X-ray electron density analysis of chemical bonding in permanent magnet Nd₂Fe₁₄B

Chemical bonding determines the intrinsic properties of materials, but despite the super-strong metallic magnet Nd₂Fe₁₄B being a vital compound in modern life, the local chemical environment is not well understood. Nd₂Fe₁₄B has a very complex crystal structure with six independent Fe sites, two independent Nd sites and one B site, which in concert are responsible for the extremely high magnetic moment. Dense inorganic materials with excellent crystal quality and heavy atoms represent a strong challenge to X-ray charge density analysis, and indeed Nd₂Fe₁₄B has a mere suitability factor of 0.02 compared with 3-5 for typical organic molecular crystals. Here, we report high-energy (λ = 0.2482 Å) 25 K single-crystal synchrotron X-ray diffraction data suitable for multipole modelling of the X-ray charge density. The X-ray electron density shows local anisotropy in the bonding environment of the Fe atoms, and topological analysis quantifies that the Nd atoms are positive (∼+1), one Fe atom and B are negative (-1.7 and -0.44, respectively), and the remaining Fe atoms are close to neutral (±0.1). The d orbitals of all Fe atoms are close to being evenly populated, and bonding analysis establishes a multidirectional `metal-like' framework. It is found that a single Fe atom is crucial for the 3D framework of the magnetic structure. Through structural refinement of synchrotron single-crystal X-ray diffraction data at 25 K, 100 K, 200 K and 300 K, anisotropic displacement parameters are obtained, and the Debye temperature is estimated to be 345-383 K.