Crystal structure, metals

Extent of deformations to the crystal structure Metal grain size Metal crystalline form... 

A phenomenological model based on crystal structure, metallic radius, melting point, and enthalpy of sublimation has been used to arrive at the electronic configuration of berkelium metal [140]. An energy difference of 0.92 eV was calculated between the 5f 7s ground state and the 5f 6d 7s first excited state. The enthalpy of sublimation of trivalent Bk metal was calculated to be 2.99 eV (288 kJmol ), reflecting the fact that berkelium metal is more volatile than curium metal. It was also concluded that the metallic valence of the face-centered cubic form of berkelium metal is less than that of the double hexagonal close-packed modification [140]. 

Another example of epitaxy is tin growdi on the (100) surfaces of InSb or CdTe a = 6.49 A) [14]. At room temperature, elemental tin is metallic and adopts a bet crystal structure ( white tin ) with a lattice constant of 5.83 A. However, upon deposition on either of the two above-mentioned surfaces, tin is transfonned into the diamond structure ( grey tin ) with a = 6.49 A and essentially no misfit at the interface. Furtliennore, since grey tin is a semiconductor, then a novel heterojunction material can be fabricated. It is evident that epitaxial growth can be exploited to synthesize materials with novel physical and chemical properties. 

The melting and boiling points of the aluminium halides, in contrast to the boron compounds, are irregular. It might reasonably be expected that aluminium, being a more metallic element than boron, would form an ionic fluoride and indeed the fact that it remains solid until 1564 K. when it sublimes, would tend to confirm this, although it should not be concluded that the fluoride is, therefore, wholly ionic. The crystal structure is such that each aluminium has a coordination number of six, being surrounded by six fluoride ions. 

The approximate calculation of the surface energies of metals as a function of crystal structure described earlier uses the enthalpy of sublimation, s, and the co-ordination number to calculate the energy as a function of the atomic concentration on the surface. The atomic areas of the principal configurations are as follows ... 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

Some metals have more than one crystal structure. The most important examples are iron and titanium. As Fig. 2.1 shows, iron changes from b.c.c. to f.c.c. at 914°C but goes... 

Table 2.2 Crystal structures of pure metals at room temperature...

Fig. 2.3. The crystal structure of the "intermetollic" compound CuAlj. The structures of compounds are usually more complicated than those of pure metals.

As we have already seen, when an alloy contains more of the alloying element than the host metal can dissolve, it will split up into two phases. The two phases are "stuck" together by interphase boundaries which, again, have special properties of their own. We look first at two phases which have different chemical compositions but the same crystal structure (Fig. 2.5a). Provided they are oriented in the right way, the crystals can be made to match up at the boundary. Then, although there is a sharp change in... 

Polymers are a little more complicated. The drop in modulus (like the increase in creep rate) is caused by the increased ease with which molecules can slip past each other. In metals, which have a crystal structure, this reflects the increasing number of vacancies and the increased rate at which atoms jump into them. In polymers, which are amorphous, it reflects the increase in free volume which gives an increase in the rate of reptation. Then the shift factor is given, not by eqn. (23.11) but by... 

Among the alkali metals, Li, Na, K, Rb, and Cs and their alloys have been used as exohedral dopants for Cgo [25, 26], with one electron typically transferred per alkali metal dopant. Although the metal atom diffusion rates appear to be considerably lower, some success has also been achieved with the intercalation of alkaline earth dopants, such as Ca, Sr, and Ba [27, 28, 29], where two electrons per metal atom M are transferred to the Cgo molecules for low concentrations of metal atoms, and less than two electrons per alkaline earth ion for high metal atom concentrations. Since the alkaline earth ions are smaller than the corresponding alkali metals in the same row of the periodic table, the crystal structures formed with alkaline earth doping are often different from those for the alkali metal dopants. Except for the alkali metal and alkaline earth intercalation compounds, few intercalation compounds have been investigated for their physical properties. 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

Fig. 10. Unpolarized Raman spectra (T = 300 K) for solid Ceo, KaCeo, RbsCeo, NaeCeo, KaCco, RbeCeo and CseCeo [92, 93], The tangential and radial modes of Ag symmetry are identified, as are the features associated with the Si substrates. From the insensitivity of these spectra to crystal structure and specific alkali metal dopant, it is concluded that the interactions between the Cao molecules are weak, as are also the interactions between the Cao anions and the alkali metal cations.

Most materials scientists at an early stage in their university courses learn some elementary aspects of what is still miscalled strength of materials . This field incorporates elementary treatments of problems such as the elastic response of beams to continuous or localised loading, the distribution of torque across a shaft under torsion, or the elastic stresses in the components of a simple girder. Materials come into it only insofar as the specific elastic properties of a particular metal or timber determine the numerical values for some of the symbols in the algebraic treatment. This kind of simple theory is an example of continuum mechanics, and its derivation does not require any knowledge of the crystal structure or crystal properties of simple materials or of the microstructure of more complex materials. The specific aim is to design simple structures that will not exceed their elastic limit under load. 

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