Question

1. Expressions for Burgers vectors for FCC and BCC crystal structures, are of the form, b= a/2 <uvw> where a is the unit cell edge length. a. Describe the magnitude of Burgers vectors of dislocations that will glide on the most effective slip system in FCC and BCC crystals respectively. b. Determine the values of bl for aluminum and chromium.

Answer 1

Given ,

b = a/2<uvw>

The Burgers vector for FCC and BCC crystal structures may be expressed as b = a/2<uvw> where a = cube edge length and <uvw> is the family of close-packed crystal directions.

Answer:- (a) Obtain the atomie radi o aluminium from the dable - Atomic radii and crystal structure to 16 wutats Reas: 0.1431 mm Perystal structuu is Fcc (face-antered cubic) We need to calculate the edge length of a Fce unit cu ca) tale know that, a = Q R 12 Here 'R' is atvucic xadi By substituting billig) mm for R à : 2X0-1031 x 1/2 => = 2X0148] x 1.Ulu + 8 = 0.4047 nm me The equation for Burger's vector for Fcc mutais is as follow: b=0/2 caww... @ d e uviw qil tule slip ploure direction 9.

FCC We need to obtain the Burgers vector for metals from equation 1.19 FCC: al CIO) --- 2 tue vaules for Comparte equatim (1) E Q) and obtain UV,W , Then lle git : v=1 ? V:1.; W=0 obtain the atomic codi ta chromium from table Read= 0.12Ag nm Crystal structure is Bcc Cbody-centered elbic) Calculate the edge length of a Bcc unit Cell a = 4 R Here R atomic cell tadir By jubitituting the 0.1249 0m for R d. 4 X0.124.9 1.7320 → a. 0:4996 1.7320 a 0.2884 nm

The equation for Burger vector for Bcc urtal bị ai Cu Val).- 3) bere U,V, w are slip Plane directions Bwigers vector for Bcc metal We Need 10. Obtain tu from equation #16 Fe = a12 (111) .--. @ By comparing equatims (6) & (4), ille get U ; V: 1 W: 1 Aluminium- calauate the magnitude of Burgers vector for aluminium as follows: lbl= a/2 (u + vt + w) 1/2 substitute Alle LV, W values in the equation 101 - 64047 (17176)2 bl. 0.40417 101 - 0 2028 nm .: Magnitude of Buager Vector for Cherian Aluminium is 0.2023 om

Chromium- calculate the magnitude of Beigers vector for chromium as follows: 101=0/2 cuivaw?)?? By substituting siue U, V, W rallies ( get values by solving (3)&(4)) 101 = 0-2884 (it i'+i+)'72 → 101.0-2884 (115) 1901 - 10.10U2)(15) * → 161 = 0.2163 nm . Magni turde of Burger vector for chromium is 0.2168 om