Hume-Rothery compounds

Table 9.4. Electron compounds (Hume-Rothery phases).

Hume-Rothery s rule The statement that the phase of many alloys is determined by the ratio.s of total valency electrons to the number of atoms in the empirical formula. See electron compounds. 

It should not be thought that the structure of every intermetallic compound can be treated so simply the discussion of such struetural features as the transfer of electrons between atoms, the occurrence of strained bonds, the significance of relative atomic sizes, and the electron-atom ratio (Hume-Rothery ratio) must, however, be postponed to later papers. 

The brittleness of these intermetallic compounds suggests an electronic structure involving a filled Brillouin zone. It was pointed out by Ketelaar (1937) that the strongest reflection, that of form 531, corresponds to a Brillouin polyhedron for which the inscribed sphere has a volume of 217 electrons per unit cube, which agrees well with the value 216 calculated on the assumption that the sodium atom is univalent and the zinc atoms are bivalent that is, calculated in the usual Hume-Rothery way. It has also been... 

In the spectrum from classical intermetaUics to valence compounds to insulators, a smooth transition in their chemical bonding (metallic to ionic) is observed. At the border between Zind phases and metaUic phases, the typical properties of Zind phases diminish and metallic conductivity appears. However, it is inaccurate to impose and define a sharp boundary between classical Zind phases and the metallic phases (e.g.. Laves and Hume-Rothery phases), and it is in the overlapping regimes where much chemistry stiU remains to be discovered and understood. 

Hume-Rothery phases (brass phases, electron compounds ) are certain alloys with the structures of the different types of brass (brass = Cu-Zn alloys). They are classical examples of the structure-determining influence of the valence electron concentration (VEC) in metals. VEC = (number of valence electrons)/(number of atoms). A survey is given in Table 15.1. 

An important class of intermetallic phases (generally showing rather wide homogeneity ranges) are the Hume-Rothery phases, which are included within the so-called electron compounds . These are phases whose stable crystal structures may be supposed to be mainly controlled by the number of valence electrons per atom, that is, by the previously defined VEC. 

The Cu5Zn8 ( Cu5Zn6 9 — Cu5Zn9 7) phase is a classical example of a Hume-Rothery phase ( electron compounds , brass-type phases) that is of a phase in which there is a structure-determining influence of the VEC (valence electron concentration, see 4.4.5). 

Metals have been considered in Chapter 4 on the elements. Some alloys are simple solid solutions, and others have the composition of intermetallic compounds. If two metals are melted together we almost always obtain a liquid solution. If the liquid is cooled it can form a solid solution, give two or more phases of the metal(s) and /or intermetallic compound(s), or a single intermetallic compound might be formed if the composition corresponds to that of the compound. Chemically similar metals of similar size have the greatest tendency to form solid solutions. The following pairs, of similar size and the same periodic group, form solid solutions for any proportions K-Rb, Ag-Au, Cu-Au, As-Sb, Mo-W, and Ni-Pd. Hume-Rothery noted that usually a metal of lower valence is likely to dissolve more of one of... 

The Cu-Zn system (brass) is complex as shown in Figure 9.1. The a phase is a ccp solid solution of Zn in Cu. The (3-brass is body-centered cubic, the composition corresponding to CuZn. Each phase exists over a range of Cu/Zn ratios corresponding to a solid solution with Zn or Cu added to the compound. The y-brass, CupZns, has a complex cubic structure and e-brass, CuZn3, has an hep structure. Hume-Rothery found that many intermetallic compounds have structures similar to (3-, y-, and e-brass at the same electron-to-atom ratio as the corresponding brass compounds. Some examples of these so-called electron... 

It is just as incomprehensible that, as appears from Table 27, compounds of completely different composition, such as Cu5Zn8, Cu9A14, Cu31Sn8, Fe5Zn21, nevertheless crystallize in the same type of lattice. Hume-Rothery pointed out that in these cases it is not the atom ratio which is characteristic but... 

The ratio 21 /13 is characteristic of compounds of the y-brass type (CuZn) and 7/4 for the e-brass type (CuZn3) (Hume-Rothery compounds). 

The circumstances under which intermetallics form were elucidated by the British metallurgist William Hume-Rothery (1899-1968) for compounds between the noble metals and the elements to their right in the periodic table (Hume-Rothery, 1934 Reynolds and Hume-Rothery, 1937). These are now applied to all intermetaUic compounds, in general. The converse to an intermetaUic, a solid solution, is only stable for certain valence-electron count per atom ratios, and with minimal differences in the atomic radii, electronegativities, and crystal structures (bonding preferences) of the pure components. For example, it is a mle-of-thumb that elements with atomic radii differing by more than 15 percent generally have very little solid phase miscibility. 

The correlation between the valence electron counts and the stabilities of intermetallic phases and stmctures were also espoused by others, like the physical chemists Neds N. Engel (b. 1904) and Leo Brewer (1919-2005), although Hume-Rothery found their result somewhat controversial. The Engel-Brewer theory asserts that the crystal stmctures of transition metals and their intermetallic compounds are determined solely by the number of valence s and p electrons. For example, Engel suggested in 1949 that the BCC stmcture correlated with (where n is the total number of valence... 

ZintI Phases. Invoking Lewis octet rule, Hume-Rothery published his 8 —N rule in 1930 to explain the crystal stmctures of the p-block elements (Hume-Rothery, 1930, 1931). In this expression, N stands for the number of valence electrons on the p-block atom. An atom with four or more valence electrons forms 8 - N bonds with its nearest neighbors, thus completing its octet. The Bavarian chemist Eduard Zintl (1898-1941) later extended Hume-Rothery s (8 - N) mle to ionic compounds (Zintl, 1939). In studying the stmcture of NaTl, Zintl noted that the Tl anion has four valence electrons and he, therefore, reasoned that this ion should bond to four neighboring ions. 

The anion connectivity of many Zintl phases can be rationalized in terms of Hume-Rothery s (8 V) mle. For example, in BaSi2 (with Si clusters), the Si anion is isoelectronic with the nitrogen group elements, that is, it has five valence electrons. The (8 N) rule correctly predicts that each silicon atom will be bonded to three other sUicon atoms. Similarly, in Ca2Si, Si is isoelectronic with the noble gas elements. Again, the 8 A mle correctly predicts that silicon will occur as an isolated ion. Indeed, this compound has the anti-PbCl2 stmcffire, in which the sUicon is surrounded by nine calcium ions at the comers of a tricapped trigonal prism. 

Unfortunately, neither Hume-Rothery s original mle, nor the generalized 8 A mle, is valid for nonpolar intermetaUics, or when an octet configuration is unnecessary for stability of the compound. In order to increase the domain of stmctures for which... 

Around 1928, Zintl had begun to investigate binary intermetallic compounds, in which one component is a rather electropositive element, e.g., an alkali- or an alkaline earth metal [1,2]. Zintl discovered that in cases for which the Hume-Rothery rules for metals do not hold, significant volume contractions are observed on compound formation, which can be traced back to contractions of the electropositive atoms [2]. He explained this by an electron transfer from the electropositive to the electronegative atoms. For example, the structure of NaTl [3] can easily be understood using the ionic formulation Na Tl" where the poly- or Zintl anion [TF] forms a diamond-like partial structure - one of the preferred structures, for a four electron species [1,2], Zintl has defined a class of compounds, which, in the beginning, was a somewhat curious link between well-known valence compounds and somehow odd intermetallic phases. 

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