  Hydrothermal synthesis is described of layered lithium iron selenide
hydroxides Li1-xFex(OH)Fe1-ySe (x ~ 0.2; 0.02 < y < 0.15) with a wide range of
iron site vacancy concentrations in the iron selenide layers. This iron vacancy
concentration is revealed as the only significant compositional variable and as
the key parameter controlling the crystal structure and the electronic
properties. Single crystal X-ray diffraction, neutron powder diffraction and
X-ray absorption spectroscopy measurements are used to demonstrate that
superconductivity at temperatures as high as 40 K is observed in the
hydrothermally synthesised samples when the iron vacancy concentration is low
(y < 0.05) and when the iron oxidation state is reduced slightly below +2,
while samples with a higher vacancy concentration and a correspondingly higher
iron oxidation state are not superconducting. The importance of combining a low
iron oxidation state with a low vacancy concentration in the iron selenide
layers is emphasised by the demonstration that reductive post-synthetic
lithiation of the samples turns on superconductivity with critical temperatures
exceeding 40 K by displacing iron atoms from the Li1-xFex(OH) reservoir layer
to fill vacancies in the selenide layer
