types of primary chemical bonds
DESCRIPTION
+. -. +. -. +. -. +. -. +. +. +. +. e-. e-. +. +. +. e-. +. +. +. Types of Primary Chemical Bonds. Isotropic, filled outer shells. Metallic Electropositive: give up electrons Ionic Electronegative/Electropositive Colavent Electronegative: want electrons - PowerPoint PPT PresentationTRANSCRIPT
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• Metallic– Electropositive: give up electrons
• Ionic– Electronegative/Electropositive
• Colavent– Electronegative: want electrons
– Shared electrons along
bond direction
Types of Primary Chemical BondsIsotropic, filled outer shells
+ - +
- + -
+ - +
+ + +
+ + +
+ + +
e-
e-
e-
Close-packed structures
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Review: Common Metal Structureshcp ccp (fcc) bcc
ABABABABCABC not close-packed
Features• Filled outer shells spherical atom cores, isotropic bonding• Maximize number of bonds high coordination number• High density
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Metals• single element, fairly electropositive• elements similar in electronegativity
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cation
anion
Ionic Compounds• elements differing
in electronegativity
CERAMICS
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Ionic Bonding & Structures
• Isotropic bonding• Maximize packing density• Maximize # of bonds, subject to constraints
– Like atoms should not touch– Maintain stoichiometry– Alternate anions and cations
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Ionic Bonding & Structures
+ –
–
––
–
–
+ –
–
––
–
–
Isotropic bonding; alternate anions and cations
––
–
– –
–+
Just barely stable
Radius Ratio “Rules”
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Cubic Coordination: CN = 8
2RA
2(rc + RA)
2 AR a
3c A
A
r RR
3 1 0.732c
A
rR
a
2( ) 3A cR r a
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Cuboctahedral: CN = 12
rc + RA = 2RA
rc = RA rc/RA = 1
2RA
rc + RA
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Radius Ratio RulesCN (cation) Geometry min rc/RA
2 none(linear)
3 0.155(trigonal planar)
4 0.225(tetrahedral)
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CN Geometry min rc/RA
6 0.414(octahedral)
8 0.732(cubic)
12 1(cuboctahedral)
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Ionic Bonding & Structures• Isotropic bonding• Maximize # of bonds, subject to constraints
– Like atoms should not touch• ‘Radius Ratio Rules’ – rather, guidelines• Develop assuming rc < RA
• But inverse considerations also apply• n-fold coordinated atom must be at least some size
– Maintain stoichiometry• Simple AaBb compound: CN(A) = (b/a)*CN(B)
– Alternate anions and cations
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Radius Ratio Rules
CN (cation) Geometry min rc/RA (f)2 linear none
3 trigonal planar 0.155
4 tetrahedral 0.225
6 octahedral 0.414
8 cubic 0.732
12 cubo-octahedral 1
if rc is smaller than fRA, then the space is too big and the structure is unstable
common in ionic compounds
sites occur within close-packed arrays
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Local Coordination Structures• Build up ionic structures from close-
packed metallic structures• Given range of ionic radii: CN = 4, 6, 8
occur in close-packed structurestetrahedral
octahedral
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HCP: tetrahedral sites
4 sites/unit cell2 sites/close-packed atom
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HCP: octahedral sites
2 sites/unit cell1 site/close-packed atom
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Sites in cubic close-packed
8 tetrahedral sites/unit cell2 tetrahedral sites/close-packed atom
4 octahedral sites/unit cell1 octahedral site/close-packed atom
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Summary: Sites in HCP & CCP
2 tetrahedral sites / close-packed atom1 octahedral site / close-packed atom
sites are located between layers: number of sites/atom same for ABAB & ABCABC
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Common Ionic Structure Types• Rock salt (NaCl) sometimes also ‘Halite’
– Derive from cubic-close packed array of Cl-
• Zinc blende (ZnS)– Derive from cubic-close packed array of S=
• Fluorite (CaF2)– Derive from cubic-close packed array of Ca2+
• Cesium chloride (CsCl)– Not derived from a close-packed array
• Complex oxides– Multiple cations
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Example: NaCl (rock salt)
• Cl- ~ 1.81 Å; Na+ ~ 0.98 Å; rc/RA = 0.54
• Na+ is big enough for CN = 6– also big enough for CN = 4,
but adopts highest CN possible
• Cl- in cubic close-packed array
• Na+ in octahedral sites
• Na:Cl = 1:1 all sites filled
CN f
4 0.225
6 0.414
8 0.732
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Rock Salt Structure
Cl
Na
CN(Cl-) also = 6RA/rc > 1 Cl- certainly large enough for 6-fold coordination
ccp array with sites shown
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Lattice Constant Evaluationccp metal
4R = 2 a
a
R
a
R
a = 2(RA + rc) > ( 4/2)RA
rock salt
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Example: ZnS• S2- ~ 1.84 Å; Zn2+ ~ 0.60 – 0.57 Å;
– rc/RA = 0.326 – 0.408• Zn2+ is big enough for CN = 4 • S2- in close-packed array• Zn2+ in tetrahedral sites• Zn:S = 1:1 ½ tetrahedral sites filled• Which close-packed arrangement?
– Either! “Polytypism”– CCP: Zinc blende or Sphaelerite structure– HCP: Wurtzite structure
CN f
4 0.225
6 0.414
8 0.732
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ZnS: Zinc Blende
x
yz = 0 z = ½
x
yz = 1 z = ½
x
S2-
x
x
x
CCPanions as CP atomsfill 4/8 tetr sites
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ZnS: Zinc Blende
CN(S2-) also = 4RA/rc > 1 S2- certainly large enough for 4-fold coordination
S2-
Zn2+
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Example: CaF2 (Fluorite)• F- ~ 1.3 Å; Ca2+ ~ 1.0 Å;
– rc/RA = 0.77
• Ca2+ is big enough for CN = 8 – But there are no 8-fold sites in close-packed arrays
• Consider structure as CCP cations– F- in tetrahedral sites– RA / rc> 1 fluorine could have higher CN than 4
• Ca:F = 1:2 all tetrahedral sites filled• Places Ca2+ in site of CN = 8• Why CCP not HCP? - same reason as NaCl
CN f
4 0.225
6 0.414
8 0.732
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Fluorite
CN(F-) = 4CN(Ca2+) = 8 [target]
F-
Ca2+
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CsCl• Cl- ~ 1.8 Å; Cs+ ~ 1.7 Å;
– rc/RA = 0.94• Cs+ is big enough for CN = 8
– But there are no 8-fold sites in close-packed arrays• CsCl unrelated to close-packed structures
– Simple cubic array of anions– Cs+ in cuboctahedral sites– RA / rc> 1 chlorine ideally also has large CN
• Ca:Cl = 1:1 all sites filled
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Cesium Chloride
Cl-
Cs+1 Cs+/unit cell1 Cl-/unit cellCN(Cs) = 8
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Why do ionic solids stay bonded?2
1 2
4electrostaicpair
o
Z Z eEr
• Solid: repulsion between like charges• Net effect? Compute sum for overall all possible pairs
• Pair: attraction only
2
12 4
i jelectrostaticsolid cluster
i j o ij
Z Z eE
r
Sum over a cluster beyond which energy is unchanged
Madelung Energy
Can show 2
0( )
4electrostaticsolid
o
ZeE Nr
For simple structures Single rij
|Z1| = |Z2| = Madelung constant
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Structures of Complex Oxides
• Multiple cations– Perovskite
• Capacitors• Related to high Tc superconductors
– Spinel• Magnetic properties
• Covalency– Zinc blende
• Semiconductors– Diamond
• Semiconductors– Silicates
• Minerals
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Perovskite– Perovskite: ABO3 [B boron]
• A2+B4+O3 A3+B3+O3 A1+B5+O3
• CaTiO3 LaAlO3 KNbO3
• Occurs when RA ~ RO and RA > RB
• Coordination numbers– CN(B) = 6; CN(A) =– CN(O) = 2B + 4A
• CN’s make sense? e.g. SrTiO3
– RTi = 0.61 Å
– RSr = 1.44 Å
– RO = 1.36 Å http://abulafia.mt.ic.ac.uk/shannon/ptable.php
12
above/below
RTi/RO = 0.45
RSr/RO = 1.06
A
BO
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Tolerance factorclose-packed directions
A
B