CENG151 Introduction to Materials Science and Selection

CENG151 Introduction to Materials Science and Selection Solutions to Quiz #1 28th September, 2007

Special Notes to Students… You should read the Examination Answer Book Instructions carefully! • Write your answer on the RIGHT-HAND page. Use the left-hand page only for rough work. Any work that appears on the left-hand page will NOT be marked. • Begin EACH question on a NEW page. Write down the question number at the top of each page. Since this is your first quiz, left-hand pages will still be marked this time. But please remember this! This is also valid for other course examinations in your other subjects!

Problem 1 (20 points) • Taking the atoms as hard spheres, please answer the following questions: • How many close-packed patterns can you have for one dimensional packing? • How many close-packed patterns can you have for two dimensional packing? • How many close-packed patterns can you have for three dimensional packing?

Problem 1 Solution • One pattern only • One pattern only • Two types of pattern: FCC & HCP. HCP FCC

Problem 2 (30 points) You are given some glue and plenty of ping-pong balls. You can make whatever crystal structure you want. A long needle will be used to pierce into the crystal model made by you. Please design three types of the cubic crystal structures, so that, when you pierce the needle into the model, you can choose a direction to let the needle pass maximum number of ball centers for a given needle length.

[111] Problem 2 Solution • BCC in [111] direction • FCC in [110] direction • SC in [100] direction [110] [100]

Problem 3 (20 points) An x-ray diffraction spectrum is show below. The 2 values for (111), (220), and (400) planes 39˚, 65˚, 97˚, respectively. The wave-length of the x-ray being used is, =1.54Å. Now if some one proposes to use a cheap and less harmful laser to do the same diffraction study, know the wave-length of the laser is 5000Å. Please use Bragg’s equation, =2dsin, to argue that the spectrum of such laser diffraction is not possible to be presented.

Problem 3 Solution First consider the stronger laser. The diffraction spectrum shows angle at 2, need to times ½ to use . ↑ These are the d-spacings of the different planes

Problem 3 Solution (cont.) The d-spacings should be calculated to be the same if the weaker laser works: Therefore, Bragg’s equation does not hold for such large numbers!

Problem 4 (10 points) • Three materials have the following three packing crystallography: • a: simple cubic • b: body-centered cubic (BCC) • c: face-centered cubic (FCC) • For the order of the actual densities of the three materials (da, db, dc), choose one correct answer from the following and give a brief justification. • da < db < dc ii) da > db > dc • iii) db < da < dc iv) da < dc < db • v) All are possible

Problem 4 Solution The answer is (v), all are possible! This is because the actual density is not related to the packing pattern only, it is mainly related to the nature of the atoms. For example, both Al and Au are FCC packing but the densities of the two are very much different: dAl = 2.7 g/cm3 dAu = 13.6 g/cm3

Problem 5 (20 points) Look back at human history, please give a chronicle order of the material development and name a key material for each period.

Problem 5 Solution • Stone Age (stone, bones) • Bronze Age (Cu) • Iron Age (Fe) • Electronic Age (Si)

Bonus Question (10 points) For Problem 2, how could you find directions in which you will let the needle pass less and less ball centers? Is it possible that you can find a direction in which the needle passes through the minimum number of ball centers?

Bonus Question Solution If one goes for the directions of larger miller indices [h,k,l] then less ball centers will be passed. Perhaps the minimum number of ball center for cubic crystals is just zero for h+k+l= (infinite).

End of Quiz #1 Thank You!

CENG151 Introduction to Materials Science and Selection