Inversion of Cubic de Haas-van Alphen Data, with an Application to Palladium

Mueller, F. M.; Priestley, M. G.

doi:10.1103/physrev.148.638

Cited by 113 publications

(29 citation statements)

References 4 publications

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“…Because of the additional rotational axes between the pole and the equator on the unit sphere, the point groups T h , O h and Y h require polyhedral (disdodecahedral, hexoctahedral and icosahedral) harmonics X L which are linear combinations of Sf with fixed / and variable m. The whole family of X L for the cubic crystal classes T, T h , O, T d and O h is called "cubic harmonics" by Kurki-Suonio and coworkers [65,66,43], consistent with our nomenclature, while Fox and Krohn [97] restrict it so far to T d (also "tetrahedral harmonics" [58]) and O h , and Mueller and Priestley [98] even to O h alone. Von der Lage and Bethe [70] use the term "kubic harmonics" for the lattice harmonics A kL of the space group 0\ = im 3m for k = 0 and k=(n/a)e z .…”

Section: Laue Class (Point Group)mentioning

confidence: 76%

Three-Dimensional Reciprocal Form Factors and Momentum Densities of Electrons from Compton Experiments I. Symmetry-Adapted Series Expansion of the Electron Momentum Density

Heuser-Hofmann

Weyrich

1985

Zeitschrift Für Naturforschung A

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All methods of reconstruction of the electron momentum density from Compton scattering data are based on a series expansion of this density in terms of symmetry-adapted surface spherical harmonics (polyhedral harmonics). Owing to the improvements of y-ray and X-ray Compton spectrometers during the last few years, measurements of Compton spectra of single crystals in a shorter time and with higher angular resolution have become feasible. Therefore, in addition to the current studies, an increased number of investigations of a greater variety of crystals with large sets of directional data will soon be performed. This work is at first concerned with the accurate and efficient computation of associated Legendre functions of the first kind, Pf, with high / and m and for the whole range of their real argument, which are needed for the description of data with high angular resolution. We further show that electron momentum densities obey Laue-class symmetries in the case of crystals and point-group symmetries with an inversion centre in general, in absence of external magnetic fields. All necessary information about the polyhedral harmonics belonging to the totally symmetric representations of these point groups is given, with particular emphasis on the group O h for which the hexoctahedral harmonics with I ^ 20 are displayed graphically. In addition, the locations of the extrema on the unit sphere are tabulated.

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Section: Laue Class (Point Group)mentioning

confidence: 76%

Three-Dimensional Reciprocal Form Factors and Momentum Densities of Electrons from Compton Experiments I. Symmetry-Adapted Series Expansion of the Electron Momentum Density

Heuser-Hofmann

Weyrich

1985

Zeitschrift Für Naturforschung A

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“…Such quantities, denoted here as f(p), can be expressed as a series of lattice harmonics F l, (,) of an appropriate symmetry [1,2] (1)…”

Section: Original Papermentioning

confidence: 99%

“…Such quantities, denoted here as f(p), can be expressed as a series of lattice harmonics F l, (,) of an appropriate symmetry [1,2] (1) where  distinguishes harmonics of the same order and (,) are the azimuthal and polar angles of the direction p with respect to the reciprocal lattice coordinate system. Isotropic distributions f 0 (p) (f(p) averaged over angles (,)) are used in calculating many physical properties, e.g.…”

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confidence: 99%

Isotropic distributions in hcp crystals

Kontrym‐Sznajd

2015

Nukleonika

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This paper is devoted to the studies of the isotropic average of quantities in the momentum space having the full symmetry of the Brillouin zone. Such quantities, denoted here as f(p), can be expressed as a series of lattice harmonics F l, (,) of an appropriate symmetry [1,2] (1) where  distinguishes harmonics of the same order and (,) are the azimuthal and polar angles of the direction p with respect to the reciprocal lattice coordinate system. Isotropic distributions f 0 (p) (f(p) averaged over angles (,)) are used in calculating many physical properties, e.g. the specifi c heat and Debye temperature [1,[3][4][5][6][7] and density of states in disorder systems [8,9], or (in some particular cases) in probing electron momentum densities via angular correlation of annihilation radiation (ACAR) [10,11], Compton scattering [12][13][14][15][16][17][18][19][20][21][22], and Doppler broadening spectra [23].In the previous paper, devoted to the cubic structures [24], we showed that for calculating the isotropic component, the common procedure of applying high symmetry directions (HSD) is the worst choice (the same occurs for the anisotropic components). In this paper, similar considerations are performed for the hcp structure, although obtained results may be generalized on all structures with the unique R-fold axes. For such structures with R = 6, 4, and 3 (hcp, tetragonal, and trigonal symmetry, respectively), the lattice harmonics having the full symmetry of the Brillouin zone have a very simple form: Isotropic distributions in hcp crystalsGrażyna Kontrym-Sznajd Abstract. Some anisotropic quantities in crystalline solids can be determined from their knowledge along a limited number of sampling directions. The importance of the choice of such directions is illustrated on the example of estimating, from angular correlation of annihilation radiation data, the isotropic electron momentum density in Gd.

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“…Using the fact that the momentum distribution p(p) must remain invariant under all operations of the point group of the crystal, p(p) may be expanded in lattice harmonics of the proper symmetry; for a cubic crystal these functions are the cubic harmonics [12] From (4) it is straight forward to show that the Compton profile can also be expanded in a series of cubic harmonics [13,2] (hkl) denotes [19] hereafter denoted HF1 and (ii) by Angonoa et al [1] hereafter denoted HF2. The third approach is a full potential augmented plane wave FLAPW calculation by Blaas [3].…”

Section: Specimensmentioning

confidence: 99%

Electron Compton scattering in a symmetric two-beam scattering geometry

Jonas

Schattschneider

1993

Microsc. Microanal. Microstruct.

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Abstract. 2014 The aim of this work is to present an experimental procedure to measure directional Compton profiles by means of electron energy-loss spectroscopy in the transmission electron microscope. In order to obtain unique profiles with a well defined orientation in momentum space a symmetric two-beam scattering geometry taking advantage of crystal symmetry was developped. Measurements on single crystal silicon are discussed in comparison to results of other Compton scattering techniques and theoretical calculations.

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Inversion of Cubic de Haas-van Alphen Data, with an Application to Palladium

Cited by 113 publications

References 4 publications

Three-Dimensional Reciprocal Form Factors and Momentum Densities of Electrons from Compton Experiments I. Symmetry-Adapted Series Expansion of the Electron Momentum Density

Three-Dimensional Reciprocal Form Factors and Momentum Densities of Electrons from Compton Experiments I. Symmetry-Adapted Series Expansion of the Electron Momentum Density

Isotropic distributions in hcp crystals

Electron Compton scattering in a symmetric two-beam scattering geometry

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