import math

# Given constants
D0 = 7.85e-5  # m^2/s
Q_d = 3.63  # eV/atom
R = 8.314  # J/(mol·K)
eV_to_J = 1.602e-19  # Conversion factor: 1 eV = 1.602e-19 J
Q_d_J = Q_d * eV_to_J  # Convert activation energy to Joules
T1 = 1175 + 273  # Temperature in Kelvin for 1175°C
T2 = 925 + 273  # Temperature in Kelvin for 925°C
delta_x = 2.35e-6  # Depth in meters (2.35 μm)
t1_hours = 2  # Time at T1 in hours
t1_seconds = t1_hours * 3600  # Convert hours to seconds

# Function to calculate diffusion coefficient
def diffusion_coefficient(D0, Q_d, R, T):
    return D0 * math.exp(-Q_d / (R * T))

# Calculate D1 at T1
D1 = diffusion_coefficient(D0, Q_d_J, R, T1)

# Calculate D2 at T2
D2 = diffusion_coefficient(D0, Q_d_J, R, T2)

# Calculate t2 at T2 using the diffusion depth formula: delta_x = sqrt(2 * D * t)
# Rearrange to solve for t: t = (delta_x^2) / (2 * D)
t2_seconds = (delta_x**2) / (2 * D2)
t2_hours = t2_seconds / 3600  # Convert seconds to hours

D1, D2, t2_hours