EXAM 1: CRYSTALLOGRAPHY

Geology 360, Fall 1993

Please answer all questions: MAKE SURE YOUR FINAL ANSWER IS CLEAR !!!

(1)

(a) (9 points) Sketch a face centered orthorhombic unit cell. Make sure you mark onto your diagram the coordinate axes (indicating their relative lengths) and a, b, g, and indicate which angles, if any, are = 90 degrees.

(b) (2 points) How many lattice points are there in your unit cell ?

(c) (6 points) If there is an atom at each lattice point, what is the plane group symmetry of the (001) face ? Answer this question by drawing a sketch of the (001) face and marking on all the symmetry elements present. The name of the plane group is not necessary.

(2)

(i) (5 points) On the following diagram, illustrate the operation of an inversion center on the comma.

Figure 1

(3)

The following illustrates the structure of a mineral when the mineral is viewed down its c-axis:

(i) (7 points) Mark onto the diagram the two dimensional unit cell and the symmetry elements present. USE the correct symbols to indicate the types of symmetry elements !

(ii) (2 points) Is the unit cell primitive ? Yes .... or No...... ?

(4)

Examine the block labelled "A".

(i) (8 points) Draw a stereographic projection of the symmetry elements present in this block:

Figure 2

(ii) (2 points) Name one cation that may occupy a site in a crystal structure with this symmetry................ and one anion that would surround that cation producing this coordination environment: .....................

(5)

(8 points) Using Pauling's second rule, determine the charge on an anion in the following crystal:

Figure 3

Note: all cations (larger dark-stippled balls) are bonded (bonds indicated by sticks) only to anions (open circles) and anions to cations; the charge on the cations is 4.

Charge on anion is .......... (specify + or - !!)

(ii) (3 points) I have a crystal that contains an ion sitting at a site in the structure that I know has no center of symmetry. Of the following coordination environments for his ion, which is the most likely:

(a) tetrahedral; (b) octahedral; (c) cubic; (d) dodecahedral

(6)

Complete the following table (2 points / entry):

Coordinate axes or symmetry present--------------------------------Crystal system

a = b = c, and alpha = beta = gamma = 90 degrees--------------------------------

a, b, and c are unequal, beta >90---------------------------------------------------

One 4-fold or one bar 4 rotoinversion axis----------------------------------------

a = b; gamma = 120; beta=alpha = 90---------------------------------------------

Four 3-fold rotoinversion axes-----------------------------------------------------

a, b, and c are unequal; alpha, beta, gamma do not equal 90 or 120-------------

(7)

(8 points) Use the symmetry elements depicted in the following stereonet to determine the multiplicity of the point group (i.e., the multiplicity of the general position) : SHOW YOUR WORKING !!!

Figure 4

Multiplicity = .......................

(8)

(10 points) All axes of a crystal are 8mm in length and a=b=g = 90 degrees. Tic marks on the axes are 8mm apart in the diagram below. Provide the Miller Indices of the planes (A) and (B). Note the stippled plane (A) has intercepts on axes marked by open circles and the unstippled plane (B) has axial intercepts marked by dark spots. SHOW YOUR WORKING !!!

Figure 5

(9)

Provide short answers to the following (2 points each):

(i) What is the difference between a point group and a space group ?

(ii) Explain how Pauling's first rule instructs us to predict the coordination number of a cation:

(iii) A silicon ion 4-coordinatedby oxygen is expected to share a maximum of one ? two ? three ? or four ? of its oxygens with a single adjacent 4-coordinated Si ?

(iv) A glide is derived by combination of what symmetry operations ?

(10)

On the coordinate axes below, mark (and label) the following directions (2 pts each):

(i) [100]

(ii) [110]

(iii)[312]

(iv) [122]

USE the single unit cell marked on the diagram to define the lengths of the a,b, and c axes:

Figure 6

(ii) (2 points) Mark onto the diagram above (or an enlargement of it) an atom with the fractional coordinates (1/2,1/2,0).