Material Science and Engineering
Performance Parameter: The property of a component that is determined by
1) Size 2) Shape 3) Material property (Materials constant) Varies with size and shape
How could I improve Hardness? How could I test Hardness?
1) You could coat it with another materials. Polycarbonate plastic scratched with steel wool. One side has been treated with chemical vapor deposited oxide coating. 2) Vickers Hardness Tester
The Coefficient of Restitution is a __________ that describes the amount of ___________. Other _________ that is not returned is lost as ________ or goes to __________
1. Performance Parameter 2. Energy returned to an object after a collision 3. energy 4. heat 5. deformation of material
What is it called when you a mechanical strain and get a voltage? What is it called when you apply a voltage and get a mechanical strain?
1. Piezoelectric effect 2. Electrostriction
Assume the coefficient of thermal expansion (CTE) of the super alloy is 8x10⁻6 m/m°C. To prevent delamination of the coating, which of the following materials would you choose?
C. Material C CTE = 10x10⁻6 m/m °C
When you have a material that is composed of brass metal on one side and iron metal on the other at room temperature what happens when you heat the bar?
The brass side of the bar expands more than the iron side, so the bar expands unevenly curving with the brass on the outside of the curve. When you cool the bar it begins to compress and straighten back out. Bimetallic strips work in household devices like thermostats because once a desired temperature has been reached the bimetallic strip begins to expand and break the circuit which causes the circuit to stop.
Magnetization of material formula/definition
M = ℵH ℵ = magnetic susceptibility H = magnetic field It is the materials response to an applied magnetic field (H) but it will be the focus of our discussion
Coercive Field
Magnetic field required to switch the direction of magnetization in a magnetic material. High coercive field materials will prevent demagnetization and enable permanent magnets.
What device quantifies color?
UV/Vis Spectroscopy You have a light source then you have slit where colors are split and a slide will cover one side of the device so only certain colors can transmit through.
Ultimate Tensile Strength (σuts) AKA
Ultimate Strength. The stress beyond which the material fails/fractures
How is the reslience described on a stress-strain curve (σ-ε)
The amount of energy we can return to a material is the area under the elastic (reversible) portion of the stress-strain curve.
When light is incident on a material, three things can happen to the light:
(1) It gets REFLECTED off the surface (2) It enters the material and gets ABSORBED inside (3) It travels through the entire material ( TRANSMITTED) and exits on the other side. IR + IA+ I T = 100%
Electrode Dielectric
(Electrical conductor) (Electrical insulator)
Thermal Conductivity
(speed of heat flow) The "Speed" of energy is J/S (power->w) The rate which heat flows through a material at a steady rate (ex: across a temperature a gradient that is constant with time). Units for Thermal Conductivity: w/(m×k) = W.m-1.K-1
Resilience is a
material property/constant
MSE provides the
materials constants the other engineers use for design
What is the relationship between Electrical Conductivity and Resistivity
σ = 1/p S = 1/Ω
Hooke's Law (Formula)
σ = E × ε --> ε = σ/E Slope of the linear portion of a stress-strain curve: E Stress (σ) Strain (ε)
Stress Formula
σ = F/A We will use critical stress values as materials constants
What is strain and its formula?
Amount of material elongation with loading ∈ = LF - Li/Li x 100% Change in length
Calcite would be able to scratch A. Fluorite B. Quartz C. Gypsum Both A & B None of these
C. Gypsum
Reflectivity, absorptivity, and transmissivity all depend on the _________ of incident light and the ___________. The color of a material depends on what wavelengths of light are _______. Wavelengths (_____) that are not _____ are the colors we see. These colors are seen either by _______ (in the case of opaque materials) or by _______ (in the case of transparent or translucent materials)
1. Wavelength (color) 2. AWhngle of incidence 3. Absorbed 4. Color 5. Absorbed 6. Reflection 7. Opaque 8. Transmission
Most modern materials are less than
100 years old
Strength
: How much force (stress) does it take to permanently deform the material
Explain the effects of a Higher thermal conductivity
A cold material with a high thermal conductivity takes heat away faster from an ice cube than another material that appears warm but actually has a lower thermal conductivity. Your body heat is what will be sensed if you touched the warm block.
What is Piezoelectricity a Cross property of and what is it?
A cross property combining both the electrical and mechanical responses of a material. Piezoelectrics are electrical insulators because they must support an internal applied voltage to work. Piezoelectric Effect is the ability of certain materials to generate an electric charge in response to applied mechanical stress. The word Piezoelectric is derived from the Greek piezein, which means to squeeze or press, and piezo, which is Greek for "push".
Plastic deformation
A deformation that is permanent (non-linear) portion of the stress-strain curve. -Does not go back to original shape at this point.
Elastic deformation
A deformation that is reversible. When load is removed material returns to original shape.
A refrigerator door is made of
A soft magnetic material
If you were asked to design a cell phone screen that could not be scratched, which material property would you try to maximize? A)Hardness B)Resilience C)Ductility D) Density
A)Hardness
The yield strength of a material... A. ...determines when a material will permanently deform. B. ...determines how stiff a material is. C. ...is the proportionality constant in Hooke's Law. D. ...is equivalent to the area under the linear portion of the stress-strain curve. Both A & B Both B & C Both C & D B, C, & D A, B, C, and D
A. ...determines when a material will permanently deformf
If you choose to use a superalloy with a CTE = 8x10⁻⁴ m/m° and a thermal barrier coating (TBC) with a CTE = 10x10 m/m°C, will the ceramic TBC be in tension or compression at the service temperature? Assume there is no strain in the coating at room temperature
A. tension
Material property or Material constant
An intrinsic property of a material that does not depend upon size or shape
Which of the following would be considered a CHEMICAL property of a material? A)Dielectric Constant B)Solubility C)Heat Capacity D) Ductility
B)Solubility
What materials property for the thermal barrier would you select to reduce the operating temperature of the turbine blade
B. a low thermal conductivity
Why are thermal barrier coating added to turbine blades
B. to increase the service temperature of superalloy turbine blades
CTE: "Bimetallic Strips"
Bonding two metals with dissimilar thermal expansion coefficients can produce useful devices for detecting and measuring temperature changes. A typical pair is brass and steel with typical expansion coefficients of 19 and 13 parts per million per degree Celsius respectively. The examples shown are straight strips, but bimetallic strips are made in coils to increase their sensitivity for use in thermostats. One of the many uses for bimetallic strips is in electrical breakers where excessive current through the strip heats it and bends it to trip the switch to interrupt the current. What matters? CTE mismatch (Difference in CTE between the two materials ---> Bigger ∆CTE ----> Bigger deflection)
The modulus of resilience of a material... A. ...is the critical stress beyond which the material permanently deforms. B. ...can be represented by the area under the elastic portion of the stress-strain curve. C. ...is the proportionality constant in Hooke's Law. D. ...describes the amount of reversible mechanical energy storage possible in a given material. Both A & B Both A & C Both B & C Both B & D B, C, & D A, B, C, & D
Both B & D
You design a rod to hold a chandelier from the ceiling, but then your boss informs you that the chandelier will be twice as heavy. Your initial design will now plastically deform under the weight. Which of the following could be done to your original design to allow it to work with the new chandelier? A. Use the same material, but shrink the diameter of the rod. B. Use the same material, but increase the diameter of the rod. C. Choose a material with a higher elastic modulus, but keep the rod diameter the same. D. Choose a material with a higher yield strength but keep the rod diameter the same. Both B & C will work. Both B & D will work. B, C, and D will all work.
Both B & D will work.
Transmission
By the time a beam of light has passed completely through a slab of material it has lost some intensity through reflection at the surface at which it entered, some in reflection at the surface at which it leaves and some by absorption in between. Its intensity is The term (1 − IR/Io) occurs to the second power because intensity is lost through reflection at both surfaces.
Design equation for capacitance (performance parameter)
C = ∈₀ x k x A/t C = capacitance ∈₀ = permittivity of free space (universal constants) k = dielectric constant
Thermal Expansion Coefficient (α) or Coefficient of Thermal Expansion (CTE) What is it a cross property of?
CTE- Change in volume of a material with change in temperature. Cross of Thermal and Mechanical. Most materials expand with increasing temperature, but some can have a negative CTE. Cubic Zirconium Tungstate, for example, contracts continuously over a previously unprecedented temperature range of 2 to 1050K. Such materials have a range of potential engineering, photonic, electronic or structural applications. If, for example, one were to mix an NTE material with a "normal" material which expands on heating one could envisage making a zero expansion composite. In addition to its negative thermal expansion, ZrW2O8 and related phases exhibit oxide ion mobility at remarkably low temperatures, unusual behaviour under applied pressure and unusual hysteresis effects.
If you apply a voltage to a piezoelectric material, it will
Change size because you ares subjecting the atoms inside to electrical pressure. They have to move to rebalance themselves, and that's why they deform when you put a voltage across them.
The properties of a material depend upon more than just? Other important factors?
Composition. Other Factors: Microstructure Defects Internal Strain Crystal Structure
When do we want high electrical conductivity? High electrical Resistivity?
Conductivity: Power lines Lightning rod Solder Resistivity: Spark Plug Capacitors
Electronic Properties
Conductors are important but don't have any other interesting properties. Insulators have more properties because the entire material feels the voltage
List of Chemical Properties
Corrosion Resistance Solubility UV Protection Rating Biocompatability
List of Price (Cost per volume) properties
Cost of raw material Cost to process the material
In the stress-strain curve shown below, which point best represents the strain at fracture? A) B) C) D)
D
Bimetallic Thermometer
Definition: The bimetallic thermometer uses the bimetallic strip which converts the temperature into the mechanical displacement. The working of the bimetallic strip depends on the thermal expansion property of the metal. The thermal expansion is the tendency of metal in which the volume of metal changes with the variation in temperature. Every metal has a different temperature coefficient. The temperature coefficient shows the relation between the change in the physical dimension of metal and the temperature that causes it. The expansion or contraction of metal depends on the temperature coefficient, i.e., at the same temperature the metals have different changes in the physical dimension. Working Principle of Bimetallic Thermometer The working principle of bimetallic thermometer depends on the two fundamental properties of the metal. The metal has the property of thermal expansion, i.e., the metal expand and contract concerning the temperature. The temperature coefficient of all the metal is not same. The expansion or contraction of metals is different at the same temperature. Constructions of Bimetallic Thermometer The bimetallic strip is constructed by bonding together the two thin strips of different metals. The metals are joined together at one end with the help of the welding. The bonding is kept in such a way that there is no relative motion between the two metals. The physical dimension of the metals varies with the variation in temperature. Since the bimetallic strip of the thermometer is constructed with different metals. Thereby, the length of metals changes at different rates. When the temperature increases, the strip bends towards the metal which has a low-temperature coefficient. And when the temperature decreases, the strip bends towards the metal which has a high-temperature coefficient. The figure below shows the bimetallic strip in the form of the straight cantilever beam. The strip fixed at one end and deflects at the other end.
List of Mechanical/Structural Properties
Density Elastic Modulus (stiffness) Yield Strength Modulus of Resilience Fracture Toughness Hardness Ductility Poisson's Ratio Coefficient fricition
Design Challenges of Thermal Expansion Coefficient (α)
Design Challenges: Buckling If a material is constrained and undergoes a temperature change then it is susceptible to buckling. σApply due to CTE > σy ----> PERMANENT BUCKLING AND PERMANENT DEFORMATION
What engineers do?
Design. Use existing knowledge to design components of systems for a given process
Important material properties for a capacitor's dielectric material
Dielectric constant (kappa) (k)---> How much charge can be stored by material Resistivity (p) (Rho) ----> Determines how long you can store charge before self discharge.
Dielectric behavior
Dielectrics are insulators. So what happens to their electrons when a field E is applied? In zero field, the electrons and protons in most dielectrics are symmetrically distributed, so the material carries no net or dipole moment. A field exerts a force on a charge, pushing positive charges in the direction of the field and negative charges in the opposite direction. The effect is easiest to see in ionic crystals, since here neighbouring ions carry opposite charges, as on the left of Figure 14.12. Switch on the field and the positive ions (charge +q) are pulled in the field direction, the negative ones (charge −q) in the reverse, until the restoring force of the inter-atomic bonds just balances the force due to the field at a displacement of Δx, as on the right of the figure. Two charges ±q separated by a distance Δx create a dipole with dipole moment, d, given by Figure 14.12 An ionic crystal in zero applied field (a), and when a field V/x is applied (b). The electric field displaces charge, causing the material to acquire a dipole moment. Even in materials that are not ionic, like silicon, a field produces a dipole moment because the nucleus of each atom is displaced a tiny distance in the direction of the field and its surrounding electrons are displaced in the opposite direction. The resulting dipole moment depends on the magnitude of the displacement and the number of charges per unit volume, and it is this that determines the dielectric constant. The bigger the shift, the bigger the dielectric constant. Thus, compounds with ionic bonds and polymers that contain polar groups like —OH− and —NH− (nylon, for example) have larger dielectric constants than those that do not.
What scientists do:
Discover Understand fundamental principles governing physical world.
List of Electrical/Magnetic Properties
Electrical Conductivity Magnetic Susceptibility Magnetization Magnetic Remanence Dielectric constant Polarization (ferroelectricity) Superconductivity
Name the weak and strong types of magnets.
Strong: Ferromagnets and ferrimagnets Weak: Paramagnets, diamagnets, antiferromagnets
16.2 The interaction of materials and radiation
Electromagnetic (e-m) radiation permeates the entire universe. Observe the sky with your eye and you see the visible spectrum, the range of wavelengths we call 'light' (0.40-0.77 µm). Observe it with a detector of X-rays or γ-rays and you see radiation with far shorter wavelengths (as short as 10−4 nm, one-thousandth the size of an atom). Observe it instead with a radio-telescope and you pick up radiation with wavelengths measured in millimeters, meters or even kilometers, known as radio and microwaves. The range of wavelengths of radiation is vast, spanning 18 orders of magnitude (Figure 16.1). The visible part of this spectrum is only a tiny part of it—but even that has entrancing variety, giving us colours ranging from deep purple through blue, green and yellow to deep red. The spectrum of electromagnetic (e-m) waves. The visible spectrum lies between the wavelengths 0.4 and 0.77 µm.
Applications of Piezoelectric effect and electrostriction
Electrostriction: Analytical tools (atomic force microscrope) Optical alignment Ink Jet printer Fuel Injector Ultrasound Piezoelectric Effect: Gas grill lighters Pick-ups for acoustics instruments Light-up shoes
Toughness
Energy per unit volume requires to rupture or break a material. The area underneath the line is the toughness Units: N/m² × m/m = J/m³ Stress is m² and Strain is m Energy/Volume
Compared to engineers, scientists usually focus more on designing new components to achieve the best performance for a given application. True False
False
Ferro-electric materials
Ferro-electrics are a special case of piezo-electric behaviour. They too have an unsymmetric structure, but have the special ability to switch asymmetry. Barium titanate, BaTiO3, shown schematically in Figure 14.16, is one of these. Below a critical temperature, the Curie9 temperature (about 120 °C for barium titanate), the titanium atom, instead of sitting at the centre of the unit cell, is displaced up, down, to the left or to the right, as in (a) and (b). Above the Curie temperature the asymmetry disappears and with it the dipole moment, as in (c). In ferro-electrics, these dipoles spontaneously align so that large volumes of the material are polarised even when there is no applied field. Ferro-electric materials have a permanent dipole moment that can switch: here the Ti+ion can flip from the upper to the lower position. Above the Curie temperature the asymmetry disappears.
Why should non-majors study MSE?
Learning a language. (It's like learning a language. Allow for better communication). Broaden your design space (Exposed to new properties = new idea. While we call them "materials constants" by changing chemical structure we can change these properties.
You are hired by a bedding company to design new mattresses. Your first project is to design a "firm" mattress (that is, one that does not compress very much when you lay on it). Below are the stress-strain curves that have been collected for three different foams loaded under compression. Amongst these three foams, which would you select to make the "firmest" mattress and why? Foam C because it has the highest yield strength. Foam B because it has the highest yield strength. Foam B because it has the highest elastic modulus. Foam A because it has the highest elastic modulus. Foam A because it has the lowest yield strength. Foam C because it has the lowest elastic modulus. Foam A because it has the highest yield strength.
Foam B because it has the highest elastic modulus.
Acoustics Engineering Why is foam used for sound insulation?
Foam(s) are low density and low elastic modulus which makes its close to air ---? lots of transmittance between air and foam.
What makes a material tough
For high toughness a material requires both a high yield strength and high ductility
Measuring Mechanical Properties: The Tensile Test
Force and elongation are proportional Tensile testing measures the stress-strain curve for a material which is a graphical representation for many of the relevant mechanical properties of the material
A good dielectric material designed for use in a capacitor should
Have a high dielectric constant be a good electrical insulator
List of Thermal Properties
Heart capacity Thermal Conductivity Melting Temperature
Stiffness:
How much force (stress) does it take to flex the material
Sound Absorption Coefficient
How much sound is absorbed into a material. Metals and Ceramics 10⁻⁶ to 10⁻⁴ Polymers and Foams 0.01 to 0.2 Higher Absorption coefficient the more sound absorbed and turned to heat.
Electrical resistance
If a field E exerts a force Ee on an electron, why does it not accelerate forever, giving a current that continuously increases with time? This is not what happens; instead, switching on a field causes a current that almost immediately reaches a steady value. Referring back to equations (14.1) and (14.2), the current density i/A is proportional to the field E: where ρe is the resistivity and κe, its reciprocal, is the electrical conductivity.
Absorption
If radiation can penetrate a material, some is absorbed. The greater the thickness x through which the radiation passes, the greater the absorption. The intensity I, starting with the initial value I0, decreases such that where β is the absorption coefficient, with dimensions of m−1 (or, more conveniently, mm−1). The absorption coefficient depends on wavelength, with the result that white light passing through a material may emerge with a color corresponding to the wavelength that is least absorbed—that is why a thick slab of ice looks blue.
Magnetic fields in materials
If the space inside the coil of Figure 15.2 is filled with a material, as in Figure 15.3, the induction within it changes. This is because its atoms respond to the field by forming little magnetic dipoles in ways that are explained in Section 15.4. The material acquires a macroscopic dipole moment or magnetisation, M(its units are A/m, like H). The induction becomes
Def. bodies
If you go above the Yield strength the object will be permanently deformed Apply some amount of load in a certain geometry and calculate the type and amount of stress in each part of the material. Atoms start to rearrange past yield strength. Ultimate tensile strength Past this point it will break
Performance Parameter:
Load (force) Can it withstand a certain force
Elastic energy
If you stretch an elastic band, energy is stored in it. The energy can be considerable: catapults can kill people. The super-weapon of the Roman arsenal at one time was a wind-up mechanism that stored enough elastic energy to hurl a 10 kg stone projectile 100 yards or more. How do you calculate this energy? A force F acting through a displacement dL does work F dL. A stress σ = F/A acting through a strain increment dε = dL/L does work per unit volume with units of J/m3. If the stress is acting on an elastic material, this work is stored as elastic energy. The elastic part of all three stress-strain curves of Figure 4.4—the part of the curve before the elastic limit—is linear; in it σ = Eε. The work done per unit volume as the stress is raised from zero to a final value σ* is the area under the stress-strain curve: This is the energy that is stored, per unit volume, in an elastically strained material. The energy is released when the stress is relaxed.
CTE: Bimetallic Strips - Uses
Image: Thermostat How can we use in design? Sense temperature and convert temperatures changes to mechanical motion. As long as the stresses do not exceed yield strength of the material, this bending is reversible (you can calibrate) . These bimetallic thermometers can also be used as temperature sensitive mechanical switches. Examples: thermostats, blinkers, toasters, x-mas lights.
Which of the following is not an example of an elastic moduli? Bulk Modulus Shear Modulus Impression Modulus Young's Modulus
Impression Modulus
Ferro-electric materials 2.0
In the absence of an external field a ferro-electric divides itself up into domains—regions in which all the dipoles are aligned in one direction—separated by domain walls at which the direction of polarisation changes (Figure 14.17). The domains orient themselves so that the dipole moment of one more or less cancels those of its neighbours. If a field is applied the domain walls move so that those polarised parallel to the field grow and those polarised across or against it shrink, until the entire sample is polarised (or 'poled') in just one direction. Figure 14.18 shows how the polarisation P changes as the field E is increased: P increases, reaching a maximum at the saturation polarisation, Ps. If the field is now removed, a large part of the polarisation remains (the remanent polarisation), which is only removed by reversing the field to the value 2Ec, the coercive field. The figure shows a complete cycle through full reverse polarisation, ending up again with full forward poling. The little inserts show the domain structures round the cycle. Ferro-electric materials have enormous dielectric constants. Those of normal materials with symmetric charge distributions lie in the range 2-20. Those for ferro-electrics can be as high as 20 000. It is this that allows their use to make super-capacitors that can store 1000 times more energy than conventional capacitors. Such is the energy density that super-capacitors now compete with batteries for energy storage.
Electrical Resistance
Is the performance parameter. The equation for electrical resistance: R = P× L/A R is in Ω (ohms)
Material properties can almost always be designed around by making a component a different size or shape ( longer, shorter, fatter, thinner, rougher, smoother pointier, rounder etc) In other words you could achieve a certain performance parameter from a certain material but
It inconvenient because it gives you an undesirable trade off in another performance parameter. For example, steel is opaque and non-bendable. Transparency glass is transparent and bendable. If you decrease the thickness of the steel then you could bend it. For bendable steel we have to give up thickness. Optical transparency from a metal is also possible if you make it thin enough but at that point it is useless.
Heat capacity
It is a materials constant. It is the heat energy required to raise the temperature of a material by 1° C (1k). AKA: Specific Heat; Cp ≈Cv for a solid. Units: J/m³ °C or J/g° C or J/mol °C Design Warning: Be careful of units, not always inuitive In the same volume you can more energy in copper than in lead even though lead has more mass.
What is a capacitor and how do they work?
It is an insulator between two conductors They store electrical energy by storing charge. Electrode: (Electrical conductor) Dielectric: (Electrical insulator) In class he hooked up plugs to a battery and a capacitor. The capacitor was able to store the energy so it could later power a light bulb. The capacitor is a component which has the ability or "capacity" to store energy in the form of an electrical charge producing a potential difference (Static Voltage) across its plates, much like a small rechargeable battery. There are many different kinds of capacitors available from very small capacitor beads used in resonance circuits to large power factor correction capacitors, but they all do the same thing, they store charge. In its basic form, a capacitor consists of two or more parallel conductive (metal) plates which are not connected or touching each other, but are electrically separated either by air or by some form of a good insulating material such as waxed paper, mica, ceramic, plastic or some form of a liquid gel as used in electrolytic capacitors. The insulating layer between a capacitors plates is commonly called the Dielectric. A Typical Capacitor Due to this insulating layer, DC current can not flow through the capacitor as it blocks it allowing instead a voltage to be present across the plates in the form of an electrical charge. The conductive metal plates of a capacitor can be either square, circular or rectangular, or they can be of a cylindrical or spherical shape with the general shape, size and construction of a parallel plate capacitor depending on its application and voltage rating. When used in a direct current or DC circuit, a capacitor charges up to its supply voltage but blocks the flow of current through it because the dielectric of a capacitor is non-conductive and basically an insulator. However, when a capacitor is connected to an alternating current or AC circuit, the flow of the current appears to pass straight through the capacitor with little or no resistance. There are two types of electrical charge, positive charge in the form of Protons and negative charge in the form of Electrons. When a DC voltage is placed across a capacitor, the positive (+ve) charge quickly accumulates on one plate while a corresponding and opposite negative (-ve) charge accumulates on the other plate. For every particle of +ve charge that arrives at one plate a charge of the same sign will depart from the -ve plate. Then the plates remain charge neutral and a potential difference due to this charge is established between the two plates. Once the capacitor reaches its steady state condition an electrical current is unable to flow through the capacitor itself and around the circuit due to the insulating properties of the dielectric used to separate the plates. The flow of electrons onto the plates is known as the capacitors Charging Current which continues to flow until the voltage across both plates (and hence the capacitor) is equal to the applied voltage Vc. At this point the capacitor is said to be "fully charged" with electrons. The strength or rate of this charging current is at its maximum value when the plates are fully discharged (initial condition) and slowly reduces in value to zero as the plates charge up to a potential difference across the capacitors plates equal to the source voltage. The amount of potential difference present across the capacitor depends upon how much charge was deposited onto the plates by the work being done by the source voltage and also by how much capacitance the capacitor has and this is illustrated below.
16.1 Introduction and synopsis
It was at one time thought that the fact that light could travel through space—from the sun to earth, for instance—must mean that space was not really empty but filled with 'luminiferous ether'. It was not until the experiments of Michelson1 and Morley in 1881 that it was realised that light did not need a 'material' for its propagation but could propagate through totally empty space at what is now seen as the ultimate velocity: 3 × 108 m/s. When radiation strikes materials, things can happen. Materials interact with radiation by reflecting it, absorbing it, transmitting it and refracting it. This chapter is about these interactions, the materials that do them best and the ways we use them. The chapter opening page shows two: a reflecting telescope and a refracting microscope, each of which depend on the optical properties of materials.
The prototypical piezoelectric material is? PZT has a piezoelectric coefficient (d₃₃) of? Quarts is piezoelectric with a d₁₁ of
Lead zirconate titanate (PZT). ~300 pm/v If we apply 1 volt to the material it will expand or contract by 0.3 nm. (small and precise) -2.3 pm/v?
Hardness is a _____________________ of a material
Surface property
Measuring magnetic properties 2.0
Magnetic materials are characterised by the size and shape of their hysteresis loops. The initial segment AB is called the initial magnetisation curve and its average slope (or sometimes its steepest slope) is the magnetic susceptibility, χ. The other key properties—the saturation magnetisation Ms, the remanence MR and the coercive field Hc—have already been defined. Each full cycle of the hysteresis loop dissipates an energy per unit volume equal to the area of the loop multiplied by μo, the permeability of a vacuum. This energy appears as heat (it is like magnetic friction). Many texts plot not the M-H curve, but the curve of inductance B against H. Equation (15.5) says that B is proportional to (M + H), and the value of M for any magnetic materials worthy of the name is very much larger than the H applied to it, so B ≈ μoM and the B-H curve of a ferro-magnetic material looks very like its M-H curve (it's just that the M-axis has been scaled by μo). There are several ways to measure the hysteresis curve, one of which is sketched in Figure 15.6. Here the material forms the core of what is, in effect, a transformer. The oscillating current through the primary input coil creates a field H that induces magnetisation M in the material of the core, driving it round its hysteresis loop. The secondary coil picks up the inductance, from which the instantaneous state of the magnetisation can be calculated, mapping out the loop.
Measuring magnetic properties 3.0
Magnetic materials differ greatly in the shape and area of their hysteresis loop, the greatest difference being that between soft magnets, which have thin loops, and hard magnets, which have fat ones, as sketched in Figure 15.7. In fact the differences are much greater than this figure suggests: the coercive field Hc (which determines the width of the loop) of hard magnetic materials like Alnico is greater by a factor of about 105 than that of soft magnetic materials like silicon-iron. More on this in the next two sections. Hysteresis loops. (a) A fat loop typical of hard magnets. (b) A thin, square loop typical of soft magnets.
Measuring magnetic properties
Magnetic properties are measured by plotting an M-H curve. It looks like Figure 15.5. If an increasing field H is applied to a previously demagnetised sample, starting at A on the figure, its magnetisation increases, slowly at first and then faster, following the broken line, until it finally tails off to a maximum, the saturation magnetisation Ms at the point B. If the field is now backed off, M does not retrace its original path, but retains some of its magnetisation so that when H has reached zero, at the point C, some magnetisation remains: it is called the remanent magnetisation or remanence MR and is usually only a little less than Ms. To decrease M further we must increase the field in the opposite direction until M finally passes through zero at the point D when the field is −Hc, the coercive field, a measure of the resistance to demagnetisation. Some applications require Hc to be as high as possible, others as low a possible. Beyond point D the magnetisation M starts to increase in the opposite direction, eventually reaching saturation again at the point E. If the field is now decreased again, M follows the curve through F and G back to full forward magnetic saturation again at B to form a closed M-H circuit called the hysteresis loop. Figure 15.5 A hysteresis curve, showing the important magnetic properties.
Consider two materials, A & B, with mechanical stress-strain curves shown below. Which of the following statements accurately describe the mechanical properties of these two materials? a) Material A and B have the same strength, but Material B will flex more at low stresses than Material A. b)Material A and B have the same stiffness, but Material B will yield at a lower stress than Material A.3 c)Material A and B have the same strength and stiffness, but Material A will fail at a lower stress than Material B. d)Material A and B have the same strength, but Material A will flex more at low stresses than Material B. e)Material A and B have the same stiffness, but Material A will yield at a lower stress than Material B.. f)Material A and B have the same strength and stiffness, but g)Material B will fail at a lower stress than Material A.
Material A and B have the same stiffness, but Material B will yield at a lower stress than Material A.
The stress-strain curves for three materials are shown below (Materials A, B, and C). Amongst these three materials, which one has the greatest toughness? Material A. Material B Material C Materials A & B have the same toughness. Materials B & C have the same toughness. Materials A & C have the same toughness.
Material B
Saturation Magnetization
Maximum magnetization that a material can obtain when placed under an electric field. (Even if magnetic field intensity is increased the material saturates at this magnetization level)
What material property might you care about when designing a widget?
Mechanical, Chemical, Thermal, Cost, Electrical, Magnetic, Optical
Specular and diffuse reflection
Metals reflect almost all the light that strikes them; none is transmitted and little is absorbed. When light strikes a reflecting surface at an incident angle θ1, part of it is reflected, leaving the surface with an angle of reflection θ2 such that
15.1 Introduction and synopsis
Migrating birds, some think, navigate using the earth's magnetic field. This may be questionable, but what is beyond question is that sailors, for centuries, have navigated in this way, using a natural magnet, lodestone, to track it. Lodestone is a mineral, magnetite (Fe3O4), that sometimes occurs naturally in a magnetised state. Today we know lodestone as one of a family of ferrites, members of which can be found in every radio, television set and microwave oven. Ferrites are one of two families of magnetic material; the other is the ferro-magnet family, typified by iron but also including nickel, cobalt and alloys of all three. Placed in a magnetic field, these materials become magnetised, a phenomenon called magnetic induction. On removal, some, called soft magnets, lose their magnetisation; others, the hard magnets, retain it. Magnetic fields are created by moving electric charge—electric current in electromagnets, electron spin in atoms of magnetic materials. This chapter is about magnetic materials: how they are characterised, where their properties come from and how they are selected and used. It starts with definitions of magnetic properties and the way they are measured. As in other chapters, charts display them well, separating the materials that are good for one sort of application from those that are good for others. The chapter continues by drilling down to the origins of magnetic behavior, and concludes with a discussion of applications and the materials that best fill them.
Hardness can be semi-quantitatively assessed using the _______________ Hardness is related to the _________ of a material: Vickers Hardness ≈
Moh's Hardness Scale. Higher numbers on the scale can stratch lower numbers.≈ ≈ σy
Why select a different material: Original material may: Require the use of _________________ material - - Be more difficult or impossible to _________________ (EX: gate oxides for MOSFETs) SiO2 Require a ____________ with another _____________-
More -Cost more (or not) - This could weigh more Process/Manufacture C = k A/B ? Trade-off and necessary property
Magnetic fields in materials 2.0
Nearly all materials respond to a magnetic field by becoming magnetised, but most are paramagnetic with a response so faint that it is of no practical use. A few, however, contain atoms that have large dipole moments and have the ability to spontaneously magnetise—to align their dipoles in parallel—as electric dipoles do in ferro-electric materials. These are called ferro-magnetic and ferri-magnetic materials (the second one is called ferrites for short), and it is these that are of real practical use.Magnetisation decreases with increasing temperature. Just as with ferro-electrics, there is a temperature, the Curie temperature Tc, above which it disappears, as in Figure 15.4. Its value for the materials we shall meet here is well above room temperature (typically 300-500 °C) but making magnets for use at really high temperatures is a problem. Figure 15.4 Saturation magnetisation decreases with temperature, falling to zero at the Curie temperature, Tc.
Great opportunity
New materials with "better" properties drive creation of new products
Material properties
Normalize performance parameter to the geometry
The electrical conductivity (σ)
Of a material is how "quickly" electrons (electricity) travel through the material. Units: S/cm (siemens)
The electrical Resistivity (p)
Of a material is the opposite of conductivty, it is the impediment to electron flow Units: Ω x cm (ohm)
Stress Strain Curve Analysis
Past the linear regime is the Yield strength. Past the yield strength is where plastic deformation occurs. The x marks the spot that is the ultimate tensile strength. If you release past yield strength you will recover elastic deformation but not elastic deformation.
Curie Temperature
Permanent magnets lose their magnetization when heated above the material's Curie Temperature This loss of magnetization is PERMANENT and the material remain demagnetized when cooled back down. When can stick it back in a magnetic field to recover it. The Curie Temperature is the Service Temperature for magnetic materials.
In the stress-strain curve for an arbitrary material shown below, which point most closely matches the ultimate tensile strength of the material? Point A Point B Point C Point D
Point C
Organization for this class
Process ---> Structure ---> Properties We will start with properties in this class and work backwards
Pyro-electric materials
Pyro-electricity—polarisation caused by change of temperature—was known to (but not understood by) the Greek philosopher Theophrastus8, who noted that certain stone, when warmed or cooled, acquired the ability to pick up straw and dry leaves. It was not until the 20th century that this strange behaviour was understood and exploited. Some materials have a permanent dipole moment because their positive and negative ions balance electrically but are slightly out of line with each other. If a thin disk of one of these is cut so that its faces are parallel to the plane in which the misalignment happens, the disk has a dipole moment of its own. The unit cells of pyro-electric materials are like this. The dipole moment per unit volume of the material is called the spontaneous polarisation Ps. This net dipole moment exists in the absence of an applied electric field and is equivalent to a layer of bound charge on each flat surface. Nearby free charges such as electrons or ions are attracted to the surfaces, neutralising the charge. Imagine that conductive electrodes are then attached to the surfaces and connected through an ampmeter. If the temperature of the sample is constant, then so is Ps and no current flows through the circuit. An increase in temperature, however, causes expansion and that changes the net dipole moment and the polarisation. Redistribution of free charges to compensate for the change in bound charge results in a current flow—the pyro-electric current—in the circuit. Cooling rather than heating reverses the sign of the current. Thus, the pyro-electric current flows only while the temperature is changing—it is the way that intruder alarms, automatic doors and safety lights are activated. In an open circuit the free charges remain on the electrodes—and that has its uses too, described in the next section. Pyro-electric materials include minerals such as tourmaline (the one Theophrastus found), ceramics such as barium titanate, polymers such as polyvinylidene fluoride and even biological materials, such as collagen.
Fourier's Law:
Q = heat flow λ = Proportionality constant is thermal conductivity (lambda) ∆x = Distance heat travels ∆T = temperature gradient
Equation for Electrical Resistance
R = P × L/A R = resistance P = resistivity L = length A= area
List of Optical Properties
Refractive Index Absorption coefficient Reflectivity Fluorescence/Emission
Hardness describes how difficult it is to _______________ a material
Scratch
Elastic modulus AKA:
Stiffness The material's resistance to stretching, bending, or flexing, (For an axial loading geometry, this is called the Young's Modulus)
Yield Stress (σ₂) AKA
Strength or Yield Strength. The stress required to permanently deform the material. Ex: Plastically deform the material. So if σ Apply >σY then the materially will be permanently deformed.
Stress-free strain
Stress is not the only stimulus that causes strain. Certain materials respond to a magnetic field by undergoing strain—an effect known as magneto-striction. Others respond to an electrostatic field in the same way—they are known as piezo-electric materials. In each case a material property relates the magnitude of the strain to the intensity of the stimulus (Figure 4.5). The strains are small but can be controlled with great accuracy and, in the case of magneto-striction and piezo-electric strain, can be changed with a very high frequency. This is exploited in precision positioning devices, acoustic generators and sensors—applications we return to in Chapters 14 and 15. Figure 4.5 Stimuli leading to strain. A more familiar effect is that of thermal expansion: strain caused by change of temperature. The thermal strain εT is linearly related to the temperature change ΔT by the expansion coefficient, α: (4.14) where the subscript T is a reminder that the strain is caused by temperature change, not stress. The term 'stress-free strain' is a little misleading. It correctly conveys the idea that the strain is not caused by stress but by something else. But these strains can nonetheless give rise to stresses if the body suffering the strain is constrained. Thermal stress—stress arising from thermal expansion—particularly, can be a problem, causing mechanisms to jam and railway tracks to buckle. We analyse it in Chapter 12.
Equation for Linear Expansion Give an example of an alternative for the equation
The image is a Thermal Expansion Joint. ∆L = αLi∆T ∆L = Change in length α = CTE ∼10⁻⁶/C PP.M/C Li =Original length ∆T = Change in temperature Alternative: ∆L/∆i = ∞∆t
16.2 The interaction of materials and radiation 2.0
The intensity I of an e-m wave, proportional to the square of its amplitude, is a measure of the energy it carries. When radiation with intensity Io strikes a material, a part IR of it is reflected, a part IA absorbed and a part IT may be transmitted. Conservation of energy requires that The first term is called the reflectivity of the material, the second the absorptivity and the last the transmittability (all dimensionless). Each depends on the wavelength of the radiation, on the nature of the material and on the state of its surfaces. They can be thought of as properties of the material in a given state of surface polish, smoothness or roughness. In optics we are concerned with wavelengths in the visible spectrum. Materials that reflect or absorb all visible light, transmitting none, are called opaque, even though they may transmit in the near visible (infrared or ultraviolet). Those that transmit a little diffuse light are called translucent. Those that transmit light sufficiently well that you can see through them are called transparent; a subset of these that transmit almost perfectly, making them suitable for lenses, light-guides and optical fibres, are given the additional title of optical quality. Metals are opaque. To be transparent a material must be a dielectric.
Stress-Strain Curve
The linear regime of a stress-strain curve is the elastic portion. The slope is the elastic modulus. Past the linear regime is the non-linear or (plastic) regime Past another point is the ultimate tensile strength where it will fracture.
REMANENCE (Remanent magnetization)
The magnitude (intensity) of the retained permanent magnetization of a material. (how much magnetization remains after you remove the magnetic field). High remanence implies having a permanent magnet
Magnetic susceptibility
The materials property, but it is complex because it is a mathematical function of magnetic field (H)
Maximum Service Temperature
The maximum "useable" temperature for a material. Above this the material can "fail" in a number of ways. How it can fail: Melt Sag Break Corrode Decompose (polymers) A material can also lose a property (a magnetic property) Service temperature are often much lower than the melting temperature.
Ductility (εf)
The maximum amount of strain (%elongation) at failure. How does the material stretch before failure?
Poisson's Ratio (v)
The negative of the ratio of the transverse (lateral) strain (eₜ) to the axial (longitudinal) strain (ε) in axial tensile loading. v = - εₜ/ε
Magnetic fields in materials 1.0
The simplicity of this equation is misleading, since it suggests that M and H are independent; in reality M is the response of the material to H, so the two are coupled. If the material of the core is ferro-magnetic, the response is a very strong one and it is nonlinear, as we shall see in a moment. It is usual to rewrite equation (15.5) in the form
If a material is deformed elastically, which of the following must be true? a)The applied stress will exceed the yield point. b)The strain length of the material varies linearly with the applied stress. c) None of the above. d) A permanent deformation occurs.
The strain length of the material varies linearly with the applied stress.
Describe the graph of a soft magnet
The top of the graph is the saturation magnetization. This graph goes to zero once the magnetic field is released.
Refraction
The velocity of light in a vacuum, co = 3 × 108 m/s, is as fast as it ever goes. When it (or any other electromagnetic radiation) enters a material, it slows down. The index of refraction, n, is the ratio of its velocity in a vacuum, co, to that in the material, c:
Piezo-electric materials
The word 'Quartz' on the face of your watch carries the assurance that its time-steps are set by the oscillations of a piezo-electric quartz crystal. Piezo-electric behaviour is found in crystals in which the ions are unsymmetrically distributed (the crystal structure lacks a center of symmetry), so that each molecule carries a permanent dipole moment (Figure 14.15(a)). If you cut a little cube from such a material, with faces parallel to crystal planes, the faces would carry charge. This charge attracts ions and charged particles from the atmosphere just as a television screen does, giving an invisible surface layer that neutralises the charge. If you now squeeze the crystal, its ions move relative to each other, the dipole moment changes and the charge on the surface changes too (Figure 14.15(b)). Given time, the newly appeared charge would attract neutralising ions, but this does not happen immediately, giving a potential difference. This provides the basis of operation of electric microphones and pick-ups. The potential difference between the faces can be large—large enough to generate a spark across a narrow gap—it is the way that gas lighters work. A piezo-electric material has unsymmetrically distributed charge, giving it a natural dipole moment. The surface charge associated with this is neutralised by pick-up of ions, but if it is deformed, as in (b), the dipole moment changes and the surfaces become charged. The inverse is also true: a field induces a change of shape, the basis of piezo-electric actuation, as in (c). A strain, then, induces an electric field in a piezo-electric material. The inverse is also true: a field induces a strain. The field pulls the positive ions and pushes the negative ones, changing their spacing and so changing the shape of the crystal (Figure 14.15(c)). If a small strain produces a large field, then a large field will produce only a very small strain. But the strain is a linear function of field, allowing extremely precise, if small, displacements, used for positioning and actuation at the sub-micron scale. Piezo-electric materials respond to a change in electric field faster than most materials respond to a stimulus of this or any other kind. Put them in a megahertz field and they respond with microsecond precision. That opens up many applications, some described later in this chapter. In particular, it opens up the world of ultrasonics—sound waves with frequencies starting at the upper limit of the human ear, 20 kHz, up to 20 000 kHz and greater.
List of Cross Properties
Thermal Expansion Curie Temperature Electro-optic Coefficient Piezoelectric Coefficient Thermoelectric Pyroelectric Emissivity Electrochemical proeprties
Thermal expansion is a cross-property. It could be categorized as both a: a)Thermal and Mechanical property b)Chemical and Thermal property c)Chemical and Mechanical property d)Thermal and Electrical property e)Mechanical and Electrical property
Thermal and Mechanical property
Thermal Diffusivity (Dth)
Thermal diffusivity describes the rate at which a material "thermalizes" with the heat source (how long does it take to reach the same temperature as the heat source) If thermal conductivity is low, then portion of material near the source will heat up, but... heat will take a "long time" to reach rest of material. If heat capacity is high... it takes a "long time" to raise temperature of material. Materials "thermalizes" quickly if: λ is high + Cp low
12.1 Introduction and synopsis
Thermal properties quantify the response of materials to heat. Heat, until about 1800, was thought to be a physical substance called 'caloric' that somehow seeped into things when they were exposed to flame. It took the American Benjamin Thompson1, backed up by none other than the formidable Carnot2, to suggest what we now know to be true: that heat is atoms or molecules in motion. In gases, they are flying between occasional collisions with each other. In solids, by contrast, they vibrate about their mean positions; the higher the temperature, the greater the amplitude of vibrations. From this perception emerges all of our understanding of thermal properties of solids: their heat capacity, expansion coefficient, conductivity, even melting. Heat affects mechanical and physical properties too. As temperature rises, materials expand, the elastic modulus decreases, the strength falls and the material starts to creep, deforming slowly with time at a rate that increases as the melting point is approached until, on melting, the solid loses all stiffness and strength. This we leave for Chapter 13. Thermal design, the ultimate topic of this chapter, is design to cope properly with the effects of heat or, where possible, to exploit them. The chapter opening page shows an example: a copper heat exchanger, designed to transfer heat efficiently between two circulating fluids.
Possible Problems with CTE: Bimetallic Strips
Thin film delaminating a substrate because of large CTE mismatch. Common temperature change situations: seasons, time of day, inside/outside, altitude.
A material with high yield strength and high ductility would be considered "tough". True False
True
Acoustic Impedance (Z)
When sound travels from one material to another, the difference in the acoustic impedance determined how much of the sound is transmitted or reflected. You will have two materials. You need to use the formula proportional to "Z" to find your Z's. Once you find it you can then plug into your Acoustic reflection (R) and Acoustic Transmission (T) formulas. Large Z mismatch ---> Most sound is reflected @interface. Small Z mismatch ---> Most sound is transmitted into sound material .
Describe the graph of a hard magnet
When we release the magnetic field and we go to zero we still have some value present for magnetization. The remanence is from the top line of the graph to the x-axis. The coercive field is from the left linear side of the graph to the y-axis.
What happens to non-magnetic materials (paramagnetic, diamagnetic, and antiferromagnetic) when you apply a magnetic field and when you remove it?
When you apply a magnetic field the negligible interactions with most magnetic fields. Nothing happens when you remove the field.
Great Challenge
Which material should you choose
What happens to magnetic materials (ferromagnetic, ferrimagnetic) that are soft magnetic materials or hard magnetic materials in a magnetic field and when you remove the field.
With both soft and hard magnetic materials the material will become magnetizes. However, when you remove the field from the soft magnetic material it will demagnetize whereas the hard magnetic material will stay magnetized.
Measurement of Young's modulus
You might think that the way to measure the elastic modulus of a material would be to apply a small stress (to be sure to remain in the linear elastic region of the stress-strain curve), measure the strain and divide one by the other. In reality, moduli measured as slopes of stress-strain curves are inaccurate, often by a factor of 2 or more, because of contributions to the strain from material creep or deflection of the test machine. Accurate moduli are measured dynamically: by measuring the frequency of natural vibrations of a beam or wire, or by measuring the velocity of sound waves in the material. Both depend on , so if you know the density ρ you can calculate E.
Young's Modulus
a) Young's Modulus (E) (Axial Loading) b) Shear Modulus (G) (Shearing) C) Bulk Modulus (K) (Hydrostatic pressure) Water
In the design of a new aircraft, which materials selection and design decision for the wings is likely most appropriate: a)A new material with a higher yield strength is chosen so that the wing's thickness can be reduced (lightweighting) without compromising its load capacity. b)A new material with a lower yield strength is chosen so that the wing's thickness can be increased (lightweighting) without compromising its load capacity. c)A new material with a lower yield strength is chosen so that the wing's thickness can be reduced (lightweighting) without compromising its load capacity.0 d)A new material with a higher yield strength is chosen so that the wing's thickness can be increased (lightweighting) without compromising its load capacity.
a)A new material with a higher yield strength is chosen so that the wing's thickness can be reduced (lightweighting) without compromising its load capacity.
Which of these lists of material constants are all examples of mechanical/structural properties? a)Poisson's Ratio, Modulus of Resilience, Density3 b)Modulus of Resilience, Refractive Index, Hardness c)Hardness, Density, Heat Capacity d)Pyroelectric Coefficient, Poisson's Ratio, Refractive Index e)Hardness, Density, Refractive Index f)Dielectric Constant, Hardness, Ductility
a)Poisson's Ratio, Modulus of Resilience, Density3
In the history of humankind, why did humans work with bronze (the Bronze Age) prior to working with iron (the Iron Age)? a)Because bronze was considered "more beautiful" than iron. b)Bronze's lower melting temperature makes it easier to process than iron. c)Because copper and zinc (the elements that make-up bronze) are more abundant than iron. d)Because bronze is more valuable than iron.
b)Bronze's lower melting temperature makes it easier to process than iron.
Based on the classroom discussion, select the BEST description for the discipline of materials science & engineering (MSE): a) MSE designs new engineering systems. b) MSE both discovers new engineering components (e.g., turbines, crankshafts, etc.) and designs new systems with these components (e.g., aircrafts, vehicles, etc.). c) MSE both discovers new physical phenomena about materials and designs new engineering materials using these phenomena. d) MSE discovers new physical phenomena in materials.
c) MSE both discovers new physical phenomena about materials and designs new engineering materials using these phenomena.
The emissivity of a material determines the spectral intensities of light emitted from the material at a temperature above absolute zero. Thus, the emissivity is an example of a material constant that crosses which two classes of properties? a)Electrical and Thermal b)Optical and Magnetic c)Magnetic and Electrical d)Optical and Thermal e)Electrical and Optical
d)Optical and Thermal
If you know the composition of a material, then you can fully predict its properties. true false
false
You have been hired by a national defense agency to help design the sonar system for a new submarine. Your first project is to select a material to be used for a sonar detector which will be installed on an external wall of the submarine. The acoustic impedance of water is about 1.5 MPa-s/m. Which of the materials listed below would you select for the submarine's sonar detection panel and why? Acoustic Impedances: Material A: 20 MPa-s/m Material B: 0.1 MPa-s/m Material C: 2 MPa-s/m a)Material A because it has the largest acoustic impedance mismatch with water and will reflect the most sound. b)Material B because it has the smallest acoustic impedance mismatch with water and will transmit the most sound. c)Material C because it has the smallest acoustic impedance mismatch with water and will reflect the most sound. d)Material A because it has the largest acoustic impedance mismatch with water and will transmit the most sound. e)Material B because it has the largest acoustic impedance mismatch with water and will reflect the most sound. f)Material B because it has a lower acoustic impedance than water which will maximize the acoustic reflectance. g)Material C because it has the smallest acoustic impedance mismatch with water and will transmit the most sound.
g)Material C because it has the smallest acoustic impedance mismatch with water and will transmit the most sound.
Materials Science and engineering studies the
inter-relationships among Processing of Materials --> Structure of Materials --> Properties of Materials
Refractive Index (Index of Refraction)
is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density. The refractive index variable is most commonly symbolized by the letter n or n' in descriptive text and mathematical equations.
Sound is transmitted through materials as ______
longitudinal Strain waves (mechanical response)
Roughening the surface of a material (by, for example, rubbing the surface with sandpaper) is an example of... a)...modifying the material constant of a material that may change its performance for a given application. b)...modifying the material constant of a material in such a way as to have no influence on its performance in a given application. c)...modifying both the shape and material constant of a material. d)...modifying the shape of a material in such a way as to have no influence on its performance in a given application. e)...modifying the shape of a material in a way that may change its performance for a given application.
modifying the shape of a material in a way that may change its performance for a given application.
