Question

A compound is formed by two elements P and Q. Atoms of Q (as anions) make hcp lattice and those of the element P (as cations) occupy all the tetrahedral voids. What is the formula of the compound?

Answer 1

There are two kinds of voids in hexagonal close packing namely, octahedral voids and tetrahedral voids. The number of these two types of voids depends upon the number of close- packed spheres. Let the number of close packed spheres be $N$ , then, the amount of octahedral voids generated is $N$ and also the quantity of tetrahedral voids generated is $\,2N\,$ .

Complete step by step answer:
-A unit is the foremost simple and least volume consuming repeating structure of any solid. When the building block repeats itself, the network is known as a lattice.
-Voids literally mean gaps between the constituent particles. Voids in solid states mean the vacant space between the constituent particles during a closed packed structure. Close packing in solids is generally tiring in three ways: $\,1D\,$ close packing, $\,2D\,$ close packing and $\,3D\,$ close packing.
-In 2 dimensional structures when the atoms are arranged in square close packing and hexagonal close packing, we see empty spaces left over between the atoms. These empty spaces are called voids and within the case of hexagonal packing, these voids are in triangular shapes and are called the triangular voids.
-There are two sorts of interstitial voids in every $\,3D\,$ structure:
-Tetrahedral voids: In cubic close packed structure, spheres of the second layer lie above the triangular voids of the primary layer. Each sphere touches the three spheres of the primary layer. By joining the centre of those four spheres, it forms a tetrahedron and also the empty space left over by joining the centre of those spheres forms a tetrahedral void.
-Octahedral voids: Adjacent to tetrahedral voids we find octahedral voids. SWhen the triangular voids of the primary layer coincides with the triangular voids of the layer above or below it, we get a void that's formed by enclosing six spheres. This vacant space formed by combining the triangular voids of the primary layer which of the second layer are called Octahedral Voids
Let the number of atoms of Q in lattice is $n$
Total Number of tetrahedral voids $= 2 \times$ no. of atoms in hcp.
Since P occupies tetrahedral voids, we can say that
Number of atoms of P In lattice will be $2$ $n$
Hence chemical formula of the Chemical compound will be
$\,{P_{2n}}{Q_n} = {P_2}Q\,$

Note: There are only fourteen different lattice structures (often brought up as Bravais lattices). These fourteen different structures are derived from seven crystal systems, which indicate the various shapes a building block takes and 4 sorts of lattices, which tells how the atoms are arranged within the unit. Both tetrahedral voids and octahedral voids are found in closed packed structures, for instance in hcp, ccp and fcc. However, in simple cubic structures, only octahedral voids are found.
-The ratio of tetrahedral void and radius of that particle is $0.225$ . The amount of void is way smaller than that of the particle. The atom within the tetrahedral void is in touch with four atoms placed in four different corners of a tetrahedron.