Atomic: number, 177 volume

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Here Pyj is the structure factor for the (hkl) diffiaction peak and is related to the atomic arrangements in the material. Specifically, Fjjj is the Fourier transform of the positions of the atoms in one unit cell. Each atom is weighted by its form factor, which is equal to its atomic number Z for small 26, but which decreases as 2d increases. Thus, XRD is more sensitive to high-Z materials, and for low-Z materials, neutron or electron diffraction may be more suitable. The faaor e (called the Debye-Waller factor) accounts for the reduction in intensity due to the disorder in the crystal, and the diffracting volume V depends on p and on the film thickness. For epitaxial thin films and films with preferred orientations, the integrated intensity depends on the orientation of the specimen. 

Atomic number Atomic volume Atomic weight Valency... 

The atomic volumes of the alkali metals increase with atomic number, as do those of the inert gases. Notice, however, that the volume occupied by an alkali atom is somewhat larger than that of the adjacent inert gas (with the exception of the lithium and helium—helium is the cause of this anomaly). The sodium atom in sodium metal occupies 30% more volume than does neon. Cesium occupies close to twice the volume of xenon. 

The volume per mole of atoms of some fourth-row elements (in the solid state) are as follows K, 45.3 Ca, 25.9 Sc, 18.0 Br, 23.5 and Kr, 32.2 ml/mole of atoms. Calculate the atomic volumes (volume per mole of atoms) for each of the fourth-row transition metals. Plot these atomic volumes and those of the elements given above against atomic numbers. 

Hie number of Compton scatters occurring in a given volume depends on the number of electrons present and is relatively independent of incident 7-energy. For the lower atomic number elements (excluding hydrogen), the number of electrons present is directly proportional to atomic wt. Thus Compton scattering on a per unit volume basis is a function of density and is independent of chem compn. The density of soils is widely variable and the density of expls falls within the normal range of soil... 

The German physicist Lothar Meyer observed a periodicity in the physical properties of the elements at about the same time as Mendeleev was working on their chemical properties. Some of Meyer s observations can be reproduced by examining the molar volume for the solid element as a function of atomic number. Calculate the molar volumes for the elements in Periods 2 and 3 from the densities of the elements found in Appendix 2D and the following solid densities (g-cuU ) nitrogen, 0.88 fluorine, 1.11 neon, 1.21. Plot your results as a function of atomic number and describe any variations that you observe. 

In the sequence of structures from the large to the small rare-earth elements, the lanthanide contraction is manifested as shown in Figs. 19a and 19b. Within a structure, the cell volume diminishes linearly with the atomic number. If a certain, limiting value is reached, there is... 

Fig. 19. Molecular-volume variation in relation to the atomic number a, sulfide iodides b, sulfide bromides. (From C. Dagron and F. Thevet, Ann. Chim. 6, 67 (1971), Figs. 2 and 3, p. 72.)...

The spatial resolution in quantitative analysis is defined by how large a particle must be to obtain the required analytical accuracy, and this depends upon the spatial distribution of X-ray production in the analysed region. The volume under the incident electron beam which emits characteristic X-rays for analysis is known as the interaction volume. The shape of the interaction volume depends on the energy of the incident electrons and the atomic number of the specimen, it is roughly spherical, as shown in Figure 5.7, with the lateral spread of the electron beam increasing with the depth of penetration. 

In this chapter we will have a closer look at the methods of the reconstruction of the momentum densities and the occupation number densities for the case of CuAl alloys. An analogous reconstruction was successfully performed for LiMg alloys by Stutz etal. in 1995 [3], It was found that the shape of the Fermi surface changed and its included volume grew with Mg concentration. Finally the Fermi surface came into contact with the boundary of the first Brillouin zone in the [110] direction. Similar changes of the shape and the included volume of the Fermi surface can be expected for CuAl [4], although the higher atomic number of Cu compared to that of Li leads to problems with the reconstruction, which will be examined. 

The variation of the Chin-Gilman parameter with bonding type means that the mechanism underlying hardness numbers varies. As a result, this author has found that it is necessary to consider the work done by an applied shear stress during the shearing of a bond. This depends on the crystal structure, the direction of shear, and the chemical bond type. At constant crystal structure, it depends on the atomic (molecular volume). In the case of glasses, it depends on the average size of the disorder mesh. 

The number of stable isotopes for the naturally occurring elements tends to increase with increasing atomic number, to a maximum of 10 for Sn (Fig. 1). Elements with low atomic numbers tend to have the lowest number of stable isotopes, limiting the possible ways in which isotopic compositions can be reported. Both H and C have only two stable isotopes (Fig. 1), and therefore isotopic compositions are reported using one ratio, D/H and C/ C, respectively. Single ratios can only be used for B and N, and data are reported as "B/ B and W N, respectively. Of the non-traditional stable isotope systems discussed in this volume, only three have just two stable isotopes (Li, Cl, and Cu Fig. 1). 

Figure 1. Number of stable isotopes relative to atomic number (Z) for the elements. Mono-isotopic elements shown in gray diamonds. Elements discussed in this volume are shown as large gray circles. Other elements that have been the major focus of prior isotopic studies are shown in small white circles, and include H, C, O, and S. Nuclides that are radioactive but have very long half-lives are also shown in the diagram.

Qualitative analysis is manifested in the identification of the elements present. It is based on Moseley s law, which points out that the energies of a pre-selected line-type (e.g. Kai) lie on a monotonic, smooth curve as a function of the atomic number. Simultaneous read-out of the positions of the many lines present in the EDS spectrum acts as identifying fingerprints and results in a list of the element present in the excited volume. 

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