Solid State PDF by Rakshita Singh

CHAPTER 15 SOLID STATE h Chapter Objectives...

CHAPTER 15 SOLID STATE h Chapter Objectives ng Classificntionofsolids, Space lattice and Unit ell, Types ofcrystal latire o Crystalline solids, Amorphous solids,Calculation ofpackingfraction, Close packing in the crystals, Calculatiom i t cell, Radius ratio,inClassificntion of particles a unit cell, ofionic structures, Bragg's equation, Iniperfections in a crystal, Electrinpropertias f mumber Si semiconductors, insulators, Magnetic properties of solids, Dielectric solids, Banud theory ofmetals, conductors, solids. STUDY MATERIAL ita sh I. Concept Clarified: For more detai Scan the cok One of the physical states of matter is solid state in which particles (molecules, ions or atoms) are ak dosely packed and held together by strong intermolecular forces of attraction. Solids -R Crystaline solids Amorphous solids Differences between Crystalline and Amorphous solids am S.No. Property Crystalline Solids Amorphous Solids 1. Shape Definite shape. Irregular shape 2. Melting point Melt at sharp and characteristic Indefinitemelting point. gr temperature. le Te Time Time 3. Heat of fusion They have a definite heat of fusion. They do not have ue fusion. to Compressibility Theyare rigid and incompressible. They may be Compressed appreciable extent. 5 Cleavage They undergo clean cleavage. undergoclean They do not Anisotropy & Isotropy Anisotropic in nature age. b. Isotropic in nature_ Nature True solids Pseudo-solid or suppe liquids bree t 8. Examples Diamond, Cu, Silica, NaCl etc. Plastics, PTFE, FiDI Glass,  i f i c a t i o n o fS o l i d s F o rmore details, Classitica of the the forces which hold For more details, upon t he nature the ions), a n be cla solid ccan classified together the structural units into four types as shown in the scan the code scan the code ding i 0 t n s ) , solid or e y e n molecules s l l o wn gt a b l e : Tipesof SolidSolid Constituent Particles Intermolecular Cations and anions Coulombic or forces Properties Examples NaCI, KCI, MgO, o Brittle, hard, high lonic electrostatic melting point, CaF, etc. insulators in solid state but conductors in molten state and in aqueous solution Non-polar molecules| Dispersion or Soft, very low melting Ar, CC1, H, CO2 h Molecular and atoms of non- London forces point, insulator etc. ng solids () Non-polar| metals Polar molecules Dipole Dipole Soft, low melting point, HCI, SO, etc. interaction insulator () Polar Si Containing Hydrogen bond Hard, low melting HO (ice) electronegative and point, insulator (ii)Hydrogen bonded small size atom (Like ita solids EO,N)_ SiO(Quartz), C Covalent solids| Atoms of non-metals Covalent bond Hard, very high melting point, insulator (Diamond), SiC,etc. Fe, Na, Zn Cu etcC. Metallic solids Metallic kernels (cations) and free Metallic bond sh Indefinite hardness, melting point depends on strength of metallic electrons ak bond, malleable, ductile, insulator or conductor (exception) -R |For more details, For more details, Unit Cell: ne smallest repeating unit of a crystal which is repeated over in different scan the code scan the code directions regenerates the whole crystal. mportantterms in unit cell: am present in unit cell. Latticepoint: The atoms, ions or molecules which are of the constituent A regular arrangement Pe1attice or crystal lattice : Formoredetails, particles of a crystal in three-dimensional space. scan the code three edges a, three-dimensional lattice is characterized by stalparameters: The unit cell in a These are known as unit cell's parameters. Thus, there are gr sivt n e interfacial angles a, B, y. parameters (a, b, c and a, B, 1) in a unit cel le Te b of unit ceil A unit celi Space lattice pes of Cryst it cells areystal Lattices are of of ple or the following two types:Particles are present at all the corners of the unit cell. e cubic unit cell :  (i) Non-primitive or centered unit cell: Particles may be present at all the corners and within the unit nit cells a6 as some other special positions. These cells may be further divided into thefollowing types: (1) Face centered Cubic (fcc): When atoms are present in all corners as well as six face centres in ac cell. cubx. ue (2) End centered cubic (ecc): When atoms are present at corners as well as centre of any two faces in. unit cell. faces in a cuby (3) Body centered cubic (bc): Atoms are present at corners as well as body centre in a cubic unit cel] Crystal Systems: The different possible geometrical shapes of crystal lattice (or crystal) are known as Crystal systems. (i) There are 230 crystal forms which are grouped on the basis of their symmetry into 32 classes. (ii) There are seven systems and arrangement of atom/ions in four different ways : (i) primitive, (i) bec, f iv) ecc. Therefore, systems x 4 ways 28 ways of arranging the atoms/ions. Out of 28 theoreticalways on. exists. These 14 unit cells are called Bravais Lattices. only '4 h The 14 Bravais Lattices are given as below: ng S.No. Crystal system BravaisLLattices Parameters of unit cell Intercepts Interfacial angle No. of No. of point Example point space groups Si groups 1. Cubic Primitive, fcc, bcc =3 a = b =c B =y = 90° 5 36 Pb, Hg Ag Au, Zns, NaCl ita Diamond 2. Orthorhombic Primitive, fcc, bc, a b c a = B =y = 90° ecc = 4 sh 59 KNO,,KS0, 3 Tetragonal Primitive, bcc =2 a = b c a = ß =y = 90 7 68 SnO, TIO 4. Monoclinic a b c ak Primitive, ecc = 2 Y = 90° 13 CaSO,2H.00 B 90° 5. Triclinic Primitive =1 ab c a B y =90° 2 2 KCr,O -R CuSO,5H0 6. Hexagonal Primitive =1 a =b #c a B 90° 27 Mg. Zn, Cd Y= 120° SiO2 7. Rhombohedral Primitive =1 a b a 90° 5 As, Sb, Br am = = c = y = 25 B 120 CaCO 32 230 gr Seven Crystal Systems and Fourteen Bravais Lattice CUBIC le Te Simple Face Centered Body Centered ORTHORHOMBIC Angles between Body Centered Face Centered End Centered the planes Simple  T E T R A G O N A L MONOCLINIC d Body Centered End Centered Simple Simple RHOMBOHEDRAL TRICLINIC HEXAGONAL h ng Si 120 ita an ofNumber of Particles and Space Occupied ie. Packing Fraction in Unit Cell: fcc Primitive or simple cubic cell (scc) sh bcc ak Ceonetry -R a = 2r 4r= 3a 4r=2a = 8 x (1x1) - 8 x+ 6x m Vumber of atoms unit cell (n) 8x=1 Corners body centre Corners facecentre corners a = 4 = 1+1=2 gr elation between 4r= 2a i and r a = 2r 4r= 3a le kang efficiency nx Te o r 52.4% 5T or 68% 3 o r 74% Va) 8 Volume=al Loordination Number: s defined as the the number of its closest neighbours (oppositely charged ions in case of ionic crystal) that an atom r2s in a unit cell. It nunmbe Simple cubic depends upon structure. Face ucture coordination no.=6 : ABodycentered cubic structu coordination no.=12 centered cubic structure : coordination ne no.=8 se tacking in Crystals: ions/molecules) are arranged in such a way that the ent haonstituent units of particles (atoms having minimum energy. Maximum stability1s attained when eachconet aximum stability must be packed as closely as possible. maximum number of neighbours i.e. crystal Ithas two types: 1. Close Packing in Two Dimensions: in two dimensions. There are two possible arrangements of close packing ) Square Close Packing In which the spheres in the adjacent row lie just one over the other and show a horizontal as well arrangement and form square. Each sphere in thin arrangement is in contact with four spheres well as vertica X Fig: Square Close Packing h (i) Hexagonal Close Packing: ng In which the spheres in every depression are seated between the spheres of the first row. The spheres in the third row are vertically aligned with the spheres of the first row. These types of arrangement are nohie over the crystal structure. ced all Si Vertical XA Ist row 2nd row Allignment ita 3rd row sh Fig: Hexagonal Close Packing Comparison between Square close packing and Hexagonal close packing ak 1. hcp is more dense than square close packing (s.c.p). 2. 60.4% available space is occupied by spheres in I cp whereas in scp, it is 52.4%. 3. In hcp arrangement, the spheres are packed in such a way that their centres are at the centres of an triangle. Each sphere is surrounded by six similar neighbours of spheres. But in scp, each sphereequilateral -R is aligned with four spheres whose centres lie at the corners of a square. 2. Close Packing in Three Dimensions: There are also two different ways to arrange spheres in three-dimensional packing: am (i) Hexagonal Close Packing (hcp): The third layer of spheres may be placed on the hollows of second that each sphere of the third layer lies layerso strictly above a sphere of the first layer ie. third layer becomes exacty identical to the first layer. This type of packing is referred to as ABABAB.... arrangement. gr le A Points -B Te at centre -A Hexagonal (ii) Cubic Close Packing (ccp):The second way to pack spheres in the third layer is to place them (unoccupied) of the first layer). In this way the fourth layer lies strictly above a sphere of the first over layerhou navu"g sequence as ABCABCABC... CBA B C A Points Cubic at center  (a) void 'b' void'a' (a) Hexagonal (a) Cubic Exploded close-packed Exploded close-packed structure view structure view (d) (C Fig: Cubic Close Packing having The spheres are arranged in the first layer closely packed h ered cubic (bcc) arrangement: of second layer At the toP of the hollows in the first layer are arranged by the spheres ng BO opened up. is in contact with four spheres of the first layer. Spheres of third layer a r e sinnhere in the second layer in each sphere is in contact with eight spheres (four cty above the first layet. lhus, this arrangement, heres a r e at the c o r ners layer. and four spheres in lower layer). In this arrangement, eight Si in upper spheres and one sphere is in the centre (or body) of the cube. of a cube A ita A sh (A) (B) Fig: Body centred cubic arrangement ak from its Edge Length: Calculation of Density of a Crystal elements: Forcubic crystals of Mass of unit cell -R unit cell Z = Let the number of atoms per D e n s i t y o f u n i t cell (P) = Volume of unit cell of Mass of unit cell No. of atoms per unit cell x = mass one atom ZM Atomic mass(M) Mass of each atom Na am Avogadro number (NA) ppm) (Let the edge length = Mass of unit cell a3x Atomic Mass Volume of unit cell (ppm) = = (a x 10-10 cm) = No. of atoms per unit cell X Avogadro No. 103 cmn^] gr ZM ZM F N ax108cm" le N Voids or crystal: holes created in packing of atoms in a Te There a packing (a) tetrahedral voids and (b) octahedral three-dimensional close VOnds. O ypes of interstitial voids in tetrahedral arrangement. between four spheres touching each other having Thedral voids: The vacant space e r of tetrahedral voids is double to the number of spheres. Tetrahedral void Tetrahedral void fcc unit cell tetrahedral voids per a lius (r Tetrahedral void in fec Number of rahedral void = 0.225R [R = Radius of sphere  (ii) Octahedral void : The vacant space between six spheres touching each other having octahedral arranpen gement Octahedral Octah Octahedral void void void Octahedral void in fcc An octahedral void at the centre of an edge in fcc unit cell. An octahedral void at the body centered position in fcc unit cell h Radius ( ) of octahedral void = 0.414 R [R = Radius of sphere] The no. of voids in terms of number of atoms in no. of octahedral voids = No. of atoms in the close packej ng arrangement. In ccp unit cell there are 8 tetrahedral voids and 4 octahedral voids but in hcp unit cell there are 12 tetrahedal Si voids and 6 octahedral voids. No. of tetrahedral voids = 2 x No. of atoms of octahedral voids. N.B. All noble gases have ccp arrangement but He(helium) has hcp arrangement ita Formore details, For more details,| Radius Ratio: scan the code scan the code Radius of cation sh Radius ratio =- Radius of anion ak -R am ideal =ideal