PHYSICAL CHEMISTRY
XII (ALL)
SOLID
STATES
r A I " A S P E C I A L L Y D E S I G N E D K I T F O R L E A R N I N G " CONTENTST H E K E Y > Basic principles of subjects. An outline ofthe topics to be
discussed in class lectures.
T H E A T L A S > Basic layout of subject. Aroute map correlating different subtopics
in coherent manner
E X E R C I S E I
P R O F I C I E N C Y T E S T
>
>
Introductory problems to get first hand experience of problem solving.
To check you newly acquired concepts.
E X E R C I S E H > A collection of good problems.
E X E R C I S E ffl > Test your objective skill.
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:
Type of Solid Intermolecular forces Properties Examples Ionic Ion-Ion forces Brittle, hard high Melting NaCl, KC1, MgCl2
Molecular
Dispersion forces/Dipole-Dipole
/H-bond
Soft, low melting
non-conducting H20, Br2, C02, CH4 Covalent
network Covalent bonds Hard: High melting C-Diamond Si02 Metallic Metallic bonds Variable hardness and melting
point conducting Na, Zn, Cu, Fe
SftiiW-iXc^e 3 Cx
*z
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
turet ^ r r w e n si c^s- . 1. Unit Cell: (>\) lest *f <»
M
Zpace (a th'cc C'ptfecfm
pm SV&uri H. CxTSUf. . <ty (Jyjlt-f |V S t>.Crystal Systems Bravais Lattice Unit Cell Parameters Crystal Systems Bravais Lattice
Intercepts Crystal Angles 4 Cubic Primitive, Face Centered,
Body Centered a = b = c a = p = y = 90°
2 Orthorhombic Primitive, Face Centered,
Body Centered, End Centered a * b * c a = p = y = '90°
3 Rhombohedral Primitive a = b = c a = P = Y * 90°
4 Monoclinic Primitive, End Centered a ^ b a = Y = 90°, P * 90°
5 Triclinic Primitive a ^ b a * p * Y * 90°
6 Tetragonal Primitive, Body Centered a = b c a = p = Y = 90°
t Hexagonal Primitive a = b c a = P = 90°, Y = 120° Simple Cubic a = b = c a = p = y = 90° k _ Z F Tetragonal a = b * c a = p = y = 90° Orthorhombic a = p = y = 90° Monoclinic a * b * c a = y = 90°, P * 90° Triclinic a * b * c
KS
Hexagonal Primitive a = b * c a = p = 90°, y = 120°^Bansal Classes
Solid State
TKere a^ 4 c ^ c c w ^ / r* Iwit
cell-( U S t y l e T t e o d b * v s « * t a * ^ o j ft, c a f c * ~
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.
Example: Polonium crystallises in simple cubic arrangement.
Z = 1 ; C.N. = 6
P J / < ]A i c v n 5
Osxe o n l y
C c r a - n e ^ . Oj. f i ^ C e l A
-1.2 Body Centered cubic (BCC) unit cell: Spheres in one layer sit in the depression made by first layer 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-
-p % f e e ? ! 2 <3cc - B c c
\-ACP CC p f f C U a - S i 2.
1.3 Face centered cubic (FCC) unit cell: Examples: Al, Ni, Fe, Pd all solid noble gases etc.
Z = 2 ; C.N. = H c P e x p C t U t ( X v \ f ttP CvJo\'ccm. (3) a * , p l u 3 ^ e a c h ^ x - e . O f C x v W
ft)
2. Density of cubic crystals:
7 T P £ O F PACKING: Z = 4 ' C N =12 A t - A ADOP4 C o h e i r s , j ! °f 1 ' c W o o c - y v ' ^ b - o o o p p ^ C . C t k ? ^ TWIT y . fei p ^
3. 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.
(i) 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) of first layer.
(ii) 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 of first layer. irVgaox^s LcAft'Cg.
( ? ) P H d t a C c AVA'CVS C*) riJM-' . A I > CUoY-f) " V^fOk void a YCA cow (c) F C C ( o o o r ejjt'cXfncyl' t V- VJaCo^vvA Spwcc [OQ - [OO Pl~ - (OOfl-PF> v o i d 'b' «sL TOVSLV \M c t e x c s . 1 M p o s s i b l e -(uWc
^r'-.S* / ^ a/2 J l feBansal Classes C l ) E f j - H O . (Di a f e ^ (V j-. i J J , , , , A u / n / h c c i ^ -Exploded view Hexagonal close-packed
( a ) structure ( " & ) ^ y u ^ A e 1 ( d l l b > S * " e + 2 -- 2 . B C C (£ ? ^ t - 4 R - c , , T W iVf) M ^ ^ F ^ c t c f i o n 04 J Uil u v , < Cubic close-packed ' 0j C ^ t O v U ' . -s t r u c t u f e ^ Exploded view C C ) s A Solid State dQ ^ 3 ( a ) V i J l J ^ = o . I T 2 x V s _
[3]
16Hexagonal primitive unit cell
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N u m b e r o f t e t r a h e d r a l v o i d s p e r F C C u n i t c e l l 4.2 Octahedral void Tc p j o w s H ( C J t m u I a J i \ x h A s c w d *0oUs c x S ^ d 0 \ o " V \ a a v K ^ ' C a l U n e C - N O . g r C e + t - H ) j V. (J / < L1 - ^ - "1 ' V N.I Q _ A i l U o i d e \\Q <v\ TVs <!s I - r p C W - p r e S e ' w i r & f " Tfub/oxJ OA b o d w < f OC5t 5. Octahedral void m£Mi .... . ^ i i .yy'r-r Octahedral Wf void * f : J.... ;'.'.'. 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 i n a F C C u n i t c e l l . Radius ratio O c t a h e d r a l v o i d A n o c t a h e d r a l v o i d a t t h e b o d y c e n t e r e d p o s i t i o n i n F C C u n i t c e l l T-c-P, (a) (b)5.1 Radius ratio for co-ordination number 3
(TriangularArrangement): r+ + r = - J j r 2 - y 3
- ^ T - 0 . 1 5 5
5.2 Radius ratio for coordination number 4 (Tetrahedral arrangement): r+ + r
/
B . // :
\!
V
// \
H D i D i 4 V 2 V 3 - V 2 V 5 0.2255.3 Radius ratio for coordination number 6:
(Octahedral Arrangement) or
Radius ratio for coordination number 4 (Square plannar arrangement)
' 2'a
T o p v i e w o f o c t a h e d r a l a r r a n g e m e n t
5.4 Radius ratio for coordination number 8 : (Body centered cubic crystal)
r + + r = V 2 r
= V 2 - 1 = 0 . 4 1 4
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 atom filling all octahedral voids.
R o c k salt s t r u c t u r e
6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.
(I)
(a) (b) **
(II) * (a) (b) *Zinc blende (sphalerite) structurer(ZnS) Larger atom formic ccp arrangement and smaller atom filling half of alternate tetrahedral voids
Fluorite structure: (CaF,,) Ca2+ forming ccp arrangement and F~ filling all tetrahedral voids.
Antifluorite structure :(Li20) O2 ion forming ccp
and Li+ taking all tetrahedral voids.
Z i n c b l e n d e s t r u c t u r e o 0 ' «
»
P*
Fluorite structure A n t i f l u o r i t e s t r u c t u r eCesium halide structure: (CsCl) CI at the corners of cube and Cs+ in the center
C e s i u m c h l o r i d e s t r u c t u r e
Corundum Structure: (A1203) O2 forming hep andAl3+ filling 2/3 octahedral voids.
Rutile structure: (Ti02) O2 forming hep while Ti4+ ions occupy half of the octahedral voids.
Pervoskite structure: (CaTi03) Ca2+ in the corner of *
cube O2' at the face center and Ti4+ at the centre of cube.
P e r v o s k i t e s t r u c t u r e
Spinel and inverse spinel structure: (MgAl204)02~ forming fee, Mg2+ filling 1/8 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.
THE ATLAS
