Diffusion in Intermetallic Compounds
Studied Using Short-Lived Radioisotopes
M. O. Zacate1, M. Deicher2, K. Johnston2, J. Lehnert2, F. Strauß2, G. S. Collins3
1
Department of Physics and Geology, Northern Kentucky University, Highland Heights, KY 41099, USA
2 Technische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
3 Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
1
Diffusion
Study of diffusion important for the understanding and controlling of
impurities in materials
• Control of useful/problematical impurities
• Activation energies
• Study of fundamental diffusion properties.
Already considerable programme of diffusion studies underway at
ISOLDE: IS489.
Use of radiotracers using short and long-lived isotopes.
2
Radiotracer Technique (IS489)
60 keV
Implantation
550 … 900 K
CdxZn1-xTe
Ø = 6 mm
d = 800
a µm
111Ag+
thermal
CdTe
treatment
Used isotopes :
30nm
111Ag, 67Cu, 24Na, 43K, 56Mn,
59Mn(59Fe), 65Ni, 61Mn(61Co), 101Cd(101Pd), 191Hg(191Pt), 193Hg(193Au)
-3
concentration (cm )
CdTe:111Ag
2 mg
1 1...30
... 30 µm
m
10
14
10
13
10
12
10
11
Tdiff = 570 K
tdiff = 30 min
DAg = 7.6·10-9 cm2/s
0
100
200
300
400
depth (µm)
3
What’s different about this work
Use of PAC (perturbed angular correlation) to examine the atomic
nature of diffusion processes.
PAC very versatile technique (as evidenced by other proposals in
this session)….but not usually used to study diffusion.
Study of intermetallic compounds:
• L12 compounds: RIn3, RGa3, RSn3
• Gd3P7
Examine on a local scale some of the unusual diffusion behaviour
associated with these compounds.
Tests last year during the Ag beamtime were encouraging.
4
Diffusion in solids
example: simple vacancy diffusion
V
EA
rate  exp  EA / kBT 
x
5
Diffusion in intermetallic compounds
Only first-neighbor jumps allowed (?)
example: 6-jump cycle
6
5
4
3
2
1
6
(EFG)
For diffusion experiments, monitor
the changes of EFG as probe
atoms move in the crystal.
7
Observing diffusion by PAC:
Reorientation of EFG tensor
G2(t)
Heating increases jump frequency...
time
...first increases, then reduces relaxation.
8
PAC measurements of Cd jump rates in L12 structured compounds*
•
•
RIn3, RGa3, RSn3 with R=rare earth
L12 structure:
1
G2(t)
EFG
Vzz
V
Vzz
zz
In
VV
Vxx xxxx
R
*Collins, Jiang, Bevington, Selim, Zacate, PRL 102,
155901 (2009) and refs. therein;
Jiang, Zacate, Collins, Def. & Diff. Forum 289-292,
725 (2009);
629oC
0
1
419oC
G2(t)
0
VVyyyyVyy 1
oC
340
G2(t)
0
1
261oC
G2(t)
0
1
156oC
G2(t)
0
0
100
200
t (ns)
300
9
PAC measurements of Cd jump rates in L12 structured compounds*
• RIn3, RGa3, RSn3 with R=rare earth
• Jump rates at phase boundaries:
Jump rate larger for Rpoorer boundary
Jump rate larger for Rrich boundary
LaIn3, CeIn3, PrIn3
LuIn3, TmIn3, ErIn3,
HoIn3, DyIn3, TbIn3,
GdIn3
LaSn3, CeSn3, SmSn3,
GdSn3
divacancy or
6-jump
mechanism
Collins, Jiang, Bevington, Selim,
Zacate, PRL 102, 155901 (2009)
Simple vacancy mechanism
10
PAC measurements of Cd jump rates in L12 structured compounds*
• RIn3, RGa3, RSn3 with R=rare earth
• Jump rates at phase boundaries indicate complex diffusion
mechanism in light rare earth tri-indides
• Possible explanation: constitutional defects differ in light and heavy
R compounds
Light R
VR and RIn
Heavy R
VIn and InR
Aim of proposed experiments is to detect which defects are present
across the RIn3 series using 111mCd
11
PAC measurements of Cd jump rates in L12 structured compounds*
Why 111mCd?
 Too few defects to be observed using 111In

111mCd
is an impurity so that association between
defects and Cd could enhance site fractions enough to
determine defect configurations
Aim of proposed experiments is to detect which defects are present
across the RIn3 series using 111mCd
12
366 °C
Ga7Pd3
0
1
314 °C
• One Pd site
• Two inequivalent Ga sites (3 & 4)
0
1
235 °C
Ga(3)
Ga(4)
0
1
111In/Cd
in Ga7Pd3
• In/Cd only on Ga sites
• No defects observed
0
156 °C
0
100
200
t (ns)
300
13
111In/Cd
in Pd3Ga7 (high temperature)
G2(t)
1
366 °C
0
1
314 °C
Damping of signal is due to loss in
coherence among spin states as
tracers jump
0
1
235 °C
0
1
0
Diffusion and Defect Data 264, 27-32
(2007)
156 °C
0
100
200
t (ns)
300
14
Cd jump rates in Ga7Pd3 – empirical
analysis
G2 t   exp  t G2,static t 
Seven distinct EFGs
• Three EFGs for Ga(3) site
parameterized by quadrupole
interaction frequency wQ(3)
• Four EFGs for Ga(4) site
parameterized by quadrupole
interaction frequency wQ(4)
Four EFG transition rates: r3→3, r4→4,
r3→4, and r4→3
Initial fraction of probes on Ga(3)
sites: f3
l
Why
difference in
jump rates?
 
Stochastic Model
1
Diffusion and Defect Data 264, 27-32 (2007)
Spectra calculated using SHIML (Comput. Phys. Commun. 182,
1061 (2011)) following the method of Winkler and Gerdau (Z.
Phys. 262, 363 (1973))
15
Cd jump rates in Ga7Pd3
• Scatter in the fits using
stochastic model.
• Need to understand this
better; Could perform DFT
calculations, but
experimental solution is
more direct
reorientation rates (MHz)
1000
400
300
T (C)
200
100
r33
r44
r34
r43
100
10
1
0.1
0.01
1E-3
15
20
25
1/kT (eV-1)
30
•
Proposal: repeat experiments using the 111mCd probe and analyze using the stochastic
model.
•
Use of 111mCd allows elimination of f3 in the model because of the principle of detailed
balance:
f3  4r34  1  f3  3r43
•
This offers a unique opportunity to measure separately inter- and intra-sublattice jump
rates.
16
Beam request
Isotope
T1/2
Target
111mCd
48 min
Sn
Yield
(ions/µC)
2×108
Ion
Shipping?
source
HP
No
(VADIS)
• 10 shifts split over 2-3 years.
Work involved:
• Collections of ~ 15 mins allow
many
experiments
to
be
performed
over
3-4
day
beamtime.
• Need to determine “good” annealing
temperatures for the compounds
following implantation.
• Easy to accommodate other
groups.
• Ga7Pd3 more focused, priority for
2011.
• Large variety of L12 compounds to be
examined, great flexibility.
17
Sample preparation
Option 1
111In
in InCl3 dissolved
in HCl
Step 1: high purity metal
foils folded together
Step 2: Arc melt at 45
DCA for ~1 sec
Option 2
111mCd
implanted
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Simple vacancy diffusion in L12
compounds
Simple vacancy jumps in L12
EFG
Vzz
Vzz
VVxxxx
VyyVyy
*Muhammed, Zacate,
Evenson, Hyperfine
Interact. 177, 45 (2007)
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Simulating Simple Vacancy Diffusion in
L12-Structured Compounds…
6-jump cycle L12
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Ga sites in Ga7Pd3
Tracer jumps that lead to a change in EFG:
Ga(4) → Ga(4)
Ga(3) → Ga(3)
Ga(3) ↔ Ga(4)
Jump distances:
Ga(4)-Ga(4): 0.280 nm (×3) and 0.273 nm
Ga(3)-Ga(3): 0.310 nm (×4)
Ga(3)-Ga(4): 0.338 nm (×4)
21