solids - crystal structures

[Zellmer, Robert]

Someone asked me about what they needed to know about
solids and where to find the information.

This is sections 11.7 and 11.8 in the 10th and 11th editions and
this same material from the 11th edition is on Carmen for those using
the 12th - 14th editions.  Remember, no matter which edition
you're using we are not using chapter 12.

I covered the primitive(simple), body-centered and face-centered
cubic structures.  I gave a lot of info about these (# particles/uc,
how the particles touch, relationship between edge-length and radius,
coordination number, % empty space, type of holes the particles
are in, etc.).  I also covered close-packing of spheres and we saw
a non-cubic type of packing (Hexagonal close-packing, hcp) and learned
the cubic-close packed (ccp) structure is the same as a fcc structure.
All of this discussion was for identical particles in the u.c. (i.e. same
size, like all Fe atoms, all CO2 molecules, etc.)

This was all covered in section 11.7 in the 10th and 11th editions
Some of this is summarized in the following link (found at the "Notes"
link on my web page):

Chapter 11/12 - Unit Cell Table for Identical Sized Particles<https://www.asc.ohio-state.edu/zellmer.1/chem1250/notes/unit_cell_table.pdf>

I covered the NaCl structure in detail and a few things about three
other ionic crystal structures.

In the 10th and 11th editions the structure of NaCl is discussed in
section 11.7 and CsCl, ZnS and CaF2 are discussed in section 11.8.
For the 12th - 14th editions use what's on Carmen (from the 11th ed.).

NaCl is described as a face-centered cubic unit cell.  The problem is
it doesn't look like the fcc unit cell described for a substance in which
all particles are identical.  I explained why it is called a fcc structure and
how it differs from the fcc unit cell for identical sized particles in lecture.
For NaCl understand the unit cells and related information given in class,
notes and the textbook for NaCl.  This includes its structure, placement
of the ions, how anions and cations touch (along an edge), relationship
between edge length and radii of the ions, number of nearest neighbors
and what they are, for both the cation and anion, type of "hole" each ion
"sits" in, unit cell calculations, etc.  I don't generally refer to NaCl as
face-centered but call it the "NaCl structure".  So in a problem I might state
something like "the substance has an NaCl like structure".  You should
know what that means.

For CsCl, ZnS and CaF2 you should know where the atoms are in the u.c.
and the number of formula units in a unit cell.

In doing unit cell calc. for ionic structures you must know how many
formula units there are in a unit cell (e.g. NaCl, ZnS and CaF2 all have
4 f.u. per unit cell, CsCl has 1 fu/uc).  For CsCl, ZnS and CaF2 you only
need to know the # fu/uc.  I've included a link to a table with all the
information for these 4 ionic structures.  You should  know what's listed
for NaCl.  For the other 3 ionic crystal structures just know the placement
of the ions and the #fu/uc.  You can find what you need for these ionic
structures marked in RED at the following link (found at the "Notes" link on
my web page):

Chapter 11/12 - Unit Cell Table for Ionic Structures (know stuff in red)<https://www.asc.ohio-state.edu/zellmer.1/chem1250/notes/ionic_unit_cell_table_filled.pdf>

Furthermore, I would highly suggest using dimensional analysis to
do unit-cell calculations rather than the way shown in the book.  I
did them this way in class and I think in the long run it makes them
easier.  You will find you can do the uc calc. for ionic structures in the
same way as you do for atoms or molecules if you think in terms of
"formula-units" (f.u.) for the ionic compounds.  NaCl is the "formula unit"
for sodium chloride.  You treat it just as if it were a molecule. For
CO2, which is a fcc structure, you have 4 CO2 molecules per u.c. and
for NaCl you have 4 NaCl f.u. per u.c.  Thus, you can do a density
calculation the same way for CO2 and NaCl as you would for something
like the Ag example I did in class (using the MW for CO2 or the formula wt.
for NaCl and the number of particles/uc in the same way you would use
the atomic wt. and # atoms/uc for an atom like Ag).

For unit cell calculations you should be able determine the following:

    1) density (g/cm^3)
    2) volume (cm^3/uc) - includes edge length and particle radius
    3) AW, MW, FW (g/mol)
    4) unit cell type (sc, bcc, fcc) - (#particles/uc)
    5) Avogadro's Number (#particles/mol)

I've included the units you're after when doing these problems using
dimensional analysis.  This includes calculations for ionic structures
(particle radius for just NaCl).

There is a web site where you can look at these structures in 3-D and
rotate them around.

http://undergrad-ed.chemistry.ohio-state.edu/xtal/index.html

Once there, click on "Crystal Structures" at the bottom.  At the top of
the page which comes up you can load the structures for a single type
of particle (sc, bcc, fcc) using the "Bravais Lattices" drop down box or
the ionic structures using the "Other Compounds" drop down box.

It's easiest to understand things if you click the "All atoms" button.
Ask for more than 1 unit cell when trying to see the nearest neighbors
(coord. #).  Also, for the ionic compounds it's much easier to see the
nearest neighbors if you click on "Connect Atoms" toward the bottom
of the window (you sometimes have to click it twice).

Also, look at the links I have for ch 11/12 ("Notes" link).  I have the three
unit cell calculation examples done in lecture.  The table given in the notes
with the info about the unit cells for identical particles (including packing) and
a table for the 4 ionic structures in the notes (with the info you should know
in red).  The links for these last two things were given above.

Also, look at the last page of the chapter 11 (12) notes.  You will find a table
summarizing the 4 types of solids and their properties.  This can be found
on my class web page ("Notes" link),

Types of Solids and Their Properties<https://www.asc.ohio-state.edu/zellmer.1/chem1250/notes/Table_13-10_solids_no_lines.pdf>


I hope this makes sense.

Dr. Zellmer
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