Mechanical Behavior · Dislocations

Stacking fault energy: why a dislocation splits in two

Start with copper in the first picture: its dislocation is two partial dislocations with a strip of wrongly stacked atoms between them. Drag the stacking fault energy down and watch the strip widen.

1 Partials and ribbon width 2 Cross-slip and planar slip 3 Measuring it Takeaways Questions References

What is stacking fault energy, and why does a dislocation split into Shockley partials?

In FCC metals a dislocation usually splits into two partial dislocations. The stacking fault energy γ is the energy per area of the strip between them.

Spheres: an atom of the layer above makes one long step b, or two short steps b1 and b2 through a C hollow. Ribbon: the split dislocation from above, to scale. Scale: screw ribbon width in each metal.
Metal (γ from the source in the table below)
Line direction (angle β between line and b)
Ribbon width d
d in partial Burgers vectors bp
bp = a/√6
Energy saved by splitting (estimate)

Try it: copper, screw: the ribbon is 1.44 nm, about 10 bp wide. Press Al: 0.30 nm. Back on copper, press Edge: 3.45 nm.

Why does low stacking fault energy make cross-slip hard?

A screw dislocation must squeeze its two partials back into one line before it can change plane, and a wide ribbon resists that.

Run: a sketch to show the idea, not a simulation. The waiting time before each squeeze is set by this page and grows steeply with ribbon width. Times and counts are not measured values. Trends: general trends with γ, not sharp limits. In alloys, short-range order can matter more (see the questions below).
Metal
Run
Screw ribbon width d
d / bp
Passed the obstacle (sketch, end of run)
Queued behind it (sketch, end of run)

Try it: press Al, then Play: all 8 dislocations squeeze and cross-slip past the obstacle. Press Brass, then Play: all 8 queue behind it on one plane.

How is stacking fault energy measured?

Weak-beam dark-field TEM shows the two partials as two bright lines; their spacing d gives γ, since γ goes as 1/d.

Image: simulated, with noise; each line is 1.4 nm wide (set on this page). Drag the red markers onto the lines. Profile: brightness averaged along the lines.
Line direction β
Image noise
Your spacing d
γ from your d
γ if d is off by ±0.5 nm
γ used to draw the image

Try it: copper, edge: drag the markers onto the two peaks, 3.45 nm apart, and read γ near 41 mJ/m2. Move one marker 0.5 nm out or in: γ becomes about 36 or 48.

What to take away

Splitting saves energyLine energy goes as b2. By Frank's rule b2 = a2/2, but b12 + b22 = a2/3, a third less. The partials push apart until the fault's pull γ stops them.
Ribbon width goes as 1/γA screw dislocation in copper (41 mJ/m2) has a ribbon about 1.4 nm wide; in aluminium (135 mJ/m2) about 0.3 nm. Halve γ and the ribbon doubles.
Low γ, harder cross-slipA wide ribbon must squeeze shut before a screw can change plane, so slip stays on fewer planes. Measured γ for one metal can differ by tens of percent between methods.
More detail: the equations, the numbers and the limits

Partials and Frank's rule. On (111), b = a/2[−1 0 1] splits into a/6[−2 1 1] + a/6[−1 −1 2]. Each partial has length bp = a/√6 and lies at 30° to b. Line energy goes as Gb2 (G is the shear modulus), so splitting lowers it from a2/2 to a2/3 (Hull and Bacon, chapter 5). Behind the first partial, ABCABC stacking becomes ABCACABC: an intrinsic stacking fault.

Ribbon width. Two straight, parallel partials repel with a force per length F = G/(2πd)·[(b1·ξ)(b2·ξ) + (b1×ξ)·(b2×ξ)/(1−ν)]. Here ξ is the line direction and ν is Poisson's ratio. Setting F = γ gives

d = G bp2/(8πγ) · (2−ν)/(1−ν) · [1 − 2ν cos 2β/(2−ν)]

β is the angle between b and the line. Screw (β = 0): factor (2−3ν)/(1−ν). Edge (β = 90°): (2+ν)/(1−ν), 2.4 times wider at ν = 0.34. This is eq. 1 of Sun et al. (2021), after Anderson, Hirth and Lothe.

Energy saved. Spreading the pair from a core radius r0 to d saves γd[ln(d/r0) − 1 + r0/d] per length. The page takes r0 = bp, a model choice, so this readout is an estimate.

Values used. γ as measured (1 erg/cm2 = 1 mJ/m2). G and ν for Al, Ni, Cu and brass are room-temperature values for a metal of many grains (Callister and Rethwisch, Table 6.1). The lattice parameter a of Al, Ni, Cu and Ag is the X-ray value at 25 °C (Swanson and Tatge 1953). G and ν for Au and Ag, and a for Au and brass, are rounded values, so treat them as approximate.

Metalγ (mJ/m2)Method, sourceG (GPa), ν, a (nm)

Spread. Rough node estimates (Howie and Swann 1961) were Cu 40, Ag 25 and Ni 150 mJ/m2. Weak beam gave 41, 16.3 and 120 to 130. For Al, Sun et al. (2021) list about 150 ± 40. Read every value as good to tens of percent.

Limits. The papers used anisotropic elasticity; this page uses isotropic elasticity, so its widths are estimates. Lines are taken as straight and infinite. Real weak-beam peaks sit slightly off the cores, so careful work matches a computed image (Cockayne, Ray and Whelan 1969 introduced the method). The Fe-Mn-C ranges in picture 2 (Allain et al. 2004) apply to that steel family only. The other bands in picture 2 are trends. In fatigued metals, dislocation cells give way to evenly spread dislocations as γ falls (Feltner and Laird 1968). In shocked Cu and Cu-Al, twins carry more of the hardening at low γ (Rohatgi et al. 2001).

Questions people ask

What is stacking fault energy?

It is the extra energy per unit area of a stacking fault. That is a plane where the ABCABC order of close-packed layers breaks, for example ABCACABC. Its unit is mJ/m2. Weak-beam TEM gives 41 ± 9 mJ/m2 for copper; the shrinkage of faulted loops gave 135 ± 20 for aluminium.

What is a Shockley partial dislocation?

It is a dislocation with Burgers vector a/6⟨112⟩, shorter than a lattice vector, so it leaves a stacking fault behind it. In FCC, a/2[−1 0 1] splits into a/6[−2 1 1] + a/6[−1 −1 2]. Each partial is at 30° to the full Burgers vector.

How does stacking fault energy affect cross-slip?

A screw dislocation can only change plane after its two partials squeeze back into one line. The ribbon is wider at low γ, so that squeeze costs more. In this page's model a copper screw ribbon is about 10 bp wide and an aluminium one about 2 bp.

Is low stacking fault energy the only cause of planar slip?

No. For solid-solution alloys, Gerold and Karnthaler (1989) argued that short-range order or clustering is the main cause. The first dislocation on a plane disturbs the order, so the next one finds that plane easier. In their view a low γ matters less. So read the slip-pattern band in picture 2 as a trend, not a rule.

How is stacking fault energy measured?

The most direct way is weak-beam TEM. You image split dislocations and convert the partial spacing to γ, as for Cu, Ag, Au and Ni. Older work used the curvature of extended dislocation nodes (Whelan 1959; Howie and Swann 1961). For Al, whose partials are too close to resolve, the shrinkage rate of faulted loops gave 135 ± 20 mJ/m2.

Why does brass twin and aluminium does not?

A twin grows by Shockley partials gliding on neighbouring (111) planes, and each one makes a stacking fault. That is cheap in Cu-30Zn brass (about 14 mJ/m2) and costly in aluminium (about 135). In shock-loaded Cu and Cu-Al alloys, the share of hardening from twins rose as γ fell (Rohatgi et al. 2001).

What stacking fault energy gives TWIP or TRIP steel?

For Fe-Mn-C steels, Allain et al. (2004) found strain-induced martensite (TRIP) below about 18 mJ/m2 and twinning (TWIP) between about 12 and 35 mJ/m2. Their γ values are calculated, and the ranges overlap. They hold for that steel family only.

Can you see the partials in aluminium?

Only just. In this page's model the Al ribbon is 0.3 to 0.7 nm wide, narrower than the 1.4 nm line width used in picture 3. High-resolution TEM can show it: Mills and Stadelmann (1989) found about 0.55 ± 0.15 nm for 60° dislocations in Al boundaries. The model gives 0.60 nm.

Related: Stacking faults and twins (ABC layers) · Dislocations and Burgers vectors · Schmid factor and FCC slip systems · Strengthening mechanisms · Reading a tensile curve · Weak-beam dark field (imaging the partials) · Two-beam defect simulator (stacking fault contrast) · Twin boundaries in EBSD

References

Show the 19 references
  1. D. J. H. Cockayne, M. L. Jenkins and I. L. F. Ray, The measurement of stacking-fault energies of pure face-centred cubic metals, Philosophical Magazine 24, 1383 to 1392 (1971). doi:10.1080/14786437108217419.
  2. M. L. Jenkins, Measurement of the stacking-fault energy of gold using the weak-beam technique of electron microscopy, Philosophical Magazine 26, 747 to 751 (1972). doi:10.1080/14786437208230118.
  3. C. B. Carter and S. M. Holmes, The stacking-fault energy of nickel, Philosophical Magazine 35, 1161 to 1172 (1977). doi:10.1080/14786437708232942.
  4. P. S. Dobson, P. J. Goodhew and R. E. Smallman, Climb kinetics of dislocation loops in aluminium, Philosophical Magazine 16, 9 to 22 (1967). doi:10.1080/14786436708229253.
  5. A. Howie and P. R. Swann, Direct measurements of stacking-fault energies from observations of dislocation nodes, Philosophical Magazine 6, 1215 to 1226 (1961). doi:10.1080/14786436108243372
  6. D. J. H. Cockayne, I. L. F. Ray and M. J. Whelan, Investigations of dislocation strain fields using weak beams, Philosophical Magazine 20, 1265 to 1270 (1969). doi:10.1080/14786436908228210
  7. M. J. Whelan, Dislocation interactions in face-centred cubic metals, with particular reference to stainless steel, Proceedings of the Royal Society A 249, 114 to 137 (1959). doi:10.1098/rspa.1959.0011.
  8. X. Sun, S. Lu, R. Xie et al., Can experiment determine the stacking fault energy of metastable alloys?, Materials & Design 199, 109396 (2021). doi:10.1016/j.matdes.2020.109396.
  9. P. M. Anderson, J. P. Hirth and J. Lothe, Theory of Dislocations, 3rd ed., Cambridge University Press (2017).
  10. P. C. J. Gallagher, The influence of alloying, temperature, and related effects on the stacking fault energy, Metallurgical Transactions 1, 2429 to 2461 (1970). doi:10.1007/BF03038370. Cu-30Zn value as quoted in the next entry.
  11. M. Sosa, L. Carvajal, V. Salinas Barrera, F. Lund, C. Aguilar and F. Castro Cerda, Acoustic assessment of microstructural deformation mechanisms on a cold rolled Cu30Zn brass, Materials 17, 3321 (2024). doi:10.3390/ma17133321
  12. D. Hull and D. J. Bacon, Introduction to Dislocations, 5th ed., Elsevier (2011): chapter 5, Dislocations in face-centered cubic metals, pages 85 to 107. doi:10.1016/B978-0-08-096672-4.00005-0
  13. M. J. Mills and P. Stadelmann, A study of the structure of Lomer and 60° dislocations in aluminium using high-resolution transmission electron microscopy, Philosophical Magazine A 60, 355 to 384 (1989). doi:10.1080/01418618908213867
  14. S. Allain, J.-P. Chateau, O. Bouaziz, S. Migot and N. Guelton, Correlations between the calculated stacking fault energy and the plasticity mechanisms in Fe-Mn-C alloys, Materials Science and Engineering A 387 to 389, 158 to 162 (2004). doi:10.1016/j.msea.2004.01.059
  15. V. Gerold and H. P. Karnthaler, On the origin of planar slip in f.c.c. alloys, Acta Metallurgica 37, 2177 to 2183 (1989). doi:10.1016/0001-6160(89)90143-0
  16. C. E. Feltner and C. Laird, Factors influencing the dislocation structures in fatigued metals, Transactions of the Metallurgical Society of AIME 242, 1253 to 1257 (1968).
  17. A. Rohatgi, K. S. Vecchio and G. T. Gray, Metallographic and quantitative analysis of the influence of stacking fault energy on shock-hardening in Cu and Cu-Al alloys, Acta Materialia 49, 427 to 438 (2001). doi:10.1016/S1359-6454(00)00335-9
  18. W. D. Callister Jr. and D. G. Rethwisch, Materials Science and Engineering: An Introduction, 10th ed., Wiley (2018): Table 6.1, room-temperature shear modulus and Poisson’s ratio (Al, Cu, Ni, brass).
  19. H. E. Swanson and E. Tatge, Standard X-ray Diffraction Powder Patterns, NBS Circular 539, vol. I, National Bureau of Standards (1953): lattice parameters of Al, Cu, Ni and Ag at 25 °C.
Cite this page: Tripathy, Manisha. “Stacking Fault Energy Lab.” untethered atom, 2026, https://untetheredatom.com/mechanical-behavior/stacking-fault-energy.
BibTeX 
@misc{tripathy2026stackingfaultenergy,
  author = {Tripathy, Manisha},
  title  = {Stacking Fault Energy Lab},
  year   = {2026},
  howpublished = {\url{https://untetheredatom.com/mechanical-behavior/stacking-fault-energy}},
  note   = {Interactive web tool}
}
Last updated 3 November 2026.