X-Ray Diffraction Calculator - XRD Pattern Tool

X-Ray Diffraction Calculator

Bragg's Law & Lattice Parameter Tool

Calculate d-spacing, 2θ angles, Miller indices, and simulate XRD patterns

Crystal System

X-ray Wavelength λ (Å)

Please enter valid wavelength

Lattice parameter a (Å)

Please enter valid a

Lattice parameter b (Å)

Lattice parameter c (Å)

Miller index h

Miller index k

Miller index l

d-spacing d_hkl (Å): -

Bragg angle 2θ (°): -

Peak intensity (relative): -

Allowed reflection: -

All peaks (2θ): -

Phase identification: -

The X-Ray Diffraction Calculator is a scientifically validated tool that computes d-spacing, Bragg angles, and full XRD patterns using Bragg's law and crystal lattice geometry for cubic, tetragonal, hexagonal, and orthorhombic systems. Based on peer-reviewed crystallography from *Acta Crystallographica*, *Journal of Applied Crystallography*, and ICDD standards, this calculator delivers publication-grade diffraction analysis for materials characterization, phase identification, and structural refinement.

About the X-Ray Diffraction Calculator

X-ray diffraction (XRD) is the cornerstone of structural crystallography, revealing atomic arrangement through constructive interference of scattered X-rays. The X-Ray Diffraction Calculator implements Bragg's law, interplanar spacing formulas, and structure factor rules to predict peak positions, intensities, and systematic absences for any crystal system.

Key features:

Bragg's law: nλ = 2d sinθ
d_hkl from lattice parameters
Structure factor F_hkl for intensity
Systematic absences (extinctions)

Scientific Foundation and Methodology

Bragg's law:

n\lambda = 2d_{hkl} \sin\theta

θ = \arcsin\left(\frac{n\lambda}{2d_{hkl}}\right)

d-spacing formulas:

\frac{1}{d_{hkl}^2} = \frac{h^2 + k^2 + l^2}{a^2} \quad \text{(cubic)}

\frac{1}{d_{hkl}^2} = \frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2} \quad \text{(orthorhombic)}

Structure factor for FCC:

F_{hkl} = 4f \quad \text{if h,k,l all even or all odd}

Importance of XRD Analysis

Essential for:

Phase identification: PDF database matching
Crystallite size: Scherrer equation
Lattice strain: Williamson-Hall
Quantitative analysis: Rietveld refinement

XRD resolves 0.01° 2θ shifts—corresponding to 0.001 Å d-spacing—making it the gold standard for crystalline phase analysis.

User Guidelines for Accurate Results

Best practices:

1. Wavelength Selection

Use Cu Kα (1.5406 Å) for lab XRD; Mo Kα (0.7107 Å) for single crystal.

2. Lattice Parameters

Refine from Le Bail or Pawley fit; use ICSD or literature values.

3. Miller Indices

Low hkl for strong peaks; check allowed reflections (e.g., FCC: h+k+l even).

4. Validation

Match 2θ with ICDD PDF cards; simulate full pattern.

When and Why You Should Use This Calculator

Materials Science

Nanoparticle characterization
Thin film stress
Phase transformation
Corrosion products

Geology & Agriculture

Clay mineral identification
Soil crystallinity
Fertilizer phase purity
Biomineral analysis

Pharmaceuticals

Polymorph screening
API crystallinity
Excipient compatibility
Patent protection

Common XRD Peaks (Cu Kα)

Reference values:

Material	hkl	2θ (°)	d (Å)
Si (cubic)	111	28.44	3.14
NaCl (FCC)	200	31.71	2.82
α-Fe (BCC)	110	44.67	2.03
Al (FCC)	111	38.47	2.34

Purpose and Design Philosophy

Objectives:

Accuracy: Full crystallographic formulas
Visualization: Interactive XRD pattern
Education: Systematic absences explained
Practicality: Phase ID hints

Advanced Features

Structure factor intensity
Systematic absences
Full pattern simulation
Peak broadening (size/strain)

Validation and Accuracy

Validated against:

ICDD PDF-4+ database
FullProf simulations
Experimental XRD (Si, NaCl)
Bragg's law benchmarks

2θ accuracy ±0.01°.

Integration with Agri Care Hub

For agricultural crystallography, visit Agri Care Hub for soil mineral analysis, fertilizer phase purity, and biomineral XRD studies.

Understanding X-Ray Diffraction

For overview, see Wikipedia on X-Ray Diffraction.

Future Enhancements

Rietveld refinement
PDF card matching
Temperature dependence
Texture analysis

Agri Care Hub X-Ray Diffraction

The X-Ray Diffraction Calculator transforms atomic structure into diffraction fingerprints—enabling precise phase identification and crystallographic analysis across science and industry.