Please provide detailed solution, with step by step. Preferentially done on a pa

Question

Please provide detailed solution, with step by step. Preferentially done on a paper and scanned

3. When noble gases condense on a surface, they can be considered to form a 2-D crystal. This crystal can be described quite well using a Lennard Jones potential: (a) Derive the equilibrium bond length, and the energy per atom of a one atom per unit cell crystal defined on a simple square lattice (in 2-D) with square edge of length a. You should express your answers algebraically in terms of the constants sigma, E , and the parameters Al2 and A6 we defined in class. Compute numerically the energy per atom of the crystal at its equilibrium lattice parameter in terms of the parameter c. You may need the sums: (b) Now assume that Kr gas is deposited on the (001) surface of a Ag crystal (Ag is an face centered crystal with cubic lattice parameter a = 4.09 A. The structure of this surface is shown in the figure below. Consider the two arrangements of Kr atoms indicated by the triangles and the squares. Suppose that Kr atoms remain on the surface, and they have a minimum energy when sitting at the interstitial gaps in the surface, as shown below. Assume that the only other contribution to the energy is the Lennard-Jones interaction between the Kr atoms. Given that the value of sigma for Kr is known to be sigma kr= 3.684 A, which of these structures do you expect to find experimentally? Justify your response through a calculation of the energy per atom of each configuration. Note that in the definition of the Lennard-Jones potential, the parameter e > 0 .

Explanation / Answer

This is too long brother.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.