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Solid state structurehttp://web.chemistry.gatech.edu/~barefield/1311/handouts.html
click on Wilkinson’s Class for the version used in classclick on handout #5 for an alternative view of material
The URL for the webpage on unit cells ishttp://www.cwru.edu/artsci/chem/chime/solids.html
The structure of metalsThe structure of most metals can be described in terms of packing hard spheres (representing atoms) in a regular array– this type of description is also used for ionic solids– these metals are crystalline
Several different simple packing arrangements are found in elemental metals– Packing arrangements of atoms in metals play an important
role in determining their mechanical properties> Ductility of copper is directly related to its packing
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The unit cell
• The atoms in a crystal are in a regular repeating pattern called the crystalline lattice.
• The crystalline lattice can be reproduced by translation of the unit cell in three dimensions. The unit cell is that unique part of the crystal structure such that when translated along parallel lines, generates the entire crystal structure.
• For a substance containing more than one kind of atom, the ratio of atoms in the unit cell must be exactly the same as in the entire crystal.
Simple cubic
body-centered cubic
face-centered cubic
Contribution of atoms to unit cell
Cubic
Body centered cubic
bcc
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Close packing
Close packed structures are built up from hexagonal arrays of atomsClose packing is the most efficient way of filling space
HCP and CCP (or FCC)Hexagonal and cubic close packing are very common. – Face Centered Cubic packing is the same as cubic close packing
FCC unit cell has four(whole) atoms in it
HCP hasABAB.. repeat
FCC hasABCABC.. repeat
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Other views of HCP and FCC
ccp hcp
Note that face centered (FCC) cubic packing and cubic close packing (CCP) are the same thing!
Not all unit cells are cubic!
There are seven unique crystal systems
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Packing efficiency
Determination of density from structural data
Aluminum has the face-centered cubic structure (to right) with a unit cell dimension of 4.041 D.
volume of unit cell = (4.041 x 10-8 cm)3 = 6.599 x 10-23 cm3
mass of atoms in the cell = 4 atoms x 1 mol/6.022 x 1023 atoms x 26.98 g mol-1= 17.922 x 10-23 g
d = mass/volume = 17.922 x 10-23 g/6.599 x 10-23 cm3 = 2.715 g cm-3
d = mass of contents of cell/volume of cell
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Ionic bonding
Many compounds can be thought of as a collection of ions (Mn+, Xn-) held together electrostaticallyThis idea arose out of experiments by Arrhenius looking at the conductivity of solutions prepared by dissolving “ionic compounds” in water– Not believed at first, but got the 1903 Nobel
prize. http://www.nobel.se/chemistry/laureates/1903/
Evidence for presence of ions in solids
•Formed from elements with )O>2
•Exist as nonvolatile solid with poor conductance at RT
•Good conductance when molten
•Process a 3-dimensional lattice with regular array of cationsand anions where nearest neighbors are of opposite charge
Electron density map of a portion of the face of NaCl unit cell
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Metals and ionic compounds: structure, bonding and energetics
• Metals adopt three basic structures; cubic closest packed (ccp), hexagonal closest packed (hcp) or body centered cubic (bcc).
• Many simple salts can be viewed as having a structure in which one ion forms a closest packed array with the oppositely charged ion occupying voids (holes) in the array.
• Properties of metals, salts and non-metallic elements/molecular compounds differ greatly.
ccp hcp
bcc NaCl
ZnS
Comparison of properties of metals, simple salts and non-metallic elements
Non-metallic elementsSaltsMetalsStructures
Loose packed, low connectivityMolecular, chain, layer or infinite
structures
Close packed, C.N. = 4-8Infinite structures
Close packed, C.N. = 8-12Infinite structures
PropertiesPoor conductorsBrittle (can be hard)Non-reflective, low tensile
strengthLarge range of densities and
melting points
Insulators as solids, good conductors molten
BrittleNon-reflective, low tensile
strengthLarge range of densities; high
melting points
Good conductorsMalleable, ductile, elasticLustrous, hard, high tensile
strengthLarge range of densities and
melting points
Chemical PropertiesTend to form anionsOxidizing agentsNever liberate H2 from waterForm salts with metalsReact with O2 to form covalent
(mostly acidic) oxides
Combination of ionsSimple salts are neither
oxidizing or reducingNever liberate H2 from waterDo not react with metalsDo not react with oxygen
Tend to form cationsReducing agentsMore electropositive liberate H2
from waterForm alloys with other metalsElectropositive react with O2 to
form (mostly ionic, basic) oxides
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Structures of ionic compoundsIt is often convenient to think about the cationslying in holes (interstices) between arrays of anionsTypically, assume ions are hard spheresUsually, a compound will adopt a structure that maximizes the number of anions around each cation without causing the anions to touch
Salts based on simple cubic packingA simple cubic array of ions contains holes that are eight coordinate– These holes can be filled by ions of opposite charge to make
salts» structures include CsCl and CaF2
Note this is not BCC packing
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More unit cells
NaCl CsCl
ZnS Li2Se
Salts based on octahedral cationcoordination
Close packed arrays of anions have both octahedral and tetrahedral interstices– filling octahedral holes in a cubic close packed
array gives the NaCl structure– filling octahedral holes in a hexagonal close
packed array gives the NiAs structure
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Holes in close packed arrays
There are one octahedral and two tetrahedral holes for every atom in a close packed array
x Marks octahedral holes x Marks tetrahedral holes
The NaCl structure
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Tetrahedral coordination
Structures based on filling tetrahedral holes in close packed anion arrays are commonly found– fill all tetrahedral sites in cubic close packed array -
ZnS zinc blende– fill all tetrahedral sites in a hexagonal close packed
array - ZnS Wurtzite
ZnS structures
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More unit cells
NaCl CsCl
ZnS Li2Se
Structure prediction from ion radius ratios
The maximum electrostatic interaction between ions occurs when they are surrounded by the maximum number of ions of opposite charge separated by the shortest distance.
Assuming a model in which ions are considered as hard spheres with the smaller ion occupying holes in an array of larger ions allows calculation of the ideal size for a sphere in each type of hole.
Cubic hole
r+/r- = 0.15 r+/r- = 0.41
r+/r- = 0.73
r+/r- = 0.22
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Radius ratio rules
It is possible to predict the type of ion coordination that you will get if you know the ratio of the cation to anion size
r+/r- values Preferred coordination number
> 0.732 8 – cubic coordination
0.414 – 0.732 6 – octahedral coordination
0.225 – 0.414 4 – tetrahedral coordination
How the limiting values were calculated
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Violations of the radius ratio rulesRadius ratio rules only work for ~2/3 known compounds– ions are not really hard spheres– covalent contribution to bonding can mess things up– ionic radius varies with coordination number
There are empirical methods that can be used to reliably predict structure– structure maps
What do the following have in common?● Push-button igniters (BBQ grills, cigarette lighters) ● Electronic beepers ● Tweeters in stereo speakers ● Sound-generating arrays for sonar, fish finders, etc. ● Crystal microphones● Nanoscale positioners (Å precision)● Functional element in time keepers (clocks, watches,
etc.)
Crystals that are piezoelectric● Piezo (Greek) means pressure; such crystals are pressure
sensitive● Piezoelectric crystals generate current when deformed
and deform when a potential is applied● Only materials whose crystal structures lack a center of
symmetry can exhibit piezoelectric properties
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Pb(Zr,Ti)O3 (PZT) phase diagram
Only structures without a center of symmetry show piezoelectric properties
0
100
200
300
400
500
0 20 40 60 80 100Percent Titanium
Tem
pera
ture
(ο C)
tetragonal
rhombohedral
cubic
The Piezoelectric Effect
Crystal
Current Meter= 0
+ - + - + -
+ - + - + -Charges canceleach other, sono current flows
Crystal material at rest: No forces applied, so net current flow is 0
Adapted from copyrighted ValpeyFisher Corp. materials
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The Piezoelectric Effect
Crystal
Current meter deflects
- - - - -
+ + + + +
Charges are net + on one end and net - on the opposite end: crystal gets thinner and longer; changing direction of applied force will shorten and fatten crystal and reverse the charges (and current).
Crystal material with forces applied in direction of arrows………..
Force
Adapted from copyrighted ValpeyFisher Corp. materials
The electromechanical effect
Crystal
…. the crystal should get longer and skinnier (shown) or shorter and fatter depending upon polarity.
Now, replace the current meter with a power source capableof supplying a current meter….
power source(battery)
- side
+ side
- - - - -
+ + + + +
Adapted from copyrighted ValpeyFisher Corp. materials
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The electromechanical effect
Crystal
With the switch open, the crystal material is now at rest again:the positive charges cancel the negative charges.
+ - + - + -
+ - + - + -
power source
switch
charges cancel
Adapted from copyrighted ValpeyFisher Corp. materials
Summary of the Piezoelectric & Electromechanical Effect
● A deformation of the crystal structure (eg: squeezing it) will result in an electrical current.
● Changing the direction of deformation (eg: pulling it) will reverse the direction of the current.
● If the crystal structure is placed into an electrical field, it will deform by an amount proportional to the strength of the field.
● If the same structure is placed into an electrical field with the direction of the field reversed, the deformation will be opposite.
Adapted from copyrighted ValpeyFisher Corp. materials
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Ionic sizeCations are always smaller than the parent atom and anions are always larger than their parent atoms– outermost electrons in a cations experience a higher effective
charge than the outer electron in the neutral atom would» Na 186 pm but Na+ 116 pm
– outermost electrons in a anions experience a lower effective charge than the outer electron in the neutral atom would
Determining ionic radiiMany different ways to do this. Each gives slightly different answers. Be consistent with the source of you data when doing calculations– A good way involves measuring electron density in
crystals. Minimum in density between ions is the boundary between ions
Electron density map for NaCl
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Effect of ion chargeIsoelectronic ions get smaller as the nuclear charge goes up
Ion Radius / pm
Νa+ 116
Mg2+ 86
Al3+ 68
Ion Radius / pm
Ν3- 132
O2- 124
F- 117
Periodic trends in size
Similar to those found for atomsIncrease down a group decrease across a period assuming the ion has the same charge
Ion Radius / pm
F- 117
Cl- 167
Br- 182
I- 206
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Trends in physical propertiesDecreasing ion size and increasing ion charge favor better binding of the solid (higher lattice energy)– this tends to give increased melting and boiling points
Compound Melting point / ºC
ΚF 857
KCl 772
KBr 735
KI 685
Compound Melting point / ºC
NaF 988
MgF2 1266
AlF3 1291 sublimes
The ionic to covalent continuumIn practice, no solid compound is fully ionicCompounds containing elements with very different electronegativities tend to be more ionic
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Polarization and covalency
“Ionic” compounds tend have a considerable covalent contribution to their bonding when they contain polarizing cations– polarizing cations are cations capable of distorting
the anion’s electron cloud towards the cation
Fajan’s rules
Fajan’s rules help us determine which species will be polarizing or polarizable– Small highly charged cations are more polarizing– Large highly charged anions are more polarizable– Polarization is favored for cations that do not have
a noble gas electron configuration» Ag+, Cu+, Zn2+, Cd2+, Hg2+, Tl+ etc.
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Charge density
The charge density of a cation is a good indication of its ability to polarize an anion– Charge density = (Charge on proton x valency)/volume
For Na+, ionic radius 1.16 Å– Charge density = (1 x 1.6 x 10-19 C)/((4/3) x π x (1.16 x 10-7mm)3) = 24
C.mm-3 (this is a low charge density)
High charge density ions form compounds displaying covalent bonding
Cation chargeHigh charge ions tend to be small. So high charge ions usually have high charge densities and form compounds with covalent bonding– +1 and +2 ions often form predominantly ionic
compounds– +3 ions more covalent except for compounds with
unpolarizable anions such as F-
– +4 charge and above, bonding is usually highly covalent
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Physical effect of covalency“Ionic” solids with a significant covalent contribution to bonding show “anomalous” physical properties– may not be water soluble AgCl, CuI etc.– AlF3 MP 1290 oC, AlI3 MP 190 oC– Often compounds with significant covalency in
their bonding have low melting points» As melting does not involved breaking the compound up
into a collection of mobile individual ions
Manganese oxides example
The effect of charge density/covalency can be illustrated by looking at manganese oxidesMnO – Mn2+, charge density 84 C/mm3
– Ionic, melting point 1785 º CMn2O7 – Mn7+, charge density 1240 C/mm3
– Covalent, liquid at room temperature
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Silver halides
Non-noble gas configuration of Ag+ makes the species polarizing and many of its compounds are at least partly covalent
AgF AgCl AgBr AgIMP/ºC 435 455 430 558
All lower melting than alkali halides due to covalent contribution to bondingAgCl, AgBr and AgI are insoluble in water. AgF dissolves in water. AgF has an hard to polarize anion so it is more ionic and hence more soluble
Structure maps
The structure of a compound can be predicted based on the difference in electronegativity between the elements and the average principle
quantum number of the valence orbitals
Structure mapfor AB compounds
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