fing 發問於 科學及數學化學 · 6 年前

[緊急]有關化學的問題, 求解答(20分)

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

1 個解答

評分
  • ?
    Lv 7
    6 年前
    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.

    ====

    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%

還有問題嗎?立即提問即可得到解答。