Solid state 12
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1) The document discusses different types of unit cell structures in crystalline solids, including simple cubic, body centered cubic, and face centered cubic unit cells. 2) It also describes the packing efficiency of each unit cell structure, with face centered cubic being the most efficient with 74% of space occupied by particles. 3) The document outlines the three stages of packing - linear packing in one dimension, planar packing arrangements, and three-dimensional packing. It provides examples of AAAA and ABAB planar arrangements and how they correspond to simple cubic and hexagonal close packed 3D structures.
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Solid state 12
- 1. Nutan junior college,wavi Tal – sinner Prof :- Mrs. VIDHATE G.B.
- 2. Simple cubic unit cell
- 4. BODY CENTRED CUBIC UNIT CELL •Body centred cubic unit cell is a modification of simple cubic unit cell.( bcc •in which one particle is at the center of the unit cell & 8 particles at the corner , each corner attached particle size is 1/8 of the particle. •Total number of sphere = no.of unit cell at the corner x size of unit cell + 1 •Total number of unit cell = = 8 x 1/8 +1 •= 1 + 1 •= 2
- 5. •face centred cubic unit cell is a modification of simple cubic unit cell.( fcc) •in which four particle is at the center of the unit cell & 8 particles at the corner , each corner attached particle size is 1/8 of the particle. •Total number of sphere = no.of unit cell at the corner x size of unit cell + Total no.of half sphere x size of half sphere •Total number of unit cell/sphere = 8 x 1/8 +6 x ½ •=1+3 •= 4 Face centered cubic unit cell
- 6. REPRESENTATION OF CRYSTAL LATTICE •The participating particles atoms,ions or molecules touche each other and form three diamentional network . •This three diamentional structure can draw with help of small circles are participating particles & connecting neighbouring particles with the help of straight line.
- 7. PACKING IN SOLIDS ï‚— In case of a crystal lattice formed by simple cubic unit cell the occupied space by constituents particles is to the extent of 52.4 % and 47.6 % space is unoccupied empty space is called void. ï‚— In case of body centered cubic str. the space occupied is 68 % and void is 32 %. ï‚— In face centered cubic str. The space occupied is 74 % & void is 26 %. ï‚— Closest packing is most efficient arrangement because most space occupied by particles & minimum space remains for void space. ï‚— There are three types of arrangement for unit cell. ï‚— 1) linear packing in one direction ï‚— 2) planar packing arrangement of sphere ï‚— 3) three dimensional packing
- 8. 1) Stage I-linear packing in one direction • The constituent particles of the crystalline solids are represented by Sphere of equal size. • The linear arrangement of sphere in one dimension can be made by arranging the sphere in one row in which each sphere is attached to two neighboring sphere ,except two ends sphere. • The co-ordination number of the particles in one dimension is two.
- 9. Stage II-planar packing arrangement of spheres AAAA TYPE ARRANGEMENT
- 10. ABAB -TYPE PACKING ARRANGEMENT ITS CLOSEST PACKING ARRANGEMENT
- 11. Three dimensional packing Three dimensional str. are made by /with the help of two dimensional AAAA/ABAB Type of crystal str. Three dimensional crystalline str. Are prepared by placing two dimensinal crystal str. One over another. There are also two types 1) AAAA type simple cubic str. 2) ABAB type Hexagonal closed packed str.
- 12. AAAA Type simple cubic str. AAAA Type of two dimensional crystal layers are placed over one another in suc A way that all the sphere of each layer are exactly above the sphere of lower lay All the sphere of different layers are aligned horizontally & also vertically. It is evident from fig. each sphere are surrounded by six sphere out of which 4 a Onded to sphere & one are above & one are below. Co-ordination is six. there are more empty space in the simple cubic str.
- 13. ABAB type Hexagonal closed packed str. ABAB Type of two dimensional crystal layers are placed over one another by A way that empty space Is reduced & packing is made most efficient. In both the str. The central sphere are surrouded by six sphere in each layer. sphere of second layer are packed into depressions between the sphere of Layer due to this packing is made most efficient & reduce empty space.
- 14. • Evidence from fig. • Only half the no. of triangular open spaces of lower layer A are completely covered • By sphere of upper layer B .this consists a tetrahedral hole in the lower layer A • Formed four sphere, three in the lower layer A & one sphere in the upper layer B. • Simultaneously new tetrahedral holes are also created by three neighboring sphere • Of the top layer & one sphere of the lower layer. • The remaining half of triangular open spaces of the lower layer are partially covered by three neighboring spheres of upper layer & a new type of open space • Is formed by total six sphere open space known as octahedral void.
- 15. Tetrahedral void
- 16. Octahedral void If the no. Of closed packed sphere are N , the no. of octahedral void are N & the no. of tetrahedral void are 2N
- 17. 1) Placing the spheres of the third layer into the tetrahedral voids