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What your software doesn't tell you
The number is the easy part.
Every page in this series starts the same way: a program prints a number, and the number
arrives with none of its assumptions attached. A zone axis. A thickness in nanometres. A composition to
two decimals. A grain count. A GND density. A hardness.
None of those are wrong, exactly. They are answers to a question the software chose on your
behalf, and the choosing is invisible. Twelve pages take one such number each and put the choosing back
on screen, so you can move it and watch the answer move with it.
Twelve numbers
TEM · Diffraction
- It prints
- Zone axis [111]
- It omits
- Whether your two measured g-vectors name one zone axis or several at the
precision you actually clicked, and whether the extra spots are a twin, double diffraction, a second
phase, or not Bragg spots at all.
Index a pattern by hand and see the degeneracy →
TEM · EELS
- It prints
- t = 87.4 nm
- It omits
- Which mean-free-path model supplied λ, and how far the answer moves between
Malis and Iakoubovskii. On most specimens that spread is wider than the digits being shown.
Run both models on one spectrum →
Atom probe tomography
- It prints
- Cr 18.42 at.%
- It omits
- Which peaks overlapped before you ranged them, and how few atoms actually sit
inside the volume that number came from. Counting statistics set a limit on what a composition can
claim, and the display does not print the limit.
Untangle a mass spectrum and a proxigram →
EBSD / TKD · Part 3
- It prints
- 1,284 grains · Σ3 = 41%
- It omits
- That a threshold you left at its default chose that grain count. The same dataset
gives a different number at 5° than at 15°, and the Brandon criterion behind the Σ3
fraction is a convention, not a measurement.
Move the threshold and watch the count →
EBSD / TKD · Part 5
- It prints
- Indexed: 100.0%
- It omits
- That cleanup improves a map up to a point and then begins inventing
microstructure, and that you cannot see where the turn happened because you never had the truth to
compare against. This page does have it: the microstructure is synthetic, so the error curve can
actually be plotted.
Watch the U-shaped error curve →
EBSD / TKD · Part 8
- It prints
- ρGND = 4.1 × 1014 m−2
- It omits
- That refining the step raises that number, because orientation noise does not
shrink when the step does: the noise floor rises as 1/step. And that a surface map can fill only
five of the nine components of the Nye tensor.
Find the coarsest step that still measures →
Tribology · Indentation, Part 1
- It prints
- H = 5.57 GPa · E = 198 GPa
- It omits
- Where the fit sat on the unloading curve, and how much H and E move when you drag
that window. On a curve whose true hardness is known, the drift is easy to measure and larger than
most people assume.
Drag the fit window against known truth →
TEM · EDS
- It prints
- Fe 68.2 · Cr 18.4 · Ni 13.4 at.%
- It omits
- Which k-factors it used and where they came from, and that Cliff-Lorimer assumes
the foil is thin enough for absorption to be ignored. That assumption fails quietly: the soft line is
absorbed more as the specimen thickens and as you tilt, so the composition drifts without the spectrum
looking any worse.
Watch a composition drift with thickness and tilt →
TEM · EELS
- It prints
- N/Ti = 0.98
- It omits
- Which cross-section model supplied the partial ionisation cross-sections, and where
the power-law background window sat. Both are choices, and the ratio moves with each of them by more
than the two decimals suggest.
Move the window and the model, watch the ratio →
TEM · STEM
- It prints
- Intensity ∝ Z1.7
- It omits
- That the exponent is not a constant of nature. It falls as the inner collection
angle falls and it changes with thickness, so the same specimen imaged on two microscopes gives two
exponents. And an intensity that is not normalised to the incident beam cannot be compared with
anything at all.
Derive the exponent for your own detector →
TEM · Diffraction
- It prints
- Camera length 200 mm
- It omits
- That the nominal camera length is a setting on the microscope, not a measurement of
your session, and that the pattern reaching the camera is slightly elliptical and rotated with respect
to the image. Every d-spacing you read carries all three.
Fit the camera constant from a ring pattern →
EBSD / TKD · Conventions
- It prints
- A map, a pole figure, RD to the right
- It omits
- Which of four coordinate frames each of those is drawn in, and that a file can
carry the map positions in one specimen frame and the Euler angles in another. Get it wrong and every
angle stays right while every direction is mirrored, which no plot will tell you.
Flip a convention and watch the map →
The numbers above are illustrative: real values from these pages depend on your own data. What is not
illustrative is the omission in each case, which is the point of the page it links to.
The series grows when a number turns out to be hiding something worth a page.
Tell me which
number you don't trust and it moves up the queue.