EBSD数据分析-共43页课件.ppt

1、Analysis of EBSD Data (L17)27-750, Fall 2009Texture, Microstructure & Anisotropy, Fall 2009B. El-Dasher*, A.D. Rollett, G.S. Rohrer, P.N. KaluCarnegie Mellon MRSECLast revised: 7th Nov. 09*now with the Lawrence Livermore Natl. Lab.Overview Understanding the program: Important menus Definition of Gra

2、ins in OIM Partitioning datasets Cleaning up the data: Types Examples of Neighbor correlation Orientation: System Definition Distribution Functions (ODFs) Plotting ODFsOverview Misorientation: Definitions - Orientation vs. Misorientation Distribution Functions (MDFs) Plotting MDFs Other tools: Plott

3、ing Distributions Interactive toolsNavigating the menus There are two menus that access virtually everything:Creates new partitionsImports data as partitionsAccess to routines that cleanup the datasetUse this to export text .ang filesCheck the scan statsRotate the orientations of each point about sa

4、mple frameCut out scan sectionsAccess to menu for: - Maps - Texture calculation - Texture plotsExport grain ID data associated with each pointCheck the partition stats & definitionChange the partition properties:- Decide which points to include- Define a “grain”Grain Definitions OIM defines a set of

5、 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 numberPoints with a CI less than specified are excluded from statistics Note: P

6、oints that are excluded are given a grain ID of 0 (zero) in exported files Grain DefinitionsExamples of definitions3 degrees15 degreesNote that each color represents 1 grainPartitioning Datasets-Choose which points to include in analysis by setting up selection formulaUse to select by individual poi

7、nt attributesUse to select by grain attributesSelection formula is explicitly written hereGrain 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

8、 a grain from being lost) Data CleanupNeighbor Orient. Correlation- Performed on all points in the datasetFor 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 sa

9、me 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 resultsNeighbor Phase Correlation- Same as Grain Dilation but instead of using the grain with most number of neighborin

10、g 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 fileNeighbor CI Correlation- Performed only on points with CI less than a given minimum - The orien

11、tation 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 existGrain 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 po

12、ints- 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 ExampleNo CleanupLevel 0Level 3Note that Higher cleanup levels are iterative (i.e. Level 3= Levels 0,1,2,3)Definition of Orientation By definition an orie

13、ntation is always relative. The OIM uses the sample surface to define the orthogonal reference frame.Quantities are transformed from sample frame to crystal framee1se2sj1Fj2NB: a more comprehensive discussion of reference frames is given laterOrientation Distribution FunctionsThe ODF displays how th

14、e measured orientations are distributed in orientation spaceTwo types of distributions can be calculated:Discrete ODF: Bin size defines the volume of each element in orientation space (5ox5ox5o) Fast calculation Suitable for most texture strengths but not weak textures if the number of grains is sma

15、ll (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 maxim

16、um) Time intensive Mostly appropriate for weaker textures Some smoothing is inherentPlotting Orientation DistributionsOne 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 on

17、e PF, they need to be added one at a time. Inverse Pole Figures are used to illustrate which crystal plane normals are p a r a l l e l t o s a m p l e directions (generally RD, TD & ND) The indices entered represent which sample reference frame plane is being considered: 100, 010 and 001 are typical

18、 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/

19、 Inverse PF PlotsChoose texture and desired plot typeU s e t o a d d multiple plots to the same image NB: a more comprehensive discussion of reference frames is given laterThe Average Orientation of the pixels in a grainis given by this equation:RD10 000 orientations near to the Brass component:repr

20、esented by a 111 pole figure and, in the complete Euler space to show the 24 equivalents resulting from application of cubic crystal symmetry111Preparation of the data for analysisi=1,24.q.qq/ )q.qq(qN21N21M(g)quivalent M(g)mesur. Si cristalCourtesy of N. BozzoloVery simple, nest-ce pas?However, the

21、re 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 (2019) Determination of a mean orientation in electron backscatter diffraction measurements, Metall. Mater. Trans. 36A 3427-38j1=0j1

22、=5j1=10j1=15.max = 5.56.Parameters for texture analysisCourtesy of N. Bozzolomax = 5.3716x16x83225max = 4.4432x32x168225max = 5.56Resolution 32x32x16Gaussian 3Lmax 22Bin Size5Effect of the binning resolutionEffect of the width of the GaussianParameters for texture analysisCourtesy of N. Bozzolomax =

23、 5.17Lmax = 16max = 5.56Lmax = 22Effect of the maximum rank in the series expansion, Lmaxmax = 2.43Lmax = 5max = 4.04Lmax = 8max = 6.36Lmax = 34Resolution 32x32x16Gaussian 3Lmax 22Bin Size5Courtesy of N. Bozzolomax = 31 !Same, with 10 binning :Direct Methodmax = 5.56In effect the harmonic method giv

24、es some ”smoothing . Without this, a coarse binning of, say, 10, produces a very “lumpy” result.j1=5Courtesy of N. Bozzoloj j0= 87.6 at 0 35 3080000 grains6.6 at 0 35 307.1 at 0 35 258.2 at 0 30 258.3 at 15 30 302000 grains5.8 at 5 30 157.3 at 345 35 5015.5 at -5 35 5016000 grains6.7 at 0 35 307.9 a

25、t 0 35 306.9 at -5 35 359.0 at -5 30 40Gaussienne de j j0= 4Triclinic sample symmetryj j0= 4j j0= 8Statistical Aspects Number of grains measured Width of the Gaussian ( and/or Lmax) Influence of the sample symmetryZirconium, equiaxedSections thru the OD at constant j1 (Lmax = 34)16.011.38.05.64.02.8

26、2.01.40.7Texture = distribution of orientations Problem of sampling!Orthorhombic sample symmetryCourtesy of N. BozzoloSingle EBSD map (1 mm2)Multiple maps, different locations ( total =1 mm2)RDTDND10.0(00.1)0.71.42.02.84.05.68.011.3asymmetry of intensityHomogeneity/heterogeneity of the specimen.equi

27、axed TiNot just the number of grains must be considered but also their spatial distribution:Statistical Aspects Courtesy of N. BozzoloTexture Microstructure CouplingExample : partial texture of populations of grains identified by a grain size criterion (zirconium at the end of recrystallization ) pa

28、rtial texture of the largest grainsPartial texture of the smallest grainsImportant 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 g

29、rains 17.9% surf.D D/2 (=2.75 m) 14255 grains 1.7% surf.Global texturej1 = 0090060Fj27.4116.011.38.05.64.02.82.01.40.7Definition of MisorientationMisorientation is an orientation defined with another crystal orientation frame as reference instead of the sample reference frameThus a misorientation is

30、 the axis transformation from one point (crystal orientation) in the dataset to another pointxzygA-1gBx,y,z are sample reference axesgA is orientation of data point A (reference orientation) w.r.t sample referencegB is orientation of data point B w.r.t. sample referenceMisorientation = gBgA-1Again t

31、he function can be either discrete or continuousMisorientation Distribution Functions Calculating MDFs is very similar to calculating ODFsCorrelated MDF: Misorientations are calculated only between neighbors If the misorientation is greater than the grain definition angle, the data point is included

32、 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 h

33、as weak textureTexture 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 MDFPlotting MDFsAgain, you need to choose what data you want to seeSele

34、ct the Texture datasetSelect the plot type (axis/angle ; Rodrigues; Euler)Use to generate plot sectionsSections through Misorientation SpaceChartsCharts are easy to use in order to obtain statistical informationIncreasing bin #Reconstructed Boundaries Data MUST be on hexagonal grid Clean up the data

35、 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

36、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 hexag

37、onal grid. Use the software called OIMTools to do this (freely available fortran program).Reference FramesThis 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

38、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 confusi

39、ng.TSL / OIM Reference Frames-TD= -yEulerND= zEuler-RD= -xEulerSample Reference Frame for Orientations/Euler AnglesReference Frame for Spatial CoordinatesCrystal Reference Frame:Remember that, to obtain directions and tensor quantities in the crystal frame for each grain (starting from coordinates e

40、xpressed in the Euler frame), one must use the Euler angles to obtain a transformation matrix (or equivalent).+Zspatial points in to the planeZEuler points out of the planexspatialRD = xEuler=100sampleTD = yEuler = 010sampleImage:Note the 180 rotation.“ “+” denotes the Origin+Physical specimen:Mount

41、ed in the SEM, the tilt axisis parallel to “xspatial”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 ImagesFrom Herb Millers notes:The axes for the TSL Euler frame are consistent with the RD-TD-ND sys

42、tem 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.010100001Conversion from spatial to Euler and vi

43、ce 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=y31TSL / OIM Reference Frames: Coordinates in Physical Frame, Conversion to Im

44、age 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 i

45、s necessary to take either the physical data and rotate it by 180, or to rotate the crystallographic information.-TD= -ysampleND= zEuler-RD= -xEulerSample 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 l

46、eft (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.+32Cart

47、esian Reference Frame for Physical MeasurementyEulerxEuler 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

48、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 r

49、otation about zsample. In this case, the z-axis points out of the plane of the page.01010000133TSL / 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 N

50、D 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