Structure, Bonding, and Properties
Rule 4: Linking of polyhedra having different cations
1.13. PROPERTIES OF MATERIALS
1.12.2. THERMODYNAMIC STABILITY
When the free enthalpy of reaction f!G for the transformation of the structure of a compound to any other structure is positive, this structure is thermodynamically stable.
The term f!G depends on the transition enthalpy W and the transition entropy f!S:
f!G
=
W - Tf!S (1.21)and W and f!S, in tum, depend on pressure p and temperature T:
(1.22) A structure is stable only within a certain pressure and temperature. By variation of the pressure and/or temperature f!G eventually becomes negative relative to some other structures and a phase transition will occur. The following rules are given for the temperature and pressure dependence of thermodynamic stable structures in general:
(a) With increasing temperature T structures with a low degree of order will be favored. Their formation involves a positive transition entropy f!S, and the value of f!G depends mainly on T f!S.
(b) Higher pressure p favors structures that occupy smaller volumes (or higher densities). For example, diamond (3.51gcm-3) is more stable than graphite (2.26 g cm - 3) at very high pressure.
On the other hand, a thermodynamically unstable structure can exist when its conversion to some other structure proceeds at a negligible rate. In this case the structure is called metastable, inert or kinetically stable. Glasses, or non-crystalline materials in a broad sense, are metastable phases, which have short-range ordering but lack of long range ordering.
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coherent, in which the two lattices can be matched with each other, or incoherent, in which the two lattices do not match. Figure 1.22a shows a grain boundary in terbium oxide. The two grains are oriented differently, as reflected by the difference in lattice spacing. In some of the materials second phases may exist at the grain boundary of a matrix material, and composition segregation usually occurs. In general, two lattices (or phases) can have coherent interfaces if the lattice mimatch is less than 15%, as shown in Fig. 1.22b, where the superstructure is seen for the upper grain only because of the difference in crystal orientations. If the lattice mismatch is greater than 15% the interface can contain a high density of mismatch dislocations. In Chapter 7 we briefly introduce 0- lattice theory for describing grain boundaries.
Interfaces playa key role in determining the properties of functional materials. First, some of the properties are determined by the transport characteristics of grain boundaries;
the critical current density in polycrystalline high-temperature superconductors, such as YBa2Cu307, is a typical example. Although the volume of a grain can carry high current density, the grain boundary may not be superconductive, preventing the flow of supercurrent across the film. Second, the domain structure is an important characteristic in some functional materials, such as BaTi03. Spontaneous polarization of the domains produces ferroelectric properties. A grain boundary could disturb the alignment of the domains, resulting in degradation or loss of ferroelectricity. Finally, functional material is usually integrated with other composite materials or systems to perform an "intelligent"
Figure 1.22. High-resolution TEM images showing typical grain boundaries in terbium oxide.
action; the structure and composition of the interfaces affect the performance of the entire system.
There are numerous books on the basic properties of various classes of materials. In this book we focus on the relationship between structure evolution and properties. We are looking for guidance in searching and developing new functional materials that have potential applications in the smart system. The evolution of bulk (or volume) structure is the focus of our discussion, and the analysis of interfaces will be illustrated with some examples. It is necessary to clarify that, hereafter, by property we mean the property of a compound or a phase excluding the effect of interfaces. In other words, we mainly discuss the performance of a single crystalline material. Readers are strongly urged to consider the effect of interfaces in a practical materials system. In Chapter 7, numerous examples will be given to show how interface and grain boundary affect the performance of a thin-film material.
The property of a compound depends on the structure, which is intimately related to its constituents and stoichiometry. The relationship between structure and property is so complex that the property sometimes may be measured but its relationship with the structure may have not been defined. High Tc superconductivity, for example, was first observed in 1986, but examining the relationship between the structure and the superconductivity may still have a long way to go. Searching or understanding the relationship between the property and the structure is a fundamental goal in solid-state chemistry, condensed matter physics, and materials science. Our discussion is focused on the basic principles governing the structural evolution. In the following sections, some of the typical properties related to functional materials are reviewed.
1.13.1. MECHANICAL PROPERTY
Mechanical properties are the response of a material to an externally applied force, including elasticity, compressivity, tensile strength, deformability, hardness, wear resistivity, brittleness, cleavability, etc. The mechanical properties depend on the chemical bonding and the structure. Anisotropic mechanical properties are possible for crystals with noncubic structures because of the directional dependence of the chemical bonding and atom arrangement in the crystal. A strong covalent bonding usually gives high hardness, compressivity, and tensile strength. The strongest tensile strength is along the covalent bonding direction. It is well known that diamond is the hardest compound due to the carbon Sp3 covalent bonding. The (111) orientations are the hardest directions.
The change in bonding will inevitably produce the structure evolution, resulting in different mechanical properties. If carbon Sp3 bonds are replaced by Sp2 bonds, the structure of carbon transforms from diamond to graphite in which the Sp2 bonding forms two-dimensional covalent bonding sheets which are held together via van der Waals bonds to form the three-dimensional network of graphite. This layered structure has strong in-plane strength but very weak interlayer bonding.
In ionic crystals, the Coulomb interaction force produces high hardness, but low brittleness. Partial covalent bonding can improve the brittleness and hardness. As covalent bonding increases the strength and hardness also increase. In metallic bonding crystals, the metal ions are embedded in an electron gas, and the attractive forces remain active even after mutual displacements of parts of a crystal. Thus, metals can be deformed without fracture.
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STRUCTURE, BONDING, AND PROPERTIES
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Dislocations, which are the linear defects serving as the boundaries between deformed and undeformed parts in metals and alloys, play an important role in the deformation process. However, dislocations in ionic crystals hardly move, and they play an important role in determining the chemical reactivity of the compounds.
1.13.2. MAGNETIC PROPERTY
Magnetic property comes from the atomic magnetic moment due to the alignment of electron spins. The electron configuration of the constituents and the structure of the compounds determine the orientation and arrangement of atomic magnetic moments, resulting in different magnetisms. Two electrons are called paired if they coincide in all of their quantum numbers except the spin quantum number; thus, the magnetic moments of the two cancel. Substances having only paired electrons are diamagnetic. When they are introduced in an external magnetic field, a force acts on the electrons and an electric current is induced; the magnetic field of this current is opposed to the external field (Lenz's rule), so the substance is repelled by the external magnetic field.
In a paramagnetic material unpaired electrons are present. When an external magnetic field acts on a paramagnetic substance, the magnetic moments of the electrons adopt the orientation of this field, and the sample is magnetized and the force pulls the substance into the field. Ferromagnetism refers to a state in which the spins of all the unpaired electrons are aligned even in the absence of a magnetic field if the temperature is below the critical temperature. Ferromagnetic material has a nonvanishing magnetic moment, or "spontaneous magnetization." In antiferromagnetism, although there is no net total moment in the absence of a field, there is a far from random spatial pattern of the individual magnetic moments, due to the antiparallel orientation of neighboring moments.
Different magnetisms can be distinguished from the behavior of their magnetic susceptibility X =MIH, where M is magnetization and H is the magnetic field.
Diamagnetic substances have negative susceptibility (X < 0) and are repelled by an applied magnetic field. Paramagnetic materials have positive susceptibility (X > 0) and are attracted by an applied field. Ferromagnetism has very high X value. The Curie-Weiss law elucidates the relationship between the magnetic susceptibility and the temperature as X
= T
C for diamagnetism and paramagnetism (1.23) X=
T _ C T for ferromagnetismc
(1.24) X
=
T+
C Tc for antiferromagnetism (1.25)Figure 1.23 shows the variation of different types of magnetic susceptibility with temperatures.
Magnetic domain is the character of ferromagnetic materials. All of the atomic magnetic moments are aligned in the same orientation within one domain, but the magnetic moment varies from domain to domain. When the spins of all domains have been oriented in parallel, saturation is reached. To achieve this state a magnetic field with some minimum field strength is required. A hysteresis curve is the typical character of ferromagnetic materials. Figure 1.24 gives three types of hysteresis curves which are the
X=+M H (a) T
X=+M H Tc
(b) T
X=+M H Tc Figure 1.23. Magnetization behaviors of (a) diamagnetic and paramagnetic, (b) ferromagnetic, and (c) antiferromagnetic materials.
(c) T t::J:j 0u> ;g~~ O ... C '1::1Zn ~9::l """>::0 Ut tnZm \C u> t:::I •
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M
Hc Hc
H H
/
./Hard magnetic Soft magnetic Soft magnetic for data storage Figure 1.24. Hysteresis loops for hard, soft, and medium hard magnetic materials, where Mr is the remnant magnetization and He the coercive force.
basis of functionality of the ferromagnetic compounds. Starting from a untreated sample, an increasing magnetic field causes an increasing magnetization until saturation is reached. After switching off the magnetic field, there is some loss of magnetization, but a remnant magnetization Mr is retained. By reversing the magnetic field the spins experience a reorientation. The minimum magnetic field required for this is the coercive force He. The remnant magnetization depends on the magnetic domain alignment, and the coercive force is related to the movability of the magnetic domain boundaries. The area enclosed by the hysteresis loop is related to the energy consumption during the magnetization circle. Magnetism is a large field of science and technology, and numerous books are available for describing its theories, characteristics, and applications.
Spinel ferrites are iron-containing spinels, M2+Fe204' The medium-hard ferrites are used in the form of pigments as data storage materials, especially y-Fe203 (diskettes, recording tapes), and y-Fe203 with additives of CoFe204 (videocassettes). y-Fe203 has a spinel structure with point defects. Hexagonal ferrites, such as BaFe12019 and Ba2Zn2Fe12022> are usually used as hard magnets. BaFe12019 also has important application in high-capacity diskettes.
1.13.3. PIEZOELECTRIC PROPERTY
To illustrate piezoelectricity, consider an atom with a positive charge surrounded tetrahedrally by anions (Fig. 1.25). The center of gravity of the negative charges is at the center of the tetrahedron. By exerting pressure on the crystal on the comers of the tetrahedron, the tetrahedron undergoes distortion and the center of gravity of the negative charges no longer coincides with the position of the positive central atom, and an electric dipole is generated. If all of the tetrahedra in the crystal have the same orientation or some other mutual orientation that does not allow for cancellation among the dipoles, the crystal has a macroscopic dipole. The two opposite faces of the crystal have opposite electric charges.
Piezoelectricity refers to a reverse process in which contraction or elongation is created in the crystal once it is positioned in an electric field. Crystals can only be piezoelectric if they are noncentrosymmetric to ensure the noncompensation among the
I t\
I \
~
1 __ -III'±
---
+
i
Figure 1.25. Mechanism of the piezoelectric effect. An external pressure causes the deformation of a coordination tetrahedron, resulting in a shift of the gravity centers of the electric charges, creating a local polarization dipole.
dipoles created by the tetrahedra. Piezoelectric effect can convert a mechanical vibration into an electric signal, or vice versa. It is widely used in quartz resonators, controlling tip movement in scanning probe microscopy, sensors for vibration waves in air and under sea, and other applications. Searching and developing new piezoelectric materials are a major area of functional materials research.
1.13.4. FERROELECTRIC PROPERTY
The ferroelectric property is similar to the ferromagnetic property. The latter, however, is based on atomic magnetic moment induced by electron spin, whereas the former originates from electric dipole moment induced by spontaneous polarization of the crystal. In ionic compounds the tetrahedra and/or the octahedra usually are the basic building blocks of the unit cells, and other coordination polyhedra can be formed by sharing the anions of the tetrahedra and octahedra. However, in some cases the centers of gravity of positive and negative charges do not coincide and uncompensated charges form a permanent electric dipole in the unit cell. If these dipoles can be canceled by the randomly oriented ferroelectric domains, the material does not exhibit a macroscopic dipole. We call it paraelectric. If these dipoles cannot cancel each other, the residual dipoles add up, forming a macroscopic dipole, which is ferroelectricity. Ferroelectricity and ferromagnetism have many common characteristics, such as domains and hysteresis loops.
Usually the dipoles in one domain are oriented in parallel, but different domains may have different dipole orientations and they can cancel each other so that the entire crystal may not exhibit any electric dipole. If an external electric field is applied to the crystal, the domains whose polarizations are parallel to the field will grow, while those whose polarizations are antiparallel and not parallel to the field will be reduced. If the external electric field is removed, the domains cannot spontaneously compensate each other again, and a remnant polarization Pr remains. The crystal now is an electret. In order to remove the remnant polarization an oppositely oriented electric field of strength Ee, called the coercive field, has to be applied to the crystal. Polarization in a domain is
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STRUCTURE, BONDING, AND PROPERTIES
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CHAPTER 1
characterized by a spontaneous polarization Ps• Ferroelectricity disappears if the specimen temperature is higher than a critical value.
The variability of coordination polyhedra is an important factor for the ferroelectric property. Distortion and symmetry reduction of the unit cell usually occur. Most of them have distorted perovskite or perovskite-related structures. Ferroelectric materials are a group of functional materials, because of their potential applications in data storage, optics, lasers, and sensors.
1.13.5. OPTICAL PROPERTY
Optical properties represent the interaction characteristics of light (e.g., electric magnetic waves) with the crystal. Refraction and reflection are the fundamental characteristics of light. By choosing materials with specific refraction indexes, a variety of optical instruments can be made. Optical waveguides, for example, are a rapidly developing area in optical communication, which uses the total reflection property of light in optic fibers. Ge02, Si02, and P20S are important materials in fiber optics.
Electromagnetic radiation causes a variety of electronic processes in solids. These processes can be loosely characterized either emission or absorption processes.
Luminescence, phosphorescence, and laser (light amplification by stimulated emission of radiation) are the three most important properties of materials. Luminescence is defined as light emission in the visible spectrum that results from the collision of incident radiation with electrons surrounding an atom. ZnS doped with Mn is an example of electroluminescence.
If the electron transition in the luminescence occurs slowly because it is temporarily trapped by impurities just below the conduction band, the light emitted is delayed and occurs over a period of time. This is phosphorescence, an important application of which is found in the materials used in television screens, such as Y 203 doped with Eu. The coating on the cathode ray tube is selected to give red, green, and blue light emissions.
The relaxation time is controlled to be short enough to preclude image overlap but long enough for the human eye to register the image.
The laser is an important tool in modem technology, such as surgical devices, optical communications, high-intensity heat, and target guide in military weapons. The solid-state laser is an example of luminescent materials in which the light emitted by the fluorescence of an excited atomic cluster stimulates other clusters to emit light in phase.
When an atom absorbs a photon with a specific frequency, the atom is excited and undergoes a transition to a higher energy level. If the absorbed energy matches the value of the energy difference between the initial and final electronic energy levels and obeys the quantum selection rules, the electron in the ground state is excited to a high energy state (called the excited state). This electron falls almost immediately to a metastable state level, where it can remain for an extended period of time. If the falls of the electrons from this metastable state to the ground state occur in a random fashion, there would be no laser because of the lack of coherence among the photons. Under certain conditions, however, when one electron undergoes transition, the photon released triggers another electron in the metastable state to make the same transition; e.g., one photons "stimulate the emission" of the second photon with the same frequency and phase. The second photon would stimulate the third one, and the chain reaction continues to produce an intensive, coherent, monochromatic light beam. A variety of oxides can generate a laser, an example being single-crystalline Ah03 doped with Cr. The electron structure of a
crystal depends on the crystallographic structure and the constituent valence states of the elements. Therefore, the optical property is also tightly related to the crystal structure.
1.13.6. ELECTRIC PROPERTY
The electric conductivity of a compound is determined by the electron band structure. If the structure has at least one partially filled band, no energy gap exists between the highest occupied level (the Fermi level) and the lowest unoccupied level.
The electron energy level can be changed easily by an external applied electric field, and it can conduct electric current.
Usually covalent compounds are insulators due to no partially filled band and, large band gap. Ionic compounds, especially mixed valent compounds, are generally semiconductors or insulators due to fully filled narrow bands and smaller band gap.
However, if the crystal structure is changed by modifying the stoichiometry and/or distortion of the coordination polyhedra, the electronic structure should also be changed.
While the energy band where the Fermi level is has been nested to form two new bands, it is possible to have a new partially filled band. The compound will then change from a semiconductor or insulator to a conductor. Compounds with narrow bands and variable valence states have this characteristic, and they are candidates for functional materials, as will be shown in Chapters 3 and 4.
Transition from an insulator to a semiconductor or to a conductor is an important aspect of some functional materials. This is the basis of numerous sensors. This transition can be driven by temperature or an externally applied magnetic/electric field. LaMn03, for example, is an insulator, but it can be metallic after doping some divalent elements (such as Ca or Sr) that replace some of the La ions, Lal-xCaxMn03, of which the conductivity depends strongly on the doping amount x. On the other hand, the conductivity of this material depends on the intrinsic magnetic coupling between Mn layers; hence, the conductivity is a function of the externally applied magnetic field. It is a magnetic field sensor material although its sensitivity is very low at low field and room temperature. High-temperature superconductors, such as YBa2Cu307 and Bi2Sr2Ca- CU20x, are insulators when the temperature is higher than the critical temperature ( '" 90 K), but they become superconductors when the temperature is lower than the critical temperature. This electric property has potential applications in many fields of science and future technology.
Another important class of materials is the dielectrics, which are generally oxides. In microelectronics packaging, small devices are necessary in integrated circuits. However, as device size decreases the breakdown voltage and interdevice interference become important. To improve these· properties materials with high dielectric constants are required so that the distance between electrodes of the capacitors can be small. PZT and BaTi03 are good candidates for these applications.