Summary
Key concepts
- Characteristic properties of the solids
- They have definite mass, volume and shape.
- Intermolecular distances are short
- Intermolecular forces are strong
- Their constituent particles (atoms, molecules or ions) have fixed positions and can only oscillate about their mean positions.
- They are incompressible and rigid
- Solids are two types :
They are 1) Amorphous solids
2)Crystalline solids- Isotropy: Amorphous solids on the other hand are isotropic in nature. It is because there is no long range order in them and arrangement is irregular along all the directions. Therefore, value of any physical property would same along any direction
- Anisotropy: Crystalline solids are anisotropic in nature, that is, some of their physical properties like electrical resistance or refractive index show different values when measured along different directions in the same crystals. This arises from different arrangement of particles in different directions.
- Classification of Crystalline Solids: A crystal is classified as ionic, covalent, metallic and molecular according to the nature of the building units, chemical bonding and the intermolecular forces in the crystal.
- Space Lattice (or) Crystal Lattice: A space lattice is an array of points showing how molecules, atoms or ions are arranged at different sites in three dimensional space.
- Lattice Point:The point that represents a molecule, an atom or an ion in a space lattice is called Lattice point.
- Unit Cell: The smallest portion of the crystal lattice which can be used as repetitive unit in three dimensional manner to get entire crystal lattice is called unit cell. Unit cells are broadly divided into two categories, primitive and centered unit cells.
- (a) Primitive unit cells :When constituent particles are present only on the corner positions of a unit cell,it is called as primitive unit cell.
- (b) Centred unit cells : When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called Centred unit cell. Centred unit cells are of three types:
(i) Body – centered unit cells : Such a unit cell contains one constituent particle (atom, molecule or ion) at its body – centre besides the ones that are at its corners.
(ii) Face – centered unit cells : Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.
(iii) End – centered unit cells : In such a unit cell, one constituent particles is present at the centre of any two opposite faces besides the ones present at its corners.
- There are 230 crystal forms possible. These forms may be classified into 32 classes on the basis of their symmetry. On the basis of inter facial angles and axes crystal systems are 7 types.
- Tetragonal Lattice There are two possible types of tetragonal lattices. Primitive and Body centered unit cells. In these lattices one side is different in length and angles between faces are equal to 90°. (a = b ≠ c; α= β = γ=90° )
- Orthorhombic Lattice Four types of orthorhombic lattice are possible. They are Primitive, End – centered, Body centered and Face centered. They have unequal sides. The Angles between their faces are equal to 90° a = b ≠ c; α= β = γ = 90°)
- Monoclinic Lattice There are two possible types of monoclinic lattice. They are Primitive and End centered. They have unequal sides and two faces have angles other than 90° ( a ≠ b ≠ c; α = γ = 90°, β ≠ 90° )
- Hexagonal lattice Hexagonal lattice is of one type only. It has one side is different in length to the other two and the angles on two faces are 120°.(a = b ≠ c; α = β= 90° γ=120)
- Rhombohedral Lattice Only one type of lattice is possible for Rhombohedral lattice. It has all sides equal and angles on two faces are less than 90°(a = b = c; α = β= γ ≠ 90°)
- Triclinic Lattice Triclinic lattice has only one type of lattice. It has unequal sides and none of the angles between faces are equal to 90°( a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90° )
- Calculation of the contribution of lattice points per unit cell of substance.
- A lattice point at the corner of a unit cell is shared by 8 vicinal unit cells.
- A face centered point is shared by two adjacent unit cells.
- A edge centered point is shared by four adjacent unit cells
- A body centered lattice point belongs completely to a specific unit cell.
- If lattice point is at corner ,contribution of lattice points per unit cell=1/8
- If lattice point is at middle of face ,contribution of lattice points per unit cell=1
- If lattice point is at middle of edge ,contribution of lattice points per unit cell = 1/4
- If lattice point is at body centre ,contribution of lattice points per unit cell = 1
- Close packed structures Packing of Solids and Voids: In solids constituent particles are arranged as spheres in close structure. In close packed structure, maximum space is occupied by constituent particles and leave minimum vacant space. When the spheres are closely packed the different crystal systems are generated
- A) Close packing in one dimension : Close packing of spheres in one dimension Co – ordination number is 2.
- B)Close packing in two dimensions : Square close packing, its coordination no.4 and hexagonal close packing its coordination no.6
- C) Close packing in three dimensions :
- (i) Three dimensional close packing from two dimensional square close – packed layers: While placing the second square close – packed layer above the first we follow the same rule that was followed when one row was placed adjacent to the other. The second layer is placed over the first layer such that the spheres of the upper layer are exactly above those of the first layer. In this arrangement spheres of both the layers are perfectly aligned horizontally as well as vertically. Similarly, we may place more layers one above the other. If the arrangement of spheres in the first layer is called 'A' type, all the layers have the same arrangement. Thus this lattice has AAA.... type pattern. The lattice thus generated is the simple cubic lattice, and its unit cell is the primitive cubic unit cell.
- (ii) Three dimensional close packing from two dimensional hexagonal close packed layers. Three dimensional close packed structure can be generated by placing layers one over the other.
(a) Placing second layer over the first layer: Let us take a two dimensional hexagonal close packed layer 'A' and place a similar layer above it such that the spheres of the second layer are placed in the depressions of the first layer. Since the spheres of the two layers are aligned differently. This is AB AB type packing. The spheres of the second layer 'B' are not covered all the triangular voids of the first layer 'A'. This gives rise to different arrangements. Wherever a sphere of the second layer is above the void of the first layer (or vice versa) a tetrahedral void is formed. These voids are called tetrahedral voids because a tetrahedron is formed when the centres of these four spheres are joined. At other places, the triangular voids in the second layer are above the triangular voids in the first layer, and the triangular shapes of these do not overlap. One of them has the apex of the triangle pointing upwards and the other downwards. Such voids are surrounded by six spheres and are called octahedral voids.
Let the number of close packed spheres be N, then : The number of octahedral voids generated = N, The number of tetrahedral voids generated = 2N
(b) Placing third layer over the second layer: When third layer is placed over the second, there are two possibilities. - (i) Covering Tetrahedral voids : Tetrahedral voids of the second layer may be covered by the spheres of the third layer. In this case, the spheres of the third layer are exactly aligned with those of the first layer. Thus, the pattern of spheres is repeated in alternate layers. This pattern is often written as ABAB.... pattern. This structure is called hexagonal close packed (hcp) structure. This sort of arrangement of atoms is found in many metals like magnesium and zinc.
- (ii) Covering octahedral voids :The third layer may be placed above the second layer in a manner such that its spheres cover the octahedral voids. When placed in this manner, the spheres of the third layer are not aligned with those of either the first or the second layer. This arrangement is called "c" type. Only when fourth layer is placed, its spheres are aligned with those of the first layer. This pattern of layers is often written as ABCABC..... This structure is called cubic close packed (ccp) or face – centered cubic (fcc) structure. Metals such as copper and silver crystallize in this structure. both these types of close packing are highly efficient and 74%space in the crystal is filled. In either of them, each sphere is in contact with twelve spheres. Thus, the coordination number is 12 in either of these two structures.
- Interstitial Voids : The empty spaces between the three dimensional layers are known as holes or voids. The holes are also referred as interstices. There are three types of holes possible.
- Tetrahedral holes : A hole formed by three spheres in contact with each other of a layer. The hole is capped by a sphere from an upper layer.(Planar triangle with vertex down wards) A hole formed by three spheres of a layer in contact with each other and also with a sphere of a next lower layer (planar triangles with vertex upward). In the above types of holes the four spheres are arranged at the vertices of a regular tetrahedron. If 'X' spheres form a solid there are a total of'2X' tetrahedral holes. Radius ratio of tetrahedral void = rvoid / rsphere = 0.225
- Octahedral hole : It is the vacant space between a group of three spheres in a layer and another set of three spheres of a next layer. These six spheres surrounding the hole, lie at the vertices of a regular octahedron. In CCP or FCC lattice, one octahedral void is at the body centre of the cube and one octahedral void at the centre of each of the 12 edges. Radius ratio of octahedral void= rvoid / rsphere = 0.414
- Types of unit cells:
Simple cubic unit cell : Let us consider edge length of primitive unit cell'a' and 'r' be the radius of atom ( lattice ) and 'd' density of unit cell . It has following characteristics
1) This lattice has AAA.... type pattern.
2) 8 atoms are occupied at 8 corners of cube
3) Number of atoms (lattice points)
per unit cell = 8 × 1/8 = 1
4) Coordination of each lattice point = 6
5)First nearest distance (along cubic lattice points ) = a = 2r
6) Number of first nearest lattice points = 6
7) Second nearest distance (along along face diagonal ) = √2a
8) Number of second nearest lattice points = 12
9) Third nearest distance (along along body diagonal ) = √3a
10) Crystallogrhaphic planes ( 1, 0, 0), (1, 1, 0), (1, 1, 1)
11) Percentage Packing fraction = 52.4 %
12) Percentage void fraction = 47.7 %
13) Density of unit cell (d) =(Z = 1) × M / N0 × a3 - Body centered unit cell : Let us consider edge length of primitive unit cell 'a' and 'r' be the radius of atom (lattice) and 'd' density of unit cell . It has following characteristics
1) This lattice has ABABAB.... type pattern
2) 8 atoms are occupied at 8 corners of cube and 1 atoms are occupied at body centre
3) Number of atoms (lattice points )(effective atom)
number per unit cell = 8 × 1/8 + 1×1 = 2
4) Coordination of each lattice point = 8
5) First nearest distance (along body diagonal ) = √3a/2
6) Number of first nearest lattice points = 8
7) Second nearest distance (adjacent crystal lattice point) = a
8) Number of second nearest lattice points = 6
9) Third nearest distance (along face diagonal) = √2a
10) Number of third nearest atoms = 12
11) Fourth nearest distance (along body diagonal) = √3a
12) Number of fourth nearest atoms = 8
13) Crystallographic planes (2, 0, 0), (1, 1, 0), (2, 2, 2)
14) Percentage Packing fraction = 68 %
15) Percentage void fraction = 32 %
16) Density of unit cell (d) = (Z = 1) × M/N0 × a3 - Face centered cubic lattice unit cell (F.C.C ): Let us consider edge length of primitive unit cell 'a' and 'r' be the radius of atom (lattice) and 'd' density of unit cell. It has following characteristics
1) This lattice has ABCABCABC... type pattern.
2) 8 atoms are occupied at 8 corners of cube and 6 atoms at middle of face
3 ) Number of atoms (lattice points )
per unit cell (EAN)= 8 × 1/8 + 6 × 1/2 = 4
4) Coordination of each lattice point = 12
5) First nearest distance (along middle of face diagonal) = √2a/2
6) Number of first nearest lattice points = 12
7) Second nearest distance (adjacent crystal lattice point) = a
8) Number of second nearest lattice points = 8
9) Third nearest distance (along face diagonal) = √3a/2
10) Number of third nearest atoms = 12
11) Fourth nearest distance (along body diagonal) = √2a
12) Number of fourth nearest atoms = 1
13) Crystallographic planes (2, 0, 0), (2, 2, 0), (1, 1, 1)
14) Percentage Packing fraction = 52.4 %
15) Percentage void fraction = 47.7 %
16) Density of unit cell (d) =(Z = 1) × M/N0×a3
Note:1)The distance between two tetrahedral voids = √3a/2
2)The distance between octahedral and tetrahedral voids = √3a/4
3)Tetrahedral voids located along body diagonal in front of corner
4)Octahedral voids located at body centre and middle of edge - Defects in Solids: Any deviation from the perfectly crystalline arrangement in a solid is known as a defect.
- Broadly speaking the defects are of two types, namely, point defects and line defects. Point defects are the irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance, whereas the line defects are irregularities or deviations from ideal arrangement in some rows of lattice points.
- Types of defects: 1) Stoichiometric defects 2) Non – stoichiometric defects
1) Stoichiometric defects: These are the defects in which stichometry of the ionic compound remains the same after the defect. The ratio of cations and anions is maintained even after the defect. Types of stoichiometric defects 1) Schottky defect 2) Frenkel defect
A) Schottky defect : This defect arises due to a vacancy at cation sites and equal number of vacancies at anion sites, In ionic crystals electrical neutrality is to be maintained Conditions for this defect. Seen in high co – ordination numbers compounds, Where the positive and negative ions are of similar size i.e Ex : NaCl, CsCl,Kcl,AgBr . Density of the crystal decreases. Stability crystal decreases
B) Frenkel defect: This type of defect arises due to a vacancy at a cation site. Actually, The cation moves to another position between two layers (intersticial position) and it is surrounded by a greater number of anions. Frenkel defect is favoured by a large difference in sizes between cation and anion Compounds having ions of different sizes i.e r+, r– is low since positive ions are smaller than negative ions, generally the positive ions are found in interstitial positions In these compounds the coordination number is low(usually 4 or 6) Ex: ZnS, AgBr, AgI, AgCl. Some ionic crystals have both the Schottky as well as Frenkel defects Ex : AgBr Consequences of Frenkel Defect: Density of the crystal is not altered Stability decreases
C) Impurity defect: If molten NaCl containing small quantity of SrCl2 is crystalized, some of the Na+ ions are replaced by Sr+2. Each Sr+2 replaces two Na+ ions. It occupies the site of one Na+ ion and the other site remains vacant. Other example is the solid solution of CdCl2 and AgCl. - Non Stoichiometric point defects : They include Metal excess defect (Due to anion vacancy) : It is due to absence of anion from lattice site leaving a hole which is occupied by electron to maintain electrical neutrality Centres, Holes occupied by electrons are called F – Centres (Colour centres). The greater the number of F – centres the greater is the intensity of colour of solid and solids are paramagnetic in nature due to F – centres. Ex: NaCl is yellow, KCl is violet, LiCl is pink Crystals showing schottky defect also show this defect. Metal excess defect due to the presence of extra cations at interstitial sites :ZnO on heating loses oxygen and turns yellow. Now there is excess of Zinc in the crystal. The excess Zn+2 ions move to interstitial sites and the electrons to neighbouring interstitial sites.
- Metal deficiency defect due to cation vacancy: It is due to absence of a metal ion from its lattice site and charge is balanced by ion having higher positive charge. Transition metals exhibits this defect. A typical example of this type is FeO which is mostly found with a composition of FeO 0.95. It may actually range from Fe 0.93 to FeO0.96. In crystals of FeO some Fe+2 cations are missing and the loss of positive charge is made up by the presence of required number of Fe+3 ions.
- Electrical Properties : Based on electrical conductivity, solids can be broadly classified into three types They are Metals, Semi – conductors and Insulators or Non – conductors Metals are conductors and have conductivity of the order of 104 to 107 ohm–1 m–1 Insulators have very low conductivity of the order of 10–20 to 10–10 ohm–1 m–1 The solids whose conductivity lies between those of Metallic conductors and insulators are called Semi – conductors. The order of conductivity of semi – conductors is 10–6 to 104 ohm–1m–1
The conductivity of semi conductors varies completely in the opposite way to that of the metals. Semi conductors conductivities increases with increase in temperature. This is due to the fact that the electrons from the valence band jump to the conduction band. Pure semi conductors which exhibit this property are known as intrinsic semi conductors. The temperature zone where the conductivity depends on the thermal electrons and the holes in the lattice of the semi conductors is known as intrinsic region. At low temperature the conductivity is mainly determined by the concentrations of the electron donors and the acceptors. This region is known as extrinsic region. - Doping: Addition of (III A Group) or P or As (VA Group) element to alter the conductivity of Ge or Si is called as doping. Pure Si or Ge are intrinsic semiconductors. In doping, group III A 13 group element element behaves as electron acceptor and group VA 15group elements element behaves as donor.
- Electron – rich impurties: When VA (or) 15th group element is added to Si , the crystal lattice does not change, but few Si atoms are replaced by group VA (or) 15th group elements, it forms covalent bonds with Si the fifth electron is delocalised, therefore Si becomes electrical conductor. Silicon doped with VA (or) 15th group element is known as'n' type semi conductor ( n = negatively charged electrons are responsible for conductivity) In doping, VA (or) III A group element is called as dopant.
- Electron – deficit impurties: III A group element has only 3 valence electrons. One more electron is required, it is left as a vacant place on the atom. This is called as electron vacancy or a hole. This electron vacancy in the crystal structure migrates from one atom to another. This is responsible for electrical conductivity of Si. 'Si' doped with III A (or) 13th group element is called p – type semiconductor.
(a) Magnetic Properties: The substances can be classified into five types depending on their response to an applied magnetic field. (a) Diamagnetic Materials : The substances which are weakly repelled by magnetic field examples NaCl, KCl, TiO2>ZnO, H2O Benzene etc.B <<< H
(b) Paramagnetic Materials:The substances which are attracted by magnetic field due to the presence unpaired electrons on atoms, ions or molecules. They lose their magnetic property when the applied field is removed. Ex: O2, Cu++, Fe+2, Fe+3, Cr+3, Na, Ti2 O3, VO2, NO etc B > H
(c) Ferromagnetic Materials:The substances which are strongly attracted by magnetic field. These substances contain domains of magnetization. All of them are oriented in the same direction. They retain their magnetism even after withdrawal of applied field. Ex : Fe, Co, Ni, CrO2, Gadalonium etc.B >>> H - Dielectric properties: A dielectric is a substance in which an electric field gives rise to net flow of electric charge. The crystals in which there is a net dipole moment when subjected to a stress, produce electricity. It is called piezoelectricity or pressure electricity. In some piezoelectric solids, dipoles are spontaneously aligned in a particular direction, even in the absence of electric field. They are called'ferroelectric substances'. Ex : Barium titanate (BaTiO3), sodium potassium tartarate, potassium hydrogen phosphate (KH2 PO4) etc. In some crystals, the dipoles align in opposite directions, then there is no net dipole movement. They are called'anti ferroelectric substances' eg : lead zirconate (PbZrO3) If electricity is produced on heating the crystal then it is called pyroelectricity .