skip to main content

Title: Ar transport and blister growth kinetics in titania-doped germania-based optical coatings

Blistering is a phenomenon sometimes observed in sputtered-deposited thin films but seldom investigated in detail. Here, we consider the case of titania-doped germania (TGO)/silica multilayers deposited by ion beam sputtering. TGO is a candidate as high refractive index material in the Bragg mirrors for the next iteration of gravitational waves detectors. It needs to be annealed at 600C for 100 h in order to reach the desired relaxation state. However under some growth conditions, in 52-layer TGO/silica stacks, blistering occurs upon annealing at a temperature near 500C, which corresponds to the temperature where Ar desorbs from TGO. In order to better understand the blistering phenomenon, we measure the Ar transport in single layers of TGO and silica. In the case of<1µm-thick TGO layers, the Ar desorption is mainly limited by detrapping. The transport model also correctly predicts the evolution of the total amount of Ar in a 8.5µm stack of TGO and silica layers annealed at 450C, but in that case, the process is mainly limited by diffusion. Since Ar diffusion is an order of magnitude slower in TGO compared to silica, we observe a correspondingly strong accumulation of Ar in TGO. The Ar transport model is used to explain some regimes of the blisters growth, and we find indications that Ar accumulation is a driver for their growth in general, but the blisters nucleation remains a complex phenomenon influenced by several other factors including stress, substrate roughness, and impurities.

more » « less
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » ; ; ; ; « less
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Classical and Quantum Gravity
Medium: X Size: Article No. 115013
Article No. 115013
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$Quasi-NP=NTIME[n(logn)O(1)]and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$C, by showing that$\mathcal { C}$Cadmits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$C. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$ixi. We show that for every sparsef, and for all “typical”$\mathcal { C}$C, faster#SAT algorithms for$\mathcal { C}$Ccircuits imply lower bounds against the circuit class$f \circ \mathcal { C}$fC, which may bestrongerthan$\mathcal { C}$Citself. In particular:

    #SAT algorithms fornk-size$\mathcal { C}$C-circuits running in 2n/nktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$(fC)-circuits of polynomial size.

    #SAT algorithms for$2^{n^{{\varepsilon }}}$2nε-size$\mathcal { C}$C-circuits running in$2^{n-n^{{\varepsilon }}}$2nnεtime (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$(fC)-circuits of polynomial size.

    Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJACC0THRcircuits of polynomial size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC0[Williams JACM’14] andACC0THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class.

    more » « less
  2. Both thin (55μm) composite and thick (350μm) all active material battery porous electrodes were prepared for estimating the diffusion coefficient of Li+(DLi+)in tellurium (Te) during electrochemical lithiation. Galvanostatic intermittent titration technique (GITT), cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS) were applied to quantify the chemical lithium solid-state diffusion coefficient within the Te active material in the electrodes. Multiple methods of GITT and EIS were assessed. For the composite Te electrodes, theDLi+was on the order of 10−11cm2s−1from both CV and GITT methods, but 10−9cm2s−1from EIS. For the thick tellurium electrodes, both GITT and EIS resulted in lithium diffusion coefficient estimates in the range of 10−11–10−12cm2s−1. The general trend across all methods that quantified the diffusion coefficient as a function of lithiation of tellurium was that theDLi+decreased rapidly when the Te material was initially lithiated. TheDLi+at the phase transition voltage plateau (∼1.7 V, vs Li/Li+, where both Te and Li2Te were expected) had the lowestDLi+,while theDLi+both before and after the plateau was generally higher. Among all the electrochemical measurements ofDLi+,the modified GITT method with modelling the relaxation region resulted in relatively low scatter in the data, provided values as a function of lithiation, and was well suited to thick electrodes with a flat discharge plateau as was the case herein.

    more » « less
  3. Cross-platform observing systems are requisite to capturing the temporal and spatial dynamics of particles in the ocean. We present simultaneous observations of bulk optical properties, including the particulate beam attenuation (cp) and backscattering (bbp) coefficients, and particle size distributions collected in the North Pacific Subtropical Gyre. Clear and coherent diel cycles are observed in all bulk and size-fractionated optical proxies for particle biomass. We show evidence linking diurnal increases incpandbbpto daytime particle growth and division of cells, with particles<<#comment/>7µ<#comment/>mdriving the daily cycle of particle production and loss within the mixed layer. Flow cytometry data reveal the nitrogen-fixing cyanobacteriumCrocosphaera(∼<#comment/>4−<#comment/>7µ<#comment/>m) to be an important driver ofcpat the time of sampling, whereasProchlorococcusdynamics (∼<#comment/>0.5µ<#comment/>m) were essential to reproducing temporal variability inbbp. This study is a step towards improved characterization of the particle size range represented byin situbulk optical properties and a better understanding of the mechanisms that drive variability in particle production in the oligotrophic open ocean.

    more » « less
  4. Abstract

    The crystal structure and bonding environment of K2Ca(CO3)2bütschliite were probed under isothermal compression via Raman spectroscopy to 95 GPa and single crystal and powder X-ray diffraction to 12 and 68 GPa, respectively. A second order Birch-Murnaghan equation of state fit to the X-ray data yields a bulk modulus,$${K}_{0}=46.9$$K0=46.9GPa with an imposed value of$${K}_{0}^{\prime}= 4$$K0=4for the ambient pressure phase. Compression of bütschliite is highly anisotropic, with contraction along thec-axis accounting for most of the volume change. Bütschliite undergoes a phase transition to a monoclinicC2/mstructure at around 6 GPa, mirroring polymorphism within isostructural borates. A fit to the compression data of the monoclinic phase yields$${V}_{0}=322.2$$V0=322.2 Å3$$,$$,$${K}_{0}=24.8$$K0=24.8GPa and$${K}_{0}^{\prime}=4.0$$K0=4.0using a third order fit; the ability to access different compression mechanisms gives rise to a more compressible material than the low-pressure phase. In particular, compression of theC2/mphase involves interlayer displacement and twisting of the [CO3] units, and an increase in coordination number of the K+ion. Three more phase transitions, at ~ 28, 34, and 37 GPa occur based on the Raman spectra and powder diffraction data: these give rise to new [CO3] bonding environments within the structure.

    more » « less
  5. Abstract

    The Gaussian elimination with partial pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical evidence strongly suggests that for atypicalsquare coefficient matrix, GEPP is numerically stable. We obtain a (partial) theoretical justification of this phenomenon by showing that, given the random$$n\times n$$n×nstandard Gaussian coefficient matrixA, thegrowth factorof the Gaussian elimination with partial pivoting is at most polynomially large innwith probability close to one. This implies that with probability close to one the number of bits of precision sufficient to solve$$Ax = b$$Ax=btombits of accuracy using GEPP is$$m+O(\log n)$$m+O(logn), which improves an earlier estimate$$m+O(\log ^2 n)$$m+O(log2n)of Sankar, and which we conjecture to be optimal by the order of magnitude. We further provide tail estimates of the growth factor which can be used to support the empirical observation that GEPP is more stable than the Gaussian Elimination with no pivoting.

    more » « less