Hume-Rothery Stabilization Mechanism Research Articles

Structure and stability of γ1-AuZn2.1: a γ-brass-related complex phase in the Au-Zn System.

γ1-AuZn2.1 in the Au-Zn binary system has been synthesized and its structure analyzed by single-crystal X-ray diffraction. It crystallizes in the trigonal space group P31m (No. 157) with ∼227 atoms per unit cell and represents a \surd3a × \surd3a × c superstructure of rhombohedrally distorted γ-Au5-xZn8+y. The structure is largely tetrahedrally closed packed. The formation of γ1-AuZn2.1 can be understood within the framework of a Hume-Rothery stabilization mechanism with a valence electron concentration of 1.68 e/a (valence electrons per atom).

Crystal structure, homogeneity range and electronic structure of rhombohedral γ-Mn5Al8

Abstract The γ-region of the Mn–Al phase diagram between 45 and 70 at.% Al was re-investigated by a combination of powder and single crystal X-ray diffraction as well as EDS analysis to establish the distribution of Mn and Al atoms. Single crystals of γ-Mn5–x Al8+x were grown using Sn-flux at 650 °C. The crystal structure, atomic coordinates and site occupancy parameters of γ-Mn5−x Al8+x phases were refined from single crystal X-ray data. The γ-Mn5-x Al8+x phase adopts the rhombohedral Cr5Al8-type structure rather than a cubic γ-brass structure. The refined compositions from two crystals extracted from the Al-rich and Mn-rich sides are, respectively, Mn4.76Al8.24(2) (I) and Mn6.32Al6.68(2) (II). The structure was refined in the acentric R3m space group (No.160, Z=6), in order to compare with other reported rhombohedral γ-brasses. In addition, according to X-ray powder diffraction analysis, at the Al-rich side the γ-phase coexists with LT–Mn4Al11 and, at the Mn-rich side, with a hitherto unknown phase. The refined lattice parameters from powder patterns fall in the range a=12.6814(7)−12.6012(5) Å and c=7.9444(2)−7.9311(2) Å from Al-rich to Mn-rich loadings, and the corresponding rhombohedral angles distorted from a pseudo-cubic cell were found to be 89.1(1)°−88.9(1)°. Magnetic susceptibility and magnetization studies of Mn4.92Al8.08(2) are consistent with moment bearing Mn and suggest a spin glass state below 27 K. Tight-binding electronic structure calculations (LMTO-ASA with LSDA) showed that the calculated Fermi level for γ-“Mn5Al8” falls within a pseudogap of the density of states, a result which is in accordance with a Hume-Rothery stabilization mechanism γ-brass type phases.

Electrons per atom ratio determination and Hume-Rothery electron concentration rule for P-based polar compounds studied by FLAPW-fourier calculations.

The extent to which reliable electrons per atom ratio, e/a, are determined and the validity of the Hume-Rothery stabilization mechanism are ensured upon increasing ionicity are studied by applying first-principles full potential linearized augmented plane wave (FLAPW)-Fourier band calculations to as many as 59 binary compounds formed by adding elements from periods 2-6 to phosphorus in group 15 of the Periodic Table. Van Arkel-Ketelaar triangle maps were constructed both by using the Allen electronegativity data and by using an energy difference between the center-of-gravity energies of FLAPW-derived s and p partial densities of states (DOSs) for the equiatomic compounds studied. The determination of e/a and the test of the interference condition, both of which play a key role in the Hume-Rothery stabilization mechanism, were reliably made for all intermetallic compounds, as long as the ionicity is less than 50%. In the A-P (A = Li, Na, K, Rb, and Cs) compounds with ionicity exceeding 50%, however, e/a determination becomes unstable, as reflected in its P concentration dependence. New Hume-Rothery electron concentration rules were theoretically found in two families of polar compounds: skutterudite compounds TMP(3), TMAs(3), and TMSb(3) (TM = Co, Ni, Rh, and Ir; cI32) with e/a = 4.34 and TM(3)P (TM = Cr, Mn, Fe, and Ni; tI32) with e/a = 2.20.

AuCd4: a Hume-Rothery Phase with VEC of 1.8 and icosahedral and trigonal-prismatic clusters as building blocks.

The η phase in the Au-Cd binary system has been synthesized, and the structure has been analyzed by single-crystal X-ray diffraction. The compound η-AuCd(4) crystallizes in the hexagonal space group P6(3)/m (No. 176). The unit cell contains ∼273 atoms. The compound AuCd(4) represents a √3a × √3a × c superstructure of the AgMg(4) type. The structure can be well described by icosahedral and trigonal-prismatic clusters. A phase transition to the high-temperature ε phase occurs exothermically at around 578 K. The compound is formed at a sharp valence electron concentration of 1.8 e/a. The compound can be understood within the framework of the Hume-Rothery stabilization mechanism.

24 electron cluster formulas as the ‘molecular’ units of ideal metallic glasses

It is known that ideal metallic glasses fully complying with the Hume-Rothery stabilization mechanism can be expressed by a universal cluster formula of the form [cluster](glue atom)1 or 3. In the present work, it is shown, after a re-examination of the cluster-resonance model, that the number of electrons per unit cluster formula, e/u, is universally 24. The cluster formulas are then the atomic as well as the electronic structural units, mimicking the ‘molecular’ formulas for chemical substances. The origin of different electron number per atom ratios e/a is related to the total number of atoms Z in unit cluster formula, e/a = 24/Z. The 24 electron formulas are well confirmed in typical binary and ternary bulk metallic glasses.

Stabilization mechanism of γ-Mg17Al12 and β-Mg2Al3 complex metallic alloys

Large-unit-cell complex metallic alloys (CMAs) frequently achieve stability by lowering the kinetic energy of the electron system through formation of a pseudogap in the electronic density of states (DOS) across the Fermi energy εF. By employing experimental techniques that are sensitive to the electronic DOS in the vicinity of εF, we have studied the stabilization mechanism of two binary CMA phases from the Al–Mg system: the γ-Mg17Al12 phase with 58 atoms in the unit cell and the β-Mg2Al3 phase with 1178 atoms in the unit cell. Since the investigated alloys are free from transition metal elements, orbital hybridization effects must be small and we were able to test whether the alloys obey the Hume-Rothery stabilization mechanism, where a pseudogap in the DOS is produced by the Fermi surface–Brillouin zone interactions. The results have shown that the DOS of the γ-Mg17Al12 phase exhibits a pronounced pseudogap centered almost exactly at εF, which is compatible with the theoretical prediction that this phase is stabilized by the Hume-Rothery mechanism. The disordered cubic β-Mg2Al3 phase is most likely entropically stabilized at high temperatures, whereas at lower temperatures stability is achieved by undergoing a structural phase transition to more ordered rhombohedral β′ phase at 214 ° C, where all atomic sites become fully occupied. No pseudogap in the vicinity of εF was detected for the β′ phase on the energy scale of a few 100 meV as determined by the ‘thermal observation window’ of the Fermi–Dirac function, so that the Hume-Rothery stabilization mechanism is not confirmed for this compound. However, the existence of a much broader shallow pseudogap due to several critical reciprocal lattice vectors that simultaneously satisfy the Hume-Rothery interference condition remains the most plausible stabilization mechanism of this phase. At Tc = 0.85 K, the β′ phase undergoes a superconducting transition, which slightly increases the cohesive energy and may contribute to relative stability of this phase against competing neighboring phases.

Hume-Rothery stabilization mechanism and e/a determination in MI-type Al–Mn, Al–Re, Al–Re–Si, Al–Cu–Fe–Si and Al–Cu–Ru–Si 1/1-1/1-1/1 approximants – a proposal for a new Hume-Rothery electron concentration rule

Full-potential linearized augmented plane wave (FLAPW) band calculations with subsequent FLAPW-Fourier analyses have been performed for five MI-type Al–TM (transition metal)-based 1/1-1/1-1/1 approximants in order to elucidate the origin of a pseudogap from the point of view of the Fermi surface–Brillouin zone (FsBz) interactions. The square of the Fermi diameter is determined from the Hume-Rothery plot to be close to 50 without exception in units of , where is the lattice constant. The FsBz interactions involving several reciprocal lattice vectors are claimed to be responsible for constituting the pseudogap structure across E F. This is referred to as the multi-zone effect. Among them, the wave, in which the Fourier coefficients are most evenly and densely distributed across E F, is selected as the critical one satisfying the matching condition . The d-states-mediated-splitting appears to be absent in spite of substantial occupations of TM-d states in the valence band. All MI-type approximants studied are found to obey the Hume-Rothery stabilization mechanism. A new Hume-Rothery electron concentration rule linking the number of atoms per unit cell, e/uc, with a critical reciprocal lattice vector is found to hold well for structurally complex intermetallic compounds obeying the Hume-Rothery stabilization mechanism.

Hume-Rothery stabilization mechanism and e/a determination for RT- and MI-type 1/1-1/1-1/1 approximants studied by FLAPW-Fourier analyses

Full-potential linearized augmented plane wave (FLAPW) electronic band calculations were performed for two RT- (rhombic triacontahedron) and five MI- (Mackay icosahedron) type 1/1-1/1-1/1 approximants plus several complex metallic compounds in Al-TM (TM = transition metal element) binary alloy systems in order to elucidate the origin of a pseudogap from the viewpoint of Fermi surface-Brillouin zone (FsBz) interactions. The square of the Fermi diameter (2k(F))(2) and square of the critical reciprocal lattice vector |G|(2) or the critical set of lattice planes, with which electrons at the Fermi level E(F) are interfering, can be extracted from the FLAPW-Fourier method. We revealed that a pseudogap in both RT- and MI-type 1/1-1/1-1/1 approximants universally originates from interference phenomenon satisfying the matching condition (2k(F))(2) = |G|(2) equal to 50 in units of (2π/a)(2), where a is the lattice constant. The multi-zone effect involving not only |G|(2) = 50 but also its neighboring ones is also claimed to be responsible for constituting a pseudogap across E(F). The value of e/a for Mn, Fe, Re and Ru elements in the periodic table is deduced to be positive in the neighborhood of unity. All 1/1-1/1-1/1 approximants, regardless of RT- or MI-type atomic cluster involved, are stabilized at around e/a= 2.7, while their counterpart quasicrystals are at around e/a= 2.2. A new Hume-Rothery electron concentration rule linking the number of atoms per unit cell, e/uc, with a critical|G|(2) holds well for all complex intermetallic compounds characterized by a pseudogap at E(F).

Origin of the DOS pseudogap and Hume–Rothery stabilization mechanism in RT-type Al48Mg64Zn48 and Al84Li52Cu24 1/1-1/1-1/1 approximants

Full-potential linearized plane wave (FLAPW) band calculations with subsequent FLAPW-Fourier analyses have been performed for two RT-type Al48Mg64Zn48 and Al84Li52Cu24 1/1-1/1-1/1 approximants containing 160 atoms per unit cell. The FLAPW-Fourier analysis revealed that the Fermi surface–Brillouin zone (FsBz) interactions involving more than two sets of lattice planes are responsible for the formation of a pseudogap across the Fermi level in both compounds. The most critical sets of lattice planes interfering with electrons at the Fermi level are deduced to be {543} + {710} + {550} with = 50 in the former and {631} with = 46 in the latter. The square of the Fermi diameter is determined to be 49.9 ± 0.1 and 47.1 ± 0.4 in units of , respectively, where a is the lattice constant. Hence, the matching condition holds well in both compounds. It is also shown that, while a shallow pseudogap in the Al48Mg64Zn48 approximant can be ascribed solely to the FsBz interactions, a much deeper one in the Al84Li52Cu24 approximant is explained as a superposition of the FsBz interactions and the formation of strongly directional bonding states between Cu-4p and Al-3p orbitals.

A comparative scanning tunneling spectroscopy investigation of the (12110)-surface of decagonal Al–Ni–Co and the (100)-surface of its approximant Y–Al–Ni–Co

We present a low-temperature scanning tunneling spectroscopy study of the local density of states (LDOS) on the (12110)-surface of the decagonal quasicrystal d–Al–Ni–Co and the (100)-surface of its structurally closely related approximant Y–Al–Ni–Co in the range of ±1 eV around the Fermi energy. The LDOS of both surfaces are dominated by a large parabolic pseudogap centered at the Fermi energy, which can be attributed to the Hume–Rothery stabilization mechanism or to an orbital hybridization. Superimposed on this large pseudogap, a spatially varying fine structure is revealed, whose spatial distribution correlates with the structures of both of the surfaces. This fine structure shows narrow peaks and pseudogaps exhibiting typical energy widths between 50 and 150 meV. The spatial extent of these localized states is of the order of the width of the topographic features, which is about 0.45 nm. Our findings show that specific electronic states are localized on equivalent topographic features regardless of the presence of periodic or quasiperiodic long-range order. We interpret this result as an indication that the fine structure in the LDOS is dominated much more by the complex short-range order than by the presence of the quasiperiodic long-range order.

Failure of the Hume-Rothery stabilization mechanism in theAg5Li8 gamma-brass studied by first-principles FLAPW electronic structure calculations

The first-principles FLAPW (full potential linearized augmentedplane wave) electronic structure calculations were performed for theAg5Li8 gamma-brass, which contains 52 atoms in a unit cell and has been known for many years asone of the most structurally complex alloy phases. The calculations were also made for itsneighboring phase AgLi B2 compound. The main objective in the present work is to examine if theAg5Li8 gamma-brass is stabilized at the particular electrons per atom ratioe/a = 21/13 in the same way as some other gamma-brasses likeCu5Zn8 and Cu9Al4, obeying the Hume-Rothery electron concentration rule. For this purpose, thee/a valuefor the Ag5Li8 gamma-brass as well as the AgLi B2 compound was first determined by means of the FLAPW-Fouriermethod we have developed. It proved that both the gamma-brass and the B2 compound possess ane/a value equal tounity instead of 21/13. Moreover, we could demonstrate why the Hume-Rothery stabilization mechanism fails for theAg5Li8 gamma-brass and proposed a new stability mechanism, in which the unique gamma-brassstructure can effectively lower the band-structure energy by forming heavily populatedbonding states near the bottom of the Ag-4d band.

Electronic structure of quasicrystalline compounds

Theoretical as well as many experimental means have been used to investigate the electronic structures of quasicrystalline compounds. In icosahedral quasicrystalline compounds a pseudo-gap at the Fermi level exists that is also present even at the surface. Its formation involves a Hume-Rothery stabilization mechanism and also Al-transition metal hybridization effects. The specific atomic arrangement in a hierarchy of interpenetrating clusters may also be invoked to participate in the formation of this pseudo-gap. For Al based decagonal quasicrystals containing transition metals, the d–d interaction is such that there is no pseudo-gap in the total density of states whereas it still exists in the Al sub-bands. The electronic states in the quasicrystals and their close approximants are of more localized-like character on both sides of the pseudo-gap than in regular intermetallics that signs a clear tendency to weak electron localization. Extended states are found more than 2 eV above and deep below the Fermi level. The pseudo-gap at the Fermi level is not a genuine characteristic of quasicrystalline compounds as it exists also in related crystalline alloys, but in conventional alloys of the same phase diagram it is less pronounced than in the quasicrystal. The Al 3p pseudo-gap is connected to the metallic character of the specimen since the larger and deeper the pseudo-gap, the less metallic is the sample. This may allow one to tune the metallic character through a series of compounds.

Investigation of the Hume–Rothery stabilization mechanism from ab initio band calculations for different electron compounds: Cu 5Zn 8 and Al–Mg–Zn, Al–Cu–Ru–Si approximants

The origin of the pseudogap formed across the Fermi level has been studied in relation to the Fermi surface–Brillouin zone interaction and the sp–d hybridization effect by performing the LMTO–ASA (Linear Muffin–Tin Orbital–Atomic Sphere Approximation) band calculations for the three electron compounds: the γ-phase Cu 5Zn 8 alloy, the free-electron-like Al 30Mg 40Zn 30 Frank–Kasper-type 1/1-1/1-1/1 approximant and the Al 68Cu 7Ru 17Si 8 Mackay–Icosahedral-type 1/1-1/1-1/1 approximant. We revealed that, in the free-electron-like Al–Mg–Zn approximant, the Fermi surface–Brillouin zone interaction is solely responsible for the formation of the pseudogap at the Fermi level. In the case of the γ-phase and the Al–Cu–Ru–Si approximant, where d-states are involved across the Fermi level, we have demonstrated that the Fermi surface–Brillouin zone interaction is still strong enough to produce the pseudogap near the Fermi level but that its depth and width are substantially enhanced by the sp–d hybridization effect which splits the d-states into the bonding and antibonding states across the Fermi level.

57Fe Mössbauer-effect studies of quadrupole splitting distributions in icosahedral Al-TM-Fe quasicrystals

Room temperature57Fe Mossbauer effect spectra of several Al-TM-Fe icosahedral quasicrystals are reported. Results of fits to discrete sites and to various distributions of quadrupole splittings are presented. Mean isomer shifts,\(\overline \delta \), and quadrupole splittings, Δ, are shown to be insensitive to the fitting procedure used. Trends in\(\overline \delta \) and\(\overline \Delta \) for the icosahedral phase may be indicative of a Hume-Rothery stabilization mechanism.