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Problem 4 (17 points) For a hexagonal lattice with primitive lattice vectors aq = aî +žaſ...

Problem 4 (17 points) For a hexagonal lattice with primitive lattice vectors aq = aî +žaſ ; a2 = - ai +ļaſ ; az = ck (a) Dete

Problem 4 (17 points) For a hexagonal lattice with primitive lattice vectors aq = aî +žaſ ; a2 = - ai +ļaſ ; az = ck (a) Determine the volume of the primitive cell (Vp). (b) Determine the primitive vectors A, B and C of its reciprocal lattice (c) Find the volume of the reciprocal lattice unit cell (d) Determine the angles between the various primitive reciprocal vectors
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(a) Volume of the primitive unit cell is V = 9, 192Xa3 V= (33 al tlap) (- Baltkal) x cle va ad + $03) C C-1(+590) + ] V= J3q²A = ait bitch B = Qzł + bajtak Ia Ia bi bz a ca AXB² = ê (b, (2- bz (1) -] (9.22-02(1) +2 (ap2-6,192)(6) The primitive vectors A, B and C of its reciprocal. lattice is H = 2Т Лхад а - 42 хаз) В= 2Tag xa а, -42 xas | (= ат ауq,С= 2та, хар а - ахад axan - Jза“ + Jза - Е (21) Ja+Ta ауа, ха, - за - 23 24°Е за? с ап ()) (c) Volume of the reciprocal lattAngle botween primitive unit cell are Coso ab Tal15) i Angle between A and B Coso = AB TALIB pat (ſt te k). 2.4(945) () (1+(and A (riis Angle between Coso C- A ICIAL (23 (CT E) (9+ Joc ) (ory (1) Jitiba Coso - 1 + 1 / 2

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