Validation of density functionals for transition metals and intermetallics using data from quantitative electron diffraction

Abstract

Accurate low-order structure factors (F g ) measured by quantitative convergent beam electron diffraction (QCBED) were used for validation of different density functional theory (DFT) approximations. 23 low-order F g were measured by QCBED for the transition metals Cr, Fe, Co, Ni, and Cu, and the transition metal based intermetallic phases γ-TiAl, β-NiAl and γ 1 -FePd using a multi-beam off-zone axis (MBOZA) method and then compared with F g calculated ab-initio by DFT using the local spin density approximation (LDA) and LDA+U, and different generalized gradient approximations (GGA) functionals. Different functionals perform very differently for different materials and crystal structures. Among the GGA functionals, PW91 and EV93 achieve the best overall agreement with the experimentally determined low-order F g for the five metals, while PW91 performs the best for the three intermetallics. The LDA+U approach, through careful selection of U, achieves excellent matches with the experimentally measured F g for all the metallic systems investigated in this paper. Similar to the band gap for semiconductors, it is proposed that experimentally determined low-order F g can be used to tune the U term in LDA+U method DFT calculations for metals and intermetallics.

How do specimen preparation and crystal perfection affect structure factor measurements by quantitative convergent-beam electron diffraction?

“…In the past three decades, quantitative convergent-beam electron diffraction (QCBED) has become established as a technique capable of very accurate and precise measurements of the low-order structure factors in crystalline materials with small unit cells (Zuo et al, 1988(Zuo et al, , 1997(Zuo et al, , 1999(Zuo et al, , 2000Bird & Saunders, 1992;Spence & Zuo, 1992;Spence, 1993;Zuo, 1993Zuo, , 2004Deininger et al, 1994;Holmestad et al, 1995;Peng & Zuo, 1995;Saunders et al, 1995Saunders et al, , 1996Saunders et al, , 1999aRen et al, 1997;Tsuda & Tanaka, 1999;Streltsov et al, 2001Streltsov et al, , 2003Tsuda et al, 2002Tsuda et al, , 2010Friis et al, 2003Friis et al, , 2005Jiang et al, 2003Jiang et al, , 2004Ogata et al, 2004;Nakashima, 2005Nakashima, , 2007Nakashima, , 2012Nakashima & Muddle, 2010b;Sang et al, 2010Sang et al, , 2011Sang et al, , 2013Midgley, 2011;Nakashima et al, 2011;Saeterli et al, 2011;Tanaka & Tsuda, 2011;Zuo & Spence, 2017). It is the low-order structure factors that contain the most information about the bonding electron distribution between the atoms, whilst at the same time being most susceptible to erro...…”

Charge Density Determination for Al-rich Composition L1o-ordered gamma-TiAl by Convergent Beam Electron Diffraction

“…Experimental details and the dynamical diffraction theory based iterative refinements for the CBED data quantifications have been described previously [1,2]. It has been shown for equiatomic γ-TiAl that DFT calculations based on the local density approximation (LDA) fail to treat accurately the 3d-electron system related bonding effects, while using the generalized gradient approximations (GGA) achieved considerably improved match and qualitatively excellent agreement with experimentally determined low-order F g and ∆ρ(r) [2,4]. However, GGA DFT calculations predicted larger electron charge delocalization than is observed in the CBED based experimentally determined Δρ(r) for equiatomic γ-TiAl [4].…”

“…The lattice parameters of the offstoichiometric γ-TiAl phase, with the tetragonal L1 0 structure, and the elemental composition have been determined by combining X-ray diffraction, locally resolved CBED HOLZ line analyses [3] and X-ray energy dispersive spectroscopy using binary standards [2,4]. Experimental details and the dynamical diffraction theory based iterative refinements for the CBED data quantifications have been described previously [1,2].…”

“…Cr, Fe, Co, Ni) and some binary intermetallic phases (e.g. NiAl, TiAl and FePd) [1,2]. The facility to determine experimentally the Δρ(r) for these d-electron materials warrants use of the CBED measurements as additional metrics in validation of density functional theory (DFT) calculations [2].…”

“…The lattice parameters of the offstoichiometric γ-TiAl phase, with the tetragonal L1 0 structure, and the elemental composition have been determined by combining X-ray diffraction, locally resolved CBED HOLZ line analyses [3] and X-ray energy dispersive spectroscopy using binary standards [2,4]. Experimental details and the dynamical diffraction theory based iterative refinements for the CBED data quantifications have been described previously [1,2]. It has been shown for equiatomic γ-TiAl that DFT calculations based on the local density approximation (LDA) fail to treat accurately the 3d-electron system related bonding effects, while using the generalized gradient approximations (GGA) achieved considerably improved match and qualitatively excellent agreement with experimentally determined low-order F g and ∆ρ(r) [2,4].…”