Materials Final
A flat head shield is designed to protect against sudden temperature surges. Its maximum allowable thickness is 10 mm. When heat is applied to one of its surfaces, the other should not start to change significantly in temperature for at least 5 minutes. Find an estimate value of the maximum thermal diffusivity for this requirement.
3.3x10^-7 m^2/s
A steel component is nickel plated to give corrosion protection. To increase the strength of the bond between the steel and the nickel, the component is heated for 4 hours at 1000*C. If the diffusion parameters for nickel in iron are Do=1.9x10^-4 m^2/s and Qd=284 kJ/mol. Find the diffusion coefficient at 1000*C
3.77x10^-16 m^2/s
(Problem 1) The cable of a hoist has a cross section of 80 mm^2. The hoist is used to lift a crate weighing 250 kg. The free length of the cable is 3 m. How much if it is made of of polypropylene, PP (modulus 1.2 GPa)? What is the stress in the cable?
30.7 MPa
The atomic volume of silicon is 2.0x10^-29 m^3 and the free electron density nv at 300 K is 1.5x10^16/m^3. What fraction of silicon atoms have provided a conduction electron?
3x10^-13
Continuing from Q15,16: The diffusivity (or effective diffusion coefficient for heat) in iron at 1000*C is a=9x10^-6 m^2/s. Find out the heat approximate distance of diffusion in time t.
3x10^-6 sqrt(t) m
Continuing from Q55 (Q15). Find out carbon approximate distance of diffusion in time t.
4.41x10^-6 sqrt(t) m
A gold interconnect 1 mm long and with a rectangular cross-section of 10 micro-m x 1 micro-m has a potential difference of 1 mV between its ends. What is the current in the interconnect? The resistivity pe of gold is 2.5 x 10^-8 omega m
4x10^-4 A
The element w the largest saturation magnetisation is holmium, with Ms=3x10^6 A/m. The density p is 8800 kg/m^3 and atomic weight Awt=165 kg/mol. What is the atomic magnetic moment nm in Bohr magnetons of holmium?
nm=10.1 Bohr magnetons
Derive an expression for the "effective modulus" (o1/E1) in this case
o1/E1 = E(1-v)/(1-v-2v^2)
(Problem 2) A cube of linear elastic material is again subjected to a vertical compressive stress o1 in the 1-direction, but is now constrained (E=0) in both the 2 and 3 directions. Find expressions for the induced transverse stress, o2 terms of o1.
o2 = o1v/(1-v)
(Problem 2) Find expressions for the induced transverse stress o3 in terms of o1
o3 = o1v/(1-v) **o2 and o3 are the same
Indicate the correct ranking of the bonds from the most covalent to the most ionic
H-C, Li-H, H-F, Na-Cl, Rb-O
A cylindrical coil with L=30 mm w n=75 turns carries a current i=0.1A. What is the field in the magnet? A silicon-iron core with a relative permeability u-R = 3000 is placed in the core of the coil. What is the magnetization of the silicon-iron? The permeability of free space uo= 4pix10^-7 H/m
H=250 A/m M=7.48x10^5 A/m
Derive the expression for fraction of light
I=Io(I-IR/Io)^2
Why do insulators not conduct electricity, at least when cold?
In insulators the force is insufficient to push electrons across the band gap, so they remain localized on the atom and are unable to move
What sort of bonding you expect in Magnesium Iodide, MgI2
Ionic
The approximate range of modulus of elastomers
10^-4 to 10^-1 GPa
Continuing from Q15-18, Within the same time, how many times larger is the distance that heat diffuses more than carbon?
10^3
Continuing from Q17-17, Roughly how many times faster than carbon, heat diffuses in iron?
10^6
If the overload is caused by inserting half a liter of water at 20*C, by how much could 100 g of this PCM reduce the temperature of the water?
11*C
A potential difference of 4 V is applied across tungsten wire 200 mm long and 0.1 mm in diameter. How much power is dissipated in the wire? The electrical conductivity Ke of tungsten is 1.8 x 10^7 S/m.
11.3 W
How long do you estimate it would take to cool by the same amount in the real component?
135 s
What time would you expect to find is required to cool the center to 50% of the new temperature interval? The thermal diffusivities of the steel and aluminum are 9x10^-6 m^2/s and 7x10^-5 m^2/s, respectively.
17 s
The stiffness S of an atomic bond in a material is 50 N/m and its center-to-center atom spacing is 0.3 nm. What, approximately, is its elastic modulus?
170 GPa
Determine carburizing time necessary to achieve a carbon concentration of 0.40 wt% at a position 4 mm into an iron-carbon alloy that initially contains 0.20 wt% C. The surface concentration is to be maintained at 0.80 wt% C, and the treatment is to be conducted at 1200*C. Use the diffusion data for -Fe in Table 6.2
18 h
(Problem 6) Calculate the weight average degree of polymerization
2,461
Continuing from Q53 (Q13): How far would you expect the nickel to diffuse into the steel in this time?
2.3 microns
A potential difference of 4 V is applied across tungsten wire 200 mm long and 0.1 mm in diameter. What current flows in the wire? The electrical conductivity Ke of tungsten is 1.8 x 10^7 S/m
2.8 A
For Q64 (Q24), calculate erf(z)
2/3
Does sound move faster in titanium or glass?
Glass
Resistivity of brass with 60 atom % copper and 40 atom % of zinc is pe=6.8 micro omega cm. Each copper atom contributes one free electron. Each zinc atom contributes two. The atomic volumes of copper and zinc are almost the same and the electron concentration is nv=8.45x10^28/m^3. What is the electron mobility micro-e in brass?
0.001087 m^2/Vs
The resistivity of pure silver is pe=1.59 micro omega.cm. Each silver atom provides one free electron. The atomic volume of silver is 1.71x10^-29 m^3. What is the electron mobility in silver.
0.0067 m^2/Vs
Estimate the drift velocity of free electrons when a potential difference of 3 V is applied between the ends of a copper wire 100 mm long. The electron mobility in copper is micro-e=0.0032 m^2/V.s
0.096 m/s
The electron mobility u-e is undoped geranium at 300K is 0.36 m^2/Vs and that of holes u-h is 0.19 m^2/Vs. The carrier density nv is 2.3x10^19/m^3. What is the conductivity of geranium at 300K? What is resistivity?
0.25 S/m
The fraction of light transmitted through a 100 mm panel is 0.97. What is absorption coefficient B of PMMA?
0.3046/m
(Problem 1) How much will it extend if it is made of steel (modulus 200 GPa)?
0.46 mm
For Q64 (Q24), calculate z
0.68
For Q64 (Q24), calculate the diffusion coefficient
1.29x10^-10 m^2/s
A new metal alloy has a density of 7,380 kg/m^3. Its specific heat is Cp=271 J/kg/K and it has a melting point of 1,540 K. Its thermal expansion coefficient has not yet been measured. How would you make an approximate estimate of its value? What value would you then report?
1.3x10^-5
The diffusion constant for carbon diffusion in FCC iron is Do=2.3x10^-5 m^2/s and the activation energy Q=148 kJ/mol. Find the diffusion coefficient D for carbon in iron at 1000*C.
1.94x10^-11 m^2/s
A gold interconnect 1 mm long and with a rectangular cross-section of 10 micro-m x 1 micro-m has a potential difference of 1 mV between its ends. How much power is dissipated in it? The resistivity pe of gold is 2.5 x 10^-8 omega m
4x10^-7 Watts
Metal zinc has free electron concentration per unit volume, nv, of 1.3x10^29/m^3 and an electron mobility micro e of 8x10^-4 m ^2/V.s. The charge carried by an electron, e, is 1.6x10^-19 coulomb. What is electrical conductivity of zinc? Resistivity of zinc as 5.9 micro omega cm.
6.01x10^-8 micro omega m
(Problem 6) The following table lists molecular weight data for a PE material. Calculate the number-average molecular weight.
64,000
(Problem 6) Calculate the weight-average molecular weight ***
69,093
The range of modulus of CFRP (carbon-fiber reinforced plastic)
80 to 200
Aluminum has a high carbon footprint - its value is 13.1 kg/kJ. What does this mean?
A carbon footprint of 13.1 kg/kg means that the mining and beneficiation of the ore (Bauxite) and its subsequent electrorefining to make aluminum releases 13.1 kg of CO2 for each kg of aluminum produced (or, more precisely, the global warming equivalent of 13.1 kg of CO2 when taking other gaseous emissions into account)
Mode of loading in bicycle forks
A column
Mode of loading in shoe soles
A column: axial compression & A shaft: twisting or torsion
What is a Bohr magneton? Its atomic volume, omega, is 3.7x10^-29 m^3. What is saturation magnetisation, Ms?
A magnetic element has two unpaired electrons and an exchange interaction that causes them to align such that their magnetic fields are parallel // magnetic moment of a lone unpaired electron in orbit around an atom. Ms=501 A/m
Mode of loading in aircraft fuselage
A shell
Identify which of the five modes of loading (Figure 4.2) is dominant in a fizzy drink container.
A shell (pressure difference across a shell: biaxial tension or compression)
Mode of loading in climbing rope
A tie
Mode of loading in overhead electric cable
A tie: axial tension
A food processing plant uses dilute acetic acid for pickling onions. The acid is piped to and from holding tanks. Use Table B2 of App B to select a suitable material for the pipes and tanks, given that, to have sufficient strength and toughness to tolerate external abuse they must be made of a metal. Stainless steel Nickel alloys Titanium alloys
AoA
Indicate the correct sentence For foams, the constraint has no effect, as no lateral expansion For rubbers, incompressible, but with lateral expansion prevented Rubber, which has the lowest Young's modulus of all solid materials, has a very stiff response when constrained
AoA
"" Carbon diffuses far more rapidly than chromium through iron. (Indicate the incorrect) (about C atoms)
C atoms will not diffuse relatively rapidly.
Suggest dielectric material (insulator) for a capacitor with the highest possible energy density. What material? Use 15.7
Ceramics, PZT, lead lanthanum zirconium titanate
Select material for a magnetostrictive actuator. Coil w length L=30mm with n=75 turns and a max current i=1A
Galfenol
What sort of bonding would you expect in Aluminum phosphide, AlP
Covalent
The gold interconnect of the previous question (length 1 mm and rectangular cross-section of 10 micro-m x 1 micro-m with a potential difference of 1 mV across its length) carries power for 10 seconds. If no heat is lost by conduction, radiation, or convection, how hot will the interconnect get? The resistivity pe of gold is 2.5 x 10^-8 omega m, its specific heat Cp is 130 J/kg.C and its density is 19300 kg/m^3.
DeltaT=159*C
What is a ferrite?
Ferri-magnetic materials. Electrical insulators. Oxides. Magnet but also contain atoms that have large dipole moments
The cases is which most CDs are sold have an irritating way of cracking and breaking. Which design limiting property was neglected? Density, stiffness, fracture toughness, ductility, strength
Fracture toughness
What are the units of specific heat?
J/Kg/K
The metal with the lowest modulus
Lead
Many metallic structures are partly or wholly buried in soil. How is the corrosive potential of a soil estimated? (Indicate the correct)
Measuring both, electrical resistivity, and pH
Why do metals conduct electricity? Indicate the wrong.
Metals are conductors because the charge-carriers are the electrons and holes.
Cobalt has density p of 8900 kg/m^3 and atomic weight Awt of 58.93 kg/kmol. The net magnetic moment of cobalt atom is nm=1.8. What is saturation magnetisation Ms of cobalt?
Ms=1517562.4 A/m
Recommend material for solid-state refrigerator to operator
Need high adiabatic temp change and operating between 2-6 La(Fe-Si)H or Gadolinium
Use the (lamda-a) chart of Figure 12.5 to identify material classes that you might use for the heat shield.
Neoprene
(Problem 4) The speed of longitudinal waves in a material is proportional to sqrt(E/p). Plot contours of this quantity onto to modulus-density chart allowing you to read off approximate value for any material on the chart. Which metals have about the same sound velocity as steel.
Nickel
The electronegativity of geranium is 1.8, that of bromine is 2.8 on the Pauling scale. Will they form on iconic bond?
No
"" Diffusion is more rapid in polycrystalline silver with a small grain size than in coarse-grained silver. (Indicate incorrect).
NoA
A linear polyethylene has a number-average molecular weight of 300,000 g/mol; compute average value of the total chain L for this material. Assume carbon-carbon bond distance of 0.514 nm and the angle bond to bond of 109*.
NoA
If you wanted to select a material for a compact heat storing device, which of the two, Cv or Cp, would you use as a criterion of choice? Indicate the incorrect. For minimum mass is the material with the greatest value of Cp For minimum volume (thus compact) is that with the greatest value of (Cp)vol Regardless, the material should meet all the other constraints A constraint to meet could be an adequate maximum service temp
NoA
Regarding the specific heat per unit volume and the specific heat per unit mass. Indicate the incorrect. When dealing with gases, it is more usual to measure the heat capacity at constant volume (Cv) For gases, Cv differs from Cp For solids, the specific heat per unit volume is the same per unit mass, Cp, multiplied by density, p Cv = CpP
NoA
Solar panels, touch-screens, and other displays use Indium to provide an electrically conducting film that is transparent to light. Use the Abundance plot to form a judgement about possible future availability of Indium. Indicate the incorrect sentence: Indium is a rare element Indium abundance in the earth's crust is comparable with that of silver Indium abundance in the earth's crust is much less than that of the Germanium Rare earths or Uranium of Uranium, all of them regarded as having a low abundance
NoA
Use your knowledge of diffusion and solid solutions to account for the following observation: The rate of diffusion of oxygen from the atmosphere into an oxide film is strongly dependent on the temperature and the concentration of oxygen in the atmosphere. (Indicate incorrect)
NoA
What in your judgement, is not a design limiting property for the material of an oven glove? Flexibility, low thermal conductivity, tolerance of water, high max operating temperature.
NoA
The diagram shows a proposed designed for an outdoor water tank. What aspects of the design might cause concern for corrosion? Indicate incorrect.
NoA (go check)
Specific heat is
NoA (the energy to heat 1 kg of a material by 1 K)
The wire frames in your fridge or dishwasher are coated to protect them from water and food-related fluids by hot-dipping: plunging the frame when hot into a fluidized bed of polymer powder, which melts and sticks to the frame. What's the polymer likely to be?
Nylon
Use Figure 12.18, top, to find a phase-change material (PCM) that could help maintain the temperature at 5*C during one of these temporary thermal over-loads.
Parafin C14
You need a flexible tube to connect a tank of diesel fuel to a burner. Use Table B2, App B, to find a suitable plastic.
Polyvinylchloride
(Problem 5) Yield strength
Processing masks any dependence with atomic number
Asked to design a heat sensing switch to turn the lights off when no one is moving around. What principle? What materials?
Pyroelectric thermal imaging, geranium
What are the characteristics required of materials for magnetic information storage?
Requires hard magnets, but with a squareness for binary storage. Induce an electric pulse.
A material is required as the magnet for a magnet soap holder. Soap is mildly alkaline. What is not a design limiting property? Ferromagnetic, Good resistance to fresh water, good resistance to mild alkali, soft magnetic behavior
Soft magnetic behavior
There have been many attempts to manufacture and market plastic bicycles. All have been too flexible. Which design-limiting property is insufficiently large? Flexibility, Stiffness, Strength, Ductility, Density
Stiffness
"" Carbon diffuses far more rapidly than chromium through iron. (Indicate the incorrect)
The diffusion of chromium in iron is faster than the one of carbon in iron
(Problem 3) Use the modulus-density chart to find, from among the materials that appear on it: The material with the highest density
Tungsten (W)
What are the necessary conditions for a material to be ferromagnetic at a temperature T?
The material must be able to maintain its dipole moment at a temperature T.
Regarding Q71 (Q31) use Table B3 of App B to select a suitable material for the pipes and tanks, given that, to have sufficient strength and toughness to tolerate external abuse they must be made of a metal. Indicate invalid.
The safest choice would be stainless steel lined with PTFE (?)
(Problem 5) The atomic volume and Young's modulus change in a cyclic way across the rows of the periodic table. Would you expect the following properties to behave in this way? Indicate incorrect. Absolute melting point and latent and heat of fusion
They are microstructure-sensitive properties
Identify a material with potential for use above 1000 C.
ZrO2
The description "solid in which the atoms or molecules are arranged in an ordered way that can be described by a geometric lattice" belongs to
a crystalline solid
The description "is one in which the bonding along the polymer chains is covalent and strong but the bonding between them is Van der Waals or hydrogen bonding and is weak." This causes the polymer to melt when heated, allowing thermal molding." belongs to
a thermoplastic
The description "one in which the polymer chains are cross-linked by strong covalent bonds that do not melt when the polymer is heated." belongs to
a thermoset
The description "it is a slightly cross-linked polymer which, at room temperature, is above its glass-transition temperature" belongs to
an elastomer
The absorption coefficient B of polyethylene for optical frequencies is 86.6 cm^-1. How thick a slab is required for half is initial value?
x=0.008 cm
The approximate ratio of the modulus of woods measured parallel to the grain and perpendicular to the grain
~10
