PHYSICAL CHEMISTRY XII (ALL)
SOLID r
STATES
" A SPECIALLY DESIGNED KIT FOR L E A R N I N G "
I
CONTENTS THE KEY
Basic principles of subjects. An outline ofthe topics to be discussed in class lectures.
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THEATLAS
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Basic layout of subject. Aroute map correlating different subtopics in coherent manner
EXERCISE I
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PROFICIENCY TEST
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Introductory problems to getfirsthand experience of problem solving. To check you newly acquired concepts.
EXERCISE H
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A collection of good problems.
E X E R C I S E ffl
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Test your objective skill.
^ E X E R C I S E IV
> A collection of previous ten years JEE problems.
A
THE KEY Crystalline solids: Crystalline solids are those whose atom, molecules or ions have an ordered arrangement extending over a Long Range. example-(Rock salt, NaCl). Amorphous solids: Amorphous solids are those whose constituted particles are randomly arrange and have no ordered long range structure, example: Rubber, Glass ect. TYPES OF CRYSTALLINE
SOLIDS: Properties
Examples
Ion-Ion forces Dispersion forces/Dipole-Dipole /H-bond
Brittle, hard high Melting
NaCl, KC1, MgCl2
Soft, low melting nonconducting
H 2 0, Br2, C0 2 , CH4
Covalent network
Covalent bonds
Hard: High melting
C-Diamond Si0 2
Metallic
Metallic bonds
Variable hardness and melting point conducting
Na, Zn, Cu, Fe
Type of Solid Intermolecular forces Ionic Molecular
TYPES OF UNIT CELL: Collection of lattice points, whose repetition produce whole lattice is called a unit cell. The whole lattice can be considered to be made by repetion of unit cell. i) C^j-odL is famed . W>teOKce *z turet
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1. (>\)
lest
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si c^s- .
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Cx
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Unit Cell: *f <»
Crystal Systems
C'ptfecfm4
Cubic
pm SV&uriH. 2
Orthorhombic
3 CxTSUf. . 4 . 6 t
Rhombohedral Monoclinic Triclinic Tetragonal Hexagonal
Unit Cell Parameters Intercepts Crystal Angles
Bravais Lattice Primitive, Face Centered, Body Centered Primitive, Face Centered, Body Centered, End Centered Primitive Primitive, End Centered Primitive Primitive, Body Centered Primitive
a=b=c
a = p = y = 90°
a*b *c
a = p = y = '90°
a=b=c a^b a^b a=b c a=b c
a = P = Y * 90° a = Y = 90°, P * 90° a * p * Y * 90° a = p = Y = 90° a = P = 90°, Y = 120°
KS k _ Z F Tetragonal a= b* c a = p = y = 90°
Simple Cubic a=b=c a = p = y = 90°
Orthorhombic a = p = y = 90°
^Bansal Classes TKere a^
4
Triclinic a* b * c
Monoclinic a* b* c a = y = 90°, P * 90°
Hexagonal Primitive a= b* c a = p = 90°, y = 120°
Solid State c
( U S t y l e T t e o d b * v s « * t
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1.1
Primitive or simple cubic (PS/SC) unit cell: Spheres in one layer sitting directly on top of those in previous layer, so that all layers are identical. Each sphere is touched by six other, hence coordination number is 6. 52% of available space occupied by spheres. P J / < ]Aicvn5 Example: Polonium crystallises in simple cubic arrangement. Osxe
only
Ccra-ne^. Oj. f i ^ C e l A - -
Z = 1 ; C.N. = 6 1.2
Body Centered cubic (BCC) unit cell: Spheres in one layer sit in the depression made byfirstlayer in a-b-a-b manner. Coordination number is 8, and 68% of available space is occupied by atoms. Example: Iron, sodium and 14 other metal crystallises in this manner. C o ^ V w ^ t o A T\0. \ fA0. Of nearest Y\e j^bours > j f c f r cm cdcm KctS dn a u^- ceM- <3cc - B c c -p % f e e ? ! 2 t U t ( X v \ f ttP Z = 2 ; C.N. = CvJo\'ccm. \-ACP CC p f f C Ua-S i 2. HcP
exp
1.3 Face centered cubic (FCC) unit cell: Examples: Al, Ni, Fe, Pd all solid noble gases etc. (3)
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Density of cubic crystals:
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PACKING:
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ADOP4
Coheirs,
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Closest packing of atoms: This is the most efficient way of packing 74% of available space is occupied by spheres and coordination number is 12. Hexagonal close pack (A-B-A-B) type packing: Each layer has hexagonal arrangement of touching sphere and 3rd layer is similar (exactly on top) offirstlayer. Cubic close pack (A-B-C-A-B-C): AB layers are similar to HCP arrangement but third layer is offset from both A and B layers. The fourth layer is exactly on top offirstlayer. irVgaox^s LcAft'Cg.
P H d t a C c AVA'CVS
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structure
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Solid State
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Cubic close-packed structufe
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c t p q c \ A \ Hexagonal primitive unit cell
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layer A
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Types of voi ds
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Tetrahedral void
i
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Tetrahedral^
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void
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Octahedral void v K ^ ' C a l
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N u m b e r o f tetrahedral voids p e r F C C unit cell
j o w s H(CJtmuIaJi \ x h A s
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Octahedral void
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Octahedral void
Octahedral void
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;'.'.'. A n o c t a h e d r a l v o i d at t h e c e n t r e o f a n e d g e in a F C C u n i t c e l l . A n o c t a h e d r a l void at the b o d y c e n t e r e d p o s i t i o n in F C C u n i t c e l l
5.
Radius ratio
(a) 5.1
T-c-P,
(b)
Radius ratio for co-ordination number 3 (TriangularArrangement):
r+ + r = - J j r
Solid State
2 - y 3 - ^ T
-0.155
[41
5.2
Radius ratio for coordination number 4 (Tetrahedral arrangement): r+ + r 4
/
V2
/:
B./
!
\
// \
V
H D i
V3-V2
0.225
V5
5.3
Radius ratio for coordination number 6: (Octahedral Arrangement) or
r+ +
r
= V2
= V2-1
r
=0.414
Radius ratio for coordination number 4 (Square plannar arrangement)
'
2'a
Top v i e w of octahedral arrangement
5.4
Radius ratio for coordination number 8 : (Body centered cubic crystal)
r+ + r = + r = V3 r
a/3-1 = 0.732
6.
Types of ionic structures
6.1
Rock salt structure: (NaCl) Larger atom formic ccp arrangement and smaller atomfillingall octahedral voids. R o c k salt s t r u c t u r e
Solid State
[5]
6.2
Zinc blende (sphalerite) structurer(ZnS) Larger atom formic ccp arrangement and smaller atom filling half of alternate tetrahedral voids Zinc blende structure
6.3
Fluorite structure: (CaF,,) Ca2+ forming ccp arrangement and F~fillingall tetrahedral voids.
0« '
o
» P*
Fluorite structure
6.4
Antifluorite structure :(Li20) O2 ion forming ccp and Li+ taking all tetrahedral voids. Antifluorite structure
6.5
Cesium halide structure: (CsCl) CI at the corners of cube and Cs+ in the center Cesium chloride structure
6.6
Corundum Structure: (A1203) O2 forming hep andAl3+ filling 2/3 octahedral voids.
6.7
Rutile structure: (Ti02) O2 forming hep while Ti4+ ions occupy half of the octahedral voids.
6.8
Pervoskite structure: (CaTi03) Ca2+ in the corner of cube O 2 ' at the face center and Ti4+ at the centre of cube.
*
Pervoskite structure
2
6.9
7.
(I) (a) (b) *
* (II) * (a) (b) *
2+
Spinel and inverse spinel structure: (MgAl204)0 ~ forming fee, Mg filling1/8 of tetrahedral voids and Al3+ taking half of octahedral voids. In an inverse spinel structure, O2" ion form FCC lattice, A2+ ions occupy 1/8 of the tetrahedral voids and trivalent cation occupies 1/8 of the tetrahedral voids and 1/4 of the octahedral voids. Crystal defects: Point defects: When ions or atoms do not hold the theoretical position, this is called point defect. Point defects are of two types: Stoichiometric defects. Schottky defect: Due to missing of ions from lattice point in pairs. Frenkel defect: It is caused due to the creation of lattice vacancy as a result of misplaced ion in interstitial site. Schottky defect common in ionic solid with high coordination number. NaCl, KC1, KBr Frenkel defect:- Solid with low coordination number ZnS, AgBr. Non-Stoichiometric defects: Ratio of positive and negative ion differ from that indicated by chemical formula. Metal-excess defect : A negative ion replaced by electron. (F-centre) Extra metal ion present in lattice and electron also present in interstitial site. Metal-deficiency defect caused by: Cation missing from lattice point, electroneutrality maintained by metal ions with higher oxidation state as Fe0 94°0.
^Bansal
Classes
Solid State
[6]
THE
fe Bansal Classes
ATLAS
Solid State
m
