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Commit 89c2cc82 authored by Nicolas Eßing's avatar Nicolas Eßing
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State of submitting my thesis. Merge MATLAB code to tex.

parents 4786a80b 74f0a9b7
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MATLAB/+materialSimulations/AistSimulation.m 0 → 100755
+ 58
− 0
View file @ 89c2cc82
classdef AistSimulation < phasefieldMethod.TestSimulation & ...
simulationModels.AllPhysicalSimulation & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.CombinedViscosity_1 & ...
simulationModels.WilsonFrenkelVelocity & ...
simulationModels.ClassicalNucleation
%AISTSIMULATION The simulation model for AIST
% TODO
properties (SetAccess = protected)
% Free energy
Lv = 878.9e6; % Latent heat [J/m^3]
L = 173e-3 * simulationModels.Constants.eV
Tm = 817; % Melting temperature [K]
% Viscosity
Tglass = 700; %TODO
ninf = 1.22e-3; % Viscosity for T -> Inf [Pa*s]
Tg = 445; % Glass transition temperature [K]
m = 128; % Fragility
Ea = 2.90 * simulationModels.Constants.eV; % Activation energy [eV]
% Velocity
jd = 1e-10;
r_atom = 1.5e-10;
R_hyd = 0.5e-10;
% Nucleation
IE = 5.5e-2; % Interfacial energy [J/m^2]
Vm;
end
properties (SetAccess = protected)
DIT; % diffuse interface thickness [m]
end
methods
function S = AistSimulation(spacing, seed)
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.AllPhysicalSimulation(spacing, seed);
S@simulationModels.WilsonFrenkelVelocity(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.CombinedViscosity_1(spacing, seed);
S.Vm = S.L / S.Lv;
end
function S = setParameters(S, DIT, T)
S.DIT = DIT;
S.T = T;
end
function S = apply(S)
S.J = S.nucleationRate();
S = apply@simulationModels.AllPhysicalSimulation(S);
end
end
end
MATLAB/+materialSimulations/GSTSimulation.m 0 → 100755
+ 106
− 0
View file @ 89c2cc82
classdef GSTSimulation < phasefieldMethod.TestSimulation & ...
simulationModels.AllPhysicalSimulation & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.CombinedViscosity11 & ...
simulationModels.CombinedVelocity & ...
simulationModels.HeterogeneousNucleation
%GSTSIMULATION A simulation for the model Zhi Yang used for GST.
properties (SetAccess = protected)
DIT; % diffuse interface thickness [m]
structf; % structure factor for nucleation
end
properties (SetAccess = protected)
IE = 0.06; % interfacial energy [J/m^2]
Lv = 625e6; % latent heat [J/m^3]
L = 625e6 * 2.9e-28; % latent heat per atom [J]
Vm = 2.9e-28; % volume per atom [m^3]
Tm = 889; % melting temperature [K]
ninf = 0.012; % viscosity for infinite temperature [Pa*s]
m = 140; % fragility
Tg = 472; % other glass transition temperature [K]
jd = 2.99e-10; % jump distance [m]
Ea = 2.3 * 1.6e-19; % activation energy [J]
Tglass = 534; % glass transition temperature [K]
r_atom = 1;
R_hyd = 1;
wa = 180; % wetting ange [degrees]
end
methods
function S = GSTSimulation(spacing, seed)
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.AllPhysicalSimulation(spacing, seed);
S@simulationModels.CombinedVelocity(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.CombinedViscosity11(spacing, seed);
end
function S = setParameters(S, DIT, T)
S = S.assertForm(DIT, 'interface thickness');
S = S.assertForm(T, 'temperature');
S.DIT = DIT;
S.T = T;
end
function S = apply(S)
neighs = phasefieldMethod.analyse_structure_27(S.phasefield);
s = (2+cosd(S.wa)) * (1-cosd(S.wa)) * (1-cosd(S.wa)) /4;
S.structf = (neighs == 0) * 1 + ...
and((neighs >= 1), (neighs < 7)) * s*(1.2^2) + ...
and((neighs >= 7), (neighs < 26)) * s*1.2 + ...
(neighs >= 26) * s;
S.J = S.nucleationRate();
S = apply@simulationModels.AllPhysicalSimulation(S);
end
function s = structfactor(S)
s = S.structf;
end
function backupParams(S, file)
% Write the settings and evolution parameters to a .mat file.
% Arguments:
% file - Handle of a .mat file
% Returns nothing
S.backupParamsCore(file);
file.IE = S.IE;
file.DIT = S.DIT;
file.L = S.L;
file.Tm = S.Tm;
file.T = S.T;
% file.Vm = S.Vm;
file.ninf = S.ninf;
file.m = S.m;
file.Tg = S.Tg;
file.jd = S.jd;
file.Ea = S.Ea;
file.Tglass = S.Tglass;
file.wa = S.wa;
end
end
methods (Static)
function S = fromBackup(paramsfile, statefile)
S = phasefieldMethod.Simulation.fromBackupCore( ...
@phasefieldMethod.GSTSimulation, paramsfile, statefile);
S.IE = paramsfile.IE;
S.DIT = paramsfile.DIT;
S.L = paramsfile.L;
S.Tm = paramsfile.Tm;
S.T = paramsfile.T;
% S.Vm = paramsfile.Vm;
S.ninf = paramsfile.ninf;
S.m = paramsfile.m;
S.Tg = paramsfile.Tg;
S.jd = paramsfile.jd;
S.Ea = paramsfile.Ea;
S.Tglass = paramsfile.Tglass;
S.wa = paramsfile.wa;
S = S.apply();
end
end
end
MATLAB/+phasefieldMethod/GeTeSimulation.m → MATLAB/+materialSimulations/GeTeSimulation.m
+ 111
− 0
View file @ 89c2cc82
classdef GeTeSimulation < phasefieldMethod.TestSimulation
classdef GeTeSimulation < phasefieldMethod.TestSimulation & ...
simulationModels.AllPhysicalSimulation & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.CombinedViscosity11 & ...
simulationModels.FrenkelSimplifiedVelocity & ...
simulationModels.ClassicalNucleation
%GETESIMULATION A simulation model for GeTe. Temperature dependent
% Arrhenius behaviour for growth velocity and nucleation rate and a
% numerically set critical radius.
......@@ -7,81 +12,65 @@ classdef GeTeSimulation < phasefieldMethod.TestSimulation
% of 1.0789e64 m^-3*s^-2 * exp(-4.3eV/kB/T) is from A. M. Mio et al
% (who also give other values for v).
properties
properties (SetAccess = protected)
DIT = 0; % interface thickness [m]
r_c = 0; % critical radius [m]
T = 0; % temperature [K]
vinf = 5.9e14; % growth velocity for infinite temperature [m/s]
Ea_v = 1.77 % activation energy for velocity [eV]
Jinf = 1.0798e+64; % nucleation rate for infinite T [1/m^3/s]
Ea_J = 4.3; % activation energy for nucleation [eV]
end
end
properties ( Constant )
kB = 1.380649e-23; % Boltzmann constant, [J/K]
eV = 1.602176634e-19 % Electron volt [J]
properties (SetAccess = protected)
% For free energy
Lv = 17.9e3 / 33.11e-6
L = 17.9e3 / 33.11e-6 * 55e-30
Tm = 1000;
% For viscosity
ninf = 10^(-3.2);
Tg = 432.1;
m = 130.7
Tglass = 454
Ea = 1.85 * simulationModels.Constants.eV;
% For velocity
Atilde = 10^(-2);
% For nucleation
Vm = 55e-30;
jd = 3.8e-10;
IE;
IE_0 = 5.7e20 * 1e-3*simulationModels.Constants.eV;
IE_m = 0.021e20 * 1e-3*simulationModels.Constants.eV;
end
methods
function S = GeTeSimulation(spacing, seed)
S = S@phasefieldMethod.TestSimulation(spacing, seed);
S.M = 1;
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.AllPhysicalSimulation(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.CombinedViscosity11(spacing, seed);
S@simulationModels.FrenkelSimplifiedVelocity(spacing, seed);
S@simulationModels.ClassicalNucleation();
end
function S = setParameters(S, DIT, r_c)
%SETPARAMETERS(DIT, r_c, T) - Set the numerical parameters
function S = setParameters(S, DIT)
%SETPARAMETERS(DIT) - Set the numerical parameters
% Arguments:
% DIT - diffuse interface thickness [m]
% r_c - critical radius [m]
% Returns:
% S - The updated object
assert(isscalar(DIT) && isnumeric(DIT), 'DIT has wrong type or size');
assert(isscalar(r_c) && isnumeric(r_c), 'DIT has wrong type or size');
S.DIT = single( DIT );
S.r_c = single( r_c );
v = S.vinf .* exp( - S.Ea_v .* S.eV ./ (S.kB .* S.T) );
S.eps = sqrt(v .* r_c ./ 2);
S.W = v .* r_c ./ (4 .* DIT .^2);
S.dGv = v ./ (6 .* DIT);
end
function S = setTemp(S, T)
% Initialise or update the temperature field
S = S.assertForm(T, 'T');
S.T = T;
v = S.vinf .* exp( - S.Ea_v .* S.eV ./ (S.kB .* S.T) );
S.eps = sqrt(v .* S.r_c ./ 2);
S.W = v .* S.r_c ./ (4 .* S.DIT .^2);
S.dGv = v ./ (6 .* S.DIT);
S.J = S.Jinf .* exp( - S.Ea_J .* S.eV ./ (S.kB .* S.T) );
end
function S = apply(S)
v = S.vinf .* exp( - S.Ea_v .* S.eV ./ (S.kB * S.T));
S.M = 1;
S.eps = sqrt(v .* S.r_c ./ 2);
S.W = v .* S.r_c ./ (4 .* S.DIT .^2);
S.dGv = v ./ (6 .* S.DIT);
S.J = S.Jinf .* exp( - S.Ea_J .* S.eV ./ (S.kB .* S.T) );
S = apply@phasefieldMethod.Simulation(S);
S.IE = S.IE_0 + S.IE_m .* S.T;
S.J = S.nucleationRate();
S = apply@simulationModels.AllPhysicalSimulation(S);
end
function exportParameters(S, folder, index)
%EXPORTPARAMETERS(folder, index) - Export the current
% parameters.
% This function does nothing, but can be overwritten to export
% parameters.
% In this class, the temperature field is exported.
% Arguments:
% folder - Name of the folder to save in. Must already exist.
% index - An index to this export. Will appear in the
......@@ -90,13 +79,12 @@ classdef GeTeSimulation < phasefieldMethod.TestSimulation
filename = fullfile(folder,sprintf('temperature_%d.vtk',index));
phasefieldMethod.mat2vtk(S.T, filename, S.spacing, ...
[0,0,0], 'grainindices');
[0,0,0], 'temperature');
end
function backupParams(S, file)
S.backupParamsCore(file);
file.DIT = S.DIT;
file.r_c = S.r_c;
file.T = S.T;
file.vinf = S.vinf;
file.Ea_v = S.Ea_v;
......@@ -112,7 +100,6 @@ classdef GeTeSimulation < phasefieldMethod.TestSimulation
paramsfile, statefile);
S.DIT = paramsfile.DIT;
S.r_c = paramsfile.r_c;
S.T = paramsfile.T;
S.vinf = paramsfile.vinf;
S.Ea_v = paramsfile.Ea_v;
......
MATLAB/+materialSimulations/SbTeSimulation.m 0 → 100755
+ 53
− 0
View file @ 89c2cc82
classdef SbTeSimulation < phasefieldMethod.TestSimulation & ...
simulationModels.AllPhysicalSimulation & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.ArrheniusVelocity & ...
simulationModels.ArrheniusViscosity & ...
simulationModels.ClassicalNucleation
%SBTESIMULATION The simulation model for Sb2Te
% TODO
properties (SetAccess = protected)
% For free energy
Tm = 837.5; % Melting temperature [K]
Lv = 296.4e6; % Latent heat [J/m^3]
L;
% For velocity
v00 = 1.89885855985e+15; % Growth velocity for T -> Inf [m/s]
Ea = 2.91633477015e-19; % Activation energy [J]
% For nucleation
IE = 7.29e-2;
n00 = 1.2e-99;
jd = 1;
Vm = 4*pi/3;
end
properties (SetAccess = protected)
DIT; % diffuse interface thickness [m]
end
methods
function S = SbTeSimulation(spacing, seed)
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.AllPhysicalSimulation(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.ArrheniusVelocity(spacing, seed);
S@simulationModels.ArrheniusViscosity(spacing, seed);
S@simulationModels.ClassicalNucleation();
end
function S = setParameters(S, DIT, T)
S.DIT = DIT;
S.T = T;
end
function S = apply(S)
S.J = S.nucleationRate();
S = apply@simulationModels.AllPhysicalSimulation(S);
end
end
end
MATLAB/+materialSimulations/ScaleableAist.m 0 → 100755
+ 60
− 0
View file @ 89c2cc82
classdef ScaleableAist < phasefieldMethod.TestSimulation & ...
simulationModels.ScaleableSimulation & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.CombinedViscosity_1 & ...
simulationModels.WilsonFrenkelVelocity & ...
simulationModels.ClassicalNucleation
%AISTSIMULATION The simulation model for AIST
% TODO
properties (SetAccess = protected)
% Free energy
Lv = 878.9e6; % Latent heat [J/m^3]
L = 173e-3 * simulationModels.Constants.eV
Tm = 817; % Melting temperature [K]
% Viscosity
Tglass = 700; %TODO
ninf = 1.22e-3; % Viscosity for T -> Inf [Pa*s]
Tg = 445; % Glass transition temperature [K]
m = 128; % Fragility
Ea = 2.91 * simulationModels.Constants.eV; % Activation energy [eV]
% Velocity
jd = 1e-10;
r_atom = 1.5e-10;
R_hyd = 0.5e-10;
% Nucleation
IE = 5.5e-2; % Interfacial energy [J/m^2]
Vm;
end
properties (SetAccess = protected)
DIT; % diffuse interface thickness [m]
r_c; % Critical radius [m]
end
methods
function S = ScaleableAist(spacing, seed)
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.ScaleableSimulation(spacing, seed);
S@simulationModels.WilsonFrenkelVelocity(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.CombinedViscosity_1(spacing, seed);
S.Vm = S.L / S.Lv;
end
function S = setParameters(S, DIT, r_c, T)
S.DIT = DIT;
S.r_c = r_c;
S.T = T;
end
function S = apply(S)
S.J = S.nucleationRate();
S = apply@simulationModels.ScaleableSimulation(S);
end
end
end
MATLAB/+phasefieldMethod/SbTeSimulation.m → MATLAB/+materialSimulations/ScaleableSbTe.m
+ 36
− 20
View file @ 89c2cc82
classdef SbTeSimulation < phasefieldMethod.TestSimulation
classdef ScaleableSbTe < phasefieldMethod.TestSimulation & ...
simulationModels.ScaleableSimulation & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.ArrheniusVelocity & ...
simulationModels.ArrheniusViscosity & ...
simulationModels.ClassicalNucleation
%SBTESIMULATION The simulation model for Sb2Te
% TODO
properties (Constant)
vinf = 1.89885855985e+15; % growth velocity for T -> Inf [m/s]
Ea = 21122.9267551; % activation energy divided by kB [K]
properties (SetAccess = protected)
% For free energy
Tm = 837.5; % Melting temperature [K]
Lv = 296.4e6; % Latent heat [J/m^3]
L;
% For velocity
v00 = 1.89885855985e+15; % Growth velocity for T -> Inf [m/s]
Ea = 2.91633477015e-19; % Activation energy [J]
% For nucleation
IE = 7.29e-2;
n00 = 1.2e-99;
jd = 1;
Vm = 4*pi/3;
end
properties (SetAccess = protected)
DIT; % diffuse interface thickness [m]
r_c; % critical radius [m]
T; % temperature [K]
end
properties (SetAccess = private, GetAccess = private)
......@@ -18,7 +34,7 @@ classdef SbTeSimulation < phasefieldMethod.TestSimulation
end
methods
function S = SbTeSimulation(spacing, seed, printNucleiSizes)
function S = ScaleableSbTe(spacing, seed, printNucleiSizes)
%SBTESIMULATION(spacing, seed, printNucleiSizes) - Create a
% simulation for Sb2Te.
% Before simulating, you need to pass parameters, define a time
......@@ -30,25 +46,25 @@ classdef SbTeSimulation < phasefieldMethod.TestSimulation
% printed into the infoLine
% Returns:
% S - An instance of this class
%
% All subclasses must define a consturctor to call this
% superclass constructor to provide these parameters.
S = S@phasefieldMethod.TestSimulation(spacing, seed);
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.ScaleableSimulation(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.ArrheniusVelocity(spacing, seed);
S@simulationModels.ArrheniusViscosity(spacing, seed);
S@simulationModels.ClassicalNucleation();
S.printNucleiSizes = printNucleiSizes;
end
function S = setParameters(S, DIT, r_c, T, J)
function S = setParameters(S, DIT, r_c, T)
S.DIT = DIT;
S.r_c = r_c;
S.T = T;
S.J = J;
v = S.vinf .* exp(-S.Ea ./ T);
S.M = 1;
S.eps = sqrt( v .* r_c ./ 2 );
S.W = v .* r_c ./ (4 * DIT .* DIT);
S.dGv = v ./ (6 * DIT);
end
function S = apply(S)
S.J = S.nucleationRate();
S = apply@simulationModels.ScaleableSimulation(S);
end
function l = infoLine(S)
......@@ -82,4 +98,4 @@ classdef SbTeSimulation < phasefieldMethod.TestSimulation
end
end
\ No newline at end of file
end
MATLAB/+materialSimulations/SimpleGeTe.m 0 → 100755
+ 111
− 0
View file @ 89c2cc82
classdef SimpleGeTe < phasefieldMethod.TestSimulation & ...
simulationModels.ScaleableSimulation & ...
simulationModels.FrenkelSimplifiedVelocity & ...
simulationModels.ThompsonSpaepen & ...
simulationModels.CombinedViscosity11 & ...
simulationModels.ArrheniusNucleation
%GETESIMULATION A simulation model for GeTe. Temperature dependent
% Arrhenius behaviour for growth velocity and nucleation rate and a
% numerically set critical radius.
% The growth velocity of 5.9e14 m/s * exp(-1.77eV/kB/T) is taken from
% Q. M. Lu and M. Libera, the nucleation rate
% of 1.0789e64 m^-3*s^-2 * exp(-4.3eV/kB/T) is from A. M. Mio et al
% (who also give other values for v).
properties (SetAccess = protected)
DIT = 0; % interface thickness [m]
r_c = 0;
end
properties (SetAccess = protected)
% For viscosity
ninf = 10^(-3.2);
Tg = 432.1;
m = 130.7
Tglass = 454
Ea = 1.85 * simulationModels.Constants.eV;
% For free energy
Lv = 17.9e3 / 33.11e-6
L = 17.9e3 / 33.11e-6 * 55e-30
Tm = 1000;
% For velocity
Atilde = 10^(-2);
% For nucleation
J_Ea = 4.3 * simulationModels.Constants.eV;
J00 = exp(103);
end
methods
function S = SimpleGeTe(spacing, seed)
S@phasefieldMethod.TestSimulation(spacing, seed);
S@simulationModels.ScaleableSimulation(spacing, seed);
S@simulationModels.ThompsonSpaepen(spacing, seed);
S@simulationModels.CombinedViscosity11(spacing, seed);
S@simulationModels.FrenkelSimplifiedVelocity(spacing, seed);
S@simulationModels.ArrheniusNucleation();
end
function S = setParameters(S, DIT, r_c)
%SETPARAMETERS(DIT, r_c) - Set the numerical parameters
% Arguments:
% DIT - diffuse interface thickness [m]
% r_c - critical radius [m]
% Returns:
% S - The updated object
assert(isscalar(DIT) && isnumeric(DIT), 'DIT has wrong type or size');
assert(isscalar(r_c) && isnumeric(r_c), 'r_c has wrong type or size');
S.DIT = single( DIT );
S.r_c = single( r_c );
end
function S = apply(S)
S.J = S.nucleationRate();
S = apply@simulationModels.ScaleableSimulation(S);
end
function exportParameters(S, folder, index)
%EXPORTPARAMETERS(folder, index) - Export the current
% parameters.
% In this class, the temperature field is exported.
% Arguments:
% folder - Name of the folder to save in. Must already exist.
% index - An index to this export. Will appear in the
% filename.
% Returns nothing.
filename = fullfile(folder,sprintf('temperature_%d.vtk',index));
phasefieldMethod.mat2vtk(S.T, filename, S.spacing, ...
[0,0,0], 'temperature');
end
function backupParams(S, file)
S.backupParamsCore(file);
file.DIT = S.DIT;
file.T = S.T;
file.vinf = S.vinf;
file.Ea_v = S.Ea_v;
file.Jinf = S.Jinf;
file.Ea_J = S.Ea_J;
end
end
methods( Static )
function S = fromBackup(paramsfile, statefile)
S = phasefieldMethod.Simulation.fromBackupCore( ...
@phasefieldMethod.SimpleSimulation, ...
paramsfile, statefile);
S.DIT = paramsfile.DIT;
S.T = paramsfile.T;
S.vinf = paramsfile.vinf;
S.Ea_v = paramsfile.Ea_v;
S.Jinf = paramsfile.Jinf;
S.Ea_J = paramsfile.Ea_J;
S = S.apply();
end
end
end
\ No newline at end of file
MATLAB/+phasefieldMethod/GSTSimulation.m deleted 100755 → 0
+ 0
− 152
View file @ 4786a80b
classdef GSTSimulation < phasefieldMethod.TestSimulation
%GSTSIMULATION A simulation for the model Zhi Yang used for GST.
% Default parameters are for GST but can be replaced.
properties
IE = 0.06; % interfacial energy [J/m^2]
DIT; % diffuse interface thickness [m]
L = 625e6; % latent heat [J/m^3]
Tm = 889; % melting temperature [K]
T; % temperature [K]
Vm = 2.9e-28; % volume of a monomer [m^3]
ninf = 0.012; % viscosity for infinite temperature [Pa*s]
m = 140; % fragility
Tg = 472; % other glass transition temperature [K]
jd = 2.99e-10; % jump distance [m]
Ea = 2.3 * 1.6e-19; % activation energy [J]
Tglass = 534; % glass transition temperature [K]
wa = 180; % wetting ange [degrees]
end
properties (SetAccess = protected)
n; % viscosity [Pa*s]
end
properties ( Constant )
kB = 1.380649e-23; % Boltzmann constant, [J/K]
eV = 1.602176634e-19 % Electron volt [J]
end
methods
function S = GSTSimulation(spacing, seed)
S = S@phasefieldMethod.TestSimulation(spacing, seed);
end
function S = apply(S)
S.eps = sqrt(6*S.IE*S.DIT);
S.W = 3*S.IE/S.DIT;
S.dGv = S.L*(S.Tm - S.T)*2.*S.T/S.Tm./(S.Tm+S.T);
dGv00 = S.L*(S.Tm - S.Tglass)*2*S.Tglass/S.Tm/(S.Tm+S.Tglass);
n00 = (10^(log10(S.ninf)+(12-log10(S.ninf))*(S.Tg/S.Tglass)*...
exp((S.m/(12-log10(S.ninf))-1)*(S.Tg/S.Tglass-1))));
n0 = n00/exp(S.Ea/S.kB/S.Tglass);
vinf = 4*S.kB*S.Tglass*(1-exp(-dGv00*S.Vm/S.kB/S.Tglass))/...
(3*pi*S.jd*S.jd*n00*dGv00)/exp(-S.Ea/S.kB/S.Tglass);
structneighbours27 = phasefieldMethod.analyse_structure_27(S.phasefield);
sf = structfactor(S.wa, gather(structneighbours27));
S.n = viscosity(n0, S.Ea, S.T, S.Tglass, S.m, S.ninf, S.Tg);
S.J = nucleationrate(S.dGv, S.IE, S.Vm, S.T, S.jd, S.n, sf);
S.M = mobility(S.W, S.eps, vinf, S.Ea, S.Tglass, S.T, ...
S.dGv, S.Vm, S.jd, S.n);
S = apply@phasefieldMethod.Simulation(S);
end
function backupParams(S, file)
% Write the settings and evolution parameters to a .mat file.
% Arguments:
% file - Handle of a .mat file
% Returns nothing
S.backupParamsCore(file);
file.IE = S.IE;
file.DIT = S.DIT;
file.L = S.L;
file.Tm = S.Tm;
file.T = S.T;
file.Vm = S.Vm;
file.ninf = S.ninf;
file.m = S.m;
file.Tg = S.Tg;
file.jd = S.jd;
file.Ea = S.Ea;
file.Tglass = S.Tglass;
file.wa = S.wa;
end
end
methods (Static)
function S = fromBackup(paramsfile, statefile)
S = phasefieldMethod.Simulation.fromBackupCore( ...
@phasefieldMethod.GSTSimulation, paramsfile, statefile);
S.IE = paramsfile.IE;
S.DIT = paramsfile.DIT;
S.L = paramsfile.L;
S.Tm = paramsfile.Tm;
S.T = paramsfile.T;
S.Vm = paramsfile.Vm;
S.ninf = paramsfile.ninf;
S.m = paramsfile.m;
S.Tg = paramsfile.Tg;
S.jd = paramsfile.jd;
S.Ea = paramsfile.Ea;
S.Tglass = paramsfile.Tglass;
S.wa = paramsfile.wa;
S = S.apply();
end
end
end
function M = mobility(W, eps, vinf, Ea, Tglass, T, dGv, Vm, jd, n)
%TODO doc
kBT = phasefieldMethod.GSTSimulation.kB.*T;
% for T < Tglass
M = sqrt(2*W)/6/eps*vinf*exp(-Ea./kBT);
% for T>Tglass
upf2 = sqrt(2*W)/6/eps*4.*kBT.*(1-exp(-dGv*Vm./kBT))./(3*pi*jd*jd*n.*dGv);
% combine
M(T > Tglass) = upf2(T > Tglass);
end
function J = nucleationrate(dGv, IE, Vm, T, jd, n, structfactor)
%TODO doc
dGv = max(dGv, 0); % change negative terms to zero
rcrit = 2 * IE ./ dGv; % critical radius matrix
nc = 4/3*pi * (rcrit).^3 /Vm; % points in critical nucleus
kBT = phasefieldMethod.GSTSimulation.kB*T;
jf = kBT./(3*pi*jd*jd*jd*n); % jump frequency
I0 = 4*jf.*(nc.^(2/3)).*sqrt(dGv*Vm./(6*pi*nc.*kBT))/Vm; % nuclatio rate prefactor
dGc = 16/3*pi*(IE^3)./(dGv.*dGv); % nucleaton barrier energy
dGc = dGc .* structfactor; % consider heterogeneous effects
J = I0.*exp(-dGc./kBT); % nucleation rate
end
function n = viscosity(n0, Ea, T, Tglass, m, ninf, Tg)
%TODO doc
kBT = phasefieldMethod.GSTSimulation.kB*T;
n = n0*exp(Ea/kBT); % viscosity for T < Tglass
n2 = 10.^(log10(ninf)+(12-log10(ninf)) ... % T > Tglass
*(Tg./T).*exp((m/(12-log10(ninf))-1)*(Tg./T -1)));
n(T > Tglass) = n2(T > Tglass);
%TODO if n goes to Inf at some points, it might be necessary to fix
end
function sf = structfactor(wa, neighs)
s =(2+cosd(wa))*(1-cosd(wa))*(1-cosd(wa))/4;
sf = (neighs == 0) * 1 + ...
and((neighs >= 1), (neighs < 7)) * s*(1.2^2) + ...
and((neighs >= 7), (neighs < 26)) * s*1.2 + ...
(neighs >= 26) * s;
end
\ No newline at end of file
MATLAB/+simulationModels/AllPhysicalSimulation.m 0 → 100755
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classdef AllPhysicalSimulation < simulationModels.PhysicalSimulation
%ALLPHYSICALSIMULATION - A simulation using only physically reasonable
% values.
%
% Properties that need to be defined by subclasses:
% DIT
% IE
%
% Methods that need to be provided by subclasses:
% volumefreeEnergy
% velocity
% nucleationRate
properties (Abstract, SetAccess = protected)
DIT;
IE;
end
methods
function S = AllPhysicalSimulation(spacing, seed)
S@simulationModels.PhysicalSimulation(spacing, seed);
end
function S = apply(S)
S.eps = sqrt(6 .* S.IE .* S.DIT);
S.W = 3 .* S.IE ./ S.DIT;
S.dGv = S.volumeFreeEnergy();
S.M = S.velocity() ./ (6 * S.DIT .* S.dGv);
S = apply@simulationModels.PhysicalSimulation(S);
end
end
end
MATLAB/+simulationModels/ArrheniusNucleation.m 0 → 100755
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View file @ 89c2cc82
classdef ArrheniusNucleation
%ARRHENIUSNUCLEATION A arrhenius approximation for the nucleation rate.
properties (Abstract, SetAccess = protected)
J_Ea;
J00;
end
methods
function J = nucleationRate(S)
kB = simulationModels.Constants.kB;
J = S.J00 .* exp( - S.J_Ea ./ kB ./ S.T );
end
end
end
MATLAB/+simulationModels/ArrheniusVelocity.m 0 → 100755
+ 27
− 0
View file @ 89c2cc82
classdef ArrheniusVelocity < simulationModels.PhysicalSimulation
%ARRHENIUSVELOCITY - A simulation with an arrhenius model for the
% growth velocity.
%
% Properties that need to be defined by subclasses:
% v00 - velocity for T -> inf [m/s]
% Ea - Activation energy [J]
%
% Methods provided:
% velocity
properties (Abstract, SetAccess = protected)
v00; % velocity for T -> inf [m/s]
Ea; % Activation energy [J]
end
methods
function S = ArrheniusVelocity(spacing, seed)
S = S@simulationModels.PhysicalSimulation(spacing, seed);
end
function v = velocity(S)
kB = simulationModels.Constants.kB;
v = S.v00 .* exp( - S.Ea ./ (kB * S.T));
end
end
end
MATLAB/+simulationModels/ArrheniusViscosity.m 0 → 100755
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classdef ArrheniusViscosity < simulationModels.PhysicalSimulation
%ARRHENIUSVISCOSITY - A simulation with an arrhenius model for the
% viscosity.
%
% Properties that need to be defined by subclasses:
% n00 - Viscosity for T -> inf [Pa*s]
% Ea - Activation energy [J]
%
% Methods provided:
% viscosity
properties (Abstract, SetAccess = protected)
n00; % Viscosity for T -> inf [Pa*s]
Ea; % Activation energy [J]
end
methods
function S = ArrheniusViscosity(spacing, seed)
S = S@simulationModels.PhysicalSimulation(spacing, seed);
end
function n = viscosity(S)
kB = simulationModels.Constants.kB;
n = S.n00 .* exp( S.Ea ./ (kB * S.T));
end
end
end
MATLAB/+simulationModels/ClassicalNucleation.m 0 → 100755
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View file @ 89c2cc82
classdef ClassicalNucleation < simulationModels.HeterogeneousNucleation
%CLASSICALNUCLEATION - A simulation using classical nucleation theory
% for the nucleation rate.
% Uses the more general heterogeneous model with a structfactor set to
% one.
%
% Properties that need to be defined by subclasses:
% jd
% IE
%
% Methods that need to be provided by subclasses:
% volumefreeEnergy
% viscosity
%
% Methods provided:
% structfactor
% nucleationRate
% apply
methods (Abstract)
volumeFreeEnergy(S)
viscosity(S)
end
methods
function s = structfactor(S)
s = 1;
end
end
end
MATLAB/+simulationModels/CombinedVelocity.m 0 → 100755
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View file @ 89c2cc82
classdef CombinedVelocity < simulationModels.ArrheniusVelocity & ...
simulationModels.WilsonFrenkelVelocity
%COMBINEDVELOCITY - A simulation with a combined model for the groth
% velocity.
%
% Properties that need to be defined by subclasses:
% jd
% r_atom
% R_hyd
% Ea
%
% Methods that need to be provided by subclasses:
% freeEnergy
% viscosity
%
% Methods provided:
% velcocity
properties (Abstract, SetAccess = protected)
Tglass; % Glass transition temperature
end
properties (SetAccess = protected)
v00;
end
methods
function S = CombinedVelocity(spacing, seed)
S@simulationModels.ArrheniusVelocity(spacing, seed);
S@simulationModels.WilsonFrenkelVelocity(spacing, seed);
% Make the transition between the models continuous
kB = simulationModels.Constants.kB;
Ttemp = S.T;
S.T = S.Tglass;
S.v00 = S.velocity() / exp( - S.Ea ./ (kB * S.Tglass));
S.T = Ttemp;
end
function v = velocity(S)
v = velocity@simulationModels.WilsonFrenkelVelocity(S);
v2 = velocity@simulationModels.ArrheniusVelocity(S);
v(S.T<S.Tglass) = v2(S.T<S.Tglass);
end
end
end
MATLAB/+simulationModels/CombinedViscosity11.m 0 → 100755
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classdef CombinedViscosity11 < simulationModels.ArrheniusViscosity & ...
simulationModels.MyegaViscosity11
%COMBINEDVISCOSITY - A simulation with a combined model for the
% viscosity, using the MYEGA model for temperatures above the glass
% transition temperature Tglass and an Arrhenius model for lower
% temperatures.
%
% Properties that need to be defined by subclasses:
% Tglass
% Ea
% ninf
% Tg
% m
%
% Methods provided:
% viscosity
properties (Abstract, SetAccess = protected)
Tglass; % Glass transition temperature
end
properties (SetAccess = protected)
n00;
end
methods
function S = CombinedViscosity11(spacing, seed)
S@simulationModels.ArrheniusViscosity(spacing, seed);
S@simulationModels.MyegaViscosity11(spacing, seed);
% Make the transition between the models continuous
kB = simulationModels.Constants.kB;
% S.n00 = S.temperaureViscosity(S.Tglass) / ...
S.n00 = (10^(log10(S.ninf)+(12-log10(S.ninf))*(S.Tg/S.Tglass)*...
exp((S.m/(12-log10(S.ninf))-1)*(S.Tg/S.Tglass-1)))) / ...
exp( S.Ea ./ (kB * S.Tglass));
end
function n = viscosity(S)
n = viscosity@simulationModels.MyegaViscosity11(S);
n2 = viscosity@simulationModels.ArrheniusViscosity(S);
n(S.T<S.Tglass) = n2(S.T<S.Tglass);
end
end
end
MATLAB/+simulationModels/CombinedViscosity_1.m 0 → 100755
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classdef CombinedViscosity_1 < simulationModels.ArrheniusViscosity & ...
simulationModels.MyegaViscosity_1
%COMBINEDVISCOSITY - A simulation with a combined model for the
% viscosity, using the MYEGA model for temperatures above the glass
% transition temperature Tglass and an Arrhenius model for lower
% temperatures.
%
% Properties that need to be defined by subclasses:
% Tglass
% Ea
% ninf
% Tg
% m
%
% Methods provided:
% viscosity
properties (Abstract, SetAccess = protected)
Tglass; % Glass transition temperature
end
properties (SetAccess = protected)
n00;
end
methods
function S = CombinedViscosity_1(spacing, seed)
S@simulationModels.ArrheniusViscosity(spacing, seed);
S@simulationModels.MyegaViscosity_1(spacing, seed);
% Make the transition between the models continuous
kB = simulationModels.Constants.kB;
S.n00 = S.temperaureViscosity(S.Tglass) / ...
exp( S.Ea ./ (kB * S.Tglass));
end
function n = viscosity(S)
n = viscosity@simulationModels.MyegaViscosity_1(S);
n2 = viscosity@simulationModels.ArrheniusViscosity(S);
n(S.T<S.Tglass) = n2(S.T<S.Tglass);
end
end
end
MATLAB/+simulationModels/Constants.m 0 → 100755
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View file @ 89c2cc82
classdef Constants
% A class that defines some general used constants.
properties (Constant)
kB = 1.380649e-23; % Boltzmann constant, [J/K]
eV = 1.602176634e-19 % Electron volt [J]
Na = 6.02214076e23 % Avogadro constant [1/mol]
zeroC = 273.15 % Zero degrees celsius [K]
end
end
\ No newline at end of file
MATLAB/+simulationModels/FrenkelSimplifiedVelocity.m 0 → 100755
+ 35
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View file @ 89c2cc82
classdef FrenkelSimplifiedVelocity < simulationModels.PhysicalSimulation
%WILSONFRENKELVELOCITY - A simulation using a velocity from the Wilson
% and Frenkel model.
%
% Properties that need to be defined by subclasses:
% Atilde
%
% Methods that need to be provided by subclasses:
% freeEnergy
% viscosity
%
% Methods provided:
% velcocity
properties (Abstract, SetAccess = protected)
Atilde
end
methods (Abstract)
freeEnergy(S)
viscosity(S)
end
methods
function S = FrenkelSimplifiedVelocity(spacing, seed)
S@simulationModels.PhysicalSimulation(spacing, seed);
end
function v = velocity(S)
kB = simulationModels.Constants.kB;
v = S.Atilde ./ S.viscosity() .* ...
(1 - exp(- S.freeEnergy() ./ (kB .* S.T)) );
end
end
end
MATLAB/+simulationModels/HeterogeneousNucleation.m 0 → 100755
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View file @ 89c2cc82
classdef HeterogeneousNucleation
%CLASSICALNUCLEATION - A simulation using classical nucleation theory
% for the nucleation rate, but includes heterogeneous effects.
%
% Properties that need to be defined by subclasses:
% jd
% IE
%
% Methods that need to be provided by subclasses:
% volumefreeEnergy
% viscosity
% structfactor
%
% Methods provided:
% nucleationRate
% apply
properties (Abstract, SetAccess = protected)
jd;
IE;
Vm;
end
methods (Abstract)
volumeFreeEnergy(S)
viscosity(S)
structfactor(S)
end
methods
function J = nucleationRate(S)
kB = simulationModels.Constants.kB;
dGv = S.volumeFreeEnergy();
sf = S.structfactor();
nc = 32 * pi ./ (3 .* S.Vm) .* (S.IE ./ dGv).^3;
disp(nc);
% It is important that the exp() term is in the middle, as the
% other factors get quite large.
J = 4 .* nc.^(2/3) .* ...
dGv.^2 .* sqrt(kB * S.T ./ S.IE.^3) .* ...
exp( -16 * pi * S.IE.^3 ./ (3 * dGv.^2 .* kB .* S.T) .* sf) ...
./ (24 * pi^2 * S.jd.^3 .* S.viscosity());
end
end
end
MATLAB/+simulationModels/MyegaViscosity11.m 0 → 100755
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View file @ 89c2cc82
classdef MyegaViscosity11 < simulationModels.PhysicalSimulation
%MYEGAVISCOSITY - A simulation using the MYEGA model for the viscosity.
%
% Properties that need to be defined by subclasses:
% ninf - Viscosity for T -> inf [Pa*s]
% Tg - Reference temperature in MYEGA equation [K]
% m - Fragility [1]
%
% Methods provided:
% viscosity
properties (Abstract, SetAccess = protected)
ninf; % Viscosity for T -> inf [Pa*s]
Tg; % Reference temperature in MYEGA equation [K]
m; % Fragility [1]
end
methods
function S = MyegaViscosity11(spacing, seed)
S = S@simulationModels.PhysicalSimulation(spacing, seed);
end
function n = viscosity(S)
n = S.temperaureViscosity(S.T);
end
end
methods (Access = protected)
function n = temperaureViscosity(S, T)
n = 10.^(log10(S.ninf) + (12-log10(S.ninf)) ...
*(S.Tg./T) .* exp((S.m/(12-log10(S.ninf)) - 1) ...
*(S.Tg./T - 1)));
end
end
end
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