Key Terms students should be familiar with, in this chapter:
Crystalline | Amorphous | Space Lattice |
Unit Cell | Simple Cube | Face Centered Cube fcc |
Body Centered Cube bcc | Rock salt | Caesium chloride type |
Zinc Blende | Fluorite | Antifluorite |
Tetrahedral Void | Octahedral Void | Hexagonalclosepacking hcp |
Cubic close packing ccp | Coordination number | Radius ratio |
Ionic radii | Ortho silicates | Pyro silicates |
Cyclic or ring silicates | Sheet silicates | 3D Silicates |
Point defects | Schotky defect | Frenkel defect |
F-Centres | Dislocation | Conductors |
Insulators | Semiconductors | Diamagnetic |
Paramagnetic | Ferromagnetic | Spinels |
Dielectric | Piezo electricity | Pyro electricity |
Ferro electricity | Antiferro electricity | Super conductivity |
12-16 Compounds | 13-15 Compounds | Amphiboles |
Pyroxenes | Radius ratio effect | N-Type of conductors |
P-Type of conductors | Semiconductors | Photovoltaics – Transducers |
Classification of Solids:
Ionic | Molecular | Covalent | Metallic |
Positive and Negative ions | Molecules | Atoms | Positive metal kernels and free electrons |
Strong Electrostatic forces of attraction | Van der Waals forces | Covalent bonds | Cohesive forces are electrostatic attraction or Metallic bonds |
... force is exerted on other charged objects. Static Electricity: Static Electricity: the buildup of charge on an object In ... Current: An electric current is induced in a conductor when the conductor moves through a magnetic field. Electromagnetic Induction: ... unbroken path through which electric charges can flow Conductors and Insulators: A conductor transfers electric charge well. An insulator does ...
KCl, NaNO3, CaF2 | Dry ice CO2, CH4, Sugar, Sulphur | Diamond, Silicon Carbide, graphite | Gold, Silver, Copper etc. |
High m.p, b.p | Low m.p, b.p | High m.p | High m.p, b.p |
CLASSIFICATION OF SOLIDS:
Molecular Solids: The forces of attraction holding the molecules are Van der Waals forces. Examples of molecular Crystals are Ice, Solid Carbon dioxide, Sulphur, CH4 , Wax.
Ionic Solids: The forces of attraction holding the ions together is electrostatic in nature. Examples are NaCl, BaCl2 , CsCl, NaNO3 etc.
Covalent Solids: The binding forces are Covalent Bonds eg. Diamond, Silicon Carbide, Quartz.
Metallic Solids: The binding forces are electrostatic attraction eg. Copper, Aluminium, Silver, Gold etc.
CLOSED PACKED STRUCTURES
In a crystal the constituent units atoms ions or molecules are arranged in such a way that the arrangement has minimum energy and thus maximum stability.
For maximum stability the constituent units in the crystal must be srrounded by maximum number of neighbours.
Three-dimensional packing of spheres
Hexagonal Close Packing hcp:- The spheres are arranged in a way such that the third layer comes vertically above the first layer the sequence may be represented as ABABABABA……. This type of arrangement is called hexagonal close packing or hcp arrangement e.g. Beryllium, Calcium, Cadmium, Zinc etc.
Cubic Close Packing ccp:- The spheres are arranged in a way such that the fourth layer comes vertically above the first layer. The sequence may be represented as ABCABCABC……. This type of arrangement is called cubic close packing or ccp arrangement.
The A,B,C represent the different layers of spheres in a three dimensional arrangement where each layer has a hexagonal close packing in 2 – dimension.
When arranging atoms in a 3D pattern there is space still unoccupied and these are regarded as holes or voids or interstices.
Tetrahedral Voids:- These are voids formed by 4 closely touching spheres.
Or one sphere resting on three touching spheres. It is called a tetrahedral void because the centres of the 4 touching are placed at the corners of a tetrahedra
... work out the formular: if n = number of figures a = number of arrangements the formular is a = ni/2 ... so if A represent arrangement, and n represent numbers of figures, x represent the number fo same number, and the formula ... the frequency 2 figure with 2 same number 1 arrangements 3 1 3 4 1 3 4 ... formula which can calculate the number of arrangement when we look at a number. Lets list all the arrangment ...
Octahedral Voids:- These are voids formed by six touching spheres.
Or Three spheres belonging to one layer and three spheres belonging to the second layer. The centres of these spheres form a regular Octahedron.
Note 1. Octahedral Voids are bigger than Tetrahedral voids
2. Number of Octahedral voids are equal to the number of spheres
3. Number of Tetrahedral voids are equal to twice the number of spheres
4. Relationship between size of the voids and spheres is
a) Radius of atom ‘r’ in a Tetrahedral void = .225 R
b) Radius of atom ‘r’ in an Octahedral void = .414 R
Where R is the radius of the sphere in the close packing arrangement.
Co-ordination Number:- The total number of nearest neighbours, atoms or ions of a particular atom or ion in a crystal lattice is called co-ordination number.
The smallest portion of a space lattice which generates the whole crystal by repeating its own dimensions in various directions is called unit cell
The smallest repeating unit in space lattice which when repeated over and over again produces the complete space lattice.
STRUCTURES OF SIMPLE IONIC COMPOUNDS:
CRYSTAL STRUCTURE | A BRIEF DETAIL WITH EXAMPLES | CO-RDINATION NUMBER | FORMULA UNITS PER UNIT CELL |
NaCl -TypeRock-Salt | Na+ ions occupy the Octahedral sites while Cl- ions are in ccp arrangement or vice versa eg. NH4Cl, AgCl, AgBr, Halides of Li, Na &Rb; CaC2 etc. | Na+ = 6Cl- = 6 | 4 |
CsCl-Type | Cs+ ions occupy cubic sites while Cl-ions are at the corners of a cube orvice versa. | Cs+ = 8Cl- = 8 | 1 |
CaF2 – TypeFluorite Structure | Ca2+ ions are in ccp while F- ions occupy Tetrahedral sites e.g. CaF2, BaF2, BaCl2, SrF2 etc. | Ca2+ = 8F – = 4 | 4 |
... committed” because its daughter cells can become any of a restricted number of cell types. All of the differentiated cell types in a human ... in concentrations is called a concentration gradient, and atoms, molecules, and ions are said to diffuse down a concentration gradient. ... - Also called simple diffusion is the tendency of atoms, molecules, and ions in a liquid or air solution to move from ...
ZnS-Typea) Zinc blende | Zn2+ ions occupy Alternate tetrahedral sites e.g. while S2- ions are in the ccp e.g. ZnS, CuCl, CuBr,CuI, AgI etc. | Zn2+ = 4S2- = 4 | 4 |
b) Wurzite | Zn2+ ions occupy Alternate tetrahedral sites while S2- ions are inhcp type of arrangement. | Zn2+ = 4S2- = 4 | 4 |
AntifluoriteStructureNa2O | Positive ions occupy all thetetrahedral sites while Negative ionsare in ccp type of arrangement. e.g. Na2O | Na+ = 4O2- = 8 | 4 |
TYPES OF UNIT CELLS:-
Simple Cubic Unit Cell: It is that unit cell in which the lattice points are present at its corners only. It is also called a primitive unit cell.
The total number of atoms in an scc unit cell is z = = 1
Face Centred Cubic Unit Cell FCC: It is that unit Cell in which the lattice points are present at its corners as well as the centre of each face.
A Particle on a face of the cube is shared by 2 faces.
The total no of atoms in an fcc unit cell is z =
Body Centred Cubic unit cell BCC: It is a unit cell in which the lattice points are present in its corners as well as the centre of the body.
The total number of atoms in a bcc unit cell is z =
| CONTRIBUTES INTO THE UNIT CELL |
ATOMS ON EDGE | 1 / 4 |
ATOMS AT CORNERS | 1 / 8 |
ATOMS ON FACES | 1 / 2 |
ATOMS IN THE UNIT CELL | 1 |
CALCULATION OF DENSITY OF UNIT CELL :
Mass of unit cell = Number of atoms in unit cell x Mass of each atom
Mass of unit cell =
Mass of each atom
Z = No of atoms in unit cell
N is Avogadro’s Number
is the Molar mass of the Crystal
is the volume of the unit cell
Where a is the edge length of a unit cell
a is the edge length of a cube usually expressed in pico metre or nano metre 1pm =10-12 m and 1nm = 10-9m
M is the molar mass of the element,
CALCULATION OF THE NUMBER OF FORMULA UNITS IN THE NACL CRYSTAL:
NaCl has FCC type of Unit cell.
... they flow freely in and out of the cell. 8. Defects in structures of the cell can lead to many diseases. Pick one ... not function properly. Cell membranes separate the interior of the cell from the outside environment. The cell membrane allows certain ions and organic molecules ... the structure of a cell, whereas in animal cells they are used to store water, waste, and ions. Animal cells have one or more ...
The Unit Cell has 12 Edges, 6 Faces and 8 Corners
Na+ ions are present at the centre of the cube and on the 12 edges.
No. of Na+ ions contributed into unit cell by the Edges is ¼ x 12 = 3 ions.
No. of Na+ ions in the centre of the unit cell is = 1
Total no. of Na+ in the Unit Cell is = 3 + 1 = 4
Cl- ions are present on the 6 Faces and 8 Corners
No. of Cl- ions contributed into unit the cell by the 6 faces are ½ x 6 = 3
No of Cl- ions contributed into the unit cell by the 8 corners are 1/8 x 8 = 1
Total No. of Cl- ions present in the unit cell are 3 + 1 = 4
Therefore there are 4 formula units of NaCl in its unit cell.
DETERMINATION OF RADIUS OF AN ATOM IN AN OCTAHEDRAL VOID
Derive a relationship between the radius r of an atom that can be placed in the
octahedral void constituted by atoms of radius R. (r = .414R)
(BC)2 = (AB)2 + (AC)2
(2R)2 = (r + R)2+ + (r + R)2
(2R)2 = 2 (r + R)2
(√2 R)2 = (r + R)2
√2 R = r + R
r = √2 R – R
r = R(√2 – 1)
r = R(1.414 – 1)
r = .414R
RADIUS RATIO EFFECT
The ratio of the radius of positive and negative ions is known as radius ratio.
The effect of this number in determining the co-ordination number and the shape of an ionic solid is known as radius ratio effect.
Limiting Radius Ratio:-
In a binary compound AB e.g. NaCl, CsCl, ZnS etc.
The co-ordination number of A+ is equal to the co-ordination number of B-.
In Binary AB2 type of compound CaF2, CaCl2 etc.
The co-ordination number of A+ is equal to 2 x co-ordination number of B-
Radius Ratio =
Radius Ratio r+/r- | Co-ordination Number | Structure | Example |
1 – 0.732 | 8 | Cubic | CsCl |
0.732 – 0.414 | 6 | Octahedral | NaCl |
0.414 – 0.225 | 4 | Tetrahedral | ZnS |
0.225 – 0.155 | 3 | Trigonal | Boron Oxide |
Inter Nuclear Distance:-
Inter Nuclear distance = Ionic radius of Cation + Ionic radius of Anion
Inter Nuclear distance of NaCl type of Crystal i.e. r+ + r-
... meaning than that to the orbital magnetic dipole moment. The magnetic moments of the electrons in the atoms that make up ... seen to change only into the corresponding neutrino. The electron has magnetic properties by virtue of (1) its orbital motion about ... classical analog of the orbital magnetic dipolemoment of a small current-carrying circuit. The electron spin magnetic dipolemoment may be thought ...
rc + ra = |
Inter Nuclear distance of CsCl type of Crystal i.e. r+ + r-
rc + ra = |
For similar kind of elements the radius of the atoms can be calculated using the following equations:
For Simple Cubic Closed packed structures (scc) a = 2r or r =
For Face Centred Cubic close packed structures (fcc) r =
For Body Centred Cubic closed packed structures (bcc) r =
IMPERFECTIONS IN SOLIDS
Intrinsic Conduction: At absolute zero Covalent and ionic compounds have their electrons in the ground state so they do not tend to conduct electric current. At higher temperatures the electrons are released into higher orbitals, creating holes and positive holes. The electrons released in the covalent bonds at higher temperatures in Silicon and Germanium brings about Intrinsic Conduction. The electrons and holes created in the crystals are electronic imperfections.
N – Type of Conductors:
The tetravalent silicon and germanium doped with pentavalent group 15 elements e.g. P, As, Sb etc brings about n-type of conduction. The pentavalent impurity has got an unsatisfied valence electron, this free electron can bring about electrical conduction it is known as an n-type (negative) of conductor. The free electron is the cause for conduction.
P-Type of Conductors:
The tetravalent silicon and germanium doped with trivalent group 13 elements e.g. Al, Ga, In etc. Brings about p-type of conduction. The trivalent impurity cannot complete the three dimensional network of the tetravalent Si or Ge this leads to the formation of a Positive hole or electron deficient centre which conducts electricity hence known as p-type of conductor.
12-16 Compounds: When a solid state compound is formed by combination of elements of group 12 and 16 the compounds are called 12 -16 compounds e.g. ZnS, CdS etc. (The effective valency of the two elements become 4 by the combination of the two group elements.)
The measurement of nuclear and electron magnetic resonance on bulk materials was made possible by Felix Bloch ... quantum mechanical property of electrons and some nuclei called spin. In the absence of an externally applied magnetic field, this property is ... quantum mechanics to include this property. Purcell looked at the magnetic resonance experiment with the eyes of an optical spectroscopist. He ...
13 – 15 Compounds: When solid state compounds are obtained by combination of elements of group 13 and 15 the compounds are called 13 – 15 Compounds e.g. AlP, GaAs, InSb etc. (The effective valency of the two elements become 4 by the combination of the two group elements.) These compounds show Solid state properties.
The imperfections in the crystal due to vacancies in the lattice or due to dislocation of a particle from one position to another position of the lattice is called Point Defect.
Stoichiometric Defects: The compounds in which the numbers of positive and negative ions are exactly in the same ratio indicated by their chemical formula are called stoichiometric compounds.
Schottky defect is observed when equal numbers of cations and anions are missing from the lattice. Presence of Schottky defect lowers the density of the solid.(It is a stoichiometric point defect)
Conditions for Schottky defects:
a) The constituent ions should have high Co-ordination number
b) The Cations and Anions Should be almost of same size
c) The compound should be strongly ionic in nature.
Examples: NaCl, KCl, KBr and CsCl.
Frenkel defect arises when a cation leaves its normal lattice site and occupies an interstitial site.
Conditions for Frenkel defect:
a) The constituent ions have low co-ordination number
b) The Anions are much larger than the Cations
Examples: AgBr, AgCl, AgI
What are the consequences of Schottky and Frenkel defects?
Solids showing these defects conduct electricity to a small extent. This is because if an ion moves from its lattice site to occupy a hole it creates a new hole. In this way a hole moves across the crystal which as a result moves the charge in the opposite direction.
Due to presence of holes, the stability of the crystal decreases
In Frenkel defect, similar charges come closer. This results in the increase of dielectric constant of the crystals.
Dislocations: When deviation in arrangement of ions extends over microscopic regions they are known as Lattice Imperfections. When a lattice imperfection extends along a line or plane the defect is also known as Dislocation.
Non stoichiometric Defects:
The compounds in which the numbers of positive and negative ions are not exactly in the same ratio indicated by their chemical formula are called stoichiometric compounds.
Metal Excess Defects.
F-Centre When alkali metal halides are heated in an atmosphere of alkali metal vapours, Anion Vacancies are produced. Electrons trapped in anion vacancies are known as F-Centres.
F-Centres are paramagnetic due to the presence of unpaired electrons.
A group of mixed metal oxides with the general formula AB2O4 where ‘A’ is divalent and ‘B’ is Trivalent. Where ‘A’ and ‘B’ can be the same or different ‘A’ can be Mg, Fe, Co, Ni, Zn and ‘B’ can be Al, Fe, Mn, Cr or Rh. The Oxygen has cubic closed packed arrangement. In Normal Spinals ‘A’ occupies Tetrahedral voids and in Inverse spinals ‘B’ occupies half the Tetrahedral voids and the other half is in Ocrahedral voids. E.g. Fe3O4, MgO Fe2O3etc.
What are F Centres? Why does ZnO turn yellow on heating? And Why does the it loose it yellow colour on cooling? What kind of defect is it?
ELECTRICAL PROPERTIES OF SOLIDS:
Semi Conductors: They are solids which are perfect insulators at absolute Zero but conduct current at room temperature.
Insulators are substances whose electrical conductivity is of the order of 10-12 Ohm-1 cm-1 and Conductors are substances whose conductivity is of the order of 106 to 108 Ohm-1 cm-1 and Semiconductors conductivity is of the order of 102 to 10-9 Ohm-1 cm-1 .
It is shown by all those substances in which atoms, ions or molecules have unpaired electrons. It is caused by the spin and orbital angular momentum coupling of electrons. Such compounds are weakly attracted by external magnetic fields and the magnetic properties are lost once the external magnetic field is removed. E.g.Oxygen
This property is shown by compounds which do not contain unpaired electrons. These materials are weakly repelled by the external magnetic field. Diamagnetic substances are independent of temperature. e.g. TiO2, NaCl and Benzene.
Substances which are strongly attracted by the magnetic field and show permanent magnetism even when the magnetic field is removed are known as Ferromagnetic Substances.
Ferromagnetism arise due to spontaneous alignment of magnetic moments due to the presence of unpaired electrons
If the alignment of magnetic moments in a compound is in a compensatory way so as to give a net magnetic moment of Zero due to the cancellation of the individual magnetic moments, the property is referred to as Anti Ferromagnetism.
When the Magnetic moments are aligned in parallel and antiparallel directions in unequal numbers resulting in a net magnetic moment the property of the compound is said to be ferrimagnetic. E.g. Fe3O4 and spinels
Effect of temperature on the magnetic behaviour:
Due to spin randomisation many compounds become paramagnetic at high temperature. Fe3O4 becomes paramagnetic at 850 K
When an insulator is placed under the influence of an external electric field the electrons in the bonds get polarised leading to the formation of a dipole. This leads to the following dielectric properties.
A crystal in which the dipoles arrange themselves in an ordered way such that the crystal has a net dipole moment are said to exhibit Piezoelectric effect.
When a dielectric crystal is subjected to a mechanical strain electrical charges develop on some parts of the crystal and thus a current is produced this current is called Piezoelectricity. The reverse is also true if opposite charges are applied on the faces of the crystal there will be a mechanical strain due to atomic rearrangement. They are therefore called as Electrical Mechanical Transducers E.g. Quartz Crystals.
These are Piezoelectric crystals in which the dipoles are permanently aligned even in the absence of an external electric field. The application of an external electric field can reverse the direction of polarisation. E.g. Barium Titanate BaTiO3, Rochelle Salt or Sodium potassium Tartarate and Potassium dihydrogen phosphate KH2PO4 .
Crystals in which there is no net dipole moment due to internal compensation since the dipoles within the alternate polyhedra cancel each other. They do not exhibit Ferroelectric character. E.g. PbZrO3 Lead Zirconate.
When a dielectric crystal like Tourmaline is heated some of its faces become electrically charged and thus a small electric current is produced known as Pyroelectricity.
An amorphous solid is a substance whose constituents do not posses a long range orderly arrangement. The orderly arrangement in them is restricted to very short distances which are of the same order of magnitude as the inter atomic distances.
e.g. Glass, Plastic, fused silica etc.
Amorphous substances are
II. Does not have definite melting points
III. Does not have definite interfacial angles
Photovoltaics They are amorphous substances viz. Silica which is capable of converting electromagnetic radiation (light)into electrical energy.
They are formed by fusing alkali metal carbonates with silica at 1775K The basic building unit in all silicates is the SiO4 4- tetrahedron. The SiO4 4- units are linked together in many ways in which the oxygen atoms of the silicate units are shared between each other in many ways given below.
Orthosilicates, Pyrosilicates or Island silicates, Chain silicates, Ring silicates and Sheet Silicates (2-Dimensional Silicates)
In simple Orthosilicates the SiO4 4- tetrahedron units do not share any of its oxygen atoms with any of the other tetrahedra units. E.g. Willmenite ZnSiO4, Zircon ZrSiO4.
Pyrosilicates or Island silicates
In Pyrosilicates one oxygen atom is shared by two silicate units General formula is (Si2O7)6-
E.g. Thortevitite Sc2[Si2O7] and Hemimorphite Zn(OH)2(Si2O7)H2O
Ring or Cyclic Silicate
It is formed when two oxygen atoms are shared by two silicate units. They have a general formula (SiO32-)n examples are Beryl Be3Al2Si6O18 and Wollastonite Ca3Si3O9 both containing 6 six silicate unit ring system. Examples of three silicate unit ring systems are Benitoite BaTi(Si3O9).
When two oxygen atoms per SiO4 tetrahedra are shared by other silicate units two kinds of chain silicates are formed. General Formula (SiO32-)n
I. Pyroxenes They contain a single stranded chain e.g. Enstatite MgSiO3, Spodumene [Li Al(SiO3)]
II. Amphiboles They contain a double stranded chain it is present in Asbestos Ca Mg3O(Si4O11) and Tremolite Ca2Mg5(Si4O11)2 (OH)2.
There are Two kinds 2D and 3Dimensional sheet silicates
2Dimensional silicates are present in Clay each silicate unit shares 3 of its oxygen atoms with three other silicate units giving an infinite sheet structure General formula (Si2O52- )n . E.g Talc Mg3(OH)3Si4O10.
3Dimensional Silicates Quartz is an example all the four oxygen atoms of the silicate unit is shared by all the four silicate units surrounding it giving rise to an infinite 3D arrangement. E.g Zeolites NaAlSi2O6.
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