X-ray Diffraction In their paper entitled \" Sodium under pressure: BCC to FCC s

Question

X-ray Diffraction

In their paper entitled "Sodium under pressure: BCC to FCC structural transition and pressure-volume relation at 100 GPa" (Phys. Rev. B, 65, 184109 (2002)), Hanfland et al. described their high-pressure x-ray diffraction measurements performed on metallic Na. They observed that Na undergoes a phase transition from the body centered cubic (BCC) to face centered cubic (FCC) structure at 62.3 GPa. Information for metallic Na is tabulated below at the bottom of this problem

(a) At room temperature and atmospheric pressure, metallic Na is known to have BCC structure. Calculate the lattice parameter at room temperature.

(b) Calculate the density of metallic Na at room temperature and atmospheric pressure.

(c) Due to the applied high pressure, the lattice parameter of the BCC structure, aBCC, decreases to 2.91

Explanation / Answer

Solution:

The metallic Na is having BCC structure at room temperature, its lattice parameter (a) can be related to the atomic radius (r) as follows

a)

a = 4r / root 3

Given the atomic radius of the sodium (Na), that is r = 190 nm = 1.9 * 10-10 m, this gives lattice parameter as a = 4.3878 A0

b)

Density of sodium can be calculated using this formula

Where n = number of atoms per BCC unit cell, V = volume of unit cell, N= Avagadro

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