Instead of silicon or germanium with four valence electrons (to yield a filled band of 4 + 4 = 8
electrons on band formation), we can form a compound from gallium (three valence electrons)
and arsenic (five valence electrons) to yield gallium arsenide with a filled valence band. In
general, however the ΔE for the band gap will differ from those of elemental semiconductors.
The band gap will increase as the tendency for electrons to become more and more localized on
atoms increases, and thus it is a function of the electronegativities of the constituents (Fig. 7.25).
Note that conductivity is a continuous property ranging from metallic conductance (Sn) through
elemental semiconductors (Ge, Si), compound semiconductors (GaAs, CdS) to insulators, both
elemental (diamond, C) and compounds (NaCl).
Fig. 7.25 Empirical relationship between energy gap and the electronegativities of the elements
present. Note that substances made from a single, fairly electronegative atom (C, diamond) or from a
very low-electronegativity metal and high-electronegativity nonmetal (NaCl) are good insulators. As
the electronegativities approach 1.75, the electronegativity function rapidly approaches zero. [From
Hannay, N. B. Solid-State Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1967. Reproduced with
permission.]
1
Extrinsic semiconductors
The number of electron carriers can be increased if atoms with more electrons
than the parent element can be introduced in the process called doping. Remarkably low
levels of dopant concentration are needed -only about one atom per 109 atoms of the
host material- so it is essential to achieve very high purity.
If As atoms are introduced into a silicon crystal, then one additional electron will be
available for each dopant atom that is substituted. Note that the doping is substitutional
in the sense that the dopant atom takes the place of a Si atom. If the donor atoms, the
As atoms, are far apart from each other, their electrons will be localized and the
donor band will be very narrow (Fig. 3.37a). Commonly the energy of the filled
dopant band is close to that of the empty band of the lattice. For T > 0, some of its
electrons will be thermally promoted into the empty conduction band. In other words,
thermal excitation will lead to the transfer of an As electron onto a neighboring Si atom
from where it will be able to migrate through the lattice in the molecular orbitals formed
by Si-Si overlap. This gives rise to n-type semiconductivity, the n indicating that the
charge carriers are negative electrons.
Fig. 7.26 Conduction by holes in
an acceptor or p-type
semiconductor.
Fig. 7.27 Conduction by electrons
in a donor or n-type
semiconductor
Fig. 3.37. The band structure in (a) a p-type semiconductor and (b) an n-type semiconductor.
2
Fig. 13.1 Schematic drawing of silicon,
showing the negative-electron and positivehole current carriers which give rise to a
small intrinsic conductivity in the pure
element.
FIGURE 13.2 Schematic drawing of n-type silicon, and the corresponding densityof-states diagram.
FIGURE 13.3 Schematic drawing of p-type silicon, and the corresponding
density-of-states diagram.
3
DEFECT SEMICONDUCTORS7
Many compounds are semiconductors because they are nonstoichiometric. For example, when
compounds such as NaCl, KCl, LiH, and δ-TiO are subjected to high-energy radiation or are heated
with an excess of their constituent metals, the compounds become deficient in the electronegative
elements and their compositions may be represented by the general formula MY1- x, where x is a small
fraction. The crystal lattice of such a compound has anion vacancies, each of which is usually occupied
by an electron. Such electron-occupied holes are called "F centers." The electron of an F center can
be thermally excited to a conduction band, thus giving rise to n-type semiconduction.
Another class of n-type semiconductor are those compounds which contain excess
interstitial metal atoms and whose compositions correspond to the formula M1+xY. The compounds
ZnO, CdO, Cr2O3, and Fe2O3 show this type of structural defect. The interstitial metal atoms
are readily ionized, allowing their valence electrons to enter a conduction band and leaving
interstitial metal ions. When a defect oxide of this type is heated in oxygen, its room-temperature
conductivity decreases because of the loss of some of the interstitial metal atoms by oxidation.
Compounds which are deficient in metal ions, of general formula M1-xY, are p-type
semiconductors. This type of semiconductor can be found in Cu2O, FeO, NiO, δ-TiO, CuI,
and FeS. Electrical neutrality is maintained in these compounds, in spite of cation vacancies, by the
presence of metal ions of higher oxidation state. Thus the composition Fe0.95O is more informatively
Ⅱ
Ⅲ
represented by the formula Fe 0.85Fe 0.10O. (See Fig. 13.4 for the iron-oxygen phase diagram.)
Electrical conductivity is achieved by the hopping of valence electrons from lower-oxidation-state metal
ions to higher-oxidation-state metal ions. However, because the Fe(III) ion concentration is much lower
than the Fe(II) ion concentration, the effective migrating unit is a positive hole in a metal ion and the
conductivity is of the p type. The energy gap for this type of semiconductor corresponds to the energy
required to move a positive hole away from the vicinity of a cation vacancy, where it is electrostatically
held. When a defect oxide of this type is heated in oxygen, its room-temperature conductivity increases
because of oxidation of some of the metal ions and the consequent increase in positive-hole concentration.
FIGURE 13.4 The iron-oxygen
phase diagram. Notice that Fe1xO is unstable with respect to
disproportionation below 560o.
However,
room-temperature
metastable Fe1-xO can be
prepared by rapid quenching of
the high-temperature phase.
(Adapted from Gmelin-Durrer,
“Metal-lurgie des Eisens,”
Band 1b, p. 59, Verlag Chemie,
Weinheim, 1964.)
4
CONTROLLED-VALENCE SEMICONDUCTORS8
Defect semiconductors are generally difficult to obtain with large deviations from stoichiometry. Hence
only limited variations in electrical properties are possible. In addition, compositions are difficult to
reproduce exactly. These difficulties can be overcome by the use of "controlled-valence" semiconductors,
first prepared by Verwey and his coworkers.
For example, consider the material formed by heating an intimate mixture of NiO and a small amount of
Li2O in air at 1200°C. Oxygen is absorbed, and a single phase of composition LixNi1-xO is formed:
Inasmuch as Li + and NiH ions have similar radii, Li + ions can substitute for Ni2+ ions in the lattice. One
Ni3+ ion is formed for every Li + ion introduced to preserve electrical neutrality. The resulting compound
Ⅲ
Ⅱ
can be represented more precisely by the expanded formula LixNi xNi 1-2x. The positive holes in the
Ni2+ ions (i.e., the Ni3+ ions) can move from one nickel ion to another and thus give rise to p-type
semiconduction. By simply controlling the ratio of lithium to nickel, the electrical conductivity can be
varied at will. The conductivity of pure
NiO is about 10-10Ω-1, whereas the compound in which 10 percent of the nickel atoms have been replaced
by lithium atoms has a conductivity of about 10-1 cm-1
Mixed-valence systems can also be obtained with compounds having the perovskite structure such as
Ⅳ
barium titanate, BaTi O3. (This compound consists of a ccp lattice of Ba2+ and O2- ions in which the
octahedral holes surrounded exclusively by O2- ions are occupied by Ti4+ ions.) If a small number of the
barium ions are replaced by +3 ions such as lanthanum ions, a corresponding number of Ti4+ ions must be
Ⅲ
Ⅳ
reduced to Ti3+, forming the system LaxBa1-xTi xTi 1-xO3. This material exhibits n-type
semiconductivity.
Compounds of the type LixMnl-xO are semiconducting, but they cannot be made by heating a mixture of
Li2O and MnO in air, because MnO is easily oxidized in air at high temperatures. In this case, the reaction
is carried out in a sealed container, and the oxygen is introduced in the form of lithium peroxide:
Various imperfections can lead to semiconductivity in analogous ways. For example, nickel(Ⅱ) oxide
may be doped by lithium oxide (see Fig. 7.12). The Ni3+ ions now behave as holes as they are reduced
and produce new Ni3+ ions at adjacent sites. These holes can migrate under a potential (indicated by the
signs on the extremes of the series of nickel ions):
The range of possibilities for semiconduction is very great, and the applications to the operation of
transistors and related devices have revolutionized the electronics industry, but an extensive discussion of
these topics is beyond the scope of this text.25 Note, however, that inorganic compounds are receiving
intensive attention as the source of semiconductors, superconductors (page 285), and one-dimensional
conductors (Chapter 16).
5
BAND GAPS
The band gap of a semiconductor is the energy difference between the top of the valence band and the
bottom of the conduction band. Values of the band gap in various substances are listed in Table 13.1.
The binding energies associated with impurities are much smaller than the band gaps. For example, the
energy required to excite an electron away from a phosphorus atom impurity in silicon to the conduction
band is about 0.044 e V Similarly, the energy required to excite a hole from an aluminum atom impurity
in silicon to the valence band is about 0.057 eV These excitation energies may be compared with the band
gap, 1.1 e V
A major advantage of gallium arsenide over silicon is the ease with which its band gap can be changed.
The gap is larger in gallium arsenide than in silicon, but it can be narrowed or widened by appropriate
substitution with other elements. If aluminum is substituted for gallium, a much wider band gap is
obtained, and partial substitutions produce gaps proportional to the fraction of aluminum. Other valuable
materials are formed by substituting some indium for gallium, some phosphorus for arsenic, or both at the
same time.
6
Created by Readiris, Copyright IRIS 2003
Fig. 12.23 Electrical resistance of a
sample of mercury as a function of
absolute temperature. These data of
Kamerlingh Onnes were the first
evidence for the phenomenon of
superconductivity
A superconductor is a substance that conducts electricity without resistance. Until 1987, the only known superconductors (which included
metals, some oxides, and some halides) needed to be cooled to below
about 20 K before they became superconducting. However, in 1987 the
first 'high-temperature' superconductors were discovered; their
superconduction is well established at 120 K and spasmodic reports of
even higher temperatures have appeared. We will not consider these
high-temperature materials at this stage (they are discussed in Chapter
18), but sketch the ideas behind the mechanism of low-temperature
superconduction.
In 1911 H. Kamerlingh Onnes,26 while studying the electrical resistance of mercury metal at very
low temperatures, discovered that when the temperature was lowered below a critical temperature (Tc) of
4.2 K, the resistivity dropped to an immeasurably small value (see Fig. 12.23). Soon this phenomenon of
superconductivity was observed for about two dozen other metals, for which the critical temperatures are
given in Table 12.8. The highest Te value for a pure metal is that observed for niobium, 9.50 K. It has also
been shown that certain alloys and metallic compounds exhibit superconductivity,
often with transition temperatures considerably higher then those found for pure
metals (see Table 12.9). It should be noted that even (SN)x, a polymer containing
no metal atoms, becomes superconducting below 0.26 K .
The central concept of low-temperature superconduction is the existence of a
Cooper pair, a pair of electrons that exists on account of their interaction
indirectly through vibrational displacements of the atoms in the lattice. Thus, if
one electron is in a particular region of a solid, the nuclei there move toward it to
give a distorted local structure (Fig. 3.38). Since that local distortion is rich in
positive charge, it is favorable for a second electron to join the first. Hence, there
is a virtual attraction between the two electrons, and they move together as a pair.
The local distortion can be easily disrupted by thermal motion of the ions, so the
virtual attraction occurs only at very low temperatures.
Fig. 3.38 The formation of a
Cooper pair. One electron
A Cooper pair undergoes less scattering than an individual electron as it travels
distorts the crystal lattice, and
through the solid, since the distortion caused by one electron can attract back the
the second electron has a
other electron should it be scattered out of its path in a collision. This has been
lower energy if it goes to that
likened to the difference between the motion of a herd of cattle, with members
region. This effectively binds
of the herd that are deflected from their path by boulders in their way, and a
the two electron into a pair
team of cattle yoked together, which will travel forward largely regardless of
obstacles. Since the Cooper pair is stable against scattering, it can carry charge
freely through the solid, and hence give rise to superconduction.
7
For many years a major obstacle to the use of superconductors was their low critical
temperatures, generally below the boiling point of helium (4.3 K) or hydrogen (20.4 K). This
27
obstacle was removed soon after Bednorz and Muller found, in 1986, that the compound
BaxLa2-xCuO4 has a superconductivity critical temperature of about 35 K. Their discovery
spurred intense synthetic activity, and in 1987 Chu and Wu28 reported the preparation of
YBa2Cu3O7-x (x ≤ 0.5), with a 95 K critical temperature (180 above the boiling
point of nitrogen). Although this material can be prepared by heating a mixture of Y2O3, CuO,
and BaCO3 to about 950˚, a better product, consisting of finer and more densely sintered
particles, can be prepared by heating an intimate mixture of precursors not containing the
difficult-to-decompose BaCO3. Thus a relatively high-density form of YBa2Cu3O7-x can be
prepared by heating the hydrolysis products of a mixture of Y(OCHMe2)3, Ba(OCHMe2)2, and
CuNBU2 .29
8
The structure of YBa2Cu3O7-x, shown in Fig. 12.24, is similar to the perovskite structure shown
in Fig. 11.19. The perovskite structure (typified by Call03) has a cubic unit cell with a calcium
atom at the center, a titanium atom
FIGURE 12.24 Idealized structure of
YBa2Cu3O7. Oxygen atoms can be
randomly removed from the top and
bottom edges of the unit cells to form
YBa2Cu3O7-x, with x ranging from 0 to
1. [Reproduced with permission from
P. P. Edwards, M. R. Harrison, and R.
Jones, Chem. Brit., 23, 962 (1987).]
at each corner, and an oxygen atom at the middle of each edge. The lattice may be looked upon
as a close-packed array of oxygen and calcium atoms, with titanium atoms in one-quarter of the
octahedral holes. The YBa2Cu3O7-x unit cell is essentially a group of three adjacent perovskite
unit cells, with an yttrium and two barilim atoms replacing the calcium atoms and copper atoms
replacing the titanium atoms. If all the oxygen positions were occupied, the formula
would be YBa2Cu3O9, and the average oxidation state of the copper would be 11/3
or 3.67. Such a composition would be extremely unstable toward loss of oxygen because of the
strong oxidizing power of +4 copper, and thus one can rationalize the oxygen vacancies in the
lattice. (Notice that the top and bottom planes of the cell contain only two oxygen atoms each,
and that there are no oxygen atoms whatever in the horizontal plane passing through the yttrium
atom.)
There are two structurally distinct sites for the copper atoms of YBa2Cu3O7-x: Cu(l) has a square
planar coordination of oxide ions, whereas Cu(2) is located near the base of a square pyramid of
oxide ions. The fivecoordinate Cu(2) is displaced about 0.3 A from the plane of the oxide ions.
This distortion, giving a dimpled CuO2 plane, may be of importance to the superconductivity
properties of the material. 30
There are difficult problems associated with the practical application of high-temperature
superconductors. When fashioned into wires for magnets or electrical transmission, these
superconductors usually have a low critical current density (the maximum current a
superconductor can carry before it loses its superconductivity). However, in thin films, critical
current densities of several million amperes per square centimeter–enough for microelectronic
applications–have been achieved, and early applications of these superconductors will probably
involve such systems.
9
10
High-Temperature Superconductivity
Superconductivity was discovered in mercury metal in 1911. Below 4.2 K the resistance of mercury
drops to zero. Currently much interest is focused on high-temperature superconductors such as
YBa2Cu3O7-δ In this case, "high-temperature" is about 100 ± 20 K, greater than the boiling point of
nitrogen (77 K), but much lower than climatic temperatures on Earth. Earlier superconductors needed to
be cooled by the more expensive and difficultly handled liquid helium (bp = 4.3 K). Superconductivity
has generated much excitement in the popular press because of the Meissner effect illustrated by
the now familiar picture of a magnet floating over the superconductor. 41
The first breakthrough superconductors were formulated as La2-xBaxCuO4-δ (x < 0.2, unspecified but
small) and have the tetragonal, layered K2NiF4 perovskite structure. They had a critical temperature of
about 35 K.42 Observation that the critical temperature increased with pressure suggested that it depended
upon lattice distances. Therefore strontium (r + = 132 pm) was substituted for barium (r + = 149) with
some increase in Te but dramatic improvement occurred when Y (r + = 104 pm) was substituted for La (r +
= 117 pm), and a new type of compound, YBa2Cu3O7-δ was formed.43 This is the so-called 1-2-3
superconductor
The 1-2-3 superconductor has a perovskite-like structure (7.33a,c). There are systematic oxygen atom
vacancies in the unit cell compared to a stack of simple perovskite unit cells (Fig. 7.33b). These occur
between adjacent copper atoms in the chains along the c axis. The vacancies are in the yttrium atom plane.
There are also vacancies between copper atoms along the a axis in the copper-and-oxygen planes
Fig. 7.33 (a) Unit cell of the 1-2-3 supperconductor, orthorhombic, space group Pmmm. Onedimensional CuO3 chain run along the b-axis, and two-dimensional CuO2 layers lie in the ab plane.
(b) The cubic structure of perovskite, SrTiO3. Three unit cells are shown stacked vertically. (c) The
unit cell of the 1-2-3 superconductor in the context of the surrounding crystal. Cooper atoms are
surrounded either by five oxygen atoms in a square pyramid or four oxygen atoms in a aquare
plans. [From Holland, G. F. Stacy, A. M. Acc.Chem. Res. 1988, 21, 8-15. Reproduced with
permission.]
44
The preparation of these superconductors is still much of an art with grinding, heating, annealing or
slow cooling, etc., and each lab has its own recipe. Mixtures are often formed with different phases
present. Procedures are given in Footnotes 40, 41, and in Porter. L. C.; Thorn. R. J.; Geiser. U.; Umezawa,
A.; Wang. H. H.; Kwok. W. K.; Kao. H-C. I.; Monaghan. M. R.; Crabtree. G. W.; Carlson. K. D.;
Williams. J. M. [norg. Chem. 1987,26. 1645-1646; Engler. E. M.; Lee. V. Y.; Nazzal, A. I.; Beyers. R. B.;
Lim. G.; Grant, P. M.; Parkin. S. S. P.; Ramirez, M. L.; Vazquez, J. E.; Savoy. R. J. J. Am. Chem. Soc.
1987. 109.2848-2849; Garbauskas. M. F.; Green, R. W.; Arendt, R. H.; Kasper. J. S. Inorg. Chem.
1988.27.871-873.
11
that lie between the planes of barium atoms. The structural unit that is thought to be responsible for the
superconductivity is the Ba2Cu3O73- slab. The odd stoichiometry, YBa2Cu3O7-δ, results from additional
oxygen vacancies (defect structure) at the 01 and 02 positions such that 0.0 < δ < 0.4; usually δ≈0.19.
More recently, other metals such as thallium, bismuth. and lead have been included in superconductor
formulation. In one interesting series, the critical temperature has been found to increase with increasing n
in suspertonductors of the type TlBa2Can-1CunO2n+2 to a maximum of 122 K for n = 4 (Fig. 7.34).45 The
current maximum critical temperature is 125 K for a closely related Tl2Ba2Cu3O10
The following generalizations can be made about all of the high-temperature superconductors examined
to date: (1) The structures can be derived by stacking different amounts and sequences of rock salt and
perovskite-like layers of metal and oxygen; (2) superconductivity occurs in the CuO2 layers; (3) the
similarity in energy between the copper 3d and oxygen 2p levels causes them to mix extensively in the
electronic band at the Fermi level; (4) the non-CuO2 layers (part of the CuO3 chains in the 1-2-3
compounds, the Tl-O and Bi-O layers in others) furnish electron density that tunes the electronic state of
the CuO2 layers.46 Detailed discussion of superconductivity theory or of band theory applied to these
crystals is beyond the scope of this
Fig. 7.34 Unit cells (with idealized atomic positions) of the first members of the homologous
series TlBa2C2n-1CunO2n+2. [From Haldar, P.; Chen, K.; Maheshwaran, B.; Roig-Janicki, A.;
Jaggi, N. K.; Markiewicz, R. S.; Giessen, B. C. Science 1988, 241, 1198-1200. Reproduced
with permission.]
12
Ferromagnetism
Some substances have permanent magnetic moments even in the absence of applied magnetic fields and
are called "ferromagnetic." Only a few elements are ferromagnetic: Fe, Co, Ni, and several lanthanides. A
density-of-states diagram for the 3d and 4s shells of Fe, Co, or Ni would look something like that
shown in Fig. 12.12. Here the upper diagram corresponds to electrons with their spins oriented one way
(say "up"), and the lower diagram corresponds to electrons with their spins oriented the opposite way (say
"down"). The remarkable thing about these metals is that the two bands are spontaneously displaced so
that they are unequally filled. Thus more electrons are aligned one way than in the opposite way, and the
metal has a permanent magnetic moment. The thermal energy of the crystal tends to misalign the
electronic spins and to bring the density-of-states
FIGURE 12.12 Density-of-states diagrams for a ferromagnetic transition metal. The upper bands
correspond to electrons with spins “up”; the lower bands correspond to electrons with spins
“down”. The points marked Cu indicate the Fermi energy of cooper, for which there is no relative
displacement of the bands.
bands together. Obviously energy is required to displace the bands relative to one another as shown in Fig.
12.12. It is believed that the source of this energy is the exchange interaction between neighboring
aligned spins. (See Chap.1.) Raising the temperature of a ferromagnet causes the magnetization to
decrease. When the temperature reaches the Curie temperature, at which the thermal energy of the crystal
tending to bring the bands together equals the exchange energy, the magnetization is zero. At
temperatures above the Curie temperature (1043, 1404, and 631 K for Fe, Co, and Ni, respectively) the
metal is no longer fegomagnetic.
Metals which are ferromagnetic have high densities of states at the Fermi energy (i.e., the energy
corresponding to the highest filled level in the band). Thus many electrons change their spin direction
(and yield exchange energy) for a small displacement of the bands. For ordinary metals, the density of
states at the Fermi energy is lower and the energy required to displace the bands is not compensated by
the exchange energy. For example, in copper metal the levels are filled to a point where the density of
states is very low (see Fig. 12.12); consequently this metal is not ferromagnetic. The reason for the high
density of states in Fe, Co, and Ni is the fact that the 3d atomic orbitals are somewhat interior
orbitals which do not overlap strongly with those on other atoms in the lattice; thus the 3d bands for
these metals are narrow.
13
The ThCr2Si2
Structure Type26
More than 400 compounds of AB2X2 stoichiometry adopt the ThCr2Si2 type structure.27 In these
A is typically an alkali, alkaline earth, or rare earth metal. B may be a transition metal or a
main-group metal. X is a group VA (15), IVA (14), or occasionally IІIA (13) nonmetal. The
compounds in which we shall be most interested are composed of an alkaline earth metal (A =
Ca, Sr, Ba), a transition metal (B = Mn, Fe, Co, Ni, Cu), and phosphorus (see Table 7.2). These
compounds are isostructural and crystallize in the ThCr2Si2 structure with space group I4/mmm.
The unit cell (Fig. 7.28) consists of eight AII ions at the corners of a rectangular parallelepiped
plus one body-centered AⅡ ion. The transition metal atoms (BII) and the phosphorus atoms
occur in [B2P2]x2- layers, each in a square array such that each metal atom is surrounded by a
tetrahedron of phosphorus "ligands":
Fig. 7.28 Unit cell of an alkaline earth (A)/
transition metal (B)/ phosphide (P) of the
ThCr2Si2-type structure.
Isolated Tetrahedron
Note the capping phosphorus atom atop the square pyramid: It is coordinated to four metal
atoms, all on one side, highly unusual for an ion. However, if we ask whether this is an
extraordinary covalent structure for a nonmetal, we note that it is not at all unusual for sulfur (cf.
SF4 Fig. 6.4).28 Although currently unknown for phosphorus in a simple molecule, a similar
structure would be expected for the isoelectronic : PF4- anion if it existed.29
14
Table 7.2
Some interatomic distances in AB2P2 com
Compound
CaFe2P2
rCa-P
rB-P
rP-P
304
224
271
CaCo2P2
299
226
245
CaNi2P2
300
229
230
CaCu1.75 P2b
305
238
225
SrFe2P2
320
225
343
SrCo2P2
318
224
342
b
SrCu1.75
P2
316
243
230
BaMn2P2
341
245
373
BaFe2P2
332
226
384
15
Fig. 7.29. Left: Energy levels of separated Mn and P atoms, Mn-P MO’s from adjacent atoms, and extended
bonding. Right: Band structure of a single [Mn2P2]x2- layer. [Modified from Hoffmann,
R.;Zheng,C.J.Phys.Chem.1985,89,4175-4181. Reproduced with permission.]
16
Fig.7.30 Total DOS of the
extended [Mn2P2]x2- layer. The
relative contributions of the
manganese(dark area) and the
phosphorus(light
area)
are
indicated. Note that the bonding
states at -19 and -15 eV are
dominated by the phosphorus, that
is, there is more electron density
on the phosphorus than on the
mangaese.[From
Hoffmann,R.;Zheng,
C.J.Phys.Chem.1985,89,41754181. Reproduced]
Fig.7.31 Phosphorus 3pz,
orbital contribution (dark
area) to the total DOS(dashed
line; cfFig.7,29 and 7.30) of
the [Mn2P2]x2- layer.
[Modified from Hoffmann,
R.;Zheng,C.J.Phys.Chem.198
5,89,4175-4181. Reproduced
with permission.]
Fig.7.32 Phosphorus 3pz orbital
contribution (dark area) to the
total DOS(dashed line) of the total
DOS (dashed line)of the three
dimentional (total) [Mn2P2]x2lattice. The P-P interactions are
labeled σ and σ . The square
bracket encloses the bands arising
principally from the manganese
3d orbitals. [Modified from
Hoffmann,
R.;Zheng,C.J.Phys.Chem.1985,89
,4175-4181. Reproduced with
permission.]
*
17
Table 7.2
Some interatomic distances in AB2P2 com
Compound
CaFe2P2
rCa-P
rB-P
rP-P
304
224
271
CaCo2P2
299
226
245
CaNi2P2
300
229
230
CaCu1.75 P2b
305
238
225
BaMn2P2
341
245
373
BaFe2P2
332
226
384
SrFe2P2
320
225
343
SrCo2P2
318
224
342
b
SrCu1.75
P2
316
243
230
18
Imperfections in Crystals
The simplest type of defect is called the Schottky or Schottky-Wagner defect. It is simply the absence of
an atom or ion from a lattice site. In an ionic crystal, electrical neutrality requires that the missing charge
be balanced in some way. The simplest way is for the missing cation, for example, to be balanced by
another Schottky defect, a missing anion, elsewhere (Fig. 7.10).
Alternately, the missing ion can be balanced by the presence of an impurity ion of higher charge. For
example, if a crystal of silver chloride is “doped” with a small
Fig.7.10 Two Schottky defects balancing
each other for no net charge.
Fig.7.11. Schottky defect (cation
vacancy) induced and balanced by the
presence of a higher valence cation.
[Hannay, N.B. Solid-state Chemistry;
Prentice-Hall: Englewood Cliffs, NJ,
1967. Reproduced with permission.]
Fig.7.12 Controlled valency
(Ni2+ → Ni3+) by addition of Li+ ions to
NiO. [Hannay, N.B. Solid-state
Chemistry; Prentice-Hall: Englewood
Cliffs, NJ, 1967. Reproduced with
permission.]
Fig.7.13 An F center: an electron
occupying an anionic site.
Fig.7.14 A Frenkel defect: a cation displaced
from its normal site.
19
Conductivity in Ionic Solids
- Conductivity by Ion Migration
Normally, ionic solids have very low conductivities. An ordinary crystal like sodium chloride must
conduct by ion conduction since it does not have partially filled bands(metals) for electronic conduction.
The conductivities that do obtain usually relate to the defacts discussed in the previous section.
The migration of the ions may be classified into three types.
1. Vacancy mechanism. If there is a vacancy in a lattice, it may be possible for an adjacent ion
of the type that is missing, normally a cation, to migrate into it, the difficulty of migration being related to
the sizes of the migrating ion and the ions that surround it and tend to impede it.
2. Interstitial mechanism. As we have seen with regard to Frenkel defects, if an ion is small
enough(again, usually a cation), it can occupy an interstitial site, such as a tetrahedral hole in an
octahedral lattice. It may then move to other interstitial site.
3. Interstitialcy mechanism. This mechanism is a combination of the two above. It is a
concerted mechanism, with one ion moving into an interstitial site and another ion moving into the
vacancy thus created. These three mechanisms are shown in Fig. 7.15.
Fig. 7.15 Mechanisms of ionic conduction in crystals with defect structures: (a) vacancy(Schottky
defect) mechanism,(b)interstitial(Frenkel defects) mechanism, (c)interstitalcy(concerted SchottkyFrenkel) mechanism.
Fig. 7.17 Relation of the spinel structure (left) to the structure of sodium beta alumina(right). The
sodium ions are free to move in open spaces between spinel blocks, held apart by Al-O-Al pillars in the
“parking garage” structure.[In part from Wells, A.F. Structural Inorganic Chemistry, 5th ed.; Oxford
University, 1984. Reproduced with permission.]
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