Hi Aditi

This is done by calculating the surface energy (γ) for each fcc plane, and then ratioing the surface energies for each plane. The surface energies for each plane depend on the number of surface atoms exposed per unit area and also the energy required to form each surface atom (remember, surface atoms are coordinatively unsaturated with respect to the bulk, thus their formation requires energy input since bonds need to broken in their formation)

γ = (Energy required per surface atom)*(number of surface atom/surface area)

I think you will find the attached references useful in your ongoing work.

Best regards

Geoff

As Dr.Geoffrey is mentioned some equations, I suggest to read and follow the following articles to calculate the surface energy of different faces of nano-particle.

Regards,

Nanoparticles have a substantial fraction of their atoms on the surface, This high surface area to volume ratio is an important factor in many of the physical properties of nanoparticles, such as their melting point and vapor pressure, and also in their reactivity. Heterogeneous catalysts, for example, are often based on nanoparticles because the catalytically reactive atoms are those that are on the surface of the particle.

Fractional composition of surface and bulk vs. nanoparticle size.

A key quantity that is connected with the chemistry of all surfaces is the surface energy. This is the (thermodynamically unfavorable) energy of making "dangling bonds" at the surface. Atoms at the surface are under-coordinated, and because breaking bonds costs energy, surface atoms always have higher energy than atoms in the bulk. This happens regardless of whether the bonding is covalent (as in a metal), ionic (in a salt), or non-covalent (in a liquid such as water). We see this effect, for example, in water droplets that bead up on a waxy surface. The droplet contracts into a sphere (against the force of gravity that works to flatten it) in order to minimize the number of dangling hydrogen bonds at the surface.

In the case of metal or semiconductor particles, strong covalent bonds are broken at the surface. For example, a gold atom in bulk face-centered cubic Au has 12 nearest neighbors, but a gold atom on the (111) surface of the crystal (the most dense crystal plane of gold) has six nearest neighbors in-plane and three underneath, for a total of 9. We might expect the surface energy of this crystal face to be a little less (because the remaining bonds will become slightly stronger) than 3/12 = 1/4 of the bonding energy of bulk Au, and this is in fact a fairly good rule of thumb for many materials. When translated into energy per unit area, the surface energy of metals and inorganic salts is usually in the range of 1-2 J/m2.

https://chem.libretexts.org/@api/deki/pages/34818/pdf/11.4%253A%2bSurface%2bEnergy.pdf?stylesheet=default

Size-dependent surface energies of Au nano particles

Useful research to learn the calculation of the surface area of the nuclear material.

  Greetings Dr Qhatan Adnan 

Dear colleagues, could you please tell me where could I find the energies of the different faces of iron oxide nanoparticles (especially Fe3O4)? I have not found them in the references that you send here.

Many thanks in advance

hi

could you plz explain for me the relation between the surface energies and chemical or physical bonds of surface? i mean is it true to say that surface with chemical bonds has more surface energy in comparison with surface with physical bonds?