Due March 6.
The whole class will be divided into 8 groups. Each group
consists 4 students. Each students will write the report for
part 1 and build a model for part 2.
Let ABCD the the vertices of a regular tetrahedron and
O be its "center". Find the angle AOB.
In this project you need repeatedly use the Pythagorean theorem and
a little bit of trigonometry. You need also to think about the use of area and
volumes.
Write a report that details your reasons.
We are still in the winter.
Do you wonder why the snowflakes have that shape?
It all starts with the crystal structure of the ice.
In this project, build a deformed hexagon prism.
(1) The top view is a perfect regular hexagon.
(2) The side view of each of the faces is
a rhombus with each edges equal to 2.76 Angstroms.
The angles of rhombus are 109^o (and 81^o)
like in the regular tetrahedron.
(3) Make it scale as 1 cm =1 Angstrom.
(4) Discuss the possible locations of oxygen and hydrogen.
You can add some artificial faces and edges so the model is more stable.
Here is some more information about ice.
Each oxygen atom has two hydrogen atoms attached to it at distances
0.95Angstrom,
thereby forming a water molecule.
Each water molecule is oriented so that its two hydrogen atoms are directed
approximately
towards two of the four oxygen which surround it as a regular tetrahedron.
There is one and only one hydrogen in between each of the pairs of neighboring oxygen atoms.
The first layer of crystal lattice is as the model.
Then next layer is the mirror image of that.
I found the following sites are useful.
A dictionary of crystal lattices
http://cst-www.nrl.navy.mil/lattice/index.html
http://www.recipnet.indiana.edu/common/Simple_stuff/water/water.htm
http://www.recipnet.indiana.edu/common/Simple_stuff/simpleindex.htm
http://kristall.uni-mki.gwdg.de/homep1.htm
http://www.nyu.edu/pages/mathmol/textbook/info_water.html
http://cwis.nyu.edu/pages/mathmol/library/math/index.html
http://cwis.nyu.edu/pages/mathmol/library/water/ice.wrl
where you can use the mouse to rotation the ice crystal.
Snowflakes at
http://www.its.caltech.edu/~atomic/snowcrystals/
Here is the dimension according to the book of B. Mitchel: Ice Mechanics, page 5-6.
Let r be the distance between bonded molecules then r=2.760A.
Each oxygen atom has two hydrogen atoms
attached to it at distances of 0.95A.