Hume intermetallic phases

The components of polar intermetallics generally include an active metal from the group 1 or 2 or the rare-earth series plus, sometimes, a late-transition metal, and a metal from the p-block. Because of the presence of an electron-poorer late transition metal, polar intermetallics generally have lower e/a values (about 2.0-4.0) than classic Zintl phases (>4.0) [45], Note these values are traditionally calculated over only electronegative atoms [45], in contrast to those of Hume-Rothery phases (<2.0) [45] and QC/ACs (2.0 0.3) [25], for which electron counts are considered to be distributed over all atoms. The former two higher values are decreased to about 1.5-2.5 and >2.5, respectively, when counted over all atoms (but with omission of any dw shells). For comparison purposes, Fig. 3 sketches the distribution of all these intermetallic phases according to e/a counted over all atoms, as we will use hereafter. 

Since all known QC systems, with e/a of about 1.75-2.20 [25], lie close to the approximate border between the Hume-Rothery and polar intermetallic phase regions, a reasonable starting place for development of new QC/AC systems is to study selected polar intermetallic systems with nearby e/a values. Synthetic explorations of such polar intermetallics have been significant only in the past few decades [42,45], Knowledge and insights developed about the diverse interplays between composition-structure-electronic structure-physical properties for these phases were expected to be a considerable aid to the discovery of novel QC/ACs. 

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 Hume-Rothery phases constitute an interesting and ubiquitous group of binary and complex intermetallic substances it was indeed Hume-Rothery who, already in the twenties, observed that one of the relevant parameters in rationalizing compositions and structures of a number of phases is the average number of valence electrons per atom (nJnM). An illustration of this fact may be found in Table 4.6, where a number of the Hume-Rothery structure types have been collected, together with a few more major structure types relevant to transition metal alloys. For each phase the corresponding VEC has been reported as njnai ratio, both calculated on the basis of the s and p electrons and of s, p and d electrons. 

Hume-Rothery (12,13) has pointed out that in some alloys the structure of the intermetallic phases are determined by the electron concentration (E.C.). The work of Hume-Rothery and others has shown that the series of changes (i.e. a phase —> (3 phase —> 7 phase — phase), which occurs as the composition of an alloy is varied continuously, takes place at electron-atom ratios of 3/2, 21/13, and 7/4, respectively. The interpretation of these changes in terms of the Brillouin zone theory has been made by H. Jones (14) and can be understood from the A (E)-curves for typical face centered cubic (a) and body centered cubic (6) structures as... 

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... 

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. 

The duster molecule has a diameter of about 3000 pm and the Ni-Ni distances in 51 lie in the range 236-312 pm. A description of the bonding in terms of the 18e rule is therefore not possible. 51 contains 448 valence electrons, which is in good agreement with the number predicted for M clusters (n > 13) on the basis of the Hume-Rothery rules for intermetallic phases (440-444e"). [26-29] This indicates that the properties of cluster complexes will approach those of metals as the number of metal atoms increases. It should be emphasized, however, that the structure of the Ni34 unit cannot be described in terms of those prindples derived for metals and intermetallic phases. 

The alloying of Cu with group IIB to IVB metals results in a series of alloy systems with a characteristic sequence of intermetallic phases characterised by their outer electron to atom ratio (e/a), as first recognised by and named after Hume-Rothery. This behavior is attributed to the fact that the electronic structure rather than ionic radius, directed bonds, or other factors of influence for alloy formation is dominating the and crystal... 

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... 

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. 

Hume-Rothery Rules. It was from observations like these that Hume-Rothery was able to develop bis Intermetallic Compound Rules (1926). He showed that the above, and other, fi-phase abnormal valency intermetallic compounds, have one common characteristic they all hare three electrons to every two atoms. Tims, in CuZn the one copper atom provides one electron and the other atom—zinc—supplies two, so that the... 

It may, incidentally, be mentioned that, in order to explain the various intermetallic compound formulae, the Hume-Eothery ratios have been simplified to whole-number ratios their derived phases, however, do, in fact, have a range of composition on either side of that of the particular individual compound concerned. 

The factors determining the particular structure adopted hy an intermetallic compound or, indeed, whether such a compound exists at all as a single-phase material, have been the subject of much discussion for a considerable period of time. The Hume-Rothery rules for electron compound formation will he very familiar and are related physically to the size of the Fermi sphere in the appropriate Brillouin zone. For example, electron compounds are expected for valence electron concentrations of , fj and l for the bcc, y-brass and cph structures, respectively. The interplay of other factors such as the atomic size, solubility and crystal structure of the components on the formation of intermetallic compounds has been considered in considerable detail by many workers, including Yao (1962), who suggested that transition metal binary systems could be classified into groups according to an excess energy dE expressed as... 

By crystallographic transformations one generally means that, when a new phase (product) forms from the old (parent), it bears certain deHnite geometrical relationships. The most widely studied crystallographic transformation is the martensitic transformation, the prototype of which occurs in quenched steels. Actually, martensite (in honor of Professor A. Martens) was the name given by Osmond in 1895 to the microstructure observed in quenched steels, but in more modern times the word martensite designates a transformation mechanism, now known to be associated with many metals, alloys, ceramics, and even some polymers. These transformations occur in a variety of intermetallics, most notably the Hume-Rothery electron compounds as found, for example, in /3-brass of near-equiatomic composition, and many similar alloys of Cu, Ag, and Au. 

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