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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