Calculator
Enter the crystal model, unit cell edge, and one known ionic radius. The calculator solves the unknown counter-ion radius using hard-sphere contact geometry.
Example data table
These examples show geometric estimates using common crystal models. Real tabulated ionic radii may differ because coordination environment and bonding effects change measured values.
| Crystal type | Edge length | Known ion radius | Solved unknown radius | Relation used |
|---|---|---|---|---|
| Rock Salt (NaCl type) | 5.64 Å | Cl− = 181 pm | Na+ ≈ 101 pm | r+ + r− = a / 2 |
| Cesium Chloride (CsCl type) | 4.12 Å | Cl− = 181 pm | Cs+ ≈ 175.8 pm | r+ + r− = (√3 × a) / 2 |
| Zinc Blende (ZnS type) | 5.41 Å | S2− = 184 pm | Zn2+ ≈ 50.3 pm | r+ + r− = (√3 × a) / 4 |
| Fluorite (CaF2 type) | 5.46 Å | F− = 133 pm | Ca2+ ≈ 103.4 pm | r+ + r− = (√3 × a) / 4 |
Formula used
The calculator assumes hard-sphere ionic contact. First, it finds the nearest unlike-ion separation from the lattice geometry. Then it subtracts the known ion radius.
Geometry factors
- Rock Salt: k = 1/2
- Cesium Chloride: k = √3/2
- Zinc Blende: k = √3/4
- Fluorite: k = √3/4
- Antifluorite: k = √3/4
Interpretation note
This method gives a geometric estimate from lattice dimensions. It is most useful for quick checks, teaching, and comparing structure assumptions with one fixed unit cell edge.
How to use this calculator
- Choose the crystal structure that matches your solid.
- Enter the unit cell edge length and its unit.
- Choose whether the unknown radius is the cation or anion.
- Enter the known counter-ion radius and optional labels.
- Pick the output unit and decimal precision.
- Press calculate to view the solved radius, comparison table, downloads, and graph.
FAQs
1) How do you calculate ionic radius from unit cell length?
Find the nearest unlike-ion contact distance from the structure geometry, then subtract the known counter-ion radius. The relation depends on the crystal type, not only on the edge length.
2) Which crystal structures does this calculator support?
It supports Rock Salt, Cesium Chloride, Zinc Blende, Fluorite, and Antifluorite models. These cover several common coordination environments used in chemistry and materials science classes.
3) Can I solve for either the cation or the anion radius?
Yes. Choose which ion is unknown, then enter the known counter-ion radius. The geometry gives the radius sum, so the missing value is found by subtraction.
4) Why can the result become negative or invalid?
A negative value means the chosen structure and inputs do not fit together physically. The known radius is larger than the available contact distance for that lattice assumption.
5) Which units can I use?
You can enter cell edge and ionic radius values in picometers, angstroms, or nanometers. The calculator converts all values internally before displaying the final answer.
6) Is this the same as Shannon ionic radius data?
Not exactly. Shannon radii are tabulated from coordination and bonding environments, while this tool uses geometric contact assumptions from the chosen unit cell model.
7) How accurate is the answer?
It is a fast structural estimate. Accuracy depends on crystal ideality, coordination assumptions, and whether hard-sphere contact is a good approximation for the material.
8) Why does the graph compare other structures too?
The graph helps you see how strongly the solved radius depends on the structure model. It is useful when you want to test alternate lattice assumptions with identical input values.