+2 Chem- Solid State

8/2/2019 +2 Chem- Solid State

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Solid materials are formed from densely-packed atoms, with intense interaction forcesbetween them. These interactions are responsible for the mechanical (e.g. hardnessand elasticity), thermal, electrical, magnetic and optical properties of solids. Depending onthe material involved and the conditions in which it was formed, the atoms may bearranged in a regular, geometric pattern (crystalline solids, which include metals andordinary water ice) or irregularly (an amorphous solid such as common window glass).The bulk of solid-state physics theory and research is focused on crystals, largely becausethe periodicity of atoms in a crystal — its defining characteristic — facilitates mathematicalmodeling, and also because crystalline materials often have electrical, magnetic, optical,or mechanical properties that can be exploited for engineering purposes.The forces between the atoms in a crystal can take a variety of forms. For example, in acrystal of sodium chloride (common salt), the crystal is made up of ionic sodium and chlorine, and held together with ionic bonds. In others, the atomsshare electrons and form covalent bonds. In metals, electrons are shared amongst the

whole crystal in metallic bonding. Finally, the noble gases do not undergo any of thesetypes of bonding. In solid form, the noble gases are held together with van der Waalsforces resulting from the polarisation of the electronic charge cloud on each atom. Thedifferences between the types of solid result from the differences between their bonding.



Many properties of materials are affected by their crystal structure. This structure can beinvestigated using a range of crystallographic techniques, including X-raycrystallography, neutron diffraction and electron diffraction.

The sizes of the individual crystals in a crystalline solid material vary depending on thematerial involved and the conditions when it was formed. Most crystalline materialsencountered in everyday life are polycrystalline, with the individual crystals beingmicroscopic in scale, but macroscopic single crystals can be produced either naturally(e.g. diamonds) or artificially.Real crystals feature defects or irregularities in the ideal arrangements, and it is thesedefects that critically determine many of the electrical and mechanical properties of realmaterials.The crystal lattice can vibrate. These vibrations are found to be quantised, the quantisedvibrational modes being known as phonons. Phonons play a major role in many of thephysical properties of solids, such as the transmission of sound. In insulating solids,

phonons are also the primary mechanism by which heat conduction takes place. Phononsare also necessary for understanding the lattice heat capacity of a solid, as in the Einsteinmodel and the later Debye model.Unit cells can be broadly divided into 2 categories: primitive and centred unit cells.



Seven primitive unit cells and their possible Variations asCentred Unit Cells



The 14 Bravais lattices



The underlying idea behind the electronic structure of solids is that the valence electronsfrom the atoms involved spread throughout the entire structure, i.e. molecular orbitals aregenerally extended over all the constituent atoms. A large number of overlapping atomic

orbitals lead to molecular orbitals very similar in energy over a certain range. This forms analmost continuous band. These bands are separated by band gaps, which are the energyvalues where there are no orbitals. (fig. 1)This continuous band arises from the molecular orbitals being slightly different in energy,which arises from the different degrees of bonding in each. At the bottom of the band wehave the lowest energy MO which has all bonding character. At the top, with highestenergy is an MO with all anti-bonding character. Therefore the rest of the band is formedfrom all the MO’s with intermediate bonding character between the two extremes. (fig. 2)



Different types of orbitals form separate bands. Therefore we can end up with an s bandand a p band. Whether or not they form two distinct bands with a band gap, or overlapdepends on the separation of the orbitals and how strong the interaction between the

atoms is. Strong interaction means wide bands and a greater chance of overlap. (fig. 3)The distinction between metallic and non-metallic solids comes from the way the orbitalsare filled. Metallic behaviour arises from a partially full band as then there is no gapbetween the top filled level (Fermi level) and the lowest empty one. However, a non-metallic solid has a completely filled level (the valence band) and an empty one (theconduction band). These two bands are separated by a band gap. (fig. 4). In the filled bandevery electron is matched by another so you get no overall net motion of electric charge.Therefore, for conduction to occur electrons have to be excited up to the conduction bandby overcoming an activation energy and hence, the conduction of these compoundsincreases with temperature.



Insulators have a full valence band separated from the next energy band, which is empty,by a large, forbidden gap. Diamond is an excellent insulator. It has a band gap of approximately 6eV which is very large. This means very few electrons have sufficient

energy to be promoted and the conductivity is negligibly small. (fig. 5) When conductivityof insulators is able to be measured it is found to increase with temperature like the non-metallic solids.IONIC SOLIDS – bonding due to transfer of charge from one atom to another. Energy bandsformed from the atomic orbitals of anions and cations.COVALENT SOLIDS – bonding due to overlap and sharing of electrons. Bands formed frombonding molecular orbitals (filled bands) and antibonding orbitals (empty bands).METALLIC SOLIDS – bonding due to orbital overlap forming a delocalised cloud of electrons.Overlap of atomic orbitals can be so strong that bands are formed which are much broaderthan the original energy separation of the orbitals. Orbitals lose their individuality and youcan look at it as the electrons moving freely.

The band gap is important as the size of it determines whether you are looking at a

semiconductor or an insulator. Band gap determines the minimum photon energy requiredto excite an electron up to the conduction band from the valence band.



The existence of bands and a map of their densities of states can be shown using eitherphotoelectron spectroscopy or x-ray analysis.Photoelectron spectroscopy can be used here in much the same way as when dealing with

discrete molecules. The densities of states of discrete molecules are made up of a set of widely separated, narrow peaks, corresponding to energies of discrete molecular orbitals.When looking at the photoelectron spectrum the peaks exist as photoelectrons withdiscrete ionisation energies.Equivalent information about solids can be obtained from X-ray emission bands. Electronsare ejected (by electron bombardment) from the inner closed shells of the atoms. Aselectrons from the valence band fall into the vacancies created x-rays are emitted. (fig. 6)



Since the valence electron falling can originate from any of the occupied levels in the band,the corresponding x-ray emissions cover a range of frequencies. Where there are manystates in the valence band with similar energies you get higher emission intensities, and

vice-versa.Therefore, the x-ray emission band gives an indication of the variation of the density of states across the band. It is not an exact match though, because you must make allowancesfor the ease with which the incoming photon may eject an electron from different types of orbital.X-ray emission gives information about the densities of states of the occupied areas of theband and x-ray absorption information about the unoccupied areas.



Semiconductors have a similar band structure to insulators but the band gap is not verylarge and some electrons have sufficient thermal energy to be promoted up to the emptyconduction band. There are two types of conduction mechanism in semiconductors.

Electrons promoted into the conduction band are classed as negative charge carriers andwould move towards a positive electrode under an applied potential. The holes theseelectrons leave behind are known as positive holes. These holes move when an electronenters them. Wherever the electron that filled the hole moved from is the new positivehole. The positive holes therefore move in an opposite direction to the electrons. (fig. 7)Semiconductors can be split into two groups. INTRINSIC and EXTRINSIC semiconductors.Intrinsic semiconductors are pure materials with the bandstructure already discussed. Thenumber of electrons in the conduction band is determined only by the size of the band gapand the temperature (more electrons with small band gap and high temperature).

Extrinsic semiconductors are materials where the conductivity is controlled by adding

dopants with different numbers of valence electrons to that of the original material.



Doping of semiconductors is achieved by introducing atoms with more or less electronsthan the parent element. Doping is substitutional, the dopant atoms directly replace theoriginal atoms. Surprisingly low levels of dopant are required, only 1 atom in 109 of the

parent atoms.Looking at silicon; if phosphorous atoms are introduced into a silicon crystal then extraelectrons will be available (one for each dopant atom introduced as p has one extra valenceelectron). The dopant atoms form a set of energy levels that lie in the band gap betweenthe valence and conduction bands, but close to the conduction band. The electrons inthese levels cannot move directly as there is not enough of them to form a continuousband. However, the levels themselves can act as donor levels because the electrons haveenough thermal energy to get up into the conduction band where they can move freely.Such semiconductors are known as n-type semiconductors, representing the negativecharge carriers or electrons.What if, instead of doping with phosphorous, we doped silicon with an element with one

less valence electron such as gallium. Now for every dopant atom there is an electronmissing, and the atoms form a narrow, empty band consisting of acceptor levels which lie just above the valence band. Electrons from the valence band may have enough thermalenergy to be promoted into the acceptor levels, which are discrete levels if theconcentration of gallium atoms is small. Therefore, electrons in the acceptor levels cannotcontribute to the conductivity of the material. However, the positive holes in the valence

band left behind by the promoted electrons are able to move.These type of semiconductors are known as a p-type semiconductors, representing the



positive holes.Representation of p-type and n-type semiconductors shown in (fig. 8).There are two fundamental differences between extrinsic and intrinsic semiconductors:

1) At standard temperatures extrinsic semiconductors tend to have significantly greaterconductivities than comparable intrinsic ones.2) The conductivity of an extrinsic semiconductor can easily and accurately be controlledsimply by controlling the amount of dopant which is introduced. Therefore materials can bemanufactured to exact specifications of conductivity.



Controlled valancy semiconductors: Some transition metal compounds can be conductors due to the presence of an element inmore than one oxidation state. NiO is a very good example. On oxidation the compound

goes black and becomes a relatively good conductor. Some of the Ni2+ ions have beenoxidised to Ni3+ and some Ni2+ ions diffuse out to maintain charge balance leaving cationholes.The reason for the conduction is the ability of electrons to transfer from Ni2+ to Ni3+ ions.This basically allows the Ni3+ ions to move and black NiO is therefore a p-typesemiconductor. Slightly different to the p-type discussed earlier this type is known asa hopping semiconductor because the transfer process is thermally controlled andtherefore highly dependent on temperature.This makes controlling the conductivity a tricky process. Therefore controlled valancysemiconductors rely on control of the concentration of, in this case, Ni3+ ions by controlledaddition of a dopant (such as lithium). Instead of having NiO, you now have Li+ x Ni2+

1-2x

Ni3+

x O, hence, the concentration of Li+ ions controls the conductivity.

The P-N junction: This occurs in the situation where a crystal has been doped such that half of it is n-type andthe other half is p-type. The two halves have different Fermi levels (n-type’s is higher) and

electrons flow from the n-type section to the p-type section to try and equalize theelectron concentrations (fig. 9). This creates a positive charge on the n-type region and a

negative charge on the p-type region which leads to an electric field pushing electrons backto the n-type region. Eventually a balance is reached (fig. 10).



If you apply an external potential difference to make the p-type region positive and the n-type region negative a continuous current can now flow. Electrons enter from the n-typeelectrode, travel through the conduction band of the n-type region, drop into the valence

band of the p-type region, continue through the positive holes and then leave at the otherelectrode. Cannot flow the other way with a relatively low voltage as the electrons areunable to jump up to the n-type conduction band.



All solids, even the most ‘perfect’ crystals contain defects. Defects are of great importance

as they can affect properties such as mechanical strength, electrical conductivity, chemicalreactivity and corrosion. There are several terms used to describe defects which we must

consider:Intrinsic defects – present for thermodynamic reasons.Extrinsic defects – not required by thermodynamics and can be controlled by purificationor synthetic conditions.Point defects – Occur at single sites. Random errors in a periodic lattice eg absence of atomfrom usual place (vacancy) or atom in a site not normally occupied (interstital).Extended defects – ordered in one, two and three dimensions. Eg errors in the stacking of planes.Every solid has a thermodynamic tendency to acquire point defects, as they introducedisorder and therefore increase entropy.

The Gibbs free energy, G = H – TS, of a solid, is contributed to by the entropy and enthalpy

of the sample (fig. 14). Entropy is a measure of disorder within a system, hence, a solid withdefects has a higher entropy than a perfect crystal.



Intrinsic point defects: Point defects are not easy to directly detect. Several techniques have been used to studythem. Two physicists, Frenkel and Schottky used conductivity and density data to identify

specific types of point defects.Schottky defect – Vacancy in an otherwise perfect lattice. Point defect where atom / ion ismissing from its usual point in the lattice. Overall stoichiometry is usually unaffected asthere is normally equal numbers of vacancies at both M and X sites preserving chargebalance.These defects are encountered more commonly when metal ions are able to easily assumemultiple oxidation states.Schottky defect shown (fig. 15)



Frenkel defect – Point defect where an atom / ion has been displaced into an interstitalsite. eg In AgCl some Ag+ ions occupy tetrahedral sites (fig. 16) which are normallyunoccupied. Stoichiometry is unchanged.

Encountered in open structures (wurtzite, sphalerite, etc) where coordination numbers arelow and open structure provides room for interstital sites to be occupied.Frenkel defect shown (fig. 17).Extrinsic point defects: These are inevitable because perfect purity is unattainable in crystals of any significant size.



We can introduce defects into a perfect crystal by adding an impurity. The addition of thedopant causes point defects to occur in the crystal. These defects are classed as extrinsic

defects.

Take NaCl heated in sodium vapour. Sodium is taken into the crystal and changes thecomposition from NaCl to Na1+x Cl. The sodium atoms taken into the crystal occupy cationsites leaving an equivalent number of unoccupied anion sites. The atoms then ionise suchthat Na+ ions occupy the cation sites as expected and the electrons now occupy the anionvacancies. This solid is now a non-stoichiometric compound as the ratio of atoms is nolonger the simple integer you expect. It is quite common for the ratios to be non-integral,eg vanadium oxide varies from VO0.79 to VO1.29. There are many other examples such asTiO x , Ni x O, UO x and Li x WO3.Covalent compounds are held to together by very strong covalent bonds which are difficultto break, so normallythese compounds do not show a wide range of composition. Ionic compounds do not

show a wide range either because a large amount of energy is required to remove / addions.However, non-stoichiometry can be caused by doping as already mentioned. There is also away of making ionic crystals non-stoichiometric: If the crystal has a multi-valent element init, changes in the number of ions can be compensated for by changes in the charge on theions, therefore maintaining charge balance but changing the stoichiometry.

Basically, non-stoichiometric compounds have formulae with non-integer ratios and canexhibit a range of compositions. They are formed by introducing an impurity (doping) or by



the ability of an element to show multi-valent character.The electronic, optical, magnetic and mechanical properties of non-stoichiometriccompounds can be controlled by varying their composition.



Group IV elements and related III / V compounds have already been discussed. Now we willlook at other compounds such as NaCl (I / VII compound) and MgO (II / VI compound).They are white, insulating solids with negligible small electronic conductivities and the

bonding is mainly ionic. Addition of dopants to these compounds often produces ionicrather than electronic conductivity. If NaCl is completely ionic you would get electronicconfigurations on the ions of;Na+: 1s22s22p6 Cl- : 1s22s22p63s23p6 Therefore the 3s, 3p valence shell of Cl- is full and that of Na+ is empty. The 3p orbitals onCl- are able to overlap slightly and form a narrow valence band, consisting of anion orbitalsonly. The 3s, 3p orbitals on Na+ may also overlap forming an empty conduction bandconsisting of only cation orbitals.

Since there is also a large bandgap (~7eV), the band structure of NaCl is very similar to thatof an insulator. Any promotion of electrons into the conduction band can be regarded asback transfer of charge from Cl- to Na+.We would therefore expect some correlation between the electronegativity differencesbetween the ions and the size of the band gap. A large electronegativity difference favoursionic bonding and in these cases back transfer should be difficult. This correlates with theobservation that ionic solids do have large band gaps.



When considering transition metals, the presence of partly filled d orbitals is an additionalfactor, which must be considered. In some cases the d orbitals are able to overlap to form aband or bands and the material could have a high conductivity. The other situation is when

the d orbital overlap is poor and the orbitals are effectively localized on the atoms. Thislatter situation is shown well by stoichiometric NiO which has low conductivity and there isno evidence suggesting there is reasonable overlap of d orbitals.The high conductivity situation is shown by TiO and VO. These both have the rock saltstructure like NiO, but here the dxy, dxz, dyx orbitals overlap strongly (fig 18) to form a broadt2g band. This band is partly filled, hence they show almost metallic conductivity. Thet2g band (capacity for 6 electrons) in NiO must be full and the 2 extra electrons of Ni2+ are ineg levels, dz2 and dx2-y2. These orbitals point directly at the oxide ions (fig 18) and due tothese oxide ions the eg orbitals on adjacent Ni2+ ions are unable to overlap to form a band,hence remain localized on the ions.



Phillips and Williams gave some general guidelines to determine whether good overlapwould occur. A d band formation is likely to occur if:(1) The formal charge of the cations is small.

Therefore TiO is metallic whereas TiO2 is an insulator.(2) The cation occurs early in the transition series. Therefore TiO and VO are metallic whereas NiO and CuO are poor semiconductors.(3) The cation is in the 2nd or 3rd transition series. Therefore Cr2O3 is a poor conductor whereas the lower oxides of Mo and W are goodconductors.(4) The anion is reasonably electropositive. Therefore NiO is a poor conductor whereas NiS and NiSe are good conductors.



Silicon has a very high affinity for oxygen which explains the existence of the large numberof silicate minerals. The silicate structures are best discussed in terms of the simple [SiO4]4-

unit. The [SiO4]4- unit has tetrahedral coordination of silicon by oxygen and is nicely

represented by a small tetrahedron (Si atom at the centre and O atoms at the vertices).In most silicates the [SiO4]4- tetrahedral link by sharing vertices, but occasionally shareedges or faces. Each terminal oxygen atom adds –1 to the charge of the unit, but eachshared oxygen contributes 0.Through sharing one or more oxygen atoms the tetrahedral are able to link and formchains, rings and layers. The negative charges on the silicate framework are balanced out

by metal cations within the lattice.The next page shows a structural classification of some mineral silicates. (fig. 19)





Further structural variety is possible when Al atoms replace some Si atoms. This leads tothe formation of aluminosilicates. The Al atom can substitute directly for an Si atom in atetrahedral site, insert into an octahedral environment outside of the silicate framework,

or, very occasionally occur with different coordination numbers.Due to aluminium being Al(III), when it replaces Si(IV) in an aluminosilicate you get anoverall charge negative by one unit. Therefore the framework contains exchangeable metalcations to balance the change in overall charge (H+, Na+, K+, 1/2Ca2+, etc) and can alsohold removable and replaceable guest molecules (water in naturally occurring zeolites).Molecular sieves are crystalline aluminosilicates which have open structures with gaps of molecular dimensions. The reason they are known as ‘molecular sieves’ is that these

molecules only absorb molecules smaller than the dimensions of the gaps in their structureand so can be used to separate different sized molecules.The zeolites are a subclass of molecular sieves. They are a class of crystalline

aluminosilicates based on rigid anionic frameworks with cations trapped inside tunnels orcages.As well as acting as molecular sieves, zeolites can also exchange their ions for those in asurrounding solution.General formula for zeolite composition is:M x/n[(AlO2) x (SiO2)y ].mH2OWhere cations M of valence n balance the charges on the aluminosilicate framework.



Zeolites are formed by corner-sharing [SiO4]4- and [AlO4]5- tetrahedral with exchangeablecations keeping overall electrical neutrality. The tetrahedral are able to link using up to all 4corners, thus forming a wide variety of different structures.

Linked tetrahedral are normally represented by drawing a straight line to represent theoxygen bridges connecting tetrahedral (fig. 20). This framework representation gives aclear view of the shapes of the cages and channels in the zeolite.Many zeolite structures are based on a building unit consisting of 24 silica or aluminatetrahedral linked together in 4- and 6-rings forming a truncated octahedron. This is asodalite unit (fig. 20).



Zeolite type A is based on sodalite units joined by O bridges between the square faces.Eight linked together in this way have a large central cavity called an alpha-cage. Thesecages share octagonal faces with an open diameter of 4.2Å. Therefore small molecules such

as water can fill them and diffuse through them. However, the cages are not able to allowentrance of molecules with van der waals diameters greater than 4.2Å. (fig. 21)The charge on the framework in zeolite type-A is neutralised by the presence of Na+ ionsand the formula is;Na12[(SiO2)12(AlO2)12].27H2ONumerous other cations can be introduced by ion exchange with aqueous solutions, which

is a very important property of zeolites. For this reason they are commonly used in laundrydetergent to remove ions which harm the effectiveness of the surfactant.



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+2 Chem- Solid State