In-situ Testing · Micropillar compression
Micropillar compression: what goes wrong and why small is strong
Squash a tiny pillar cut by a focused ion beam (FIB) and see how its shape, base and size change the measured stress.
What goes wrong in a micropillar compression test?
Change the pillar's shape and watch the picture and the curve react.
Try it: set the taper to 0°: the three stresses agree. Set the aspect ratio to 5: the pillar buckles.
Why are smaller pillars stronger?
Pick a metal and shrink the pillar: strength climbs as a power of the diameter.
Try it: with Ni, go from 1 to 0.1 µm: the stress rises 4.6 times. W's line is almost flat.
How much of a small pillar is FIB damage?
The Ga beam leaves a damaged, Ga-rich shell on every surface it cuts.
Try it: at t = 25 nm, go from D = 1 to 0.2 µm: the shell grows from 10% to 44%.
What to take away
Say which diameter
At 3° taper and aspect ratio 2.5, the bottom-diameter stress reads 37% below the top. Report which diameter you used.
Correct for the base
The pillar sinks into its base. Without the Sneddon correction a straight pillar's modulus reads 19 to 26% low.
Small is strong, and damaged
FCC strength rises about as D−0.66. Below 1 µm a 25 nm FIB shell is over 10% of the pillar.
More detail: the equations, the numbers used and the limits
The model pillar
Picture 1 uses a nickel-like single crystal: top diameter 2 µm, E = 200 GPa, ν = 0.31, the same material in the base. It yields at 350 MPa, the Dou and Derby value for a 2 µm [001] Ni pillar (picture 2), and hardens slowly. The test is load-controlled, so each strain burst is a flat step. Burst sizes are random. The picture's shapes (mushroom top, buckling, bending) are drawn from the settings and are not a finite element calculation.
Taper
With top diameter Dt, height H and taper angle θ (each side), the bottom diameter is Db = Dt + 2H tan θ. The stress P/A is highest at the top, so the top yields first. Using the mid-height or bottom diameter spreads the load over a larger area and reads low by 1 − (Dt/D)2. Zhang et al. (2006) showed with finite elements that taper also gives a modulus that reads high, false strain hardening and a higher apparent yield.
Base sink-in (Sneddon)
The pillar acts as a flat punch pressed into its base. Sneddon's flat-punch solution gives δbase = (1 − νb2) P / (Eb Db), written by some papers as √π (1 − ν2) P / (2E√A), which is the same thing. Zhang et al. (2006) and Frick et al. (2008) use this correction. The page subtracts it from the measured displacement. The pillar's own elastic shortening for a straight taper is 4PH / (π E Dt Db). Zhang et al. (2006) found a better fit with an effective contact radius that includes the fillet at the pillar foot; treat the simple form as a first correction. The punch's own contact compliance (the diamond on the pillar top) is not included.
Misalignment
A punch tilted by θm first touches one edge. Full contact needs a further Dt tan θm of travel. The page assumes the contact stiffness grows in proportion to the travel until then, which gives a curved "toe" at the start of the curve and a low loading slope. The edge that touches first yields early.
Size effect
For FCC metals Dou and Derby (2009) fitted τ/μ = 0.71 (D/b)−0.66 to many pillar studies (τ = resolved shear stress, μ = shear modulus, b = Burgers vector). The page turns τ into an axial stress for a [001] pillar by dividing by the Schmid factor 0.408. Shear moduli and b: Au 27 GPa, 0.288 nm; Ni 76 GPa, 0.249 nm; Cu 48 GPa, 0.256 nm. For Mo the page uses n = 0.44 (Kim, Jang and Greer 2010, compression) through an approximate 2.0 GPa at D = 300 nm; treat the Mo level as illustrative. For W the page uses the data of Schneider et al. (2011): [235] pillars, stress at 2.5% strain, about 2.8 GPa at 200 nm and 1.65 GPa at 4 µm, fitted with n = 0.16. Kim et al. (2010) found n = 0.44 for their W pillars, so BCC exponents differ between studies. They depend on orientation, strain level, how the pillar was made and the test temperature (Schneider et al. 2009).
FIB damage
The shell share of a cylinder with a damaged side layer of thickness t is 1 − (1 − 2t/D)2; the top face is left out. Kiener et al. (2007) found up to 20 at.% Ga a few nanometres below a Cu surface and more than 2 at.% Ga down to about 50 nm. The damage depth depends on the metal, the beam energy and the angle; low-kV final cuts make it thinner. A damaged shell can harden the pillar or add dislocation sources, so it can raise or lower the measured strength.
On this site: FIB specimen prep artifacts · Microcantilever bending · Strengthening mechanisms · Dislocations and Burgers vectors · Nanoindentation beyond hardness
Questions people ask
What is micropillar compression?
A small pillar, usually 0.2 to 10 µm across, is cut into a material with a focused ion beam. A nanoindenter with a flat punch presses it along its axis. Load over area and shortening over height give a stress-strain curve from a single grain or phase.
What aspect ratio should a micropillar have?
Most studies use a height about 2 to 3 times the diameter, following Zhang et al. (2006). Shorter pillars are held back by friction and the stiff base, so the stress reads high. Taller pillars can buckle, especially if the punch is not flat on the top.
Why do micropillar stress-strain curves have strain bursts?
Plastic flow in a small crystal comes from a few dislocation sources. When one operates, many dislocations run out of the pillar at once, and the pillar shortens in a sudden step. Under load control this shows as a flat jump in strain.
Which diameter should I use for a tapered pillar?
There is no single right answer. The top diameter gives the stress where yielding starts; the mid-height diameter is also common. Report which one you used and the taper angle, and keep the taper as small as you can: Zhang et al. (2006) found a 2.9° taper already distorts the curve.
Why are smaller crystals stronger?
In a small pillar, dislocation sources are short, because the free surface cuts them off, and dislocations escape quickly through the surface. More stress is needed to keep plastic flow going. For FCC metals the strength rises about as D−0.6 to D−0.7.
Does FIB damage change micropillar results?
It can. Ga implantation and ion damage leave a layer tens of nanometres thick. In pillars under about 1 µm this layer is a large share of the volume and can harden the pillar or add dislocation sources. Low-kV final cuts and comparisons with pillars made by other methods help.
References
Show the 12 references
- M. D. Uchic, D. M. Dimiduk, J. N. Florando and W. D. Nix, Sample dimensions influence strength and crystal plasticity, Science 305, 986 to 989 (2004). doi:10.1126/science.1098993
- J. R. Greer, W. C. Oliver and W. D. Nix, Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients, Acta Materialia 53, 1821 to 1830 (2005).
- H. Zhang, B. E. Schuster, Q. Wei and K. T. Ramesh, The design of accurate micro-compression experiments, Scripta Materialia 54, 181 to 186 (2006): aspect ratio 2 to 3, taper, misalignment within 0.5°, and the Sneddon base compliance.
- C. P. Frick, B. G. Clark, S. Orso, A. S. Schneider and E. Arzt, Size effect on strength and strain hardening of small-scale [111] nickel compression pillars, Materials Science and Engineering A 489, 319 to 329 (2008).
- R. Dou and B. Derby, A universal scaling law for the strength of metal micropillars and nanowires, Scripta Materialia 61, 524 to 527 (2009): τ/μ = 0.71 (D/b)−0.66 for FCC metals.
- D. Kiener, C. Motz, M. Rester, M. Jenko and G. Dehm, FIB damage of Cu and possible consequences for miniaturized mechanical tests, Materials Science and Engineering A 459, 262 to 272 (2007).
- M. D. Uchic, P. A. Shade and D. M. Dimiduk, Plasticity of micrometer-scale single crystals in compression, Annual Review of Materials Research 39, 361 to 386 (2009).
- J.-Y. Kim, D. Jang and J. R. Greer, Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale, Acta Materialia 58, 2355 to 2363 (2010). doi:10.1016/j.actamat.2009.12.022
- J. R. Greer, C. R. Weinberger and W. Cai, Comparing the strength of f.c.c. and b.c.c. sub-micrometer pillars: compression experiments and dislocation dynamics simulations, Materials Science and Engineering A 493, 21 to 25 (2008). doi:10.1016/j.msea.2007.08.093
- A. S. Schneider, D. Kaufmann, B. G. Clark, C. P. Frick, P. A. Gruber, R. Mönig, O. Kraft and E. Arzt, Correlation between critical temperature and strength of small-scale bcc pillars, Physical Review Letters 103, 105501 (2009). doi:10.1103/PhysRevLett.103.105501
- A. S. Schneider, C. P. Frick, B. G. Clark, P. A. Gruber and E. Arzt, Influence of orientation on the size effect in bcc pillars with different critical temperatures, Materials Science and Engineering A 528, 1540 to 1547 (2011): W pillars about 2.8 GPa at 200 nm and 1.65 GPa at 4 µm ([235], 2.5% strain), n = 0.16.
- I. N. Sneddon, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, International Journal of Engineering Science 3, 47 to 57 (1965).
BibTeX
@misc{tripathy2026micropillar,
author = {Tripathy, Manisha},
title = {Micropillar Compression Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/insitu/micropillar-compression}},
note = {Interactive web tool}
}