Imaging Atoms with HRTEM

From a pattern of spots to a picture of atoms

Guide 1 spent its whole length in the shadow world. Selected-area diffraction gave a grid of spots, convergent-beam discs carried point- and space-group symmetry, and Kikuchi lines steered the crystal — but every one of those was a photograph of the reciprocal lattice, never a picture of the atoms themselves. This guide flips a single switch on the same transmission electron microscope and asks it for the other thing it can do: a real-space image, magnified until the atomic columns show up as dots. The switch is literally a matter of which plane the lenses focus on — the back focal plane gives the diffraction pattern of guide 1, the image plane gives the picture we are after here.

Why can electrons image atoms at all, when X-rays cannot be focused into a picture this way? Two reasons, both from earlier in this rung. First, wavelength: fast electrons at 200 kilovolts have a wavelength near 2.5 picometres, about sixty times shorter than a Cu K-alpha X-ray (1.54 angstrom = 154 pm), so the fineness they can in principle resolve is far below one atom's width. Second, strength of interaction: electrons feel the electric field of every nucleus directly and scatter roughly ten thousand times more strongly than X-rays. That strong interaction is both the gift and the curse of the whole enterprise — it gives plenty of signal from a whisker-thin sample, but it also means the beam scatters many times over, the dynamical scattering that will haunt every image we make.

How a lattice image is made: many beams interfering

The ordinary defect-imaging mode of the TEM lets only ONE beam through an aperture and maps its intensity — that is diffraction-contrast imaging, and it shows dislocations and faults as light and dark lines. High-resolution TEM (HRTEM) does the opposite: it opens the aperture wide so that many diffracted beams pass together, then lets them recombine and interfere down in the image plane. Where the waves reinforce you get a bright fringe; where they cancel, a dark one. Line the crystal up along a zone axis — beam straight down a low-index direction, so whole columns of atoms stack neatly behind one another — and the fringes from different plane families cross to weave a two-dimensional grid of dots, one dot sitting more or less on each column of the atomic structure.

FORMING A LATTICE IMAGE  (phase contrast, many beams)

  thin crystal      objective lens     back focal plane      image plane
  ||||||||   ==beam=>  ( lens )  ==>   . . o . .   ==recombine=>  lattice
  atom columns                         diffraction spots        image (dots)
                                       ( a*, b*, c* grid )
                                            |
         aperture placed HERE selects HOW MANY beams recombine:
              1 beam   -> diffraction-contrast image  (see defects)
              many     -> HRTEM phase-contrast lattice image

  the many beams INTERFERE in the image plane:
       waves add   -> bright fringe        waves cancel -> dark fringe
       down a zone axis the fringes cross -> 2D grid of dots ~ columns

  BUT a dot is an interference fringe, NOT a photographed atom:
       Scherzer (optimum) defocus + very thin -> dots faithfully = columns
       wrong focus  /  thicker foil           -> contrast can REVERSE

  worked:  silicon viewed down [110], at Scherzer defocus
       two dark dots (a 'dumbbell') spaced 0.136 nm = 1.36 angstrom
       shift the focus by ~30 nm  ->  those same columns turn BRIGHT

Here is the single most important, most-often-missed truth of the whole guide: an HRTEM lattice image is an interference pattern, not a literal snapshot of atoms. Whether the columns come out bright on a dark background or dark on a bright one, and even whether the dots sit exactly over the columns, is decided not by the atoms alone but by the microscope's focus, the specimen's thickness, and its lens aberrations. The dots are real and repeatable, but reading them as 'the atoms' is a claim you have to earn, not a free gift of the picture.

The catch: focus, thickness, and the contrast transfer function

There is one magic setting where the picture behaves. It is called Scherzer defocus — a specific, slightly underfocused value chosen so that a broad band of fine detail is transferred into the image all with the same sign. For a thin enough specimen at Scherzer defocus, the dark dots really do line up faithfully with the atomic columns, which is exactly why operators hunt for that focus before trusting anything. The rule that governs which spatial details pass, and with what plus-or-minus sign, is the microscope's contrast transfer function — think of it as a filter that lets some fine spacings through cleanly, blurs others, and even flips the contrast of others to the wrong sign. On a good uncorrected instrument this gives a point resolution around 0.2 nm.

Feel the danger with a concrete case. View a very thin silicon crystal down its [110] direction at Scherzer defocus and the image shows the famous 'dumbbells' — pairs of dark dots spaced just 0.136 nm apart, faithfully marking silicon's paired atomic columns. Now change the focus by only a few tens of nanometres and those very same columns can turn bright. Nothing moved in the crystal; only the interference conditions changed. This is why careful HRTEM never trusts the eye: you compare the recorded image against computer simulations across a whole range of focus values and thicknesses, and only believe the dots are atoms where image and simulation agree.

STEM and Z-contrast: a more honest map

There is a second way to image atoms that sidesteps much of that headache. Instead of flooding the sample with a broad beam, scanning transmission electron microscopy (STEM) focuses the electrons into an extremely fine probe — below one angstrom in an aberration-corrected instrument — and scans it across the thin foil point by point, building the image one pixel at a time. The magic is a ring-shaped detector that catches only the electrons flung out to high angles. High-angle scattering is largely incoherent, so it does not suffer the focus-dependent contrast reversals of HRTEM: brighter simply means more scattering, with no simulation gymnastics required just to know which way is up.

This high-angle mode is the basis of Z-contrast imaging, and its payoff is remarkable: brightness reads off the chemical element directly. Electrons flung to large angles scatter close to the nucleus, and the strength of that scattering climbs steeply with the atomic number Z — roughly as Z^2 (in practice somewhere between Z^1.7 and Z^2). So a column of lanthanum (Z = 57) outshines a column of aluminium (Z = 13) by about (57/13)^2, close to a factor of twenty. You can quite literally read the chemistry off an atomic-resolution image, and while the probe dwells on a column you can simultaneously collect its energy-loss spectrum or emitted X-rays, mapping structure and composition together, column by column.

But be honest about the blind spot, because it is a big one. The very Z^2 that makes heavy atoms blaze makes LIGHT atoms nearly invisible: oxygen, nitrogen, lithium, and hydrogen most of all, scatter far too weakly to register beside heavy neighbours. To see light atoms you switch to a complementary mode such as annular bright field, or turn to spectroscopy. So HRTEM and STEM are not rivals but partners — the phase-contrast lattice image and the Z-contrast chemical map answer different questions, and a full atomic-scale story usually needs both.

What atomic imaging reveals — and where it can mislead

The payoff of all this care is that you get to look, in real space and near-atom by near-atom, at exactly the features earlier rungs described only in the abstract. HRTEM and STEM let you watch how atomic planes bend and terminate at a dislocation core, how two crystals stitch together across a coherent interface or an epitaxial film-on-substrate, where a stacking fault or a twin interrupts the neat pattern, and how a dopant sits in its host lattice. This is the great gift: the microstructural defects that control a material's strength and behaviour, seen directly rather than inferred.

1. Thin the specimen until it is electron-transparent — typically under about 50 nm — by grinding, ion milling, or focused-ion-beam cutting. Too thick and dynamical scattering scrambles the image.
2. Tilt to a low-index zone axis, using the Kikuchi lines from guide 1 as a steering map, so whole atomic columns line up behind one another along the beam.
3. For a lattice image, set Scherzer (optimum) defocus on a thin region — or use an aberration-corrected instrument where the interpretable window is far wider.
4. For a chemistry-sensitive map, switch to HAADF-STEM for Z-contrast, and add energy-loss (EELS) or X-ray (EDS) signals to identify the element on each column.
5. Before you claim the dots are atoms, compare the image against simulations over a focus-and-thickness series. Agreement earns the interpretation; a single striking picture does not.

Two honest limits shape how far you can trust any of this, and both point to the same lesson: choose the probe to fit the question (structure characterization is always about matching tool to target). First, every TEM image is a two-dimensional projection through the whole thickness of the foil, so overlapping features add together and true depth is lost — you are seeing a shadow-play of a slice, not a 3D solid. Second, the thin foil may not behave like the bulk: thinning can relax stresses and let defects move, and the intense beam can heat, charge, or damage delicate samples. So reach for HRTEM or STEM when the question is the atomic structure of one tiny, sacrificable region; reach for EBSD in guide 3 to map orientation over whole grains, for neutrons in guide 4 to see light atoms and magnetism, and for scanned-probe methods in guide 5 to feel real surface atoms. Every probe trades something away — the skill is knowing which trade your question can afford.