Metals atomic radii

Simple criteria for surface segregation in alloys (relative melting points, enthalpies of sublimation, metal atom radii, surface free energies of the pure metals) all indicate that surface segregation of titanium should occur on Pt/Ti alloys in vacuo. However, this is inadequate because of the large departures from ideality in Pt/Ti alloys. Analysis (11) of a broken bond model of the system, especially with the use of data directly determined with Pt/Ti alloys, gives a more reliable result. 

The metal atomic radii are smaller than those of the Group I metals owing to the increased nuclear charge the number of bonding electrons in the... 

The calculated dissociation energy of H2 increases linearly with decreasing energy e. Because of the mismatch between metal atom radii and substrate metal atom distances, the overlayer metal-metal atom distances can he very different compared to the case where the metal overlayer and substrate are the same... 

Table 3.3 Carbon/Metal Atomic Radii Ratio of Interstitial Carbides...

Chromium carbide, with a carbon/metal atomic-radii ratio of 0.61, is a borderline case and, strictly speaking, belongs to the intermediate class of carbides (reviewed in Ch, 2, Sec. 5.3). Yet, unlike other intermediate carbides, it meets the refractory criteria and is a material of major industrial importance. For these reasons, it is included in this book (see Ch. 7). 

Group IV Carbides Lowest carbon/metal atomic radii ratio... 

Highest carbon/metal atomic radii ratio Several compositions fee, hep, and hexagonal structures Host metal has only one structure bcc... 

Another structure is the simple hexagonal structure (hex) such as that of tungsten mononitride (8WN) where the metal atom layers form a sequence of layers AA or BB. Such structures are not close-packed and do not form octahedral sites the available interstitial sites are trigonal prisms (see Fig, 3.13 of Ch. 3). This structure cannot form if the ratio of the nitrogen/ metal atomic radii is small, as is the case in the Zr-N and Hf-N systems. 

Symbol Fe atomic number 26 atomic weight 55.847 a Group VIII (Group 8) metallic element transition metal atomic radius 1.24A electron configuration [Ar]3d 4s2 most common valence states +2 and -i-3 other oxidization states -1, 0, -1-1, +4 and -i-6 are known but rare most abundant isotope Fe-56 natural isotopes and their abundances Fe-54 (5.90%), Fe-56 (91.52%), Fe-57 (2.245%), Fe-58 (0.33%). 

Symbol Mg atomic number 12 atomic weight 24.305 a Group II A (Group 2) alkaline-earth metal atomic radius 1.60A ionic radius (Mg2+) 0.72A atomic volume 14.0 cm /mol electron configuration [Ne]3s2 valence +2 ionization potential 7.646 and 15.035eV for Mg+ and Mg2+, respectively three natural isotopes Mg-24(78.99%), Mg-25(10.00%), Mg-26(11.01%). 

The carbon-metal atomic radius ratio for the room temperature form of iron, a-Fe, is 0.60, just in excess of the Hagg limit. Consequently, the ability of a-Fe to accept interstitial C is marginal only 0.022 weight % or 0.06 atom % C can be accommodated in the random solid solution known... 

Figure 1. Calculated properties of hydride of BCC metal (atomic radius unity) as a function of radius R of hydrogen in octahedral sites (1/2,1/2, 0) and (0,0,1/2)...

The correlation between the so-called phosphine radius rP and the metal atom radius results in the following relationships102 ... 

As subtraction of the appropriate metal atom radius from d(M-N) leads to an effectively constant value of 1.47. A, bonding in both classes of molecule may be regarded as predominantly ionic202. The small differences between calculated and experimental... 

Different ethylidyne species bond distances and angles (fQ = carbon covalent radius rj = bulk metal atomic radius)... 

Metallic Atomic radius number Element q>m) Atomic (g) config. Effective ionic radius Oxidation states... 

Fig. 1. Space filling representation of Qq and the hollow cavity within it, shown next to a transition metal atom (radius = 2.0 A) for size comparison. The structures were ray-traced with POV-Ray Tracer 3 downloadable at http //www.povray.org. Note that the atoms are not hard as perhaps suggested here by the metallic surfaces metal atoms can bury themselves significantly within the 71-cloud of the carbon shell through metal-to-carbon bonding...

The octahedral hole, surrounded by six metal atoms, has a radius that is 41.4% of the metal atom radius. By contrast, the hole in the center of a cube in the simple cubic stmcture has a radius that is 73% of the metal atom radius. The number of octahedral holes in a closest-packed stmcture is equal to the number of metal atoms. 

Because this hole is surrounded by only four atoms, the hole is smaller than the octahedral interstitial hole. We can apply geometric considerations similar to those used previously for the octahedral hole to determine that the tetrahedral hole has a radius that is 23% of the metal atom radius. 

Metal (Me) metal atom Radius of metalloid atom Rx, A ... 

The data in Table 7.1 show that, as expected, density, ionic radius, and atomic radius increase with increasing atomic number. However, we should also note the marked differences in m.p. and liquid range of boron compared with the other Group III elements here we have the first indication of the very large difference in properties between boron and the other elements in the group. Boron is in fact a non-metal, whilst the remaining elements are metals with closely related properties. 

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

The most common oxidation state of niobium is +5, although many anhydrous compounds have been made with lower oxidation states, notably +4 and +3, and Nb can be reduced in aqueous solution to Nb by zinc. The aqueous chemistry primarily involves halo- and organic acid anionic complexes. Virtually no cationic chemistry exists because of the irreversible hydrolysis of the cation in dilute solutions. Metal—metal bonding is common. Extensive polymeric anions form. Niobium resembles tantalum and titanium in its chemistry, and separation from these elements is difficult. In the soHd state, niobium has the same atomic radius as tantalum and essentially the same ionic radius as well, ie, Nb Ta = 68 pm. This is the same size as Ti ... 

The atomic radius of silver (144 pm) is within about 15% of many elements, permitting sofid solutions with Al, Au, Be, Bi, Cu, Cd, Ge, In, Mn, Pb, Pd, Pt, Sb, Sn, Th, and Zn. These metals form useful braziag, jewelry, and soldering alloys. Copper is the only metal with which silver forms a simple eutectic between two sofid solutions (Pig. 3). Silver has extremely limited solubiUtyia B, C, Co, Cr, Pe, Ge, Ir, Ni, Mg, Mo, Se, Si, Te, Ti, and W. Thus these metals may be brazed by silver alloys without serious erosion during welding (qv). 

Some metals are soluble as atomic species in molten silicates, the most quantitative studies having been made with Ca0-Si02-Al203(37, 26, 27 mole per cent respectively). The results at 1800 K gave solubilities of 0.055, 0.16, 0.001 and 0.101 for the pure metals Cu, Ag, Au and Pb. When these metal solubilities were compared for metal alloys which produced 1 mm Hg pressure of each of these elements at this temperature, it was found drat the solubility decreases as the atomic radius increases, i.e. when die difference in vapour pressure of die pure metals is removed by alloy formation. If the solution was subjected to a temperature cycle of about 20 K around the control temperamre, the copper solution precipitated copper particles which grew with time. Thus the liquid metal drops, once precipitated, remained stable thereafter. 

The radius of the 24-coordinate metal site in MBs is too large (215-225 pm) to be comfortably occupied by the later (smaller) lanthanide elements Ho, Er, Tm and Lu, and these form MB4 instead, where the metal site has a radius of 185-200 pm. The structure of MB4 (also formed by Ca, Y, Mo and W) consists of a tetragonal lattice formed by chains of Bs octahedra linked along the c-axis and joined laterally by pairs of B2 atoms in the xy plane so as to form a 3D skeleton with tunnels along the c-axis that are filled by metal atoms (Fig. 6.11). The pairs of boron atoms are thus surrounded by trigonal prisms of... 

Atomic radii. The radii are determined by assuming that atoms in closest contact in an element touch one another. The atomic radius is taken to be one half of the closest internuclear distance, (a) Arrangement of copper atoms in metallic copper, giving an atomic radius of 0.128 nm for copper, (b) Chlorine atoms in a chlorine (Cl2) molecule, giving an atomic radius of 0.099 nm for chlorine. 

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