Question

Al is metal, silvery in colour, with a resistivity of 2.65 μΩ.cm at room temperature. it has the so-called face centred cubic (FCC) structure, in which the fractional coordinates of the atoms within the (conventional cubic, side length of a 4.046 A) unit cell are: (0,0,0), (12%,0), (12,0,%), (0,%,%) The intermetallic compound AbAu is bright purple in colour, has a melting point of 1060°C, is rather brittle, and has a resistivity of p-8 u2.cm.1 the repeating unit is also cubic with a side length we shall denote a), and has atoms at fractional coordinates: 4, 74, 74), (74,74,74), (74, 74, 74), (74, 74,4 74, 74,74),74,74,74 Au: (0,0,0), (%,%,0), (14,0,%), (0,%,%) 74,74,74, 74, 74,74 Fig shows simulated powder diffraction pattern profiles for three different samples using Cu Ka (X-ray) radiation with a wavelength of 1.54 Å. Powder diffraction is reminiscent of the polycrystalline diffraction patterm shown in lectures: the sample comprises many small crystals in random orientations and the resultant diffraction pattern only varies in one dimension 1.0 0.8 0.6 0.4 0.2 0.0 (A)2 20 25 35 40 45 26(degrees) (B)10 0.8 0.6 0.4 0.2 0.0 35 45 2θ (degrees) 0.8 2 0.6 0.2 0.0 35 50 20(degrees) Fig. 2: Simulated powder diffraction patterns. Note: Consistent with the standard experimental geometry , the horizontal axis is given in units of 20 rather than θ.) a. Which of the three diffraction pattern profiles in Fig. 2 is consistent with the A2Au profiles in Fig. 2 is consistent with the AlbAu structure? Justify your answer Further, use this information to determine the lattice parameter a', the side length of the repeating unit. You must show your working. b. Would Al and Al2Au be distinguishable from the pattern of allowed and forbidden reflections alone? Would they be distinguishable on the basis of the actual Bragg angles 6? Would they be distinguishable on the basis of the peak heights? Justify your answers. C. Of the physical properties of A2Au provided, which are most typical of a metal and which are less so? For question (d), use the classical free electron gas model applied to pure (FCC) aluminium. d. Using the background information provided and assuming that each aluminium atom donates three electrons to the electron gas, calculate the average time between collisions of the electrons. Using the electron thermal velocity at room temperature, further calculate the mean free path (mean distance between collisions). Compare the mean free path to the

Answer 1

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