Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that, on choosing the de Donder functional, the resulting boundary operator involves projection operators jointly with a nilpotent operator. Moreover, the elliptic operator acting on metric perturbations is symmetric. Other choices of mixed boundary conditions, for which the normal components of metric perturbations can be set to zero at the boundary, are then analysed in detail. Lastly, the evaluation of the 1-loop divergence in the axial gauge for gravity is obtained. Interestingly, such a divergence turns out to coincide with the one resulting from transverse-traceless perturbations.
Pb(Zr,Ti)O3 (PZT) films were deposited on Pt/Ti/SiO2/Si
substrates by electron cyclotron resonance (ECR) plasma enhanced DC
magnetron reactive sputtering. Various seed layers with different
compositions were formed by varying the target power of each element at
the initial stage of the deposition process, and the effects of the seed
layers on the properties of the PZT films subsequently deposited on them
were studied. The seed layers were fabricated in three ways: increasing
Pb flux at a particular Zr/Ti flux ratio which is kept constant in the
subsequent PZT film deposition process, increasing Pb flux with decreasing
the Zr/Ti flux ratio to make the layer composition below the morphotrophic
phase boundary (Zr/Ti=1.08) value and finally maintaing a Zr flux of zero
for the PbTiOx seed layer. It was found that the PZT seed layer is more
effective than a PbTiOx seed layer and the effectivity of the seed layer is
increased not by just increasing the supply of Pb, but by increasing the
Pb supplement in the presence of low Zr/Ti flux ratio. However, too
much excess supplement of Pb element during the seed layer deposition
degrades the crystallinity and capacitance properties of overlying PZT films.
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