2P32 – Principles of Inorganic Chemistry
Dr. M. Pilkington
Lecture 24 – The Solid State 1. A-type lattices 2. Ionic crystals – ABn crystal lattices 3. Predicting structure types of ionic compounds: radius ratios 4. Examples of common structure types of ionic solids 5. Surveying the four main classes of crystalline solids:
metallic, covalent network, molecular and ionic solids
Three A-type Lattices
A second type of lattice is called body-centered cubic (bcc) and, as the name implies, differs from the simple cubic lattice in that a second sphere is placed in the centre of the cubic cell.
In this case the eight spheres at the corners are only one-eighth in the unit cell, the center sphere is completely incorporated into the body of the cell and therefore has a coordination number of 8.
The third arrangement is face centered cubic (fcc) where the coordination number of a given sphere is 12.
Cubic packing is not the most efficient way to pack spheres in a layer.
To increase the efficiency of the packing we fit a given sphere in the crevice or depression between two others.
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We can consider this to be layer A of the cubic close packed and hexagonal close packed structures. The second layer is laid down such that a given sphere fits in the hole left by three spheres in layer A. There are now two types of holes in layer B: those which have no spheres below them, holes a and those which have layer spheres directly below them, holes b. If the third layer is placed in the a depressions, they create a new layer C. The resulting packing scheme is known as the face centred cubic closepacked (ccp) structure ABCABCABC (c). If the spheres of the third layer are placed in the b depressions, they generate another layer A, the same as the first and the ABABAB hexagonal close packing scheme results (d).
The ABABAB and ABCABC closed packed structures – remember here that in the A, B and C layers the spheres have all the same size or are of the same type.
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2. Ionic Crystals
Most ionic crystals can be described as layers of anions containing cations within holes. The holes can be tetrahedral or octahedral.
There are a number of packing arrangements that are very commonly found in ionic crystals.
ABn-Type Crystal Lattices The spheres representing the atoms, ions or molecules are two different sizes. The most common example of these lattices are ionic crystals in which the anion is larger than the cation. It is best to picture the anions forming an A-type lattice and the cations fitting into “holes” in that lattice.
The crystal in this case is ionic and the holes in the anionic lattice must be of proper size to adequately accommodate the cations.
We have to then be able to identify the number and type of holes present in the A-type lattice.
A face centered cubic unit cell showing the positions and numbers of octahedral and tetrahedral holes per unit cell.
There are octahedral holes in the centre and in the middle of the 12 edges of the unit cell.
There is a tetrahedral hole associated with each corner of the unit cell.
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ABn structures - 1:1 compounds are the easiest to visualise (NaCl, BaO etc… they contain 1 cation and 1 anion). There are three main structural types: 1. NaCl – Na+ is coordinated by 6 Cl- - OCTAHEDRAL COORDINATION 2. CsCl – Cs+ is coordinated by 8 Cl- - CUBIC COORDINATION 3. ZnS – Zn2+ is coordinated by 4 S2- - TETRAHEDRAL COORDINATION
3. Radius Ratios A tetrahedral hole must be quite small, but an octahedral hole is a little larger. The ratio of the radius of the cation to the radius of the anion gives us values which enable us to determine the hole size and coordination number and thus structural type of the ionic structure:
If the cation is very small r cation/r anion = 0.225- 0.414 – Coordination No 4 e.g. ZnS type structure. If r cation/r anion = 0.414 - 0.732 – coordination No 6 e.g. NaCl type structure If the cation and anion are large r cation/r anion = > 0.732- Coordination No 8 e.g. CsCl type structure.
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4. Examples of ABn Structures AB structures
1. Sodium Chloride “rock salt”
Both ions have the same packing pattern, the stoichiometry is 1:1.
The sodium cations occupy octahedral holes (in both the centre and at the cell edges of the unit cell) in the cubic closed packed lattice of chloride ions.
The ABCABC layer structure of chlorides which is consistent with a fcc unit cell.
2. Zinc Blende
1:1 stoichiometry, four sulfide ions to match four zinc cations found completely within the unit cell.
Zinc cations occupy tetrahedral holes (not octahedral) in the sulfide lattice.
The sulfides form a cubic close packed array – an ABCABC arrangement of the fcc unit cell of anions.
The zinc cations occupy only four of the eight tetrahedral holes (four tetrahedral holes are empty).
Has a diamond like structure and there is some covalent nature to this structure, not purely ionic.
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3. Caesium Chloride Cs cations form a simple cubic lattice and the chloride ions occupy the holes or, Cl- anions can be pictured as forming the A-type lattice with Cs cations in the cubic holes.
The coordination number for both the anion and the cation is 8.
AB2 Structures - In AB compounds the coordination numbers and stoichiometries of anions and cations are equal. This is not the case for AB2 compounds -
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1. Consider CaF2 (Flourite) Due to the stoichiometry, a larger unit cell of fcc calcium ions with flourides filling tetrahedral holes is consistent with the 1:2 stoichiometry. The coordination number of the flourides is 4. The calcium ions occupy cubic holes formed by flouride ions. 2. Rutile structure (TiO2) is not close packed. This is not a cubic unit cell, but rather a tetragonal. The coordination number of the oxides is 3.
5. Types of Crystals
The realm of inorganic chemistry was considerably expanded in the early 20th Century when X-ray diffraction revealed information on the structure of solids.
Solids are composed of atoms, molecules, or ions arranged in a rigid, repeating geometric pattern of particles known as the crystal lattice.
Crystals are usually categorized by the type of interactions operating among the atoms, molecules or ions of the substance.
These interactions include ionic, metallic, and covalent bonds as well as intermolecular forces such as hydrogen bonds, dipole-dipole forces and London dispersion forces.
In the classification of crystals as well as categorizing them by their lattice types, i.e. monoclinic, cubic, tetragonal etc… we can also classify them according to their chemical and physical properties. In this respect, we have four types of crystals, metallic, covalent, (covalent) molecular, and ionic.
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1. Metallic Crystals
Metals – elements from the left side of the periodic table form crystals in which each atom has been ionized to form a cation and a corresponding number of electrons. The cations are pictured to form a crystal lattice that is held together by a “sea of electrons” – sometimes called a Fermi sea. The electrons of the sea are no longer associated with any particular cation but are free to wander about the lattice of cations. We can therefore define a metallic crystal as a lattice of cations held together by a sea of free electrons. The sea analogy allows us to picture electrons flowing from one place in the lattice to another.
If we shape the metal (copper is a good example) into a wire. If we put electrons in one end of the wire, electrons will be bumped along the lattice of cations until some electrons will be pushed out of the other end.
The mobility of the delocalized electrons accounts for electrical conductivity.
Metals are characterized by their tensile strength and the ability to conduct electricity.
Both properties are the result of the special nature of the metallic bond. Bonding electrons in metals are highly delocalized over the entire crystal.
The great cohesive force resulting from the delocalization is responsible for the great strength noted in metals.
The bonding strength in metals varies with the number of electrons available as well as with the size of the atoms. i.e. Na – 1 valence electron m.p. 980C Mg – 2 valence electrons m.p. 6490C W – 6 valence electrons m.p. 60000C
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Metal crystals all have a high density which means that they usually have the hcp or fcc structure.
Magnesium, scandium, titanium, cobalt, zinc and cadmium have the hcp structure.
Aluminium, calcium, nickel, copper, palladium, silver, platinum, gold and lead have the fcc structure.
Alkali metals, iron, chromium, barium, and tungsten have the bcc structure.
2. Covalent Network Crystals
A covalent network crystal is composed of atoms or groups of atoms arranged into a crystal lattice that is held together by an interlocking network of covalent bonds.
Covalent bonds (the result of the sharing of one or more pairs of electrons in a region of overlap between two or perhaps more atoms) are directional interactions as opposed to ionic and metallic bonds, which are non directional.
For example diamond – each carbon is best thought of as being sp3-hybridized and that to maximize the overlap of these hybrid orbitals, a C-C-C bond angle of 109.50 is necessary.
Hence the interactions are directional in nature.
Other examples of compounds that form covalent network crystals are silicon dioxide (quartz), graphite, elemental silicon, boron nitride (BN) and black phosphorous.
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The structure of diamond is based on a fcc lattice. There are 8 C atoms at the centre of the cube, 6 C atoms in the face centre, and 4 more within the unit cell. Each C is tetrahedrally bonded to four others. This tightly bound lattice contributes to diamond's unusual hardness. In graphite each C is bonded to three others and the layers are held together only weakly.
Covalent crystals are hard solids that possess very high melting points. They are poor conductors of electricity.
3. Molecular crystals
Very soft solids that possess low melting points.
They are poor conductors of electricity.
Molecular crystals consist of such substances as N2, CCI4, I2 and benzene.
Generally, the molecules are packed together as closely as their size and shape will allow.
The attractive forces are mainly van der Waals (dipole-dipole) interactions.
Water molecules are held together by directional H-bonds.
Intermolecular forces in this case can either be nondirectional as is the case of crystals of argon, or directional, as in the case of ice.
In the latter case, the H-O···H angle is 109.50, an angle determined by the geometry of the individual water molecules.
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Examples of molecular crystals:
4. Ionic crystals
Hard and brittle solids.
They possess high melting points.
They are poor conductors of electricity, but their ability to conduct increases drastically in melt. The packing of spheres in ionic crystals is complicated by two factors :
charged species are present
anions and cations are generally quite different in size
Some general conclusions can be drawn from ionic radii :
within the same period the anions always have larger radii than the cations the radius of the trivalent cation is smaller than that of the divalent cation, which is smaller than that of the monovalent cation
It should be realized that the value of any ionic radius only serves as a useful but approximate size of the ion.. The fact that the ionic radius of Na+ is 0.98Å does not mean that the electron cloud of the ion never extends beyond this value. It is significant because when it is added together with the radius of an anion, e.g. Cl-, the sum is approximately equal to the observed interionic distance.
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Formation of an Ionic Crystal – when two elements, one a metal with a low ionization energy and the other a nonmetal with a highly exothermic electron affinity are combined, electrons are transferred to produce cations and anions.
These forces are held together by non-directional, electrostatic forces known as ionic bonds. A hypothetical view of the formation of sodium chloride, the constituent elements are combined, electrons are transferred and ionic bonds among the sodium and chloride ions are formed.
Examples of compounds that form ionic crystals are CsCl , CaF2, KNO3, alumina, Al2O3, zirconia, ZrO2 (very hard).
Cubic zirconia is an imitation diamond, when crystallized it can be used as a jewel or it can be used as an industrial product for abrasion.
Melting Points of a Class of Ionic Compounds. LiF – 8450
BeO - 25300
NaF – 9930
MgO - 28520
KF – 8580
CaO - 26140
RbF – 7950
SrO - 24300
CsF- 6820
BaO – 19180
Next lecture - examine the factors that influence the melting points of these solids?
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