LECTURE -3 SOLID STATE PHYSICS DATE: 07-12-2021 TIME: 04:00 PM-06:00 PM 07 2 2021 THREE DIMENSIONAL BRAVAIS LATTICES: 7Crutal kysung fr 3D, twe ha 14 Bruni Lottieg 6utice Consaaa distantes LCubic Edges and angles 3 Orthorhombic 2Tetragonal abzC bC a anglaket6lc B y = 90 a=B-y=90* aghbt"cla Titnad 6. Monoclinic 07 b= aB=yz90" a=bzc azb*c ay90:B 4 Rhortbohedral 2, Hexagonal a =B= 90,y= 120 a ßy-90 -2021 Sr. Name of the Crystal Bravais Lattices symbol length and interaxial angles No. System 1. Cubic Lattice Nature of unit cell [Axial Examples idie 2 . Tetragonal 1. Simple cubic Cu, NaCl, Ag. latic a=ß=y = 90° 2. Body-centered Ltice 3. Face-centered Lattice F 1. Simple tetragonal Lalice P 3 . Orthorhombic SnO2, NiSO4 a 2. Body-centered Lattioe = B =y =90° KNOg, Ba50 1. Simple orthorhombicldsc P 2.Body-centered oe. LatiaI 3. Face-centered ordbo,latiot 4 . Basc-centered arte.Latitt a=ß=y =90° F c or Ed-eslood ortho.ldiido 4 . Rhombohedral (Trigonal) 07 12 202 1. Simple rhombohedral (Trigonal) Latice AL lal=6l=lEl a =ß=y 90° As, Sb, Bi, Calcite, Quartz Sr.Name No. theBravais Lattices o Crystal System 1. Simple hexagonal lattica Hexagonal Nature of unit cell [Axial symbol length and interaxial angles| Zn, Cd, Mg, Sio2 P a 6. 1. Simple monoclinic Liica Monoclinic 2. Base-centered Mooclinic Examples Lattice = B 90°.y = 120° CaSo, Borax, P C a =Y= 90° * B FeSO4 al=6lte Cuso, K,Cra0 or Erd- Cartbed Morcdiie 7. 1. Simple triclinie Triclinic Litice P aBy* 90° 07 12 202 Cubic Crual Sytimk (4), Smph daic Lalioe(P)= Jattice (). otitin pous an In Latia ot arailabe at Comta Se latice, othe Cukic Jauwik coll a=b C (2). hartut distacs de dan Lattoe ois 12 Shnzdhat digbict t* Jtios padnt 2021 ( Ne =a ltika pabt1 (okd) pu 2aik cell heft= ho o 6 Cmdx ndikekin. Unik cell \foot ur corm Lattice Kimcbive ut call (b) For the simple cubic erystal structure. (a) a hard-sphere unit ell. and (h) a reduced-sphere unit cell. Monoaimic batis) Efp Nodan (tenoatwie saui) pur unt celt 814 =1 atn r uik cal (4R bet r and a a= 2r (5) No. 4 Nanust nuighboos CCordlnatim. huarbth) G hanest úghbe at distanee a 6.N2 hial 12 Jund naighenau at distna-2a fem 07-12 2021 Neaust Aobnns »0 Becd naizdbomas 07-12202 ).No.3 nuigkas 07 12 207 8 thbd naisksewo at distbau a pon 8) Btmic Packing fractim (fr Movodtbmic. kanis)> Atbnic Packing tracton (APF) = Auit cel - VeluatVoluns 6Aauik coll a Aphor, elp= ho. ams pr i k cell 1x 202 APF o. Exanpk > ly or o52 a 52 Pooniun ekibik Se fr Catl icir, se ShuctoneSc Mtice a nenom hae Se Lttaeáth disbmie hasi. 07 12 202 I. &dycoxtöal aubie Lalic (I) > = hckon Lattio painti ot oin ane ljng Comd call. Cntb &oie uik The ot Jkirtkdian 4o-diagenala dodyecenlbv aiaurunit tell 07 12 2021 1 4 Body-centered +l= 2 cubic (bcc) (3) shatut distauca Or hactust tabea tao Jtice sata= a atms Con Kolatin iloen rand a > 2r= 2 4r=3a (5). Noeadust naiboos orCN Namt CNo 12 2d huigkos 2021 naighbaod at di|zha 12a ton kpea alom eUnd nighteos at diutace t a an eloece an (F). No.3d uighbeuss 12 thtrd nugnboud at 34 2a atm APf 4xar 2 T 7 0722 2021 BTr68 L0oRe-acked 9.Ta Packing 11o Ex Na, K, Chromiun, Fe 07 12 2021 exhi bit ,-. BccAtructisa- 3. Face-Centered Cubic (FCC) Structure: (F) o . uitin 4 Latia jo basid) aloma (fr monoalamic In tia tee or slrucin, d ane availabe at &Cmeu& atint or tice ja- canlos Cubie Aik cell. (2) M. atans or latieefoitl fur uanik elln= ix+ cx! 07 122 (3 Rlutin ket r and a 2a distaree hatrtn atns shashst (4 (51. No.umet noughaoid8 = a2 =4r = a 12 tust uighkoau at distaa amkoce atim. (GNo. o2hd Nighbhuhd G econd a pon a ntighbtu u c e don.12 07 12 2021 2 Nemet naughbeut! 07-1-20 adt diuarce (. N. 3" noighbess Home hloe. Atomie Packina fracton APF= Xnr a3 4x 07 12 2021 (9 Tye o, Sx. 3 4ln)_ 2 = o.74 | RPF % =74% Clae-Packad Structina acking 1, Ni, A, z, P, Ncl. Fcc sruchort is alto called as Paskud). ccP structs ( Cukic-clote 07-12-2021 sOLID STATE PHYSICS Assignment-1 1 The packing fraction ofasimplecubiclattice is approximately (a) 0.74 2. b)0.68 34 Given that ris the mdius of the atoms and a is the lattice constant ofa solid having a cubic structure, which one of the following relations is true for (a)a-2r 3. O.52 abodycentredcubic structure? (b) a = 2 r 2 (c) a = 2r a-4r5 What is the second nearest-neighbour distance in a face centred cubic lattice whose conventional unit cell parameter iIs a? (a) a/ V 1. (d) /a (b) a2 For a closed packed BCCstructure of hard spheres, the lattice constant a is related to the sphere rndius R as a=4R/V 07 12 2021 (b) a = 4R3 (c) a = 4R/2 (d) a = 2R2 sOLID STATE PHYSIcs Assignment-1 68. The third-nearest neighbour distance in aBCC (Body Centered Cubic) crystal with kattice constanta, is b) 3a 2 (a) a Third-naahtst 3a, NET June 2019 heigkea. distak h a BCe cratal =2a, 07 12 2021 sOLID STATE PHYSICs Assignment-1 69. Sodum (Na) exhibits body-centered-cubic (BCC) crystal structure with atomic radius 0.186 nm. The lattice nm. (Round off to 2 decimalplaces) parameter ofNa unit cel is r 14. o-186 nn, a = ¢ = 4X0-18% nm = 0-43 hm Which is loosepackedstructure? Body centred cubic structure b) Hexagonal close-packed structure (c)Face-centred cubic structure (d) None ofthese 07 12-2021 sOLID STATE PHYSICS Assignment-2 Consider a regular arangement of identical spheres in aface-centred cubic(fcc)structure in whichthe centres of the respective spheres are located at each of the eight comers and the centres ofthe six surfaces of a unit cube. The fraction of each cubic unit cell occupied by the spheres in the ckose-pack configurationis (b)0.62 0.74 d)0.88 (a) 0.50 APF= 0-74 07 12 2021 sOLID STATE PHYSICS Assignment-2 . The ratio ofthe second-neighbour distance to the nearest-neighbour distance in an fcc lattice 1s (a) 22 b)2 Becnd nihbour ciutinca (c)3 n Fec a noanest 9. The fraction of volume unoccupied in the unit cell of the body centered cubic lattice is (d)32 BcC : o68 Occubed vekhant traclnu =13 = 1-d =8-BT =032 uOCCupied 8 = 5 07 12 2021 sOLID STATE PHYSICS Assignment-2 Atoms, which can be assumed to be hard spheres of radius R. are aranged in anfcc lattice with kattice constant a, such that each atom touches its nearest neighbours. Take the center of one of the atoms as the origin. Another atom of radius r (assumed to be hard sphere) is to be accommodated at a position (0. a / 2. 0) without distorting the lattice. The maximum value of r/ R is_ (Giveyour answer upto two IGATE 2016 decimalplaces). 07-12 2021 THANK YOU 07 12 2021
