Hi Michael

In general high SFE materials deform easy by a slip of the screw or edge dislocations on define slip systems in the materials, i.e., aluminum alloys, .   In contrast , low SFE materials deform by twinning of partial dislocations because of undefined slip systems in the materials, I,e, copper alloys.   This is the reason behind observations of twins in microstructures of copper alloys,  but not in aluminum alloys. 

Dear Michael,

I wrote a comment to a similar question on Researchgate before. So I apologize if I am repeating most of it below.

Stacking fault energy, at the most fundamental level, depends on the free electron density distribution. Calculation of it realistically, i.e. by considering the presence of different atomic species together in any solid solution for example, not to mention that the presence of crystal defects of different types, is an impossible task with today's capacity. People are doing ab initio calculations using computer models in system that are 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. Admittedly, such an approach is far from being perfect but nevertheless the effort is worth as the results are still very useful.

As a physical picture it may help us understand better if we consider the following… First of all free electron distribution is usually pictured as a “sea of electrons” or “a cloud of electrons” when we teach the concept. But this is distorting the fact that such a “sea” is not uniform (may be not the cloud, but a cloud has no order at all anyway, and therefore it too wrong). In reality free electron distribution changes depending on the path one walks from one atom to a particular neighboring atom. As a result, if free electron density distribution creates a high polarity around lattice points in particular planes/directions, than the stacking fault energy (SFE) measured would be high, and vice versa. This also tells us that instead of speaking about a general SFE value, it would be more meaningful to understand how the SFE changes for individual planes. This becomes even more crucial a point in crystals of lower symmetry, like hexagonal. In any case, a lower SFE implies that creation of crystal defects (their birth) becomes easier.

SFE influences every property of materials. 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 becomes easier. 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 due to smaller strain field they have. Lower SFE (larger dislocation core size) makes the dislocations less mobile and lesser number of them can be accumulated on a particular slip plane. SFE modifies the ability of a dislocation to glide onto an intersecting slip plane. The common perception in the literature is that lower SFE materials display wider stacking faults and have more difficulties for cross-slip and climb. So it is said, for example, that lower SFE leads to lower creep rate in FCC. And these are the properties that are highly relevant to creep deformation. However, I am not convinced about climb getting more difficult with lower SFE (to my best knowledge, I have not seen any study/experiments that would directly prove this). I am just thinking that lower SFE increases the stress field around a dislocation. Since a dislocation has a compressive stress field below and tensile above it, I am inclined to think that atoms that sit along the dislocation lines would be under greater compressive stresses with lower SFE and therefore climb may actually be fascilitated.   

One may extend the discussions by saying that larger dislocation core size (lower SFE) size can allow for somewhat faster pipe-diffusion. It should also be kept in mind that a different SFE level would also change the distribution and the number of dislocations, with lower SFE being more “homogeneously” distributed and with less number of them on an individual plane. So an assessment becomes rather complicated especially for creep.

Well… I think I should stop at this point.  Best regards.

 Dear Khaled and Ali

Thank you both for your answers I do appreciate the time taken to write on this topic.  

With regard to climb becoming more difficult with a large stacking fault I suppose the common perception is that it is much easier to move a line of atoms than a whole plane of atoms.   Nevertheless, I can see your point if there is sufficient driving force (applied stress, local stress field and temperature) then moving a whole plane should not be so hard, after all it happens in slip.  

I guess the climb of a stacking fault could be modelled?  

Dear Michael,

Yes it would be interesting to model climb. I am not aware of any work if there exist any.

Best regards

I would recommend you read "Mechanical Behaviour of crystalline solids at elevate temperature" by OD Sherby and PM Burke, in Progress in Materials Science, Vol. 13, No. 7, 1967, Pergamon Press. -(or more recent summaries - for instance from M. Kassner (2015). Fundamentals of creep in metals and alloys, Butterworth-Heinemann.) The Sherby-Burke article states that ... it has been suggested that widely extended dislocations would have difficulty climbing because the partials must first combine before climb becomes possible . Dislocations in BCC metals are, in general, not believed to be extended. For this reason it has been suggested that the higher creep resistance of FCC metals over BCC is due to the difference in stacking fault energy.  However it appears that the main reason for the superiority of FCC metals (or HCP metals) lies in the lower rate of atomic diffusion in those close packed structures. However when the steady state creep rate of Al, Ni, Cu, Ag is plotted as a function of stacking fault energy at constant stress over modulus and at constant diffusivity the creep rate is found to be proportional to stacking fault to the 3.5 power. Sherby suggested that low stacking fault energy may contribute to fine subgrain formation which in turn results in higher creep resistance.

Dear Eiselstein,

Thank you for your illuminating-for-me contribution. The explanation for more difficult climb in case of lower SFE and a concurrent lower diffusion rate seems very satisfactory indeed. However, referring to Sherby's interpretation, regarding low SFE leading to fine subgrain formation and therefore a higher creep resistance, seemed questionable. Even only looking from the perspective of lower SFE and subgrain formation we have the case of magnesium for example that skips the subgrain formation, a phenomenon which is explain based on low SFE. Larger strain fields with low SFE prevents grouping of dislocations to form cell walls during recrystallization (more homogeneous distribution of dislocation due to low SFE).

The counter argument to Sherby's reasoning may be extended further. How can fine subgrain formation which would eventually lead to fine grain structure give higher creep resistance?

Thank you for your attention.

Higher stacking fault energy implies lower stacking fault width and thus it would facilitate dislocation movements and thus might lead to plasticity and creep!

It has been quite a long time since I reviewed this research area.  I would recommend that you consider reviewing the review articles from Conrad, Robinson, and Sherby and the more recent review article by Mike Kassner.  In brief, Young, Robinson, and Sherby, “Effect of subgrain size on the high temperature strength of polycrystalline aluminium as determined by constant strain rate tests”, Acta Metallurgica, Volume 23, Issue 5, May 1975, Pages 633-639) state that the influence of subgrain size, λ, on the creep strength, σ. of high purity polycrystalline aluminum was studied by a unique method involving instantaneous strain rate change tests. The results obtained reveal that the strength at a given strain rate increases as the subgrain size decreases following the relation σ ∝ λ-p/N, where p and N are creep parameters about equal to 3.2 and 7.4 respectively. These values of p and N are in close agreement with those obtained from stress reduction tests in creep experiments. Attention is drawn to the need for new creep models which identify the importance of subgrain boundaries to the creep process.

(Kasner and Pearez-Prado, Five-power-law creep in single phase metals and alloys, Progress in Materials Science 45 (2000). pages 1-102) provides a more recent good review.  He states, in part, that for constant-stress transients, the network dislocations cause hardening but the fraction of mobile dislocations may decrease, leading to strain-rate decreases not necessarily associated with subgrain formation. 304 has a relatively low stacking fault energy while aluminum is relatively high. In both cases, the average subgrain size (considering the entire volume) decreases over primary creep. The lower stacking fault energy 304 austenitic stainless steel, however, requires substantially more primary creep strain (0.4 vs. 0.2) to achieve steady-state at a comparable fraction of the melting temperature. It is possible that the subgrain size in 304 stainless steel continues to decrease during steady-state. Under constant-strain rate conditions, the density of dislocations not associated with subgrain boundaries monotonically increases with increased flow stress for both austenitic stainless steel and high purity aluminum. I think you will find these article quite illuminating  Best regards Larry

Hi everyone,

This tread of discussions was some time ago but I would like to add a detail that I think it is important.

Prof. Roberts of Oxford University, Department of Materials, once made a very important contribution (here in Researchgate) to the question of relationship between the mobility of dislocations and SFE. Prof. Roberts, referring to his lecture notes, correctly indicated that smaller SFE, which leads to a larger dislocation core size, actually is a case where less stress is needed to mobilize a dislocation. This is true as an individual dislocation "feels" higher stresses due to larger bending (large core size) of the neighboring planes around itself. So, relatively speaking only a small additional stress is needed to mobilize such a dislocation. But on the other hand, the common observation is that in materials of smaller SFE, dislocation mobility is less. In fact, despite an apparent contradiction here there is no contradiction. Prof. Robert's explanation is absolutely correct for an individual dislocation. However, in real cases (or in real materials) we very rarely have such a situation where a material has dislocations that sit sufficiently far apart from each other. And even if such a picture is true at the beginning of deformation, the picture quickly changes and we get into a situation where dislocation density becomes high enough to the extent that low SFE with dislocations of large core size (large stress fields around them) hinders the mobility of the dislocations. Thus, what is said as 'with lower SFE dislocation mobility is less' becomes true.

Thank you for reviving the topic Prof. Kaya. This clarification is quite illuminating; after all we typically deal with clusters or forests of dislocations in practice, hence the observation for low SFE materials can be explained.

On the previous point about SFE and climb, the reasoning that climb needs to be prefaced by combination of partials seems quite satisfactory. I wonder if the reasoning based on dislocation core size (and hence mobility) is applicable in thermally activated climb as well? Or does the core size affect only the in-plane deformation?

The reason I ask is, the mobility of screw dislocations is reported to be lower than edge dislocations, despite their ability to cross-slip. So I wonder if the SFE of a material affects edge and screw dislocations differently.