Aimless Wanderin’? – Part One

Dr. Stuart Wright, Senior Scientist, EDAX

On a recent transatlantic flight I passed the time watching one of my favorite movies: Oh Brother! There are a lot of great quotable lines in this movie. One that seems appropriate for this blog entry is from the lead character: Ulysses Everett McGill

“Say, uh, any a you boys smithies? Or, if not smithies per se, were you otherwise trained in the metallurgic arts before straitened circumstances forced you into a life of aimless wanderin’?”

Source: Rudy Wenk

While, in theory, I am “trained in the metallurgic arts”, my travels sometimes feel like “aimless wanderin’” and sometimes my mind follows suit – especially on long flights. In this series of entries for the EDAX Blog, I would like to take you on some “wanderin’s” through some of the terminology, history and personalities surrounding EBSD. Let’s begin with “texture”.

My global wanderings aren’t always aimless and I often learn some interesting things. At some recent conferences, I saw several interesting textures measured using neutron diffraction; for example, works by Heinz-Günther Brokmeier, Sven Vogel, Raul Bolmaro and others. Generally, these textures were measured over large volumes, such as from a section of a pipe, or an entire automobile component. It struck me that the use of the word “texture” has evolved to mean different things to different people.

My source of most early historical texture knowledge is Rudy Wenk. Rudy informs me that he believes the first use of the word was in an 1833 textbook by a Belgian geologist – d’Halloy to describe a directional microstructure. This seems a little ironic now as geologists tend to use the term “fabric” to describe what a metallurgist would refer to as “texture” but the evolution of these terms has also seen some wanderin’ as described in section 6 in Chapter 1 of Rudy’s 1985 book, Preferred Orientation in Deformed Metal and Rocks: An introduction to Modern Texture Analysis. I had the great fortune of learning from Rudy during a short-course on texture held at BYU when I was an undergrad as well as during his visits to Los Alamos National Lab when I was a Post-Doc. I am excited for a symposium in his honor at this year’s edition of ICOTOM in St George, Utah.

I was first introduced to the term texture in 1985 by Peter Morris, who was a visiting researcher at BYU working with Professor Brent Adams. At the time, I was employed by a Professor in the Physics Department, Dorian Hatch, to track down papers in the library (long before libraries went digital and on-line search and retrieval tools were available). I was a junior Mechanical Engineering student but had become a bit disenchanted with my coursework. I expressed to Dorian my frustration and that I was considering switching my major (Dorian was one of my leaders in our local church congregation when I was a teenager and was very helpful in offering good advice to a young university student). He recommended I go and visit with a new Professor in Mechanical Engineering named Brent Adams. When I knocked on Brent’s office door he was busy and recommended I speak with Peter. I still remember being completely lost as Peter tried to talk to me about which kind of mathematical functions would be appropriate to describe the r-dependence of the Two-Point Orientation Coherence function. Luckily, Brent popped in before I left Peter’s office completely befuddled; he brought things down a little closer to my level (if you can imagine Brent doing such a thing) and introduced me to texture. Brent was looking for someone with programming skills which I happened to have and so I joined his research team. (I got to know Peter better as part of Brent’s team particularly on a long drive from Provo, Utah to Santa Fe, New Mexico for ICOTOM 8. At one point in the drive I thought I would try out my German on Peter but was very surprised to learn that he didn’t speak German – remarkable, because if you dig out a copy of Bunge’s Texture Analysis in Materials Science you will note it was translated from German to English by Peter).

My personal introduction to texture was through the ODF or Orientation Distribution Function (another odd description as in the formal statistical sense it is actually a density function as opposed to a distribution function) per Bunge (“Zur Darstellung allgemeiner Texturen”, Zeitschrift der Metallkunde, 56, 872-874 (1965)):

“Die Orientierungsvertailung oder Textur eines polykristallinen Materials wird charakterisiert durch den Volumenateil derjenigen Kristalle, deren Orientierung zwischeng g and g + dg liegt.”

My best attempt at a translation is “the orientation distribution or texture of polycrystalline materials is characterized through the volume fraction of the constituent crystals, with orientations lying between g and dg.”

Bunge further explains in Chapter 4 of Rudy’s book entitled Preferred Orientation in Deformed Metal and Rocks: An Introduction to Modern Texture Analysis (1985):

“The texture is thus, per definition, the orientation distribution of all crystals present in the sample irrespective of their arrangement in the sample. Since the texture is defined as a statistical quantity, the sample must at least be big enough, compared to the grain size, to allow a statistically significant description. This, in turn, depends on the degree of relevance required. If we have a sample much bigger that what is required by statistical relevance, then it may be divided into volume elements V big enough to allow the statistical description of the texture. The texture can then be measured in each of these volumes elements separately. If the textures of all volume elements of the big sample are statistically identical, then the big sample is said to have a homogeneous texture. If we speak about he the texture of a material without further specification, the homogeneity is assumed. In may important cases, however, the textures of the volume elements are not the same. Such textures are called inhomogeneous, and the definition of the term “texture” become more complex (e.g., Bung, 1982c).”

In the world of EBSD, we measure textures on surfaces. We hope this is representative of the volume but oft times we know it is not. For instance, consider the following (111) pole figure measured from the surface of an aluminum sheet. It has some of the characteristics we expect for a rolled fcc material but does not exhibit the symmetry we would expect for the texture through the volume of the sheet.

(111) pole figures from two samples of rolled aluminum. Left: recent EBSD measurements on the surface of a sample. Right: X-Ray measurements from the cross-section (this pen plot is from my M.S. Thesis which formed the basis of the paper S. I. Wright and B. L. Adams (1990) An Evaluation of the Single Orientation Method for Texture Determination in Materials of Moderate Texture Strength”, Textures and Microstructures 12, 65-76.

Could the lack of symmetry be due to a lack of statistics – i.e. the volume element investigated is too small? I don’t believe so as the average grain size for this material is approximately 25 microns (always a bit tricky to estimate in deformed materials with elongated grains and with a well-defined subgrain structure) and the step size was 4µm. The scan area was 2.1 x 1.6 mm (~250,000 orientation measurements) and thus, approximately 6900 grains were sampled. In addition, the pole figure is fairly symmetric horizontally. Rather, I assume the lack of vertical symmetry in the pole figure comes from a texture gradient from the surface to the center of the sheet. So rather than calling this a texture in the classic volumetric sense it would be more correct to add “surface” as a qualifier – i.e. a surface texture.

One concern I have, is the use of the term micro-texture. I understand the point, it is the texture measured at the “micro-scale” – in the language of the quote from Bunge, a volume element at the micro-scale. But, if the area contains just a few grains, is it really a “texture”? That isn’t to say we can’t learn a lot from such measurements but, in my mind, the term texture has a statistical component to it in terms of the number of grain orientations sampled. For example, consider the following texture measurements from the same sample. Each measurement contains approximately 250,000 EBSD measurements of orientation but the step sizes are 4µm, 400nm, 40nm and 4nm. Clearly, as the sampled area becomes smaller and smaller, the measured texture becomes less and less representative of the sample as a whole. Actually, it is remarkable that the fcc rolling texture is recognizable in all but the 4nm step size. At the smallest step size, the “texture” contains just 3 grains and thus the oscillations around the major peaks arising from the spherical harmonics used to calculate the texture are relatively prominent.

(111) pole figures and orientation maps from the surface of rolled aluminum sheet from EBSD measurements at step sizes of 4µm, 400nm, 40nm and 4nm each with just over 250,000 orientation measurements.

My concern is not enough to protest the use of the word micro-texture as I think most who use the term understand the implications, but as a community we need to be aware of sampling and statistical reliability as we draw conclusions from our EBSD measurements so that our scientific wanderin’s don’t become aimless but, to quote another classic movie, “stay on target”.

(Stay tuned for some thoughts on the term “meso-texture” 😊)

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