MECHANICAL 560-The melting temperature on the surface of nanoparticles (Tm)

The melting temperature on the surface of nanoparticles (Tm) is affected by decreasing nanoparticle size over the melting temperature of the bulk material (Tb). The relationship can be modeled by the follow equation:Tm = Tb {1 — [(20 — D)/2D]},Where D is the diameter of the nanoparticle for D < 20nm. The melting point of gold (Au) bulk material is 1340 K.(a) Plot to scale on linear graph paper or using Excel the melting temperature of gold as a function of diameter for spherical nanoparticles between 2 – 20nm.(b) What is the melting temperature for 2nm diameter Au particles? {How much is the melting temperature reduced for 2nm diameter particles from bulk at 20nm?(c) Give a physical explanation for this reduced melting temperature for Au nanoparticles.

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