Calculator Inputs
Choose a sizing method, fill the fields, then press calculate. The calculator area uses three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
| Method | Example input | Example output | Engineering use |
|---|---|---|---|
| XRD Scherrer | K = 0.9, λ = 1.5406 Å, 2θ = 38.2°, FWHM = 0.24°, instrumental = 0.05° | 35.8155 nm crystallite size | Estimate coherent domain size from diffraction broadening. |
| Surface area | SSA = 120 m²/g, density = 4.2 g/cm³, shape factor = 1 | 11.9048 nm equivalent diameter | Check average size from surface area data. |
| Image statistics | 18, 20, 19, 21, 22, 24, 20, 23, 25, 21 nm | 21.3 nm mean diameter | Summarize microscopy measurements and dispersion. |
Formula Used
1) XRD Scherrer equation
D = Kλ / (β cos θ)
Here, D is crystallite size, K is shape factor, λ is wavelength, β is corrected peak broadening in radians, and θ is the Bragg angle.
If instrumental broadening is known, the calculator first applies: βcorrected = √(βmeasured2 − βinstrument2).
2) Specific surface area method
D(nm) = 6000 × shape correction / (SSA × density)
This assumes a particle model close to spherical behavior. It returns an equivalent diameter, which is useful for process comparison and rough engineering screening.
3) Image statistics
Mean = Σx / n
Standard deviation = √[Σ(x − mean)² / n]
The calculator also estimates D10, D50, D90, coefficient of variation, and span to describe particle size spread from microscopy measurements.
How to Use This Calculator
- Select the nanoparticle sizing method that matches your data source.
- Enter XRD peak values, surface area data, or microscopy diameters.
- Press the calculate button to generate the result summary.
- Review the result table, interpretation, and Plotly graph.
- Download the report as CSV or PDF when needed.
- Compare methods carefully, because each method represents different physical assumptions.
Important Engineering Notes
- Scherrer size reflects crystallite domain size, not always full agglomerate size.
- Surface area sizing is most reliable when morphology assumptions fit the material.
- Image statistics depend on representative sampling and proper segmentation quality.
- Use multiple methods together for stronger engineering validation.
FAQs
1) What does this calculator measure?
It estimates nanoparticle or crystallite size using XRD broadening, specific surface area, or direct image measurements. Each method represents a different physical viewpoint, so results may differ.
2) Is Scherrer size the same as particle size?
Not always. Scherrer analysis estimates coherent crystallite domain size. A real particle can contain several crystallites or exist as an agglomerate, making the observed physical particle larger.
3) Why include instrumental broadening?
Instrumental broadening removes part of the peak width caused by the diffractometer itself. Without correction, the Scherrer method can underestimate crystallite size.
4) When should I use the surface area method?
Use it when you know the specific surface area and density, and when a simple particle shape assumption is acceptable. It works well for fast engineering estimates and comparisons.
5) What does D10, D50, and D90 mean?
These percentiles describe the spread of image-based diameters. D50 is the median size. D10 and D90 show the smaller and larger ends of the measured distribution.
6) Why can different methods return different values?
Each method captures a different feature: crystallite size, equivalent diameter from surface area, or direct visible particle dimensions. Material shape, porosity, aggregation, and measurement noise also matter.
7) Does the calculator support exportable reports?
Yes. After calculation, use the CSV button for spreadsheet-friendly output or the PDF button for a compact engineering report with the summary table and graph.
8) What is the best method for engineering work?
The best method depends on your instrument, material, and decision goal. For stronger confidence, compare XRD, microscopy, and surface area results instead of relying on one value alone.