From c408663b7d4f33e03623ac52509053c3b75147ad Mon Sep 17 00:00:00 2001 From: jhiscocks Date: Wed, 11 Aug 2021 15:31:42 -0400 Subject: [PATCH] Update ODFTutorial.m Note for line 7: not sure if g is a percentage or fraction - I expect fraction is more accurate. Check Line 44: not familair with ODF display methods. --- doc/Tutorials/ODFTutorial.m | 72 ++++++++++++++++++------------------- 1 file changed, 36 insertions(+), 36 deletions(-) diff --git a/doc/Tutorials/ODFTutorial.m b/doc/Tutorials/ODFTutorial.m index 241ad7ac3..ed85cb6af 100644 --- a/doc/Tutorials/ODFTutorial.m +++ b/doc/Tutorials/ODFTutorial.m @@ -2,24 +2,24 @@ % %% Theory % -% The orientation distribution function (ODF) is a function on the -% orientation space that associates to each orientation $g$ the volume -% percentage of crystals in a polycrystaline specimen that are in this +% The orientation distribution function (ODF) is a function in +% orientation space that associates each orientation $g$ with the volume +% fraction of crystals in a polycrystaline specimen that are in this % specific orientation, i.e., % % $$\mathrm{odf}(g) = \frac{1}{V} \frac{\mathrm{d}V(g)}{\mathrm{d}g}.$$ % -% In MTEX an entirely random texure will have an ODF constant to one. In +% In MTEX a perfectly random texure will have an ODF equal to a value of one for all orientations. In % other word the values of ODFs in MTEX can be interpreted as multiples of % the random distribution (mrd). % %% Computing an ODF from Individual Orientations % -% Individual orientations data may be obtained by experimental by EBSD, -% ACOM or 3d X-ray imaging; or from simulations, like VPSC. In the -% following we consider an EBSD map of an Titanium alloy. +% Individual orientation data may be obtained experimentally by EBSD (orientation mapping in a SEM), +% ACOM (orientation mapping in a TEM) or 3d X-ray imaging; or from computer simulations involving texture modeling, such as VPSC. In the +% following example we consider an EBSD map of an Titanium alloy. Note that this test data is based on hexagonal layout rather than the more common x-y grid. -% import the titanium data +% import the titanium test data downloaded with the MTEX package mtexdata titanium % plot an orientation map @@ -30,67 +30,67 @@ % using the command % . -% extract the orientations +% copy the EBSD orientations to a separate variable ori = ebsd.orientations; % compute the ODF odf = calcDensity(ori) %% -% There many different ways to visualize ODF: or , , and % . The most common but not -% recommended way are sections with respect to the third Euler angle +% recommended method uses sigma sections, slices with respect to the third Euler angle % $\varphi_2$ plot(odf) %% Computing an ODF from Pole Figure Data % -% Pole figure data arises when textured materials are measured via x-ray, -% neutron or syncrotron radiation. Generaly, for $3$ to $10$ diffraction -% planes specified by Miller indices $(hk\ell)$ diffraction intensities are -% measured at a spherical grid of specimen directions. In the example below -% each dot corresponds to one diffraction intensity at the plane indicated -% at the top of the spherical plots measured from the direction -% corresponding to the pixel position. - -% import pole figure data +% Pole figure data is often generated when textured materials are measured via x-ray, +% neutron or syncrotron radiation. When performing this type of diffraction experiment, +% diffraction intensities are measured over a spherical grid of specimen directions for $3$ to $10$ diffraction +% planes specified by Miller indices $(hk\ell)$ . In the example below, for each plane indicated +% at the top of the spherical plot, each dot colour corresponds to a measured diffraction intensity +% at the position corresponding to the dot location. + +% import the PTX pole figure test data downloaded with the MTEX package mtexdata ptx -% plot the data +% plot the pole figures, representing the experimental data acquired plot(pf) +% show the colour bar. Note the maximum intensity is different for each pole figure. mtexColorbar %% % The of an ODF from pole figure data -% requires the solution of an ill posed inverse problem. This mean the -% reconstruction problem has in general , but there are several ODFs that correspond to the same -% set of pole figure data. MTEX applies to identify among all solutions the physically most -% reasonable. - -% compute an ODF with default settings +% requires the solution of an *ill posed inverse problem*. This means the +% reconstruction problem generally , and there are several ODFs that may be constructed from the same +% set of pole figure data. MTEX generates multiple possibilities, and then applies to identify the physically most +% reasonable result. + +% compute an ODF from the three input pole figures with default settings odf = calcODF(pf) %% -% Once an ODF is reconstructed we can check how well its pole figures fit -% the measured pole figures +% Once an ODF is reconstructed we can check how well the ODF's pole figures fit +% the experimentally measured pole figures -% plot the recalculated pole figures +% plot the pole figures of the calculated ODF plotPDF(odf,pf.h) %% ODF Modelling % -% Besides from experimental data MTEX allows also the definition of model -% ODFS of different type. These include , -% , +% Aside from using experimental data, MTEX also allows the definition of model +% ODFs of different types. These include , +% , % and any . -% define a fibre symmetric ODF +% define a gamma fibre ODF odf = fibreODF(fibre.gamma(odf.CS)) % plot it in sigma sections