EBSD数据分析

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Analysis of EBSD Data (L17),27-750, Fall 2009,Texture, Microstructure & Anisotropy, Fall 2009,B. El-Dasher*, A.D. Rollett, G.S. Rohrer, P.N. Kalu,Last revised,:,7,th,Nov. 09,*,now with the Lawrence Livermore Natl. Lab.,Overview,Understanding the program:,Important menus,Definition of Grains in OIM,Partitioning datasets,Cleaning up the data:,Types,Examples of Neighbor correlation,Orientation:,System Definition,Distribution Functions (ODFs),Plotting ODFs,Overview,Misorientation:,Definitions - Orientation vs. Misorientation,Distribution Functions (MDFs),Plotting MDFs,Other tools:,Plotting Distributions,Interactive tools,Navigating the menus,There are two menus that access virtually everything:,Creates new partitions,Imports data as partitions,Access to routines that cleanup the dataset,Use this to export text .ang files,Check the scan stats,Rotate the,orientations,of each point about,sample frame,Cut out scan sections,Access to menu for:,- Maps,- Texture calculation,- Texture plots,Export grain ID data associated with each point,Check the partition stats & definition,Change the partition properties:,Decide which points to include,Define a “grain”,Grain Definitions,OIM defines a set of points to constitute a grain if:,- A path exists between any two points (in the set) such that it does not traverse a misorientation angle more than a specified tolerance,- The number of,points,is greater than a specified number,Points with a CI less than specified are excluded from,statistics,Note:,Points that are excluded are given a grain ID of 0 (zero) in exported files,Grain Definitions,Examples of definitions,3 degrees,15 degrees,Note that each color represents 1 grain,Partitioning Datasets,Choose which points to include in analysis by setting up selection formula,Use to select by individual point attributes,Use to select by grain attributes,Selection formula is explicitly written here,Grain CI Standardization:,Changes the CI of all points within a grain to be that of the highest within each grain,Most useful if a minimum CI criterion is used in analyzing data (prevents low CI points within a grain from being lost),Data Cleanup,Neighbor Orient. Correlation,Performed on all points in the dataset,For cleanup level,n:,Condition 1: Orientation of 6-,n,nearest neighbors is different than current point (misorientation angle chosen),Condition 2: Orientation of 6-,n,nearest neighbors is the same as each other,If both conditions are met, the points orientation is chosen to be a neighbors at random,Repeat low cleanup levels (,n=3,max,) until no more points change for best results,Neighbor Phase Correlation,- Same as Grain Dilation but instead of using the grain with most number of neighboring points, the phase with the most number of neighboring points is used,Output Options:,Overwrite current dataset,Create “cleaned up” dataset as a new dataset,Write the “cleaned up” dataset directly to file,Neighbor CI Correlation,Performed only on points with CI less than a given minimum,The orientation and CI of the neighbor with highest CI is assigned to these points,Use when majority of points are high CI, and only a few bad points exist,Grain Dilation:,Acts only on points that do not belong to any grain as defined,A point becomes part of the grain with the most number of surrounding points,Takes the orientation and CI of the neighboring point with highest CI,Use to remove bad points due to pits or at G.Bs,Neighbor Correlation Example,No Cleanup,Level 0,Level 3,Note that Higher cleanup levels are iterative (i.e. Level 3= Levels 0,1,2,3),Definition of Orientation,By definition an orientation is always relative. The OIM uses the sample surface to define the orthogonal reference frame.,Quantities are transformed,from,sample frame to,crystal,frame,e,1,s,e,2,s,j,1,F,j,2,NB: a more comprehensive discussion of reference frames is given later,Orientation Distribution Functions,The ODF displays how the measured orientations are distributed in orientation space,Two types of distributions can be calculated:,Discrete ODF:,Bin size defines the volume of each element in orientation space (5,o,x5,o,x5,o,),Fast calculation,Suitable for most texture strengths but not weak textures if the number of grains is small (consider the number of data points per cell required to achieve reasonably low noise),Continuous ODF:,Generalized Spherical Harmonic Functions: Rank defines the “resolution” of the function,Equivalent to a Fourier transform,Calculation time rises steeply with rank number (32 is an effective maximum),Time intensive,Mostly appropriate for weaker textures,Some smoothing is inherent,Plotting Orientation Distributions,One must select the types of data visualization desired,Pole figures show the distribution of specific crystal planes w.r.t. sample reference frame,For the generation of more than one PF, they need to be added one at a time.,Inverse Pole Figures are used to illustrate which crystal plane normals are parallel to sample directions (generally RD, TD & ND),The indices entered represent which sample reference frame plane is being considered: 100, 010 and 001 are typical choices,Multiple planes also need to be entered one at a time,Euler space plot shows the distribution of intensity as a function of the Euler angles,Used to visualize pockets of texture as well as “fiber” textures,Resolution defines how many slices are possible in the plot,Types of ODF/Pole Figure/ Inverse PF Plots,Choose texture and desired plot type,Use to add multiple plots to the same image,NB: a more comprehensive discussion of reference frames is given later,The,Average Orientation,of the pixels in a grainis given by,this equation:,RD,10 000 orientations near to the Brass component:,represented,by a 111 pole figure,and, in the complete Euler space to show the 24 equivalents resulting from application of cubic crystal symmetry,111,Preparation of the data for analysis,i=1,24,Courtesy of N. Bozzolo,Very,simple, nest-ce pas?,However, there is a problem.,As a consequence of the crystal symmetry, there are several equivalent orientations.This example illustrates the point:,Cho J H, Rollett A D and Oh K H (2005) Determination of a mean orientation in electron backscatter diffraction measurements,Metall. Mater. Trans,.,36A,3427-38,1,=0,1,=5,1,=10,1,=15,.,max = 5.56,.,Parameters for texture analysis,Courtesy of N. Bozzolo,max = 5.37,16x16x8,3,22,5,max = 4.44,32x32x16,8,22,5,max = 5.56,Resolution 32x32x16,Gaussian 3,L,max,22,Bin Size5,Effect of the binning resolution,Effect of the width of the Gaussian,Parameters for texture analysis,Courtesy of N. Bozzolo,max = 5.17,L,max,= 16,max = 5.56,L,max,= 22,Effect of the maximum rank in the series expansion, L,max,max = 2.43,L,max,= 5,max = 4.04,L,max,= 8,max = 6.36,L,max,= 34,Resolution 32x32x16,Gaussian 3,L,max,22,Bin Size5,Courtesy of N. Bozzolo,max = 31 !,Same, with,10,binning,:,Direct Method,max = 5.56,In effect the harmonic method gives some ”smoothing . Without this, a coarse binning of, say, 10, produces a very “lumpy” result.,1,=5,Courtesy of N. Bozzolo,0,=,8,7.6,at,0 35 30,80000 grains,6.6,at,0 35 30,7.1 at 0 35 25,8.2 at 0 30 25,8.3,at,15 30 30,2000 grains,5.8,at,5 30 15,7.3 at 345 35 50,15.5 at -5 35 50,16000 grains,6.7,at,0 35 30,7.9 at 0 35 30,6.9 at -5 35 35,9.0 at -5 30 40,Gaussienne de,0,=,4,Triclinic sample symmetry,0,=,4,0,=,8,Statistical Aspects,Number of grains measured,Width of the Gaussian ( and/or L,max,),Influence of the sample symmetry,Zirconium, equiaxed,Sections thru the OD at,constant ,1,(L,max,= 34),16.0,11.3,8.0,5.6,4.0,2.8,2.0,1.4,0.7,Texture = distribution of orientations, Problem of sampling!,Orthorhombic sample symmetry,Courtesy of N. Bozzolo,Single EBSD map (1 mm,2,),Multiple maps, different locations ( total =1 mm,2,),RD,TD,ND,10.0,(00.1),0.7,1.4,2.0,2.8,4.0,5.6,8.0,11.3,asymmetry of intensity,Homogeneity/heterogeneity of the specimen.,equiaxed Ti,Not just the number of grains must be considered but also their spatial distribution:,Statistical Aspects,Courtesy of N. Bozzolo,Texture Microstructure Coupling,Example : partial texture of populations of grains identified by a grain size criterion,(zirconium at the end of recrystallization ),partial texture of the,largest grains,Partial texture of the,smallest grains,Important for texture evolution during grain growth: the large grains grow at the expense of the small grains. Since the large grains have a different texture, the overall texture also changes during growth.,D 2D (=11 m),3496 grains,17.9% surf.,D D/2 (=2.75 m),14255 grains,1.7% surf.,Global texture,j,1,= 0,0,90,0,60,F,j,2,7.41,16.0,11.3,8.0,5.6,4.0,2.8,2.0,1.4,0.7,Definition of Misorientation,Misorientation is an orientation defined with another crystal orientation frame as reference instead of the sample reference frame,Thus a misorientation is the axis transformation from one point (crystal orientation) in the dataset to another point,x,z,y,g,A,-1,g,B,x,y,z,are sample reference axes,g,A,is,orientation,of data point A (reference orientation) w.r.t sample reference,g,B,is,orientation,of data point B w.r.t. sample reference,Misorientation = g,B,g,A,-1,Again the function can be either discrete or continuous,Misorientation Distribution Functions,Calculating MDFs is very similar to calculating ODFs,Correlated MDF:,Misorientations are calculated only between neighbors,If the misorientation is greater than the grain definition angle, the data point is included,This effectively only plots the misorientations between neighboring points across a G.B.,Uncorrelated MDF:,Misorientations are calculated between all pairs of orientations in dataset,This is the “texture derived” MDF as it effectively is calculated from the ODF,Only effectively used if the sample has weak texture,Texture Reduced:,Requires both Correlated and Uncorrelated MDFs to be calculated,for the same plot type,This MDF is simply the Correlated / Uncorrelated values,May be used to amplify any features in the correlated MDF,Plotting MDFs,Again, you need to choose what data you want to see,Select the Texture dataset,Select the plot type (axis/angle ; Rodrigues; Euler),Use to generate plot sections,Sections through Misorientation Space,Charts,Charts are easy to use in order to obtain statistical information,Increasing bin #,Reconstructed Boundaries,Data MUST be on hexagonal grid,Clean up the data to desired level,Choose boundary deviation limit,Generate a map with reconstructed boundaries selected,Export g.b. data into text file,This type of data is required for stereological analysis of 5-parameter grain boundary character,The software includes an analysis of grain boundaries that outputs the information as a (long) list of line segment data.,use of the GB segment analysis is an essential preliminary step before performing the stereological 5-parameter analysis of GBCD.,The data must be on a hexagonal/triangular grid. If you have a map on a square grid, you must convert it to a hexagonal grid. Use the software called OIMTools to do this (freely available fortran program).,Reference Frames,This next set of slides is devoted to explaining, as best we can, how to relate features observed in EBSD images/maps to the Euler angles.,In general, the Euler frame is not aligned with the,x-y,axes used to measure locations in the maps.,The TSL and Channel,softwares,both rotate the image 180 relative to the original physical sample.,Both TLS and Channel,softwares,use different reference frames for measuring spatial location versus the the Euler angles, which is, of course, extremely confusing.,TSL / OIM Reference Frames,-TD= -y,Euler,ND= z,Euler,-RD= -x,Euler,Z,spatial,x,spatial,y,spatial,Sample Reference Frame for Orientations/Euler Angles,Reference Frame for Spatial Coordinates,Crystal Reference Frame:,Remember that, to obtain directions and tensor quantities in the crystal frame for each grain (starting from coordinates expressed in the Euler frame), one must use the Euler angles to obtain a transformation matrix (or equivalent).,+,Z,spatial,points,in,to the plane,Z,Euler,points,out,of the plane,x,spatial,y,spatial,RD = x,Euler,=100,sample,TD = y,Euler,= 010,sample,Image:,Note the 180 rotation.,“,+” denotes the Origin,+,Physical specimen:,Mounted in the SEM, the tilt axisis parallel to “x,spatial,”,The purple line indicates a direction, associated with, say, a scratch, or trace of a grain boundary on the specimen.,TSL / OIM Reference Frames for,Images,From Herb Millers notes:,The axes for the TSL Euler frame,are,consistent with the RD-TD-ND system in the TSL Technical Manual, but only with respect to maps/images, not the physical specimens.,The axes for the HKL system,are,consistent with Nathalie Bozzolos notes and slides. Here, x is in common, but the two y-axes point in opposite directions.,Conversion from spatial to Euler and vice versa (TSL only),Notes: the image, as presented by the TSL software, has the vertical axis inverted in relation to the physical sample, i.e. a 180 rotation.,Note that the transformation is a 180 rotation about the line,x=y,31,TSL / OIM Reference Frames:,Coordinates in,Physical Frame,Conversion to,Image,The previous slides make the point that a transformation is required to align spatial coordinates with the Euler frame.,However, there is also a 180 rotation between the physical specimen and the image. Therefore to align physical markings on a specimen with traces and crystals in an image, it is necessary to take either the physical data and rotate it by 180, or to rotate the crystallographic information.,-TD= -y,sample,ND= z,Euler,-RD= -x,Euler,Z,spatial,x,spatial,y,spatial,Sample Reference Frame for Orientations, How to measure lines etc. on a physical specimen?, Answer: use the spatial frame as shown on the diagram to the left (which is NOT the normal, mathematical arrangement of axes) and your measured coordinates will be correct in the images, provided you plot them according to the IMAGE spatial frame. The purple line, for example, will appear on the image (e.g. an IPF map) as turned by 180 in the x-y plane.,+,32,Cartesian Reference Frame,for,Physical Measurement,y,Euler,x,Euler,x,Cartesian,y,Cartesian, How to measure lines etc. on a physical specimen using the standard,Cartesian frame,with,x,pointing right, and,y,pointing up?, Answer: use the,Cartesian frame,as shown on the diagram to the left (which IS the normal, mathematical arrangement of axes and is NOT the,frame used for point coordinates,that you find in a .ANG file). Apply the transformation of axes (passive rotation) as specified by the transformation matrix shown and then your measured coordinates will be in the same frame as your Euler angles. This transformation is a +90 rotation about,z,sample,. In this case, the z-axis points out of the plane of the page.,33,TSL / OIM Reference Frames: Labels in the TSL system, What do the labels “RD”, “TD” and “ND” mean in the TSL literature?, The labels should be understood to mean that RD is the x-axis, TD is the y-axis and ND the z-axis, all for Euler angles (but,not,spatial coordinates)., The labels on the Pole Figures are consistent with the maps/images (but NOT the physical specimen)., The labels on the diagram are consistent with the maps/images, but NOT the physical specimen, as drawn., The frame in which the spatial coordinates are specified in the datasets is different from the Euler frame (RD-TD-ND) see the preceding diagrams for information and for how to transform your spatial coordinates into the same frame as the Euler angles, using a 180 rotation about the line,x=y,.,= x,spatial,= y,Euler,= y,spatial,= x,Euler,The diagram is reproduced from the TSL Technical Manual; the designation of RD, TD and ND is only correct for Euler angles in reference to the plotted maps/images,not,the physical specimen,TSL versus HKL Reference Frames,+,Z (x),x,spatial,y,spatial,RD=100,sample,= x,Euler,TD=010,sample,= y,Euler,TSL,HKL,+,Z (x),x,spatial,y,spatial,RD=100,sample,= x,Euler,TD=010,sample,= y,Euler,The two spatial frames are the same, exactly as noted by Changsoo Kim and Herb Miller previously. The figures show,images,(as opposed to physical specimen).,The Euler angle references frames differ by a rotation of +90 (add 90 to the first Euler angle) going from the TSL to the HKL frames (in terms of an axis transformation, or passive rotation). Vice versa, to pass from the HKL to the TSL frame, one needs a rotation of -90 (subtract 90 from the first Euler angle).,The position of the “sample” axes is critical. The names “RD” and “TD” do not necessarily correspond to the physical “rolling direction” and “transverse direction” because these depend on how the sample was mounted in the microscope.,Test of Euler Angle Reference Frames,TSL,1,A simple test of the frames used for the Euler angles is to have the softwares plot pole figures for a single orientation with small positive values of the 3 angles. This reveals the position of the crystal x-axis via the sense of rotation imposed by the second Euler angle,F,.,Clearly, one has to add 90 to,1,to pass from HKL coordinates to TSL coordinates.,Note that the CMU TSL is using the x/1120 convention (“X convention”), whereas the Metz Channel/HKL software is using the y/1120 convention (“Y convention”).,HKL,1,Euler angles: 17.2, 14.3, 0.57,Hexagonal crystal symmetry (no sample symmetry),36,The Axis Alignment Issue,The issue with hexagonal materials is the alignment of the Cartesian coordinate system used for calculations with the crystal coordinate system (the Bravais lattice).,In one convention (e.g. popLA, TSL), the x-axis, i.e. 1,0,0, is aligned with the crystal,a,1,axis, i.e. the 2,-1,-1,0 direction. In this case, the y-axis is aligned with the 0,1,-1,0 direction.,In the other convention, (e.g. HKL, Univ. Metz software), the x-axis, i.e. 1,0,0, is aligned with the crystal 1,0,-1,0 direction. In this case, the y-axis is aligned with the -1,2,-1,0 direction.,See next page for diagrams.,This is important because texture analysis can lead to an ambiguity as to the alignment of 2,-1,-1,0 versus 1,0,-1,0, with apparent 30 shifts in the data.,Caution: it appears that the axis alignment is a choic