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Tutorial on Chapter 1 gives the typical numerical problems in Crystal Growth-Bulk and Epitaxial.

Tutorial on Chapter 1-Crystal and Crystal Growth.

  1. Give the percentage packing of Face-Centered-Cube ? [Ans.74%]

Method:

FCC crystal has 8 atoms at the 8 corners of the cube and 6 atoms on the 6 faces (4 on side faces+2 on the upper and lower faces].

Therefore N = the coordination Number = the number of atoms per unit cell = (8×1/8+6×1/2)= 4 atoms per unit cell.

The atoms are solid spheres and are closely packed so that the atom at the center of the face are touching the 4 atoms on the four corners of the face as shown in the Figure I.

Inspecting the Figure we find that:

4R=diagonal of the face=a√2.

Therefore R/a = √2/4=1/(2√2)

Therefore packing percentage in FCC crystals is 74%.

  1. Give the percentage packing of Body-Centered-Cube ? [Ans.68%]

Method:

BCC crystal has 8 atoms at the 8 corners of the cube and 1 atom at the center of the Cube. Therefore N = the coordination Number = the number of atoms per unit cell = (8×1/8+1)= 2 atoms per unit cell.

The atoms are solid spheres and are closely packed so that the atom at the center of the Cube is touching the 2 atoms on the two corners of the cross diagonal of the cube as shown in the Figure 2.

Inspecting the Figure we find that:

4R= cross diagonal of the Cube =a√3.

Therefore R/a = √3/4;

Therefore packing percentage in FCC crystals is 68%.

  1. Determine the conducting electrons density in FCC Cu where the lattice parameter is 3.6 Angstrom ? [Ans. 8.5734×10 28 /m 3 ]

Copper is univalent crystal hence each atom contributes one electron. Therefore atomic density gives the conducting electron density.

Coordination Number of Cu = N = 4 atoms per unit cell.

Unit cell volume is a 3 .

Therefore atomic density = conducting electron density = 4 / (a 3 ) = 8.5734×10 28 /m 3 = 8.5734×10 22 /cc.

  1. Si, Ge and GaAs are all diamond crystal structure. Diamond structure is two interpenetrating FCC crystals with one sub-lattice displaced w.r.t. the other along the cross diagonal of the cube by a quarter of the cross diagonal length. In case of Ga As it is ZincBlende cubic structure which has one sub-lattice of Ga and the other sub-lattice of As.

Find the weight density of Si,Ge and GaAs. Given Avogadro Number = N Avo =6.02×10 23 atoms/gm-mole, Si, Ge and GaAs have atomic weight of 28.1, 72.6 and 144.63(mean=72.315 respectively and the lattice parameters are 5.43A°, 5.646A° and 5.6533A° respectively.

[Ans. 2.33gm/cc, 5.37gm/cc and 5.32gm/cc respectively]

Method:

Coordination Number =N= 8 corner atoms + 6 face center atoms + 4 body center atoms= (1/8×8 + 1/2×6+ 4)= 8 atoms per unit cell.

Therefore Number density = N * = 8/a 3 = 4.9967×10 22 atoms/cc, 4.445 ×10 22 atoms/cc, 4.4277 ×10 22 atoms/cc,of Si, Ge and GaAs respectively.

Weight of one atom= (AW gm/mole)÷ (N Avo atoms/mole)= 4.66×10 -23 gm/atom. 1.157×10 -22 gm/atom. 1.244×10 -22 gm/atom of Si, Ge, GaAs respectively.

Therefore weight density = Wt of one atom× N * = Weight Density = ρ

Therefore density of Si=4.9967×10 22 atoms/cc×4.6677×10 -23 gm/atom=2.33gm/cc.

Questions & Answers

the definition for anatomy and physiology
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What is a cell
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what is cell
Mohammed
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Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
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Mercy Reply
studies of microbes
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How bacteria create energy to survive?
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Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
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the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
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Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
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en français
Adama
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Source:  OpenStax, Electrical and electronic materials science. OpenStax CNX. May 01, 2014 Download for free at http://cnx.org/content/col11615/1.14
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