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A crystal of formula AB3 has A ions at the cube corners and B ions at the edge centres. The coordination numbers of A and B, respectively, are x and y, then the sum of x and y is:

Last updated date: 21st Jun 2024
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Hint: This question is based on the concept of crystal structure theory. Hans Bethe and John Von Vlech developed a model called Crystal Field Theory(CFT). A particular arrangement of atoms in a crystal is called a crystal structure. A crystal structure consists of a unit cell, a group of atoms arranged in a particular fashion, which is replicated on a lattice regularly in three dimensions.

Complete Step by step answer: Each A atom in a cubic crystal in the centre is surrounded by 6 B atoms at the vertices to which it is linked where 2 are in plane, 2 are above and 2 are below the planes. Therefore, A has the coordination number, A=6 ie., x=6
Each B atom present at the centre of the edge is surrounded at the corners by 2 A atoms. Therefore, B has the coordination number, B=6 i.e. y=2

Thus, the sum of x and y results in 8. i.e x + y = 8.

Additional information: -CFT(Crystal Field Theory) model is used to explain the stability and bonding of complex compounds. It is based on degeneracies of d-orbitals. When these orbitals split, ligands approach the central metal ion.
-There are seven types of crystal structures in CFT. They are: monoclinic,triclinic, orthorhombic, hexagonal, trigonal, tetragonal and cubic.
-Some of the postulates used in crystal theory are noted below. According to crystal field theory, the bond between metal and ligand is electrostatic in nature. The force of attraction between metal and ligand is ion-ion interaction or ion-dipole interaction.

Note: The crystal structures of $A{B_3}$ and ${A_2}{B_7}$ are considered to be rare earth elements. In a crystal structure, the arrangement of atoms depends not only on the charge on the ion and the form of the bond between the atoms, but also on the size of the atoms or ions. The number of ions or atoms that surround an atom or ion of interest immediately is referred to as the coordination number.