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From Wikipedia

Ionic radius, rion, is a measure of the size of an atom's ion in a crystal lattice. It is measured in either picometres (pm) or Angstrom (Ã…), with 1&nbsp;Ã…&nbsp;= 100&nbsp;pm. Typical values range from 30&nbsp;pm (0.3&nbsp;Ã…) to over 200&nbsp;pm (2&nbsp;Ã…).

The concept of ionic radius was developed independently by Victor Goldschmidt and Linus Pauling in the 1920s to summarize the data being generated by the (at the time) new technique of X-ray crystallography: it is Pauling's approach which proved to be the more influential. X-ray crystallography can readily give the length of the side of the unit cell of a crystal, but it is much more difficult (in most cases impossible, even with more modern techniques) to distinguish a boundary between two ions. For example, it can be readily determined that each side of the unit cell of sodium chloride is 564.02&nbsp;pm in length, and that this length is twice the distance between the centre of a sodium ion and the centre of a chloride ion:

2[rion(Na+) + rion(Clâˆ’)] = 564.02&nbsp;pm

However, it is not apparent what proportion of this distance is due to the size of the sodium ion and what proportion is due to the size of the chloride ion. By comparing many different compounds, and with a certain amount of chemical intuition, Pauling decided to assign a radius of 140&nbsp;pm to the oxide ion O2âˆ’, at which point he was able to calculate the radii of the other ions by subtraction.

A major review of crystallographic data led to the publication of a revised set of ionic radii in 1976, and these are preferred to Pauling's original values. Some sources have retained Pauling's reference of rion(O2âˆ’)&nbsp;= 140&nbsp;pm, while other sources prefer to list "effective" ionic radii based on rion(O2âˆ’)&nbsp;= 126&nbsp;pm. The latter values are thought to be a more accurate approximation to the "true" relative sizes of anions and cations in ionic crystals.

The ionic radius is not a fixed property of a given ion, but varies with coordination number, spin state and other parameters. Nevertheless, ionic radius values are sufficiently transferable to allow periodic trends to be recognized. As with other types of atomic radius, ionic radii increase on descending a group. Ionic size (for the same ion) also increases with increasing coordination number, and an ion in a high-spin state will be larger than the same ion in a low-spin state. Anions (negatively charged) are almost invariably larger than cations (positively charged), although the fluorides of some alkali metals are rare exceptions. In general, ionic radius decreases with increasing positive charge and increases with increasing negative charge.

An "anomalous" ionic radius in a crystal is often a sign of significant covalent character in the bonding. No bond is completely ionic, and some supposedly "ionic" compounds, especially of the transition metals, are particularly covalent in character. This is illustrated by the unit cell parameters for sodium and silverhalides in the table. On the basis of the fluorides, one would say that Ag+ is larger than Na+, but on the basis of the chlorides and bromides the opposite appears to be true. This is because the greater covalent character of the bonds in AgCl and AgBr reduces the bond length and hence the apparent ionic radius of Ag+, an effect which is not present in the halides of the more electropositive sodium, nor in silver fluoride in which the fluoride ion is relatively unpolarizable.

## Generalization

The concept of ionic radii is based on the assumption of a spherical ion shape. However, from a group-theoretical point of view the assumption is only justified for ions that reside on high-symmetry crystal lattice sites like Na and Cl in halite or Zn and S in sphalerite. A clear distinction can be made, when the point symmetry group of the respective lattice site is considered, which are the cubic groups O6 and Td in NaCl and ZnS. For ions on lower-symmetry sites significant deviations of their electron density from a spherical shape may occur. This holds in particular for ions on lattice sites of polar symmetry, which are the crystallographic point groups C1, C1h, Cn or Cnv, n = 2, 3, 4 or 6. A thorough analysis of the bonding geometry was recently carried out for pyrite-type disulfides, where monovalent markup languagesSGML, HTML, XHTML and XML, a character entity reference is a reference to a particular kind of named entity that has been predefined or explicitly declared in a Document Type Definition (DTD). The "replacement text" of the entity consists of a single character from the Universal Character Set/Unicode. The purpose of a character entity reference is to provide a way to refer to a character that is not universally encodable.

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## Concepts

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Question:What is the relationship between electro-negativity and the ionic character of a chemical bond?

Answers:The greater the electronegativity difference, the greater the percent ionic character in a bond. Percent ionic character = 100(1-e^-DEN^2/4))

Question:The property useful in the prediction of percentage of ionic character in a covalent molecule is 1. electron gain enthalpy 2. electronegativity 3. ionisation potential 4. ionic radii

Answers:Electronegativity. The greater the electronegativity difference between two bonded atoms, the greater the percentage ionic character.

Question:What is the percent ionic character of al2o3 and what type of bonding is expected from al? al2o3?

Answers:Percent ionic character is determined by finding the difference in electronegativity values (can be found in data tables) and then relating this to percentage ionic character data in another table. This http://www2.ucdsb.on.ca/tiss/stretton/database/electronegativity.htm gives you both. Al: el. neg 1.5 and O: el.neg 3.5 so difference is 2 which gives 63% ionic character. (if you want to see how these numbers are calculated see http://www.chemistry.mcmaster.ca/esam/Chapter_7/problems.html) Given the percent ionic character I would describe the Al-O bond as highly polar covalent.