Aluminum is considered to approach an "ideal" metal or free electron gas. The valence electrons move freely, as if unaffected by the presence of the metal ions. Therefore, the electron redistribution due to chemical bonding is subtle and has proven extremely difficult to determine. Experimental measurements and ab initio calculations have yielded substantially different results. We applied quantitative convergent-beam electron diffraction to aluminum to provide an experimental determination of the bonding electron distribution. Calculation of the electron distribution based on density functional theory is shown to be in close agreement. Our results yield an accurate quantitative correlation between the anisotropic elastic properties of aluminum and the bonding electron and electrostatic potential distributions.

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Al-Fe-Si intermetallic particlesinboth unmodified and highly modified sand-cast eutectic Al-11.7pct Si alloys were characterizedusing scanning and transmission electron microscopy,energy-dispersive X-ray spectroscopy,and convergent beam and selected area electron diffraction. The only twoAl-FeSi intermetallics observed in this particulara lloy are (1) ''Chinese-script''m orphology,c onsistent with ad escription of body-centered cubic a -Al 19 Fe 4 MnSi 2 and (2) plate-shaped, consistent with tetragonal d -Al 3 FeSi 2 .T he authors are unaware of any otherc haracterization of d -Al 3 FeSi 2 using convergent beam electron diffraction (CBED) and selected area diffraction (SAD) techniques.

This article begins with pure aluminum and a discussion of the form of the crystal structure and different unit cells that can be used to describe it. Measurements of the face-centered cubic lattice parameter and thermal expansion coefficient in pure aluminum are reviewed and parametrizations are given which allow the reader to evaluate them across the full range of temperatures where aluminum is a solid. A new concept called the “vacancy triangle” is introduced and demonstrated as an effective means for determining vacancy concentrations near the melting point of aluminum. The Debye–Waller factor, quantifying the thermal vibration of aluminum atoms in pure aluminum, is reviewed and parametrized over the full range of temperatures where aluminum is a solid. The nature of interatomic bonding and the history of its characterization in pure aluminum are reviewed with the unequivocal conclusion that it is purely tetrahedral in nature. The crystallography of aluminum alloys is then discussed in terms of all of the concepts covered for pure aluminum, using prominent alloy examples. The electron density domain theory of solid-state nucleation and precipitate growth is introduced and discussed as a new means of rationalizing phase transformations in alloys from a crystallographic point of view.

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Current X-ray diffraction techniques intended for "ideally imperfect" specimens provide structure factors only on a relative scale and ever-present multiple scattering in strong low-angle Bragg reflections is difficult to correct. Multiple scattering is implicit in the quantitative convergent beam electron diffraction (QCBED) method, which provides absolutely scaled structure factors. Conventional single crystal X-ray diffraction has proved adequate in softer materials where crystal perfection is limited. In hard materials, the highly perfect nature of the crystals is often a difficulty, due to the inadequacy of the conventional corrections for multiple scattering (extinction corrections). The present study on alpha-Al2O3 exploits the complementarity of synchrotron X-ray measurements for weak and medium intensities and QCBED measurement of the strong low-angle reflections. Two-dimensional near zone axis QCBED data from different crystals at various accelerating voltages, thicknesses, and orientations have been matched using Bloch-wave and multislice methods. The reproducibility of QCBED data is better than 0.5%. The low-angle strong QCBED structure factors were combined with middle and high-angle extinction-free data from synchrotron X-ray diffraction measurements. Static deformation charge density maps for alpha-Al2O3 have been calculated from a multipole expansion model refined using the combined QCBED and X-ray data.

A new way of filtering electron diffraction patterns has been discovered. Patterns from slightly different specimen thicknesses beyond the mean free path for inelastic scattering are subtracted. Only thickness sensitive information (dominantly elastic) remains. Thermal diffuse scattering and Borrmann effects are removed in addition to the inelastic signal eliminated by conventional energy filtering. One application is quantitative convergent beam electron diffraction without an energy filter. Structure factors for alpha - Al(2)O(3) have been measured with an average uncertainty of 0.25%.

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