From the literature I have read, I can understand that stacking fault energy is an intrinsic property of a material. But what I do not understand is the origin of SFE? The width of a stacking fault is related to SFE, but is this (metallurgy) the only origin? Do bond energies and other electronic phenomena play a role in the SFE of the material?
As required, I restrict myself only to the origin of SFE which is a net resultant of five mutually related phenomenons:
[i]Defect in packing,
[ii]Galling
[iii] Slip and Twinning
[iv] Intermetallic forces
[v] e/a ratio*
[A] It is well known that ideally metals pack either as ABCABC--[ccp]or ABABA---[hcp] . Suppose, ideally a metal has ABCABC packing but the stacking fault changes it to ABCBC--.This changes adhesion so that some metal is pulled with the contacting surface due to a large force compressing the surfaces together causing simultaneous friction and adhesion in between the surfaces followed by slipping and tearing of crystal structure beneath the surface[ Galling]. This leaves some material stuck to the adjacent surface while the galled material appears as torn lumps. Some metals are more prone to galling due to their crystal structure and ductility. No doubt, both Al and Cu are FCC but Al being softer is easy to galling ,i.e. has a greater tendency to produce dislocations
[B]Next comes to the number of stacking faults. If the metal has a high number of stacking faults [ width of stacking fault is a consequence of the balance between the repulsive force between two partial dislocationson on one hand and the attractive force due to the surface tension of the stacking fault on the other hand ], it will be more prone to cross-slip at the dislocations. The material's resistance to galling is usually determined by its Stacking –Fault Energy[γSFE] ( J/m^2). A material with high SFE such as Al(160- 200J/m^2) will be far more susceptible to galling than materials with low stacking-fault energy like Cu(70-78J/m^2) .
[C] Then come the two primary methods of deformation in metals areSLIP and TWINNING . SLIP occurs by dislocation glide of either screw or edge dislocations within a slip plane. It is by far the most common mechanism.TWINNING is less common but readily occurs under some circumstances.A TWIN is a very large stacking fault and occurs when there are not enough slip systems to accommodate deformation and/or when the material has a very low SFE . A material with high SFE such as Al(160- 200J/m^2) will be less susceptible to twinning than materials with low stacking-fault energy like Cu(70-78J/m^2). Twins are abundant in many low SFE metals like copper alloys, but are rarely seen in high SFE metals like aluminum because when the SFE is low, the mobility of dislocations in a material decreases.
[D] As a metal bond[band theory; sea of electrons], is a spread over force holding kernels of a layer with its upper and lower layers in metal depending upon packing of the layers, the size of the kernel snd the coordination number( number of nearest neighbours), the deformation caused in the various layers of the metal is strongly dependent on the strength of the metal bond. Keeping the other factors constant, the stronger the metal bond, the more difficult it will be to to form stacking defects in the metals.
[E] Thornton [1962] concluded that the valence-electron to atom ratio is a good predictor of stacking fault energy.Zn is a heavier element and only has two valence electrons, whereas Al is lighter and has three valence electrons. Thus each weight percent of aluminum has a much greater impact on the SFE than does zinc.
* Mainly determines the SFE of alloys.
As required, I restrict myself only to the origin of SFE which is a net resultant of five mutually related phenomenons:
[i]Defect in packing,
[ii]Galling
[iii] Slip and Twinning
[iv] Intermetallic forces
[v] e/a ratio*
[A] It is well known that ideally metals pack either as ABCABC--[ccp]or ABABA---[hcp] . Suppose, ideally a metal has ABCABC packing but the stacking fault changes it to ABCBC--.This changes adhesion so that some metal is pulled with the contacting surface due to a large force compressing the surfaces together causing simultaneous friction and adhesion in between the surfaces followed by slipping and tearing of crystal structure beneath the surface[ Galling]. This leaves some material stuck to the adjacent surface while the galled material appears as torn lumps. Some metals are more prone to galling due to their crystal structure and ductility. No doubt, both Al and Cu are FCC but Al being softer is easy to galling ,i.e. has a greater tendency to produce dislocations
[B]Next comes to the number of stacking faults. If the metal has a high number of stacking faults [ width of stacking fault is a consequence of the balance between the repulsive force between two partial dislocationson on one hand and the attractive force due to the surface tension of the stacking fault on the other hand ], it will be more prone to cross-slip at the dislocations. The material's resistance to galling is usually determined by its Stacking –Fault Energy[γSFE] ( J/m^2). A material with high SFE such as Al(160- 200J/m^2) will be far more susceptible to galling than materials with low stacking-fault energy like Cu(70-78J/m^2) .
[C] Then come the two primary methods of deformation in metals areSLIP and TWINNING . SLIP occurs by dislocation glide of either screw or edge dislocations within a slip plane. It is by far the most common mechanism.TWINNING is less common but readily occurs under some circumstances.A TWIN is a very large stacking fault and occurs when there are not enough slip systems to accommodate deformation and/or when the material has a very low SFE . A material with high SFE such as Al(160- 200J/m^2) will be less susceptible to twinning than materials with low stacking-fault energy like Cu(70-78J/m^2). Twins are abundant in many low SFE metals like copper alloys, but are rarely seen in high SFE metals like aluminum because when the SFE is low, the mobility of dislocations in a material decreases.
[D] As a metal bond[band theory; sea of electrons], is a spread over force holding kernels of a layer with its upper and lower layers in metal depending upon packing of the layers, the size of the kernel snd the coordination number( number of nearest neighbours), the deformation caused in the various layers of the metal is strongly dependent on the strength of the metal bond. Keeping the other factors constant, the stronger the metal bond, the more difficult it will be to to form stacking defects in the metals.
[E] Thornton [1962] concluded that the valence-electron to atom ratio is a good predictor of stacking fault energy.Zn is a heavier element and only has two valence electrons, whereas Al is lighter and has three valence electrons. Thus each weight percent of aluminum has a much greater impact on the SFE than does zinc.
* Mainly determines the SFE of alloys.
Thank you for the insightful answers. So basically the atomic interactions such as bond energy, e/a ratios and alloying decide the SFE of the material?
Dear Rohit,
Stacking fault energy, at the most fundamental level, depends on the free electron density distribution, a value which is very difficult, even impossible with today's capacity, to estimate unless the system considered is very small, e.g. system considered is composed of some small number of atoms, and dilute to the extend that only one, and may be two foreign atom (I am not even sure about two atom case) is embedded into such model. One should also note that crystal defects are also neglected in such models. Admittedly, such an approach is far from being perfect but nevertheless still very useful.
Now, if free electron density distribution creates a high polarity around lattice points, than the stacking fault energy (SFE) measured would be high, and vice versa. SFE influences every materials property. High SFE would result in smaller dislocation core size (consider a dislocation as a pipe, and its diameter is the core size). Lower SFE means otherwise of course. In each case a metal behaviour changes dramatically. Higher SFE means generation of dislocations is more difficult, but dislocation mobility is requires a different analysis. Aluminum is an example to high SFE. Magnesium represents a lower SFE case. Smaller dislocation core size (high SFE) creates greater mobility for dislocations and more number of dislocations can be accumulated in each slip plane as they can come closer to each other. Lower SFE (larger dislocation core size) makes the dislocations less mobile and lesser number of them can be accumulated on a slip plane. Lower SFE materials display wider stacking faults and have more difficulties for cross-slip and climb. The SFE modifies the ability of a dislocation in a crystal to glide onto an intersecting slip plane.
I hope this helps you in some way.
i have a doubt regarding stackingfault energy.Is it changes with temperature(high and low) and high strain rates?if so what type of changes we can expect.Based on the above scenariao how the SFE contribures to strengthen the material that to in different crystals structures(like FCC,BCC,HCP).
Dear Nataraj,
I should first say that we cannot say SFE contributes to strength or weakens it. SFE governs, with regard to mechanical properties, how material behaves during deformation processes. Although it is much more meaningful to discuss the SFE values of specific planes in a metal, just for the sake of argument consider the following comparisons: Aluminum has a higher SFE value compared to magnesium and also has a higher yield strength. Cooper on the other hand has a lower SFE value compared to magnesium but again has a higher yield strength. So the SFE value does not immediately compare the strength levels. It should be born in mind that strength is the sum of a number of contributing factors (please consider the strengthening mechanisms). SFE, on the other hand is a value governed by the free electron density distribution. A change in the stacking order, although does not change the coordination number of the atoms at the fault plane but at least the bond angles changes. Hence the fault plane, i.e. SF, is a more energetic location compared to the regions having the usual stacking order. This is, at the same time, a plane where free electron density distribution in any walk from one atom to any of the neighboring atom has also changed now.
In this scenario, one would understand that SFE would also change whenever other players/factors are introduced. For example, if the fault plane (SF) involves foreign atoms, if near to other crystal defects, when extrinsic factors such as temperature, strain (or strain rate, for that matter) are in play, we may expect SFE to change by some degree. However, all this is not to say that SFE is such an ambiguous parameter that we should ignore it. On the contrary, one should remember that SFE is a relative term that we use it in a comparative way when different metals, or different alloys of a metal-base are considered. Again it is more useful to compare the SFE values of planes that are operative in slip or twinning (or whatever the atomistic process considered is) rather than making comparisons on basis of the crystal systems (remember the example of FCC-copper, FCC-aluminum and HCP-magnesium). I should also indicate the in a low symmetry system like HCP (magnesium being one) SFE of individual crystal planes becomes more distinctive, and must be considered specifically. Therefore, changes, if and when possible, in the SFE values of basal, prismatic or pyramidal planes would have extremely important consequences in terms of the overall mechanical behavior of magnesium alloys, for example.
I hope this helps.
Dear Rohitt,
The followed article seems useful for what you are searching for. It contains great ideas.
Article The origin of negative stacking fault energies and nano-twin...
Good luck.
The nature of the bonding in solid state material is electrostatic where the valence electrons are attracted by the surrounding positive ion cores. If the atoms of the materials are correctly stacked to each other all the bond will be complete and no bond is broken. This corresponds to the minimum potential energy of the material. If any bond is broken it will increase the potential energy of the material with an amount of energy corresponding to break this bond. In the stacking fault there are many broken bonds surrounding the the stacking faults which means that internal energy will be higher with the presence of the stacking fault compared to its value with stacking fault.
Best wishes
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