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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Introduction
This notebook demonstrates how to perform phase and electrochemical assessments starting from a VASP calculation using Python Materials Genomics (pymatgen) and the Materials Project database (via the Materials API). These notebooks are described in detail in
Deng, Z.; Zhu, Z.; Chu, I.-H.; Ong, S. P. Data-Driven First-Principles Methods for the Study and Design of 
Alkali Superionic Conductors. Chem. Mater. 2017, 29 (1), 281–288 DOI
Step1:  Preparation
We will first read the results from the vasprun.xml output file from our VASP calculations. Only the lowest energy result is used here.
Step2:  To construct the phase diagram, we need all entries in the Li-P-S-Cl chemical space. We will use the MPRester class to obtain these entries from the Materials Project via the Materials API.
Step3:  In addition to all the MP entries, here we also load the computed entries of O/S substituted Li-P-O tenary compounds.
Step4:  Next, we need to combine all the entries and postprocess them using MaterialsProjectCompatibility. This postprocessing step corrects the energies to account for well-known DFT errors, e.g., in the sulfur binding energy.
Step5:  Phase diagram construction
The phase diagram can then be constructed using the PhaseDiagram class, and plotted using the PDPlotter class.
Step6:  We may observe from the above phase diagram that Li6PS5Cl is not a stable phase (red nodes) in the calculated 0K phase diagram.
The pseudo-ternary Li2S-P2S5-LiCl is constructed using the CompoundPhaseDiagram class.
Step7:  Calculating $E_{\rm hull}$ of Li6PS5Cl
We may evaluate the $E_{\rm hull}$ of Li6PS5Cl using the PDAnalyzer.
Step8:  Electrochemical Stability
The electrochemical stability can be assessed using a similar phase diagram approach, but using the lithium grand potential instead of the internal energy.
First, we need to identify a reference for lithium chemical potential using the bulk Li energy $\mu_{\rm Li}^0$.
Step9:  The PDAnalyzer class provides a quick way to plot the phase diagram at a particular composition (e.g., Li6PS5Cl) as a function of lithium chemical potential called get_element_profile.
Step10:  This element profile can be plotted as a Li evolution versus voltage using matplotlib as follows.
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Python Code:
%matplotlib inline
from pymatgen.core import Composition, Element
from pymatgen.ext.matproj import MPRester
from pymatgen.io.vasp import Vasprun
from pymatgen.phasediagram.maker import PhaseDiagram, CompoundPhaseDiagram
from pymatgen.phasediagram.analyzer import PDAnalyzer
from pymatgen.phasediagram.plotter import PDPlotter
from pymatgen.entries.computed_entries import ComputedEntry
from pymatgen.entries.compatibility import MaterialsProjectCompatibility
from pymatgen.util.plotting_utils import get_publication_quality_plot
import json
import re
import palettable
import matplotlib as mpl
Explanation: Introduction
This notebook demonstrates how to perform phase and electrochemical assessments starting from a VASP calculation using Python Materials Genomics (pymatgen) and the Materials Project database (via the Materials API). These notebooks are described in detail in
Deng, Z.; Zhu, Z.; Chu, I.-H.; Ong, S. P. Data-Driven First-Principles Methods for the Study and Design of 
Alkali Superionic Conductors. Chem. Mater. 2017, 29 (1), 281–288 DOI: 10.1021/acs.chemmater.6b02648.
If you find these notebooks useful and use the functionality demonstrated, please consider citing the above work.
Let's start by importing some modules and classes that we will be using.
End of explanation
vasprun = Vasprun("aimd_data/vasprun.xml.relax2.gz")
# include structure so proper correction can be applied for oxides and sulfides
entry = vasprun.get_computed_entry(inc_structure=True)  
Explanation: Preparation
We will first read the results from the vasprun.xml output file from our VASP calculations. Only the lowest energy result is used here.
End of explanation
rester = MPRester()
mp_entries = rester.get_entries_in_chemsys(["Li", "P", "S", "Cl"])
Explanation: To construct the phase diagram, we need all entries in the Li-P-S-Cl chemical space. We will use the MPRester class to obtain these entries from the Materials Project via the Materials API.
End of explanation
with open("aimd_data/lpo_entries.json") as f:
    lpo_data = json.load(f)
lpo_entries = [ComputedEntry.from_dict(d) for d in lpo_data]
Explanation: In addition to all the MP entries, here we also load the computed entries of O/S substituted Li-P-O tenary compounds.
End of explanation
compatibility = MaterialsProjectCompatibility()
entry = compatibility.process_entry(entry)
entries = compatibility.process_entries([entry] + mp_entries + lpo_entries)
Explanation: Next, we need to combine all the entries and postprocess them using MaterialsProjectCompatibility. This postprocessing step corrects the energies to account for well-known DFT errors, e.g., in the sulfur binding energy.
End of explanation
pd = PhaseDiagram(entries)
plotter = PDPlotter(pd)
plotter.show()
Explanation: Phase diagram construction
The phase diagram can then be constructed using the PhaseDiagram class, and plotted using the PDPlotter class.
End of explanation
cpd = CompoundPhaseDiagram(entries, 
                           [Composition("P2S5"), Composition("Li2S"), Composition("LiCl")])
cplotter = PDPlotter(cpd, show_unstable=True)
cplotter.show()
Explanation: We may observe from the above phase diagram that Li6PS5Cl is not a stable phase (red nodes) in the calculated 0K phase diagram.
The pseudo-ternary Li2S-P2S5-LiCl is constructed using the CompoundPhaseDiagram class.
End of explanation
analyzer = PDAnalyzer(pd)
ehull = analyzer.get_e_above_hull(entry)
print("The energy above hull of Li6PS5Cl is %.3f eV/atom." % ehull)
Explanation: Calculating $E_{\rm hull}$ of Li6PS5Cl
We may evaluate the $E_{\rm hull}$ of Li6PS5Cl using the PDAnalyzer.
End of explanation
li_entries = [e for e in entries if e.composition.reduced_formula == "Li"]
uli0 = min(li_entries, key=lambda e: e.energy_per_atom).energy_per_atom
Explanation: Electrochemical Stability
The electrochemical stability can be assessed using a similar phase diagram approach, but using the lithium grand potential instead of the internal energy.
First, we need to identify a reference for lithium chemical potential using the bulk Li energy $\mu_{\rm Li}^0$.
End of explanation
el_profile = analyzer.get_element_profile(Element("Li"), entry.composition)
for i, d in enumerate(el_profile):
    voltage = -(d["chempot"] - uli0)
    print("Voltage: %s V" % voltage)
    print(d["reaction"])
    print("")
Explanation: The PDAnalyzer class provides a quick way to plot the phase diagram at a particular composition (e.g., Li6PS5Cl) as a function of lithium chemical potential called get_element_profile.
End of explanation
# Some matplotlib settings to improve the look of the plot.
mpl.rcParams['axes.linewidth']=3
mpl.rcParams['lines.markeredgewidth']=4
mpl.rcParams['lines.linewidth']=3
mpl.rcParams['lines.markersize']=15
mpl.rcParams['xtick.major.width']=3
mpl.rcParams['xtick.major.size']=8
mpl.rcParams['xtick.minor.width']=3
mpl.rcParams['xtick.minor.size']=4
mpl.rcParams['ytick.major.width']=3
mpl.rcParams['ytick.major.size']=8
mpl.rcParams['ytick.minor.width']=3
mpl.rcParams['ytick.minor.size']=4
# Plot of Li uptake per formula unit (f.u.) of Li6PS5Cl against voltage vs Li/Li+.
colors = palettable.colorbrewer.qualitative.Set1_9.mpl_colors
plt = get_publication_quality_plot(12, 8)
for i, d in enumerate(el_profile):
    v = - (d["chempot"] - uli0)
    if i != 0:
        plt.plot([x2, x2], [y1, d["evolution"] / 4.0], 'k', linewidth=3)
    x1 = v
    y1 = d["evolution"] / 4.0
    if i != len(el_profile) - 1:
        x2 = - (el_profile[i + 1]["chempot"] - uli0)
    else:
        x2 = 5.0
        
    if i in [0, 4, 5, 7]:
        products = [re.sub(r"(\d+)", r"$_{\1}$", p.reduced_formula)                     
                    for p in d["reaction"].products if p.reduced_formula != "Li"]
        plt.annotate(", ".join(products), xy=(v + 0.05, y1 + 0.3), 
                     fontsize=24, color=colors[0])
        
        plt.plot([x1, x2], [y1, y1], color=colors[0], linewidth=5)
    else:
        plt.plot([x1, x2], [y1, y1], 'k', linewidth=3)  
plt.xlim((0, 4.0))
plt.ylim((-6, 10))
plt.xlabel("Voltage vs Li/Li$^+$ (V)")
plt.ylabel("Li uptake per f.u.")
plt.tight_layout()
Explanation: This element profile can be plotted as a Li evolution versus voltage using matplotlib as follows.
End of explanation
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