School Science Lessons
34. Materials, bridges, elasticity, crystals, environment pollution, heat treatment, mechanical properties, stress, Hooke's law
2012-05-12 SPwp
Please send comments to: J.Elfick@uq.edu.au
Table of contents
34.0.0 Materials science
34.6.1 Bridges
3.66 Cement
34.5.4 Coefficient of restitution
3.61 Construction materials
34.5.5 Crystal structure
34.4.0 Environment pollution
34.2.0 Heat treatment of metals
34.3.0 Materials from the earth
34.5.0 Mechanical properties of materials
35.4.0 Rocks and minerals, properties
34.5.3 Shear stress
34.5.2 Tensile and compressive stress
34.6.1 Bridges
34.6.1 Classification of bridges, (GIF)
34.6.2 Test the strength of a simple bridge
34.6.4 Truss systems, (GIF)
34.6.3 Simple cantilever, often used in the building of porches, (GIF)
34.5.4 Coefficient of restitution
34.5.4 Coefficient of restitution (coefficient of elasticity)
34.5.4.1 Bouncing balls, Silly putty, silicone, bouncing putty, (Dow Corning 3179 dilatant compound) "Tricky Putty"
34.5.4.2 Dead and live balls
3.4.1.0 Rubber, natural rubber, latex
34.5.5 Crystal structure
Order online: Nitinol Memory Wire, solid state chemistry
34.5.5.6 Crystal faults, crushing salt
34.5.5.5 Crystal growth in a film
34.5.5.2 Ice model
34.5.5.4 Ice nuclei
34.5.5.1 Solid models, sphere packing
34.4.0 Environmental pollution
34.4.5 Electrostatic precipitation
34.4.2 Noise sources, Test A
34.4.3 Noise control, Test B
34.4.4 Pollution from light of buildings
34.4.1 Pollution from noise, noise effects thinking and learning, white noise
34.2.0 Heat treatment of metals
34.2.2 Annealing
34.2.1 Heat treatment of needles
34.2.1.1 Heat treatment of razor blades or steel knitting needles
34.2.3 Quenching
34.2.4 Tempering
34.3.0 Materials from the Earth
34.3.0 Materials from the Earth
23.4.0 Materials at low temperature
3.66.3 Alkalinity of concrete
3.66.1 Change in weight of setting cement
35.21.0 Igneous rocks (Geology)
34.3.1 Lime (quicklime and slaked lime)
35.23.0 Metamorphic rocks (Geology)
35.2.0 Minerals, (different minerals), (Geology)
34.3.2 Prepare quicklime
35.3.0 Properties of minerals (Geology)
35.22.0 Sedimentary rocks (Geology)
35.5.0 Soils
3.66.2 Strength of cement with changing water content
3.65 Strength of mud, clay and sand bricks
3.67 Strength of plaster of Paris
34.3.3 Test for quicklime by slaking
34.5.0 Mechanical properties of materials
34.5.0 Mechanical properties of materials, elastic, ductile, malleable
34.5.1.5 Breaking strains, brittleness
34.5.03 Bulk modulus, modulus of incompressibility, K
34.5.01 Elasticity, (Tension, Compression, Shear)
34.5.02 Hooke's law, elastic limit, deforming force, stress and strain
34.5.06 Poisson's ratio, v
3.44 Potato masher squeeze (Primary)
34.5.05 Shear modulus, modulus of rigidity, G
34.5.1.3 Strain gauge
34.6.3 Strength of paper, relationship between the shape of material and its mechanical strength
34.5.1.2 Stretch a spring
34.5.1.1 Stretch a wire
3.4.1.1 Stretched rubber band
34.5.04 Young's modulus, linear modulus, elastic modulus, E
34.5.3 Shear stress
34.5.3.3 Plywood sheets
34.5.3.1 Shear book, foam block
34.5.3.2 Spring cube
34.5.3.4 Torsion rod, modulus of rigidity, bending and twisting
34.5.2 Tensile and compressive stress
34.5.2.5 Bending beams, bending the metre stick, rectangular bar under stress, different woods
34.5.2.8 Bologna bottle, squeeze the bottle
34.5.2.1 Breaking threads
34.5.2.9 Prince Rupert's Drops, tempered glass, toughened glass
34.5.2.6 Sagging board, aluminium / steel elasticity paradox
34.5.2.7 Stretch a hole, deformation under stress, stress on a brass ring
35.4.0 Rocks and minerals, properties
35.9 Cleavage, fracture, twin crystals, crystal face
35.5 Colour
35.8 Crystal systems, crystal habit, crystal form
35.11 Density (relative density) of minerals
35.13.6 Feel and conductivity
35.13.5 Grain size and roundness
35.10 Hardness, Mohs' scale of hardness
35.13.1 Hydrochloric acid test, effervescence
35.13.4 Luminescence
35.6 Lustre (metallic lustre, non-metallic lustre)
35.13.2 Magnetism test
35.13.3 Odour and taste
35.4.1 Mineral origin
35.13.7 Shape or form
35.12 Streak
35.13.8 Tenacity
35.12.1 Touchstone, gold streak
35.7 Transparency (transparent, translucent, opaque, refraction)
34.1.0 Alloys
Lower melting alloys. These may be produced by using a Bunsen burner. Where both bismuth and lead occur together in an alloy, the bismuth and lead are melted together, and then the other ingredients added. The temperature should not be higher than necessary to prevent excess oxidation. The parts shown are by weight. The higher melting alloys. e.g. bronze and brass, are produced in a furnace with the copper melted first and the other metals added.
Alloy Bi Cd Cu Pb Sn Zn
Wood's metal 7 1 - 4 2 -
Solder - - - 1 1 -
Electric fuse alloy 1.3 - - 8.5 2.5 -
Bronze - - 80 - 5 15
Brass. malleable - - 58 - - 42
Brass, casting - - 72 - 4 24
34.2.1 Heat treating needles
Heating steel material to "red heat" then cooling it slowly is called annealing. Putting steel material heated to red heat into cold liquid to cool it quickly is called quenching. Reheating steel material quenched to the temperature slightly lower than "red heat" temperature then cooling it slowly is called temper. Anneal, quenching and temper are heat treating material to change its rigidity, brittleness and toughness by changing the range of iron atoms. Annealing: This is a form of heat treatment to soften a metal and make it easier to work Annealing is often used to soften steel to relax its inner stress to change its shape by forging, pressing and machining. Obtain some sewing needles about four to 5 cm long. These needles are alloys of iron and carbon, but the proportion of carbon is very small. Try bending a needle. It is tough and springy. These properties of this carbon steel are dependent on the arrangement of the carbon
atoms among the iron atoms. The effect of annealing, quenching and tempering is to alter this arrangement in a specific way. Some types of razor blades can be used in place of the needles.
34.2.1.1 Heat treatment of razor blades or steel knitting needles
The properties of steel whether it is hard, tough, springy depend on the manner in which the steel has been treated previously and, in particular, on how it has been heated or cooled.
1. Hold one end of a razor blade in a pair of pliers and try to bend the other with a pair of pincers. The blade snaps because it is brittle, although the steel is extremely hard.
2. Hold one corner of a razor blade in a pair of pliers and heat it strongly over a Bunsen burner flame until it is red hot. When it has been red hot for half a minute make the flame gradually less hot and smaller, so that the blade cools down very slowly. The
gradual cooling should occupy at least five minutes. When the blade is cold it is found to have lost its hard and brittle character. It can now be bent easily without breaking, and it stays bent. This process of slow cooling is called “annealing” the steel.
3. Straighten the blade used in the foregoing experiment, and once more heat it until it is red hot. Have available cold water in an old cup or mug. When the blade has been red hot for a short time put it into the cold water. The rapid cooling in this treatment makes the blade hard and brittle.
4. Dry the blade after the quick cooling in the previous experiment. Rub it with emery paper until the surface is bright and clean. Holding the corner of the blade in the pliers. Heat it by holding it an inch above a medium Bunsen burner flame until a blue sheen just appears over the surface. Let the blade cool. It is now strong and springy. This moderate heating followed by cooling is called “tempering” the steel.
34.2.2 Annealing
1. Heat a needle to bright red heat. Hold it vertically in the flame and then very slowly raise it out of the flame taking about one minute. When it is cool, try bending it. It should be soft and easily bent round a pencil.
2. Use pliers to clamp a needle's tail and forcibly insert a needle into the hard block then try to bend the needle. You may find it is very difficult because the needle has strong rigidity and toughness. Now use the pliers to clamp its tail and place it on an alcohol burner to heat. About one minute later, its most part changes dark red. Lay it aside to cool slowly. When its temperature lowers to the room temperature, insert it into the block. You may find that it is easy to bend it.
34.2.3 Quenching
1. Neither the soft needle nor the brittle needle is very useful. However, the tough springy form can be restored. Heat and quench a needle as before to obtain the hard, brittle form. Carefully clean and shine the surface with emery cloth. The needle must now be heated very gently until a deep blue oxide film appears on the surface. This colour is an indication of the temperature at which the needle is tempered. When the needle is cool, try bending it. Is it tough and springy like the original needles?
2. Heat a needle to bright red heat and, while it is still hot, plunge it completely into cold water. Try to bend it now. It should be brittle and easily broken into small pieces.
3. Use the pliers to clamp the tail of another needle and heat it on an alcohol to dark red. Place it into cold water at a beaker to cool it quickly. Insert it into the block then bend it. You may find that it becomes very hard but brittle and easy to break.
34.2.4 Tempering
Polish the needle quenched at Test B with the sand paper then reheat it on the alcohol burner. When it becomes blue black, take it from the burner and lay it aside to cool slowly. When its temperature lowers to the room temperature, insert it into the block to bead it. You may find that it becomes tough.
34.3.0 Materials from the Earth, cement
1. Types of materials: 1.1 solid, liquid, gas, plasma, 1.2 crystals, fibres, fabrics, plastics, wood, 1.3 metals, non-metals, 1.4 polymers, acids/bases, 1.5 building materials
2. Properties of materials: 2.1 taste, odour, colour, 2.2 lustre, texture, acoustic 3. characteristics: 3.1 absorbent, porous, 3.2 transparent, translucent, opaque, 3.3 magnetic, non-magnetic, 3.4 density light / heavy, floats / sinks, 3.5 solubility 3.6 strength, hardness, flexibility, 3.7 viscosity, 3.8 conduction / insulation, 3.9 heat/electricity reactivity with other substances
1. Natural materials
1.1 Organic: 1.1.1 plants: wood, fibres, 1.1.2 animals: wool, leather, glue
2. Inorganic rocks, ores, minerals
2. Processed materials: metals, alloys, plastics, salts, synthetic fibres, paper, glass, brick, cement
3. Uses: building, tools, clothing, food, cleaning, medicine, recreation
4. Changes made to properties of materials to meet required uses
34.3.1 Lime (quicklime and slaked lime)
Chemical names: quicklime, calcium oxide; slaked lime calcium hydroxide. Chemical formula: quicklime CaO; slaked lime Ca(OH)2. The word “lime” is commonly used for both quicklime and slaked lime, and for convenience we shall consider the substances together. Quicklime is manufactured by roasting chalk or limestone in a lime kiln. It has the property of giving out a brilliant light when strongly heated, and fifty years ago was used for lighting stages (hence the phrase "to be in the limelight"). Slaked lime, or calcium hydroxide, is made from quicklime by adding water to the latter. This process is called “slaking” the quicklime. Slaked lime is used to make limewater and mortar; it is also used by gardeners to “sweeten” the soil.
34.3.2 Prepare quicklime
Use a lump of marble, chalk (not blackboard chalk), or limestone twice the size of a thimble, and 20 cm of iron wire. Copper wire is not suitable, because it melts with the heat. The wire used for tying up bundles of firewood answers the purpose. Tie one end of the wire round the lump and hold the other end in a pair of pliers or fasten it in a metal stand. Put a sheet of asbestos or a metal tray below the Bunsen burner in case the lump falls out of the wire. Suspend the lump just inside a very hot flame and heat it for ten to fifteen minutes. In a short time the lump begins to glow as quicklime forms. After heating let the lump to cool on the asbestos or metal. tray. Test the quicklime as described in the next experiment. Another method of making quicklime is to put the lump of marble, chalk, or limestone into a glowing fire with a pair of tongs and leave it there for twenty minutes. Quicklime can also be made from powdered chalk with the help of a home- made blowpipe, as described. The making of quicklime from marble, chalk, or limestone is represented by the following chemical action:
Calcium carbonate -> calcium oxide + carbon dioxide.
34.3.3 Test for quicklime by slaking
Put one or two small lumps of fresh quicklime into an evaporating dish or watch glass. Use a test-tube to add drops of water. Clouds of steam is produced, accompanied by a hissing noise. Finally the solid will break up into a fine, dry powder. The water has
combined chemically with the quicklime, and slaked lime remains. The word “quick” in quicklime means “alive” in "the quick and the dead" and “quicksands.” the superstitious people of the middle ages believed that quicklime was inhabited by a "spirit". When water was added to it the "spirit" was released and a "dead: substance remained. To this day, slaked lime is often called “killed lime.”
34.4.1 Pollution from noise, noise effects thinking and learning, white noise Often people use the word "sound" for something they want to hear, and "noise" for what they do not want to hear. In general, musical sounds are made up of a certain limited number of frequencies. They are regarded as sounds even though some people may not want to hear them. Motor traffic, aircraft and trains all produce a complex range of sounds of many unrelated frequencies at the same time. This is described as noise. It is a random mixture of sounds of different frequencies and amplitudes. Study the reasons causing noise and the ways lowering noise.
34.4.2 Noise sources, test A
Use a knock-down [be able to be dismantled] transformer. Install its primary coil and secondary coil well and let its iron core in not closed state (viz. do not install the upper iron frame). Turn on the AC electrical source for the primary coil and observe the vibration and sound of the iron core. Make the iron core closed but do not screw the screws tightly and note the change in sound. Screw the screws tightly. You may find noise lowers observably. Many noises are caused by disordered vibration of some components without being fixed well. Be careful not to touch the metal parts of the transformer because it carries AC of more than 36V. Place a plastic ruler on a tabletop flat and let it spread 1/3 long out of the table and vertical to the table rim. Press the end at the table with your left hand and take a press on another one with your right to make the ruler vibrate. Note the vibration on the tabletop and the noise
it emits. Place a large, thin, sponge pad under the ruler to separate the ruler and the table. Repeat the above experiment. You may hear only the sound the ruler vibrates. Adding some elasticity materials under vibrating objects may lower vibration noise effectively because elasticity materials may absorb vibration energy.
34.4.3 Noise control, test B
Use a small radio and a box Turn on the radio to the most volume. Place the radio into the box then cover its cap. Listen to the sound. You may find the sound decreases slightly.. Separately put some cotton, sponge and broken stones in the space between
the radio and box wall. Listen to the sound again. You may find cotton and sponge make the sound decrease more observably. Actually many spongy materials are sound absorption materials. If place them at the places transferring noise, they can lower noise
effectively.
34.4.4 Pollution from light of buildings
Many modern buildings' outside walls are decorated with glass mirrors. Thus there is much sunlight being reflected to fixed direction. The inhabitants living at the places opposite to the buildings are under the strong light pollution. For example, their rooms are hotter in summer, their children's eyesight lowers due to the strong light's stimulation. To study how reflected sunlight makes the temperature at a small space increase in summer obtain two same large boxes. For paper boxes, wrap a layer of thin heat insulation materials such as foam sponge and cotton pad to imitate the walls of a room. Cut a window at a side of each box, making sure the two windows with the same size. Shade the windows with transparent glass paper or plastic film. Place the boxes in the sunlight in summer but without sunlight shining in the boxes directly. Insert a thermometer into each box. Place a large mirror and adjust its position to
make reflected sunlight into a box through its "window". You may find the temperature at the box shined by reflected sunlight increases quickly. Carefully note the difference in temperature of the two "rooms" until the temperature at this box increases no longer.
Record the readings of the temperatures and calculate the difference in temperature between two boxes. Remove the transparent glass paper shading each window to imitate "opening windows to air". After a while, you may find the temperature at the
box shined by reflected sunlight decreases more slowly than another box. Carefully note the difference in temperature of the two "rooms" until the temperature at each box decreases no longer. Record the readings of the temperatures and calculate the difference in temperature between two boxes.
34.4.5 Electrostatic precipitation
See diagram: 34.4.3: Precipitators
To build a model to show the action of an electrostatic precipitator you need concentrated hydrochloric acid, concentrated ammonia solution, gas jar or measuring cylinder, test-tubes, thin metal rod, glass and plastic tubing, stoppers, induction coil and leads, aquarium pump and aluminium foil. The aluminium foil making up the outer electrode should be in the form of a cylinder inside the walls of the jar, but if you want to see what is happening inside, you may leave a space. Turn on the pump. Hydrogen chloride from the acid reacts with ammonia from the next test-tube to form a smoke of ammonium chloride. Notice the amount of smoke emerging from the
chimney. Gradually increase the flow of air from the pump then turn on the induction coil to supply the high voltage. Note any change in the smoke from the chimney.
34.5.0 Mechanical properties of materials, elastic, ductile, malleable
See 3.64: Heat treatment of steel needles, annealing, quenching, tempering
1. If forces are applied to a body remaining in equilibrium, the length volume or shape alters temporarily or permanently, i.e. it becomes deformed. If the forces applied to the body stop and the body regains its original length, volume and shape then the
deformation occurred within the elastic limit of the body. The magnitude of the elasticity of the body or the material comprising the body is expressed as a modulus of elasticity.
2. Ductility is the ability of metals or alloys to keep their strength and be permanently distorted and not crack or fracture when their shape is altered. Some ductile metals, e.g. copper, can be drawn through a die to reduce the cross-section by plastic flow and form wire, but other metals lose their strength and crack. Gold is among the most ductile metals. One gram of gold can be drawn into a wire 2 km long. The atoms of a ductile metal can slide past each other without causing the material to break into pieces. Also it can be hammered so finely that light can pass through it. Only metals are ductile.
3. A malleable metal can be hammered, pressed or extruded out of the original shape and not tend to return to the original shape or to fracture or break. Both ductile and malleable metals or alloys have large crystals. Metals have a regular pattern of fixed particles consisting of the nucleus of an atom and inner electrons around the atom. Outer electrons, (delocalized electrons, valence electrons) are held only loosely by the nuclei of the atoms so they can mover freely between the fixed particles allowing metals to have good heat conductivity and good electrical conductivity. Metals are malleable and ductile because distorting metallic crystals doe not completely break all the metallic bonds. Many metals have high melting points and high boiling points because their chemical bonds are strong. The greater the number of outer shell valence electrons the higher the boiling point.
34.5.01 Elasticity, (Tension, Compression, Shear)
Order online: Balloon Racer (Use elastic potential energy to power a racing car)
See diagram 34.5.0: Three types of stress, Hooke's law
The three types of stress
1. Tension: Equal and opposite forces acting away from each other along the same line of action that tend to elongate the body
2. Compression: Equal and opposite forces acting away towards each other along the same line of action that tend to shorten the body
3. Shear: Equal and opposite forces acting along different lines of action that tend to twist the body without changing its volume.
The amount of deformation is proportional to the applied stress only until the applied stress reaches the elastic limit. Within the elastic limit when the deforming force is removed the body returns to its original shape and volume. At some stage applied stress beyond the elastic limit the body can no longer be deformed and so it breaks. For example, stretch springs of copper and brass. The copper spring remains extended because it has reached its elastic limit.
34.5.02 Hooke's law, elastic limit, deforming force, stress and strain
See diagram 34.5.1: Young's modulus
Materials that recover their original shape after an applied force is removed show elastic deformation. Materials that do not recover their original shape after an applied force is removed show plastic deformation because the applied force was greater than
the elastic limit. Stress is the applied force per unit area of a material. Stress may cause a strain. Strain is the change in dimensions of a material / original dimensions of the material, e.g. change in volume per unit volume. Hooke's law states that, within the elastic limit, the stress is proportional to the strain. The constant of proportionality, elastic constant, for a material is called Young's modulus, E. With wires made of iron or annealed steels, at the elastic limit, (yield point), a sudden plastic deformation occurs. The wire "gives" and despite decrease of stress the wire does not return to its previous shorter length. Hooke's law does not apply to polymers or rubber. When a small stress results in a big strain, the material is soft. When a big stress results in a small strain, the material is
hard. When a small stress results in permanent deformation, the material is plastic. A modulus is a numerical quantity representing some quality of a substance equal to the ratio of the magnitude of the cause to the magnitude of its effect on the substance. The
bulk modulus of a material is often expressed for convenience in GPa, gigapascals.
1 gigapascal = 1000000000 pascal, 109 pa.
34.5.03 Bulk modulus, modulus of incompressibility, K
Compressive stress / Volumetric strain =
Deformed force per unit area / Change in volume per unit volume =
K. so K = (F/A) / (change in volume v / original volume V) =
PV /v = K
[Compressibility = 1/K]. Unlike gases, liquids and solids have little space between the particles so are difficult to compress. Solids are more difficult to compress than liquids. Some bulk modulus approximate values: steel 160 GPa, glass 35 -55 GPa, water 2.2 GPa, (so water is not completely incompressible!)
34.5.04 Young's modulus, linear modulus, elastic modulus, E
Linear stress / Linear strain =
Deforming force per unit area / Change in length per unit area =
(F/A) / (increase in length e / original length L) = FL/eA = E
Some Young's modulus values: steel 200 GPa, glass 65 GPa, aluminium 70 GPa, polystyrene 3 GPa.
The Young's modulus values of different types of chemical bonds can be measured:
Covalent bonds, e.g. C-C bonds 200 - 1000 GPa,
Metallic bonds, e.g. all metals 60 - 300 GPa,
Ionic bonds, e.g. Alumina, Al203 32 - 96 GPa,
Hydrogen bonds, e.g. Polyethylene 2 - 12 GPa,
Van der Walls bonds, e.g. waxes 1- 4 GPa.
34.5.05 Shear modulus, modulus of rigidity, G
Shearing stress /Shear strain = (F/A) / change in an angle of π/2 radians (90oC)
If forces are applied tangentially to the upper and lower surfaces of a cube causing the shape to change without change in volume, section of the cube at right angles to those two faces will have their angles changed from π/2 to (π/2 + θ) or (π/2 - θ).
Young's modulus is related to shear modulus, G, Poisson's ratio v, and bulk modulus,
K, by the formula: E = 2G(1+ v) = 3K(1-2v) = 9KG / (3K + G).
Solids have modulus K, modulus E and modulus G. Liquids have modulus E and modulus K only. Gases have modulus K only.
Some shear modulus values at room temperature: steel 79 GPa, glass 26 GPa, aluminium 25 GPa, polyethylene 0.117 GPa.
34.5.06 Poisson's ratio, v
A longitudinal pull in one direction produces an extension in that direction and a contraction at right angles to that direction. the stretched body becomes thinner. The ratio of the lateral contraction per unit breadth to the longitudinal extension per unit length in the line of the applied force is the Poisson's ratio for the material., v. Stretch a rubber hose to show lateral contraction with increasing length. Use a two-dimensional spring model to show Poisson contraction in crystals.
34.5.1.1 Stretch a wire
1. Pull on a horizontal spring with a spring scale. Use 2 metres of copper wire, e.g. 32 SWG, stretched by weights attached to the end the wire through a pulley. Plot a graph of load against extension of the wire. The graph is a straight line to show that Hooke's law applies, extension is proportional to stretching force. Take off weights and observe that the wire returns to its previous lengths at the same tensions.
2. Repeat the experiment by adding weights until the wire suddenly "gives" or "runs". This is called the yield point. The wire has stretch proportionally much more than previously for the load added. The wire can support heavier loads. However, when the
weights are removed, the wire can no longer return to its original lengths. At the yield point the wire had reached its elastic limit and Hooke's law no longer applies. In engineering, metal components should carry loads only within their elastic limits.
34.5.1.2 Stretch a spring
Add masses to a pan balance and measure the deflection with a vernier or cathetometer (travelling microscope). Examine the force / displacement curve at small extensions. Add 10, 20 and 30 newton to a large spring.
34.5.1.3 Strain gauge
Pull to various lengths a spring attached to a dynamic force transducer and show the resulting force on a voltmeter.
34.5.1.4 Ductility and elongation of metal
Use pieces or iron wire and copper wire. Beat the wire flat with a hammer to make them thinner. Note the thickness at which they break. Repeat the experiment with folded zinc and lead sheet.
34.5.1.5 Breaking strains, brittleness
A material distorted by forces acting on it is in a state of strain, is strained. So strain is the ratio: change in dimension / original dimension., and has no units.
Direct tensile or compressive strain = elongation or contraction / original length.
Shear strain causes a rectangle to become a parallelogram.
Volumetric strain, bulk strain = change in volume / original volume.
Approximate breaking strain in kg of some metals and wires hard-drawn through the same gauge (No. 23):
Copper, breaking strain 12 kg, Tin, breaking strain < 3 kg, Lead, breaking strain < 3 kg, Tin-lead (20% lead) 3 kg,
Tin-copper (12% copper) 3 kg, Copper-tin (12% tin) 40 kg, Gold (12% tin) 9 kg, Gold-copper (8.4% copper) 32 kg,
Silver (8.4% copper) 20 kg, Platinum (8.4% copper) 20 kg, Silver-platinum (30% platinum) 34 kg
However, the malleability, ductility, and power of resisting oxygen of alloys is generally diminished. The alloy formed of two brittle metals is always brittle. The alloys formed of metals having different fusing points are usually malleable while cold and brittle while hot. The action of the air on alloys is generally less than on their simple metals, unless the former are heated. A mixture of 1 part of tin and 3 parts of lead is scarcely acted on at common temperatures, but at a red heat it readily takes fire, and continues to burn for some time. Similarly, a mixture of tin and zinc, when strongly heated, rapidly decomposes both moist air and steam. Brittleness is the tendency for metals or alloys to have a brittle fracture when under tension, without plastic deformation, i.e. still keeping its shape. Brittleness mean a low value of fracture toughness, toughness. A brittle fracture is causes bu cracks leading to more cracks usually along certain crystal planes.
34.5.2.1 Breaking threads
1. Place a broom handle across two stools. Attach a thread to be tested to the centre of the broom handle. Attach the lower end of the thread to a large plastic bottle. Add water to the jar until the thread breaks. Note the volume of water needed to break the
thread
2. Add heavy masses to different threads until they break, e.g. cotton thread, copper wire (fuse wire), fishing line, dental floss, wool yarn, catgut, piano wire. Compare the breaking strain of the fishing line with this information on the packet.
34.5.2.3 Test the shear strength of thin sheets
See diagram 34.5.2.3: Clothes-pag tester
Cut sheets of material to be tested so that they just fit around a spring clothes peg, e.g. newspaper, paper towel, potato chip packet, thin plastic, cling film. All the sheets should have the same shape and area. Wrap each sheet around the spring clothes peg and squeeze the ends of the clothes peg handles with the thumb and first finger. Note which materials stretch or break.
34.5.2.5 Bending the metre stick, rectangular bar under stress, bending beams, different woods
Hang 2 kg from the centre of a metre stick supported at the ends. Place the metre stick on edge and then on the flat bending beam. Load a rectangular cross-section bar in the middle while resting on narrow and broad faces. Hang weights at the ends of
extended beams. Use beams of different lengths and cross-sections. Use different woods
34.5.2.6 Sagging board, aluminium / steel elasticity paradox
Place the ends of a thin board on blocks then add mass to the centre. Show that copper and brass rods sag by different amounts under their own weight but steel and aluminium do not.
34.5.2.7 Stretch a hole, deformation under stress, stress on a brass ring
See 2.05: Conic sections, ellipse
Stretch holes arranged a circle in a rubber sheet to deform into an ellipse. Paint a pattern on a sheet of rubber and deform by pulling on opposite sides. Use a strain gauge bridge to measure the forces required to deform a brass ring.
34.5.2.8 Squeeze the bottle
Fit a bottle with a stopper and a small bore tube. Squeeze the bottle and watch the coloured water rise in the tube.
34.5.2.9 Prince Rupert's Drops, tempered glass, toughened glass
Bubbles made by dropping molten glass into water. The shape is like that of a tadpole. If the smallest portion of the end of the tail is nipped off, the whole bubble explodes into fine dust. This novelty was introduced into England by Prince Rupert (1619 -
1682), grandson of James I. He also introduced Prince Rupert's metal, an alloy of brass.
Cool a drop of molten glass very quickly. Hit the round bulb of the glass with a hammer. It does not break. Break off the sharp tip of the drop. The glass shatters. This phenomenon is a form of tempered glass, (toughened glass) that are manufactured into sheets that break into small granular chunks instead of dangerous pointed shards. The sheets are used in buildings, telephone box windows and the side windows of cars. Car windscreens are made of laminated toughened glass. Another method of producing toughened glass for complex shapes, e.g. drinking glasses, involves treating glass in molten potassium nitrate.
Commercial:
Tumbler, toughened glass, 230 mL, pack / 6
34.5.3 Shear stress
Shear is a kind of deformation of materials where parallel plates of the material are displaced in a direction parallel to themselves, but the parallel plates remain parallel. So the adjacent planes of parallel plates slide over each other. If a shearing force is applied parallel to one side of a rectangle it becomes a parallelogram. Shear stress is the applied force divided by the area of the material parallel to the applied force, i.e. F / 1.
34.5.3.1 Shear book, foam block
Use a very thick book or stacks of cards to show shear. Push on the top of a large book or a large foam block to show shear.
34.5.3.2 Spring cube
A cube of cork balls fastened together with springs.
34.5.3.3 Plywood sheets
Use a stack of plywood sheets with springs at the corners to show shear torsion bending.
34.5.3.4 Torsion rod, modulus of rigidity, bending and twisting
Twist a rod by a mass hanging off the edge of a wheel. Wind a copper strip around a rod and then remove the rod and pull the strip straight to show twisting bending and twisting. Twist rods of various materials and diameters in a torsion lathe.
34.5.4 Coefficient of restitution (coefficient of elasticity)
1. Newton found experimentally that if two smooth spheres collide with velocities u1 and u2 and rebound with velocities v1 and v2 then - (v2 - v1) / (u2 - u1) is a positive constant, e, independent of the initial velocities, called the coefficient of elasticity or coefficient off restitution. The value of the constant e depends on the substances, e.g. 0.9 for glass and 0.2 for lead.
2. The coefficient of restitution can be used to measure of the elasticity of the collision between ball and racquet. Elasticity is a measure of bounce, i.e. how much of the kinetic energy of the colliding objects remains after the collision. With an inelastic collision, some kinetic energy is transformed into deformation of the material, heat, sound, and not available for movement. For a perfectly elastic collision, coefficient of restitution = 1, e.g. two diamonds colliding. For a perfectly plastic, i.e. inelastic, collision, coefficient of restitution = 1, e.g. two lumps of Plasticine (modelling clay) that do not bounce but stick together. The coefficient of restitution = difference in velocities of two colliding objects after the collision / difference in velocities of two colliding objects after the collision. For a racquet and ball, v1 = velocity racquet centre before impact, s1 = velocity ball before impact, v2 = velocity racquet centre
after impact, s2 = velocity ball after impact
Coefficient of Restitution = (s2 - v2) / (v1 - s1)
For a falling object bouncing off the floor, coefficient of restitution = √ (bounce height / drop height), e.g. for a particular bouncing ball, coefficient of restitution = 0.85
34.5.4.1 Bouncing balls, Silly putty, silicone, bouncing putty (Dow Corning 3179
dilatant compound) "Tricky Putty"
See 7.2.6: Silly putty
Drop balls of different material on plates of various materials. Observe loss of mechanical energy in the coefficient of restitution. Drop balls on a glass plate. Drop glass, steel, rubber, brass, and lead balls onto a steel plate. Drop rubber balls of differing elasticity and silly putty on a steel plate. Observe variation in coefficient of restitution n baseballs.
34.5.4.2 Dead and live balls
See 3.4.04: Super ball
Drop a black super ball and a ball rolled from a piece of wax. Make a non-bounce ball by filling a hollow sphere with iron filings or tungsten powder.
34.5.5.1 Solid models, sphere packing
Use tetrahedral and octahedral building blocks construct crystal shapes. Use Styrofoam balls and steel ball bearings to make crystal models. Stack balls on vertical rods mounted on a board to build crystal models. Build crystal models with a combination of compression and tension springs. Use old tennis balls glued together to show close-packed crystals. Examine lattice models of sodium chloride, calcium carbonate, graphite and diamond.
34.5.5.2 Ice model
Make ball and stick water molecules that you can stick together to make ice..
34.5.5.4 Ice nuclei
Let large ice crystals form on the surface of a supercooled saturated sugar solution.
34.5.5.5 Crystal growth in a film
Observe crystal growth on a freezing soap film through crossed Polaroid.
34.5.5.6 Crystal faults, crushing salt
Arrange one layer of small ball bearings between two Lucite, (perspex), sides. Examine natural faults in a calcite crystal then the single layer of small spheres model faults. Crush a large salt crystal in a big clamp
34.6.2 Test the strength of a simple bridge
See diagram 34.6.2: Simple beam bridge
1. Use C-clamps and blocks of wood to fix one piece of knotless wood (lathe), e.g. 0.5 cm × 5 cm × 60 cm, with the wider width (5 cm) down (flat board), between two tables 0.5 m apart. Use rope to attach an empty bucket to the centre of the bridge. Add sand to the empty bucket until the wood bends downward 1 cm at the centre. Weigh the bucket and sand. Add sand until the wood breaks. If the wood does not break just use the data Weight to bend down 1 cm.
2. Repeat the experiment decreasing and increasing the distance between the two tables to find the weight needed to bend the wood downward 1 cm and the weight to break the wood. All the pieces of wood must be free of knots.
3. Repeat the experiment with the narrower width (0.5 cm) down (vertical board).
4. Drill two holes vertically in the board and repeat the above experiments.
Distance between tables Weight to bend down 1 cm Weight to break wood
50 cm .
 .
55 cm .
 .
45 cm .
 .
34.6.3 Strength of paper, relationship between the shape of material and its
mechanical strength
See diagram 34.3.1: Folded paper, crossbeams
A flat piece of paper placed over two rods can support only light weight. However, if the piece of paper is folded into many alternate ditches and edges it can support heavier weight. Draw parallel lines on A4 paper 1 cm apart. Fold the paper alternately each way along the parallel lines. Cut out a 4 cm square of cardboard and put it on folded paper. Add weights to the cardboard or put an empty glass on it and add water until the paper begin to change its shape. Repeat the experiment with paper folds 0.5 cm apart and 2.0 cm apart. Compare the results of the two experiments. Crossbeams made of reinforced concrete are used in building construction as in diagram 34.3.1.(b), not as in diagram 34.3.1.
35.4.0 Rocks and minerals, classification, origin
A mineral has a definite chemical composition and may have a characteristic shape. A rock is a composite of more than one mineral. Pieces of the same rock might be composed of different minerals. Some rocks are composed of elements, e.g. gold or silver, but most rocks are combinations of elements in minerals. For example, the mineral quartz is a combination of the elements silicon and oxygen. Use the following testing and descriptive techniques to identify minerals.
Minerals can be classified as:
1. Elements
2. Sulfides (selenides, tellurides, arsenides, antimonides, bimuthides)
3. Halides
4. Oxides, hydroxides
5. Nitrates, carbonates, borates
6. Sulfates (chromates, molybdates, wolframates)
7. Phosphates, arsenates, vanadates
8. Silicates
9. Organic substances
35.4.1 Mineral origin
1. Crystallization from magma, e.g. magnetite, mica, quartz,
2. Physical, chemical and biological changes caused by weathering, e.g. serpentine, malachite
3. Sedimentary and evaporation processes, e.g. rock salt, calcite
4. Biological accumulation of salts, e.g. limestone, pyrite
35.5 Colour
The colour is an obvious physical property but it varies too much to be a reliable property for identification. However, rock colour charts are available, usually based on the "Munsell colour system". The names of some colours come from the characteristic colour of minerals, e.g. emerald, ruby, azure, amethyst. Quartz, calcite and rock salt are colourless if they do not contain impurities. However, some pure minerals may have different colours, e.g. fluorspar, apatite and beryl. The colour of some minerals may be changed by sunlight, artificial light, ultraviolet light, turning in the light, radioactivity, surface tarnish, heat, and dyes.
35.6 Lustre (metallic lustre, non-metallic lustre)
The lustre is the appearance of the surface of a mineral in reflected light, depending on the reflection and refraction of light. The lustre often distinguishes minerals from one another. Minerals are divided into two great groups on the basis of their lustre. One
group is opaque and has a metallic lustre like that of a metal. The other group may be opaque or transparent but does not have a metallic lustre. Most of the ore minerals have a metallic or a sub-metallic lustre. Others may be vitreous or glassy; resinous, like
resin; pearly or silky.
Minerals may be:
1. Opaque and with a metallic lustre, like a metal, e.g. pyrite, galena,
2. Opaque or transparent but without a metallic lustre, subdivided as: adamantine (diamond-like) lustre, vitreous (glassy) lustre, greasy (oily) lustre, dull lustre, silky lustre, e.g. asbestos and pearly lustre (layered).
A gem with changeable lustre, chatoyancy, is called a cat's eye, e.g. chrysoberyl, a form of quartz. The lustre of a diamond used in jewellery is called its "water". So the best diamonds are called "diamonds of the first water".
35.7 Transparency (transparent, translucent, opaque, refraction)
Transparent minerals allow passage of light without much deviation or absorption, like a window glass. You can read through a transparent mineral, e.g. quartz (rock crystal), rock salt, topaz. Translucent minerals allow passage of some light, but not images, like frosted glass used in bathrooms. Translucent minerals may be a transparent mineral containing impurities or finely granular transparent minerals. The minerals gypsum and mica may be translucent or opaque if finely granular but transparent if big crystals. Opaque minerals allow no passage of light and have a metallic or dull lustre. Each mineral has a characteristic refractive index. An anisotrtopic crystal may split incident light to produce double refraction, e.g. calcite crystal.
35.8 Crystal systems, crystal habit, crystal form
See diagram 35.8.1: Orthogonal axes
See diagram 35.8.2: Non-orthogonal axes, and 120o axes
See diagram 35.8.3: Tabular, prismatic, and pyramidal habit
See diagram 35.8 4: Crystal form of the seven crystal systems
See diagram 5.8.1: Orthogonal axes (Not labelled)
See diagram 5.8.2: Non-orthogonal axes (Not labelled)
See Diagram 5.8.3: Crystal form (Not labelled)
Most minerals are crystalline. The patterns of the internal atomic structures result in a definite external shape. Some minerals are amorphous, non-crystalline. However, silica, SiO2, may occur as quartz crystals, irregular sand grain crystals, fine grain chalcedony aggregate, and amorphous opal deposit.
Crystal habit refers to the relative width and length of the crystal faces (development of the faces of a crystal) and includes:
pyramidal, e.g. native sulfur, columnar, tabular (flat slab), e.g. mica, acicular (needle-like), fibrous, lamellar (plate-like), prismatic (elongated), e.g. most silicates.
Crystallographic axes can be described by looking at a crystal so that "axis a" is front to back, "axis b" is right to left, and "axis c" is top to bottom. Orthogonal axes are mutually at right angles, i.e. the cubic, tetragonal, and orthorhombic (rhombic) crystal systems. Non-orthogonal axes have one or more axes not at right angles to the others, i.e. the monoclinic and triclinic crystal systems. The hexagonal and trigonal crystal systems have three horizontal axes mutually at 120o and at right angles to the vertical, axis c. Let α = angle between axis b and axis c, β = angle between axis a and axis c, and γ = angle between axis a and axis b.
The seven crystal systems and examples of crystal form (geometric shape of the crystal):
1. Cubic (isometric): a = b = c, and α = β = γ = 90o, e.g. galena, garnet, halite, fluorite, magnetite, pyrite, sphalerite, uraninite
2. Tetragonal: a = b not = c, and α = β = γ = 90o, e.g. cassiterite, chalcopyrite, rutile, scheelite, zircon
3. Orthorhombic: a not = b not = c, and α = β = γ = 90o, e.g. barytes, marcasite, olivine, stibnite, sulfur
4. Monoclinic: a not = b not = c, and α = γ = 90o not = beta, e.g. augite, gypsum, hornblende, micas, orthoclase feldspar, serpentine, talc
5. Triclinic: a = b = c, and α not = β not = γ, e.g. axinite, plagioclase feldspar, rhodonite
6. Hexagonal: a = b not = c, and α = β = γ = 90o, e.g. apatite, beryl
7. Trigonal: a = b not = c, and α = β = γ not = 90o, e.g. ilmenite, tourmaline
35.9 Cleavage, fracture, twin crystals, crystal faces
See diagram 35.9: Twin crystals, striations, cleavage
1. Cleavage is the tendency to split along certain definite planes is a very useful distinguishing property reflecting the crystalline structure of a mineral and which can be related to the packing together of its atomic constituents. Minerals may cleave in
one, two, three or more directions with various degrees of perfection. A cleavage occurs when you can split a mineral in a plane parallel to a crystal face leaving a smooth flat surface along this planes. Some minerals have only one cleavage direction,
e.g. mica. Other minerals may have two or more cleavages. For example, galena has three cleavages. The direction of cleavage may be indicated by fine cleavage rifts running along the planes of cleavage. Some fine grain rocks have a cleavage, e.g. slate.
2. Fracture is any breakage or rupture other than a cleavage. Some minerals break evenly, others have an uneven or jagged hackly fracture. The fracture may feel even, uneven, jagged and conchoidal. Conchoidal is the shell-like pattern seen on chipped
glass. The fractures are curved as often in quartz.
3. Twin crystals may occur in a regular way with internal angles consistently at more than 180o, e.g. fluorite, gypsum, cassiterite.
4. Crystal faces may have characteristic striations, e.g. pyrite, quartz and tourmaline.
35.10 Hardness, Mohs' scale of hardness
Minerals differ greatly in hardness. The hardness refers to the resistance of a mineral to scratching, scratch hardness. The Mohs' scale of hardness (Friedrich Mohs 1773 - 1839) has a range from 1 (softest) to 10 (hardest). Hold a specimen of a mineral with forceps and try to scratch the following substances with it:
fingernail hardness 2.5,
piece of copper or copper coin hardness 3,
steel knife blade hardness 35.5,
window glass hardness 35.5 to 6.0,
steel file hardness 6, diamond hardness 10.
American coins have hardness 2.5 but the old "Indian heads" penny has hardness 3.35.
Hardness 7 substances produce sparks when hit with steel.
When hardness testing with glass, do not hold the glass in the hand but place it on a flat surface.
The Mohs' scale of hardness of minerals: 1. talc, 2. gypsum, 3. calcite, 35. fluorite, 35. apatite, 6. orthoclase feldspar, 7. quartz. 8. topaz. 9. corundum. 10. diamond.
The Mohs' scale of hardness of gemstones: topaz 7, emerald 8, sapphire 9, ruby 9, diamond 10.
This hardness test can be applied only to fresh unweathered specimens. The columnar mineral kyanite is unusual because has hardness 4-4.5 vertically but hardness 6-7 horizontally. Fibrous and porous aggregates may have a deceptively lower harness
because of the spaces between grains. Determining the hardness of earthy minerals, fine grain minerals and needle-shaped fibrous minerals is almost impossible.
Engineers do not use Mohs' scale. They define harness as resistance to indentation by a tool tipped with a pyramid-shaped diamond. The scales include "Vickers", "Rockwell" and "Knoop", in units of force (newton) / diameter2 of the indentation, at an angle of
136o. For example, the Australian "kangaroo" $1 Aluminium Bronze coin blanks have Vickers harness 80.
35.11 Density (relative density) of minerals
The relative density, r.d., of a mineral is a number that expresses the ratio between its mass and the mass of an equal volume of water at 4oC. If a mineral has a relative density of 2, it means that a given specimen of that mineral has twice as much mass as the same volume of water. Most common minerals have a relative density of 2.5 to 4.0.
The following substances have their densities expressed in g / cm3: sulfur: 2.0, quartz: 2.6, calcite: 2.7, copper: 8.9, lead: 11.35. Some ores are not uniform in density because they contain variable quantities of quartz, feldspar and other minerals, e.g. malachite, cassiterite and cerussite. Minerals less than 2.5 feel "light" and those more than 3.0 feel "heavy" for their relative size. The relative density of a mineral of fixed composition is constant and its determination is frequently an important aid in identification of the mineral. To find accurately the relative density of a mineral, it must be pure and it must also be compact, with no cracks or cavities where bubbles or films of air can exist.
35.12 Streak
The streak refers to the colour of the ground or powdered mineral and is sometimes a reliable test. To see the streak, rub the mineral on a ceramic streak plate or building tile or unglazed porcelain to leave a coloured scratch. Porcelain has Mohs hardness 6-6.5 so harder minerals will only leave a streak of white porcelain powder. Grind the harder minerals to see the streak colour. The colour of the streak may be different from the colour of the gross mineral in the ground. Colourless and white minerals always have white streak. Minerals with metallic lustre show the greatest difference between the true colour of the mineral and streak colour, e.g. black haematite gives a red streak powder. A mineral usually has a constant streak colour even if the colour of the mineral varies. So streak is much more reliable quality than colour of the mineral. The iron mineral haematite gives a brick-red streak and limonite gives a yellow streak.
35.12.1 Touchstone, gold streak
Touchstone is a form of schist used to assay gold by comparing the streak of the sample to the streak of "touch needles" with known gold content.
35.13.1 Hydrochloric acid test, effervescence
Cold, dilute hydrochloric acid or white vinegar (acetic acid, ethanoic acid) causes bubbles, effervescence, with sedimentary rocks containing mostly carbonates, i.e. limestone, e.g. calcite CaCO3, dolomite Ca(CO3).Mg(CO3), witherite BaCO3, malachite CuCO3Cu(OH)2.
35.13.2 Magnetism test
Note whether the powdered mineral is strongly or weakly attracted to a magnet, e.g. magnetite Fe3O4, attracts iron dust. Haematite becomes magnetic when heated.
35.13.3 Odour and taste
See 16.3.4.1b: Earth smells, rain smells and cut grass smells, geosmin
See 35.22.11: Argillaceous rock
Some minerals have a characteristic odour when rubbed, e.g. arsenopyrite FeAsS, fluorite. sulfur has a distinctive odour and clay minerals have an "earthy" smell. Minerals soluble in water have a characteristic taste. Some people claim that the amalgam fillings in their teeth allow them to taste certain minerals. A "metallic taste" in the mouth may be caused by antibiotics, drugs, oral diseases and even mercury poisoning. Usually the metallic taste disappears within days.
Some common examples include the following:
1. Chalcanthite, sweet metallic taste and slightly poisonous, CuSO4.5H2O, it is a water-soluble sulfate
2. Epsomite, Epsom salts, bitter taste, MgSO4.7H2O, hydrated magnesium sulfate
3. Glauberite, bitter and salty taste, Na2Ca(SO4)2, sodium calcium sulfate
4. Halite, rock salt, saline taste, NaCl
5. Hanksite, salty taste, Na22K(SO4)9(CO3)2, sodium potassium sulfate carbonate
6. Melanterite, sweet, astringent and metallic taste, FeSO4.7H2O, hydrated iron sulfate, Sylvite, (sylvine) bitter taste, KCl
35.13.4 Luminescence
Fluorescent minerals absorb ultraviolet light and emit longer wavelength visible light, e.g. scheelite. Phosphorescent minerals continue to emit light after the ultraviolet light ceases. Triboluminescent minerals emit light when squeezed, e.g. sphalerite. Calcite glows when heated. Thermoluminescent substance emit light when heated by do not themselves decompose chemically, e.g. calcium oxide (limelight), magnesium oxide, phosphorus (V) oxide (phosphorus pentoxide), fluorite, calcite.
35.13.5 Grain size and roundness
Measure size and roundness with a sand gauge. Size classification systems include the logarithmic "Wentworth scale" and the "USCS scale" (United Soil Classification System). For example, e.g. boulder > 256 mm, cobble 64 to 256 mm, pebble 4 to 64 mm, gravel (granule) 2 to 4 mm, sand 1/16 to 2 mm, silt 1/256 to 1/16 mm, and clay < 1/256 mm.
35.13.6 Feel and conductivity
Experienced handlers of minerals, e.g. gemstone workers, claim to be able to recognize minerals from the feel against the fingers or the cheek. For example they say that talc and graphite feel smooth and greasy while kaolin (China clay) and chalk feel rough and dry. Copper feels colder than amber against the cheek because copper is a better conductor of heat. Similarly, they can distinguish real gemstones from glass imitations by feel against the cheek.
35.13.7 Shape or form
Minerals may be. found in a number of different shapes. They may be crystals, parts of crystals or groups of crystals which may be just massive or grouped haphazardly or in a particular way. If the crystals radiate from a point we may call them radiating. They may form networks or be reticulated. Tree-like or moss-like shapes are described as mossy or dentritic. Many other descriptive terms are used to describe mineral aggregates.
35.13.8 Tenacity
Most minerals are brittle but some are sectile-cut easily with a knife; malleable flattened out under a hammer; flexible or elastic.