Bonjour, j'étudie actuellement à Oslo et j'ai un rapport à rendre. Je planche dessus depuis plusieurs semaines déjà. Mon professeur m'a dit que mes réponses étaient fausses et qu'il ne pouvait pas accepté mon rapport. J'ai besoin d'aide s'il vous plaît.
Merci par avance de votre aide!
Task 1 – Crystal structures, crystallography and chemical bonding
CrAs (chromium arsenide) crystallises with MnP-type structure. MnP-type structure can be described as a deformed NiAs-type structure.
CrAs has unit cell dimensions a = 5.549 Å, b = 3.461 Å, c = 6.208 Å, and is described with the space group Pnma.
Relative atomic positions for CrAs are:
Cr in 4c: (x, ¼, z), with x = 0.007 and z = 0.200
As in 4c: (x, ¼, z), with x = 0.200 and z = 0.577
Information given in “International Table of Crystallography” for space group no. 62 (Pnma) can be found on Fronter or by searching the internet.
a) Describe the space group symbol and its corresponding point group. Also, give the crystal system.
b) Sketch the Bravais lattice for CrAs as a projection on the ac-plane.
c) Name the other types of lattices that exist and give the number of lattice points per unit cell for each lattice. Feel free to make sketches.
d) Draw the crystal planes described with Miller indices (101) and (102) projected on the ac-plane. Draw at least three parallel planes in the figure.
e) Show, with the help of a stereographic projection, the number of general positions generated for the corresponding point group of Pnma. You can use the additional information in the appendix. Also, give the number of equivalent atoms that will be generated in the unit cell when they are described with a general position in the space group Pnma.
f) Calculate the relative atomic coordinates of all the atoms in the unit cell for CrAs, and sketch the crystal structure as a projection on the ac-plane. Note; include atoms inside, and also those right outside the unit cell of your drawing (the last one is done to more easily being able to identify important structural features, coordination, and much more).
g) Look at the sketch in f). For CrAs there are several relatively short Cr-Cr distances. Indicate on your figure (for example with bold lines between the atoms) where these distances are, and then calculate the bonding length for these relatively short Cr-Cr distances (2 + 2). The Cr-As distances are in the size order of 2.5 Å.
h) Evaluate the bond type in CrAs based on the sketch(es) you have made and the following information:
Electron negativity: Cr: 1.66, As: 2.18
Metallic radius Cr: 1.17 Å
Ionic radius Cr3+: 0.76 Å, As3−: 1.4 Å
Covalent radius Cr: 1.20 Å, As: 1.25 Å
Metallic chromium (bcc) has a Cr-Cr distance of 2.5 Å.
i) What types of interstitial positions can you find in the NiAs-type structure?
j) On the basis of what you know about the NiAs-type structure, discuss whether or not the non-stoichiometric composition Cr1.10As can exist.
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