Solid State 1: Course Material - IIT-JEE, AIEEE, Boards Chapters & Discussions

Solid State #1 by Sanjay Sharma

  • A solid is defined as that form of matter which possesses rigidity and due to which possesses a definite volume and a definite shape. �
  • The solids can be classified into -
  • (a) Amorphous solids (b) Crystalline solids

  • The solids which do not have any definite shape geometrically are called AMORPHOUS (Morpha = form) solids. Infact these have a random and disordered arrangement of atoms. These solids are also called �super cooled liquids� and are without sharp melting points i.e., these have �short range order� of their constituent atoms like that in the liquids. e.g. Glass, Rubber, Plastics etc.
  • Amorphous solids are isotropic i.e., their physical properties are same in all directions. Actually, here the particles are randomly arranged and disordered due to which all directions are equivalent hence all the properties remain same in all directions.
  • A crystal is a solid which is composed of atoms arranged in an orderly repetitive array i.e., A homogeneous anisotropic substance having a definite geometrical shape with surfaces that are usually plane with sharp edges.
  • In many solids, we may not clearly see the shape of crystals, because several small or micro-sized crystals are tightly packed together without any specific order. Such a substance which is infact crystalline but is superfine to be seen as crystals is called MICRO-CRYSTALLINE or POLYCRYSTALLINE SOLID. e.g. many metals and alloys. A copper wire have microcystalline structure.
  • On the basic of nature of bonding, the crystallien solids have been classified into following 4 types
    1. IONIC CRYSTALS : With (+) ve and ( - ) ve ions as constituent particles (which are bonded together by strong electrostatic
    2. MOLECULAR CRYSTALS : With molecules as constituent particles (bonded by vander Waals�forces). For Example : I2 ,Dry Ice (Solid CO2), Solid CH4 Ice etc.
    3. COVALENT CRYSTALS : With atoms as constitutent particles (bonded together by coralent bonds) For Example : Diamond, Graphite, Silicon etc.
    4. METALLIC CRYSTALS : With positive metal ions (Kernels) and free electrons as constituent particle (bonded together by metallic bonds) For Example : All Metals and alloys.
  • The external features of a crystals include -
    1. 1. Faces,
      2. Forms
      3. Edge
      4. Solid angle
      5. Interfacial angle
      6. Zone and Zone-axis

  • The crystals are bounded by surfaces which are usually planer and arranged in definite pattern. These surfaces are called faces. Faces are of two types namely like and unlike faces. The crystals with all similar surfaces is said to have like faces e.g. Alums, fluorspar etc. while galena crystal have unlike faces i.e., if have a combination of cubical and octohedral faces.
  • All the faces corresponding to a crystal are said to constitute a form. The forms may be SIMPLE (with like faces) or in COMBINATION (with unlike faces).
  • In a crystal, when two adjacent faces intersect, we get an edge and when three or more edges intersect we get a SOLID ANGLE.
  • The angle between the normals to the two intersecting faces is called an interfacial angle.
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    (i) AB type structures
    (ii) AB2 or A2B type structures.

  • The AB type structures designate equality in no. of cations and the no. of anions. The examples of this type of structes include - NaCl with coordination No. 6 - 6, CsCl with coordination no. 8 - 8 and ZnS with coordination no. 4 - 4.
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  • The AB2 or A2B type of ionic crystals contain the ions in the ratio 1:2 or 2 : 1 respectively. For Example : CaF2 populary called to have fluorite structure with other examples like SrF2, BaF2, PbF2and BaCl2 etc. The coordination number of Ca++ in CaF2 is 8 while that of F- is 4. On the contrary Na2O have antifluorite structure i.e., here the place of cations in occupied by anions and vice versa.
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  • The size of the unit cell and arrangement of atoms in a crystal is determined with the help of measurement of differaction of x-rays by the crystal. When a beam of monochromatic x-ray strikes two planes of atoms in a crystal at a certain angle Q, It is reflected. The intensity of reflected beam will be maximum if -
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    In actual practice it is difficult to grow a perfect crystal. Even single crystals grown with-all care are found to contain
    many internal irregularities. These irregularities are called crystal defects and can be defined as “Any departure from
    perfectly ordered arrangement of atoms in a crystal in called IMPERFECTION or DEFFECT”.These imperfections
    not only modify the properties but also sometimes impart new properties to the solids.

  • In an ionic crystal, the electrons are mostly concentrated around the electronegative component. Some of these electrons have the tendency of thermal release i.e., the property of loosing its position on increase in temperature. These thermally released electrous become mobile resulting to increase in conductivity of solid
  • When an electron is thermally removed from its position the electron deficient site thus formed is called a HOLE. Holes also impart electrical conductivity but their movement is opposite in direction to which the electrons move. The electrons and holes in solids give rise to electronic imperfections.
  • The defect discussed above is/are called point defects and can be categorised to following 3 types -
    (A) Stoichiometric defects
    (B) Non - stoichiometric defects
    (C) Impurity defects.
  • If imperfections in crystals are such that the ratio between the cations and the anions remains the same as described in its molecular formula, the defect will be called STOICHIOMETRIC DEFECT. These can be further categorised to-
    (a) Schottky defect (b) Frenkel defect.
  • In an ionic crystal of A+B- type, if equal no. of cations and anions are missing from their lattice sites, the defect is called SCHOTTKY DEFECT. In this defect electrical neutrality is maintained due to disappearence of similar no. of cations and anions (Lattice Vacancy).
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  • The schottky defect is shown by highly ionic compounds having -
    (i) High co-ordination number
    (ii) Small difference in the size of cations and anions
  • For Example : NaCl, KCl, KBr, CsCl etc.
    Due to such a defect density of the solid decreases.

  • In an ionic crystal when an ion is missing from its lattice site (causing a hole or vacancy there) and occupies interstitial site the defect is called FRENKEL’S DEFECT. In this defect the electrical neutrality and stoichiometry of the compound is maintained as ion does not leave the crystal completely.
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  • This type of defect is seen in those crystals where the difference in the size of cations and anions is very large and their coordination no. is low for example AgCl, AgBr, ZnS etc. Due to such a defect the density of the solid remains unchanged.
  • When the ratio of cations and anions due to imperfection differ from that indicated by their molecular formula, the defects are called Non-stoichiometric defects. These defects results in either excess of metal atom of excess of non metal atom.
  • The metal excess may occur in either of the following two ways -
    (i) Due to missing of a negative ion from its lattice site,
    thus leaving a hole which is occupied by an electron.
    The electrons thus trapped in the anion vacancies
    are called F.Centres (F=Farbe=German word for color) as these are responsible for imparting color to the crystals.
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    This defect is similar to frenkel defect

  • Metal defeciency or Non metal excess occurs where the metal shows variable valency i.e., transition metals. The defect usually occur due to missing of a cation from its lattice site and presence of the cation having higher charge at different lattice site thus balancing the loss.
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    e.g. FeO, FeS, NiO etc.

  • Another common method of introducing defects in ionic solids is by adding impurity ions having different change than host ion. These foreign atoms are present at lattice site in substitutional solids and at vacant interstitial sites in interstitial solids.
  • The faces, edges and interfacial angles are related as
  • f + C = e + 2

    where, f = Number of faces

    e = Number of edges

    c = Number of interfacial angles.

  • The faces of a crystal occur in sets. These sets are called ZONES. Each zone forms a complete belt around a crystals. A line drawn through the centre of a crystal in a direction parallel to the edges of a zone is known as ZONE
  • Some other terms related with solids include
    1. 1.Unit cell and space Lattice
      2. Coordination Number
      3. Crystallographic axes
      4. Standard or unit plane
      5. Axial ratio.

  • The regular arrangement of the constituent particles of a crystalline solid in the 3 dimensional space is called the space lattice or crystal lattice.
  • The smallest portion of the complete space which when repeated again and again in different directions produces the complete space lattice, is called the unit cell.
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  • The unit cells are of the following 2 types -
    1. Simple or primitive unit cell.
    2. Non primitive or multiple unit cell.
  • The simplest unit cell which has the lattice points at the corners or in the other words we can say when particles are present only at the corners of the unit cell. It is denoted by P.
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  • When a unit cell contains more than one additional lattice point (additional to those defined in simple unit cell) it is called non-premitive or multiple unit cell. It is further sub divided into -
    (i) Face centred unit cell (F)
    (ii) End face centred unit cell (C)
    (iii) Body centred unit cell (I)
  • When there particles or lattice points are present at the centre of each face in addition to particles at the corner the unit cell is called FACE CENTERED.
  • When in the unit cell, besides the points or particles at the corner of cell, the points or particles are located at the centre of any two parallel faces of the unit cell, it is called side - centred or end face unit cell.
  • In a unit cell when, beside the points or particles at the corner there is one particle located at the centre within its body, it is called body centred arrangement and the unit cell is called body centred unit cell.
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  • The geometry of a crystal can be best described in terms of 3 non-coplaner coordinate axes, called CRYSTALLOGRAPHIC AXES. These axes, namely X,Y and Z, may be mutually at right angles to each other or may be inclined to each other at different angles. As per convention the angle between Y and Z axes is called a, between Z and X is called b and between X and Y is called g.
  • On the basis of different possible values of a, b and g and different axial distances or edge lengths a, b and c following 7 types of 3 dimensinal primitive cells or crystal systems are given -
    1. Cubic : Where a = b = c & a = b = g = 90� for
    Example NaCl, KCl Diamond, Copper, Zinc
    blende etc.
    2. Tetragonal : Where a = b c and a = b = g = 90�
    For Example : Canssiterite (SnO2), white Tin, T1O2 (Rutile) etc.
    3. Orthorhombic : Where a b c and `a = b = g =90�.
    (Rhombic) For Example : Rhombic Sulfur, BaSO4
    (Baryta) CaCO3, PbCO3 (cerrusite) etc.
    4. Monoclinic : Where a b � c and a = g = 90�, b 90�
    For Example : Monoclinic sulfer, PbCrO2 etc.
    5. Hexagonal : Where a = b � c and a = b = 90�, g = 120
    For Example : Mg, Beryl, ZnO (Zincite) PbI2, Graphite etc.
    6. Rhombohedral : Where a = b = c and a = b = g� 90�
    (Trigonal) For Example : NaNO3,CaCO3(Calcite)
    MgS(Cinnabar) etc.
    7. Triclinic : Where a� b� c and a b g � 90�
    For Example: K2Cr2O77,H3BO3,CuSO4,5H2O etc.
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  • As there are 5 possible 2 dimensional lattice, similarly there are only 14 possible 3 dimensional lattices. These are called Bravais lattices (after the French Mathematician who first described them).
  • In different types of unit cells, the no. of atoms per unit cell can be calculated as follows :
    (a) In Primitive or Simple cubic unit cell -
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    from the above figure it is clear that here eight atoms which are present at 8 corners are shared by 8 unit cells. Hence,
    contribution of each atom present at the corner =

    total no. of atoms present per unit cell = 8 x = 1atom

    (b) In body centred cubic unit cell.

    from the above figure it is clear that this unit cell has 1 complete atom additional to that present in simple cubic unit . Hence, the total no. of atom present = 1+1=2 atoms per unit cell.
    (c) In face centred cubic unit cell :

    From the above figure it is clear that here -

    (i) 8 corner atoms x atoms per unit cell = 1 atom

    (ii) 6 face atoms with representation of 1/2 atom
    per face per unit cell, thus - 6x1/2 = 3 atoms
    Total atoms present per unit cell = 1+3 = 4 atoms

    (d) In end face centred cubic unit cell :
    Similarly end face centred cubic unit cell have 1
    instead of 3 face atoms present in face centred cubic
    unit cell. Rest distribution is same (because here only
    2 parallel face have one atom each at the centre of
    face shared by two unit cells). Thus, the total no. of
    atoms present per unit cell here is = 1 + 1 = 2 atoms
    per unit cell.

  • If we represent atoms by sphere, the no. of sheres surrounding a particular sphere is called the co-ordination number of that sphere i.e., in simple words it is the no. of atoms or ions or molecules surrounding a particular atom in a crystal lattice.
  • Any face of the crystal may cut into one or more crystallographic axes. The face which cuts all the three axes in called STANDARD or UNIT PLANE. The distances of the points where the standard plane cuts the three axes from the origin are called intercepts. The intercepts a,b and c and axis x, y and 2 respectively are called CRYSTAL PARAMETERS.
  • The actual practice the ratio a : b : c is called the AXIAL RATIO and it depends upon the point where all the three axes meet.
  • To understand the packing of particles in a crystal it is assumed that these particles are hard spheres of identical size. This packing can be seen in one of the following ways-
    (a) The simplest way is if spheres are placed in a
    horizontal row, touching each other as seen below -
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    Thus an edge of crystal is formed.
    (b) When the above written rows combine, 2 type of combinations are possible -
    (i) With a horizontal as well as vertical alignment as shown below -

    Thus particles form square and the packing is called Square close packing. The empty space between the the partivles in a close packing is called a VOID as seen above.


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