untethered atom · The series

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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

SAED indexing, g-vectors and real vs. fake spots

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

EELS thickness calculator

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

Data and analysis: peaks, proxigrams and counting

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

Misorientation, boundaries and CSL

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

Cleaning data honestly

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

KAM, GNDs and the step size

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

How a hardness number gets made

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

EDS quantification

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

EELS core-loss quantification

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

Quantitative HAADF

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

Ring pattern calibration

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

EBSD reference frames and 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.