Chapter 2: Phase Diagrams and Phase Transformations of Alloys

print("=" * 70)
print("Degrees of Freedom Calculation Using Gibbs Phase Rule")
print("=" * 70)

# Gibbs Phase Rule: F = C - P + 2
# For binary system at constant pressure: F = C - P + 1 = 2 - P + 1 = 3 - P

C = 2  # Number of components
pressure_fixed = True  # Constant pressure

print(f"\nGibbs Phase Rule: F = C - P + 2")
print(f"Number of components C = {C}")
print(f"At constant pressure: F = C - P + 1 = 3 - P")

cases = [("Single-phase region (liquid phase only)", 1),
         ("Two-phase region (liquid + alpha solid)", 2),
         ("Eutectic point (liquid + alpha + beta)", 3)]

print("\n" + "=" * 70)
print("[Calculation Results]")
print("=" * 70)

for i, (description, P) in enumerate(cases, 1):
    F = 3 - P
    print(f"\n({i}) {description}")
    print(f"    Number of phases P = {P}")
    print(f"    Degrees of freedom F = 3 - {P} = {F}")

    if F == 2:
        print(f"    -> Both temperature and composition can be varied independently")
    elif F == 1:
        print(f"    -> When temperature is fixed, composition of each phase is determined")
        print(f"       (or when composition is fixed, temperature is determined)")
    elif F == 0:
        print(f"    -> Both temperature and composition are fixed (invariant point)")

print("\n" + "=" * 70)
print("[Physical Interpretation]")
print("=" * 70)
print("\nThe degrees of freedom F represents the number of independent variables")
print("needed to specify the state of the system.")
print("")
print("F = 2: In single-phase regions, both temperature and composition can be varied.")
print("       Represented as an area (2D region) on the phase diagram.")
print("")
print("F = 1: In two-phase regions, when temperature is fixed, the composition")
print("       of each phase is thermodynamically determined (lever rule gives fractions).")
print("       Represented as a line (1D) on the phase diagram.")
print("")
print("F = 0: At three-phase coexistence points, both temperature and composition are fixed.")
print("       Represented as a point (0D) on the phase diagram.")
print("       Examples: Eutectic point, eutectoid point, peritectic point")
print("=" * 70)

# Figure
import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots(figsize=(10, 8))

# Simplified phase diagram
composition = np.linspace(0, 100, 300)
T_liquidus_1 = 1000 - 5 * composition[:150]
T_liquidus_2 = 250 + 5 * (composition[150:] - 50)
liquidus = np.concatenate([T_liquidus_1, T_liquidus_2])

ax.plot(composition, liquidus, 'r-', linewidth=3, label='Liquidus')
ax.axhline(250, color='blue', linestyle='--', linewidth=2, label='Eutectic Temperature')

# Region labels
ax.text(50, 800, 'F = 2\n(Single-phase region)', fontsize=14, fontweight='bold',
        ha='center', bbox=dict(boxstyle='round', facecolor='yellow', alpha=0.7))
ax.text(25, 400, 'F = 1\n(Two-phase coexistence)', fontsize=13, fontweight='bold',
        ha='center', bbox=dict(boxstyle='round', facecolor='lightblue', alpha=0.7))
ax.text(75, 400, 'F = 1\n(Two-phase coexistence)', fontsize=13, fontweight='bold',
        ha='center', bbox=dict(boxstyle='round', facecolor='lightgreen', alpha=0.7))

ax.plot(50, 250, 'ko', markersize=15, label='Eutectic Point (F=0)')

ax.set_xlabel('Composition (mass% B)', fontsize=13, fontweight='bold')
ax.set_ylabel('Temperature (deg C)', fontsize=13, fontweight='bold')
ax.set_title('Relationship Between Degrees of Freedom and Phase Diagram',
             fontsize=15, fontweight='bold', pad=15)
ax.set_xlim(0, 100)
ax.set_ylim(200, 1100)
ax.legend(fontsize=12)
ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.savefig('gibbs_phase_rule_degrees_of_freedom.png', dpi=300, bbox_inches='tight')
plt.show()

print("\n Graph saved as 'gibbs_phase_rule_degrees_of_freedom.png'")

# Requirements:
# - Python 3.9+
# - numpy>=1.24.0, <2.0.0

"""
Example: Phase fraction calculation for Fe-0.6% C steel

Purpose: Demonstrate lever rule application
Target: Beginner to Intermediate
Execution time: 2-5 seconds
Dependencies: numpy, matplotlib
"""

import numpy as np
import matplotlib.pyplot as plt

# Given values
C_steel = 0.6       # Carbon content of steel (mass% C)
C_ferrite = 0.022   # Carbon content of ferrite (mass% C)
C_pearlite = 0.76   # Eutectoid composition (pearlite) (mass% C)
T = 727             # Temperature (deg C)

print("=" * 80)
print("Microstructure Calculation for Fe-0.6 mass% C Steel (Lever Rule)")
print("=" * 80)
print("\n[Problem Statement]")
print(f"Steel composition: {C_steel} mass% C (Hypoeutectoid Steel)")
print(f"Cooling temperature: 900 deg C -> room temperature")
print(f"Evaluation temperature: {T} deg C (just below eutectoid temperature)")

print("\n[Given Values]")
print(f"  C_Steel: {C_steel} mass% C")
print(f"  C_Ferrite: {C_ferrite} mass% C")
print(f"  C_Pearlite: {C_pearlite} mass% C (eutectoid composition)")

# Lever Rule application
# f_alpha = (C_Pearlite - C_Steel) / (C_Pearlite - C_Ferrite)
# f_Pearlite = (C_Steel - C_Ferrite) / (C_Pearlite - C_Ferrite)

f_ferrite = (C_pearlite - C_steel) / (C_pearlite - C_ferrite)
f_pearlite = (C_steel - C_ferrite) / (C_pearlite - C_ferrite)

print("\n[Lever Rule Calculation]")
print("\nFerrite mass fraction:")
print(f"  f_Ferrite = (C_Pearlite - C_Steel) / (C_Pearlite - C_Ferrite)")
print(f"           = ({C_pearlite} - {C_steel}) / ({C_pearlite} - {C_ferrite})")
print(f"           = {C_pearlite - C_steel:.2f} / {C_pearlite - C_ferrite:.3f}")
print(f"           = {f_ferrite:.4f}")
print(f"           = {f_ferrite * 100:.2f}%")

print("\nPearlite mass fraction:")
print(f"  f_Pearlite = (C_Steel - C_Ferrite) / (C_Pearlite - C_Ferrite)")
print(f"            = ({C_steel} - {C_ferrite}) / ({C_pearlite} - {C_ferrite})")
print(f"            = {C_steel - C_ferrite:.3f} / {C_pearlite - C_ferrite:.3f}")
print(f"            = {f_pearlite:.4f}")
print(f"            = {f_pearlite * 100:.2f}%")

print("\n[Verification]")
total = f_ferrite + f_pearlite
print(f"  f_Ferrite + f_Pearlite = {f_ferrite:.4f} + {f_pearlite:.4f}")
print(f"                        = {total:.4f}")
if abs(total - 1.0) < 1e-6:
    print("  Confirmed to equal 1.0")
else:
    print(f"  Error: {total - 1.0:.6f}")

# Detailed analysis of pearlite microstructure
# Pearlite = Ferrite (0.022% C) + Cementite (6.67% C)
# Pearlite composition = 0.76% C
C_cementite = 6.67  # Carbon content of cementite

f_ferrite_in_pearlite = (C_cementite - C_pearlite) / (C_cementite - C_ferrite)
f_cementite_in_pearlite = (C_pearlite - C_ferrite) / (C_cementite - C_ferrite)

print("\n[Detailed Analysis of Pearlite Microstructure]")
print("Pearlite is a lamellar structure of ferrite and cementite.")
print(f"\nFerrite fraction in pearlite:")
print(f"  = ({C_cementite} - {C_pearlite}) / ({C_cementite} - {C_ferrite})")
print(f"  = {f_ferrite_in_pearlite:.4f} = {f_ferrite_in_pearlite * 100:.2f}%")
print(f"\nCementite fraction in pearlite:")
print(f"  = ({C_pearlite} - {C_ferrite}) / ({C_cementite} - {C_ferrite})")
print(f"  = {f_cementite_in_pearlite:.4f} = {f_cementite_in_pearlite * 100:.2f}%")

# Total phase fractions in steel
f_ferrite_total = f_ferrite + f_pearlite * f_ferrite_in_pearlite
f_cementite_total = f_pearlite * f_cementite_in_pearlite

print("\n[Total Phase Mass Fractions in Steel]")
print(f"  Proeutectoid ferrite: {f_ferrite * 100:.2f}%")
print(f"  Pearlite: {f_pearlite * 100:.2f}%")
print(f"    - Ferrite in pearlite: {f_pearlite * f_ferrite_in_pearlite * 100:.2f}%")
print(f"    - Cementite: {f_cementite_total * 100:.2f}%")
print(f"  ----------------------------------------")
print(f"  Total ferrite: {f_ferrite_total * 100:.2f}%")
print(f"  Total cementite: {f_cementite_total * 100:.2f}%")

# Visualization
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 6))

# Left figure: Lever Rule diagram
compositions = [C_ferrite, C_steel, C_pearlite]
labels = ['Ferrite\n(alpha)', 'Steel Composition\n(0.6% C)', 'Pearlite\n(Eutectoid)']
colors = ['blue', 'red', 'purple']

for c, label, color in zip(compositions, labels, colors):
    ax1.axvline(c, color=color, linestyle='--', linewidth=2, alpha=0.7)
    ax1.text(c, 0.9, label, ha='center', fontsize=12, fontweight='bold',
             bbox=dict(boxstyle='round', facecolor=color, alpha=0.3))

ax1.plot([C_ferrite, C_pearlite], [0.5, 0.5], 'k-', linewidth=3)
ax1.plot(C_steel, 0.5, 'ro', markersize=15, label='Fulcrum point')

ax1.annotate('', xy=(C_ferrite, 0.35), xytext=(C_steel, 0.35),
             arrowprops=dict(arrowstyle='<->', color='blue', lw=2.5))
ax1.text((C_ferrite + C_steel) / 2, 0.28, f'{C_steel - C_ferrite:.3f}%',
         ha='center', fontsize=11, color='blue', fontweight='bold')

ax1.annotate('', xy=(C_steel, 0.35), xytext=(C_pearlite, 0.35),
             arrowprops=dict(arrowstyle='<->', color='purple', lw=2.5))
ax1.text((C_steel + C_pearlite) / 2, 0.28, f'{C_pearlite - C_steel:.2f}%',
         ha='center', fontsize=11, color='purple', fontweight='bold')

ax1.text(C_ferrite - 0.1, 0.7, f'Mass Fraction\n{f_ferrite * 100:.1f}%',
         ha='center', fontsize=13, fontweight='bold',
         bbox=dict(boxstyle='round', facecolor='lightblue', alpha=0.9))
ax1.text(C_pearlite + 0.1, 0.7, f'Mass Fraction\n{f_pearlite * 100:.1f}%',
         ha='center', fontsize=13, fontweight='bold',
         bbox=dict(boxstyle='round', facecolor='lightcoral', alpha=0.9))

ax1.set_xlabel('Carbon Content (mass% C)', fontsize=13, fontweight='bold')
ax1.set_title('Lever Rule Calculation', fontsize=15, fontweight='bold', pad=15)
ax1.set_xlim(0, 1.0)
ax1.set_ylim(0, 1)
ax1.set_yticks([])
ax1.grid(axis='x', alpha=0.3)

# Right figure: Microstructure pie chart
phases = ['Proeutectoid Ferrite', f'Pearlite\n({f_pearlite * 100:.1f}%)']
sizes = [f_ferrite * 100, f_pearlite * 100]
colors_pie = ['lightblue', 'lightcoral']
explode = (0.05, 0.05)

wedges, texts, autotexts = ax2.pie(sizes, explode=explode, labels=phases,
                                    colors=colors_pie, autopct='%1.1f%%',
                                    startangle=90,
                                    textprops={'fontsize': 12, 'fontweight': 'bold'})
for autotext in autotexts:
    autotext.set_color('white')
    autotext.set_fontweight('bold')
    autotext.set_fontsize(14)

ax2.set_title('Fe-0.6% C Steel Microstructure Composition',
              fontsize=15, fontweight='bold', pad=15)

plt.tight_layout()
plt.savefig('fe_06c_microstructure_calculation.png', dpi=300, bbox_inches='tight')
plt.show()

print("\n" + "=" * 80)
print("[Conclusion]")
print("=" * 80)
print(f"When Fe-{C_steel} mass% C steel is slowly cooled to just below the eutectoid temperature:")
print(f"  Proeutectoid ferrite: {f_ferrite * 100:.1f} mass%")
print(f"  Pearlite: {f_pearlite * 100:.1f} mass%")
print("")
print("This is a typical hypoeutectoid steel microstructure.")
print("Proeutectoid ferrite is soft, while pearlite (lamellar structure) is harder,")
print(f"so this steel has moderate strength and hardness.")
print("")
print(f"As carbon content approaches 0.76% (eutectoid steel), the pearlite fraction increases,")
print("resulting in higher strength and hardness.")
print("=" * 80)
print("\n Graph saved as 'fe_06c_microstructure_calculation.png'")

# Requirements:
# - Python 3.9+
# - numpy>=1.24.0, <2.0.0

"""
Example: Phase transformation of Fe-1.2% C hypereutectoid steel

Purpose: Demonstrate cooling transformation and lever rule
Target: Intermediate to Advanced
Execution time: 10-30 seconds
Dependencies: numpy, matplotlib
"""

import numpy as np
import matplotlib.pyplot as plt

# Given values
C_steel = 1.2       # Carbon content of steel (mass% C) - Hypereutectoid steel
C_eutectoid = 0.76  # Eutectoid composition (mass% C)
C_cementite = 6.67  # Carbon content of cementite (mass% C)
T_eutectoid = 727   # Eutectoid temperature (deg C)

print("=" * 80)
print("Cooling Transformation of Fe-1.2 mass% C Steel (Hypereutectoid Steel)")
print("=" * 80)

print("\n[Steel Classification]")
print(f"Carbon content: {C_steel} mass% C")
print(f"Classification: Hypereutectoid steel ({C_eutectoid} mass% C < C < 2.14 mass% C)")

# Cooling process explanation
cooling_stages = [
    ("1000 deg C", "gamma phase (austenite) single phase"),
    ("~850 deg C", "gamma + Fe3C boundary line; proeutectoid cementite starts to precipitate"),
    ("850-727 deg C", "gamma + Fe3C two-phase coexistence; proeutectoid Fe3C precipitation continues"),
    ("727 deg C (eutectoid temperature)", "Eutectoid reaction: gamma -> alpha + Fe3C (pearlite forms)"),
    ("Below 727 deg C", "Proeutectoid Fe3C + pearlite; room temperature microstructure")
]

print("\n[Microstructure Changes During Cooling]")
print("=" * 80)
for i, (temp, description) in enumerate(cooling_stages, 1):
    print(f"\n{i}. {temp}")
    print(f"   {description}")

# Lever Rule calculation (just below 727 deg C)
# For hypereutectoid steel: Proeutectoid cementite + Pearlite
# f_Fe3C = (C_Steel - C_Eutectoid) / (C_Cementite - C_Eutectoid)
# f_Pearlite = (C_Cementite - C_Steel) / (C_Cementite - C_Eutectoid)

f_cementite = (C_steel - C_eutectoid) / (C_cementite - C_eutectoid)
f_pearlite = (C_cementite - C_steel) / (C_cementite - C_eutectoid)

print("\n" + "=" * 80)
print("[Lever Rule Calculation (just below 727 deg C)]")
print("=" * 80)

print(f"\nOverall composition: {C_steel} mass% C")
print(f"Pearlite composition (gamma phase at eutectoid): {C_eutectoid} mass% C")
print(f"Cementite composition (Fe3C): {C_cementite} mass% C")

print("\n[Phase Fraction Calculation]")
print("\nProeutectoid cementite:")
print(f"  f_Fe3C = (C_Steel - C_Eutectoid) / (C_Cementite - C_Eutectoid)")
print(f"        = ({C_steel} - {C_eutectoid}) / ({C_cementite} - {C_eutectoid})")
print(f"        = {f_cementite:.4f} = {f_cementite * 100:.2f}%")

print("\nPearlite:")
print(f"  f_Pearlite = (C_Cementite - C_Steel) / (C_Cementite - C_Eutectoid)")
print(f"            = ({C_cementite} - {C_steel}) / ({C_cementite} - {C_eutectoid})")
print(f"            = {f_pearlite:.4f} = {f_pearlite * 100:.2f}%")

print(f"\n[Verification]")
total = f_cementite + f_pearlite
print(f"  f_Fe3C + f_Pearlite = {total:.4f}")
if abs(total - 1.0) < 1e-6:
    print("  Confirmed to equal 1.0")

# Pearlite internal structure analysis
C_ferrite_eutectoid = 0.022
f_ferrite_in_pearlite = (C_cementite - C_eutectoid) / (C_cementite - C_ferrite_eutectoid)
f_cementite_in_pearlite = (C_eutectoid - C_ferrite_eutectoid) / (C_cementite - C_ferrite_eutectoid)

print("\n[Pearlite Internal Structure]")
print(f"  Ferrite in pearlite: {f_ferrite_in_pearlite * 100:.2f}%")
print(f"  Cementite in pearlite: {f_cementite_in_pearlite * 100:.2f}%")

# Total cementite in steel
total_cementite = f_cementite + f_pearlite * f_cementite_in_pearlite

print("\n[Total Phase Composition in Steel]")
print(f"  Proeutectoid cementite: {f_cementite * 100:.2f}%")
print(f"  Pearlite: {f_pearlite * 100:.2f}%")
print(f"  Total cementite: {total_cementite * 100:.2f}%")

# Visualization
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 7))

# Left figure: Cooling curve with microstructure changes
temperatures = [1000, 900, 850, 727, 500, 25]
time = np.arange(len(temperatures))

ax1.plot(time, temperatures, 'ro-', linewidth=2.5, markersize=10)
ax1.axhline(T_eutectoid, color='purple', linestyle='--', linewidth=2, alpha=0.7,
            label='Eutectoid Temperature (727 deg C)')
ax1.axhline(850, color='green', linestyle='--', linewidth=2, alpha=0.7,
            label='gamma + Fe3C boundary (~850 deg C)')

ax1.text(0.5, 1050, 'gamma phase\n(Austenite)', fontsize=12, fontweight='bold',
         ha='center', bbox=dict(boxstyle='round', facecolor='yellow', alpha=0.7))
ax1.text(2, 800, 'gamma + Proeutectoid Fe3C\nPrecipitation', fontsize=11, fontweight='bold',
         ha='center', bbox=dict(boxstyle='round', facecolor='lightgreen', alpha=0.7))
ax1.text(4, 650, 'Proeutectoid Fe3C\n+ Pearlite', fontsize=12, fontweight='bold',
         ha='center', bbox=dict(boxstyle='round', facecolor='lightcoral', alpha=0.7))

ax1.set_xlabel('Cooling Time (arbitrary units)', fontsize=13, fontweight='bold')
ax1.set_ylabel('Temperature (deg C)', fontsize=13, fontweight='bold')
ax1.set_title('Fe-1.2% C Steel Microstructure Changes During Cooling',
              fontsize=15, fontweight='bold', pad=15)
ax1.set_ylim(0, 1100)
ax1.legend(fontsize=11)
ax1.grid(True, alpha=0.3)

# Right figure: Microstructure pie chart
phases = ['Proeutectoid Cementite', f'Pearlite\n({f_pearlite * 100:.1f}%)']
sizes = [f_cementite * 100, f_pearlite * 100]
colors_pie = ['darkgray', 'lightcoral']
explode = (0.1, 0)

wedges, texts, autotexts = ax2.pie(sizes, explode=explode, labels=phases,
                                    colors=colors_pie, autopct='%1.2f%%',
                                    startangle=90,
                                    textprops={'fontsize': 12, 'fontweight': 'bold'})
for autotext in autotexts:
    autotext.set_color('white')
    autotext.set_fontweight('bold')
    autotext.set_fontsize(14)

ax2.set_title('Fe-1.2% C Steel Microstructure Composition (Lever Rule)',
              fontsize=15, fontweight='bold', pad=15)

plt.tight_layout()
plt.savefig('fe_12c_hypereutectoid_cooling.png', dpi=300, bbox_inches='tight')
plt.show()

print("\n" + "=" * 80)
print("[Hypereutectoid Steel Characteristics]")
print("=" * 80)
print("Hypereutectoid steel differs from hypoeutectoid steel in that:")
print("  - Proeutectoid cementite (hard, brittle) forms instead of proeutectoid ferrite (soft)")
print("  - Due to the hard cementite network, steel has high hardness (HV 200+)")
print("  - However, the continuous cementite network reduces toughness")
print("  - Spheroidizing annealing can improve toughness by fragmenting cementite")

print("\n[Comparison with Hypoeutectoid Steel]")
print("Hypoeutectoid steel: Proeutectoid ferrite (soft) + Pearlite")
print("  - Good balance of ductility and strength")
print("Hypereutectoid steel: Proeutectoid cementite (hard) + Pearlite")
print("  - High hardness, lower toughness")
print("=" * 80)
print("\n Graph saved as 'fe_12c_hypereutectoid_cooling.png'")