Nanoparticle Melting Point Calculator

Calculator Inputs

Use the responsive grid below. It shows three columns on large screens, two on smaller screens, and one on mobile.

Material preset

Choose a preset or keep custom values.

Material name

Bulk melting point

Particle diameter

Solid-liquid interfacial energy

J/m²

Solid density

Latent heat of fusion

Shape factor

For spheres, a common starting value is 4.

Graph range minimum

Graph range maximum

Graph points

Chart temperature unit

Decimal precision

Example Data Table

These example values are illustrative starting points for trend analysis. Replace them with experimental data for serious materials work.

Material	Bulk MP (°C)	Diameter (nm)	Interfacial Energy (J/m²)	Density (g/cm³)	Latent Heat (kJ/kg)	Shape Factor	Predicted Nano MP (°C)
Gold	1064.18	10	0.132	19.32	64.5	4	1006.10
Silver	961.78	8	0.125	10.49	104.7	4	881.33
Copper	1084.62	12	0.177	8.96	205.0	4	985.37
Lead	327.46	6	0.055	11.34	24.7	4	280.04
Tin	231.93	5	0.066	7.31	59.2	4	198.03

Formula Used

Gibbs-Thomson style relation

T_m(d) = T_m,bulk × [1 - (S × γ_sl) / (ρ_s × ΔH_f × d)]

Where:

T_m(d) = melting point of the nanoparticle
T_m,bulk = bulk melting point
S = shape factor, often 4 for spheres
γ_sl = solid-liquid interfacial energy
ρ_s = solid density
ΔH_f = latent heat of fusion per unit mass
d = particle diameter

The calculator also reports a size constant, K = (S × γ_sl) / (ρ_s × ΔH_f), which helps explain how strongly size changes alter melting temperature. Larger interfacial energy raises suppression. Larger density, latent heat, and particle size reduce suppression.

How to Use This Calculator

Select a preset material or enter a custom material name.
Enter the bulk melting point and choose Celsius or Kelvin.
Enter particle diameter and select the matching size unit.
Provide interfacial energy, density, latent heat, and shape factor.
Set the graph range to explore melting behavior across sizes.
Press Calculate Melting Point to display the result above the form.
Review the summary cards, sensitivity table, and Plotly graph.
Use the CSV and PDF buttons to export the result summary.

Frequently Asked Questions

1) What does this calculator estimate?

It estimates how a nanoparticle’s melting point changes as size decreases. Smaller particles generally melt below their bulk melting temperature because surface effects become more important.

2) Which formula is used here?

The page uses a Gibbs-Thomson style relationship. It links melting point suppression to particle size, interfacial energy, density, latent heat of fusion, and an optional shape factor.

3) Why is the nanoparticle melting point lower than bulk?

Nanoparticles have a much larger surface-to-volume ratio. That increases the influence of surface energy, making the solid phase less stable and lowering the temperature needed for melting.

4) What is the shape factor used for?

The shape factor adjusts the suppression strength for particle geometry. Spherical particles often use a value near 4, while other shapes may require different calibrated values.

5) Can I use this for oxides, ceramics, or alloys?

Yes, for trend studies. However, the model is simplest for systems with reasonably known interfacial data. Complex alloys, coatings, or phase-separating particles may need more advanced treatment.

6) Why do I need interfacial energy and latent heat?

They govern the strength of the size effect. Higher interfacial energy tends to increase melting-point depression, while higher latent heat tends to resist that depression.

7) What does the critical diameter mean?

It is an approximate threshold from the model’s size constant. Near or below that scale, suppression becomes very strong, and the simple equation may predict extremely low values.

8) Are the preset values exact?

No. They are reasonable starting points for comparison and demonstration. For research work, replace them with your own experimentally measured or literature-validated property values.