Early work on Laves phases in East Germany

Paufler, P.

doi:10.1016/j.intermet.2010.11.032

Cited by 37 publications

(43 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The C15 structure was first observed in a molecule structure by Friauf [19] and Laves (see, e.g., [42]). The fundamental structure of C15 is constructed from 24 vertices, listed in Table 1.…”

Section: Tablementioning

confidence: 93%

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

Räbinä¹,

Mönkölä²,

Rossi³

2015

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. We consider the computationally efficient time integration of Maxwell's equations using discrete exterior calculus (DEC) as the computational framework. With the theory of DEC, we associate the degrees of freedom of the electric and magnetic fields with primal and dual mesh structures, respectively. We concentrate on mesh constructions that imitate the geometry of the close packing in crystal lattices that is typical of elemental metals and intermetallic compounds. This class of computational grids has not been used previously in electromagnetics. For the simulation of wave propagation driven by time-harmonic source terms, we provide an optimized Hodge operator and a novel time discretization scheme with nonuniform time step size. The numerical experiments show a significant improvement in accuracy and a decrease in computing time compared to simulations with well-known variants of the finite difference time domain method.

show abstract

Section: Tablementioning

confidence: 93%

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

Räbinä¹,

Mönkölä²,

Rossi³

2015

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…cubic (cF24), hexagonal (hP12) and double-hexagonal (hP24) [2]. Since the discovery of this phase, more than a thousand binary and ternary Laves phase forming compounds with a range of interesting properties and varying crystal chemistry have been reported in the literature [4]. These attributes could be exploited to design single-phase or multiphase alloys [5] and thin films based on Laves phase [6].…”

Section: Introductionmentioning

confidence: 99%

Structure imaging and vanadium substitution in cubic TiCr₂Laves phase

Ghosh

Sharma

Basu

et al. 2015

Philosophical Magazine

View full text Add to dashboard Cite

Properties of Laves phase compounds can be tailored by alloying and microstructural engineering. V-substituted cubic TiCr 2 Laves phase has been studied to understand the location of V atoms in the lattice, by structural imaging and first-principle computations. Even though Ti, V and Cr appear next to each other in the periodic table, V preferentially replaces the Ti lattice producing anti-site defects. The defect formation energy for V substitution in Ti and in Cr lattice is 0.29 and 0.40 eV, respectively. V replacement in the Ti lattice generates atomic scale strain. Atomic numbers of V, Ti and Cr being very close, this phase is not quite suitable for incoherent imaging for understanding the structure and the chemistry. Instead, difference in channelling behaviour of electron waves along the Ti columns and along the Cr columns could be exploited to preferentially image the individual atom columns. Nature of the exit phase wave, phase and amplitude has been used to understand the contrast qualitatively. The intensity distribution of any particular atom column that is disturbed by the presence of foreign atom has been used to detect the position of V atoms. This method could be extended to study other Laves phases and complex intermetallic structures to understand their structure, defects and interfaces. IntroductionLaves phases, a group of topologically close-pack hard intermetallic compounds with AB 2 stoichiometry, are known to form at a particular radius ratio of A and B (r A /r B = 1.22) atoms [1]. However, a considerable deviation from ideal radius ratio (r A /r B = 1.05-1.67) [2] is observed in practice and the phase can often accommodate non-stoichiometry [3]. There are three allotropic polymorphs of Laves phase i.e. cubic (cF24), hexagonal (hP12) and double-hexagonal (hP24) [2]. Since the discovery of this phase, more than a thousand binary and ternary Laves phase forming compounds with a range of interesting properties and varying crystal chemistry have been reported in the literature [4]. These attributes could be exploited to design single-phase or multiphase

show abstract

“…This provided the final (U B) Al -matrix and the corresponding cubic cell parameter: a Al = (4.0550 ± 0.0005) Å at ambient temperature. The actual U B-matrices for the four η orientational variants were then established by the use of Equation (2). Sets of intensity profiles of η could then accurately be measured in various scan modes using the point detector.…”

Section: Methodsmentioning

confidence: 99%

“…It is the prototype Laves structure (C14 in Strukturbericht designation) [2]. The Guinier-Preston zones, formed in the initial stage of the precipitation process, are not explicitly considered in this work, where the main focus is on average structural description(s) of the equilibrium phase precursors; the so-called η .…”

Section: Introductionmentioning

confidence: 99%

Average crystal structure(s) of the embedded meta stableη′-phase in the Al–Mg–Zn system

Larsen

Thorkildsen

Natland

et al. 2014

Philosophical Magazine

View full text Add to dashboard Cite

Meta stable embedded nano-sized η -particles within a single grain extracted from an alloy having the nominal composition Al 0.88 Zn 0.10 Mg 0.02 have been examined with X-ray diffraction. By applying the orientational and metric relationships that exist between the hexagonal unit cell of the η -particles and the cubic unit cell of the Al-matrix, it has been proven possible to directly collect diffracted intensity data from the η -particle ensemble. This has been done using synchrotron radiation and a κ-diffractometer having a scintillator point detector setup. The approach has resulted in improved data quality compared to previous experiments. The interpretation of the data set, based on a combination of Patterson syntheses, direct methods and geometrical restraints, yielded two possible average structural representations: one Al-rich with the approximate stoichiometric composition Mg 2 Zn 5 Al 2 and one Al-depleted with approximate stoichiometric composition Mg 2 Zn 7 Al. Both structures are realized in the same space group, P6 3 /mmc, and are most probably superimposed in the crystalline system examined. The geometries are discussed within the atomic environment approach where icosahedral or near-icosahedral configurations are encountered. Comparison with previous published models and the equilibrium structure reveals a main difference related to the distribution of the Zn-sites in the unit cell. A possible transformation path is also suggested. Various aspects and challenges regarding data collection, data reduction and data quality are specifically addressed.

show abstract

Early work on Laves phases in East Germany

Cited by 37 publications

References 72 publications

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

Structure imaging and vanadium substitution in cubic TiCr₂Laves phase

Average crystal structure(s) of the embedded meta stableη′-phase in the Al–Mg–Zn system

Contact Info

Product

Resources

About

Early work on Laves phases in East Germany

Cited by 37 publications

References 72 publications

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences

Structure imaging and vanadium substitution in cubic TiCr2Laves phase

Average crystal structure(s) of the embedded meta stableη′-phase in the Al–Mg–Zn system

Contact Info

Product

Resources

About

Structure imaging and vanadium substitution in cubic TiCr₂Laves phase