mse 342f chapter # 4 properties part i 2014-15

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Properties of 3-D Nanomaterials

(Chapter # 4 Part I)

Uwe Erb Materials Science and Engineering,

University of Toronto, Toronto, Ontario, Canada.

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Before looking at details of properties you should consider that there are structurally three different types of 3-D nanomaterials.

1) Consolidated Powder Materials

These materials have been prepared by two-step processes. First nanopowders are made by techniques such as inert gas condensation, ball milling or chemical precipitation. In the second step these particles are consolidated under high pressures and at elevated temperatures. There is considerable residual porosity in these materials in addition to grain boundaries and tripe junctions.

2) Fully Dense Equiaxed Materials

These materials are made in one step such as electrodeposition or severe plastic deformation. The materials are usually fully dense with negligible porosity. Grain boundaries, triple junctions (and dislocations) are the main defects.

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3) Nanocrystallized Materials

The materials are produced by crystallization of amorphous precursor material. In addition to grain boundaries and triple junctions they contain residual amorphous matrix.

The properties of these materials are not always the same and direct comparisons are sometimes difficult.

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Consolidated Powder Material

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Fully Dense Equiaxed Material

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Nanocrystallized Material

amorphous

crystalline

clusters

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Thermal Stability

Nanomaterials contain very high interface contents (e.g. surfaces in 0-D nanomaterials, grain boundaries in 3-D nanomaterials). The associated interfacial energy gives the nanomaterial a very high driving force for crystal or grain growth. Therefore, for any nanomaterial, one of the key questions is their thermal stability with increasing temperature.

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Grain Growth in Conventional Materials

W.D. Callister, 6th ed., Materials Science and Engineering, Willey, NY, 2003

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Grain Growth in Conventional Materials

L.H. van Vlack, Elements of Materials Science and Engineering, 3rd ed., Addison-Wesley, Reading, MA, 1975

Larger grains grow Smaller grains shrink

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Driving Force for Grain Growth

Curvature Induced

L.H. van Vlack, Elements of Materials Science and Engineering, 3rd ed., Addison-Wesley, Reading, MA, 1975

Higher coordination number in growing grain

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Driving and Dragging Forces

Driving Force

Curvature Induced F ~ / d

Dragging Forces

Solute Drag F ~ C0 / r

Zener Drag F ~ f / R

interfacial energy r atomic radius of solute

d average grain size R particle diameter

C0 average concentration f particle volume fraction

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Normal Grain Growth Kinetics

dn – don = Kt n = 1.5 – 8

K = Ko exp (-Q/kBT)

d average grain size after time t Ko pre-exponential factor

do average starting grain size kB Boltzmann’s constant

K constant Q activation energy

T temperature

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Ex-situ TEM

Normal Grain Growth

100 nm 100 nm 250 nm

Ni – 2.5 % P

TEM bright field images of a) as-plated, b) DSC annealed, 50C/min to 4000C, c) annealed to 5000C.

a) b) c)

Y. Zhou, Ph.D. Thesis, University of Toronto, 2006

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(c) (d)

(b) (a)

300 nm

Ex-Situ TEM

Abnormal Grain Growth

Ni – 800ppm S

U. Klement, U. Erb, A.M. El-Sherik, K.T. Aust,Mat. Sci. Eng., A203 (1995) 177

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Time Exponents for Grain Growth

C. Suryanarayana & C.C. Koch, Hyperfine Interactions 130, (2000) 5

Time exponent: 1 / n

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Activation Energies

Kissinger Analysis

The curve was obtained for the Ni-P sample with starting grain size of 6.9 nm at the DSC

heating rate of 50 C/min

d = 6.9 nm

Temperature ( 0C)

0 100 200 300 400 500 600

He

at R

ele

ase

(W

/g)

0.00

0.02

0.04

0.06

0.08

0.10

DSC @ 5 to 80 0C/min 420

0 to 467

0

TP

Ni – 2.5% P

Y. Zhou, Ph.D. Thesis, University of Toronto, 2006

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Activation Energy

Modified Kissinger Analysis

where b: heating rate

Tp: peak temperature

C: constant

k: Boltzmann’s constant

T: Temperature

Q: Activation energy

L.C. Chen, F. Spaepen, Appl. Phys., 69 (1991) 679)

CkTQTb pp /)/ln(

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Peak Temperatures

280

320

360

400

440

480

0 20 40 60 80

Scanning rate (oC/min)

Pea

k t

emp

era

ture

(oC

)Ni

Ni-20%Fe

Ni-1.2%P

G.H. Hibbard, U. Erb, K.T. Aust, U. Klement, G. Palumbo, Mat. Sci. Forum, 386-388 (2002) 387

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Kissinger Analysis

Activation Energies

-5

-4.5

-4

-3.5

-3

-2.5

-2

15 16 17 18 19 20 21

1/ k B T p

Hea

tin

g r

ate

(b

/Tp )

Ni-1.2%P

2.25 eV

Ni

1.46 eV

Ni-20%Fe

2.53 eV


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Activation Energies

System Grain size

(nm) Tp (

0C) Q (eV)

Ni 20 290 1.36

Ni 26 266 1.20

Ni 20 269 1.22

Ni 15 293 1.42

Ni 20 296 1.46

Ni-1.2 wt% P 10 432 2.25

Ni-1.9 wt% P 9 412 2.63

Ni-2.5 wt% P 7 420 2.58

Ni-20 wt% Fe 13 379 2.53

Co 20 355 1.63


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Young’s Modulus

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Physical Meaning of Young’s Modulus

Young’s modulus ~ slope in force curve at a0

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Grain Boundaries

Very important for many properties of 3-D nanocrystals

W.D. Callister, 6th ed., Materials Science and Engineering, Willey, NY, 2003

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Nanocrystalline Ni and Ni-P

GRAIN SIZE (nm)

100 101 102 103 104 105

YO

UN

G'S

MO

DU

LU

S (

GP

a)

0

100

200

300

400

minor reductions

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Normalized Young’s Modulus for Nanocrystals

Region II: High Porosity

Region I: Low Porosity

Y. Zhou, U. Erb, K. T. Aust, G. Palumbo, Z. Metallk., 94 (2003) 10

major reductions

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Effect of Porosity Strong Solids (e.g., ceramics)

V. Krstic, U. Erb and G. Palumbo, Scripta Metall. Mater., 29 (1993) 1501

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Effect of Porosity Elastic Theory


1)21(41

VEE o

)57(254

)/1()57(29/1

2

3

RSRS

V : Pore volume fraction : Poisson’s ratio

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Effect of Porosity

Atomistic Modeling: Pore in Single Crystal

R. Zugic, B. Szpunar, V.D. Krstic, U. Erb, Phil. Mag., A75 (1997) 1041

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Effect of Porosity

Atomistic Modeling: Pore at 5 grain boundary


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Effect of Porosity

Atomistic Modeling Elastic Theory


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Effect of Porosity

data from

Region II


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Effect of Grain Size

Fully Dense Nanomaterials

Young’s modulus (normalized with respect to Young’s modulus of polycrystalline nickel, E0) of nanocrystalline Ni-2.5 wt% P alloys, pure nanocrystalline nickel and amorphous Ni-15 wt% P.

U. Erb, K. T. Aust, G. Palumbo, Z. Metallk., 94 (2003) 10

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Composite Model

f’s: Volume fractions

E’s: Modulus values

G: Grain

GB: Grain boundary

TJ: Triple junctions

TJTJGBGBGGm fEfEfEE


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Composite Model

Results for Nano Ni-2.5% P

GPaE

GPaE

GPaE

TJ

GB

G

151

157

208


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Young’s Modulus Summary

1) Grain boundaries and triple junctions have some effect on elastic properties. For the case of Ni it was shown that their Young’s Modulus is reduced by about 20% at grain sizes of ~ 5nm.

2) Fully dense 3-D nanomaterials produced by electrodeposition show some grain size dependence below 20 nm and virtually no grain size dependence above 20 nm.

3) 3-D nanomaterials produced from 1-D precursor material contain considerable porosity. Their Young’s modulus decreases rapidly with increasing porosity levels.

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Hardness, Strength, Ductility

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Vickers Hardness

Electrodeposited Ni

GRAIN SIZE (nm)

100 101 102 103 104 105

VIC

KE

R'S

HA

RD

NE

SS

(G

Pa

)

0

1

2

3

4

5

6

7

8

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Hall-Petch Relationship

regular strength

regular hardness

where d: grain size

k, k: constants

since 1989: k, k’ negative (inverse Hall-Petch)

21

0

/ dk

21

0

/ dkHH

E. O. Hall, Proc. Phys. Soc., London, B54 (1951) 747 N. J. Petch, J. Iron Steel Inst., 174 (1953) 25

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Hall-Petch Plot

Electrodeposited Ni

A. M. El-Sherik, U. Erb, G. Palumbo, K. T. Aust, Scripta Metal., 27 (1992) 1185

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Hall-Petch Plot

Electrodeposited Ni-P

G. Palumbo, U. Erb, K. T. Aust, Scripta Metal., 24 (1990) 2347

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Normal Crystalline Cu

Regular Hall-Petch

A. H. Chokshi, A. Rosen, J. Karch, H. Gleiter, Scripta Metal, 23 (1989) 1679

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Comparison with Gas Condensed Pd, Cu

Inverse Hall-Petch

A. H. Chokshi, A. Rosen, J. Karch, H. Gleiter, Scripta Metal, 23 (1989) 1679

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Hall-Petch Plot

Various Materials

R. W. Siegel, G. E. Fougere,, Nanostruct. Mat., 6 (1995) 205

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Hall-Petch Plot

Various Materials


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Yield Strength

Electrodeposited Ni

GRAIN SIZE (nm)

100 101 102 103 104 105

YIE

LD

ST

RE

NG

TH

(M

Pa

)

0

200

400

600

800

1000

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Yield Strength

Electrodeposited Ni

N. Wang, Z. Wang, K. T. Aust, U. Erb, Mat. Sci., A237 (1997) 150

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Grain Boundaries: Dislocation Barriers

S: source

At small grain size: no longer dominant deformation mechanism

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Constitutive Equations for Diffusional Mechanisms

23

5102

d

b

kT

bDx

dt

dgb

22

1

6108

d

b

kT

bDx

dt

d

n

kT

bDx

dt

d

1

510833.

12

114D

dkTdt

d

gbDdkTdt

d3

14

Nabarro-Herring

Coble creep

GB Sliding

GB Sliding

Dislocation Climb

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Constitutive Equations for Diffusional Mechanisms

strain rate

applied stress

grain size

volume of vacancy

grain boundary thickness

lattice diffusion coefficient

grain boundary diffusion coefficient

shear modulus

Burgers vector

:dt

d

:

:d

:

:1D

:gbD

:

:b

:

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Nabarro-Herring Creep, Coble Creep

Nabarro-Herring: lattice diffusion

Coble: grain boundary diffusion

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Grain Boundary Sliding

grain boundary or lattice diffusion controlled

C. R. Barrett, W. D. Nix, A. S. Tetelman, in The Principles of Engineering Materials, Prentice-Hall, Inc., Englewood Cliffs, NJ (1973)

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Ductility

Electrodeposited Ni (early results)

N. Wang, Z. Wang, K. T. Aust, U. Erb, Mat. Sci., A237 (1997) 150

very disappointing

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Ductility

Electrodeposited Ni (early results)

GRAIN SIZE (nm)

100 101 102 103 104 105

TE

NS

ILE

ELO

NG

AT

ION

(%

)

0

10

20

30

40

50

60

very disappointing

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Comparison with Gas Condensed Pd


very disappointing

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Elongation to Failure

Various Nanomaterials

C. Suryanarayana & C.C. Koch, Hyperfine Interactions 130, (2000) 5

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However: More Recently

Conventional and Nanodeposit Co

A. A. Karimpoor, Ph.D. Thesis, University of Toronto

good news

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Stress – Strain Curve

Electrodeposited Ni-Fe

H. Wei, M.A.Sc. Thesis, U of T, 2006

good news

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Hardness, Strength,Ductility

Summary

1) All 3-D nanocrystalline materials show significant increases in hardness, yield strength and tensile strength, regardless of synthesis method. Depending on the system, increases by factors of 3-10 are commonly observed.

2) All 3-D nanomaterials exhibit regular Hall-Petch behavior for larger grain sizes. Changes in the Hall-Petch slope are observed at smaller grain sizes (<100 nm). Some materials show the inverse Hall-Petch relationships at very small grain sizes(<10 nm).

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3) At very small grain sizes dislocation slip is no longer the dominant deformation mechanism.

4) The inverse Hall-Petch relationship can be explained on the basis of diffusional creep (Nabarro-Herring, Coble) and grain boundary sliding which become important at very small grain sizes even at room temperature.


Summary

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Summary

5) Early results on the ductility of 3-D nanomaterials were very disappointing. Most materials showed low ductility in tension (<5%), regardless of synthesis technique. However, these results were obtained using very small tensile samples.

6) Recent advances in electrodeposition processes have resulted in better materials and larger sample sizes for meaningful tensile tests. As a result tensile elongations in excess of 10% have been observed.

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7) Recent advances in other synthesis methods have also resulted in materials with better ductility.

8) Current efforts towards higher ductility include the synthesis of materials with much broader grain size distributions or even bimodal distributions. In these materials a compromise between high strength and reasonable ductility is achieved, whereby the smaller grains in the distribution are responsible for strengthening while the larger grains retain some ductility in the system.


Summary

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Summary

Changes in Hall-Petch Behavior

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50 µm

a

1) Dislocation slip

2) Twinning

Summary

Low Temperature Deformation Mechanisms

Polycrystals

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Summary

Low Temperature Deformation Mechanisms

1) Dislocation slip

2) Twinning

3) Coble

4) Nabarro-Herring

5) GB sliding

6) Grain rotation

50 nm

b

Nanocrystals

mse 342f chapter # 4 properties part i 2014-15

Documents

growing grain mse

grain boundaries

uwe erb materials science

nanocrystallized materials

conventional materials

grain growth curvature

elements of materials

dense equiaxed materials