Answer to Question #287391 in Material Science Engineering for jay

Question

Ouestion 5

A.                Describe THREE (3) applications where tensile strength is primarily factor in material selection. What material would you select for what application and state why?

B.                 Copper has the atomic radius of Oa 128 nm, an FCC crystal structure and an atomic weight of 63.5 g/mol. Calculate the following:

i.       Cell edge length ii.      Vc - Unit cell volume iii.   Vs — Sphere volume iv.          Density,

v.       APF - Atomic Pack Factor via    Write the Avagador's Number

c.         Briefly explain what the factors that caused imperfection in solids are.

Answer 1

A. It is imperative to know the tensile strength of a particular metal or any material to ensure it is the right choice for an application. This ensures an incident-free service life.

The results of choosing materials with lower tensile strength than what the application demands can be disastrous.

Engineers turn to yield strength in the design phase to make sure the stress never reaches any higher than that. Otherwise, the structure suffers permanent deformations. But ultimate tensile strength tells us the value that is necessary for complete failure and breaking.

Thus, a roof construction that comes under more stress because of a higher than normal snow load may bend the structure. At the same time, surpassing the tensile strength value means that the roof may fall in.

The tensile strength of materials varies significantly. Mechanical engineers use mostly metals because they offer a good return for value and other great properties besides relatively high tensile strength. But it is evident that the range within different types of metals alone is huge.

B.

From the right figure above we see that there is 1/8 of an atom at each of 8 corners of the unit cell and 1/2 atom at each of 6 faces.

This gives (8 x 1/8) + (6 x 1/2) = 4 atoms per crystal cell.

We also see that the atoms are packed so that for a closely packed structure, the atoms touch each other along the body diagonal of the lattice. As such we have

a/r = 2√2; a is length of side of cube and r as the radius of atom and atomic packing factor, which is the fraction of the volume of the cell actually occupied by the hard spheres = 0.74

Hence volume of unit cell =

4 x 4/3$\pi$ (0.128 x 10^-9)³ / 0.74 m³ = 4.75 x 10^-29 m³

Mass of copper atom is found from Molar mass and Avogadro’s number =

63.5 g/mol / (6.02 x 10²³) x 10^-3 = 1.055 x 10^-25 kg

Calculate Density =

$\rho$ = 4 x Mass of copper atom / Volume of unit cell = 8890.5 kg/m³

C. Any irregularity in the pattern of crystal arrangement in a solid lattice is called imperfection in solids. The occurrence of defects takes place when crystallization (the process of formation of crystals) occurs at a very fast or at an intermediate rate. This is because particles don’t get enough time to arrange themselves in a regular pattern.

Basically, defects fall out in two forms: Point Defect and Line Defect

Point Defect occurs when an atom is missing or is irregularly arranged in a crystal lattice. In other words, the deviations and irregularities observed around an atom or a point are known as a Point Defect.

Point Defects are classified into two defects, namely:

• Stoichiometric Defects
• Nonstoichiometric Defects

The defects due to which the stoichiometry of solids remains undisturbed are called stoichiometric Defects. After stoichiometric defect, the ratio of cation and anions remain same in a solid. They are also known as intrinsic or thermodynamic defects.

Stoichiometric Defects are further classified into two defects:

• Vacancy Defect
• Interstitial Defect
• Schottky Defect
• Frenkel Defect

Formation of vacancy defects take place due to vacant lattice sites. This defect generally occurs when we heat a solid. Vacancy defect also decreases the density of solid.

When some extra constituent particles (atoms, molecules or ions) are acquainted in the interstitial sites, the solid lattice is said to have an interstitial defect. Interstitial Defects are responsible for increasing density of the substance.

Both vacancy and interstitial defects are depicted by non-ionic solids whereas in ionic solids these defects occur in form of Schottky and Frenkel Defect. Remember electrical neutrality is of utmost importance for the existence of ionic solids.

If in an ionic lattice equal number of cations and anions are missing from the lattice site, the lattice is said to have Schottky defect. In Schottky Defect the electrical neutrality is maintained and it generally takes place in ionic solids. The compounds in which the size of cation and anion are nearly equal tend to show this type of defect. Some common examples of compounds depicting Schottky Defect are:

• Sodium Chloride (NaCl)
• Potassium Chloride (KCl)
• Cesium Chloride (CsCl)
• Silver Bromide (AgBr)

Schottky Defect also decreases the density of the crystal lattice.

Just like Schottky defect Frenkel defect is also observed in ionic solids. When a smaller ion (generally cation) is moved from its normal position to a new interstitial site, Frenkel Defect occurs. This dislocation of ion creates vacancy defect at its original site and interstitial defect at its new position. The density of the crystal lattice remains same in Frenkel Defect. Ionic solids in which there are vast size differences between cation and ion tend to depict Frenkel Defect. Some common examples of compounds depicting Frenkel Defect are as follows:

• Zinc Sulphide (ZnS)
• Silver Chloride (AgCl)
• Silver Bromide (AgBr)
• Silver Iodide (AgI)

The defect in which the ratio of cation and anion in an ionic lattice is variable is known as a non-stoichiometric defect. They are of two types, namely:

• Metal Excess Defect
• Metal Deficiency Defect

Metal Excess Defect occurs in two ways:

• Due to anionic vacancies
• Due to presence of extra cations at interstitial sites

Metal Excess Defect can be seen in alkali halides like NaCl and KCl. In this type of defect, the anionic vacancies are missing and are filled by an electron to ensure electrical neutrality. For example, when a NaCl crystal is heated in presence of sodium vapor, the sodium atoms are deposited on the surface of the metal. The Cl^- ions diffuse out from the crystal surface and combines with Na atom to give NaCl. To make this happen sodium loses electrons to become Na⁺ and the released electrons occupy the anionic vacancies. As a result, crystal gets excess sodium.

The anionic sites or vacancies which are filled by unpaired electrons are called F-centers and are responsible for imparting a yellow color to the flame of NaCl. Similarly in KCl excess of potassium is responsible for making KCl crystal flame violet.

In this type of defect, extra positive ions and electrons occupy interstitial sites and maintain electrical neutrality. In other words, this defect is losing non-metal atoms leaving their electrons behind and excess metal occupies interstitial positions. For example, in white zinc oxide on heating, it leaves oxygen and becomes yellow.

ZnO → Zn⁺² + O₂ + 2e^-

Now due to excess of zinc in the crystal, the formula of ZnO becomes Zn_1+xO.

This defect occurs in metals containing less number of cations than anions. It is mostly seen in compounds depicting variable oxidation states. Due to unequal number of cations and anions the metals obtained are non-stoichiometric. Some common examples falling under this category of defect are Fe_0.95O, Fe_0.93O etc.