Draft version
where K is a dimensionless shape factor, λ is the wavelength and θ is the Bragg angle. There are multiple other
factors beyond crystallite size that can affect the peak broadening which is why the estimations should be
considered tentative. It should be noted that the instrumental peak broadening are taken into account for the
estimations here. The instrumental peak broadening was measured as a function of the Bragg angle with a Si
powder reference. The Scherrer calculator in HighScore Plus from PANalytical.4 The peak broadening was
estimated from three Au peaks: (111), (220) and (113). The three broadenings lead to average crystallite sizes
of 1.9±0.2 and 2.8±0.3 nm. Due to the inaccuracy of the method, the sizes are shown as 2 and 3 nm,
respectively.
Model for estimation of Mn-Au sites
The number of sites with Mn and Au in close vicinity could have a strong impact on the activity. For the two
concentrations of Au in MnOx it is therefore interesting to estimate this number. For Au(30%)-MnOx we will
assume that spherical 2 nm particles are half immersed and dispersed on a flat Mn3O4 surface, so that the Au
particles never touch each other. For Au(50%)-MnOx the same assumptions are made but for 3 nm particles.
The ratios found from XPS will be used to evaluate the gold surface area. In this way the maximum
circumference, C, of the particles are in contact with the oxide while accessible for the electrolyte. The total
circumference, Ctot, of all gold particles present at the surface is therefore proportional to the number of Mn-
Au sites. Then the ratio between the total circumference for Au(50%)-MnOx and Au(30%)-MnOx is a measure of
the difference in interacting sites for the two concentrations. This ratio can be written as:
����������������,50%
����������������,30%
=
���������������� ∙ ��������������������,50%
����(3��������
2 )2
���� ∙ 3��������
���������������� ∙ ��������������������,30%
����(2��������
2 )2
���� ∙ 2��������
=
3 ∙ ������������������,50%
2 ∙ (1.5)2��������������������,30%
≈ 1.3
Where Atot is total area, AuXPS,50% is the ratio of Au from XPS measurements and 3 or 2 nm comes from the
domain size estimations from using the Scherrer equation as described above. For cube shaped particles the
result is the same. From this model it is therefore estimated that the samples with 50 % gold has 1.3 times as
many Mn-Au sites as the sample with 30 %. This difference is not enough to explain a factor 3 difference in
current density. If the gold particles are allowed to touch other gold particles the ratio will instead be close to
1.1 and the difference is therefore lower.
16