WS Structure and Properties of Pure Iron- iron, bcc - iron, bcc Effect of pressure on the equilibrium phase diagram of pure iron. Under atmospheric conditions, the hcp phase may be

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Lecture 2

Structure and Properties

of Pure Iron

Dr. Javad Mola

Institute of Iron and Steel Technology (IEST)

Tel: 03731 39 2407

E-mail: [email protected]

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Elemental Iron

Atomic number: 26

Atomic radius: 0.124 nm

Atomic mass: 55.845 g/mol

No. of neutrons: 28, 30, 31, 32 (5.84%,

91.75%, 2.12%, 0.28% respectively)

Density: 7.870-7.876 g/cm3

Fe

Orbital filling order for Fe atoms: 1s22s22p63s23p63d64s2

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Fe Allotropes under Atmospheric Pressure

1300

1600

1100

1500

900

1400

700

1200

500

1000

300

800

200

600

100

400

0

Te

mp

era

ture

, °C

Ferromagnetic - Fe or Ferrite (BCC)

- Fe or - Ferrite (BCC)

Paramagnetic - Fe or - Ferrite (BCC)

- Fe or Austenite (FCC)

Im3m symmetry

Im3m symmetry

Fm3m symmetry

Im3m symmetry

Liquid Fe

769 °C

911 °C

1392 °C

1536 °C

Curie Temperature (Tc, or A2)

Hans-Joachim Eckstein, Wärmebehandlung von Stahl, VEB Leipziger Druckhaus, Leipzig, 1969.

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Thermodynamic Stability

G

G

Gibbs free

energy (G)

Temperature

- Fe

- Fe

- Fe

A3 A4

At any given temperature and pressure, the phase with the lowest Gibbs free

energy has the highest thermodynamic stability.

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Stability of Fe Allotropes at High Pressures

2000

1200

800

400

0

1600

25 50 75 100 125 150 175

Pressure, kbar

Tem

pera

ture

, °C

Liquid iron

- iron, fcc

- iron,

hcp - iron,

bcc

- iron, bcc

Effect of pressure on the equilibrium phase diagram of pure iron.

Under atmospheric

conditions, the hcp phase

may be stabilized by adding

certain alloying elements

such as Mn.

Atmospheric

pressure, 1 bar

15 GPa

D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, Chapman & Hall, London, 1992.

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Body-centered cubic

(BCC), Im3m symmetry

Face-centered cubic

(FCC), Fm3m symmetry

BCC and FCC Crystal Structures

a

~ 0.360 nma

~ 0.288 nm

Coordination number

(number of nearest

neighbor atoms)

BCC FCC

8 12

Atomic packing factor

(volume fraction

occupied by atoms)

BCC FCC

0.68 0.74

National University of Singapore blog: http://blog.nus.edu.sg/kyawthetlatt/files/2013/08/h12_27-1xstpdn.jpg

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Close-Packed Planes and Directions

Body-centered cubic (BCC), Im3m symmetry

<110>: close-packed direction

in FCC <111 >: close-packed

direction in BCC

{111} plane

(maximum

possible

packing

density

{110}

plane

Face-centered cubic (FCC), Fm3m symmetry

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Interstitial SitesBCC FCC

Regular (all faces are equilateral triangles)

Tetrahedral sites

Octahedral sites

Irregular (faces are not equilateral triangles)

8 sites

per unit cell

12 sites

per unit cell

4 sites

per unit cell

6 sites

per unit cell

V. Läpple, Wärmebehandlung des Stahls: Grundlagen, Verfahren und Werkstoffe, 9., veränd. Aufl., Europa-Lehrmittel, Haan-Gruiten, 2006.

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Interstitial Sites

FCC BCC

Octahedral Tetrahedral Octahedral Tetrahedral

Sites per unit cell 4 8 6 12

Sites per Fe atom 1 2 3 6

Diameter of interstitial space, nm 0.1044 0.0568 0.0388 0.0734

Tetr

ah

ed

ral

Octa

hed

ral

BCC FCC

ElementAtom

diameter𝒅𝒂𝒕𝒐𝒎 , nm

𝒅𝒂𝒕𝒐𝒎𝒅𝜸𝒐𝒄𝒕.

𝒅𝒂𝒕𝒐𝒎𝒅𝜶𝒐𝒄𝒕.

H 0.092 0.88 2.37

B 0.174 1.67 4.48

C 0.154 1.47 3.97

N 0.142 1.36 3.66

O 0.120 1.15 3.09

V. Läpple, Wärmebehandlung des Stahls: Grundlagen, Verfahren und Werkstoffe, 9., veränd. Aufl., Europa-Lehrmittel, Haan-Gruiten, 2006.

In spite of the smaller size of octahedral sites, they are preferred

interstitial sites in bcc. This is related to the irregularity of octahedral sites

which enables to host interstitial atoms by a uniaxial expansion.

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0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040

1E-44

1E-38

1E-32

1E-26

1E-20

1E-14

1E-8

Dif

fus

ion

Co

eff

icie

nt,

cm

2.s

-1

1/T, K-1

G

A3 TC

𝐷 = 𝐷0 . 𝑒−𝑄𝑅𝑇

D0: Pre-

exponential factor

Q: activation

energy for

diffusion

R: universal gas

constant

T: absolute

temperature, K

D0=0.5 cm/s

Q=239.5 kJ/mole

D0=0.18 cm/s

Q=270 kJ/mole

D0=1.90 cm/s

Q=239.5 kJ/mole

Diffusivity

Self-diffusion (iron diffusion in iron lattice) is faster in bcc-iron with a lower

atomic packing factor (lower density).

273 K

Higher temperatures

B.C. De Cooman, J.G. Speer, Fundamentals of Steel Product Physical Metallurgy, Association for Iron and Steel Technology, Warrendale, 2011.

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Diffusivity

5

Inverse Temperature, 104 K-1

Dif

fus

ion

Co

eff

icie

nt,

cm

2. s

-1

6 7 8 9 10 11

1600 1400 1200 1000 800 600

Temperature, °C

Interstitial

diffusion

Substitutional

diffusion

Diffusion in

BCC-Fe faster

than in FCC-Fe

Diffusion of

interstitial

elements faster

than

substitutionals

B.C. De Cooman, J.G. Speer,

Fundamentals of Steel Product

Physical Metallurgy,

Association for Iron and Steel

Technology, Warrendale, 2011.

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HCP Crystal Structure

Close-packed

layer of spheres

ABAB layer stacking

ABCABC layer stacking

Hexagonal Close-Packed

Face-Centered Cubic

Fm3m symmetry

P63/mmc symmetry

http://www.learneasy.info/MDME/focus/materials/enmat/LECTURES/Lecture-04/webpages/crystals.html

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Lattice Parameter

BCC

FCC

a

~ 0.360 nm

a

~ 0.288 nm

Latt

ice P

ara

mete

r, n

m

Temperature, °C

0 400 800 12000.28

0.30

0.32

0.34

0.36

0.38

Hans-Joachim Eckstein, Wärmebehandlung von Stahl, VEB Leipziger Druckhaus, Leipzig, 1969.

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Lattice Parameter

Temperature, K

Latt

ice c

onsta

nt

(nm

)

Latt

ice c

onsta

nt

(nm

)

Temperature, K

α γ

Lattice parameters of α-iron and γ-iron based on high

temperature X-ray diffraction measurements

Seki I, Nagata K. Lattice Constant of Iron and Austenite Including Its Supersaturation Phase of Carbon. ISIJ Int 2005;45:1789–94.

- Fe

a=0.2860 + 1.60210-9 T2 + 2.05910-6 T (in the temperature range 295-1183 K)(temperature in kelvin, lattice parameter in nm)

- Fe

a=0.35519 + 8.159310-6 T (in the temperature range 1183-1550 K)(temperature in kelvin, lattice parameter in nm)

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Lattice Parameter and Atomic Volume

PhaseTemp.,

°CLattice parameter a,

nmAtomic Volume Va,

10-3nm3

Molar volume, cm3/mol

22 0.286 a3/2=11.697 7.046

22 0.3562 a3/4=11.295 6.802

22a=0.2523, c=0.4044, c/a=1.603

a2c(cos30)/2=11.15 6.714

Reduced

atomic

volume,

increased

atomic

packing density

γ αcontraction expansion

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Packing Factor vs Atomic Volume

- Fe

Calculated atomic packing factor (APFbcc)= 0.68

Measured atomic volume (AV)= 11.7 10-3 nm3

- Fe

Calculated atomic packing factor (APFfcc)= 0.74

Measured atomic volume (AV)= 11.3 10-3 nm3

Theoretical AVα / AV = 1.088

Approximate experimental AVα / AV = 1.035

The atomic volumes of ferrite and austenite are closer than the values predicted

based on the atomic packing factors of fcc and bcc structures. The reason for this

discrepancy is that the atomic radius of iron in the bcc structure is slightly smaller

than that in the fcc structure (check this with the lattice parameters of austenite and

ferrite given in the previous slide). This reduces the AVα / AV to below 1.088.

Ferrite:Austenite:

A

BD

Cdistance AB ≠ distance CD

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Thermal Expansion

A4

TCurie

A3

Reduced thermal expansion in the

vicinity of TC

0 500 1000 1500

Temperature, K

Coefficient of Thermal Expansion (CTE or ) for -Fe smaller than -Fe

CTE of -Fe almost independent of temperature at temperatures above RT

Lower CTE is associated with a better dimensional stability.

calc.

Pepperhoff W, Acet M. Constitution and Magnetism of Iron and Its Alloys. 1st ed. Springer; 2001.

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Thermal Expansion

Atomic volume (volume per atom)

A3

TC

A4

Ac3

Experimental dilatometry length

changes for an interstitial-free

steel (IF steel or a steel with

almost no C and N, i.e. almost pure

iron). Note the steeper slope in the

range.

Pepperhoff W, Acet M. Constitution and Magnetism of Iron and Its Alloys. 1st ed. Springer; 2001.

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Thermal Conductivity

Thermal conductivity

of pure iron

Th

erm

al c

on

du

cti

vit

y, W

att

m-1

K-1

20

40

60

80

100

Temperature, K

0 400 800 1200 1600

TC A3

Recommended trend

Commercial austenitic steels have a lower thermal conductivity than their ferritic

counterparts.

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Mechanical Properties

Annealing treatment Yield strength

at 0.2% offset,

MPa

Ultimate

Tensile

Strength, MPa

Reduction in

area, %

Elongation, %

Temp., °C Time, h

870 1.5 86-128 203-252 81-91 37-42

870 4 56-59 197-205 85-94 36-46

1000 1.5 41-54 191-206 91-93 36-41

Modulus of elasticity

Cold-worked: 194 GPa

Annealed 1.5 h at 870 °C: 197 GPa

High-purity iron

Tensile properties

H.E. Cleaves, J.M. Hiegel, Properties of high-purity iron, Journal of Research of the National Bureau of Standards, vol. 28, 1942, 643-667.http://nvlpubs.nist.gov/nistpubs/jres/28/jresv28n5p643_A1b.pdf

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Magnetic Properties: Dia- and Para-MagnetismD

iam

ag

neti

sm

Pa

ram

ag

neti

sm

In the absence of an external field, no dipoles exist in a diamagnetic material; in the

presence of a field, dipoles are induced that are aligned opposite to the field direction.

Examples are water, wood, copper, mercury, gold, and bismuth.

In the absence of an external magnetic field, the orientations of atomic magnetic moments in a

paramagnetic material is random and there is no net macroscopic magnetization. These

atomic dipoles are free to rotate, and paramagnetism results when they preferentially align

with an external field. Examples are magnesium, molybdenum, lithium, and tantalum.

Weakly repelled by magnetic fields

Weakly attracted to magnetic fields

William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetic Properties: Ferromagnetism

Certain metallic materials possess a permanent magnetic moment in the absence

of an external field, and manifest very large and permanent magnetizations. These

are the characteristics of ferromagnetism, and they are displayed by the

transition metals iron, cobalt, nickel, and some of the rare earth metals such as

gadolinium (Gd). Ferromagnets are noticeably attracted to magnetic fields.

Schematic illustration of the

mutual alignment of atomic

dipoles for a ferromagnetic

material, which will persist

even in the absence of an

external magnetic field.

Plot of saturation magnetization as a

function of temperature for iron and

Fe3O4.

TC

for p

ure

Fe


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Magnetic Domains

Gradual change in magnetic dipole

orientation across a domain wall

Domains in a ferromagnetic material; arrows

represent atomic magnetic dipoles. Within each

domain, all dipoles are aligned, whereas the

direction of alignment varies from one domain to

another. The net macroscopic magnetization is

the average of all domains.


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Magnetization Process

Domain configuration during several stages of magnetization of a ferromagnetic

material.

Growth of domains that are oriented in directions nearly parallel to the applied magnetic field (H)

Domain rotation and alignment with the direction of the applied magnetic field (H)


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Magnetization Cycle and Hysteresis

The hysteresis loop is represented by the solid red curve; the dashed blue curve indicates

the initial magnetization. The area within a loop represents the magnetic energy loss per

unit volume of material per magnetization-demagnetization cycle; this energy loss is

manifested as heat that is generated within the magnetic specimen and is capable of

raising its temperature.

Remanence, Br

Coercive force, Hc

Soft magnet

(easily

magnetized-

demagnetized)Hard magnet

(high resistance to

demagnetization)William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetic (Magnetocrystalline) Anisotropy

111

100

110

<100>, easy magnetization direction

Iron

Nickel

<110>

<111>

Anisotropy of magnetization behavior in Fe and Ni single crystals with

their <100>, <110>, and <111> crystallographic axes parallel to the

external magnetic field (H) direction.

easy

magnetization

direction


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Iron-Base Transformer Cores

Fabrication process of silicon steels used in transformer cores (typically

Fe-3 mass-%Si steel) aims at developing a texture in which the <100>-

type directions of sheets are parallel to the direction of magnetization.

<001>


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Documents

WS Structure and Properties of Pure Iron- iron, bcc - iron, bcc Effect of pressure on the equilibrium phase diagram of pure iron. Under atmospheric conditions, the hcp phase may be