B2 structure

Figure 4.15. Shock pressure versus specific volume for calcia and fused quartz indicating three regimes fused quartz, low-pressure regime is fused quartz, mixed phase regime, and high-pressure regime representing stishovite. In the case of calcia, the low-pressure phase is the B1 structure, mixed phase is indicated, and the high-pressure phase regime is in the B2 structure.

We have studied the fee, bcc, and hep (with ideal eja ratio) phases as completely random alloys, while the a phase for off-stoichiometry compositions has been considered as a partially ordered alloy in the B2 structure with one sub-lattice (Fe for c < 50% and Co for c > 50%) fully occupied by the atoms with largest concentration, and the other sub-lattice randomly occupied by the remaining atoms. 

We have considered the fee and bee phases for both random and ordered (partially ordered) alloys. The ordered bee phase is based on the B2 structure. In this structure only the FcsoXso (X = Co, Ni or Cu) alloys can be perfectly ordered. For the off-stoichiometry compositions partially ordered alloys have been considered with one... 

Figure 1. Representation of unit cells for (a) FeaNi and (b) CuZn. Corresponding to a tetragonal symmetry in the case of FeaNi (Ni atoms are marked black) and to the LI2 (CuaAu) structure in the case of c/a = 1. CuZn shows also tetragonal symmetry, whereby c/a = 1 corresponds to the B2 structure (black circles represent Cu atoms). In (b) a frozen phonon in [001] direction is indicated for the Zn atom.

The interatomic interaction is described by an EAM potential specifically developed for NiAl in the B2 structure [12]. Compared to the older potential [16], which was used in most of the previous atomistic studies, our new potential gives considerably higher antiphase boundary (APB) energies = 0.82 J/m, yj pg = 1.06 J/m in good agreement with the APB... 

Threonine, stereoisomers of, 302-303 structure and properties of, 1019 Threose. configuration of, 982 molecular model of, 294 Thromboxane B2. structure of,... 

The crystal structure of NiAl is the CsCl, or (B2) structure. This is bcc cubic with Ni, or A1 in the center of the unit cell and Al, or Ni at the eight comers. The lattice parameter is 2.88 A, and this is also the Burgers displacement. The unit cell volume is 23.9 A3 and the heat of formation is AHf = -71.6kJ/mole. When a kink on a dislocation line moves forward one-half burgers displacement, = b/2 = 1.44 A, the compound must dissociate locally, so AHf might be the barrier to motion. To overcome this barrier, the applied stress must do an amount of work equal to the barrier energy. If x is the applied stress, the work it does is approximately xb3 so x = 8.2 GPa. Then, if the conventional ratio of hardness to yield stress is used (i.e., 2x3 = 6) the hardness should be about 50 GPa. But according to Weaver, Stevenson and Bradt (2003) it is 2.2 GPa. Therefore, it is concluded that the hardness of NiAl is not intrinsic. Rather it is determined by an extrinsic factor namely, deformation hardening. 

Considering Fig. 17.4, the development of the B2 structure creates two sublattices from the original A2 structure. One of the B2 sublattices consists of the b.c.c. unit-cell centers (indicated by /3 in Fig. 17.4) are displaced from the b.c.c. corners (a in Fig. 17.4) by a/2(lll). An ordering transformation produces sublattices, a and /3, with differing site fractions, xB and Xg. Their difference becomes a structural order parameter ... 

Fig. 22. Showing how the inhomogeneous shear proposed (Fig. 21) in 1972 to apply in TiNi in the formation of twin and antiphase boundaries. This paper was published in 1973, more than 10 years before Goo et al claimed to have observed for the first time twining in B2 structure of TiNi (see Fig. 23). J.Appl.Phys. vol 44, p.3013 (1973).

Abstract—Pseudo-twinning and mechanical twinning have been observed in a transmission electron microscopy study of TiMNi47Fe3 and Ti49Ni5i alloys which have the B2(CsCI) structure. Observation of twinning in ordered alloys is rare and this is the first observation of twinning reported in a B2 structure. The twin planes are the 112 and 114 planes. For 112 pseudo-twins, the composition plane is not the twin plane and the pseudo-twin does not have the B2 structure. For 114 mechanical twins, the composition plane is the twin plane and the twin does have the B2 structure. It is shown that a shear on the 114 plane plus a shuffle of the atoms results in the ordered B2 structure in the twinned region. 

Fig. 23. Published in 1985 ( 12 years after Wang s paper on the same subject). Yet, no mention whatsoever (or reference made on Wang s paper-Figs. 21,22). These authors claim that they are the first discoverer of twining in B2 structure in TiNi Acta Met. Vol. 33. page 1725.

To account for this, a full-profile fit of the XRD pattern was made for three different crystallographic models (1) pure B structure (2) pure B2 structure (3) cubic structure with the fee sublattice for the lead atoms and two different positions for the sulfur atoms. The last model allows sulfur atoms to occupy not only octahedral interstitials in the fee sublattice as it is common for the B structure, but also the occupation of tetrahedral interstitials, which is common for the 53 structure. The best fit to experimental XRD pattern in the case of the third model is shown in Fig. 1. 

Fig. 15. FCEM calculated variations with temperature in the average A1 concentration at the (110) siuface of bcc aluminides (B2 structure - solid lines, B32 structure - dashed lines). 1 -ScAl, RuAl, RhAl, NiAl, CoAl, 2 - FeAl, 3 - CrAl, 4 - MoAl, 5 - TcAl. The surface concentrations were calculated in accordance with data of Table 3.

In Sect. C, the band structure data based on self-consistent relativistic augmented-plane-wave calculations performed by the author " are presented. Besides the electronic bands and the densities of states, the nature of the chemical bond is discussed. In Sect. D the electronic states in Zintl phases are compared with those having the B2 type of structure. As shown in Sect. B the B2 structure is closely related to the B32 structure. For intermetallic compounds the B2 structure seems to be the more natural because in this lattice all nearest neighbours of an atom A are B atoms. The reason why the compounds mentioned above crystallize in the B32 structure whereas similar compounds like LiTl and KTl form B2 phases has been frequently discussed in the literature 5 ... 

The first term is the difference in the sum of the one-electron energies deduced from band structure calculations for the B32 and B2 structures, respectively. The second term is a coulombic interaction of the charge densities inside the muffin-tin spheres, AE . is an exchange-correlation correction, and AEpu, is an interatomic energy difference which... 

Fig. 69. (a) Part of the body-centered cubic lattice ordered in the B2 structure (left part) and in the Dtp structure (right part). Left part shows assignment of four sublattices a, b, c and d, In the B2 structure (cf. also fig. 66a), the concentrations of A atoms are the same at the a and c sublatticcs, but differ from the concentrations of the b, d sublattices, while in the DOj structure the concentration of the b sublattice differs from that of the d sublatlice, but both differ from those of the a, c sublattices (which are still the same). In terms of an Ising spin model, these sublattice concentrations translate into sublattice magnetizations mu, mu, mc, m,i, which allow to define three order parameter components / = ma + mL- — mu — m,/, fa = m - mc + mu — m,j, and fa = -ma + m., + mu — nij. 

Figure 6.1. In (a) is shown calculations for the mixing energy of the ferromagnetic ordered alloys on the B2 and Llo lattices, as well as for the ferromagnetic random fee alloy with 50% Fe and 50% Ni. In (b) is shown the calculated results for the paramagnetic fee FeCo alloy over the whole concentration range, as well as experimental values and one point of the paramagnetic ordered B2 structure.

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