Pext

compress

dV dV,dAflow to backfill

broken bonds

broken bonds

broken bondsbrok

en b

onds

Stress = 0

As happy as it can be, if only displacive motion allowed (no diffusion)

if diffusion is allowed, though

4

Solids can flow as well as eliminate surface sites by dislocation climb (absorbing & emitting vacancies).

Take out one column of atoms & heal the crystal, removing two surface sites in the process.

Break the column up into two smaller columns, rotate 90, then insert them back inside. This would create internal pressure > 0.

6

means broken bonds (Kossel springs)

Wulff plot ofKossel crystal

John WulffMIT faculty 1931-1985

8

9

10

Tangent circle theorem in Wulff plot: for a particular n’, (n’)=(n’) if and only if a circle through the origin and

tangent to (n)n at n’ lies completely within (n)n.

Wulff plot (n) Stable Wulff plot (n)

11

Conyers Herring, “Some theorems on the free energies of crystal surfaces,” Phys. Rev. 82 (1951) 87.

h1h2

1 2

1 2 2P

h h

12

Wulff plane

Equilibrium shape of free-standing nanocrystal is the inner envelopof all Wulff planes

13

truncated octahedron bounded by eight (111) and six (100) facets

14

15

16Water drop on glass (from Wikipedia)

17

z

r

LSS

L

R

r0

h

18

S LS – L: =180, complete non-wettingS LS + L: =0, complete wetting

In 1774 Benjamin Franklin reported the following to the British Royal Society:

"At length at Clapham where there is, on the common, a large pond, which I observed to be one day very rough with the wind, I fetched out a cruet of oil, and dropped a little of it on the water. I saw it spread itself with surprising swiftness upon the surface.. the oil, though not more than a teaspoonful, produced an instant calm over a space several yards square, which spread amazingly and extended itself gradually until it reached the leeside, making all that quarter of the pond, perhaps half an acre, as smooth as a looking glass.“ - Phil. Transactions 64 (1774) 445

Over a century later, Rayleigh calculated that the thickness of the oil film was 2nm by knowing the volume of oil (4ml) dropped and the area of coverage (2000m2). Franklin-Rayleigh have come up with the first physical measurement that gives a nanometer.

Langmuir-Blodgett film: monolayer of organic molecules on surface (Langmuir won Nobel Prize Chemistry in 1932)

Clapham pond in south London

Franklin, 1762, 14 years before revolution

Andre Geim, Konstantin NovoselovNobel Prize in Physics 2010

Graphene

AFM scan of Ni-43 at.% Al; 1 h at 1400C. matwww.technion.ac.il/Rabkin/Topics.html

Supercond. Sci. Tech. 13 (2000) L1

20

(inclination)

21

22

Read & Shockley, “Dislocation models of crystal grain boundaries,”

Phys Rev 78 (1950) 275.

specialhigh-angle

vicinal

high-angle“random”

low-angle

23

From: Guy & Hren, Elements of Physical Metallurgy (1974)

24

a0

a0

d(x)

25

51 planes

50 planes

26

a

a0

27

Fully coherent, nanoscale, Guinier-Preston (GP) zones

Al alloys

Nanotechnology?

28

Ni-Alloys: Aerospace and Airplane Engine Applications

Ni high pressure compressor stages,3 back stages-spool and air foils

Ni high pressure turbineDisks and air foils

Ni low pressure turbineDisks and air foils

High By-Pass Ratio Turbofan EngineCourtesy of Jim Williams (OSU)

Ni combustor liner,case and swirlers

29

400F/min 3029

50nm 50nm

from Mike Mills, OSU

Ni-based superalloys

secondary ’precipitate(Ni3Al)

tertiary ’precipitate

matrix (Ni-Al-Cr-Co-Ti-W)

These fully coherent nanoprecipitates are typically “blocky” shaped because Wulff plot not so anisotropic

30

a0

a0

d(x)no force

no forceno force

force

no force

no force

no force

31a0

a0

32

51 planes

50 planes

33

van der Merwe, “On the stresses and energies associated with inter-crystalline boundaries,”Proc. Phys. Soc. London A 63 (1950) 616.

34

horrendous glue energy

zero elastic energy

small glue energy (coherent interface)

long-range elastic energy V

intermediate glue energy (semicoherent interface)

local elastic energy A

35

habit plane

’: hcp Matrix: fcc

Common OR: (0001)hcp // (111)FCC[2110]hcp // [110]FCC

- - -

Widmanstätten (plate-like) morphology of semi-coherent precipitates could also be partly due to growth kinetics

36

Selected Area Diffraction

Gao et al., “Conversion of Zinc Oxide Nanobelts into Superlattice-Structured Nanohelices,” Science 309(2005) 1700.

Orientation Relationship

≡Two sets ofdiffraction

pattern

37

(001)tetragonal

Orientation Relationship

OR1: (001)tetragonal // (001)FCC[100]tetragonal // [100]FCC

or [010]FCC

[100]tetragonal

OR2: (001)tetragonal // (010)FCC[100]tetragonal // [100]FCC

or [001]FCC

OR3: (001)tetragonal // (100)FCC[100]tetragonal // [010]FCC

or [001]FCC

Al-Cu random solution

Tetragonal ’ phase:CuAl2 intermetallic compound

Different variants

38

=BCC with =FCC

Kurdjumov-Sachs OR:

(110)BCC // (111)FCC[111]BCC // [110]FCC

--

Nishiyama-Wasserman OR:

(110)BCC // (111)FCC[001]BCC // [110]FCC

-rotated from each other by 5.26

39

40

n3

n1

n2

a1

a2

a3

41

3-1n3

1-1n12

-1n2

3-1: unstable

3-1: stable

42

Common tangent lineconstruction in

inverse Wulff plot

43

3n3

1n12n2

’Correspondingly, in Wulff plot space

44R

bulk

competitor

RC

weighted integral = G

Integral vs Differential free energies

Ionic Liquid in TEM:

1,2-dimethyl-3-propylimidazolium (DMPI)

-bis(trifluoromethylsulfonyl)

imide (TFSI)

Nano-Capillary/Electrokinetic

Flow

Nature Nanotechnology 8 (2013) 277

46Liquid spreading on solid nanowire surface in the complete wetting (=0) limit

Rayleigh instability: why is flat Precursor Film stable?

47

Liquid-solid van der Waals interaction

Liquid surface energy

Bulk liquid reservoir

smooth film flow

Rayleigh bead flow

W(e) = const + A/12e2

A: Hamaker constant

Disjoining pressure (e) ≡ -dW(e)/de = A/6e3

2

2 1/2 2 3/2

1γ( )[1+( ) ] [1+( ) ]

z

z z

eb

b ebe e e e

smooth Precursor Film (PF) flow → Rayleigh Bead (RB) flow →

solid nanowire

3

Lubrication Approximation in Fluid Flow:3η 1 / ( μ)t z ze b e e