research papers
Structure factors for a small holmium diiron HoFe2 Laves crystal were measured with focused λ = 0.75 Å synchrotron X-radiation using a fast avalanche photodiode (APD) counter. The deformation electron density (Δρ) maps are remarkable for significant excess electron density midway between the Ho atoms, which is not dissimilar to the peaks attributed to classic `covalent bonding' in C and Si crystals. These residual electrons accumulate at the centres of the kagomé net hexagons and form, with the Fe atoms, a triangular lattice which is characterized by more stable magnetic order than the kagomé net. Similar peaks occur along the Ho–Fe and Fe–Fe contacts. These results confirm the hypothesis that 5d electrons of the rare-earth atoms are important in the spin-coupling mechanism for HoFe2-type compounds. The 5d electrons are far less localized than the 4f electrons, and considerable 5d–5d and 5d–3d orbital overlap occurs between neighbouring atoms. Aspherical electron density near the Ho nuclei can be associated with the Ho 4f subshell electrons. Strong depletions of the Δρ near the atoms along the Ho–Ho, Ho–Fe and Fe–Fe vectors are indications of exchange repulsion. The effect of anharmonicity on the Δρ is insignificant.
Supporting information
Crystallographic Information File (CIF) | |
Structure factor file (CIF format) |
Computing details top
Data collection: BL14A_Photon_Factory; data reduction: xtal_DIFDAT_ADDREF_SORTRF_ABSORB; program(s) used to solve structure: Xtal; program(s) used to refine structure: xtal_CRYLSQ; molecular graphics: Xtal; software used to prepare material for publication: xtal_CIFIO.
(lsx) top
Crystal data top
Fe2Ho | Dx = 9.411 Mg m−3 |
Mr = 276.62 | Xray_vertical_wiggler radiation, λ = 0.75 Å |
Cubic, Fd3m | Cell parameters from 6 reflections |
Hall symbol: -F 4vw 2vw 3 | θ = 24.2–24.2° |
a = 7.3091 (6) Å | µ = 60.63 mm−1 |
V = 390.47 (10) Å3 | T = 293 K |
Z = 8 | , black |
F(000) = 952 | 0.02 × 0.02 × 0.0032 mm |
Data collection top
BL14A 4 circle diffractometer | 116 reflections with I > 2σ(I) |
Radiation source: BL14A_Photon_Factory | Rint = 0.067 |
Si(111)_double monochromator | θmax = 55.2°, θmin = 5.1° |
ω–2θ scans | h = −16→16 |
Absorption correction: analytical xtal_ABSORB | k = −16→16 |
Tmin = 0.433, Tmax = 0.823 | l = −16→16 |
3381 measured reflections | 6 standard reflections every 94 reflections |
116 independent reflections | intensity decay: 3.7% |
Refinement top
Refinement on F | 0 constraints |
Least-squares matrix: full | w = 1/σ2(F) |
R[F2 > 2σ(F2)] = 0.010 | (Δ/σ)max < 0.001 |
wR(F2) = 0.011 | Δρmax = 1.58 e Å−3 |
S = 1.40 | Δρmin = −0.70 e Å−3 |
116 reflections | Extinction correction: Maslen & Spadaccini (1993) |
4 parameters | Extinction coefficient: 0.00000 |
0 restraints |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | ||
Ho | 0.12500 | 0.12500 | 0.12500 | 0.006726 (18) | |
Fe | 0.50000 | 0.50000 | 0.50000 | 0.00667 (4) |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
Ho | 0.006726 (18) | 0.006726 (18) | 0.006726 (18) | 0.00000 | 0.00000 | 0.00000 |
Fe | 0.00667 (4) | 0.00667 (4) | 0.00667 (4) | 0.00012 (5) | 0.00012 (5) | 0.00012 (5) |
Bond lengths (Å) top
Ho—Hoi | 3.1649 (2) | Fe—Feii | 2.5842 (2) |
Ho—Feii | 3.0302 (2) |
Symmetry codes: (i) −y, x+1/4, z+1/4; (ii) −x+3/4, y, −z+3/4. |