[緊急]有關化學的問題, 求解答(20分)

Question

1. (a) Calculate the atomic packing factor (APF) of a body centered cubic crystal.

(b) If you increase the atomic radius by 15%, how will the APF change?

2.Pure Fe forms a b.c.c. structure at room temperature and then at 910 °C, it transforms to an f.c.c. . Assuming that the radius of the atom increase by 10% due to the transformation from b.c.c. to f.c.c. with an increase in temperature, calculate the change in atomic packing factor due to transformation from b.c.c. to f.c.c. Fe

Answer 1

最愛解答

1.

(a)

Let R be the radius of an atom in a unit cell, and a be the edge of a unitcell.

Consider a b.c.c. unit cell.

In Geometry :

Length of diagonal² = 3a²

Length of diagonal = (√3)a

Along the diagonal, each atom touches their neighboring atoms.

Length of the diagonal = r + 2r + r = 4r

Hence : (√3)a = 4r

r = (√3)a/4

Number of atoms in a unit cell

= Number of atoms inside + Number of atoms at the corn

= 1 + 8 × (1/8)

= 2

Total volume of atoms in a unit cell

= 2 × [(4/3) × π × r³]

= (8/3) × π × [(√3)a/4]³

= (√3)πa³/8

Volume of a unit cell

= a³

APF of b.c.c. crystal = [(√3)πa³/8]/a³ = (√3)π/8 = 0.680

(b)

APF = (√3)π/8

APF is independent of r.

When atomic radius is increased, APF is unchanged.

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2.

Consider a f.c.c. unit cell.

In Geometry :

Length of diagonal of a face² = 2a²

Length of diagonal of a face = (√2)a

Along the diagonal of a face, each atom touches their neighboring atoms.

Length of the diagonal of a face = r + 2r + r = 4r ... [2]

(√2)a = 4r

r = (√2)a/4

Number of atoms in a unit cell

= Number of atoms on the face + Number of atoms at the corn

= 6 × (1/2) + 8 × (1/8)

= 4

Total volume of atoms in a unit cell

= 4 × [(4/3) × π × r³]

= (16/3) × π × [(√2)a/4]³

= (√2)πa³/6

Volume of a unit cell

= a³

APF of f.c.c. crystal = [(√2)πa³/6]/a³ = (√2)π/6 = 0.740

Change in APF = [(0.740 - 0.680)/0.680] × 100% = +8.82%