Zirconium alloys are used a cladding (surrounding) material for nuclear fuels du

Question

Zirconium alloys are used a cladding (surrounding) material for nuclear fuels due to their near transparency to neutrons. Calculate the diffusion coefficient for hydrogen in high purity zirconium at 250 degree C. b) If it takes 1 year to diffuse a certain amount of oxygen into zirconium at 250 degree C, how long will it take for the same amount of diffusion to occur at 500 degree C? Some information: Q_d = 11.4 kcal/mol D_o = 1.09 cm^2/sec Zr and H both have the HCP structure The diffusion mechanism is interstitial.

Explanation / Answer

1. The following equation expresses data for diffusion of hydrogen in zirconium:

D = Do * exp[Q/RT]

Given: Q=11.4, Do=1.09

So, D = 1.09 *exp[11.4/0.695*523.15]

= 1.09 * exp[0.03135]

= 1.09 * 0.08521

= 0.092 cm2/s

2. Using Stokes-Einstein equation,

     D1/D2 = T12/T21

   So, D1/D2 = T1/T2 ( is same)

      0.092/D2 = 523.15/773.15

      D2 = 0.135 cm2/s

Also, For same amount of diffusion,

D1/t    (t = time taken for diffusion)

   So, D1/D2 = t2/t1

0.092/0.135 = t2/1

t2 = 0.68 years

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