Lattice constants elements

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. 

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.

Table 1. Parameters of the interatomic potentials. Distances are given in as, densities in flg, charges in e and energies in Ry. ri4s and Vc have been set to 0.57 and 8.33 ag for iron. The corresponding values for nickel are 0.85 and 8.78 ag ao denotes the equilibrium lattice constant of the elements po is the electron density at equilibrium for the perfect lattices, i.e. 0.002776 ag and 0.003543 ag for iron and nickel respectively.

In connection with a discussion of alloys of aluminum and zinc (Pauling, 1949) it was pointed out that an element present in very small quantity in solid solution in another element would have a tendency to assume the valence of the second element. The upper straight line in Fig. 2 is drawn between the value of the lattice constant for pure lead and that calculated for thallium with valence 2-14, equal to that of lead in the state of the pure element. It is seen that it passes through the experimental values of aQ for the alloys with 4-9 and 11-2 atomic percent thallium, thus supporting the suggestion that in these dilute alloys thallium has assumed the same valence as its solvent, lead. 

Numerous ternary systems are known for II-VI structures incorporating elements from other groups of the Periodic Table. One example is the Zn-Fe-S system Zn(II) and Fe(II) may substimte each other in chalcogenide structures as both are divalent and have similar radii. The cubic polymorphs of ZnS and FeS have almost identical lattice constant a = 5.3 A) and form solid solutions in the entire range of composition. The optical band gap of these alloys varies (rather anomalously) within the limits of the ZnS (3.6 eV) and FeS (0.95 eV) values. The properties of Zn Fei-xS are well suited for thin film heterojunction-based solar cells as well as for photoluminescent and electroluminescent devices. 

In general, we use only the lattice constants to define the solid structure (unless we are attempting to determine its S5nnmetry). We can then define a structure factor known as the translation vector. It is a element related to the unit cell and defines the basic unit of the structure. We will call it T. It is defined according to the following equation ... 

The XRD analyses revealed presence of AEO and Nd203, SrC03 (about 62 wt%) in SrNd-SG sample, CaC03 and Ca(OH)2 (about 5 wt%) in CaNd-SG. Solid solutions of Nd in AEO and of AEE in Nd203 were observed in all samples. The calculation of lattice constants and unit cell volumes (UCV) showed modification of the oxide lattice by foreign cations. The formation of solid solutions obviously depended of the relative ionic radii of the elements equal to 0.0995 nm for Nd3+, 0.072 for Mg2+, 0.1 for Ca2+,... 

The muonium centers observed in the curpous halides (see Table II) are unusual in several respects compared with Mu in other semiconductors and insulators. Figure 12 shows the reduced hyperfine parameters for Mu in semiconductors and ionic insulators plotted as a function of the ionicity (Philips, 1970). The positive correlation is especially apparent for compounds composed of elements on the same row of the periodic table where the lattice constants and valence orbitals are similar (see solid points in Fig. 12). Note however that the Mu hyperfine parameters in cuprous halides lie well below the line and in fact are smaller than in any other semiconductor or insulator (Kiefl et al., 1986b). The reason for this unusual behaviour is still uncertain but may be related to other unusual properties of the cuprous halides. For example the upper valence band is believed... 

Au is an excellent electrode material. It is inert in most electrochemical environments, and its surface chemistry is moderately well understood. It is not, however, the substrate of choice for the epitaxial formation of most compounds. One major problem with Au is that it is not well lattice matched with the compounds being deposited. There are cases where fortuitous lattice matches are found, such as with CdSe on Au(lll), where the Vs times the lattice constant of CdSe match up with three times the Au (Fig. 63B) [115,125]. However, there is still a 0.6% mismatch. A second problem has to do with formation of a compound on an elemental substrate (Fig. 65) [384-387]. Two types of problems are depicted in Fig. 65. In Fig. 65A the first element incompletely covers the surface, so that when an atomic layer of the second element is deposited, antiphase boundaries result on the surface between the domains. These boundaries may then propagate as the deposit grows. In Fig. 65b the presence of an atomically high step in the substrate is seen to also promote the formation of antiphase boundaries. The first atomic layer is seen to be complete in this case, but when an atomic layer of the second element is deposited on top, a boundary forms at the step edge. Both of the scenarios in Fig. 65 are avoided by use of a compound substrate. 

The use of a lattice-matched II-VI compound as a substrate works if lattice-matched substrates are available. However, even in the case of HgTe on CdTe there is a slight mismatch. Frequently the solution has been to alloy in a third element to adjust the lattice constant. For example, substrates used to make MCT detectors (Hg Cdi-xTe) frequently have at least a very thin buffer layer of CdTe alloyed with Zn to provide a better lattice match [388,389]. 

A third lattice-matching scenario is to use a corresponding III-V compound for a substrate. For instance, the lattice constants for CdTe and InSb are both listed as 0.648 nm [390], and similar lattice matches are found between the other II-VI and III-V compounds. As with the II-VI compounds, there are a number of situations where the lattice constants of the substrate can be incrementally adjusted by alloying with a third element. In addition, some high-quality wafers of III-V compounds are available commercially at reasonable prices. 

Pure iron is a fairly soft silver/white ductile and malleable moderately dense (7.87 gcm ) metal melting at 1,535 °C. It exists in three allotropic forms body-centered cubic (alpha), face-centered cubic (gamma), and a high temperature body-centered cubic (delta). The average value for the lattice constant at 20 °C is 2.86638(19)A. The physical properties of iron markedly depend on the presence of low levels of carbon or silicon. The magnetic properties are sensitive to the presence of low levels of these elements, and at room temperature pure iron is ferromagnetic, but above the Curie point (768 °C), it is paramagnetic. 

Cox, B. Lattice constants of some complex fluorides of Lithium, Sodium and Quadrivalent elements. J. Chem. Soc. 3251 (1954). 

Fig. 27. Lattice constants a and c of RN12B2C for various elements R versus the ionic radii of /t3+ ions. In the case of R = Ce (open symbols), both the radii of Ce3+ and Ce4+ do not fit the curve observed for the other rare...

Fig. 6. Relationship existing between Young s modulus and their lattice constants for elements with fee crystal structure.

Berkelium metal exhibits two stable crystallographic modifications, double hexagonal closest packed (dhcp) and face-centered cubic (fee). Thus it is isostructural with the two preceding elements, all of which exhibit the fee structure at high temperature. The room-temperature lattice constants of the dhcp form are ao = 0.3416 0.0003 nm and c0 = 1.1069 0.0007 nm, yielding a calculated density of 1.478 x 104 kg/m3 and a metallic radius (CN = 12) of 0.170 nm (119). The room-temperature fee lattice parameter is a0 = 0.4997 0.0004 nm from which the... 

The berkelium monopnictides have been prepared on the multimicrogram scale by direct combination of the elements (138). In all cases, the lattice constants of the NaCl-type cubic structures were smaller than those of the corresponding curium monopnictides but comparable to those of the corresponding terbium compounds. This supports the semimetallic classification for these compounds. One additional report of BkN has appeared (139). The lattice parameter derived from the sample exhibiting a single phase was 0.5010 0.0004 nm, whereas that extracted from the mixed-phase sample of BkN resulting from incomplete conversion of a hydride was 0.4948 0.0003 nm. Clearly, additional samples of BkN should be prepared to establish more firmly its lattice constant. 

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