text: A common concept in materials science is that, at ambient conditions, smaller features (like grain size or absolute size) generally lead to stronger materials (see Hall-Petch strengthening, Weibull statistics). However, due to the high-level of porosity in the dealloyed materials, their strengths and stiffnesses are relatively low compared to the bulk counterparts. The decrease in strength due to porosity can be described with the Gibson-Ashby (GA) relations, which give the yield strength and Young's modulus of a foam according to the following equations:
  where  and <math>C_E
   and <math>n_E
   is the relative density of the foam.
  The GA relations can be used to estimate the strength and stiffness of a given dealloyed, porous material, but more extensive study has revealed an additional factor: ligament size. When the ligament diameter is greater than 100 nm, increasing ligament size leads to greater agreement between GA predictions and experimental measurements of yield stress and Young's modulus. However, when the ligament size is under 100 nm, which is very common in many dealloying processes, there is an addition to the GA strength that looks similar to Hall-Petch strengthening of bulk polycrystalline metals (i.e., the yield stress increases with the inverse square root of grain size). Combining this relationship with the GA relation from before, an expression for the yield stress of dealloyed materials with ligaments smaller than 100 nm can be determined:
  where A and m are empirically determined constants, and  is the ligament size. The  represents the Hall-Petch-like contribution.
  There are two theories for why this increase in strength occurs: 1) dislocations are less common in smaller sample volumes, so deformation requires activation of sources (which is a more difficult process), or 2) dislocations pile-up, which strengthens the material. Either way, there would be significant surface and small volume effects in the ligaments <100 nm, which lead to this increase in yield stress. A relationship between ligament size and Young's modulus has not been studied past the GA relation.
  Occasionally, the metastable nature of these materials means that ligaments in the structure may "pinch off" due to surface diffusion, which decreases the connectivity of the structure, and reduces the strength of the dealloyed material past what would be expected from simply porosity (as predicted by the Gibson-Ashby relations).