CuZn, ordering

The existence of very small energy differences ( 0.5 mRy) between the fct and bcc phase in CuZn, forces us to take a suffir intly large k-mesh with 2500 k-points per cell, whereas for the FeaNi system we may use a much smaller k-mesh (between 500 and 900) for good convergence. In order to get this high precision for the CuZn total... 

In order to determine the phonon dispersion of CuZn and FeaNi we made use of an expanded tight binding theory from Varma and Weber . In the framework of a second order perturbation theory the dynamical matrix splits in two parts. The short range part can be treated by a force constant model, while the T>2 arising from second order perturbation theory is given by... 

Disordered alloys may form when two metals are mixed if both have body-centered cubic structures and if their atomic radii do not differ by much (e.g. K and Rb). The formation of ordered alloys, however, is usually favored at higher temperatures the tendency towards disordered structures increases. Such an arrangement can even be adopted if metals are combined which do not crystallize with body-centered cubic packings themselves, on condition of the appropriate composition. /J-Brass (CuZn) is an example below 300 °C it has a CsCl structure, but between 300 °C and 500 °C a A type transformation takes place resulting in a disordered alloy with a body-centered cubic structure. 

The order-disorder transition of a binary alloy (e.g. CuZn) provides another instructive example. The body-centred lattice of this material may be described as two interpenetrating lattices, A and B. In the disordered high-temperature phase each of the sub-lattices is equally populated by Zn and Cu atoms, in that each lattice point is equally likely to be occupied by either a Zn or a Cu atom. At zero temperature each of the sub-lattices is entirely occupied by either Zn or Cu atoms. In terms of fractional occupation numbers for A sites, an appropriate order parameter may be defined as... 

Well-ordered intermetallic compounds (alloys), when processed in high-energy ball mills exhibit atomic (chemical) disordering in the early stages of ball milling [153]. Let us take as an example ordered AlRu intermetallic crystals that are of B2 type and P-CuZn structure. This structure consists of two simple cubic interpenetrating... 

P-Brass, CuZn, has the CsCl cubic structure. It is an electron compound with 21 valence electrons for 14 atoms. The disordered structure (stable above 460° C) has each site equally occupied by Cu and Zn. The ordered structure has Zn (or Cu) at the center of the cube. For both cases the notation is 3 2PTOT. For the ordered... 

Five common ordered structures (A) L20-type CuZn, (B) L12-type Cu3Au, (C) L1o-type CuAu, (D) D03-type Fe3AI, and (E) DO-ig-type Mg3Cd. From W. F. Hosford, Physical Metallurgy (Boca Raton, FL CRC Press, 2004), p. 97, figure 5.6. 

While the commercial catalysts and technologies described above are successfully applied in the industry, some major drawbacks exist with these catalysts such as the low activity of the otherwise robust ferrochrome catalyst at low temperatures, and the susceptibility to poisoning and sintering of the CuZn shift catalyst. Additionally, both classes of catalysts are pyrophoric, generating serious safety problems in the case of accidental air exposure. Furthermore, both catalysts require a special, carefully controlled activation treatment in order to achieve the optimal active phase configuration, with the CuZn catalyst being particularly sensitive to accidental shutdowns, accidental water condensation, or temperature or concentration transients. 

Fig. 13-4 Variation of the long-range order parameter S with temperature, for AuCus and CuZn. (AuCua from Keating and Warren [13.2] CuZn data from Chipman and Warren [13.3]).

Before considering the ordering transformation in AuCu, which is rather complex, we might examine the behavior of j5-brass. This alloy is stable at room temperature over a composition range of about 46 to almost 50 atomic percent zinc, and so may be represented fairly closely by the formula CuZn. At high temperatures its structure is, statistically, body-centered cubic, with the copper and zinc atoms distributed at random. Below a critical temperature of about 460°C, ordering occurs the cell corners are then occupied only by copper atoms and the cell centers only by zinc atoms, as indicated in Fig. 13-6. The ordered alloy therefore has the CsCl structure and its Bravais lattice is simple cubic. Other alloys which have the same ordered structure are CuBe, CuPd, and FeCo. 

Figure 13-4 indicates how the degree of long-range order in CuZn varies with the temperature. The order parameter for CuZn decreases continuously to zero as T approaches T, whereas for AuCus it remains fairly high right up to and... 

Fig. 13-6 Unit cells of the disordered and ordered forms of CuZn.

But in CuZn, even when fully ordered, the situation is much worse. The atomic numbers of copper and zinc are 29 and 30, respectively, and, making the same assumptions as before, we find that... 

This ratio is so low that the superlattice lines of ordered CuZn can be detected by x-ray diffraction only under very special circumstances. (The powder pattern of this alloy, ordered or disordered, ordinarily appears to be that of a body-centered cubic substance.) The same is true of any superlattice of elements A and B which differ in atomic number by only one or two units, because the superlattice-line intensity is generally proportional to (/a — /b). ... 

Calculate the ratio of the integrated intensity of the 100 superlattice line to that of the 110 fundamental line for fully ordered -brass, if Cu Ka radiation is used. Estimate the corrections to the atomic scattering factors from Fig. 13-8. The lattice parameter of iff-brass (CuZn) is 2.95 A. 

Fig. 13.08. The variation with temperature, on heating, of the specific heat of initially ordered phases (a) CuZn (b) Cu3Au.

The major or exclusive constituent of yellow brass is P brass which is the intermetallic CuZn phase. It exhibits an A2 structure at high temperatures and a B2 structure at low temperatures, i.e. there is an order-disorder transition at about 460°C (Flinn, 1986 Massalski et al., 1990). Its range of homogeneity - between about 40 and 50 at.% Zn at higher temperatures - depends sensitively on temperature and does not include the stoichiometric 50 at.% composition at intermediate temperatures. This order-disorder transition has been used to study the effect of ordering, e.g. on elastic behavior (Westbrook, 1960 a Quillet and Le Roux, 1967), diffusion (Qirifalco, 1964 Hagel, 1967 Wever et al., 1989 Wever, 1992), recrystallization (Cahn, 1991), and hardness (Westbrook, 1960 a). 

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