10. Solids Questions

Michael Mombourquette

10. Solids Questions

When you rapidly cool a pure material from the liquid phase to the solid phase, what is most likely to happen at the phase transition?
What are the differences between a molecular solid and a covalent solid? What things are similar?
Lithium crystals take a body-centered cubic structure. What is the coordination number for a lithium atom in crystal form?
Nickel has a face centred cubic structure and it’s density is 8.90 g/cm³. What is the atomic radius of Nickel? [125 pm]
What is the edge length of a simple cubic cell made up of atoms with a 128 pm radius.
What is the coordination number of the two “closest Packed structures”, cubic closest packing and hexagonal closest packing.
Which type of solid, covalent network crystal, covalent network glass, ionic crystal, metalic crystal, molecular crystal, makes the hardest material and why? Explain for each type of solid why or why not they are hardest.

Answers

when you rapidly cool a pure material, the atoms or molecules may not have enough time to find their optimal (lowest energy) location. As a result, the most common result will be a glass or amorphous structure. This will apply for all types of solids, covalent network, ionic, molecular, metallic.
A Molecular solid is made up of individual molecules (covalently bonded atoms forming a single entity), which are held together in the solid form by intermolecular forces. A covalent solid has all the atoms throughout the crystal held together by a continuous network of covalently bonded atoms. There are no individual molecules.
Any monatomic crystal structure (like Lithium) that forms a bcc structure has a coordination number of 8. look to the diagram below. The body centred atom is in contact with the 8 vertex atoms. Since all atoms are identical, any atom can be found to be connected to (touching) 8 other atoms.
An fcc structure is a closest packing structure with 4 atoms in the unit cell (see diagram). The density is calculated using the mass of the cell (four times the mass of Ni) divided by the volume of the cell ( $a^3$ ).
$\rho = \frac{m}{V}=\frac{4\times M_{Ni}}{a^3\times N_A} = \frac{4\times 58.693 \mathrm{\frac{g}{mol}}}{a^3\times 6.0221\times10^{23}\mathrm{\frac{1}{mol}}} =8.90 \mathrm{\frac{g}{cm^3}}$

We can cancel out the units of g and of mol, leaving us with units of cm. That needs to be converted to a more convenient measure for atomic radii.

$a^3 = \frac{4\times 58.693 }{6.0221\times10^{23}\times8.90}\mathrm{cm^3}}=3.52\times10^{-7} cm^3$

$a=353\timesrm{ pm}$

Do the math and take the cube root of both sides. (raise to the power of .33333 on your calculator)
but we want the radius of the atom, not the cell parameter, $a$ . the body diagonal, $b^2=2a^2$ and $b=4r$
so we combine these to get:

$r = 125 \timesrm{ pm}$
A simple cubic cell has edge length $a =2r$ so $a = 2\times 128\textrm{ pm} = 256\textrm{ pm}$
both ccp and hcp have coordination numbers of 12.
A covalent network crystal has all atoms connected by covalent bonds (the strongest kind of bonds) in an unbroken network of atoms. This makes for a very strong but unbendable (brittle) solid in its crystalline form.
A covalent network glass is like a Covalent network crystal except that the atoms are not in any repeatable form. It would have very similar if slightly less strong/more brittle solid than it’s close cousin, the covalent network crystal.
An ionic crystal will have a regular array of anions and cations. This crystal can be somewhat weaker than the covalent network solids above. Depending on the ions, it can be quite brittle or quite soft
A metallic crystal has electrons in mobile locations, meaning that small dislocations of the atoms don’t necessarily break any bonds. A metallic solid can be much softer than the above while remaining structurally intact through the deformations (ductile, malleable)
A molecular solid is molecules held together by intermolecular forces (the weakest of bonds). this kind of solid both in crystal and amorphous form tends to be the weakest of solids.