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How hydrogen enhances dislocation mobility and dislocation
generation rate
(Solid solution softening and hardening)
Reiner Kirchheim
Institut für Materialphysik
Georg-August-Universität Göttingen
www.uni-goettingen.de
I2CNER
Kyushu-University, Japan
Outline:
1.
Introduction
2.
Dualism of solute/defect-interaction, the defactant concept
3.
Hydrogen embrittlement (during fatigue)
4.
Direct evidence for softening by hydrogen (nanoindentation and internal friction)
5.
Solid solution softening and hardening by mobile defactants
Present and future activities in the area of hydrogen in metals
1,4x10
-6
1,2x10
-6
release rate ([H]/[Fe]/s)
heat rate
1. Analysing electrochemical permeation techniques
and thermal desorption spectroscopy
2. Interaction of hydrogen with dislocations in
iron and nickel (with MPIE)
sample
3. Developing a hydrogen probe
and using it for friction and wear
(with KircTec)
a) 1x10
b) 3x10
1,0x10
-6
8,0x10
-7
6,0x10
-7
4,0x10
-7
2,0x10
-7
c) 1x10
-3
-3
d) 3x10
e) 1x10
f) 3x10
-2
-4
-4
-5
g) 1x10
-5
0,0
0
100
200
300
400
500
600
700
temperature (K)
4. Modeleling hydrogen embrittlement
(with I2CNER, Brian Somerday)
6
H-Probe
4
3
2
1
5
YUKITAKA MURAKAMI, TOSHIHIKO KANEZAKI, and YOJI MINE
METALLURGICAL AND MATERIALS TRANSACTIONS A, 41A (2010) 2548
Fatigue of stainless steel
softening hardening
no H
23 wppm
70 wppm
89 wppm
“Can hydrogen both soften and strengthen a material in the same test? This apparently
is so and is proposed to be a consequence of the dual nature of softening associated with
smaller activation energies and hardening associated with the nature of localized slip.“
New results and methods since 1980
1.
2.
3.
4.
H-H interaction und increasing excess affects dislocation motion
First principle calculations
Defactant concept
Nanoindentation
The defactant concept
R. Kirchheim, Acta Materialia 55 (2007) 5129
hydogen, boron,
carbon, oxygen,
scandium,...
solute A ↔ defect
surface, grain bond.,
stack. fault, disloc.,
vacancies
(attractive interaction 
gain energy by segregation)
Who is gaining this energy?
gain information about
solute binding energy
gain information about
changing defect energy
Dualism of solute defect interaction!
H-interacting with defects and lowering its own energy
material
structure
potential trace
energy distribution
energy distribution
n(E)dE=
E
single crystal
 (E  E o )
Eo
n(E)
single crystal
+ vacancy
o
E
E
t
E
(1  ct ) ( E  E o ) 
ct ( E  Et )
n(E)
E
single crystal
+ dislocation
K2
Eo
E
single crystal +
grain boundary
(1  ct ) ( E  E o ) 
2
Eo
Et
n(E)
E
amorphous state
2
Eo

c
 ( E  Et ) 2 
exp 

 
 2 

ct
 (E  E o )2 
exp 

 
2


1
n(E)
Apply Fermi-Dirca-Statistics to evaluate µ(c)
or use measured µ(c) to evaluate n(E)
( E  E o )3
n(E)
n( E )dE
1  exp[( E   ) / kT ]
1
2
cf/c
D/Do
rH/ rH o
0.8
1.6
r2 (nm2)
ratio of quantities (deformed/anneald
various techniques to measure H/dislocation-interaction in Pd
0.6
0.4
SANS
1.2
0.8
0.4
0.2
0
-7
-6
-5
-4
ln(H/Pd)
0
102
103
10
concentration atppm H/Pd
1
rH
rH
0

D
D
0

cf
c
Only free hydrogen atoms contribute
to resistance and diffusivity
104
cH, H
Interaction of hydrogen with dislocations,
Site energy distribution & Fermi-Dirac Statistics
q
r
const.
Fermi-Dirac & T=0 approximation
r
 (c)  K
c
chemical potential,  kJ/Mol
R
-60
core interaction
H in Pd
-40
strain field interaction
disloc. density r
-20
H-H interaction
0
with H-H interaction
0
2
4
6
8
reciprocal square root of concentration, 102 (H/Pd)-0.5
( c )  Wc loc  K
r
c
What is the binding energy of hydrogen to dislocations?
What about iron?
10
Modelling kinetics of hydrogen embrittlement
no traps
with traps
internal H (same H)
external H (same H)
same diffusible H
same diffusible H
same permeation
cdDd
same permeation
cdDd
fast supply,
internal sources
low supply,
internal sinks
same diffusible H
same permeation
cd D d
same diffusible H
same permeation
cdDd
low supply,
no sources
fast supply,
no sinks
Modelling mechanisms of hydrogen embrittlement
1. Hydrogen enhanced decohesion
2. Increasing dislocation generation rate and/or
mobility
with hydrogen
no hydrogen
Formation energy of dislocation
is decreased!
 contributes to HELP (Birnbaum,
Robertson, Sofronis)
but also to AIDE (Lynch)
3. Ease of void generation
no hydrogen
with hydrogen
Surface energy of newly
formed voids is decreased
 ductile fracture
Voids may be formed more
easily in the presence of
vacancies, Nagumo et al.
The defactant concept
R. Kirchheim, Acta Materialia 55 (2007) 5129
hydogen, boron,
carbon, oxygen,
scandium,...
solute A ↔ defect
surface, grain bond.,
stack. fault, disloc.,
vacancies
(attractive interaction 
gain energy by segregation)
Who is gaining this energy?
gain information about
solute binding energy
gain information about
changing defect energy
Dualism of solute defect interaction!
Surface energy reduction:
generation of interfaces
Germany has a long lasting tradition
in reducing the liquid/air interfacial
energy by natural solutes (surfactants)
Grease =
oil/water
emulsion
A competitor for segregation of
surfactant molecules is the
oil/liquid interface
annihilation of interfaces
Gibbs Adsorption Equation
d   Γ Ad A   Γ A RTd ln cA
GA=0
GA= Gsat
dA=0
D/kT
Can we use the Gibbs equation
for other discontinuities
(vacancies, dislocations, ….)
of matter as well?
Hydrogen interacting with defects and changing their formation energy
dΦ  d ( F  nH  H )
 2


r H  H
  SdT  PdV  Vdr   M dnM  nH d H
New!
definition of measurable GA:
i.e. dislocations:
ΓA 
nh
r

T ,V , nM ,  H
Pd
V ,T , nM ,  H
applicable to all defects (stacking faults, dislocations, kinks, vacancies etc.):
d   Γ H d h
 = defect formation energy
GH = solute excess (number of A-atoms per area, length or number)
alloying addition stabilizing a defects =
Defactant (defect acting agent)
nH
r
H2
T ,V , nM ,  M
How does hydrogen effect plasticity of metals?
1. Hydrogen is a defactant regarding dislocations
Hydrogen reduces the line energy
increases the rate of disln. generation
decreases the rate of disln. annihilation
higher dislocation densities
Cold rolling Pd-H sheets (reducing thickness by 50%)
0.0 H/Pd
1.0 at.-% H/Pd
0.5 at.-% H/Pd
3 µm
3 µm
3 µm
1.2
140
Vickers hardness
relative dislocation density
Increasing dislocation density in the presence of defactant hydrogen
1.0
0.8
0.6
0.4
0.2
0 0
130
120
110
100
90
0.2 0.4 0.6 0.8
H-concentration (at.-%)
0
0.2
0.4
0.6
H-concentration (at.-%)
0.8
Carbon and nitrogen as defactants
for grain boundaries in iron
N C aΓ C N gC 3 Γ C
c



 c gP
V
V
V
d
0 w%C
0.2 w%C
C-atoms in
grains
C-atoms
in gb
8
0.4 w%C
carbon (this work, Fe+graphite)
nitrogen (Mittemeijer, Fe+Fe3N)
cgP
1
c


d 3ΓC 3ΓC
8
2x10
5
8
10
1x10
20
0
0
5000
10000
0.8 w%C
3
carbon (Takaki, Fe-C)
8
3x10
15000
3
solute concentration (mole/m )
grain size (nm)
inverse grain size, 1/d (1/m)
4x10
METALS AND MATERIALS International
10 (2004) 533~539
Setsuo Takaki, Toshihiro Tsuchiyama,
Koichi Nakashima, Hideyuki Hidaka,
Kenji Kawasaki, and Yuichi Futamura
Consequences: dislocation formation
t
100 mV
Increasing chemical potential of hydrogen
Barnoush & Vehoff (Al, Ni, FeAl)
Nibur et al. & Yokogawa et al. (steel)
P
-900 mV
-1100 mV
Defect generation by solutes (hydrogen)
dislocation generation in V-H
Nanoindentation (Berkovich Indents)
d   Γ H dH
Uniaxial compression tests (UCT)
0 H/V
0.03 H/V
Pd-H
2 m
0 H/V
0.03H/V
BI:
Pop-in load goes down → Dislocation energy (DE) is lower
UCT: Lower DE → higher r → less localized shear slip → barrel shape
1 m
“pop-ins in the load displacement curves“
0,40
cH = 0
cH = 0.01 H/V
Pop-in Load, P (mN)
0,35
Load (nm)
0,30
0,25
0,20
0,15
0,10
0,05
0,00
0
10
20
30
40
50
60
0,34
0,32
0,30
0,28
0,26
0,24
0,22
0,20
0,18
0,16
0,14
0,12
0,10
0,08
0,06
0,04
0,02
0,00
RTip = 250
3x(RTip = 77
1/ 3
t max
0,00
0,01
0,02
0,03
0,04
0,05
 6 Er2 
 0.31 3 2 P 
 R 
0,06
Hydrogen Concentration, cH (H/V)
Displacement (nm)
0,65
9
line energy (nJ/m)
Maximum Shear Stress, tmax (GPa)
10
8
7
6

o
3-4 H-atoms/b
0,60
0,55
0,50
d   Γ Ad A
0,45
5
0,00
0,01
0,02
0,03
0,04
0,05
Hydrogen Concentration, cH (H/V)
 disl 
exp( 3)
rcorebt max
8
0,06
0,40
-10
0
-9
-8
+
-7
-6
-5
-
ln(H/V)=D/RT
-4
A
-3
-2
speed of tip = 10 m/s = 10 nm/ns
time to first pop-in ≈ 0.1 ns
a2
Hydrogen jump time: t 
6D
H-Diff.-Coeff. D=5.10-10 cm2/s
Jump distance: a = 0,25 nm
t = 2.10-7 s
= 200 ns
How do dislocations move
after their generation?
Studying dislocation motion by measuring internal friction
edge dislocation
b
dl
b
f
dl
f
dl
f
b=
Burgers vector
dl =
line element
f=
Peach-Koehler
force
srew dislocation
b
b
f
dl
f
f
dl
How does hydrogen effect plasticity of metals?
1. Hydrogen is a defactant regarding dislocations
Hydrogen reduces the line energy
increases the rate of disln. generation
decreases the rate of disln. annihilation
higher dislocation densities
2. Hydrogen is a defactant regarding kinks
Hydrogen reduces the kink formation energy
increases the rate of double kink generation
higher dislocation mobility, if controlled
by kink formation
Kink generation studied b internal friction (bcc metals Nb, Ta, Mo, Fe)
Example: Niobium (+ Hydrogen)
G. Funk, PhD thesis, University of Stuttgart, 1985
720 K
S-K(O)
-peak: double kink generation on 71o dislocations
-peak: double kink generation on screw dislocations
S-K-peak (Snoek-Köster- or coldwork-peak) :
double kink generation and movement of kinks
on dislocations in the presence of solute atoms
Example: Iron (+ Hydrogen)
I.G. Ritchie et al., phys. stat. sol. (a)
52 (1979) 331
(suggested first in the 50‘s that the activation energy of the - and
-relaxations are equal to the formation energies of kink pairs)
Alfred Seeger
Relaxation time for the S-K-peak:
H HM
t SK
 2H K  H KM  H HM
 T cd exp 
RT

2



2 H K  double kink formation energy, H KM  kink migration energy
 hydrogen (solute) migration energy, cd  H  concentrat ion at dislocatio n
 H dB 

cd  cb exp 
 RT 
H dB  hydrogen binding energy
cb  bulk concentrat ion
H SK
 2 H K  H KM  H HM  H dB for cd  1

M
M
2
H

H

H
for cd  1
K
K
H

Conclusions:
S-K peaks appear at higher temperatures compared to the peak of the naked dislocation,
because
2 H K  H KM  H HM  2 H K  H KM
Thus in iron and niobium the S-K peak arises from 71o dislocations.
Already Alfred Seeger realized the peculiar behavior of hydrogen:
“The kink-pair formation enthalpy in 71o dislocations in -Fe has been determined by
Kronmüller et al. [63] as 0.048 eV. The activation enthalpy of about 0.21 eV observed in
some experiments [22, 23, 64] may be associated with the above process. The difference
between the two activation enthalpies is larger than the range of possible migration
enthalpies of H in -Fe [28]. This is an indication that in the case of hydrogen the theory
needs further refinement.”
“We suggest also that H adsorption to the core of screw
dislocations makes double-kink nucleation easier and shifts
the peak from ~300 K to 120 to 200 K. Only a few
hydrogen atoms on a typical segment length would be
required to enhance the double-kink nucleation, …“
John Hirth
The defactant-concept provides the proof for Hirth‘s hypothesis!
What are the consequences
on the macroscopic scale?
Softening and hardening by solutes (hydrogen)
Orowan equation modified by Argon:
without solutes:
d
 brv  bra t g  t m
dt

t g  characteri stic time of kink formation
t m  characteri stic time of kink motion
increasing solute concentration:
t g decreases because of the defactant concept
t m increases because of solute drag
d
1
 brv  brat g  t m   bra / t m

1
 bra / t g
t g  t m
t g  t m
dt
d
 bra t g  t m
dt


1
t g  t m  bra / t g and t g  (solute softening)

t m  t g  bra / t m and t m  (solute hardening)
tg
tm
1) srew dislocation
t g1  t m1
time constant for kink pair generation
b dl
time constant for kink motion
tg tm
d
bra
bra


dt t g  t m t g
b
f
f
f
dl
2) low solute content
t g 2  t g1 and t m2  t m1 but t g 2 t m2
 solute softening
tg tm
d
bra
bra


dt t g  t m t m
 solute hardening
3) high solute content
t g 3  t g 2 and t m3  t m2 but t g 3 t m3
?
?
?
?
Missing reliable evaluation procedures for trapping measurements in steel!
Promote the defactant concept as a tool for microstructural engineering!
R. Kirchheim, In Solid State Physics, eds. H. Ehrenreich and F. Spaepen,
Elsevier, Amsterdam (2004), Vol. 59, 203-305
R. Kirchheim, Acta Materialia 55 (2007) 5129
R. Kirchheim, Int. J. of Materials Research 100 (2009) 483-487
Financial support: DFG and State of Lower Saxonia
Thank you for your attention!