Hume-Rothery phase

Superstructure of the CsCl type with eightfold unit cell. Left, lower half and right, upper half of the cell in projection onto the plane of the paper, a, b, c, and d designate four different kinds of atomic sites that can be occupied in the following ways  

A1 Mn Cu Cu MnCu2Al (Heusler alloy) Fm3m LiNi2Sn, TiCo2Si 

T1 Na T1 Na NaTl (Zintl phase) Fd3m LiAl, LiZn 

As Mg Ag MgAgAs (Zintl phase) F43m LiMgAs, NiZnSb, BAlBe, SiCN 

When covalent bonds favor neighbors of the same element, the positions c and d can also be occupied by atoms of the same kind as in a or b. This applies to diamond and to the Zintl phase NaTl NaTl can be regarded as a network of Tl particles that form a diamond structure which encloses Na+ ions (cf. Fig. 13.3, p. 134). 

Ca F F CaF2 (fluorite) F m3m BaCl2, ThO2, TiH2, Li2O, Be2C, Mg2Sn 

Fifteen metals crystallize in this structure and many alloys prefer this structure for geometric reasons because of the different sizes of the components. 

Inspecting the structure of copper-zinc alloys, Hume-Rothery observed that the transformation between different phases followed a change in the ratio of the number of valence electrons to the number of atoms in the Wigner-Seitz cell (Hume-Rothery,  

The formula Cu i Zn describes the composition. The structure of pure copper (x = 0) is the face centered cubic lattice (fee, Pearson symbol cF4). Upon an increase in the zinc concentration, a solution of zinc in copper is observed (a-phase). The solubility extends up to X = 0.38 depending on the temperature. The zinc atoms are statistically distributed in the copper lattice. 

For a copper/zinc ratio of 1 1 (x = 0.5, CuZn), the face centered cubic structure is no longer stable and transforms into a body centered cubic structure, the P-Phase 

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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. 

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. 

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. 

Remarks on the alloy crystal chemistry of the 11th group metals. A selection of the phases formed in the binary alloys of Cu, Ag and Au and of their crystal structures is shown in Tables 5.54a and 5.54b. For a number of these phases, more details (and a classification in terms of Hume-Rothery Phases ) are given in 4.4.5 and in Table 4.5 (structure types, valence electron concentration, etc.). Table 5.54a and 5.54b show the formation of several phases having a high content... 

The same structure is formed in a number of binary (or ternary) phases, for which a random distribution of the two (or three) atomic species in the two equivalent sites is possible. Typical examples are the (3-Cu-Zn phase (in which the equivalent 0,0,0 A, A, A positions are occupied by Cu and Zn with a 50% probability) and the (3-Cu-Al phase having a composition around Cu3A1 (in which the two crystal sites are similarly occupied, on average by Cu, with a 75% occupation probability, and by Al, with a 25% occupation probability). A number of these phases can be included within the group of the Hume-Rothery phases (see 4.4.5). 

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). 

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

The binary system Cd-Ag is known to form Hume-Rothery phases [3.324]. The phase diagram of this system and the AE relation are shown in Fig. 3.55. AE... 

In this chapter we present a survey of our current understanding of interrelations between the electronic and ionic structure in late-transition-polyvalent-element metallic glasses. Evidence of a strong influence of conduction electrons on the ionic structure, and vice versa, of the ionic structure on the conduction electrons, is presented. We discuss as well the consequences to phase stability, the electronic density of states, dynamic properties, electronic transport, and magnetism. A scaling behaviour of many properties versus Z, the mean electron number per atom, is the most characteristic feature of these alloys. Crystalline alloys which are also strongly dominated by the conduction electrons are often called electron phases or Hume-Rothery phases. The amorphous alloys under consideration are consequently described as an Electron Phase or Hume-Rothery Phase with Amorphous Structure. Similar theoretical concepts as applied to crystalline Hume-Rothery alloys are used for the present amorphous samples. 

After presenting the sample preparation in Sect. 5.2, we give an introduction to the theoretical background in Sect. 5.3. In Sect. 5.4, we briefly review the electronic influence on structure and phase stability of crystalline Hume-Rothery phases. In Sect. 5.5, we discuss the properties of non-magnetic amorphous alloys of the type just mentioned. The electronic influence on structure (5.5.1) and consequences for the phase stability (5.5.2) are also discussed. Structural influences on the electronic density of states are shown in 5.5.3. Electronic transport properties versus composition indicate additionally the electron-structure interrelation (5.5.4), and those versus temperature, the influence of low-lying collective density excitations (5.5.5). An extension of the model of the electronic influence on structure and stability was proposed by Hdussler and Kay [5.21,22] whenever local moments are involved as, for example, in Fe-containing alloys. In Sect. 5.6, experimental indications for such an influence are presented, and additional consequences on phase stability and magnetic properties are briefly discussed. 

The electronic model for phase stability has been extrapolated from the region of the crystalline HR-phases to the amorphous state considered here, indicating the latter as a limiting case of the crystalline Hume-Rothery phases for Z 1.8 e/a. The scaling behaviour with Z of all properties is explained along these lines. 

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