  Gadolinium has long been believed to undergo a high pressure phase transition
with a volume collapse around 5%. Theoretical explanations have focused on the
idea of electrons transferring from the extended s-orbital to the compact
f-orbital. However, experimental measurement has been unable to detect any
associated change in the magnetic properties of the f-electrons. Here we
resolve this discrepancy by showing that there is no significant volume
collapse, beyond what is typical in high pressure phase transformations. We
present density functional theory calculations of solid gadolinium under high
pressure using a range of methods, and revisit the experimental situation using
X-ray diffraction (XRD). The standard lanthanide pressure-transformation
sequence involving different stackings of close-packed planes: hcp to 9R to
dhcp to fcc to d-fcc is reproduced. The so-called "volume collapsed"
high-pressure phase is shown to be an unusual stacking of close-packed planes,
with Fddd symmetry and a density change less than 2%. The distorted fcc (d-fcc)
structure is revealed to arise as a consequence of antiferromagnetism. The
theoretical results are shown to be remarkably robust to various treatments of
the f-electrons. The key result is that there is no XRD evidence for volume
collapse in Gadolinium. The sequence of phase transitions is well described by
standard DFT. There is no need for special treatment of the f-electrons or
evidence of f-electron bonding. Noting previous spectroscopic evidence is that
there is no change in the f-electrons we conclude that high pressure Gadolinium
has no complicated f-electron physics such as Mott-Hubbard, Kondo or valence
transition.
