The stacking-fault energy (SFE) is a materials property on a very small scale. It is noted as γ_SFE in units of energy per area. A stacking fault is an interruption of the normal stacking sequence of atomic planes in a close-packed

crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pattern ...

. These interruptions carry a certain stacking-fault energy. The width of stacking fault is a consequence of the balance between the repulsive force between two partial

dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...

s on one hand and the attractive force due to the

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) t ...

of the stacking fault on the other hand. The equilibrium width is thus partially determined by the stacking-fault energy. When the SFE is high the dissociation of a full dislocation into two partials is energetically unfavorable, and the material can deform either by dislocation glide or cross-slip. Lower SFE materials display wider stacking faults and have more difficulties for cross-slip. The SFE modifies the ability of a dislocation in a

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...

to glide onto an intersecting slip plane. When the SFE is low, the mobility of dislocations in a material decreases. {, class="wikitable" border="1" , - ! Material !Brass !Stainless Steel ! Ag (

Silver Silver is a chemical element with the symbol Ag (from the Latin ', derived from the Proto-Indo-European ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical ...

) ! Au ! Si (

Silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ...

) ! Ni (

Nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...

) ! Cu (

Copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pink ...

) ! Mg (

Magnesium Magnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic ...

) ! Al (

Aluminum Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It ha ...

) , - ! SFE ( mJ m⁻²) , <10{{Cite book, last=Hertzberg, first=Richard W., title=Deformation and Fracture Mechanics of Engineering Materials, last2=Vinci, first2=Richard P., last3=Hertzberg, first3=Jason L., publisher=John Wiley & Sons, Inc, year=2013, isbn=978-0-470-52780-1, pages=80 , <10 , 25 , 75 , >42 , 90 , 70 -78 , 125 , 160-250

Stacking faults and stacking fault energy

A stacking fault is an irregularity in the planar stacking sequence of atoms in a crystal – in FCC metals the normal stacking sequence is ABCABC etc., but if a stacking fault is introduced it may introduce an irregularity such as ABCBCABC into the normal stacking sequence. These irregularities carry a certain energy which is called stacking-fault energy.

Influences on stacking fault energy

Stacking fault energy is heavily influenced by a few major factors, specifically base metal, alloying metals, percent of alloy metals, and valence-electron to atom ratio.Thornton, P. R., Mitchell, T.E., Hirsch, P.B., (1962). The dependence of cross-slip on stacking fault energy in face centered cubic metals and alloys. Philosophical Magazine, 7, (80), 1349-1369.

Alloying elements effects on SFE

It has long been established that the addition of alloying elements significantly lowers the SFE of most metals. Which element and how much is added dramatically affects the SFE of a material. The figures on the right show how the SFE of copper lowers with the addition of two different alloying elements; zinc and aluminum. In both cases, the SFE of the brass decreases with increasing alloy content. However, the SFE of the Cu-Al alloy decreases faster and reaches a lower minimum.

e/a ratio

Another factor that has a significant effect on the SFE of a material and is very interrelated with alloy content is the e/a ratio, or the ratio of valence electrons to atoms. Thornton showed this in 1962 by plotting the e/a ratio vs SFE for a few Cu based alloys. He found that the valence-electron to atom ratio is a good predictor of stacking fault energy, even when the alloying element is changed. This directly supports the graphs on the right.

Zinc Zinc is a chemical element with the symbol Zn and atomic number 30. Zinc is a slightly brittle metal at room temperature and has a shiny-greyish appearance when oxidation is removed. It is the first element in group 12 (IIB) of the periodi ...

is a heavier element and only has two valence electrons, whereas

aluminum Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It ha ...

is lighter and has three valence electrons. Thus each weight percent of aluminum has a much greater impact on the SFE of the Cu-based alloy than does zinc.

Effects of stacking fault energy on deformation and texture

The two primary methods of deformation in metals are slip and twinning. Slip occurs by dislocation glide of either screw or edge dislocations within a slip plane. Slip is by far the most common mechanism. Twinning is less common but readily occurs under some circumstances. Twinning occurs when there are not enough slip systems to accommodate deformation and/or when the material has a very low SFE. Twins are abundant in many low SFE metals like copper alloys, but are rarely seen in high SFE metals like aluminum. In order to accommodate large strains without fracturing, there must be at least five independent and active slip systems. When cross-slip frequently occurs and certain other criteria are met, sometimes only three independent slip systems are needed for accommodating large deformations.Dillamore, I., Butler, E., Green, D., (1968). Crystal rotations under conditions of imposed strain and the influence of twinning and cross-slip. Metal Science Journal, 2 (1), 161-167.Groves, G., Kelly, A., (1963). Independent slip systems in crystals. Philosophical Magazine, 8 (89), 877-887. Because of the different deformation mechanisms in high and low SFE materials, they develop different textures.

High SFE materials

High SFE materials deform by glide of full dislocations. Because there are no stacking faults, the screw dislocations may cross-slip. Smallman found that cross-slip happens under low stress for high SFE materials like aluminum (1964). This gives a metal extra ductility because with cross-slip it needs only three other active slip systems to undergo large strains. This is true even when the crystal is not ideally oriented. High SFE materials therefore do not need to change orientation in order to accommodate large deformations because of cross-slip. Some reorientation and texture development will occur as the grains move during deformation. Extensive cross-slip due to large deformation also causes some grain rotation.Smallman, R., Green, D., (1964). The dependence of rolling texture on stacking fault energy. Acta Metallurgica, 12 (2), 145-154. However, this re-orientation of grains in high SFE materials is much less prevalent than in low SFE materials.

Low SFE materials

Low SFE materials twin and create partial dislocations. Partials form instead of screw dislocations. Screws which do exist cannot cross-slip across stacking faults, even under high stresses. Five or more slip systems must be active for large deformations to occur because of the absence of cross-slip. For both the <111> and <100> directions there are six and eight different slip systems, respectively. If loading is not applied near one of those directions, five slip systems might be active. In this case, other mechanisms must also be in place to accommodate large strains. Low SFE materials also twin when strained. If deformation twinning is combined with regular shear deformation, the grains eventually align towards a more preferred orientation.Heye, W., Wassermann, G., (1966). Mechanical twinning in cold-rolled silver crystals. Physica Status Solidi, 18 (2), K107-K111. When many different grains align a highly anisotropic texture is created.

Notes

Materials science