text: For a spherical particle the surface area will scale as the square of the size, while the volume scales as the cube. Therefore surface contributions to the energy can become important at small sizes in nanoparticles. If the energy of the surface atoms is lower when they are closer, this can be accomplished by shrinking the whole particle. The gain in energy from the surface stress will scale as the area, balanced by an energy cost for the shrinking (deformation) that scales as the volume. Combined these lead to a change in the lattice parameter that scales inversely with size. This has been measured for many materials using either electron diffraction or x-ray diffraction. This phenomenon has sometimes been written as equivalent to the Laplace pressure, also called the capillary pressure, in both cases with a surface tension. This is not correct since these are terms that apply to liquids.
  One complication is that the changes in lattice parameter lead to more involved forms for nanoparticles with more complex shapes or when surface segregation can occur.