Phase stability in the systems AeAl(2-x)Mgx (Ae = Ca, Sr, Ba): electron concentration and size controlled variations on the laves phase structural theme.

The systems AeAl(2-x)Mgx (Ae = Ca, Sr, Ba) display electron concentration induced Laves phase structural changes. However, the complete sequence MgCu2 --> MgNi2 --> MgZn2 with increasing x (decreasing electron count) is only observed for Ae = Ca. Compounds SrAl(2-x)Mgx (0 < x < or = 2) and BaAl(2-x)Mgx (x = 0.85 and 2.0) were synthesized and structurally characterized by X-ray diffraction experiments. For the Sr system the structural sequence CeCu2 --> MgNi2 --> MgZn2 occurs with increasing Mg content x. Thus, larger Sr does not allow the realization of the MgCu2 structure at low x. For Ae = Ba a binary compound BaAl2 does not exist, but more Ba-rich Ba7Al13 forms. The reinvestigation of the crystal structure of Ba7Al13 by selected area and convergent beam electron diffraction in a transmission electron microscope revealed a superstructure, which subsequently could be refined from single X-ray diffraction data. The formula unit of the superstructure is Ba21Al40 (space group P31m, Z = 1, a = 10.568(1) angstroms, c = 17.205(6) angstroms). In Ba21Al40 a size match problem between Ba and Al present in Ba7Al13 is resolved. The structure of Ba7Al13 (Ba21Al40) can be considered as a Ba excess variant of the hexagonal MgNi2 Laves phase type structure. An incommensurately modulated variant of the MgNi2 structure is obtained for phases BaAl(2-x)Mgx with x = 0.8-1. At even higher Mg concentrations a structural change to the proper MgZn2 type structure takes place.

Structure and bonding of Sr3In11: how size and electronic effects determine structural stability of polar intermetallic compounds.

The binary compound Sr(3)In(11) (SrIn(3.667)) was synthesized and structurally characterized by X-ray diffraction experiments. It crystallizes in the orthorhombic La(3)Al(11) structure type (space group Immm, Z = 2; a = 4.9257(6), b = 14.247(2), c = 11.212(2) A). The crystal structure of Sr(3)In(11) bears features of the monoclinic EuIn(4) structure, which is adopted by SrIn(4), and the prominent tetragonal BaAl(4) structure. Sr(3)In(11) is stable until 550 degrees C. At higher temperatures it decomposes peritectically into SrIn(2) and In. Structural stability and bonding properties of Sr(3)In(11) were investigated by first principles calculations and compared to SrIn(4) in the monoclinic EuIn(4) and the tetragonal BaAl(4) structure. All three structures consist of a three-dimensional, polyanionic, network formed by In atoms and Sr cations encapsulated in cages. For the BaAl(4)-type SrIn(4), In-In network bonding is perfectly optimized. In contrast, the networks of EuIn(4)-type SrIn(4) and Sr(3)In(11) appear hypo- and hyperelectronic, respectively. The formation of Sr(3)In(11) with a composition close to 1:4 and the nonexistence of BaAl(4)-type SrIn(4) is explained by a delicate interplay of size and electronic factors governing structural stability in the In-rich part of the Sr-In system.

Laves-phase structural changes in the system CaAl2-xMgx.

Compounds CaAl(2)(-)(x)Mg(x) (0 < or = x < or = 2) were synthesized and structurally characterized by X-ray diffraction experiments. With increasing Mg content x the sequence of Laves phase structures MgCu(2) --> MgNi(2) --> MgZn(2) is revealed. The homogeneity ranges of the underlying phases were determined to be 0 < or = x < 0.24(1) (MgCu(2) type), 0.66(2) < x < 1.07(3) (MgNi(2) type), and 1.51(5) < x < or = 2.0 (MgZn(2) type). Mg/Al site occupancies in CaAl(1.34)Mg(0.66) and in CaAl(0.44)Mg(1.56) were refined from neutron powder diffraction experiments and exposed a pronounced segregation of Al and Mg in MgNi(2)-type CaAl(1.34)Mg(0.66) where Al atoms preferentially occupy the positions corresponding to trigonal bipyramids. In MgZn(2)-type CaAl(0.44)Mg(1.56), however, the Mg/Al distribution was found to be nearly uniform. Structural stability in the quasi-binary system CaAl(2)(-)(x)Mg(x) was investigated by first-principles calculations in which random occupational disorder of Mg and Al was modeled with the virtual crystal approximation. The theoretical calculations reproduced the experimental compositional stability ranges of the three different Laves phase structures very well. Structural changes in the quasi-binary system CaAl(2)(-)(x)Mg(x) are induced by the electron concentration, which decreases with increasing x. The stability of the different Laves phase structures as a function of electron concentration was analyzed by the method of moments.

The s-p bonded representatives of the prominent BaAl4 structure type: a case study on structural stability of polar intermetallic network structures.

This work presents a detailed, combined experimental and theoretical study on the structural stability of s-p bonded compounds with the BaAl4 structure type (space group I4/mmm, Z = 2) as part of a broad program to investigate the complex questions of structure formation and atomic arrangements in polar intermetallics. From ab initio calculations employing pseudopotentials and a plane wave basis set, we extracted optimized structural parameters, binding energies, and the electronic structure of the systems AeX(III)4, AeX(II)2X(IV)2, AeX(II)2X(III)2 (Ae = Ca, Sr, Ba; X(II) = Mg, Zn; X(III) = Al, Ga; X(IV) = Si, Ge). For all systems we found a pronounced pseudo-gap in the density of states separating network X42- bonding from antibonding electronic states that coincides with the Fermi level for an electron count of 14 electrons per formula unit, the optimum value for stable BaAl4-type polar intermetallics. However, the synthesis and structural characterization (from X-ray single crystal and powder diffraction data) of the new compounds AeZn2-Al2+, AeZn2-deltaGa2+delta (Ae = Ca, Sr, Ba; delta = 0-0.2) and AeMg0.9Al3.1, AeMg1.7Ga2.3 (Ae = Sr, Ba) manifested that electron deficiency is rather frequent for BaAl4-type polar intermetallics. The site preference for different "X" elements in the ternary systems was quantified by calculating "coloring energies", which, for some systems, was strongly dependent on the size of the electropositive Ae component. The Ae2+ cations decisively influence the nearest neighbor distances in the encapsulating polyanionic networks X4(2-) and the structures of these networks are surprisingly flexible to the size of the Ae component without changing the overall bonding picture. A monoclinically distorted variant of the BaAl4 structure occurs when the cations become too small for matching the size of encapsulating X4(2-) cages. An even larger size mismatch leads to the formation of the EuIn4 structure type.