Question

What is the relation between atomic radius r and lattice constant a in the case of face- centered cubic (FCC) structure? State the number of atoms in a unit cell for FCC structure and hence deduce the atomic packing factor.

Answer #1

A certain material has a FCC crystal structure with an atomic
radius of 1.44 A° (1 A° = 10-8 cm), and an atomic mass of 197.
Calculate:
a) The lattice constant ‘a’ of unit cell in cm,
b) The atomic packing factor of the material.

Hetero atom
(1) calculate radius of atom which forms simple cubic crystal
structure. Lattice constant=4.0Å
(2) calculate radius of atom which forms HCP crystal
structure. Lattice constant a=3.0Å
(3) calculate nuclear distance of body-centered
tetragonal(Lattice constant a=b=5Å, c=6Å), and
atomic packing factor.

Calculate the atomic packing factor (APF) for the following:
(a) simple cubic unit cell with 1 atom per lattice point
(b) BCC unit cell with 1 atom per
lattice point
(c) FCC unit cell with 1 atom per lattice point

Iron (Fe) crystallizes in a body-centered cubic structure with
a lattice constant of 0.287 nm:
Use drawing to show how the iron atoms are packed in the unit
cell. How many iron atoms are contained in each unit
cell?
Use drawings to show how the iron atoms are arranged on the
(100) and (110)
planes.
Determine the density of iron (g/cm3) by dividing
the total mass of iron atoms in the unit cell by the volume of the
unit cell....

Iron (Fe) crystallizes in a body-centered cubic structure with a
lattice constant of 0.287 nm:
a. Use drawing to show how the iron atoms are packed in the unit
cell. How many iron atoms are contained in each unit
cell?
b. Use drawings to show how the iron atoms are arranged on the
(100) and (110)
planes.
c. Determine diameter of iron atom
d. Determine the density of iron (g/cm3) by dividing
the total mass of iron atoms in...

Iron (Fe) crystallizes in a body-centered cubic structure with a
lattice constant of 0.287 nm:
a. Use drawing to show how the iron atoms are packed in the unit
cell. How many iron atoms are contained in each unit
cell?
b. Use drawings to show how the iron atoms are arranged on the
(100) and (110)
planes.
c. Determine diameter of iron atom
d. Determine the density of iron (g/cm3) by dividing
the total mass of iron atoms in...

Germanium has a
lattice constant of 0.565 nm.
a) Draw the portion of
the (110) plane that resides inside a cubic unit cell flat on the
page. Label the lengths of the edges. Show the arrangement of atoms
whose centers lie on the plane and label the distances between the
centers of the nearest neighbor atoms on the plane. Determine the
value of the atomic radius.
b) Calculate the
planar atomic density of atoms on the (110) plane in atoms/cm2....

1) For a metal that has the face-centered cubic (FCC) crystal
structure, calculate the atomic radius if the metal has a density
of (8.000x10^0) g/cm3 and an atomic weight of
(5.80x10^1) g/mol. Express your answer in
nm.
2) Consider a copper-aluminum solid solution containing
(7.82x10^1) at% Al. How many atoms per cubic centimeter
(atoms/cm^3) of copper are there in this solution?
Take the density of copper to be 8.94 g/cm3 and the
density of aluminum to be 2.71 g/cm3.

Chromium metal crystallizes as a body-centered cubic lattice. If
the atomic radius of Cr is 1.25 angstroms, what is the density of
Cr metal in g/cm3?

Calculate the density of Ca (s) in a face centered cubic unit
cell. (The atomic radius of Ca is 1.97 Å)

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