Variation of Elastic modulus with size

[vinven7]

It is generally well known that the elastic modulus of most materials become larger with decreasing size. This could be due to decreased number of dislocations, surface effects etc. Does anyone know how exactly does this increase? Considering a ceramic or an oxide, how does the Elastic modulus E vary with a size parameter H?

 

[CWatters]

Not my field but I found an example here with explanation on the right..

http://openi.nlm.nih.gov/detailedresult.php?img=2801994_ijms-10-05257f10&req=4

The elastic (Young’s) modulus also varies pronouncedly with the thickness of film which is less than about 10 μm, but it approaches a constant when the thickness is more than about 10 μm. The relationship between elastic modulus and the thickness is shown in Figure 10. The main reason of this phenomenon seems to associate with the growth mechanism and its influence factors of the Pth films. When the thickness is less than 10 μm, the Pth mainly grows up in a stable manner on the base layer. But with increasing thickness, more and more agglomerated molecule groups are formed away from the base layer. Therefore, many micro-defects such as micro-cracks and micro-voids easily exist in the adjacent surface layer. At the same time, the binding energy of these agglomerated molecule groups becomes smaller and smaller because of the electrochemical influence or the influence of the metal substrate. Therefore, the microstructures of Pth films will change as the thickness increases. A thin film with the thickness of about 4 μm generally has a perfect microstructure with few defects