Fermi surface-Brillouin Zone Interaction Research Articles

From simple to complex crystal chemistry in the RE-Au-Tt systems (RE = La, Ce, Pr, Nd; Tt = Ge, Pb).

Polar intermetallics are an intriguing class of compounds with complex relationships between composition and structure that are not fully understood. This work reports a systematic study of the underexplored ternary composition space RE-Au-Tt (RE = La, Ce, Pr, Nd; Tt = Ge, Pb) to expand our knowledge of the intriguing chemistry and diversity achievable with these metallic constituents. These composition spaces are particularly interesting because of the potential to find Au-bearing, highly polar intermetallic compounds. The elements were first reacted through arc welding under an inert atmosphere, followed by annealing at 850 °C. X-ray diffraction of the products identified seven unreported compounds ranging from the simple NaTl-type compounds La1.5Au2Pb0.5 and Nd2-x Au2Pb x to the more structurally complex La5AuPb3 in the Hf5CuSn3-type structure and Pu3Pd4-type RE3Au3Ge (RE = La, Ce, Pr, Nd). First-principles electronic structure calculations investigate the combination of Fermi surface-Brillouin zone interactions, electrostatic interactions, and delocalized metallic bonding that contributes to the formation of these phases. These calculations show that a mixture of electrostatic and metallic bonding plays a dominant role in these phases. The RE-Au-Tt composition space remains full of potential for discovering materials with relevant magnetic and quantum properties, provided the crystal chemistry can be comprehended.

Electron-Poor Polar Intermetallics: Complex Structures, Novel Clusters, and Intriguing Bonding with Pronounced Electron Delocalization.

Intermetallic compounds represent an extensive pool of candidates for energy related applications stemming from magnetic, electric, optic, caloric, and catalytic properties. The discovery of novel intermetallic compounds can enhance understanding of the chemical principles that govern structural stability and chemical bonding as well as finding new applications. Valence electron-poor polar intermetallics with valence electron concentrations (VECs) between 2.0 and 3.0 e-/atom show a plethora of unprecedented and fascinating structural motifs and bonding features. Therefore, establishing simple structure-bonding-property relationships is especially challenging for this compound class because commonly accepted valence electron counting rules are inappropriate. During our efforts to find quasicrystals and crystalline approximants by valence electron tuning near 2.0 e-/atom, we observed that compositions close to those of quasicrystals are exceptional sources for unprecedented valence electron-poor polar intermetallics, e.g., Ca4Au10In3 containing (Au10In3) wavy layers, Li14.7Mg36.8Cu21.5Ga66 adopting a type IV clathrate framework, and Sc4MgxCu15-xGa7.5 that is incommensurately modulated. In particular, exploratory syntheses of AAu3T (A = Ca, Sr, Ba and T = Ge, Sn) phases led to interesting bonding features for Au, such as columns, layers, and lonsdaleite-type tetrahedral frameworks. Overall, the breadth of Au-rich polar intermetallics originates, in part, from significant relativistics effect on the valence electrons of Au, effects which result in greater 6s/5d orbital mixing, a small effective metallic radius, and an enhanced Mulliken electronegativity, all leading to ultimate enhanced binding with nearly all metals including itself. Two other successful strategies to mine electron-poor polar intermetallics include lithiation and "cation-rich" phases. Along these lines, we have studied lithiated Zn-rich compounds in which structural complexity can be realized by small amounts of Li replacing Zn atoms in the parent binary compounds CaZn2, CaZn3, and CaZn5; their phase formation and bonding schemes can be rationalized by Fermi surface-Brillouin zone interactions between nearly free-electron states. "Cation-rich", electron-poor polar intermetallics have emerged using rare earth metals as the electropositive ("cationic") component together metal/metalloid clusters that mimic the backbones of aromatic hydrocarbon molecules, which give evidence of extensive electronic delocalization and multicenter bonding. Thus, we can identify three distinct, valence electron-poor, polar intermetallic systems that have yielded unprecedented phases adopting novel structures containing complex clusters and intriguing bonding characteristics. In this Account, we summarize our recent specific progress in the developments of novel Au-rich BaAl4-type related structures, shown in the "gold-rich grid", lithiation-modulated Ca-Li-Zn phases stabilized by different bonding characteristics, and rare earth-rich polar intermetallics containing unprecedented hydrocarbon-like planar Co-Ge metal clusters and pronounced delocalized multicenter bonding. We will focus mainly on novel structural motifs, bonding analyses, and the role of valence electrons for phase stability.

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 stabilisation mechanism and d-states-mediated Fermi surface–Brillouin zone interactions in structurally complex metallic alloys

The stability of Co2Zn11 and Al8V5 gamma-brasses, both of which are composed of a transition metal element and polyvalent elements Zn or Al, can be discussed in terms of d-states-mediated Fermi surface–Brillouin zone (FsBz) interactions in the context of first-principles full-potential linearised augmented plane wave (FLAPW) band calculations. A FsBz-induced pseudogap is revealed in the FLAPW-Fourier spectrum, though it is hidden behind a much larger d-band in the total density of states. The stability range of three families of complex metallic alloys (CMAs) that include gamma-brasses, RT-, MI- and Tsai-type 1/1-1/1-1/1 approximants and 2/1-2/1-2/1 approximant, each of which is characterised by = 18, 50 and 125, respectively, can be well scaled in terms of the number of electrons per unit cell (e/uc) given by the product of the number of atoms per unit cell and the e/a value determined by the Hume-Rothery plot on the basis of the FLAPW-Fourier method. This is taken as the evidence for the justification of the Hume-Rothery stabilisation mechanism for all these CMAs having a pseudogap at the Fermi level.

On the parameters of glass formation in metallic systems

We have recently noted the structural similarities between the dominant clusters of bulk metallic glasses (BMGs) with those present in icosahedral phase and intermetallics with large unit cell volume based on the diffraction studies available in literature. Latter belongs to any one of the five space groups. These are I4/ mcm (tI12), P6/ m (hP68), Fddd (oF48), Fd3 m (cF24) and an orthorhombic structure (Al 11Sm 3) whose space group is not known. We are unaware of such discussion in literature. We also present a Venn diagram based on compositionally dependent and independent parameters to classify the BMG alloy systems. It has been observed that there are two distinct categories of BMGs. One class displays Fermi surface–brillouin zone interaction whereas the other does not follow this criterion. We believe that such a classification will be helpful in knowing their characteristics with respect to some of their applications.

Simple metals at high pressure: the Fermi sphere – Brillouin zone concept

Crystal structure sequences at high pressure are analyzed for simple sp-elements and some binary alloys. Structure stability in these metals is related to effects of Fermi surface Brillouin zone (FS-BZ) interactions [1]. These effects increase under pressure and lead to formation of structures with a decrease of symmetry and packing density. Structural similarities of alkali and alkali-earth metals to polyvalent group IV and V elements under pressure are considered. Correlations between structural and physical properties (resistivity and superconductivity) for these metals are discussed within the model of FS-BZ interactions. Complex high-pressure structure Li cI16 [2] is considered as Hume-Rothery phase of gamma-brass type in the Cu-Zn alloy system. The underlying physics relates to formation of BZ by 24 planes with wave vector q211 close to 2kF (here kF is FS radius) accommodating well the FS (see Figure). The filling of BZ by electron states is ∼89%. These characteristics define specific physical properties of the Li cI16 phase.

Origin of the complex crystal structures of elements at intermediate pressure

We present a unifying theory for the observed complex structures of sp-bonded elements under pressure on the basis of nearly free electron picture. In the intermediate pressure regime, the dominant contribution to crystal structure arises from Fermi-surface Brillouin zone interactions—structures which allow this are favoured. This simple theory explains the observed crystal structures, transport properties and the evolution of internal and unit cell parameters with pressure and appears to hold for elements in groups I–VI. We illustrate it with experimental data for these elements and ab initio calculations for Li.

Orbital hybridizations versus the Fermi surface–Brillouin zone interaction in strongly hybridizingAl−Li−Cu1∕1−1∕1−1∕1approximant

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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.

Determination of Spatially Hybridized Charge Distribution and its Effect on Electron Transport in the Al-Cu-Ru-Si 1/1-Approximant ---Theoretical Basis for the Hume-Rothery rule---

AbstractThe origin of the pseudogap across the Fermi level was investigated by analyzing the electronic structure calculated in the framework of the LMTO-ASA method for the RT-type Al-Mg-Zn and MI-type Al-Cu-Ru-Si 1/1-approximants. The pseudogap in the former is proved to originate from the interaction of electronic states with the Brillouin zone planes associated with reciprocal lattice vectors matching with the Fermi sphere in the extended zone scheme. In the latter, the Fermi surface-Brillouin zone interaction coupled with the hybridization effect between the Al-3p and transition metal d-states produces a deep pseudogap at the Fermi level. The real-space charge distribution for electrons at the Fermi level is calculated for the Al-Cu-Ru-Si 1/1-approximant. The charge distribution thus obtained could explain not only the possession of a large resistivity of this approximant but also evidenced that the icosahedral clusters play a key role in reducing the electronic energy in favor of quasicrystalline and approximant phases.

Role of the pseudogap in the electron transport of quasicrystals and their approximants

There are two routes in the opening of the pseudogap: one due to the band separation in a disordered system such as expanded liquid mercury and amorphous alloys and the other due to the Fermi surface-Brillouin zone interaction in quasicrystals and their approximants. The role of the pseudogap in the electron transport has been studied by plotting resistivities at 4.2 and 300 K against the electronic specific heat coefficient for a total of 49 quasicrystals and their approximants on the log-log diagram in comparison with those for the amorphous alloys. Among them, 32 data points are for sp-electron quasicrystals and their approximants like Al-Mg-Zn, Al-Li-Cu, Mg-Zn-Ga while 17 data points are for the Mackay icosahedral-type quasicrystals like Al-Cu-Fe and Al-Cu-Ru. All the data except for the Al-Pd-Re quasicrystal of high quality are found to fall on a straight line with a slope of -2. Whether or not the data for the Al-Pd-Re quasicrystal of high quality can be treated on the same footing is left for further investigation. From this we conclude that the resistivity changes in proportion to the square of the density of states (DOS) at the Fermi level in conformity with the Mott theory for all systems characterized by the pseudogap across the Fermi level.

Hybridization Effect On Electron Transport Properties Of Rhombic Triacontahedral-Type Al60-xMg40Xx. (X = Zn, Cu, Ag, and Pd) 1/1-Cubic Approximants

AbstractWe have measured in this experiment the XPS (x-ray photoemission spectroscopy) and SXES (soft x-ray emission spectroscopy) valence spectra, the electrical resistivity, the Hall coefficient and the Rietveld structural analysis for a series of the RT-type (Rhombic Triacontahedron) Al60-xMg40Xx (X = Zn, Cu, Ag and Pd; x = 5 - 40) 1/1-approximants. The electrical resistivity at 300 K is successfully analyzed in terms of the carrier concentration per atom e/a and the ratio of the lattice constant over the “ideal” lattice constant defined as LCR. The latter is chosen as a quantitative measure of the degree of the hybridization between Al and transition metal elements Cu, Ag and Pd. We show that a sharp resistivity increase with increasing the concentration of the transition metal element can be attributed to the deepening of the pseudogap at the Fermi level, which is brought about by the combination of the Fermi surface-Brillouin zone interaction and the growth of the hybridization effect.

Electronic structure and elastic properties of Au/Cr(001) superlattices.

We present a first-principles calculation of the electronic structure and elastic properties of a series of Au/Cr(001) superlattices with modulation wavelengths between 30 and 60 \AA{}. The electronic-structure calculations are performed with the linear muffin-tin-orbital method in the atomic-sphere approximation. Results for the density of states and the charge transfer at the interfaces as a function of the modulation wavelength are presented. The force theorem has been used in the investigation of the elastic behavior of the system. We have performed a detailed analysis of the variation of the band contribution to the shear elastic constant ${\mathit{c}}_{44}$, with particular reference to the Fermi-surface contribution. This analysis allows us to investigate the role of the electronic-structure variations induced by layering in the elastic anomalies experimentally observed in metallic superlattices. We show that the origin of the enhancement of the ${\mathit{c}}_{44}$ elastic constant observed in Au/Cr at small modulation wavelengths cannot be ascribed to a Fermi-surface Brillouin-zone interaction mechanism.

Electronic specific heat measurements for quasicrystals and Frank-Kasper crystals in Mg-Al-Ag, Mg-Al-Cu, Mg-Al-Zn, Mg-Ga-Zn and Al-Li-Cu alloy systems

The electronic specific heat coefficient was measured for sp electron quasicrystals and the corresponding Frank-Kasper crystals in Mg-Al-Ag, Mg-Al-Cu, Mg-Al-Zn, Mg- Ga-Zn and Al-Li-Cu alloy systems. It turned out that the ratio gamma exp/ gamma F plotted against the average number of electrons per atom is essentially identical between the quasicrystalline and Frank-Kasper phases: it decreases with decreasing electron concentration per atom, e/ a, and is extrapolated to zero at about e/a=2.0. A unique e/a dependence of the gamma exp/ gamma F in the Frank-Kasper phase is discussed in terms of the Fermi surface-Brillouin zone interaction specific to this structure. Judging from the identical e/a dependence of gamma exp/ gamma F the authors conclude that a similar Fermi surface-Brillouin zone interaction ought to be essential in determining the density of states at the Fermi level in the quasicrystalline phase. The electronic structure near the Fermi level is essentially determined by the local atomic structure, which happens to be similar between these two intriguing phases.

Electronic structure and transport properties of sp-electron quasicrystals in comparison with the Frank-Kasper crystals and amorphous alloys

The electron transport properties and the density of states at E F have been studied on various sp-electron quasicrystals (QC) and Frank-Kasper (FK) crystals. A comparison was made with the data for sp-electron amorphous alloys. A similarity with amorphous alloys is found in the magnitude of ϱ, the interrelation between γ and ϱ and the ϱ - T dependence. This is attributed to the breakdown of the Bloch condition. On the other hand, a similarity with the FK crystals is found in the γ versus e / a relation. A Fermi surface-Brillouin zone interaction similar to that in FK crystals is suggested. It is concluded that QCs exhibit features characteristic of an amorphous alloy or of a crystal, depending on the electronic properties studied.

Electronic properties of icosahedral quasicrystals in Mg-Al-Ag, Mg-Al-Cu and Mg-Zn-Ga alloy systems

The electronic structure and the electron transport properties of sp-electron quasicrystals have been studied, using in total, 20 quasicrystals in the three alloy systems Mg-Al-Ag, Mg-Al-Cu and Mg-Zn-Ga. The authors revealed that the temperature dependence of the electrical resistivity changes its characteristic features with increasing resistivity in the same manner as that in the nonmagnetic amorphous alloys. This is apparently consistent with the generalised Faber-Ziman theory, but this simple model poses difficulties in explaining a definite increase in the resistivity upon improvement in the quasicrystallinity, brought about by the heat-treatment of the Mg39.5Zn40Ga20.5 quasicrystal. The Hall coefficient exhibits the sizable temperature dependence when its magnitude deviates from the free electron value, suggesting the important role of the Fermi surface-Brillouin zone interaction. The temperature dependence of the thermoelectric power below 300 K is found to be nonlinear, as opposed to a more linear one in the amorphous alloy. The electronic specific heat coefficient plotted against the electron concentration e/a exhibits a universal trend regardless of the alloy system and decreases with decreasing e/a from the free electron value to about one-third of the free electron value. It is noted that a thermally stable quasicrystal apparently possesses a reduced electronic specific heat coefficient.

Electronic and Mechanical Properties of DC Sputtered Compositionally Modulated Metal Films

ABSTRACTWe describe a recently constructed apparatus for the measurement of the Young's modulus and Poisson's ratio of free-standing sputtered multilayer films. In comparison with more conventional methods, this is expected to permit both measurement with lower uncertainties and interpretation which is more straightforward. A separate apparatus for the accurate measurement of the conductivity, magnetoresistance, and Hall coefficient of such systems has been prepared which will enable the contribution of Fermi surface-Brillouin zone interactions to the behaviour of these materials to be assessed.

Experimental observation of the fermi surface–Brillouin zone interaction in pure zinc by means of X‐ray photoelectron spectroscopy

AbstractThe 4s–4p valence band of pure zinc is studied by means of X‐ray photoelectron spectroscopy. A fine structure is revealed near the Fermi edge and interpreted in terms of the van Hove singularity due to the Fermi surface–Brillouin zone interaction. The observed peak is attributed to the Fermi surface contacts with the {10.1} zone planes, combined with the electron overlaps across the {10.0} zone planes. This supports the model proposed in the interpretation of the trends of the electronic specific heat coefficients in the h.c.p. Hume‐Rothery alloy phases.

Anomalies in the enthalpy of mixing in alpha-phase indium-tin due to brillouin zone effects

Enthalpies of crystallization have been measured for indium-tin alloys containing 7–9 at.% tin using differential thermal analysis (DTA). From the values obtained the enthalpies of mixing, ΔH m' in the solid state were calculated. In the ΔH m vs. composition curve there is a change in slope at 7.80 at.% tin, a maximum at 8.10% and a sharp minimum at 8.31%. This behaviour is qualitatively explained by varying electronic and lattice energies in connection with Fermi surface-Brillouin zone interaction. New pieces of Fermi surface in the third zone are assumed to appear at 8.10 at.% tin. The height of the dip is about 1.2 meV atom .

Fermi surface-brillouin zone effect in f.c.c. BiTl alloys

Anomalies in the lattice parameter, superconducting and thermo-electric properties vs. composition in f.c.c. BiTl alloys indicate that a kind of Fermi surface-Brillouin zone interaction occurs.