Question

Work function of metals and crystal planes The work function of a metal o represents the energy needed to eject and electron from the Fermi level to the vacuum level. However, this energy depends on the surface of the crystal involved on extracting the electron. O depends on the crystal plane from which the electron is ejected. Surface conditions such as a thin oxide layer or contaminants on the surface would obviously modify the observed O. Measurements of O are therefore done under high vacuum condition on clean crystal surfaces. Table 4.6 lists measured O for single crystal and polycrystalline samples of AI, Au, and Ag that have a cubic crystal structure (FCC). O has been obtained for three different planes in the case of single crystals. (a) What are the average Pay and mean standard deviation of the work function for the three planes for each crystal? (b) What is the percentage difference between the O for the polycrystalline sample and Pav? (c) In (a), your averaging gave equal weighting to each plane, Pav = (P001 + 2011 + 0.111)/3. How would you modify the averaging process to represent the different percentages of crystal planes that appear on the surface of a polycrystalline sample? Table 4.6 The work function 0 (in eV) of aluminum, gold, and silver for single crystal and polycrystalline samples Sample Aluminum (AI) Gold (Au) Silver (Ag) (100) 4.41 5.47 4.64 (110) 4.06 5.37 4.52 (eV) (111) 4.24 5.31 4.74 Polycrystalline 4.28 5.40 4.65