Solid State : Structure of Crystalline Solids

Crystal structures and Method of determination

Ionic compounds consist of positive and negative ions arranged in a manner so as to acquire minimum potential energy (maximum stability). To achieve the maximum stability, ions in a crystal should be arranged in such a way that forces of attraction are maximum and forces of repulsion are minimum. Hence, for maximum stability the oppositely charged ions should be as close as possible to one another and similarly charged ions as far away as possible from one another. Among the two ions constituting the binary compounds, the larger ions (usually anions) form a close-packed arrangement (hcp or ccp) and the smaller ions (usually cations) occupy the interstitial voids. Thus in every ionic compound, positive ions are surrounded by negative ions and vice versa. Normally each ions is surrounded by the largest possible number of oppositely charged ions. This number of oppositely charged ions surrounding each ions is termed its coordination number.

Classification of ionic structures : In the following structures, a black circle would denote an anion and a white circle would denote a cation. In any solid of the type A_x B_y the ratio of the coordination number of A to that of B would be y : x.

(1) Rock salt structure : The NaCl structure is composed of Na⁺ and Cl^–. The no. of Na⁺ ions is equal to that of Cl^–. The radii of Na⁺ and Cl^– are 95 pm and 181 pm respectively $\frac { r{ N }^{ + } }{ r{ Cl }^{ - } } =\frac { 95pm }{ 181pm }$ = 0.524. The radius ratio of 0.524 for suggests an octahedral voids. Chloride is forming a fcc unit cell in which Na⁺ is in the octahedral voids. The coordination number of Na⁺ is 6 and therefore that of Cl^– would also be 6. Moreover, there are 4 Na⁺ ions and 4 Cl^– ions per unit cell. The formula is Na₄Cl₄ i.e., NaCl. The other substances having this kind of a structure are halides of all alkali metals except cesium, halides and oxides of all alkaline earth metals except berylium oxide.

(2) Zinc blende structure : Sulphide ions are face centred and zinc is present in alternate tetrahedral voids. Formula is Zn₄S₄, i.e., ZnS. Coordination number of Zn is 4 and that of sulphide is also 4. Other substance that exists in this kind of a structure is BeO.

The zine sulphide crystals are composed of equal no. of Zn⁺² and S²⁺ ions. The radii of two ions (Zn⁺² = 74pm and S^2– = 184pm) led to the radius ratio (r⁺/r^–) as 0.40 which suggests a tetrahedral arrangement $\frac { r{ Zn }^{ +2 } }{ r{ S }^{ 2- } } =\frac { 74pm }{ 184pm }$

(3) Fluorite structure : Calcium ions are face centred and fluorite ions are present in all the tetrahedral voids. There are four calcium ions and eight fluoride ions per unit cell. Therefore the formula is Ca₄F₈, (i.e. CaF₂). The coordination number of fluoride ions is four (tetrahedral voids) and thus the coordination number of calcium ions is eight. Other substances which exist in this kind of structure are UO₂ and ThO₂.

(4) Anti-fluorite Structure : Oxide ions are face centred and lithium ions are present in all the tetrahedral voids. There are four oxide ions and eight lithium ions per unit cell. As it can be seen, this unit cell is just the reverse of fluorite structure, in the sense that, the position of cations and anions is interchanged. Other substances which exist in this kind of a structure are Na₂O, K₂O and Rb₂O.

(5) Spinel and inverse spinel structure : Spinel is a mineral (MgAl₂O₄). Generally they can be represented as M²⁺M₂³⁺O₄. Where M²⁺ is present in one-eighth of tetrahedral voids in a fcc lattice of oxide ions and present in half of the octahedral voids. M²⁺ is usually Mg, Fe, Co, Ni, Zn and Mn, M³⁺ is generally Al, Fe, Mn, Cr and Rh. e.g., ZnAl₂O₄, Fe₃O₄, FeCr₂O₄ etc.

(6) Cesium halide Structure : Chloride ions are primitive cubic while the cesium ion occupies the centre of the unit cell. There is one chloride ion and one cesium ion per unit cell. Therefore the formula is CsCl. The coordination number of cesium is eight and that of chloride is ions is also eight. Other substances which exist in this kind of a structure are all halides of cesium.

The CsCl crystal is composed of equal no. of Cs⁺ and Cl^– ions. The radii of two ions (Cs⁺= 160pm and Cl^– = 181pm) led to radius ratio of rCs⁺ to rCl^–as 0.884

$\frac { r{ Cs }^{ + } }{ r{ Cl }^{ - } } =\frac { 160pm }{ 181pm }$ = 0.884

Suggests a body centred cubic structure cubic structure having a cubic hole.

(7) Corundum structure : The general formula of compounds crystallizing in corundum structure is Al₂O₃. The closest packing is that of anions (oxide) in hexagonal primitive lattice and two-third of the octahedral voids are filled with trivalent cations. e.g., Fe₂O₃, Al₂O₃ and Cr₂O₃.

(8) Pervoskite structure : The general formula is ABO₃. One of the cation is bivalent and the other is tetravalent. e.g., CaTiO₃, BaTiO₃. The bivalent ions are present in primitive cubic lattice with oxide ions on the centres of all six square faces. The tetravalent cation is in the centre of the unit cell occupying octahedral void.

Note :

On applying high pressure, NaCl structure having 6:6 coordination number changes to CsCl structure having 8:8 coordination number similarly, CsCl having 8:8 coordination number on heating to 760 K changes to NaCl structure having 6:6 coordination number.

$\underset { 6:6\quad Co-ordination\quad number }{ NaCl }$ $\xrightleftharpoons[\text{Temp.}]{\text{Pressure}}$ $\underset { 8:8\quad Co-ordination\quad number }{ CsCl }$

Depending upon the relative number of positive and negative ions present in ionic compounds, it is convenient to divide them into groups like AB, AB₂, AB₃, etc. Ionic compounds of the type AB and AB₂ are discussed below.

Crystal Structure	Brief description	Examples	Co-ordination number	Number of formula units per unit cell
Type AB Rock salt (NaCl) type	It has fcc arrangement in which ions occupy the corners and face centres of a cube while Na⁺ ions are present at the body and edge of centres.	Halides of Li, Na, K, Rb, AgF, AgBr, NH₄Cl, NH₄Br, NH₄I etc.	Na⁺ = 6 Cl^– = 6	4
Zinc blende (ZnS) type	It has ccp arrangement in which S^2–ions form fcc and each Zn²⁺ ion is surrounded tetrahedrally by four S^2–ions and vice versa.	CuCl, CuBr CuI, AgI, BeS	Zn⁺² = 4 S^2– = 4	4
Type AB₂ Fluorite (CaF₂) type	It has arrangement in which Ca²⁺ ions form fcc with each Ca²⁺ ions surrounded by 8F^– ions and each ions by 4Ca²⁺ ions.	BaF₂, BaCl₂, SrF₂ SrCl₂, CdF₂, PbF₂	Ca²⁺ = 8 F^– = 4	4
Antifluorite type	Here negative ions form the ccp arrangement so that each positive ion is surrounded by 4 negative ions and each negative ion by 8 positive ions	Na₂O	Na⁺ = 4 O^2– = 8	4
Caesium chloride (CsCl) type	It has the bcc arrangement with Cs⁺ at the body centre and Cl^– ions at the corners of a cube or vice versa.	CsCl, CsBr, CsI, CsCN. TlCl, TlBr, TlI and TlCN	Cs⁺ = 8 Cl^– = 8	1

(iii) Crystal structure of some metals at room temperature and pressure :

Solid State : Structure of Crystalline Solids

Solid State : Structure of Crystalline Solids

About Exam Pattern

Syllabus

Theory

Practice Assignments & Papers

Previous Years Papers

Video Lectures

Online Quizzes