示例#1
0
def runLeveler(kLeveler=0.018,
               bulkLevelerConcentration=0.02,
               cellSize=0.1e-7,
               rateConstant=0.00026,
               initialAcceleratorCoverage=0.0,
               levelerDiffusionCoefficient=5e-10,
               numberOfSteps=400,
               displayRate=10,
               displayViewers=True):

    kLevelerConsumption = 0.0005
    aspectRatio = 1.5
    faradaysConstant = 9.6485e4
    gasConstant = 8.314
    acceleratorDiffusionCoefficient = 4e-10
    siteDensity = 6.35e-6
    atomicVolume = 7.1e-6
    charge = 2
    metalDiffusionCoefficient = 4e-10
    temperature = 298.
    overpotential = -0.25
    bulkMetalConcentration = 250.
    bulkAcceleratorConcentration = 50.0e-3
    initialLevelerCoverage = 0.
    cflNumber = 0.2
    cellsBelowTrench = 10
    trenchDepth = 0.4e-6
    trenchSpacing = 0.6e-6
    boundaryLayerDepth = 98.7e-6
    i0Suppressor = 0.3
    i0Accelerator = 22.5
    alphaSuppressor = 0.5
    alphaAccelerator = 0.4
    alphaAdsorption = 0.62
    m = 4
    b = 2.65
    A = 0.3
    Ba = -40
    Bb = 60
    Vd = 0.098
    Bd = 0.0008

    etaPrime = faradaysConstant * overpotential / gasConstant / temperature

    mesh = TrenchMesh(cellSize=cellSize,
                      trenchSpacing=trenchSpacing,
                      trenchDepth=trenchDepth,
                      boundaryLayerDepth=boundaryLayerDepth,
                      aspectRatio=aspectRatio,
                      angle=numerix.pi * 4. / 180.)

    distanceVar = GapFillDistanceVariable(name='distance variable',
                                          mesh=mesh,
                                          value=-1.)

    distanceVar.setValue(1., where=mesh.electrolyteMask)

    distanceVar.calcDistanceFunction()
    levelerVar = SurfactantVariable(name="leveler variable",
                                    value=initialLevelerCoverage,
                                    distanceVar=distanceVar)

    acceleratorVar = SurfactantVariable(name="accelerator variable",
                                        value=initialAcceleratorCoverage,
                                        distanceVar=distanceVar)

    bulkAcceleratorVar = CellVariable(name='bulk accelerator variable',
                                      mesh=mesh,
                                      value=bulkAcceleratorConcentration)

    bulkLevelerVar = CellVariable(name='bulk leveler variable',
                                  mesh=mesh,
                                  value=bulkLevelerConcentration)

    metalVar = CellVariable(name='metal variable',
                            mesh=mesh,
                            value=bulkMetalConcentration)

    def depositionCoeff(alpha, i0):
        expo = numerix.exp(-alpha * etaPrime)
        return 2 * i0 * (expo - expo * numerix.exp(etaPrime))

    coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
    coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)

    exchangeCurrentDensity = acceleratorVar.interfaceVar * (
        coeffAccelerator - coeffSuppressor) + coeffSuppressor

    currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity

    depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant

    extensionVelocityVariable = CellVariable(name='extension velocity',
                                             mesh=mesh,
                                             value=depositionRateVariable)

    kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
    kAcceleratorConsumption = Bd + A / (numerix.exp(Ba *
                                                    (overpotential + Vd)) +
                                        numerix.exp(Bb * (overpotential + Vd)))
    q = m * overpotential + b

    levelerSurfactantEquation = AdsorbingSurfactantEquation(
        levelerVar,
        distanceVar=distanceVar,
        bulkVar=bulkLevelerVar,
        rateConstant=kLeveler,
        consumptionCoeff=kLevelerConsumption * depositionRateVariable)

    accVar1 = acceleratorVar.interfaceVar
    accVar2 = (accVar1 > 0) * accVar1
    accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))

    acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
        acceleratorVar,
        distanceVar=distanceVar,
        bulkVar=bulkAcceleratorVar,
        rateConstant=kAccelerator,
        otherVar=levelerVar,
        otherBulkVar=bulkLevelerVar,
        otherRateConstant=kLeveler,
        consumptionCoeff=accConsumptionCoeff)

    advectionEquation = TransientTerm() + FirstOrderAdvectionTerm(
        extensionVelocityVariable)

    metalEquation = buildMetalIonDiffusionEquation(
        ionVar=metalVar,
        distanceVar=distanceVar,
        depositionRate=depositionRateVariable,
        diffusionCoeff=metalDiffusionCoefficient,
        metalIonMolarVolume=atomicVolume)

    metalVar.constrain(bulkMetalConcentration, mesh.facesTop)

    bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
        bulkVar=bulkAcceleratorVar,
        distanceVar=distanceVar,
        surfactantVar=acceleratorVar,
        otherSurfactantVar=levelerVar,
        diffusionCoeff=acceleratorDiffusionCoefficient,
        rateConstant=kAccelerator * siteDensity)

    bulkAcceleratorVar.constrain(bulkAcceleratorConcentration, mesh.facesTop)

    bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
        bulkVar=bulkLevelerVar,
        distanceVar=distanceVar,
        surfactantVar=levelerVar,
        diffusionCoeff=levelerDiffusionCoefficient,
        rateConstant=kLeveler * siteDensity)

    bulkLevelerVar.constrain(bulkLevelerConcentration, mesh.facesTop)

    eqnTuple = ((advectionEquation, distanceVar, (),
                 None), (levelerSurfactantEquation, levelerVar, (), None),
                (acceleratorSurfactantEquation, acceleratorVar, (),
                 None), (metalEquation, metalVar, (), None),
                (bulkAcceleratorEquation, bulkAcceleratorVar, (),
                 GeneralSolver()), (bulkLevelerEquation, bulkLevelerVar, (),
                                    GeneralSolver()))

    narrowBandWidth = 20 * cellSize
    levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
                                  cflNumber / 2)

    totalTime = 0.0

    if displayViewers:
        try:
            raise Exception
            from mayaviSurfactantViewer import MayaviSurfactantViewer
            viewers = (MayaviSurfactantViewer(distanceVar,
                                              acceleratorVar.interfaceVar,
                                              zoomFactor=1e6,
                                              datamax=0.5,
                                              datamin=0.0,
                                              smooth=1,
                                              title='accelerator coverage'),
                       MayaviSurfactantViewer(distanceVar,
                                              levelerVar.interfaceVar,
                                              zoomFactor=1e6,
                                              datamax=0.5,
                                              datamin=0.0,
                                              smooth=1,
                                              title='leveler coverage'))
        except:

            class PlotVariable(CellVariable):
                def __init__(self, var=None, name=''):
                    CellVariable.__init__(self, mesh=mesh.fineMesh, name=name)
                    self.var = self._requires(var)

                def _calcValue(self):
                    return numerix.array(self.var(self.mesh.cellCenters))

            viewers = (Viewer(PlotVariable(var=acceleratorVar.interfaceVar)),
                       Viewer(PlotVariable(var=levelerVar.interfaceVar)))

    for step in range(numberOfSteps):

        if displayViewers:
            if step % displayRate == 0:
                for viewer in viewers:
                    viewer.plot()

        if step % levelSetUpdateFrequency == 0:
            distanceVar.calcDistanceFunction()

        extensionVelocityVariable.setValue(depositionRateVariable)

        extOnInt = numerix.where(
            distanceVar.globalValue > 0,
            numerix.where(distanceVar.globalValue < 2 * cellSize,
                          extensionVelocityVariable.globalValue, 0), 0)

        dt = cflNumber * cellSize / extOnInt.max()

        distanceVar.extendVariable(extensionVelocityVariable)

        for eqn, var, BCs, solver in eqnTuple:
            eqn.solve(var, boundaryConditions=BCs, dt=dt, solver=solver)

        totalTime += dt

    point = ((1.25e-08, ), (3.125e-07, ))
    value = 2.02815779e-08
    return abs(float(distanceVar(point, order=1)) - value) < cellSize / 10.0
示例#2
0
文件: gold.py 项目: xinxinboss/fipy
def runGold(faradaysConstant=9.6e4,
            consumptionRateConstant=2.6e+6,
            molarVolume=10.21e-6,
            charge=1.0,
            metalDiffusion=1.7e-9,
            metalConcentration=20.0,
            catalystCoverage=0.15,
            currentDensity0=3e-2 * 16,
            currentDensity1=6.5e-1 * 16,
            cellSize=0.1e-7,
            trenchDepth=0.2e-6,
            aspectRatio=1.47,
            trenchSpacing=0.5e-6,
            boundaryLayerDepth=90.0e-6,
            numberOfSteps=10,
            taperAngle=6.0,
            displayViewers=True):
    
    cflNumber = 0.2
    numberOfCellsInNarrowBand = 20
    
    mesh = TrenchMesh(cellSize = cellSize,
                      trenchSpacing = trenchSpacing,
                      trenchDepth = trenchDepth,
                      boundaryLayerDepth = boundaryLayerDepth,
                      aspectRatio = aspectRatio,
                      angle = numerix.pi * taperAngle / 180.)

    narrowBandWidth = numberOfCellsInNarrowBand * cellSize

    distanceVar = GapFillDistanceVariable(
       name = 'distance variable',
       mesh = mesh,
       value = -1.)

    distanceVar.setValue(1., where=mesh.electrolyteMask)
    distanceVar.calcDistanceFunction()

    catalystVar = SurfactantVariable(
        name = "catalyst variable",
        value = catalystCoverage,
        distanceVar = distanceVar)

    metalVar = CellVariable(
        name = 'metal variable',
        mesh = mesh,
        value = metalConcentration)

    exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.interfaceVar
    
    currentDensity = metalVar / metalConcentration * exchangeCurrentDensity

    depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant

    extensionVelocityVariable = CellVariable(
        name = 'extension velocity',
        mesh = mesh,
        value = depositionRateVariable)   

    catalystSurfactantEquation = AdsorbingSurfactantEquation(
        catalystVar,
        distanceVar = distanceVar,
        bulkVar = 0,
        rateConstant = 0,
        consumptionCoeff = consumptionRateConstant * extensionVelocityVariable)

    advectionEquation = TransientTerm() + FirstOrderAdvectionTerm(extensionVelocityVariable)

    metalEquation = buildMetalIonDiffusionEquation(
        ionVar = metalVar,
        distanceVar = distanceVar,
        depositionRate = depositionRateVariable,
        diffusionCoeff = metalDiffusion,
        metalIonMolarVolume = molarVolume)

    metalVar.constrain(metalConcentration, mesh.facesTop)

    if displayViewers:

        try:
            from mayaviSurfactantViewer import MayaviSurfactantViewer
            viewer = MayaviSurfactantViewer(distanceVar, catalystVar.interfaceVar, zoomFactor = 1e6, datamax=1.0, datamin=0.0, smooth = 1, title = 'catalyst coverage', animate=True)
            
        except:
            
            class PlotVariable(CellVariable):
                def __init__(self, var = None, name = ''):
                    CellVariable.__init__(self, mesh = mesh.fineMesh, name = name)
                    self.var = self._requires(var)

                def _calcValue(self):
                    return numerix.array(self.var(self.mesh.cellCenters))

            viewer = MultiViewer(viewers=(
                    Viewer(PlotVariable(var = distanceVar), datamax=1e-9, datamin=-1e-9),
                    Viewer(PlotVariable(var = catalystVar.interfaceVar))))
    else:
        viewer = None

    levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2)
    step = 0

    while step < numberOfSteps:

        if step % 10 == 0 and viewer is not None:
            viewer.plot()

        if step % levelSetUpdateFrequency == 0:
            
            distanceVar.calcDistanceFunction()

        extensionVelocityVariable.setValue(numerix.array(depositionRateVariable))

        dt = cflNumber * cellSize / max(extensionVelocityVariable.globalValue)
        distanceVar.extendVariable(extensionVelocityVariable)

        advectionEquation.solve(distanceVar, dt = dt)

        catalystSurfactantEquation.solve(catalystVar, dt = dt)

        metalEquation.solve(metalVar, dt = dt)
                    
        step += 1

    point = ((5e-09,), (1.15e-07,))
    value = 1.45346701e-09
    return abs(float(distanceVar(point, order=1)) - value) < cellSize / 10.0
示例#3
0
文件: leveler.py 项目: LWhitson2/fipy
def runLeveler(kLeveler=0.018, 
               bulkLevelerConcentration=0.02, 
               cellSize=0.1e-7, 
               rateConstant=0.00026, 
               initialAcceleratorCoverage=0.0, 
               levelerDiffusionCoefficient=5e-10, 
               numberOfSteps=400, 
               displayRate=10, 
               displayViewers=True):

    
    kLevelerConsumption = 0.0005
    aspectRatio = 1.5
    faradaysConstant = 9.6485e4
    gasConstant = 8.314
    acceleratorDiffusionCoefficient = 4e-10
    siteDensity = 6.35e-6
    atomicVolume = 7.1e-6
    charge = 2
    metalDiffusionCoefficient = 4e-10
    temperature = 298.
    overpotential = -0.25
    bulkMetalConcentration = 250.
    bulkAcceleratorConcentration = 50.0e-3
    initialLevelerCoverage = 0.
    cflNumber = 0.2
    cellsBelowTrench = 10
    trenchDepth = 0.4e-6
    trenchSpacing = 0.6e-6
    boundaryLayerDepth = 98.7e-6
    i0Suppressor = 0.3
    i0Accelerator = 22.5
    alphaSuppressor = 0.5
    alphaAccelerator = 0.4
    alphaAdsorption = 0.62
    m = 4
    b = 2.65
    A = 0.3
    Ba = -40
    Bb = 60
    Vd = 0.098
    Bd = 0.0008

    etaPrime = faradaysConstant * overpotential / gasConstant / temperature

    mesh = TrenchMesh(cellSize = cellSize,
                      trenchSpacing = trenchSpacing,
                      trenchDepth = trenchDepth,
                      boundaryLayerDepth = boundaryLayerDepth,
                      aspectRatio = aspectRatio,
                      angle = numerix.pi * 4. / 180.)

    distanceVar = GapFillDistanceVariable(
        name = 'distance variable',
        mesh = mesh,
        value = -1.)

    distanceVar.setValue(1., where=mesh.electrolyteMask)
    
    distanceVar.calcDistanceFunction()
    levelerVar = SurfactantVariable(
        name = "leveler variable",
        value = initialLevelerCoverage,
        distanceVar = distanceVar)

    acceleratorVar = SurfactantVariable(
        name = "accelerator variable",
        value = initialAcceleratorCoverage,
        distanceVar = distanceVar)

    bulkAcceleratorVar = CellVariable(name = 'bulk accelerator variable',
                                      mesh = mesh,
                                      value = bulkAcceleratorConcentration)

    bulkLevelerVar = CellVariable(
        name = 'bulk leveler variable',
        mesh = mesh,
        value = bulkLevelerConcentration)

    metalVar = CellVariable(
        name = 'metal variable',
        mesh = mesh,
        value = bulkMetalConcentration)

    def depositionCoeff(alpha, i0):
        expo = numerix.exp(-alpha * etaPrime)
        return 2 * i0 * (expo - expo * numerix.exp(etaPrime))

    coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
    coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)

    exchangeCurrentDensity = acceleratorVar.interfaceVar * (coeffAccelerator - coeffSuppressor) + coeffSuppressor

    currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity

    depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant

    extensionVelocityVariable = CellVariable(
        name = 'extension velocity',
        mesh = mesh,
        value = depositionRateVariable)   

    kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
    kAcceleratorConsumption =  Bd + A / (numerix.exp(Ba * (overpotential + Vd)) + numerix.exp(Bb * (overpotential + Vd)))
    q = m * overpotential + b

    levelerSurfactantEquation = AdsorbingSurfactantEquation(
        levelerVar,
        distanceVar = distanceVar,
        bulkVar = bulkLevelerVar,
        rateConstant = kLeveler,
        consumptionCoeff = kLevelerConsumption * depositionRateVariable)

    accVar1 = acceleratorVar.interfaceVar
    accVar2 = (accVar1 > 0) * accVar1
    accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))

    acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
        acceleratorVar,
        distanceVar = distanceVar,
        bulkVar = bulkAcceleratorVar,
        rateConstant = kAccelerator,
        otherVar = levelerVar,
        otherBulkVar = bulkLevelerVar,
        otherRateConstant = kLeveler,
        consumptionCoeff = accConsumptionCoeff)

    advectionEquation = TransientTerm() + FirstOrderAdvectionTerm(extensionVelocityVariable)

    metalEquation = buildMetalIonDiffusionEquation(
        ionVar = metalVar,
        distanceVar = distanceVar,
        depositionRate = depositionRateVariable,
        diffusionCoeff = metalDiffusionCoefficient,
        metalIonMolarVolume = atomicVolume)

    metalVar.constrain(bulkMetalConcentration, mesh.facesTop)

    bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
        bulkVar = bulkAcceleratorVar,
        distanceVar = distanceVar,
        surfactantVar = acceleratorVar,
        otherSurfactantVar = levelerVar,
        diffusionCoeff = acceleratorDiffusionCoefficient,
        rateConstant = kAccelerator * siteDensity)

    bulkAcceleratorVar.constrain(bulkAcceleratorConcentration, mesh.facesTop)
    
    bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
        bulkVar = bulkLevelerVar,
        distanceVar = distanceVar,
        surfactantVar = levelerVar,
        diffusionCoeff = levelerDiffusionCoefficient,
        rateConstant = kLeveler * siteDensity)

    bulkLevelerVar.constrain(bulkLevelerConcentration, mesh.facesTop)
    
    eqnTuple = ( (advectionEquation, distanceVar, (), None),
                 (levelerSurfactantEquation, levelerVar, (), None),
                 (acceleratorSurfactantEquation, acceleratorVar, (), None),
                 (metalEquation, metalVar,  (), None),
                 (bulkAcceleratorEquation, bulkAcceleratorVar, (), GeneralSolver()),
                 (bulkLevelerEquation, bulkLevelerVar, (), GeneralSolver()))

    narrowBandWidth = 20 * cellSize
    levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2)

    totalTime = 0.0

    if displayViewers:
        try:
            raise Exception
            from mayaviSurfactantViewer import MayaviSurfactantViewer
            viewers = (
                MayaviSurfactantViewer(distanceVar, acceleratorVar.interfaceVar, zoomFactor = 1e6, datamax=0.5, datamin=0.0, smooth = 1, title = 'accelerator coverage'),
                MayaviSurfactantViewer(distanceVar, levelerVar.interfaceVar, zoomFactor = 1e6, datamax=0.5, datamin=0.0, smooth = 1, title = 'leveler coverage'))
        except:
            class PlotVariable(CellVariable):
                def __init__(self, var = None, name = ''):
                    CellVariable.__init__(self, mesh = mesh.fineMesh, name = name)
                    self.var = self._requires(var)

                def _calcValue(self):
                    return numerix.array(self.var(self.mesh.cellCenters))

            viewers = (Viewer(PlotVariable(var=acceleratorVar.interfaceVar)),
                       Viewer(PlotVariable(var=levelerVar.interfaceVar)))

        
    for step in range(numberOfSteps):

        if displayViewers:
            if step % displayRate == 0:
                for viewer in viewers:
                    viewer.plot()
            
        if step % levelSetUpdateFrequency == 0:
            distanceVar.calcDistanceFunction()

        extensionVelocityVariable.setValue(depositionRateVariable)

        extOnInt = numerix.where(distanceVar.globalValue > 0,
                                 numerix.where(distanceVar.globalValue < 2 * cellSize,
                                               extensionVelocityVariable.globalValue,
                                               0),
                                 0)

        dt = cflNumber * cellSize / extOnInt.max()

        distanceVar.extendVariable(extensionVelocityVariable)

        for eqn, var, BCs, solver in eqnTuple:
            eqn.solve(var, boundaryConditions = BCs, dt = dt, solver=solver)

        totalTime += dt

    point = ((1.25e-08,), (3.125e-07,))
    value = 2.02815779e-08
    return abs(float(distanceVar(point, order=1)) - value) < cellSize / 10.0