Cubic lattice parameter

In the 2incblende stmcture the bond length is related to the cubic lattice parameter as (3a/4). ... 

The thermal behavior of tetraborides is based on two factors the saturation vapor pressure of the metal, an increase of which increases the dissociation, and the stability of the B—B bonds within the boron sublattice, the strength of the B—B bonds decreasing as the size of the cubic lattice parameter increases. 

La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Figure 2. Cubic lattice parameters of the rare-earth and alkaline-earth hexaborides. 

Figure 1. Metallic radii of rare-earth metals and cubic lattice parameters of the rare-earth hexaborides.

For example, consider the sample specified in the top line of Table 1.1, with an oxygen iron ratio of 1.058, a measured density of 5728 kg m-3 and a cubic lattice parameter, a, of 0.4301 nm. 

It has been noted that the conductivity and activation energy can be correlated with the ionic radius of the dopant ions, with a minimum in activation energy occurring for those dopants whose radius most closely matches that of Ce4+. Kilner et al. [83] suggested that it would be more appropriate to evaluate the relative ion mismatch of dopant and host by comparing the cubic lattice parameter of the relevant rare-earth oxide. Kim [84] extended this approach by a systematic analysis of the effect of dopant ionic radius upon the relevant host lattice and gave the following empirical relation between the lattice constant of doped-ceria solid solutions and the ionic radius of the dopants. 

It has been reported that the value of the cubic lattice parameter, which is directly related to the average oxidation state of the manganese, is critical to obtain effective cycling. The lattice parameter should preferably be 8.23A or less, and such values are associated with lithium-rich materials, Lii+Mriz-jOi, where the average manganese oxidation state is 3.58 or higher this value minimizes dissolution of manganese and also the impact of the... 

Subsequently the transition has been called the Verwey transition and the transition temperature the Verwey temperature Ty. Verwey also guessed that, below Ty, the mobile electrons order as Fe on [110] rows and Fe on [llO] rows of B-site cations to produce a distortion to orthorhombic symmetry with lattice parameters approximately y/2 + 6)ao X (V2 - 6)ao x ao, where 5 is a small fraction and ao is the cubic lattice parameter. Although Bickford was able to confirm that Fc304 is magnetically orthorhombic at temperatures T < Ty, it is now known that the low-temperature structure is in fact monoclinic with lattice parameters V2ao x y/lz x 2ao and that the electronic ordering is more complex than originally proposed by Verwey. 

Figure 7.31 Variation of with the cubic lattice parameter in doped fullerides.

Fig. 1. Temperature variation of the cubic lattice parameter of GdAl2 measured by x-ray powder diffraction (this work). The small points connected by a line indicate the corresponding values of the isostructural YAI2 (nonmagnetic reference), scaled to coincide with GdAl2 at 230 K, in order to allow a direct comparison.

Figure 3 shows the variation of the cubic lattice parameter, measured by x-ray powder diffraction. As can be seen, there is no volume effect or only a small negative one with an absolute value at 0 K smaller than 0.3 x 10-3. 

Enthalpy of fusion. b Decomposition temperature at which the equilibrium pressure of MCl4(g) reaches latm. c Enthalpy of the completing reaction 2M X(s) + MX4(s)- d Cubic lattice parameter. 

The obvious case to be considered first is that of synthetic faujasites, which come in a range of compositions, and for which a considerable amount of spectral information is available. Evidence of Si, A1 ordering in zeolites X and Y is provided by the presence of discontinuities in the plot of the (cubic) lattice parameter versus the Si/Al ratio (60), which indicates stepwise rather than gradual change in Si, A1 distribution. This effect is even more pronounced in synthetic faujasitic gallosilicates (61). 

The room-temperature cubic lattice parameter a as a function of the exposure time of the uninterrupted intercalation process is plotted on Figure 1. 

Figure 2. Temperature dependences of pure fullerite C60 cubic lattice parameter (o) [8] and fullerite C 60 intercalated with helium (A).The error of the pure and intercalated fullerite lattice parameter determination was 0,02 %.

The X-ray patterns taken from the two sections of the intermetallic layer adjacent to the Ni phase were also closely comparable, though this layer is visually seen in Fig. 3.13 to consist of three sublayers. One of these sections corresponded to a layer composition of 16.0 at.% Ni and 84.0 at.% Zn, while the other to 19.0 at.% Ni and 81.0 at.% Zn. The experimental interplanar distances were found to be in better agreement with the calculated values from the orthorhombic lattice parameters of =3.3326 nm, b=0.8869 nm and c=1.2499 nm reported by G. Nover and K. Schubert,279 rather than from the cubic lattice parameter =0.892 nm. Moreover, a few diffraction lines, including the strong line corresponding to the interplanar distance 0.207 nm, could not be indexed on the basis of the cubic structure. 

X-ray diffractogram patem in the range 0=5-40° shows the presence of wide peak of amorphous carbon phase and three narrow peaks of Pt. According to X-ray diffraction data, bimetallic nanosized particles are alloys with simple cubic lattice (parameter a=3.888 A for Pt-Ru and a=3.899 A for Pt-Re). 

The only other crystallographic result reported for a berkelium chal-cogenide besides those summarized in Table II is a cubic lattice parameter of 0.844 nm for Bk2S3 (155). The microscale synthesis of the brownish-black sesquisulfide was carried out by treatment of berkelium oxide at 1400 K with a mixture of H2S and CS2 vapors. In later work (136,137), the higher chalcogenides were prepared on the 20- to 30-jug scale in quartz capillaries by direct combination of the elements. These were then thermally decomposed in situ to yield the lower chalcogenides. The stoichiometries of these compounds have not been determined directly. 

Cubic lattice parameter vs. composition for the hydrated sodium form of ZK4. 

The preparation of trivalent nitrogen was achieved in 2004 by Eremets et al. in a diamond cell at 1150 000 bar and 2000 K [47-49]. The crystallographic data for the trivalent nitrogen is cubic, lattice parameter a = 3.4542(9) A. A three-dimensional structure which consisted of trivalent nitrogen atoms (Fig. 9.5) was found. The N—N bond length at l.lMbar is 1.346 A, and the NNN angle is 108.8°. The nitrogen atoms form screws of trivalent atoms which are connected to form a three-dimensional network. 

A NUMBER OF isosTRUCTURAL Binary and pseudobinary alkali metal-Cfio superconductors have been discovered that have onset temperatures ranging from 18 to 33 K (/). Their general formulas are M3.. C6o, and their face-centered-cubic lattice parameters a range from 14.25 to 14.49 A at atmospheric pressure and 300 K. A monotonic increase of with alkali size is inferred from an empirical linear correlation between and a at constant pressure (/). Moreover, decreases with increasing pressure for the binary compounds witii M = K (2, 3) and Rb (4), and the two sets of T iP) data can be superposed... 

In general, a non-stoichiometric compound can be defined as one with variable composition. However, the major structural features are maintained. For example, Figure 6.4 shows the variation in the cubic lattice parameter (a) with oxygen content of Fej 0, which crystallizes with the rock-salt structure. A smooth variation is apparent, gradually reducing as the iron content decreases. 

The oxide NiAl204 adopts the spinel structure, with a cubic lattice parameter of 0.8048 nm. The structure is derived from a face-centred cubic lattice. Making use of Table 6.4, calculate the angles of diffraction of the first six lines expected on a powder diffraction pattern. 

The method can be illustrated by reference to a classical study of the defects present in iron monoxide1. Iron monoxide, often known by its mineral name of wiistite, has the halite (NaCl) structure. In the normal halite structure, there are four metal and four non-metal atoms in the unit cell, and compounds with this structure have an ideal composition MX 0, (see Chapter 1, Section 1.8). Wiistite has an oxygen-rich composition compared to the ideal formula of FeOi.o- Data for an actual sample found an oxygen iron ratio of 1.059, a density of 5728 kg m 3, and a cubic lattice parameter, a, of 0.4301 nm. Because there is more oxygen present than iron, the real composition can be obtained by assuming either that there are extra oxygen atoms in the unit cell, as interstitials, or that there are iron vacancies present. 

The cubic SrSi2 structure shows no characteristic axial ratio from which a change in the pyramidal group of Si atoms can be deduced. For BaSi2-III in diamond anvil cell experiments up to 420 kbar, only the decreases in both the cubic lattice parameters and the specific volumes VIVo are apparent (Table... 

The electrical resistivity of gold, at 273 K, is 2.05 X 10 0 m. Gold adopts the A1 structure with a cubic lattice parameter, oq, of 0.4078 nm. The velocity of electrons at the Fermi surface is 1.40 x 10 ms. Each gold atom contributes one electron to the structure. Calculate the relaxation time, t,... 

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