7/30/2019 One and a Half Century Of

1/42

One and a Half Century ofDiffusion

FICK, EINSTEIN

before and beyond

Jean Philibert

Diffusion Fundamentals I, LeipzigSeptember 2005

7/30/2019 One and a Half Century Of

2/42

Some MILESTONES

Thomas Graham A Scottish Chemist1830 (gas) 1863 (liquids)

Adolf Fick 1855 A German Physiologist Josef Stefan 1879 An Austrian Physicist

W.C. Roberts-Austen 1896 An EnglishMetallurgist

G. Von Hevesy 1920 A Hungarian Physicist

7/30/2019 One and a Half Century Of

3/42

Random Walk

Robert Brown 1828 J.C. Maxwell 1867

Albert Einstein 1905

Maryan Smoluchowski 1906

Jean Perrin 1912

J. Bardeen , C. Herring 1950

7/30/2019 One and a Half Century Of

4/42

Temperature dependence

Svante Arrhenius 1889 Henry Eyring 1935 / 1941

C. Wert, C. Zener 1949 G.H. Vineyard 1957

7/30/2019 One and a Half Century Of

5/42

7/30/2019 One and a Half Century Of

6/42

Fruitful as the miscibility of the gases has been an interesting

speculation,the experimental information we possess on thesubject amounts to little more than the well established fact,

that gases of different nature, when brought into contact, do not

arrange themselves according to their density, .

but they spontaneouly diffuse, mutually and equally,

through each other

and so remain in the intimate state of mixture for any length

of time.

Thomas Graham, 1829

7/30/2019 One and a Half Century Of

7/42

7/30/2019 One and a Half Century Of

8/42

Adolf FICK1829-1901

7/30/2019 One and a Half Century Of

9/42

7/30/2019 One and a Half Century Of

10/42

7/30/2019 One and a Half Century Of

11/42

7/30/2019 One and a Half Century Of

12/42

Ficks experimental Set-up

7/30/2019 One and a Half Century Of

13/42

Ficks results (tube)

1

1.05

1.1

1.15

1.2

specific

gravity

0 50 100 150 200 250depth under surface (mm)

FICK ( cylindrical tube)

y = 1.0045 + 0.00088321x R= 0.99908

7/30/2019 One and a Half Century Of

14/42

FICK / funnel

d

2

cdx

2 = dlnAdxdcdx

Cone :

d2

cdx

2= 2

x + dO

dcdx

c(x)

csat =

dO

d dO 1+

d

x + dO

7/30/2019 One and a Half Century Of

15/42

Ficks results (funnel)250 mm is a guess for the position of the cone apex

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Specific

gravity

(-1)

0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011(250-depth)

-1( mm

-1)

Fick (funnel)

y = -0.078707 + 17.248x R= 0.99922

7/30/2019 One and a Half Century Of

16/42

Fick revisited Theory and Simulation of Ficks historical

verification of the 2ndLaw

M.E. Glicksman, R. DiDomizio, A. Lupulescu

This Conference

Ficks Diffusion Experiments revisited

T.W. Patzak,

unpublished, available athttp://petroleum.berkeley.edu/papers/patzek/Fick%20

Revisited%20V2.pdf

7/30/2019 One and a Half Century Of

17/42

7/30/2019 One and a Half Century Of

18/42

Joseph Fourier1768-1830

7/30/2019 One and a Half Century Of

19/42

7/30/2019 One and a Half Century Of

20/42

.

Josef STEFAN

1836-1893

7/30/2019 One and a Half Century Of

21/42

7/30/2019 One and a Half Century Of

22/42

7/30/2019 One and a Half Century Of

23/42

7/30/2019 One and a Half Century Of

24/42

Is solid state diffusion possible ?

Corpora non agunt nisi soluta

Gay-Lussac, 1846

However, diffusion in solids has been usedfor centuries in many metallurgical processes

: e.g. cementation described by the Roman

author PLINY.

7/30/2019 One and a Half Century Of

25/42

W C ROBERTS AUSTEN

7/30/2019 One and a Half Century Of

26/42

W.C. ROBERTS-AUSTEN

Chemist and essayer, The Mint, London

Bakerian Lecture on the Diffusion in Metals

1) Diffusion of molten Metals2) Diffusion of solid Metals

London, 1896To make accurate experiments on diffusion is one of the most

difficult problems in practical physics

Ostwald, 1891My long connection with Grahams researches made it almost

a duty to attempt to extend is work on liquide diffusionto

metalsRoberts-Austen, 1896

7/30/2019 One and a Half Century Of

27/42

W. C. ROBERTS-AUSTEN

Diffusion of Gold

In Lead

7/30/2019 One and a Half Century Of

28/42

The evidence gathered by the metallurgist of active atomic

movements in fluid and solid metals sustain hope of thePhysiologist that

he will ultimately be able to measure theatomic movements upon which vitality

and thoughtdepend.

Roberts-Austen

7/30/2019 One and a Half Century Of

29/42

7/30/2019 One and a Half Century Of

30/42

Robert BROWN

1773-1858

7/30/2019 One and a Half Century Of

31/42

Robert Brown

Havingfound motion in the particles of the pollenof allthe living plantswhich Ihad examined, I was led next to inquire whether this property continued after thedeath of the plant, and for what length of time it was retained In plants, either

dried or immersed in spirit for a few days only, the particles of pollen of bothkinds were found in motion equally evident with that observed in the living plant; specimens of several plants, some of which had been driedand preserved in an

herbarium for upwards of twenty years, and others not less than a century, stillexhibited the molecules or. smaller spherical particles in considerable numbers,and in evident motion,

7/30/2019 One and a Half Century Of

32/42

Albert EINSTEIN1879-1955

7/30/2019 One and a Half Century Of

33/42

7/30/2019 One and a Half Century Of

34/42

7/30/2019 One and a Half Century Of

35/42

7/30/2019 One and a Half Century Of

36/42

Drunkards walkfrom G. GAMOW

7/30/2019 One and a Half Century Of

37/42

Jean PERRIN1870-1942

7/30/2019 One and a Half Century Of

38/42

7/30/2019 One and a Half Century Of

39/42

7/30/2019 One and a Half Century Of

40/42

Fractal trajectory D =2Si on faisait des points

des intervalles de temps100 fois plus rapprochs,chaque segment seraitremplac par un contour

polygonal relativementaussi compliqu que ledessin entier, et ainsi desuite. On voit comment

svanouit la notion detrajectoire.

Jean Perrin

7/30/2019 One and a Half Century Of

41/42

7/30/2019 One and a Half Century Of

42/42

Gyrgy HEVESY

1885-1966

1920: natural radioactive

Lead

Pb*/PbCl21935: artificial 32P