can you use values of a=3, b=3, c=7

1. Using the lattice basis LB and the reciprocal lattice basis RLB given for graphite in Examples 3.1.1 and 3.1.2, you wish to (1 determine the location of a point of interest within the lattice given by [V] RLB = b , where a, (Land C are integers, not C all zero, to be chosen by you and such that the vector is different from that chosen in any other posts on this topic . Give the coordinates of this point both with respect to the standard basis vectors for R3, and with respect to the lattice basis LB. Explain your steps carefully. Which basis of the three seems most natural for this point of interest? Be sure to include your chosen values for a, b,and C in the Subject Heading of your post. EXAMPLE 3.1.1: FINDING A COORDINATE VECTOR OF AN ATOM RELATIVE To A LATTICE BASIS FOR GRAPHITE x/E/2 /z 0 o A lattice basis for graphite is given by LB 2 a, 1 / 2 , a 1/2 , C 0 , where a = 2. 46 A (angstroms), and 0 0 1 0 c = 6. 71 A. a / 2 3 An atom within a unit cell is located at V = a, / 2 . The following video shows how to nd the coordinates of this atom c/2 relative to the lattice basis. EXAMPLE 3.1.2: CONVERTING FROM THE LATTICE BASIS FOR GRAPHITE To THE RECIPROCAL LATTICE BASIS x//z n 0 We begin again with the lattice basis for graphite given by LB 2 a 1/2 , a 1/2 , C 0 0 0 1 2 This time, we are given a coordinate vector with respect to the lattice basis, [V] LB 2 0 , and we want to know the coordinates 1 of V with respect to the reciprocal lattice basis given by 211'1/3 27r1/3 271' 0 RLB= _1 , 1 , 0 a a C 1 0 0