The metallic bond in aluminium
PNH Nakashima1,2,3, AE Smith2,4, J Etheridge1,3, BC Muddle2,3.
1. Monash Centre for Electron Microscopy, Monash University, Victoria 3800, Australia.
2. ARC Centre of Excellence for Design in Light Metals, Monash University, Victoria 3800, Australia.
3. Department of Materials Engineering, Monash University, Victoria 3800, Australia.
4. School of Physics, Monash University, Victoria 3800, Australia.
[email protected]
Keywords: Differential QCBED, DFT, Bonding Electron Density
The nature of the metallic bond in aluminium has been a mystery for more than 80 years. There
have been about 30 experimental and theoretical studies of the electron density distribution in
aluminium since the 1920s [1] and the spread of conclusions about the nature of the metallic bond
in this excellent approximation to an ideal free electron gas metal can be seen in figure 1.
The central problem of past experimental studies (all by X-ray diffraction) is the lack of sensitivity
to the very subtle redistribution of electrons in the formation of interatomic bonds. The peak
bonding density in aluminium is of the order of 0.05e-Å-3 (as per the density scale in figures 1 and
2). This is more than an order of magnitude smaller than the peak bonding density in diamond for
example (~0.65e-Å-3), a material in which bonding was very accurately characterised by X-ray
diffraction almost 50 years ago [2].
Quantitative convergent beam electron diffraction (QCBED) is now a well-established technique
for probing bonding in small unit cell materials [3]. Even though it eliminates the extinction and
scale problems of X-ray diffraction [4], the inability of even the most sophisticated energy-filtering
optics to remove all effects of inelastic scattering has limited QCBED’s accuracy and precision.
The advent of differential QCBED [1, 5 – 8] has allowed more complete extraction of the bonding
information contained in near-zone axis CBED patterns and paved the way to solving the mystery of
the metallic bond in aluminium. This most recent work, accompanied by a density functional theory
(DFT) calculation, concluded that the bonding electron density is centred entirely in the tetrahedral
interstices of aluminium (see figure 2).
The inherent difficulty of studying bonding in metals in general has led to widespread boycotting
of the description of metallic bonds in high school and university textbooks [9 – 11] and even
arguments to remove the term “metallic bond” from the physico-chemical vernacular altogether [12].
With the increased experimental sensitivity of differential QCBED and rapid advances in solid state
theory, the type of work described here may help save the metallic bond from obscurity. This paper
will describe the key aspects of the differential QCBED method and its application here to aluminium
and related materials.
References
[1] PNH Nakashima, AE Smith, J Etheridge and BC Muddle, Science 331 (2011), p. 1583.
[2] B Dawson, Proc. R. Soc. London A 298 (1967), p. 264.
[3] JM Zuo, Rep. Prog. Phys. 67 (2004), p. 2053.
[4] P Coppens, “X-ray Charge Densities and Chemical Bonding”, (Oxford Univ. Press, New York,
1997).
[5] PNH Nakashima, Phys. Rev. Lett. 99 (2007), 125506.
[6] PNH Nakashima and BC Muddle, Phys. Rev. B 81 (2010), 115135.
[7] PNH Nakashima and BC Muddle, J. Appl. Cryst. 43 (2010), p. 280.
[8] PA Midgley, Science 331 (2011), p. 1528.
[9] B Silvi and C Gatti, J. Phys. Chem. A 104 (2000), p. 947.
[10] WB Jensen, J. Chem. Ed. 86 (2009), p. 278.
[11] JM de Posada, Science Ed. 83 (1999), p. 423.
[12] JC Schön, Angew. Chem. Int. Ed. Engl. 34 (1995), p. 1081.
[13] H Bensch, H Witte and E Wölfel, Z. Phys. Chem. 4 (1955), p. 65.
[14] JP Walter, CY Fong and ML Cohen, Solid St. Commun. 12 (1973), p. 303.
[15] E Rantavuori and V-P Tanninen, Phys. Scr. 15 (1977), p. 273.
[16] S Chakraborty, A Manna and AK Ghosh, Phys. Status Solidi B 129 (1985), p. 211.
[17] The authors thank the Australian Research Council for funding (LE0454166 and FT110100427
– PNHN). PNHN thanks Prof. JM Zuo for sharing his program RefineCB. We are grateful to the
Victorian Partnership for Advanced Computing.
Figure 1. (A – D) 3-D plots of the bonding electron density in aluminium as determined by 4 examples from
the literature (A and C: X-ray diffraction experiments [13] and [15] respectively; B and D: theoretical studies
-3
[14] and [16] respectively). Iso-surfaces are drawn at levels above 0 e-Å to show where the highest bonding
densities are located in the structure and the nature of bonding. The densities at the centres of the octahedral
and tetrahedral interstices (o and t respectively in the plot inset at right) are plotted for all known electron
density studies since 1929 in the graph. The examples A – D are labeled accordingly in the plot, as are the
results from the present work (circled crosses). The hexagon-hatched region indicates a stronger tetrahedral
bonding character and the cross-hatched region, octahedral bonding. Outside these regions, bonding has a
nearest neighbor bridge character as exemplified by C and D, which show transverse bridge bonding and
longitudinal bridge bonding respectively.
Figure 2. An example of an angular difference CBED pattern [1, 6] used for differential QCBED (at left) and
the 3-D bonding electron density plots in aluminium from the present results (at right). The iso-surface is
plotted at 50% of the maximum bonding density in each case.