site preferences of indium impurity atoms in intermetallics having al 3 ti and al 3 zr crystal...
TRANSCRIPT
Site preferences of indium impurity atoms in intermetallics having Al3Ti and Al3Zr crystal structures
John P. Bevington, Farida Selim and Gary S. Collins
Department of Physics, Washington State University, Pullman, WA, USA
OC-1
Supported in part by the National Science Foundation under grant DMR 05-04843 (Metals Program) and Praveen Sinha Fund for Physics Research.
L12 DO22 DO23 Cu3Au Al3Ti Al3Zr
Outline
• Indium was doped in samples of Al3V and Al3Ti (Al3Ti structure) and Al3Zr (Al3Zr structure) by arc-melting; doping at 10 ppb level.
• Inequivalent Al-sites occupied by indium solutes were identified by measuring nuclear quadrupole interactions using PAC.
• Differences between vibrational entropies and enthalpies of solutes at different sites are obtained from temperature dependences of ratios of site fractions.
• Enthalpy differences appear to be explained by volume mismatch between transition-metal and aluminum atoms.
Perturbed angular correlation of gamma rays (PAC)
1 1 1
C d
e c
247 ke V
173 ke V
120 ns3/2
1 1 1
In (4.0 d )
1
5/2
/2
2 3
1
5/2
P , = 0)2
t
1
Anisotropy in emission of 2nd -ray
Long-lived intermediate state
4
+1/2
-5/2
-3/2
+5/2
-1/2
+3/2
2/5
2/3
2/1
2/5
1
2 3
t0 100 ns
Spin precessions detected in time domain
Spin 5/2 nucleus, US football shape, in electric field gradient
Quadrupole interaction in PAC (spin 5/2)
ttttG 0355
03510
03513
51
2 3cos2coscos)( Static PAC perturbation function for axial symmetry
0=0 for cubic symmetry
13:10:5 ratio of amplitudes applies for random polycrystalline texture
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Laves phase: C15 (Cu2Mg), cubic, 2 sites
Gd-site (green): cubic point symmetry ( =0) Al-site: (brown): three-fold symmetry ( ≠0)
A model system:Al, In, Gd are all trivalentV(Al) < V(In) < V(Gd)
Easy to identify signals with sites…
Related previous work: Indium in Al2Gd
So, where does indium go??
Matthew O. Zacate and Gary S. Collins, Physical Review B69, 174202(1-9) (2004).
Indium goes to either site, depending on composition andtemperature !
1. Five samples: A (more-Al-rich) ..to.. E (less Al-rich)
2. Different temperatures
Thermally activated:Transfer enthalpy= 0.343(2) eV
fGd/fAl
Sample B
Matthew O. Zacate and Gary S. Collins, Physical Review B69, 174202(1-9) (2004).1
What the ratio of site fractions means:
1. Transfer reaction:
2. Law of mass action: [ ] ≡ mole fraction
on sublattice
3. Ratio of site fractions:
fGd/fAl
AlGdGdAl AlInAlIn
)/exp()/exp()/exp(]][[
]][[TkHkSTkG
AlIn
AlInBtrBtrBtr
GdAl
AlGd
)/exp(][][2
][TkGAl
In
In
f
fBtrGd
Al
Gd
Al
Gd
What about [AlGd] ??
1. A strong function of composition. It may be a constitutional defect if composition is not stoichiometric (constitutional defect).
2. It might be thermally activated itself;e.g., AlGd GdAl 0
Need additional information to interpret activation enthalpy…3
This work: Indium in Al3V, Al3Ti, Al3Zr
Tetragonal structures
Three or four sites: one TM site, 2 or 3 inequivalent Al-sites
Local environments:
TM site has 12 Al near-neighbors (nn)Al(1) has 4 TM nn in squareAl(2) has 4 TM nn in tetrahedronAl(3) has 4 TM nn in square (Al3Zr only)
c-axis
Sites: TM Al(1) Al(2) Al(3) EFG symmetry: axial axial axial non-axial EFG axis: c (tetragonal) c c a (transverse)
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Identifying sites: EFG calculations in point-charge approximation guide identification of sites
4.0 4.2 4.4 4.6 4.80
2
4
6
8
10
12
14
16
18
20
4.0 4.4 4.80
1
Qua
drup
ole
inte
ract
ion
freq
uenc
y 1
Axial ratio
Al(1)
Al(3)
Al(2)
Zr
2.0 2.1 2.2 2.3 2.40
2
4
6
8
10
12
14
16
18
20
Qu
ad
rup
ole
inte
ract
ion
fre
qu
en
cy 1
Axial ratio
Ti
Al(2)
Al(1)
Al3Ti structure Al3Zr structure
No indium on TM site: a. TM site surrounded by 12 nn Al-atoms, as in Al-metal. b. Indium insoluble in Al, ruling out preference for Tm site.
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This work: Indium in Al3V, Al3Ti, Al3Zr
Sites: TM Al(1) Al(2) Al(3)
Tetragonal structures
Three or four sites: one TM site, 2 or 3 inequivalent Al-sites
Local environments:
TM site has 12 Al-near-neighbors (nn)Al(1) has 4 TM nn in squareAl(2) has 4 TM nn in tetrahedronAl(3) has 4 TM nn in square (Al3Zr only)
EFG symmetry: axial axial axial non-axial EFG axis: c (tetragonal) c c a (transverse) EFG magnitudes: very low high intermediate high
c-axis
Transfer of solutes between inequivalent sites of one element:
Transfer reaction:
Law of mass action: [ ] ≡ mole fraction
Ratio of site fractions: (factor of 2 for Al3Ti)
)/exp(][
][
]][[
]][[
1
2
21
12 TkGIn
In
AlIn
AlInBtr
Al
Al
AlAl
AlAl
)/exp(2][
][2
1
2
1
2 TkGIn
In
f
fBtr
Al
Al
Al
Al
InAl2 + AlAl1 ↔ InAl1 + AlAl2
Much simpler result !
1. independent of composition
2. directly gives differences of vibrational entropies and enthalpies of solute on the two sites:
S2-S1= difference of vibrational entropies of solute
H2-H1= difference of enthalpies of solute in the two sites
)/)(exp()/)exp(()/exp(][
][
2 12121
2
1
2 TkHHkSSTkGIn
In
f
fBBBtr
Al
Al
Al
Al
3
Measurements: Al3Zr (3 Al-sites) measured at 725 K and 1210 K
725K: Single signal dominates; attributed to Al(2) due to low frequency. Non-random polycrystalline texture.
1210K: Two new signals. Neither has significant EFG asymmetry, but one signal had non-random amplitudes just like Al(2); attribute to Al(1). Third signal attributed to Al(3) by default.
All measurements in thermal equilibrium (changes in site fractions reversible)
Results: Arrhenius plot of ratios of site fractions
Equilibrium above ~300 C
Fitted enthalpy differences given in figure
Intercepts at T= ∞ give
)/)exp(( 12 BkSS
Interpretation of site preferences in Al3Zr:
Three-level quantum system
Al2
Al1Al3
0
0.20 eV5
0.24 eV
Degeneracies:
1)/)exp((
5.2)/)exp((
21
23
B
B
kSS
kSS
Large degeneracy of site Al(3) attributed to low frequency vibrational modes; enhanced population of Al(3) sites at low temperature. Lower enthalpy of site Al(1) “wins out” at high temperature.
Atom Relative volume
V 0.75
Al 1.00
Ti 1.07
Zr 1.30
In 1.46
H correlated with volume mismatch of TM and Al-atoms
Al(1) Al(2) Al(3)
In-solute is oversized. Oversized TM atoms create additional lattice strain.Strain more anisotropic for “square” configurations, greater strain energy. H ≈ 0 if TM atom is undersized.
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Summary
Site fractions of indium solutes on inequivalent Al-sites in intermetallic compounds were measured using PAC.
Temperature dependences of ratios of site fractions were observed to be thermally activated. Activation enthalpies and prefactors are interpreted in terms of differences in enthalpies and vibrational entropies of solutes on different sites using a thermodynamic model.
The magnitude of site-enthalpy differences was shown to be correlated with atomic volume mismatches.
These appear to be the first measurements of differences of entropies and enthalpies of solutes on inequivalent sites of one element.
Thank you
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