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- a) Consider a plane in a body-centered cubic lattice where a = 4.225 Å. State the Miller indices and the direction vector of this plane. b) What is the distance between adjacent planes in this cubic crystal?For a BCC crystal, determine (a) Linear density along [111] and [101] (b) Linear packaging density along [110] and [1 11] (c) Planar density on (100) and (011) (d) Atomic packing factor (APF)constant = 1. If 1 × 1015 boron atoms per cm³ are uniformly added to silicon (diamond structure, lattice 0.543 nm) as a substitutional impurity, determine what percentage of the silicon atoms are displaced in the single crystal lattice, i.e., the concentration of boron as an impurity in silicon.
- Given: The BCC crystal structure Required: Determine the relationship between the atomic radius, R, and the unit cell width, a. Determine the APF for the BCC crystal.b) Find the directional indices for the two vectors as shown in Figure Q3(b). 0.4 nm 0.3 nm +x -0.5 nm Direction 2 Fig. Q3(b) c) Calculate the atomic packing factor for the face-centered cubic (FCC) crystal structure. Formula Sheet nA V.NA dh Direction 1 p= hkl nλ = 2d sin 0 hkl V APF = $ Ve = +y a √h² +k² +1²c) If f(aa) = 12 (sin aa) + cos aa for 0 ≤ aa ≤ 4n of large crystal is mVoba Find the height of P koa A² aa given by f(aa) = cos ka, where P' = potential.
- (a) How many silicon atoms are there in each unit cell? (b) How many silicon atoms are there in one cubic centimeter? (c) Knowing that the length of a side of the unit cell (the silicon lattice constant) is 5.43 Å, Si atomic weight is 28.1, and the Avogdaro's number is 6.02 × 10²3 atoms/mole, find the silicon density in g/cm³.A:08 الرسائل المحفو. . . 1 03: Rhenium has a Hexagonal Close-Packed crystal structure with an atomic radius of 0.137 nm and a ratio c/a of 1.615, compute: a) The volume of the unit cell. b) The theoretical density c) Atomic packing factor Note: Avogadro's' number = 6.023×10²³ Atomic weight = 186.21 g/mol إضافة وصف.. . IIIBody-centered cubic structure. (a) Show that for BCC the lattice length a in terms of the atomic radius is 4R/√3. (b) Calculate the volume of a BCC unit cell in terms of the atomic radius R. (c) Show that the atomic packing factor for the BCC crystal structure is 0.68.
- 0.4 nm 0.3 nm +x -0.5 nm- Direction 2 Fig. Q3(b) c) Calculate the atomic packing factor for the face-centered cubic (FCC) crystal structure. Formula Sheet nA V.NA p= djkl Direction 1 APF = = V V nλ = 2d hk sin 0 S +y a √h² +k² +1²Consider spherical nanoparticles of copper with diameters of 10 and 100 nm. A) Calculate the total number of atoms in the particles,considering the lattice parameter of bulk Cu. B) Calculate the number of atoms at the grain boundaries for a typical grain boundary thickness of 1nm.Consider a Face Centered Cubic (FCC) lattice structured Nickel crystal. We are looking to find the surface energy of the new surface that is formed after it is sliced at the (100) plane. a- Find the value of R as function of the lattice constant a. 4R Oa = 2R Oa = 4R Oa = = 2/2R V2 Find the area A11 of (111) surface as function of R. 04R? O16R? O8R? OR? How many atoms lie on the plane (111) within the unit cell? N111 = atoms within the unit cell Find the number of atoms per unit surface area. 2 2 R2 8R2 16R? 4R? Which of the following represents the expression of the surface energt? ON BEPA