Potassium in the deep Earth: Radioactivity
under pressure
Kanani K. M. LeeDOANOW, March 23-25, 2007
http://www.physics.nmsu.edu/~kanani
Lamb & Sington (1994)
Earth’s Deep Interior
www.gridclub.com/fact_gadget/ 1001/earth/earth/99.html
Heat Dynamics
SOURCES
Primordial:
• accretion
• differentiation
Radioactivity:
• K, U, Th
What we “know”:
•Chondritic K/U ratio ~8 x 104 (Wasserburg et al., 1964)
•Terrestrial K/U ratio ~1 x 104
What we don’t know:
•Why is there a discrepancy in the K/U ratios?
•K lost to space during accretion?!?
•K incorporated in the deep Earth during accretion?!?
Lee & Jeanloz, GRL, 2003; Lee et al., GRL, 2004
Fe-K alloying at high P/T
Diamond-Anvil Cell experiments
Ab-initio QM calculations
www.gridclub.com/fact_gadget/ 1001/earth/earth/99.html
Heat Dynamics
Up to 20% of the Earth’s power generated from 40K decay in the core!!
•Geodynamo•Mantle convection
•Long-lived magma ocean?•Core-Mantle boundary reactions?
Very HOT early Earth.
Earth’s current P/T conditions
300 K
~2000 K
~3000 K ?
~6000 K ?
or greater?
€
n→ p+ e−
p→ n + e+
p+ e− → n
- decay
+ decay
e- capture
radioactive decay schemes
•1947: Electron capture decay of 7Be predicted to be affected by extra-nuclear environments: Segré, Daudel
•Late 1940’s-1950’s: lots of theory, measurements on chemical environment effect on 7Be decay
•1963: first pressure-dependent measurement on 7Be decay (Gogarty et al., ONR)
•1970’s: more theory (40K, e.g., Bukowinski, 1976), another P measurement (7Be, Hensley et al., 1973)
•2000’s: more theory, another P measurement (Liu et al., 2000)
A bit of Electron Capture History
€
δλec =ρ e,totalρ e,total ,0
−1 ⎡
⎣ ⎢
⎤
⎦ ⎥λ ec,0€
λec ∝ total electron charge density ρ e,total
EC decay is dependent on pressure, temperature, chemistry, ionization, etc.
e.g., Bukowinski, 1979
Electron orbitals
cougar.slvhs.slv.k12.ca.us/. ../firstsemass.html
6s
5s
4s
3s
2s
1s
5p
4p
3p
2p
5d
4d
3d
En
erg
y
Relative energies of atomic orbitals
In collaboration with Gerd Steinle-Neumann, BGI
•Structures fully relaxed using VASP
•All-electron method, full potential (LAPW), Wien2k
•Both GGA and LDA approximations to many-body interactions VXC
•Energy convergence to ~1 meV/atom
Computational Method
1/2 ~ 53.3 days100% electron capture decay
= 0.478 MeVBe, BeO, BeCl2
7Be
€
7Be→7Li + γ
1.0
0.8
0.6
0.4
0.2
0.0
percent difference,
λec
50403020100
( )Pressure GPa
, Be hcp , BeO hcp BeCl2 , orth
., 1963Gogarty et al ., 1973Hensley et al & , 2000Liu Huh
7Be under pressure
Prediction: ~0.1 days decrease in 1/2 at 50 GPa forBe, BeO in hcp structure and BeCl2 in orth structure
€
7Be→7Li + γ
7Be
www.gridclub.com/fact_gadget/ 1001/earth/earth/99.html
Heat Dynamics
SOURCES
Primordial:
• accretion
• differentiation
Radioactivity:
• K, U, Th
1940K +e−→18
40Ar +γ
1940K→ 20
40Ca+e− +γ
12total~1.25 billion years!!!
Decay energy and concentration relevant to the Earth
40K long-lived radioactive decay
Electron capture
- decay
1940K +e−→18
40Ar +γ
40K long-lived radioactive decay
Electron capture
Decay is dependent on pressure, temperature, chemistry, ionization, etc.
With pressure a 4s 3d
electronic transition makes K, an alkali metal, more like a
transition metal (Bukowinski, 1976)
Transition metals
s d electronic transition in K
6s
5s
4s
3s
2s
1s
5p
4p
3p
2p
5d
4d
3d
En
erg
y
Relative energies of atomic orbitals
6s
5s
4s
3s
2s
1s
5p
4p
3p
2p
5d
4d
3d
Relative energies of atomic orbitals
K
En
erg
y
6s
5s
4s
3s
2s
1s
5p
4p
3p
2p
5d
4d
3d
Relative energies of atomic orbitals
K
En
erg
y
1/2,total ~ 1.25 Gyr1/2,EC ~ 11.9 Gyr1/2,- ~ 1.4 Gyr
~11% electron capture decay
= 1.461 MeVK, K2O, KCl
40K
€
40K→40Ar + γ
40K under pressure
0.02
0.01
0.00
percent difference,
λec
50403020100
( )Pressure GPa
, K bcc , K fcc K2 , O fcc
, 1KCl B , 2KCl B
5395.0
5394.5
5394.0
5393.5
total electron charge density,
ρe
80604020
(Volume Å3)
1.0
0.8
0.6
0.4
0.2
0.0
- number of d orbital electrons
05102550 ( )Pressure GPa
40K under pressure
sdelectronictransition
fcc K
5395.0
5394.5
5394.0
5393.5
total electron charge density,
ρe
80604020
(Volume Å3)
1.0
0.8
0.6
0.4
0.2
0.0
- number of d orbital electrons
05102550 ( )Pressure GPa
40K under pressure
fcc K
start of sd electronic transition: ~1% of electrons are in d orbital
40K
€
40K→40Ar + γ
Prediction: ~3 Myr decrease in 1/2,ec at 25 GPa for K and
~0.6 Myr decrease for K2O and KCl
sd transition matters!
Are these changes measurable?
7Be: Yes! ~40 billion decays/min
40K: Probably not. ~40 decays/day
Periodic Table of Elements
Comparable EC system: 22Na
1/2,total ~ 2.6 yr1/2,EC ~ 27.7 yr1/2,- ~ 2.8 yr
~9.4% electron capture decay = 1.275 MeVNa, Na2O, NaCl
~32 billion decays/day!!
22Na under pressure0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
percent difference,
λec
100806040200 ( )Pressure GPa
, Na bcc , Na fcc , 1NaCl B , 2NaCl B Na2 , O fcc
22Na under pressure
0.3
0.2
0.1
0.0
number of d-orbital electrons
40302010
Volume (Å3)
893
892
891
890
889
888
total electron charge density,
ρe
010251001000
, Na fcc total electron density 4 - th order polynomial fit - d orbital occupancy
( )Pressure GPa
0.25
0.20
6543
892
891
1000
22Na under pressure
0.3
0.2
0.1
0.0
number of d-orbital electrons
40302010
Volume (Å3)
893
892
891
890
889
888
total electron charge density,
ρe
010251001000
, Na fcc total electron density 4 - th order polynomial fit - d orbital occupancy
( )Pressure GPa
sdelectronic
transition!?!
22Na under pressure
0.3
0.2
0.1
0.0
number of d-orbital electrons
40302010
Volume (Å3)
893
892
891
890
889
888
total electron charge density,
ρe
010251001000
, Na fcc total electron density 4 - th order polynomial fit - d orbital occupancy
( )Pressure GPa
start of sd electronic transition: ~2% of electrons are in d orbital
Are these changes measurable?
7Be: Yes! ~40 billion decays/min
22Na: Yes! ~32 billion decays/day
40K: Probably not. ~40 decays/day
DIAMOND ANVIL CELL
Diamond• Strength• Transparency
=
ForceArea
Pressure
Ge
detector
Ge
detector
measurements under high P
Ge
detector
Ge
detector
measurements under high P
1400
1200
1000
800
600
400
200
0
counts
300025002000150010005000
Energy (keV)
1-day background spectraof empty diamond cell
1400
1200
1000
800
600
400
200
0
counts
300025002000150010005000
Energy (keV)
511 keV e+ emission
1275 keV 22Na -ray emission: 3+ billion
counts per day!!!
1-day expected spectra
1400
1200
1000
800
600
400
200
0
counts
300025002000150010005000
Energy (keV)
511 keV e+ emission
1275 keV 22Na -ray emission: 3+ billion
counts per day!!!
661 keV: 137Cs 1461 keV:
40K2615 keV: 232Th208Tl
•Pressure and chemistry DO have an effect on electron capture radioactive decay, although small
•7Be predictions are compatible with previous experiments, although lower
•Na and K as pure metals are predicted to show more P-dependence than respective simple oxides and chlorides
•Pressure, chemical environment effects are measurable for longer-lived isotope systems
Conclusions
Funded by:
Alexander von Humboldt Foundation
Bayerisches Geoinstitut (Bayreuth)
CDAC (Department of Energy)
Special thanks to:
Gerd Steinle-Neumann (BGI)Sofia Akber-Knutson (UCSD)Ron Nelson (LANL)Bob Rundberg (LANL)Boris Kiefer (NMSU)Allen Knutson (UCSD)David Dolejs (BGI)Innokenty Kantor (BGI)Artem Oganov (ETH)