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

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

Alloys

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

Types of Alloys

●Combination of two metals/elements­ Binary Alloy

● Combination of three metals/elements­ Ternary Alloy

●And so on

Classification of Metals alloys

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.

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

Allotropes of Iron

– Ferrite Alpha iron (α-Fe) T< 770 oC, Ferromagnetic, BCC

–Beta iron (β-Fe) T = 770 – 912 oC paramagnetic, BCC

–Austenite Gamma iron (γ-Fe) T = 912 – 1394 oC FCC

–Delta iron (δ-Fe) T = 1394 – 1538 oC BCC

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)

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

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

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 (415-550 MPa)

Medium Carbon Steel–Contain 0.25 – 0.6 wt % C

–Stronger than low- C steels but of low ductility and toughness

–Good wear resistance

Application: Railway wheel and tracks, gears, Crankshaft etc.

High Carbon Steel– 1.4 wt % C

– 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.

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 18-4-1 HSS: 18% tungsten, 4% chromium, 1% vanadium with a carbon content of 0.6 - 0.7%.Cobalt content of 0.6 - 0.7%Cobalt high speed steel-Increased heat resistanceMolybdenum high speed steel-Mo increases hardness and water resistance.

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% nickelApplicationFood processing equipmentsGas turbines partsHigh-temperature steam boilersHeat-treating furnacesNuclear power generating units.

Cast Iron

–Grey Cast Iron–Carbon content varies from 2.5-4.0 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 120 -280 MPa

Application: Based structures for machines and heavy equipment that are exposed to vibration

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.

Malleable Cast Iron

–Formed by heating white C.I between 800 – 900 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 = 350-450 MPa can be hammered to small thicknessApplicationConnecting rods, transmission gear, and pipe fittings, and valve parts.

Ductile or Nodular Cast Iron– Obtained by adding small amount of magnesium (0.1 – 0.8%) to the molten grey C.I (leading to the formation of graphite in the forms of spheres)

–Highly fluidity–High Tensile strength (400 - 900MPa)– Tough, wear resistant.–Good machinability and weldability

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.

Limitations of Ferrous alloys

–Relatively high density

–Comparatively low electrical conductivity

–An inherent susceptibility to corrosion in certain environment

Light Group (Non-Ferrous alloys)Aluminium–Crystal Structure: Face Centered Cubic (FCC)–Melting Points – 660 oC–Density: 2700 kg/m3 (Light)–Elastic Modulus 70 GPa–Silvery grey lustrous metal–High thermal & electrical conductivity

ApplicationsBeverage can, Sheet, wires

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 AlloysCommon alloying elements: Copper, Magnesium, Silicon, Manganese and Zinc.

Wrought Alloys

Series Alloying element1 xxx series Pure aluminium (min 99%)2 xxx series alloyed with copper (Duralium)3 xxx Series alloyed with manganese4 xxx Series alloyed with silicon5 xxx Series alloyed with Mg6 xxx series alloyed with Mg and Si7 xxx series alloyed with Zn8 xxx series other elements such as LiT-Series Heat treated

Titanium

–Pure Titanium- low density (4500 kg/m3)–High melting point (1660 oC)–Elastic Modulus 107 GPa–Tensile Strength 150 – 500 MPa

Appearance: Silvery grey-white metallic lustreAlloying required to reduce cost, increase strength and common phase

Applications: High strength & temperature components, biomedical, jewellery etc.

Two crystal forms; below 883 oC, alpha structure (HCP) and beyond 883 oC beta (BCC).

Four alloys: Alpha, Near Alpha, Alpha-Beta and Beta.

-Alpha Phase stabilizers: Al, Ga, Ge, C and NBeta Phase stabilizers: Mo, V, Ta, Nb, Mn, Fe, Cr and Co.

Zinc–Crystal Structure: Hexagonal close packed (hcp)–Melting points: 420 oC–Density: 7140 kg/m3

–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.

Heavy (Non-Ferrous alloys) Copper (Cu)

-Crystal structure: Face Centered Cubic (FCC)-Melting point: 1085 oC-Density: 8920kg/m3

-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.-99.99% pure copper used for wiring application.Possess around 97 % conductivity of silver (Ag) at 1/8th cost.

Copper alloysBrass: 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 tubeCartridge brass (~30% of Zn) Annunition carridge cases, automotive, radiators, lamp fixtures.

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 impurityPosses superior mechanical properties and corrosion resistance than brass.Comparatively hard and resist surface wear.

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.

Nickel (Ni)–Crystal Structure: Face centered Cubic (FCC)–Melting point: 1455 oC–Density: 8900 kg/m3

–Silvery-white lustrous metal with a slight golden colour.

ApplicationsNickel metal hydride metal rechargeable batteries.

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. 1100 oC) – turbine blade

Cobalt–Crystal structure: Hexagonal close packing–Density 8900 kg/m3

–Melting point-1495 oC–Elastic modulus – 209 GPaMain application: Production of high performance alloysCobalt based alloys are also corrosion and wear and wear resistant.Some high speed steel also contain Cobalt for increase heat wear-resitance.

Heusler Alloys

Definitions of Heusler alloy General Formula X

2YZ and XYZ

L21 Structure

C1b Structure

Heusler Alloys from the Periodic Table

X,Y are Transition metals and Z non­magnetic elements

Arrangement of Heusler alloys in crystals

ATOMIC_POSITIONS of L21

structureX 0.000000 0.000000 0.000000X 0.500000 0.500000 0.500000Y 0.250000 0.250000 0.250000Z 0.750000 0.750000 0.750000

ATOMIC_POSITIONS of C1b

structure X 0.00 0.00 0.00 Y 0.25 0.25 0.25 Z 0.75 0.75 0.75

Building Supercells

– Change unit of repetition to translational asymmetric unit via menuDisplay-->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 printedin the "ATOMS" section.

ATOMIC_POSITIONSFe 0.000000 0.000000 0.000000Fe 0.000000 0.500000 0.500000Fe 0.500000 0.000000 0.500000Fe 0.500000 0.500000 0.000000Fe 0.500000 0.500000 0.500000Fe 0.500000 0.000000 0.000000Fe 0.000000 0.500000 0.000000Fe 0.000000 0.000000 0.500000Ti 0.250000 0.250000 0.250000Ti 0.750000 0.750000 0.250000Ti 0.750000 0.250000 0.750000Ti 0.250000 0.750000 0.750000Al 0.750000 0.750000 0.750000Al 0.250000 0.250000 0.750000Al 0.250000 0.750000 0.250000Al 0.750000 0.250000 0.250000

ATOMIC_POSITIONSFe 0.000000 0.000000 0.000000Fe 0.000000 0.500000 0.500000Fe 0.500000 0.000000 0.500000Fe 0.500000 0.500000 0.000000Fe 0.500000 0.500000 0.500000Fe 0.500000 0.000000 0.000000Fe 0.000000 0.500000 0.000000Fe 0.000000 0.000000 0.500000Ti 0.250000 0.250000 0.250000Ti 0.750000 0.750000 0.250000Ti 0.750000 0.250000 0.750000Mn 0.250000 0.750000 0.750000Al 0.750000 0.750000 0.750000Al 0.250000 0.250000 0.750000Al 0.250000 0.750000 0.250000Al 0.750000 0.250000 0.250000

The crystal structure of Fe2TiAl and F e

2Ti

0.75 Mn

0.25Al Heusler alloys

ATOMIC_POSITIONSFe 0.000000 0.000000 0.000000Fe 0.000000 0.500000 0.500000Fe 0.500000 0.000000 0.500000Fe 0.500000 0.500000 0.000000Fe 0.500000 0.500000 0.500000Fe 0.500000 0.000000 0.000000Fe 0.000000 0.500000 0.000000Fe 0.000000 0.000000 0.500000Ti 0.250000 0.250000 0.250000Ti 0.750000 0.750000 0.250000Mn 0.750000 0.250000 0.750000Mn 0.250000 0.750000 0.750000Al 0.750000 0.750000 0.750000Al 0.250000 0.250000 0.750000Al 0.250000 0.750000 0.250000Al 0.750000 0.250000 0.250000

ATOMIC_POSITIONSFe 0.000000 0.000000 0.000000Fe 0.000000 0.500000 0.500000Fe 0.500000 0.000000 0.500000Fe 0.500000 0.500000 0.000000Fe 0.500000 0.500000 0.500000Fe 0.500000 0.000000 0.000000Fe 0.000000 0.500000 0.000000Fe 0.000000 0.000000 0.500000Ti 0.250000 0.250000 0.250000Mn 0.750000 0.750000 0.250000Mn 0.750000 0.250000 0.750000Mn 0.250000 0.750000 0.750000Al 0.750000 0.750000 0.750000Al 0.250000 0.250000 0.750000Al 0.250000 0.750000 0.250000Al 0.750000 0.250000 0.250000

ATOMIC_POSITIONSFe 0.000000 0.000000 0.000000Fe 0.000000 0.500000 0.500000Fe 0.500000 0.000000 0.500000Fe 0.500000 0.500000 0.000000Fe 0.500000 0.500000 0.500000Fe 0.500000 0.000000 0.000000Fe 0.000000 0.500000 0.000000Fe 0.000000 0.000000 0.500000Mn 0.250000 0.250000 0.250000Mn 0.750000 0.750000 0.250000Mn 0.750000 0.250000 0.750000Mn 0.250000 0.750000 0.750000Al 0.750000 0.750000 0.750000Al 0.250000 0.250000 0.750000Al 0.250000 0.750000 0.250000Al 0.750000 0.250000 0.250000

FIG. 9: The crystal structure of (a) Fe2TiAl and

(b) F e2Ti

0.75 Mn

0.25Al Heusler alloys

Spin Polarized Calculations

NM

FM

AFM

nspin = 2starting_magnetization(1) = 0.5, starting_magnetization(2)= 0.5,

Applications of Heusler Alloys

–spintronic –optoelectronic–

&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/

OPTICAL PROPERTIESThe complex refractive index and dielectric

constantThe 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

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:˜˜

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

Absorption spectra was calculated using the equation 12:

The optical conductivity is calculated from the equation:

Infrared Absorption I(ω) was calculated using:

and finally, we determined the reflection and transmission coe cients respectively through the use of the following ffiequations:

Elastic Constants

a1 = a(0 0.5 0.0), a

2 = a(0.5 0.0 0.5) and a

3 = a(0.5 0.5 0.0)

The elastic anisotropy is defined for cubic crystals by:

Young’s modulus Y can be evaluated using:

The Poisson’s ratio v can be obtained using:

Here, the shear modulus G is given as:

Thank you for your kind attention!