Introduction to Materials Science and Engineering
Homework Number 1 – Atomic and Crystal Structure
1.
(a) Briefly describe the 4 types of quantum numbers and what they represent.
(b)State the Pauli exclusion principle and what it means for the periodic table of elements.
(c) Beryllium is a metallic element with atomic number 4. Briefly describe the atomic structure
of Be, and write out the electronic configuration of beryllium in terms of its filled states.
(d) Briefly explain why beryllium is a metal and chlorine is a non metal.
2.
(a) Using specific examples, briefly describe the different types of primary and secondary
describe the concept of electronegativity and how it affects primary and secondary bonds that
can occur in nature.
(b) The attractive energy for sodium and chlorine ions sodium chloride is given by EA = -A/r, if A
is given by (Z1e)(Z2e)/(40), where 0 is the permittivity of a vacuum (8.85 X 10-12 F/m), e is the
electronic charge (1/602 X 10-19 C) and Z1 and Z2 are the valences of sodium and chlorine ions
respectively, estimate the attractive energy of sodium and chlorine ions in NaCl crystals.
(c) Explain the concept of hybridization and how it applies to the types of bonds that can be
formed between carbon and other elements.
(d) Explain the differences between the strength and tribological properties (potential to act as
lubricants) of diamond and graphite in terms of their intermolecular and intramolecular bonds.
3.
(a) Using basic ideas from potential theory, derive an expression for the binding energy of a soild
that is bound by primary covalent bonds. Identify a key materials property that is controlled by
the binding energy.
(b) Sketch the force-separation curves and the energy separation curves for a typical covalently
bonded solid. Use these curves to explain why many materials exhibit linear elastic behavior.
(c)By idealizing the force-separation curve as a sinusoidal curve in part (a), derive an expression
for the work of adhesion.
(d)Using the concept of energy-separation curves, explain the reasons for the equilibrium
separation of atoms and the thermal expansion of solids.
4.
Without referring to the periodic table, identify which os the following elements is a metal,
alkali metal, alkaline metal, inert gas, halogen or transition metal. Explain the reasons for your
choices.
(a) 1s22s2sp63s23p63d74s2
(b) 1s22s22p63s23p6
(c) 1s22s22p63s2
(d) 1s22s22p63s23p63d24s2
(e) 1s22s22p63s23p64s1
5.
(a) Briefly describe the concept of a unit cell.
(b) Describe the 7 types of crystal structures that are found in nature. Explain how the
differences in crystal symmetry can affect the overall elastic properties of crystals.
(c) Derive an expression for the atomic packing factor of a face centered cubic solid.
(d) Estimate the density of face centered cubic copper from knowledge of the number of atoms
in its unit cell. You may assume that the atomic weight of copper is 63.5 g/mol and the
Avogadro’s number is 6.022 X 1023 atoms/mol.
6.
(a) Sketch out the different types of <110> directions and {111] planes that can occur in a face
centered cubic lattice.
(b) Explain the significance of the <110> directions and {111} planes for plasticity in face
centered cubic structures.
(c) Sketch out and label the basal, prismatic and pyramidal planes in a hexagonal closed packed
structures.
(d) Explain why hexagonal closed packed structures are generally not as ductile as face centered
cubic structures.