V₂O₃ Lattice Parameter Estimation

A small reference-style estimation page for V₂O₃ lattice constants from two diffraction peaks.

Peak 1

Peak 1 Section

Upload the first XY file, select its fit window, and tune the fit model.

Min 2θ (°)

Max 2θ (°)

Peak 1 plot

Points loaded 0

2θ center -

FWHM -

Range -

Peak 2

Upload the second XY file, select its fit window, and fit it independently from Peak 1.

Min 2θ (°)

Max 2θ (°)

Peak 2 plot

Points loaded 0

2θ center -

FWHM -

Range -

Inputs

X-Ray Wavelength λ (Å):

2θ₁ (degrees)

2θ₂ (degrees)

Calculated Lattice Parameters:

Theory & Method

The calculation follows a two-step process to solve for the hexagonal lattice constants where a = b ≠ c and γ = 120°.

Bragg's Law: First, the interplanar spacing (d) is calculated for each peak:
d = λ / (2 * sin(θ))
The Quadratic Form: We set up a system of two equations based on:
1/d² = (4/3) * [(h² + hk + k²)/a²] + (l²/c²)
Matrix Solution: Let X = 1/a² and Y = 1/c². We solve the linear system:
Constant1 * X + l1² * Y = 1/d1²
Constant2 * X + l2² * Y = 1/d2²
where Constant = (4/3) * (h² + hk + k²).