[i]['energy']
                mu_vals = [ln_def_conc * k_B * T - vac_flip_en]
                mu_vals.append((e0 - spec_mult[0] * mu_vals[0]) / spec_mult[1])
                comp_ratio = yvals[0]

                # Test if the trial mus are good
                vector_func = [comp_ratio - c_ratio[0]]
                vector_func.append(omega)
                try:
                    mu_vals = nsolve(vector_func, mu, mu_vals)
                    if mu_vals:
                        mu_vals = [float(mu_val) for mu_val in mu_vals]
                    break
                except Exception:  # Go for antisite as dominant defect
                    mu_gs = [Symbol('mu_gs' + j.__str__()) for j in range(m)]

                    eqs = [mu_gs[0] - mu_gs[1] - (ln_def_conc * k_B * T - antisite_defs[i]['energy'])]
                    eqs.append(spec_mult[0] * mu_gs[0] + spec_mult[1] * mu_gs[1] - e0)
                    x = solve(eqs, mu_gs)
                    # mu_names = sorted([key.name for key in x.keys()])
                    mu_vals = []
                    for key in sorted(x.keys(), key=lambda inp: inp.name):
                        mu_vals.append(x[key])
                    vector_func = [comp_ratio - c_ratio[0]]
                    vector_func.append(omega)

                    try:
                        mu_vals = nsolve(vector_func, mu, mu_vals)
                        if mu_vals:
                            mu_vals = [float(mu_val) for mu_val in mu_vals]
                        break
                    except Exception:  # Go to the default option (search the space)
                        pass
            else:
                mu_vals = compute_mus_by_search()

        else:
            try:
                mu_vals = [trial_chem_pot[element] for element in specie_order]
            except Exception:
                mu_vals = compute_mus_by_search()

        # Compile mu's for all composition ratios in the range
        # +/- 1% from the stoichiometry
        result = {}
        i = 0
        failed_y, failed_i = [], []
        for y in yvals:
            vector_func = [y - c_ratio[0]]
            vector_func.append(omega)
            try:
                x = nsolve(vector_func, mu, mu_vals, module="numpy")
                if x:
                    mu_vals = [float(mu_val) for mu_val in x]
            except Exception:
                failed_y.append(y)
                failed_i.append(i)
                continue
            result[y] = list(mu_vals)
            x = None
            i += 1

        def get_next_mu_val(i):
            if i >= len(yvals):
                return None

            y = yvals[i + 1]
            x = result.get(y, None)
            if x:
                mu_vals = [float(mu_val) for mu_val in x]
                return mu_vals
            else:
                return get_next_mu_val(i + 1)

        def get_prev_mu_val(i):
            if i <= 0:
                return None

            y = yvals[i - 1]
            x = result.get(y, None)
            if x:
                mu_vals = [float(mu_val) for mu_val in x]
                return mu_vals
            else:
                return get_next_mu_val(i - 1)

        # Try to get better trial mus for failed cases
        for j in range(len(failed_y)):
            i = failed_i[j]

            prev_mu_val = get_prev_mu_val(i)
            if not prev_mu_val:
                continue
            next_mu_val = get_next_mu_val(i)
            if not next_mu_val:
                continue

            y = failed_y[j]
            vector_func = [y - c_ratio[0]]
            vector_func.append(omega)
            trial_mu = list(map(lambda x: float(sum(x)) / len(x), zip(prev_mu_val, next_mu_val)))
            try:
                x = nsolve(vector_func, mu, trial_mu, module="numpy")
                if x:
                    mu_vals = [float(mu_val) for mu_val in x]
            except Exception:
                continue
            result[y] = mu_vals
            x = None

        # Alternate way of calculating trial mus for failed cases
        # by taking average of trial mus at extremes.
        # for j in range(len(failed_y)):
        #    y = yvals[0]
        #    prev_mu_val = result[y]
        #    y = yvals[-1]
        #    next_mu_val = result[y]
        #
        #    trial_mu = list(map(lambda x: float(sum(x))/len(x),  \
        #            zip(prev_mu_val,next_mu_val)))
        #    y = failed_y[j]
        #    vector_func = [y-c_ratio[0]]
        #    vector_func.append(omega)
        #    try:
        #        x = nsolve(vector_func,mu,trial_mu,module="numpy")
        #        if x:
        #            mu_vals = [float(mu_val) for mu_val in x]
        #    except Exception:
        #        continue
        #    result[y] = list(mu_vals)

        if len(result.keys()) < len(yvals) / 2:
            raise ValueError('Not sufficient data')

        res = []
        new_mu_dict = {}
        # Compute the concentrations for all the compositions
        for key in sorted(result.keys()):
            mu_val = result[key]
            total_c_val = [total_c[i].subs(dict(zip(mu, mu_val))) for i in range(len(total_c))]
            c_val = c.subs(dict(zip(mu, mu_val)))
            res1 = []
            # Concentration of first element/over total concen
            res1.append(float(total_c_val[0] / sum(total_c_val)))
            new_mu_dict[res1[0]] = mu_val
            for i in range(n):
                for j in range(n):
                    if i == j:  # Vacancy
                        vac_conc = float(exp(-(mu_val[site_mu_map[i]] + dE[i, i]) / (k_B * T)))
                        res1.append(vac_conc)
                    else:  # Antisite
                        res1.append(float(c_val[i, j] / c0[j, j]))
            res.append(res1)

        res = np.array(res)
        dtype = [(str('x'), np.float64)] + [(str('y%d%d' % (i, j)), np.float64) for i in range(n) for j in range(n)]
        res1 = np.sort(res.view(dtype), order=[str('x')], axis=0)

        conc_data = {}
        """Because all the plots have identical x-points storing it in a
        single array"""
        conc_data['x'] = [dat[0][0] for dat in res1]  # x-axis data
        # Element whose composition is varied. For x-label
        conc_data['x_label'] = els[0] + " mole fraction"
        conc_data['y_label'] = "Point defect concentration"
        conc = []
        for i in range(n):
            conc.append([])
            for j in range(n):
                conc[i].append([])
        for i in range(n):
            for j in range(n):
                y1 = [dat[0][i * n + j + 1] for dat in res1]
                conc[i][j] = y1

        y_data = []
        for i in range(n):
            data = conc[i][i]
            specie = els[i]
            specie_ind = site_mu_map[i]
            indices = specie_site_index_map[specie_ind]
            specie_ind_del = indices[1] - indices[0]
            cur_ind = i - indices[0] + 1
            vac_string = "$Vac_{"
            if not specie_ind_del - 1:
                label = vac_string + specie + '}$'
            else:
                label = vac_string + specie + '_' + str(cur_ind) + '}$'
            # Plot data and legend info
            y_data.append({'data': data, 'name': label})

        for i in range(n):
            site_specie = els[i]
            specie_ind = site_mu_map[i]
            indices = specie_site_index_map[specie_ind]
            specie_ind_del = indices[1] - indices[0]
            cur_ind = i - indices[0] + 1
            for j in range(m):  # Antisite plot dat
                sub_specie = specie_order[j]
                if sub_specie == site_specie:
                    continue
                if not specie_ind_del - 1:
                    label = '$' + sub_specie + '_{' + site_specie + '}$'
                else:
                    label = '$' + sub_specie + '_{' + site_specie + '_' + str(cur_ind) + '}$'
                inds = specie_site_index_map[j]
                # TODO: Investigate the value below
                data = np.sum([conc[ind][i] for ind in range(*inds)], axis=0)
                data = data.tolist()
                y_data.append({'data': data, 'name': label})

        conc_data['y'] = y_data

        # Compute the  formation energies
        def compute_vac_formation_energies(mu_vals):
            en = []
            for vac_def in vac_defs:
                site_specie = vac_def['site_specie']
                ind = specie_order.index(site_specie)
                uncor_energy = vac_def['energy']
                formation_energy = uncor_energy + mu_vals[ind]
                en.append(float(formation_energy))
            return en

        en_res = []
        for key in sorted(new_mu_dict.keys()):
            mu_val = new_mu_dict[key]
            en_res.append(compute_vac_formation_energies(mu_val))

        en_data = {'x_label': els[0] + ' mole fraction', 'x': []}
        en_data['x'] = [dat[0][0] for dat in res1]  # x-axis data

        i = 0
        y_data = []
        for vac_def in vac_defs:
            data = [data[i] for data in en_res]
            site_specie = vac_def['site_specie']
            ind = specie_order.index(site_specie)
            specie_ind = site_mu_map[i]
            indices = specie_site_index_map[specie_ind]
            specie_ind_del = indices[1] - indices[0]
            cur_ind = i - indices[0] + 1
            vac_string = "$Vac_{"
            if not specie_ind_del - 1:
                label = vac_string + site_specie + '}$'
            else:
                label = vac_string + site_specie + '_' + str(cur_ind) + '}$'
            y_data.append({'data': data, 'name': label})
            i += 1

        def compute_as_formation_energies(mu_vals):
            en = []
            for as_def in antisite_defs:
                site_specie = as_def['site_specie']
                sub_specie = as_def['substitution_specie']
                ind1 = specie_order.index(site_specie)
                ind2 = specie_order.index(sub_specie)
                uncor_energy = as_def['energy']
                form_en = uncor_energy + mu_vals[ind1] - mu_vals[ind2]
                en.append(form_en)
            return en

        en_res = []
        for key in sorted(new_mu_dict.keys()):
            mu_val = new_mu_dict[key]
            en_res.append(compute_as_formation_energies(mu_val))
        i = 0
        for as_def in antisite_defs:
            data = [data[i] for data in en_res]
            site_specie = as_def['site_specie']
            sub_specie = as_def['substitution_specie']
            specie_ind = site_mu_map[i]
            indices = specie_site_index_map[specie_ind]
            specie_ind_del = indices[1] - indices[0]
            cur_ind = i - indices[0] + 1
            if not specie_ind_del - 1:
                label = '$' + sub_specie + '_{' + site_specie + '}$'
            else:
                label = '$' + sub_specie + '_{' + site_specie + '_' + str(cur_ind) + '}$'
            y_data.append({'data': data, 'name': label})
            i += 1

        en_data['y'] = y_data

        # Return chem potential as well
        mu_data = {'x_label': els[0] + ' mole fraction', 'x': []}
        mu_data['x'] = [dat[0][0] for dat in res1]  # x-axis data

        y_data = []
        for j in range(m):
            specie = specie_order[j]
            mus = [new_mu_dict[key][j] for key in sorted(new_mu_dict.keys())]
            y_data.append({'data': mus, 'name': specie})
        mu_data['y'] = y_data

        return conc_data, en_data, mu_data

    def compute_defect_density(structure, e0, vac_defs, antisite_defs, T=800, trial_chem_pot=None, plot_style="highcharts"):
        """
        Wrapper for the dilute_solution_model.
        The computed plot data is prepared based on plot_style.

        Args:
            structure: pymatgen.core.structure.Structure object representing the
                primitive or unitcell of the crystal.
            e0: The total energy of the undefected system.
                This is E0 from VASP calculation.
            vac_defs: List of vacancy defect parameters in the dictionary format.
                The keys of the dict associated with each vacancy defect are
                1) site_index, 2) site_specie, 3) site_multiplicity, and
                4) energy. 1-3 can be obtained from
                pymatgen.analysis.defects.point_defects.Vacancy class.
                Site index is expected to start with 1 (fortran index).
            antisite_defs: List of antisite defect parameters in the dictionary
                format. The keys of the dict associated with each antisite defect
                are 1) site_index, 2) site_specie, 3) site_multiplicity,
                4) substitution_specie, and 5) energy. 1-3 can be obtained
                from pymatgen.analysis.defects.point_defects.Vacancy class.
            T: Temperature in Kelvin
            trial_chem_pot (optional): Trial chemical potentials to speedup
                the plot generation. Format is {el1:mu1,...}
            plot_style (string): Allowed options are
                1) highcharts (default)
                2) gnuplot

        Returns:
            The plot data is generated and returned in asked format.
        """
        conc_data, en_data, mu_data = dilute_solution_model(
            structure, e0, vac_defs, antisite_defs, T, trial_chem_pot=trial_chem_pot)

        if plot_style == 'highcharts':
            "Energy data is ignored in this mode"
            hgh_chrt_data = {}
            hgh_chrt_data['xAxis'] = conc_data['x_label']
            hgh_chrt_data['yAxis'] = conc_data['y_label']

            series = []
            x = conc_data['x']
            for y_data in conc_data['y']:
                y = y_data['data']
                xy = zip(x, y)
                xy = [list(el) for el in xy]
                name = y_data['name'].strip('$')
                flds = name.split('_')
                def_string = flds[0]
                site_string = flds[1].strip('{}')
                name = def_string + "<sub>" + site_string + "</sub>"
                # series.append({'data':xy, 'name':y_data['name']})
                series.append({'data': xy, 'name': name})
            hgh_chrt_data['series'] = series
            return hgh_chrt_data
        elif plot_style == 'gnuplot':

            def data_to_rows(inp_data):
                rows = []
                labels = []
                labels.append(inp_data['x_label'])
                labels += [y['name'] for y in inp_data['y']]
                # labels.sort()
                rows.append('#' + '\t'.join(labels))
                m = len(inp_data['x'])
                for i in range(m):
                    data = []
                    data.append(inp_data['x'][i])
                    data += [y['data'][i] for y in inp_data['y']]
                    data = [float(x) for x in data]
                    rows.append('\t'.join(list(map(str, data))))
                return rows

            conc_rows = data_to_rows(conc_data)
            en_rows = data_to_rows(en_data)
            mu_rows = data_to_rows(mu_data)

            return conc_rows, en_rows, mu_rows

    # solute_site_preference_finder is based on dilute_solution_model and so most
    # of the code is same. However differences exist in setting up and processing
    # hence new function
    def solute_site_preference_finder(structure,
                                      e0,
                                      T,
                                      vac_defs,
                                      antisite_defs,
                                      solute_defs,
                                      solute_concen=0.01,
                                      trial_chem_pot=None):
        """
        Compute the solute defect densities using dilute solution model.
        Args:
            structure: pymatgen.core.structure.Structure object representing the
                primitive or unitcell of the crystal.
            e0: The total energy of the undefected system.
                This is E0 from VASP calculation.
            T: Temperature in Kelvin
            vac_defs: List of vacancy defect parameters in the dictionary format.
                The keys of the dict associated with each vacancy defect are
                1) site_index, 2) site_specie, 3) site_multiplicity, and
                4) energy. 1-3 can be obtained from
                pymatgen.analysis.defects.point_defects.Vacancy class.
                Site index is expected to start with 1 (fortran index).
            antisite_defs: List of antisite defect parameters in the dictionary
                format. The keys of the dict associated with each antisite
                defect are 1) site_index, 2) site_specie, 3) site_multiplicity,
                4) substitution_specie, and 5) energy. 1-3 can be obtained
                from pymatgen.analysis.defects.point_defects.Vacancy class.
            solute_defs: List of solute defect parameters in the dictionary
                format. Similary to that of antisite defs, wtih solute specie
                specified in substitution_specie
            solute_concen: Solute concentration (in fractional value)
            trial_chem_pot: Trial chemical potentials to speedup the plot
                generation. Format is {el1:mu1,...}

        Returns:
            plot_data: The data for plotting the solute defect concentration.
        """

        if not _check_input(vac_defs):
            raise ValueError('Vacancy energy is not defined')
        if not _check_input(antisite_defs):
            raise ValueError('Antisite energy is not defined')

        formation_energies = {}
        formation_energies['vacancies'] = copy.deepcopy(vac_defs)
        formation_energies['antisites'] = copy.deepcopy(antisite_defs)
        formation_energies['solute'] = copy.deepcopy(solute_defs)
        for vac in formation_energies['vacancies']:
            del vac['energy']
        for asite in formation_energies['antisites']:
            del asite['energy']
        for solute in formation_energies['solute']:
            del solute['energy']
        # Setup the system
        site_species = [vac_def['site_specie'] for vac_def in vac_defs]
        solute_specie = solute_defs[0]['substitution_specie']
        site_species.append(solute_specie)
        multiplicity = [vac_def['site_multiplicity'] for vac_def in vac_defs]
        m = len(set(site_species))  # distinct species
        n = len(vac_defs)  # inequivalent sites

        # Reduce the system and associated parameters such that only distinctive
        # atoms are retained
        comm_div = gcd(*tuple(multiplicity))
        multiplicity = [val / comm_div for val in multiplicity]
        multiplicity.append(0)
        e0 = e0 / comm_div
        T = Float(T)

        # c0 = np.diag(multiplicity)
        c0 = np.diag(np.ones(n + 1))
        c0[n, n] = 0
        mu = [Symbol('mu' + str(i)) for i in range(m)]

        # Generate maps for hashing
        # Generate specie->mu map and use it for site->mu map
        specie_order = []  # Contains hash for site->mu map    Eg: [Al, Ni]
        site_specie_set = set()  # Eg: {Ni, Al}
        for i in range(len(site_species)):
            site_specie = site_species[i]
            if site_specie not in site_specie_set:
                site_specie_set.add(site_specie)
                specie_order.append(site_specie)
        site_mu_map = []  # Eg: [mu0,mu0,mu0,mu1] where mu0->Al, and mu1->Ni
        for i in range(len(site_species)):
            site_specie = site_species[i]
            j = specie_order.index(site_specie)
            site_mu_map.append(j)
        specie_site_index_map = []  # Eg: [(0,3),(3,4)] for Al & Ni
        for i in range(m):
            low_ind = site_species.index(specie_order[i])
            if i < m - 1:
                hgh_ind = site_species.index(specie_order[i + 1])
            else:
                hgh_ind = len(site_species)
            specie_site_index_map.append((low_ind, hgh_ind))
        """
        dC: delta concentration matrix:
        dC[i,j,k]: Concentration change of atom i, due to presence of atom
        j on lattice site k
        Special case is [i,i,i] which is considered as vacancy
        Few cases: dC[i,i,i] = -1 due to being vacancy special case
                    dC[k,k,i] = +1 due to increment in k at i lattice if i
                                   lattice type is of different element
                    dC[i,k,i] = -1 due to decrement of ith type atom due to
                    presence of kth type atom on ith sublattice and kth type
                    atom specie is different from ith sublattice atom specie
                    dC[i,k,k] = 0 due to no effect on ith type atom
                    dC[i,j,k] = 0 if i!=j!=k
        """
        dC = np.zeros((n + 1, n + 1, n), dtype=np.int)
        for i in range(n):
            for j in range(n):
                for k in range(n):
                    if i == j and site_species[j] != site_species[k] and \
                            site_species[i] != site_species:
                        dC[i, j, k] = 1
            for j in range(n + 1):
                for k in range(n):
                    if i == k:
                        dC[i, j, k] = -1
        for k in range(n):
            dC[n, n, k] = 1
        for k in range(n):
            for j in range(n):
                if i != j:
                    if site_species[i] == site_species[k]:
                        dC[i, j, k] = 0

        for ind_map in specie_site_index_map:
            if ind_map[1] - ind_map[0] > 1:
                for index1 in range(ind_map[0] + 1, ind_map[1]):
                    for index2 in range(ind_map[0]):
                        for i in range(n):
                            dC[i, index1, index2] = 0
                    for index2 in range(ind_map[1], n):
                        for i in range(n):
                            dC[i, index1, index2] = 0

        # dE matrix: Flip energies (or raw defect energies)
        els = [vac_def['site_specie'] for vac_def in vac_defs]
        dE = []
        for i in range(n + 1):
            dE.append([])
        for i in range(n + 1):
            for j in range(n):
                dE[i].append(0)

        for j in range(n):
            for i in range(n):
                if i == j:
                    dE[i][j] = vac_defs[i]['energy']
                else:
                    sub_specie = vac_defs[i]['site_specie']
                    site_specie = vac_defs[j]['site_specie']
                    if site_specie == sub_specie:
                        dE[i][j] = 0
                    else:
                        for as_def in antisite_defs:
                            if int(as_def['site_index']) == j + 1 and \
                                    sub_specie == as_def['substitution_specie']:
                                dE[i][j] = as_def['energy']
                                break
            # Solute
            site_specie = vac_defs[j]['site_specie']
            for solute_def in solute_defs:
                def_site_ind = int(solute_def['site_index'])
                def_site_specie = solute_def['site_specie']
                if def_site_specie == site_specie and def_site_ind == j + 1:
                    dE[n][j] = solute_def['energy']
                    break

        dE = np.array(dE)
        # np.where(dE == np.array(None), 0, dE)

        # Initialization for concentrations
        # c(i,p) == presence of ith type atom on pth type site
        c = Matrix(n + 1, n, [0] * n * (n + 1))
        for i in range(n + 1):
            for p in range(n):
                c[i, p] = Integer(c0[i, p])
                site_flip_contribs = []
                for epi in range(n + 1):
                    sum_mu = sum([mu[site_mu_map[j]] * Integer(dC[j, epi, p]) for j in range(n + 1)])
                    flip = dC[i, epi, p] * exp(-(dE[epi, p] - sum_mu) / (k_B * T))
                    if flip not in site_flip_contribs:
                        site_flip_contribs.append(flip)
                        c[i, p] += flip
        host_c = Matrix(n, n, [0] * n * n)
        for i in range(n):
            for p in range(n):
                host_c[i, p] = Integer(c0[i, p])
                site_flip_contribs = []
                for epi in range(n):
                    sum_mu = sum([mu[site_mu_map[j]] * Integer(dC[j, epi, p]) for j in range(n)])
                    flip = dC[i, epi, p] * exp(-(dE[epi, p] - sum_mu) / (k_B * T))
                    if flip not in site_flip_contribs:
                        site_flip_contribs.append(flip)
                        host_c[i, p] += flip

        # specie_concen = [sum(mult[ind[0]:ind[1]]) for ind in specie_site_index_map]
        # total_c = [sum(c[ind[0]:ind[1]]) for ind in specie_site_index_map]
        total_c = []
        for ind in specie_site_index_map:
            val = 0
            for i in range(*ind):
                sum_i = sum([c[i, j] * multiplicity[j] for j in range(n)])
                val += sum_i
            total_c.append(val)

        c_ratio = [total_c[i] / sum(total_c) for i in range(m)]

        host_total_c = []
        for ind in specie_site_index_map[:-1]:
            val = 0
            for i in range(*ind):
                sum_i = sum([host_c[i, j] * multiplicity[j] for j in range(n)])
                val += sum_i
            host_total_c.append(val)

        host_c_ratio = [host_total_c[i] / sum(host_total_c) for i in range(m - 1)]

        # Expression for Omega, the Grand Potential
        omega1 = e0 - sum([mu[site_mu_map[i]] * sum(c0[i, :]) * multiplicity[i] for i in range(n)])
        omega = omega1

        used_dEs = []
        for p_r in range(n):
            for epi in range(n):
                sum_mu1 = sum([mu[site_mu_map[j]] * Integer(dC[j, epi, p_r]) for j in range(n)])
                sum_mu = sum_mu1 - mu[site_mu_map[n]] * dC[n, epi, p_r]
                if p_r != epi and site_mu_map[p_r] == site_mu_map[epi]:
                    continue
                if dE[epi, p_r] not in used_dEs:
                    omega1 -= k_B * T * multiplicity[p_r] * exp(-(dE[epi, p_r] - sum_mu1) / (k_B * T))
                    omega -= k_B * T * multiplicity[p_r] * exp(-(dE[epi, p_r] - sum_mu) / (k_B * T))
                    used_dEs.append(dE[epi, p_r])

        # Compute composition ranges
        max_host_specie_concen = 1 - solute_concen
        mult = multiplicity
        specie_concen = [sum(mult[ind[0]:ind[1]]) for ind in specie_site_index_map]
        host_specie_concen_ratio = [specie_concen[i] / sum(specie_concen) * max_host_specie_concen for i in range(m)]
        host_specie_concen_ratio[-1] = solute_concen
        li = specie_site_index_map[0][0]
        hi = specie_site_index_map[0][1]
        comp1_min = sum(multiplicity[li:hi]) / sum(multiplicity) * max_host_specie_concen - 0.01
        comp1_max = sum(multiplicity[li:hi]) / sum(multiplicity) * max_host_specie_concen + 0.01
        delta = (comp1_max - comp1_min) / 50.0

        # def reduce_mu():
        #    omega = [e0 - sum([mu[site_mu_map[i]]*sum(c0[i,:]) for i in range(n)])]
        #    x = solve(omega)
        #    return x
        def reduce_mu():
            host_concen = 1 - solute_concen
            new_c0 = c0.astype(float)
            for i in range(n):
                new_c0[i, i] = host_concen * c0[i, i]
            new_c0[n, n] = 2 * solute_concen
            omega = [e0 - sum([mu[site_mu_map[i]] * sum(new_c0[i, :]) for i in range(n + 1)])]
            x = solve(omega)
            return x

        def compute_solute_mu_by_lin_search(host_mu_vals):
            # Compute trial mu
            mult = multiplicity
            specie_concen = [sum(mult[ind[0]:ind[1]]) for ind in specie_site_index_map]
            max_host_specie_concen = 1 - solute_concen
            host_specie_concen_ratio = [specie_concen[i] / sum(specie_concen) * max_host_specie_concen for i in range(m)]
            host_specie_concen_ratio[-1] = solute_concen
            y_vect = host_specie_concen_ratio
            vector_func = [y_vect[i] - c_ratio[i] for i in range(m)]
            vector_func.append(omega)
            mu_vals = None
            m1_min = -20.0
            if e0 > 0:
                m1_max = 10  # Search space needs to be modified
            else:
                m1_max = 0
            for m1 in np.arange(m1_min, m1_max, 0.1):
                trial_mus = host_mu_vals + [m1]
                try:
                    x = nsolve(vector_func, mu, trial_mus, module="numpy")
                    if x:
                        mu_vals = [float(mu_val) for mu_val in x]
                    break
                except Exception:
                    continue
            else:
                raise ValueError()
            return mu_vals

        def compute_mus():

            # Compute trial mu
            mu_red = reduce_mu()
            mult = multiplicity
            specie_concen = [sum(mult[ind[0]:ind[1]]) for ind in specie_site_index_map]
            max_host_specie_concen = 1 - solute_concen
            host_specie_concen_ratio = [specie_concen[i] / sum(specie_concen) * max_host_specie_concen for i in range(m)]
            host_specie_concen_ratio[-1] = solute_concen

            y_vect = host_specie_concen_ratio
            vector_func = [y_vect[i] - c_ratio[i] for i in range(m)]
            vector_func.append(omega)
            mu_vals = None
            m_min = -15.0
            if e0 > 0:
                m_max = 10  # Search space needs to be modified
            else:
                m_max = 0
            for m1 in np.arange(m_min, m_max, 0.3):
                for m2 in np.arange(m_min, m_max, 0.3):
                    m0 = mu_red[mu[0]].subs([(mu[1], m1), (mu[2], m2)])
                    try:
                        mu_vals = nsolve(vector_func, mu, [m0, m1, m2], module="numpy")
                        # Line needs to be modified to include all mus when n > 2
                    except Exception:
                        continue
                    break
                if mu_vals:
                    mu_vals = [float(mu_val) for mu_val in mu_vals]
                    break
            else:
                raise ValueError("Couldn't find mus")
            return mu_vals

        if not trial_chem_pot:
            # Try computing mus by assuming one of the defects is dominant at 0.01
            # concen.  First vacancy is tried and then antisite

            # Generate trial mus assuming vacancy as dominant defect
            # for specie-0 at lower yval
            li = specie_site_index_map[0][0]
            hi = specie_site_index_map[0][1]
            li1 = specie_site_index_map[1][0]
            hi1 = specie_site_index_map[1][1]
            spec_mult = [sum(multiplicity[li:hi]), sum(multiplicity[li1:hi1])]
            ln_def_conc = 4.60517
            for i in range(li, hi):
                vac_flip_en = vac_defs[i]['energy']
                mu_vals = [ln_def_conc * k_B * T - vac_flip_en]
                mu_vals.append((e0 - spec_mult[0] * mu_vals[0]) / spec_mult[1])
                comp_ratio = comp1_min

                # Test if the trial mus are good
                vector_func = [comp_ratio - host_c_ratio[0]]
                vector_func.append(omega1)
                try:
                    host_mu_vals = nsolve(vector_func, mu[:-1], mu_vals)
                    if host_mu_vals:
                        host_mu_vals = [float(mu_val) for mu_val in host_mu_vals]
                    compute_solute_mu_by_lin_search(host_mu_vals)
                    break
                except Exception:  # Go for antisite as dominant defect
                    mu_gs = [Symbol('mu_gs' + j.__str__()) for j in range(m - 1)]

                    eqs = [mu_gs[0] - mu_gs[1] - (ln_def_conc * k_B * T - antisite_defs[i]['energy'])]
                    eqs.append(spec_mult[0] * mu_gs[0] + spec_mult[1] * mu_gs[1] - e0)
                    x = solve(eqs, mu_gs)
                    host_mu_vals = []
                    for key in sorted(x.keys(), key=lambda inp: inp.name):
                        host_mu_vals.append(x[key])
                    vector_func = [comp_ratio - host_c_ratio[0]]
                    vector_func.append(omega1)

                    try:
                        host_mu_vals = nsolve(vector_func, mu[:-1], host_mu_vals)
                        if host_mu_vals:
                            host_mu_vals = [float(mu_val) for mu_val in host_mu_vals]
                        mu_vals = compute_solute_mu_by_lin_search(host_mu_vals)
                        break
                    except Exception:  # Go to the default option (search the space)
                        pass
            else:
                mu_vals = compute_mus()

        else:
            try:
                mu_vals = [trial_chem_pot[element] for element in specie_order]
            except Exception:
                mu_vals = compute_mus()

        # Compile mu's for all composition ratios in the range
        # +/- 1% from the stoichiometry
        result = {}
        for y in np.arange(comp1_min, comp1_max + delta, delta):
            y_vect = []
            y_vect.append(y)
            y2 = max_host_specie_concen - y
            y_vect.append(y2)
            y_vect.append(solute_concen)
            vector_func = [y_vect[i] - c_ratio[i] for i in range(1, m)]
            vector_func.append(omega)

            try:
                x = nsolve(vector_func, mu, mu_vals)
                if x:
                    mu_vals = [float(mu_val) for mu_val in x]
            except Exception:
                continue
            result[y] = mu_vals

        res = []

        # Compute the concentrations for all the compositions
        for key in sorted(result.keys()):
            mu_val = result[key]
            total_c_val = [total_c[i].subs(dict(zip(mu, mu_val))) for i in range(len(total_c))]
            c_val = c.subs(dict(zip(mu, mu_val)))
            # Concentration of first element/over total concen
            res1 = []
            res1.append(float(total_c_val[0] / sum(total_c_val)))

            for i in range(n + 1):
                for j in range(n):
                    if i == j:  # Vacancy
                        vac_conc = float(exp(-(mu_val[site_mu_map[i]] + dE[i, i]) / (k_B * T)))
                        res1.append(vac_conc)
                    else:  # Antisite
                        res1.append(float(c_val[i, j] / c0[j, j]))
            res.append(res1)

        res = np.array(res)
        dtype = [(str('x'), np.float64)] + [(str('y%d%d' % (i, j)), np.float64) for i in range(n + 1) for j in range(n)]
        res1 = np.sort(res.view(dtype), order=[str('x')], axis=0)

        conc = []
        for i in range(n + 1):
            conc.append([])
            for j in range(n):
                conc[i].append([])
        for i in range(n + 1):  # Append vacancies
            for j in range(n):
                y1 = [dat[0][i * n + j + 1] for dat in res1]
                conc[i][j] = y1

        # Compute solute site preference
        # Removing the functionality
        # site_pref_data = {}
        """Because all the plots have identical x-points storing it in a
        single array"""
        # site_pref_data['x'] = [dat[0][0] for dat in res1]         # x-axis data
        # Element whose composition is varied. For x-label
        # site_pref_data['x_label'] = els[0]+ "_mole_fraction"
        # site_pref_data['y_label'] = "$"+solute_specie+"_{"+els[0]+"}/("+\
        #    solute_specie+"_{"+els[0]+"}+"+solute_specie+"_{"+els[1]+"})$"

        # y_data = []
        # inds = specie_site_index_map[m-1]
        # data1 = np.sum([multiplicity[0]*conc[ind][0] for ind in range(*inds)],axis=0)
        # data2 = np.sum([multiplicity[1]*conc[ind][1] for ind in range(*inds)],axis=0)
        # frac_data = data1/(data1+data2)
        # frac_data = frac_data.tolist()
        # y_data.append({'data':frac_data})

        # site_pref_data['y'] = y_data

        #  Return all defect concentrations
        conc_data = {}
        """Because all the plots have identical x-points storing it in a
        single array"""
        conc_data['x'] = [dat[0][0] for dat in res1]  # x-axis data
        # Element whose composition is varied. For x-label
        conc_data['x_label'] = els[0] + " mole fraction"
        conc_data['y_label'] = "Point defect concentration"

        y_data = []
        # Vacancy
        for i in range(n):
            data = conc[i][i]
            specie = els[i]
            specie_ind = site_mu_map[i]
            indices = specie_site_index_map[specie_ind]
            specie_ind_del = indices[1] - indices[0]
            cur_ind = i - indices[0] + 1
            vac_string = "$Vac_{"
            if not specie_ind_del - 1:
                label = vac_string + specie + '}$'
            else:
                label = vac_string + specie + '_' + str(cur_ind) + '}$'
            # Plot data and legend info
            y_data.append({'data': data, 'name': label})

        # Antisites and solute
        for i in range(n):
            site_specie = els[i]
            specie_ind = site_mu_map[i]
            indices = specie_site_index_map[specie_ind]
            specie_ind_del = indices[1] - indices[0]
            cur_ind = i - indices[0] + 1
            for j in range(m):
                sub_specie = specie_order[j]
                if sub_specie == site_specie:
                    continue
                if not specie_ind_del - 1:
                    label = '$' + sub_specie + '_{' + site_specie + '}$'
                else:
                    label = '$' + sub_specie + '_{' + site_specie + '_' + str(cur_ind) + '}$'
                inds = specie_site_index_map[j]
                # TODO: Investigate the value below
                data = np.sum([conc[ind][i] for ind in range(*inds)], axis=0)
                data = data.tolist()
                y_data.append({'data': data, 'name': label})

        conc_data['y'] = y_data
        # return site_pref_data, conc_data
        return conc_data

    def solute_defect_density(structure,
                              e0,
                              vac_defs,
                              antisite_defs,
                              solute_defs,
                              solute_concen=0.01,
                              T=800,
                              trial_chem_pot=None,
                              plot_style="highchargs"):
        """
        Wrapper for the solute_site_preference_finder.
        The computed plot data is prepared based on plot_style.

        Args:
            structure: pymatgen.core.structure.Structure object representing the
                primitive or unitcell of the crystal.
            e0: The total energy of the undefected system.
                This is E0 from VASP calculation.
            vac_defs: List of vacancy defect parameters in the dictionary format.
                The keys of the dict associated with each vacancy defect are
                1) site_index, 2) site_specie, 3) site_multiplicity, and
                4) energy. 1-3 can be obtained from
                pymatgen.analysis.defects.point_defects.Vacancy class.
                Site index is expected to start with 1 (fortran index).
            antisite_defs: List of antisite defect parameters in the dictionary
                format. The keys of the dict associated with each antisite defect
                are 1) site_index, 2) site_specie, 3) site_multiplicity,
                4) substitution_specie, and 5) energy. 1-3 can be obtained
                from pymatgen.analysis.defects.point_defects.Vacancy class.
            solute_defs: List of solute defect parameters in the dictionary
                format. Similary to that of antisite defs, wtih solute specie
                specified in substitution_specie
            solute_concen: Solute concentration (in fractional value)
            T: Temperature in Kelvin
            trial_chem_pot (optional): Trial chemical potentials to speedup
                the plot generation. Format is {el1:mu1,...}
            plot_style (string): Allowed options are
                1) highcharts (default)
                2) gnuplot

        Returns:
            The plot data is generated and returned in asked format.
        """

        # solute_site_pref_data, def_conc_data = solute_site_preference_finder(
        def_conc_data = solute_site_preference_finder(
            structure,
            e0,
            T,
            vac_defs,
            antisite_defs,
            solute_defs,
            solute_concen=solute_concen,
            trial_chem_pot=trial_chem_pot)

        if plot_style == 'highcharts':
            "Energy data is ignored in this mode"
            hgh_chrt_data = {}
            hgh_chrt_data['xAxis'] = def_conc_data['x_label']
            hgh_chrt_data['yAxis'] = def_conc_data['y_label']

            series = []
            x = def_conc_data['x']
            for y_data in def_conc_data['y']:
                y = y_data['data']
                xy = zip(x, y)
                xy = [list(el) for el in xy]
                name = y_data['name'].strip('$')
                flds = name.split('_')
                def_string = flds[0]
                site_string = flds[1].strip('{}')
                name = def_string + "<sub>" + site_string + "</sub>"
                # series.append({'data':xy, 'name':y_data['name']})
                series.append({'data': xy, 'name': name})
            hgh_chrt_data['series'] = series
            return hgh_chrt_data
        elif plot_style == 'gnuplot':

            def data_to_rows(inp_data, y_lbl_flg):
                rows = []
                labels = []
                labels.append(inp_data['x_label'])
                if y_lbl_flg:
                    labels.append(inp_data['y_label'])
                else:
                    labels += [y['name'] for y in inp_data['y']]
                rows.append('#' + '\t'.join(labels))
                m = len(inp_data['x'])
                for i in range(m):
                    data = []
                    data.append(inp_data['x'][i])
                    data += [y['data'][i] for y in inp_data['y']]
                    data = [float(x) for x in data]
                    rows.append('\t'.join(list(map(str, data))))
                return rows

            # solute_site_pref_rows = data_to_rows(solute_site_pref_data, True)
            pt_def_conc_rows = data_to_rows(def_conc_data, False)
            # return solute_site_pref_rows, pt_def_conc_rows
            return pt_def_conc_rows