solstatess06exer
Exercises(I) for Solid State Chemistry (WP I/II/IV), SS 2006
1. The Coulomb part of lattice enthalpy (VAB) accounts for the bulk of the lattice enthalpy of an ionic compound. Neglect the Born repulsion and estimate the order of increasing lattice enthalpy for the following compounds assuming them to crystallize in the rocksalt structure with appropriate charges for cations and anions: BeS, AlN, LiF
2. Calculate the lattice enthalpy for KCl (Born exponent n = 7) crystallizing in the rocksalt structure. Calculate a reasonable r value from ionic radii given in standard text books. Estimate the influence of the Born repulsion with respect to the Madelung part of lattice enthalpy.
3. Describe in keywords some important aspects of the interplay between lattice enthalpy and solubility of an ionic solid in water based on informations given in Shriver-Atkins.
4. Calculate the electron affinity for Cl based on the Born-Haber cycle for LiCl: Assume the following values (all values in kJ mol-1)
Enthalpy of formation for LiCl: - 408.7
sublimation: 138.9
½ atomization 121.3
ionization 520.1
Lattice enthalpy - 837.6
5. Calculate the enthalpy of formation for the hypothetical CaCl from the Born-Haber cycle. Assume the same lattice enthalpy as for NaCl and take reasonable values for the ionisation enthalpy of Ca etc from standard textbooks.
6. Explain in a simple band model why Sr and Rb are metallic conductors. Explain the term "Fermi-Energy" and the principal difference between the temperature dependence of the electrical receptivity for a semiconductor and a metal.
7. The DOS is a "fingerprint" for several physical and chemical properties of a solid material. Sketch the DOS of a semimetal and a semiconductor for T > 0K (examples). Explain the term DOS and illustrate bonding and antibonding regions in an electronic band.
8. What types of conductivity are found in solid materials? Which are the charge carriers? How can the conductivity of a given material can be calculated from its basic characteristics like density of charge carriers and others? Give a rough scale for the order of magnitude of the specific conductivity for some typical materials.
9. Explain the physical law that describes the temperature dependence of the conductivity. How can it be plotted most conveniently for evaluation of the activation energy? Explain the relation between activation energy and the movement of the charge carriers.
10. Name at least two relevant ionic conductors. How can one understand the high conductivity of -AgI from its crystal structure ? Explain the term YSZ and how ZrO2 can be manipulated chemically in order to make it an ionic conductor: What type of ionic conductor is YSZ ?
11. Which names are important in connection with the history of electon microscopy?
12. Which general interactions occur if a high energy electron beam interacts with matter?
13. Describe the principle shape of the interaction volume of an electron beam in matter. Which factors determine the interaction depth. Which are the information depths of the different kind of electrons (Auger-, backscattered-, secondary) and the X-ray radiation? Which are the main differences between an Energy Dispersive X-ray detector (EDX) and a Wave Length Dispersive X-ray detector (WDX)?
14. Which are the main differences between a secondary electron image and a backscattered electron image? Explain the term "X-ray mapping".
15. Which resolution is possible with scanning electron microscopes, which with transmission electron microscopes?
16. How does the image formation takes place in a scanning electron microscope?
17. Which factors are important for an exact quantitative analysis with a WDX system? Which corrections are necessary?
18. Concept of unit cell
a) Sketch the primitive unit cell of the following 2D structures
b) Sketch one centered unit cell of the structure depicted in a)
c) Explain the term crystal system
d) Numerate the characteristic symmetry elements of the crystal systems, specify the orientation of the characteristic symmetry elemnts
19. Indexation of directions and planes
a) Sketch following planes and directions in a cubic unit cell: a1) (11-1), a2) [111], a3) (211), a4) [211], a5) (-110), a6) [110]. Specify the position of the origin and the unit cell vectors in any case
b) What is the correlation of a hkl plane in reciprocal space?
20. Atomic coordinates, counting of atoms
a) The atoms (A, B and C) of a cubic structure are located on : 01/20 (A), 1/21/20 (B) and 000 (C). Sketch the unit cell along [001]
b) Determine the composition of a crystal with this structure
c) Specify the ration of the numbers in the Wyckoff notations of the sites occupied by A, B and C
d) Describe the environment of C by (coordination number, geometry of C-A and C-B arrangement)
21. Composition of crystals a) Determine the composition of a crystal using the following data
Atom
Wyck.
Occ.
x
Y
z
Cu1
2a
0.4
0
0
0
In1
4d
0.5
0
½
1/4
In2
2b
0.2
0
0
1/2
Se1
8i
0.5
1/4
¼
1/8
b) Determine the composition of a structure containing the following structural building units (SiO4-tetrahedra)
c) Determine the composition of a crystal with the following unit cell (sphaerite type structure)
22. Crystal classes, space groups a) Determine the crystal classes of the following objects (basis: cuboctaehdron)
b) Explain the term “Laue group”. What is the Laue group of the monoclinic system?
c) Determine the crystal classes, Laue groups and crystal systems of the following space groups: c1) Pa-3, c2) Fm-3m, c3) Pmna, c4) Fddd, c5) Pna21, c6) I4/mnm
d) Specify the centrosymmetric spacegroups of c)
23. Structure factor calculation, extinctions a) Explain the experimental significance of the structure factor, specify the formula of the structure factor.
b) Explain X-ray diffraction by a vectorial representation in the complex plane
c) Why is the structure factor of a centrosymmetric structure a real number?
d) Calculate the structure factor for a NaCl crystal, derive the extinction rules
e) Explain the differences in the intensity in the diffraction patterns of NaCl and KCl quantitatively
KCL
NaCl
24. Diffraction patterns of disordered crystals a) Explain the term statistical disorder
b) What kind of structured diffuse scattering occurs for 1D and 2D structures, respectively?
25. Synthesis: shake and bake a) Explain the conditions for reactive sintering
b) How would you prepare the samples TlInS2 and TlIn3S5?
c) Explain the terms nucleation, topotaxy, epitaxy
d) Give examples for the use of CVT in solid state synthesis
26. Synthesis by soft chemistry
a) Describe the synthesis of Zeolites and MOF
b) Explain the term reticular synthesis
27. Ceramics a) Specify the general formula of Zeolites. Explain the fundamental structural properties of Zeolites
b) Give two examples for industrial applications of Zeolites
c) Describe different kinds of selectivity that occur for Zeolites in catalytic reactions
d) Explain the term “Zeotype”, give one example
e) Explain the structural relation between Perovskite and YBa2Cu3O7, describe the properties of YBa2Cu3O7.
f) Describe the properties of ZrO2
28. Alloys and intermetallics a) Describe the structure of solid solutions. Numerate the prerequisites for the formation of a solid solution. Give one example. Sketch a phase diagram for a solid solution.
b) Sketch the unit cell of CuZn and Cu3Au
c) Describe the structure of Laves phases