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Unit Cell of Crystal Structure # Definition of “Unit Cell”: AL Chemistry p. 1 A unit cell is the smallest basic portion of the crystal lattice that, repeatedly.

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Presentation on theme: "Unit Cell of Crystal Structure # Definition of “Unit Cell”: AL Chemistry p. 1 A unit cell is the smallest basic portion of the crystal lattice that, repeatedly."— Presentation transcript:

1 Unit Cell of Crystal Structure # Definition of “Unit Cell”: AL Chemistry p. 1 A unit cell is the smallest basic portion of the crystal lattice that, repeatedly stacked together in three dimensions, can generate the entire crystal structure. [2003 Paper I, Q.4(b)]

2 Common Types of Unit Cell # 2 common types for Ionic Crystals … AL Chemistry p. 2 Face-centered Cubic closed packed (fcc) Simple Cubic closed packed (sc)

3 Counting Ions in a Unit Cell p. 3 general principle: at corners = 1/8 along edges = 1/4 in faces = 1/2 at cubic centre = 1 at corners = 8(1/8) = 1 along edges = 0 in faces = 6(1/2) = 3 at cubic centre = 0 total no. = 4 AL Chemistry at corners = 8(1/8) = 1 along edges = 0 in faces = 0 at cubic centre = 0 total no. = 1 SC FCC

4 Generating of entire Lattice p. 4 AL Chemistry

5 Ionic Crystals  the 3-dimensional arrangement of ions. ** General Bonding considerations The bonding forces should be maximized by packing as many cations around each anion, and as many cations around each anion as is possible. but it depends on the relative size of cation and anion. AL Chemistry p. 5

6 To visualize the structures in terms of a closed packed arrangement of the larger anions (FCC or SC), AL Chemistry p. 6 How do the anion and cation pack together? with the cations occupying the vacant sites between the close packed layers. The number of nearest neighbor ions of opposite charge is called the coordination number.

7 anions are packed in form of “FCC” AL Chemistry p. 7 Closed packed of Anions & Cation: if the cation is smallif the cation is not small anions are packed in form of “SC” cations fill into “octahedral holes” cations fill into “tetrahedral holes” cations fill into the “cubic centre site” governed by the “radius ratio” of cation and anion !

8 Stacking of two closed packed anion layers produces 2 types of “holes”. p. 8 Types of “cation site” (holes) available in closed packed anions arrays: AL Chemistry (a)octahedral hole ---- coordinated by 6 anions (b)tetrahedral hole ---- coordinated by 4 anions

9 p. 9 “Stuffing” the holes by Cations: AL Chemistry Octahedral or Tetrahedral hole? ► determined by the radius ratio (= r cation / r anion ) [radius ratio rule] FCC (for small cations) SC

10 p. 10 Stable Bonding Configuration : AL Chemistry For a stable coordination, the bonded cation and anion must be in contact with each other. #If the cation is larger than the ideal radius ratio … ► the cation and anion remain in contact, but the cation forces the anion apart.  STABLE!

11 p. 11 AL Chemistry #If the cation is too small … ► cation would not be in contact with the surrounding anion.  repulsion between anions  UNSTABLE!

12 p. 12 Holes available in “FCC” unit cell closed packed of anions: #“O” – octahedral hole : The unit cell has 4 octahedral sites. AL Chemistry #“T” – tetrahedral hole : The unit cell has 8 tetrahedral sites.

13 p. 13 Example 1: Sodium Chloride (NaCl) radius: Na + = 1.02nm, Cl - = 1.81nm AL Chemistry radius ratio =  FCC 4 Cl - packed in FCC, Na + will fit into the octahedral hole of the anion arrays. Cl - Na + Cl - Na + Since stiochiometry of cation and anion = 1:1, 4 Na + ions fit into the cell. i.e. all the octahedral sites are occupied! 6:6 coordination !

14 p. 14 Example 2: Zinc Blende (ZnS) radius: Zn 2+ = 0.60nm, S 2- = 1.84nm AL Chemistry radius ratio =  FCC 4 S 2- packed in FCC, Zn 2+ will fit into the tetrahedral hole of the anion arrays. Since stiochiometry of cation and anion = 1:1, 4 Zn 2+ ions fit into the cell. i.e. half the tetrahedral sites are occupied! S 2- Zn 2+ 4:4 coordination ! #(Cations fills in the diagonally opposite sites to minimize repulsion.)

15 p. 15 Example 3: Cesium Chloride (CsCl) radius: Cs + = 1.74nm, Cl - = 1.81nm AL Chemistry radius ratio =  SC ► Anions occupy the corners of a unit cell, the centre of the cube is larger than the tetrahedral and octahedral sites, therefore the large Cs + ion can fit in.

16 p. 16 AL Chemistry 8:8 coordination ! Simple Cubic closed packed (SC) Cl - Cs + Since stiochiometry of cation and anion = 1:1, 8 Cs + ions will fit into the cell. i.e. all the cubic center sites are occupied! Each unit cell has 8 anions and 8 cubic centre sites.

17 p. 17 AL Chemistry Cl - Cs + Two Inter-penetrating Lattices in CsCl: unit cell of CsCl

18 p. 18 Practice: Calcium Fluoride (CaF 2 ) radius: Ca 2+ = 1.12nm, F - = 1.31nm AL Chemistry radius ratio = Simple Cubic (SC) closed packed Since stiochiometry of cation and anion = 1:2, only 4 Ca 2+ ions will fit into the cell. i.e. half the cubic center sites are occupied! Each unit cell has 8 anions and 8 cubic centre sites.

19 p. 19 (CaF 2 ) AL Chemistry Coordination no.: each Ca 2+ surrounded by 8 F -, each F - surrounded by 4 Ca 2+.

20 AL Chemistry p. 20 anions are packed in form of “FCC” Closed packed of Anions & Cation: if the cation is smallif the cation is not small anions are packed in form of “SC” cations fill into “octahedral holes” cations fill into “tetrahedral holes” cations fill into the “cubic centre site” Conclusion ….. e.g. NaCl e.g. ZnS e.g. CsCl, CaF 2


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