Download Homework 1 - Devin Gatherwright IET 307 Portfolio

Devin Gatherwright
9/8/2012
Materials Science Homework #1
1. What is metallic bonding? How is it formed? What are its characteristics?
Answer: According to our Materials Science textbook, metallic bonding can be defined as a “primary
interatomic bond that involves the non-directional sharing of valence electrons that are shared mutually
between all atoms in the metallic solid;” and is exclusively found in metals and their alloys. Now, in
metallic bonding, metallic materials contain 1, 2, or 3 valence electrons at the most. These valence
electrons are not bound to any of the atoms in the metallic material, which means they are freely
floating through the metallic material. The non-valence electrons that are remaining create an ion core
with the atomic nuclei. These ion cores possess a net positive charge that is equivalent to the total
valence electron charge per atom. Now the free electrons protect the positive charged ion cores from
the positive charged electrostatic forces, which are repulsive to the ion cores due to their identical
charge (like charges repel). Also, these free electrons act as a type of adhesive by holding all the ion
cores together, thus creating the metallic bond. Some characteristics of metallic bonds are as follows:
metallic bonds are great conductors of both heat and electricity, which is due to all the free valence
electrons that are flowing throughout the material as aforementioned above. Also, another
characteristic of metallic bonds is the failure of metals and alloys in regards to the ductility of the
material at certain temperatures. This means that they will fracture if they are bent.
2. What is ionic bonding? How is it formed? What are its characteristics?
Answer: According to our Materials Science textbook, ionic bonding can be defined as a “coulombic
interatomic bond that occurs between two adjacent ions with opposing charges (both negative and
positive,” and are found in compounds that contain both metallic and nonmetallic elements. Now, the
atoms of the metallic element easily give up their free valence electrons to the atoms of the nonmetallic
element. In the process, all the atoms involved acquire secure configurations and also an electrical
charge (either positive or negative), thus becoming ions. Ionic bonding is known as being nondirectional, meaning the enormity of the bond is the same all directions across the ion. This means that
in order for an ion to be stable in nature, all the positive ions in the material must be in close proximity
to the negative ions in the material, thus creating the ionic bond. Some characteristics of ionic bonds are
as follows: ionic bonds are very hard and brittle, as well as being poor conductors of electricity and heat,
but good insulators of both.
3. What is covalent bonding? How is it formed? What are its characteristics?
Answer: According to our Materials Science textbook, covalent bonding can be defined as “a primary
interatomic bond that is created by the sharing of electrons between atoms that are close in proximity
to each other.” In order to create a covalent bond, two neighboring atoms must contribute at least one
electron each to the bond, with the shared electrons now belonging to both the neighboring atoms.
Covalent bonds are directional in nature, meaning that the bond exists between specific atoms and can
only exist in the direction between one atom and the neighboring atom that takes part in the sharing of
the electron. Some characteristics of covalent bonding are as follows: covalent bonding is that they can
either be a very strong bond (such as a diamond,) or a very weak bond (such as barium.) Also, covalent
bonds, like ionic bonds, are good insulators of heat and electricity.
4. What is Van der Waals bonding? How is it formed? What are its characteristics?
Answer: According to the Materials Science textbook, Van der Waals or Secondary bonding is defined as
a “secondary interatomic bond between neighboring molecular dipoles that may be either permanent
or induced.” Van der Waals bonds are relatively weak in nature, and occur between virtually all atoms.
However, its presence is often obscured by the presence of any of the three aforementioned primary
interatomic bonds. Van der Waals bonds are the result of attractive forces between dipoles, which are
the result of some separation of the positive and negative portions of an atom or molecule. There are
three types of Van der Waals bonding: Fluctuating Induced Dipole Bonds, Polar Molecule-Induced Dipole
Bonds, and Permanent Dipole Bonds. Materials with fluctuating induced dipole bonds characteristically
have low melting and boiling temperatures and are the weakest of the bonds. These bonds also cause
the solidification and liquid faction of inert gases. In contrast, melting and boiling temperatures for
permanent dipole bonds are incredibly high due to their low molecular weights.
5. What are unit cell, lattice constant and the number of atoms per unit cell? What is the number of
atoms per unit cell for BCC, FCC and HCP?
Answer: Unit cells can be defined as small repeat entities that describe crystal structures. Unit cells are
usually parallelepipeds or prisms that have three sets of parallel faces, with one face drawn within the
collective of spheres. So, in short, according to our textbook, a unit cell is the basic structural/building
block of a crystal structure and describes the crystal structure by virtue of its geometry and atom
positions within. The lattice constant is used to describe the three-dimensional array of points that
correspond with the atom positions in a crystal structure. The Face Centered Cubic crystal structure has
4 atoms per unit cell; the Body Centered Cubic crystal structure has 2 atoms per unit cell; lastly, the
Hexagonal Close-Packed crystal structure has 6 atoms per unit cell.
6. What is the atomic packing factor? What are the atomic packing factors of BCC, FCC and HCP? Dose
the volume increase or decrease when FCC iron changes to BCC iron? Why?
Answer: According to our materials science textbook, the atomic packing can be defined as “the fraction
of the volume of a unit cell that is occupied by hard sphere atoms or ions.” The atomic packing factor of
FCC is 0.74; the atomic packing factor of HCP is 0.74 as well. The atomic packing factor of BCC is 0.68.
No, it will neither increase nor decrease due to the fact that both HCP and FCC have the same atomic
packing factor.
7. What is the meaning of families of crystal directions and planes?
Answer: The families of crystal directions and crystal planes are groups of equivalent directions that are
bounded by angle brackets and for general convenience. Also, the directions in cubic crystal structures
that have the same indices, as well as having the no regard to neither sign or order are considered to be
equivalent and therefore are also considered to be a “family.”
8. What is the closest packed crystalline direction for BCC and FCC? What is the closest packed
crystalline plane for BCC and FCC?
Answer: The closest packed crystalline direction for BCC and FCC crystal structures are commonly either
[100], [110], and [111]. The closest packed crystalline plane for BCC and FCC is (111).
9. What are the similarities and differences between FCC and HCP crystal structures?
Answer: The key similarities between HCP and FCC crystal structures are that they both have the same
coordination number, 12, as well as having the same atomic packing factor of 0.74. Also, FCC and HCP
crystal structures can be created by stacking close-packed planes on top of each other. Now, in contrast
to one another, HCP’s stacking sequence is ABABAB while FCC’s stacking sequence is ABCABCABC.
Another contrast between FCC and HCP crystal structures is that an FCC crystal structure has unit cells
with a cubic symmetry, while an HCP crystal structure has unit cells with a hexagonal symmetry.
10. What is the Miller index of the crystal plane in the following figure? Explain the steps used.
Answer: First, I observed in the plane in question passed through the origin. It didn’t. Next I observed
the edges of the shape and their intersection of the 3 axes. One corner touched the z axis at three 2C,
one corner touched the x axis at 1A, and the other corner touched the y axis 3B. I then take the
reciprocals of these three numbers, making them 1/1, 1/3, and 1/2. Then I multiply each reciprocal by a
common to achieve the set of smallest integers, now making the numbers 6, 2, and 3. No reduction is
necessary, so I enclose the numbers in parentheses, thus giving me an answer of (623).
11. If the atomic radius of aluminum is 0.143 nm, calculate the volume of its unit cell in cubic meters.
𝑉𝑐 = 𝑎3 = (2𝑅√2)3 = 16𝑅3 √2
= 16(0.143)3 √2
= 16(.002924207)√2
= 16(. 002924207)1.1414213562
= .046787312 𝑋 1.414213562
= 0.661672512 𝑛𝑚3
12. Calculate the radius of an Iridium atom, given that Iridium has a FCC crystal structure, a density of
22.4 g/cm3, and an atomic weight of 192.2 g/mol.
Answer:
𝑔
𝑐𝑚3 = 0.1165 𝑚𝑜𝑙 𝑝𝑒𝑟 𝑐𝑚3 × 6.022 × 1023 = 7.018 × 1022 𝑎𝑡𝑜𝑚𝑠 𝑝𝑒𝑟 𝑐𝑚3
𝑔
192.2
𝑚𝑜𝑙
22.4
𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 =
1
1.755 ×1022
7.108 ×1022
4
= 1.755 × 1022 𝑐𝑚3
= 5.699 × 10−23 𝑐𝑚3 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙
3
𝑒𝑑𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ √5.699 × 10−23 𝑐𝑚3 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 = 3.848 × 10−8 𝑐𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑖𝑑𝑒𝑠.
2
2
√3.848 × 10−8 + 3.848 × 10−8 = 1.4807104 × 10−15 2
1.4807104 ×10−15
4
= 3.701776 × 10−16 𝑐𝑚/𝑎
13. Rhenium has an HCP crystal structure, an atomic radius of 0.137 nm, and a c/a ratio of 1.615.
Compute the volume of the unit cell for Re.
Answer:
3
3(0.137)2
2
𝑉𝑜𝑙 = √
× 1.615 = 0.709 𝑛𝑚/𝑎6
14. Explain why the properties of polycrystalline materials are most often isotropic?
Answer: Polycrystalline materials are often isotropic in nature because according to our materials
science textbook, the crystallographic orientation of the polycrystalline material’s individual grains are
completely random in their alignment. Even though the individual grains in question may be in
anisotropic in their alignment, the polycrystalline specimen composed of these individual grains will
behave isotrophically due to the randomness of the individual grains being independent of the direction
measured.
15. Why are covalently bonded materials generally less dense than ionically or metallically bonded
ones?
Answer: It is because covalent bonds occur between non-metal elements and not metallic elements. If
you look at a periodic table, non-metal elements have lower atomic weights than the metal elements
that take up the majority of the periodic table. Also, ionic and metallic bonds contain metallic elements,
which makes them denser.