Advanced School on Applications of First Principles and Molecular Simulations in Physical Sciences

Transcription

1 Advanced School on Applications of First Principles and Molecular Simulations in Physical Sciences Simulations of metals and alloys Paul O. ADEBAMBO, Dept. of Physics, FUNAAB

2 Content Classification of Metals alloys Classification of ferrous alloy Type of steel Cast Iron Non ferrous alloys Light alloys Heavy alloys Methods of simulations of some basics properties of alloys

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4 Alloys In contrast to dope/doping (addition of impurity), an alloy is a combination of two or more metals/elements from the periodic table.

5 Types of Alloys Combination of two metals/elements Binary Alloy Combination of three metals/elements Ternary Alloy And so on

6 Classification of Metals alloys

7 Iron Iron was discovered over 3,000 years ago. It is by far one of the most common metal on earth. Iron is the most widely used of all metals. Its low cost and high strength make it indispensable in engineering applications such as the construction of machinery and machine tools, automobiles and structural components for buildings.

8 Carbon forms an Interstitial solid solution with Iron to form steel

9 Allotropes of Iron Ferrite Alpha iron (α-fe) T< 770 o C, Ferromagnetic, BCC Beta iron (β-fe) T = o C paramagnetic, BCC Austenite Gamma iron (γ-fe) T = o C FCC Delta iron (δ-fe) T = o C BCC

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11 Effect of increasing carbon content in steel are: Increasing in hardness and strength Decrease in weldability Decrease in ductility Decreased mechinability (about 0.2 to 0.25 wt. %C provides the best mechinablity)

12 Low alloys steel In addition to C alloying element Cu, V, Ni, Mo present. Total alloy concentration is around 10% Stronger than plain alloy Ductile, machinable Better resistance to corrosion than plain steel

13 Application in Beams, channels, nuts, bolts, wires, tin can etc.

14 Low Carbon Steel Contain less than about 0.25 wt. % C (mild steel) Relatively soft and weak Outstanding ductility and toughness High mechanability and weldability Least expensive to produce Tensile strength ( MPa)

15 Medium Carbon Steel Contain wt % C Stronger than low- C steels but of low ductility and toughness Good wear resistance Application: Railway wheel and tracks, gears, Crankshaft etc.

16 1.4 wt % C High Carbon Steel Hardest, strongest, and least ductile carbon steel Can be alloyed with carbon and other metals to form very hard and wear resistance material (e.g. Cr, Ni, W, Mo and V) Application: cutting tools, embossing dies, saw, concrete, drills etc.

17 High Alloy steel (> 10% wt % alloys): Tool steel Commonly used in drill bits and other rotating cutting tools. It can withstand higher temperature without losing its hardness and toughness. Examples HSS: 18% tungsten, 4% chromium, 1% vanadium with a carbon content of %. Cobalt content of % Cobalt high speed steel-increased heat resistance Molybdenum high speed steel-mo increases hardness and water resistance.

18 High Alloys steel-stainless steel Highly resistance to corrosion in a variety of environment. Pre-dominant alloy: Chromium (at least 11 wt %) Example 18/8 stainless steel i.e. 18% Chromium and 8% nickel Application Food processing equipments Gas turbines parts High-temperature steam boilers Heat-treating furnaces Nuclear power generating units.

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20 Cast Iron Grey Cast Iron Carbon content varies from wt % Graphites exist in the form of flakes Graphite flakes gives self-lubricating property and vibration damping capability Strength and ductility are much higher compressive loads Tensile Strength MPa Application: Based structures for machines and heavy equipment that are exposed to vibration

21 White/Chilled Cast Iron No graphite, Carbon in the form of Carbide Formed by rapidly cooling molten Iron Very hard, wear and corrosion resistant Almost non-machinable Application: Rollers in rolling mills.

22 Malleable Cast Iron Formed by heating white C.I between o C for a prolonged time in a neutral atmosphere (to prevent oxidation) leads to the decomposition of the cementire, forming graphite in the form of clusters. Highly shock resistance or tough Tensile Strength = MPa can be hammered to small thickness Application Connecting rods, transmission gear, and pipe fittings, and valve parts.

23 Ductile or Nodular Cast Iron Obtained by adding small amount of magnesium ( %) to the molten grey C.I (leading to the formation of graphite in the forms of spheres) Highly fluidity High Tensile strength ( MPa) Tough, wear resistant. Good machinability and weldability

24 Mottled or Compacted Cast Iron Product in between Grey and ductile C.I Carbon partly free and combined form Graphite has worm-like appearance Higher thermal conductivity Better resistance to thermal shock Lower oxidation at elevated temperatures Applications: diesel engine block, exhaust manifolds, gearbox housings, flywheel etc.

25 Relatively high density Limitations of Ferrous alloys Comparatively low electrical conductivity An inherent susceptibility to corrosion in certain environment

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27 Light Group (Non-Ferrous alloys) Aluminium Crystal Structure: Face Centered Cubic (FCC) Melting Points 660 o C Density: 2700 kg/m 3 (Light) Elastic Modulus 70 GPa Silvery grey lustrous metal High thermal & electrical conductivity Applications Beverage can, Sheet, wires

28 The success story of Aluminium Reduced Fuel Consumption Lower energy consumption and gas emissions through reduced weight Extensive use of Aluminium can result in up to 300 kg weight reduction in a medium size vehicle (1400 kg) For every 100 kg reduction in the automotive sector there is 200% lower exhaust emissions Proportionally reduced operating costs Aluminium Alloys Common alloying elements: Copper, Magnesium, Silicon, Manganese and Zinc.

29 Wrought Alloys Series Alloying element 1 xxx series Pure aluminium (min 99%) 2 xxx series alloyed with copper (Duralium) 3 xxx Series alloyed with manganese 4 xxx Series alloyed with silicon 5 xxx Series alloyed with Mg 6 xxx series alloyed with Mg and Si 7 xxx series alloyed with Zn 8 xxx series other elements such as Li T-Series Heat treated

30 Titanium Pure Titanium- low density (4500 kg/m 3 ) High melting point (1660 o C) Elastic Modulus 107 GPa Tensile Strength MPa Appearance: Silvery grey-white metallic lustre Alloying required to reduce cost, increase strength and common phase Applications: High strength & temperature components, biomedical, jewellery etc.

31 Two crystal forms; below 883 o C, alpha structure (HCP) and beyond 883 o C beta (BCC). Four alloys: Alpha, Near Alpha, Alpha-Beta and Beta. -Alpha Phase stabilizers: Al, Ga, Ge, C and N Beta Phase stabilizers: Mo, V, Ta, Nb, Mn, Fe, Cr and Co.

32 Zinc Crystal Structure: Hexagonal close packed (hcp) Melting points: 420 o C Density: 7140 kg/m 3 Silver grey lustrous appearance Easy castability Applications of Zn alloys -Galvanic coating on steel (hot-dip) -Corrosion protection of structure by attaching as sacrificial anode -Zinc carbon dry battery.

33 Heavy (Non-Ferrous alloys) Copper (Cu) -Crystal structure: Face Centered Cubic (FCC) -Melting point: 1085 o C -Density: 8920kg/m 3 -Distinctive reddish orange colour -Good corrosion resistance -soft, malleable, ductile and very tough -Good machinability -High electrical and thermal conductivity -Thermal conductivity order: Ag > Cu > Al % pure copper used for wiring application. Possess around 97 % conductivity of silver (Ag) at 1/8 th cost.

34 Copper alloys Brass: Contain zinc(zn) as a main substitutional impurity to 45 wt % Sn, Al, Si, Mg, Ni, and Pb are also added. -As Zn content increases, the strength hardness, ductility increases while the conductivity reduces. -Commercially used Brass is divided in two categories. α Brass (contain up to 30 % Zn) -Gun medal (~ 2% Zn) bearing, bushes -Gliding metal (~5% Zn) coins, medals and jewellery. -Admiralty brass (~28% Zn, 1% Sn) condenser, Evaporator and Heat exchanger tube Cartridge brass (~30% of Zn) Annunition carridge cases, automotive, radiators, lamp fixtures.

35 α + β Brass (more than 30% Zn) -Muntz metal (~ 40% Zn) valve stem, architectural works -Naval brass (39.25% Zn, 0.75 % Sn): Marine construction & propeller shaft) -Bronze: contains Tin (Sn) as a main substitutional impurity Posses superior mechanical properties and corrosion resistance than brass. Comparatively hard and resist surface wear.

36 Important of copper alloys are: Beryllium Copper (up to 3% Be)-highest resilence sprin, screwdrivers, pliers, wrenches. German silver (60% Cu, 20% Ni and 20% Zn) silvery appearance but no silver Ni increases electrical resistivity, improves strength and corrosion resistance.

37 Nickel (Ni) Crystal Structure: Face centered Cubic (FCC) Melting point: 1455 o C Density: 8900 kg/m 3 Silvery-white lustrous metal with a slight golden colour. Applications Nickel metal hydride metal rechargeable batteries.

38 Monel metal Primarily composed of Ni & Cu with traces of Fe, Mn, Si, and C Strong corrosion resistant. Heat exchanges tubes, food processing plant,etc applications Superalloys (Ni-Cr) high creep and oxidation resistance at elevated temperature (approx o C) turbine blade

39 Cobalt Crystal structure: Hexagonal close packing Density 8900 kg/m 3 Melting point-1495 o C Elastic modulus 209 GPa Main application: Production of high performance alloys Cobalt based alloys are also corrosion and wear and wear resistant. Some high speed steel also contain Cobalt for increase heat wear-resitance.

40 Heusler Alloys Definitions of Heusler alloy General Formula X 2 YZ and XYZ L2 1 Structure C1 b Structure

41 Heusler Alloys from the Periodic Table X,Y are Transition metals and Z non magnetic elements

42 Arrangement of Heusler alloys in crystals ATOMIC_POSITIONS of L2 1 structure X X Y Z ATOMIC_POSITIONS of C1 b structure X Y Z

43 Building Supercells Change unit of repetition to translational asymmetric unit via menu Display-->Unit of repetition >Translation asymmetric unit Generate the supercell via menu: Modify >Number of units drawn Save the XSF file via: File >Save XSF structure then in the so generated file the atoms within the supercell are printed in the "ATOMS" section.

44 ATOMIC_POSITIONS Fe Fe Fe Fe Fe Fe Fe Fe Ti Ti Ti Ti Al Al Al Al

45 ATOMIC_POSITIONS Fe Fe Fe Fe Fe Fe Fe Fe Ti Ti Ti Mn Al Al Al Al

46 The crystal structure of Fe 2 TiAl and F e 2 Ti 0.75 Mn 0.25 Al Heusler alloys

47 ATOMIC_POSITIONS Fe Fe Fe Fe Fe Fe Fe Fe Ti Ti Mn Mn Al Al Al Al

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49 ATOMIC_POSITIONS Fe Fe Fe Fe Fe Fe Fe Fe Ti Mn Mn Mn Al Al Al Al

50 ATOMIC_POSITIONS Fe Fe Fe Fe Fe Fe Fe Fe Mn Mn Mn Mn Al Al Al Al

51 FIG. 9: The crystal structure of (a) Fe 2 TiAl and (b) F e 2 Ti 0.75 Mn 0.25 Al Heusler alloys

52 Spin Polarized Calculations NM FM AFM nspin = 2 starting_magnetization(1) = 0.5, starting_magnetization(2)= 0.5,

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54 spintronic optoelectronic Applications of Heusler Alloys

55 &bands prefix='xyz' outdir='./' no_overlap=.true. filband= 'XYZbandsup.dat' spin_component = 1 / &bands prefix='xyz' outdir='./' no_overlap=.true. filband= 'XYZbandsdown.dat' spin_component = 2 /

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57 OPTICAL PROPERTIES The complex refractive index and dielectric constant The absorption and refraction of a medium can be described by a single quantity called the complex refractive index. This is usually defined through the equation: We can relate the refractive index of a medium to its relative dielectric constant by using the standard result derived from Maxwell s equations

58 This shows that if n is complex, then relative dielectric constant must also be complex. We therefore define the complex relative dielectric constant according to: By analogy with eqn 2, we see that complex refractive index and relative dielectric constant are related to each other through: We can now work out explicit relationships between the real and imaginary of part of complex refractive index and relative dielectric constant by combining eqns 1, 2 and 3. These are:

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60 Note that if the medium is only weakly absorbing, then we can assume that K is very small, so that eqns 5 and 6 simplify to: The reflectivity depends on both n and K and is given by

61 Absorption spectra was calculated using the equation 12: The optical conductivity is calculated from the equation:

62 Infrared Absorption I(ω) was calculated using: and finally, we determined the reflection and transmission coefficients respectively through the use of the following equations:

63 Elastic Constants a 1 = a( ), a 2 = a( ) and a 3 = a( )

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68 The elastic anisotropy is defined for cubic crystals by: Young s modulus Y can be evaluated using:

69 The Poisson s ratio v can be obtained using: Here, the shear modulus G is given as:

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71 Thank you for your kind attention!