CHEM 681 Homework Assignment #1
i) each
problem needs to be on a separate sheet of paper (for grading purposes)
(1) - Determine the Hermann-Maugin point group
for the following:
i) NO3- v) cyclohexane (chair conformation)
ii) SF4 vi) SF6
iii) 1-chloronaphthalene vii) methane
iv) C3H4
alllene viii) ferrocene (eclipsed conformation)
a) which of the above are polar?
b) which of the above are centrosymmetric?
c)
what is the crystal system of each point group?
(2) - Use stereograms and matrix mathematics to
show the resultant symmetry operation when
the following symmetry operations are combined.
a) 2-fold
rotation along a-axis combined with
an inversion center.
b) 2-fold
rotation along c-axis combined with a
2-fold rotation along b-axis.
c) 4-fold rotation along c-axis combined with a 2-fold rotation
along b-axis.
3) Perform the following matrix calculations.
a) A chlorine atom is at fraction
coordinates (0.2, 0.7, 0.3). What is the
equivalent atom location upon multiplication
with the augmented matrix:
b) What is the determinant of the
following 3x3 matrix?
c) Space group P212121
has the following equivalent positions.
Determine the augmented matrix associated with
each equivalent position.
4) On the
"black and white dog" M.C. Escher print included answer the
following:
a) Draw two different unit cells.
b) determine all symmetry elements present
inside your unit cells.
5) Baddeleyite
(ZrO2) crystallizes in space group P21/c with the
following unit cell parameters:
a = 5.1454 Å, b = 5.2075 Å, c = 5.3107
Å, β = 99.140
the
atoms crystallized with the following fraction coordinates:
Zr 0.2758, 0.0404, 0.2089
O(1) 0.069, 0.342, 0.345
O(2) 0.451, 0.758, 0.479
Answer
the following questions (the page from the International Tables is included)
a) For each atom determine the distance
down each axis the atom resides in angstroms.
b) How many zirconium and oxygen atoms are
in the unit cell? What are the fractional coordinates of each atom?
6) Derive
the non-standard space group P21/a.
Show the derivation step by step.
a) show all symmetry elements.
b) provide the fractional coordinates for
all equipoints.
7) A
compound crystallized in space group P63/mmc (No 194) with atoms at
the following fractional coordinates:
Cs(1) 1/3 2/3 0.750
Cs(2) 1/3 2/3 0.432
Fe 0 0 0.151
F(1) 0.131 0.262 0.250
F(2) 0.149 0.298 0.549
a) What is the empirical formula of the
compound?
8) Find two
published manuscripts that include the space group of the compound. Describe
the symmetry down each axis. What are
the point group associated with the space
group? What is the point group
associated with the compound? Include a photocopy of the abstract page
(with author information).
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