Advanced XRD Sample Displacement Calculator

Calculate sample displacement errors in X-ray diffraction accurately now.

Example Inputs

Use these standard values to test the calculator functionality:

  • Theta ($\theta$): 15.5°
  • Displacement ($s$): 0.15 mm
  • Radius ($R$): 240 mm
  • Wavelength: 1.5406 Å
Quick Tips

Ensure your goniometer radius matches your specific laboratory instrument configuration.

Configure Parameters

Formula Used

In X-ray powder diffraction (XRD), sample displacement errors occur when the surface of the specimen is displaced from the focusing circle of the goniometer. For a flat specimen in a Bragg-Brentano geometry, the systematic peak shift $\Delta 2\theta$ is calculated using the following trigonometric relationship:

$$\Delta 2\theta = -\frac{2s \cos(\theta)}{R}$$

Where $s$ represents the linear displacement distance, $\theta$ is the Bragg angle, and $R$ denotes the goniometer radius.

How to Use This Calculator

  1. Input your measured Bragg angle ($\theta$) in degrees into the designated input field.
  2. Enter the estimated vertical or horizontal sample displacement value ($s$) in millimeters.
  3. Provide your diffractometer's goniometer radius ($R$), with default standard settings pre-populated at 240 mm.
  4. Select your specimen geometry option and click the submit button to immediately evaluate structural shifts.

Understanding X-Ray Diffraction Sample Displacement

X-ray powder diffraction is a cornerstone analytical technique utilized across materials science, chemistry, and physics for phase identification and crystal structure determination. However, quantitative accuracy can be heavily compromised by instrumental and specimen aberrations. Among these, sample displacement error represents one of the most prominent sources of systematic peak shifts, directly skewing calculated lattice parameters and unit cell dimensions.

When preparing powder samples, ensuring exact coplanarity with the goniometer axis can be exceptionally challenging. Even microscopic height variations introduce proportional shifts in the registered peak angles. Understanding these geometric corrections ensures high-fidelity data interpretation, robust Rietveld refinements, and precise phase analysis.

Frequently Asked Questions

Sample displacement occurs when the mounting surface of the specimen holder sits either above or below the focusing circle axis of the goniometer, often due to overfilling or underpacking powder holders.