Nucleosynthesis of the
nuclides
Chart
2nd Generation Stars (Our Sun)
Fusion by CNO reaction
+ 1H  13N + g
13N  13C + b+ + v
13C + 1H  14N + g
14N + 1H  15O + g
15O  15N + b+ + v
15N + 1H  12C + 4He
12C
12C
+ 4 1H  12C + 3 g + 2 b+ + 2 v
Then by combustion of 16O ( < 1 yr),
a reaction that produces higher mass
elements, including Si and Mg
16O
+ 16O  28Si + 4He + g
12C
+ 16O  24Mg + 4He + g
chart
Fusion is limited at mass 56Fe by the
diminishing return of energy of fusion and
increased energy of nuclear bonds
p = proton = 1.007593 u = 1.6726234 E–27 kg
n = neutron = 1.008982 u = 1.6749287 E–27 kg
u = 1 atomic mass unit = 1/12 12C = 1.660018 E–27 kg
56
26Fe30 = 26p
A 56Fe = 56
+ 30n
Mais le poid atomique de 56Fe = 55.934942
(http://csnwww.in2p3.fr/AMDC/web/masseval.html)
26 x 1.007593 = 26.197418 u
30 x 1.008982 = 30.269460 u
56.466878 u
56.466878 – 55.934942 = 0.531936 u = 0.883 E–27 kg = masse perdue
Converti en énergie de liason nucléaire: E = mc2
Energy of nuclear bonding
• maximum at 56Fe
• beyond, fusion is an endothermic reaction
• nucleosynthesis beyond 56Fe by neutron capture
reactions and by fission of the nuclides with
Z > 90 (uranium and the transuranics)
http://www.chem.uidaho.edu/~honors/nucbind.html
End as a red giant and
a supernova
Supernova remnants
Cas A in x-rays
(Chandra)
Cygnus Loop (HST):
green=H, red=S+,
blue=O++
Vela
Remnant of SN386, with
central pulsar (Chandra)
SN1998bu
Nucleosynthsis in 2nd generation stars:
Inventory – 1H, 4He, 12C, 13C, 14N, 15N, 16O, 20Ne, 24Mg,
28Si, 32S, 36Ar, 40Ca, 44Ca,48Ti, 52Cr, 56Fe
Production of neutrons:
13C
+ 4He  16O + n
Nucleosynthesis by neutron and
proton capture
Process S – slow neutron capture (2nd generation stars)
Production of elements up to Bi
Process R – capture of fast neutrons (red giants)
Production of heavy elements – to U.
After is limited by fission
Process P – proton capture (1H)
Production of nuclides poor in neutrons
s
50
Very unstable nuclides (T½ < 1 day)
Unstable nuclides (T½ > 1 day)
40
Atomic Number (Z) m
Z=N
Stable nuclides
30
20
Isotopes
10
Isobars
Isotones
0
0
10
20
30
Neutrons (N)
40
50
The Stable Environmental Isotopes
Isotope Ratio
2H
3He
13C
15N
18O
34S
37Cl
% natural
abundance
2H/1H
0.015
3He/4He
0.000138
13C/12C
1.11
15N/14N
0.366
18O/16O
0.204
34S/32S
4.21
37Cl/35Cl
24.23
Reference
VSMOW
Atmospheric He
VPDB
AIR N2
VSMOW, VPDB
CDT
SMOC
Routine and non-routine stable environmental isotopes
Isotope
Ratio
D
2
13
13
1.11
11,100
15
15
0.366
3,660
AIR N2 (3.677·10–3)
18
18
0.204
2,040
34
34
4.21
42,100
VSMOW (2.0052 · 10–3)
VPDB (2.0672 · 10–3)
CDT (4.5005 · 10–2)
3
He
3
He/4He
0.000138
6
Li
6
Li/7Li
7.5
75,000
C
N
O
S
H/1H
C/12C
N/14N
O/16O
S/32S
0.015
150
Reference
(abundance ratio)
Commonly analysed compounds
VSMOW (1.5575 · 10–4)
H2O in water and ice, CH4 and other
hydrocarbons, mineral hydration waters,
DIC, DOC, carbonate minerals, organics,
CO2, CH4 and other hydrocarbons,
N2 in groundwater, NO3–, NH4+, N2O,
organic compounds
H2O, dissolved O2, SO42–,
NO3–,
Carbonate minerals (VPDB)
SO42–, H2S, sulfate and sulfide minerals
VPDB (1.1237 · 10–2)
1.38
AIR (0.00000138)
Groundwater, minerals
L-SVEC (0.08362)
Seawater, brines, groundwater, minerals,
hydrothermal water
Seawater, carbonates, groundwaters,
bines,
Cl– and chloride minerals, chlorinated
hydrocarbons, perchlorate compounds
Seawater,
brines,
groundwaters,
carbonates, Ca-minerals and rocks.
11
11
80.1
801,000
NBS 951 (4.044)
37
37
24.23
242,300
SMOC (0.324)
87
87
B
Cl
Sr
B/10B
natural abundance
%
ppm
Cl/35Cl
Sr/86Sr
7.0 and 9.8
Direct measurement
Delta - permil: d - ‰
m ( O / O ) sam ple  m ( O / O ) reference
18
d
18
O sam ple 
d 18 O sam ple
16
18
18
16
16
m ( O / O ) reference
 ( 18 O / 16 O ) sam ple

  18
 1  1000
16
 ( O / O ) reference

‰ VSMOW
What is the relative enrichment or depletion of
crustal rocks (~0.204%) relative to VSMOW






d
18
18O
O
 R crustal  0.00204

16
O  crustal
18
O
 R V SM O W  0.0020052

16
O  V SM O W
18
O crustal
 R crustal

 0.00204

3
3
 
 1   10  
 1   10
 0.0020052

 R V SM O W

= 17.4‰ VSMOW
 crustal rocks are enriched in 18O by 17.4‰
or 1.7% relative to the standard VSMOW
in
Isotope Ratio Mass Spectrometry
Laser attenuation isotope analyser
(Wavelength-Scanned Cavity Ring Down
Spectroscopy – WS-CRDS)
• Laser absorption
• Reads fraction of heavy isotope bonds
• Direct reading of BOTH
• Do it in the field!
18O
and D ratios
Laser attenuation isotope analyser
(Wavelength-Scanned Cavity Ring Down
Spectroscopy – WS-CRDS)
and Picarro – nice
Los Gatos – the original black box
small footprint
Laser attenuation isotope analyser
(Wavelength-Scanned Cavity Ring Down
Spectroscopy – WS-CRDS)
Check out the sample requirements – 2 mL.
Fill a tray of 100! – lots of good data.
Distribution of isotopes in nature
• Isotope fractionation during reaction
• Rayleigh distillation during reservoir
depletion
Isotope fractionation, a
H2Owater « H2Ova po ur
R reactant
a
R product
a
18
O water
 vapor





O

16
O  water




O

16
O  vapor
18
18
a
18
O water
d 18 O sam ple
a
18
 vapor





O

16
O  water




O

16
O  vapor
18
18
 ( 18 O / 16 O ) sam ple

  1000
  18

1

16
(
O
/
O
)


reference
O w ater  vapor 



O

16
O  w ater



O

16
O  vapor
18
18

d
d
18
18
O w ater  1000
O vapour  1000
Physico-chemical fractionation
16
K 
[
18
[
16
O water +
O ] wat [
16
O ] wat [
18
K 
18
O vap o r 
O ] vap

O ] vap
 [ 18 O ] wat

 [ 16 O ]
wat





 [ 18 O ] vap

 [ 16 O ]
vap





[
18
[
16

18
O water +
O ] wat
O ] wat
R wat
R vap

[
16
[
18
16
O vap o r
O ] vap
O ] vap

 [ 18 O ] wat

 [ 16 O ]
wat





 [ 18 O ] vap

 [ 16 O ]
vap





 a wat  vap  1
Isotope partitioning functions
 = symmetry value
m = mass of isotope
E = the energy state summed from the
zero-point to the energy of the
dissociated molecule (J·mole–1)
k = Boltzmann constant
(gas constant per molecule)
= n · 1.380658 · 10–23 JK–1
T = thermodynamic temperature K
(Q
(Q
*
X
*
Y
)
)
e
 E / kT
Energy absorbed
m
3/2
Energy released
Q 
1
0
zero point
of enegy
/ QX
RX
=
= a XY
RY
/ QY
bond w ith heavy isotope
Interatomic istance
Diffusive fractionation
v 
kT
2 m
v = molecular velocity (cm · s–1)
k = Boltzmann constant (gas constant per molecule)
= n · 1.380658 · 10–23 JK–1
m = molecular mass (e.g. 7.3665 · 10–26 kg for 12C16O2)
T = absolute temperature K
Diffusive Fractionation
e.g.
13C
during CO2 diffusion
Diffusion in a vacuum
a
13
C CO
2

kT
v (1 3 CO
2
v (1 2 CO
2)
)

2  45
kT

44
 0 . 9888
45
2  44
Diffusion in air
a
13
C CO
2

m 12 ( m 13  m air )
m 13 ( m 12  m air )

44  ( 45  28 . 8 )
45  ( 44  28 . 8 )
 0 . 9956
Metabolic (biologic)
Fractionation
• 13C during photosynthesis
• sulphate reduction
• methanogenesis . . .
Units
Isotope Enrichment (e)
• Isotope difference in permil units between two reacting
phases at equilibrium
e X Y
RX

3
3



 1   10  ( a  1)  10
RY

• when a is small, then we can use:
e X  Y  10 ln a X  Y
3
Units
Isotope Separation (D)
• Isotope difference in permil units between any two phases
D X Y  d X  d Y
For a water – vapor exchange at 25°C
what is the d18O of vapor, where:
• water d18Ow = 0.0 ‰ VSMOW
For a water – vapor exchange at 25°C
what is the d18O of vapor, where:
• water d18Ow = 0.0 ‰ VSMOW
The fractionation factor (a) is:
a18Ow-v = 1.0093
The isotopic enrichment (e):
and
e18Ow-v = (a–1) ·103 = 9.3‰
e18Ov-w = – 9.3‰
For a water – vapor exchange at 25°C
what is the d18O of vapor, where:
• water d18Ow = 0.0 ‰ VSMOW
e18Ow-v = (a–1) ·103 = 9.3‰
d18Ovapor = d18Owater – e18Owater-vapor
= 0.0 – 9.3‰
= – 9.3‰
• vapor d18Ov = –9.30‰ VSMOW
For most reactions in hydrogeology:
• d values are typically –50 to +50 ‰
• a values are close to 1 (0.98 to 1.02)
• e values are typically –20 to +20 ‰
Except for some extreme reactions and light isotopes . . .
e.g. hydrogen gas produced from water is strongly
depleted in 2H and has a fractionation factor a2HH2O-H2 =
3.76 at 25°C.
What will be the d2H value for H2 produced from water
with d2HH2O = –75‰ at 25°C?
a 2 H H 2O  H 2 
3.76 
R H 2O

R H2
d 2 H H 2 O  1000
d H H 2  1000
2
 3.76
(  75 )  1000
d 2 H H 2  1000
d2HH2 = –754‰ VSMOW
(but using e, d2HH2 = –75 – 2760 = –2835‰)
So, use the e simplification . . .
• when a is close to 1
• when the d-values are not too different from
the reference (i.e. within a few tens of permil of
0)
Fractionation and Temperature
Q 
(Q
(Q
40
30
T °C
20
18
10
O w-v
*
X
*
Y
1
m
3/2
)
)

e
 E / kT
/ QX
RX
=
= a XY
RY
/ QY
lnaX-Y = aT–2 + bT–1 + c
0
18
-10
O i-v
-20
8
10
12
14
103 lna18O
16
18
Fractionation and Temperature
103 lna2H
60
80
100
140
160
40
40
30
30
2
20
H w-v
20
18
O w-v
10
10
0
0
2
18
-10
O i-v
-20
H i-v
T °C
T °C
120
-10
-20
8
10
12
14
103 lna18O
16
18
Fractionation and Temperature
eD ‰
60
80
100
140
160
40
40
30
30
2
18
10
O
H w-v
20
w-v
10
0
0
2
18
-10
O
i-v
-20
H i-v
T °C
20
T °C
120
-10
-20
8
10
12
14
e 18O ‰
16
18
T°C
2
H
water-vapour
AA 1
A
150
25
??
??
??
??
13C
10°-40°
73.2
-303.9
-204.34
-8.949
25
-60
-7.69
181.264
346
151
6.1
-90.888
-223
-38
88.4
1
0
0
0
1.137
1.534
5.9702
290.498
2.1
23.9
21.3
-0.4156
-3.206
-32.801
-127.9
-22
-7.9
2.8
-2.0667
2.644
52.227
1.137
-0.0206
2.78
-1.8034
-0.4156
17.9942
0
10.611
1.0
-19.97
-2.89
-2.7798
3.2
0.45
0
3.25
2.88
2.88
3.88
0
0
2.3
0
0
0
0
-1.5
-0.4
-3.7
-5.1
-4.1
-3.6
-2.9
29.1
2.8
4.0
31.5
28.3
28.8
25.0
1.029571
1.002836
1.004022
1.031958
1.0287
1.029215
1.025278
50
50
200
3.52
1.9189
3.55
0
8.582
0
-4.350
-18.977
-2.570
29.4
26.0
13.3
1.029791 Kita et al., 1985
1.026294 Kawabe, 1978
1.013375 Shiro and Sakai, 1972
34°-93°
0°-100°
195°-573°
Alkali feldspar-H2O
Ca- feldspar-H2O
Kaolinite-H2O
Smectite-H2O
Chlorite-H2O
500
500
200
150
25
3.13
2.09
2.5
2.67
1.56
0
0
0
0
0
-3.7
-3.7
-2.87
-4.82
-4.7
1.5
-0.2
8.3
10.1
12.8
1.001537
0.999796
1.008331
1.010142
1.012931
Bottinga and Javoy, 1973
Bottinga and Javoy, 1973
Land and Dutton, 1978
Yeh and Savin, 1977
Wenner and Taylor, 1971
500°-800°
500°-800°
CO2(g)-CO2(aq)
HCO3-CO2(g)
HCO3-CO2(aq)
CO3-HCO3
CO3-CO2(g)
CO3-CO2(g)
CaCO3-HCO3
CO2-CaCO3
"
25
25
25
25
25
25
25
25
25
25
200
200
0.942
0
0
0
0
0.87
0
0
-2.988
-0.42615
-1.04
-4.2
-8.815
0.373
9.552
9.866
-0.867
0
9.037
-4.232
7.6663
-6.4449
-2.45
12.079
18.393
-0.19
-24.10
-24.12
2.52
-3.40
-22.73
15.10
-2.46
16.30
9.90
-5.95
-8.9
1.1
7.9
9.0
-0.4
6.4
7.6
0.9
-10.4
-10.1
-10.0
0.8
-0.5
1.001062
1.007968
1.00901
0.999612
1.006407
1.007608
1.000907
0.989693
0.989942
0.990034
1.000819
0.999492
Vogel, Grootes and Mook, 1970
Mook, Bommerson and Staverman (1974)
Mook, Bommerson and Staverman (1974)
Mook, Bommerson and Staverman (1974)
Deines et al. (1974)
IAEA (1983) Thode et al., 1965
Mook, 1986
Bottinga, (1968)
Bottinga, (1969)
Bottinga, (1969)
Bottinga (1969)
Bottinga (1969)
200
0.8914
-8.557
18.11
-8.27
0.2
300
300
-0.62
2.28
6.616
15.176
6.04
-8.38
-3.08
SiO2(amorph)-H2O
SiO2(quartz)-H2O
SiO2(quartz)-H2O
CO2-CaCO3
CO2-CH4
CO2-CH4
34S
Temperature Ran
2
2
1.011231
1.078511
#NUM!
1.019487
1.020814
1.020814
1.135457
2.583595
3.485485
3.762008
2.11556
2.419961
1.02008
1.022608
1.027229
2.357616
0.985154
1.177903
1.16855
1.009373
1.009189
1.009416
1.003105
1.002804
1.014859
1.040966
1.031062
1.012601
Majzoub (1971)
Kakiuchi and Matsuo, 1979
Northrop and Clayton, 1966
Sheppard and Schwarcz, 1970
Fontes (1965)
Lloyd (1968)
McKenzie and Truesdell (1977)
Mitzutani and Rafter (1969)
Lloyd (1968)
Fractionation - Other Systems
ice-vapour
water vapour - hydrogen gas
"
water-hydrogen gas
methane-hydrogen gas 1
"
water vapour-methane
water vapour-methane
Water-methane
water-H2S
water-gypsum
water-horneblend
water-biotite
water-vapour
"
"
water-ice
"
ice-vapour
CO2-H2O
Calcite-H2O
CO2-Calcite
Aragonite-H2O
Dolomite-H2O
Dolomite-Calcite
water-gypsum
SO4-H2O
"
"
anhydrite-H2O
0
0
0
0
100
25
25
100
100
25
25
25
25
25
100
100
25
25
25
0
0
0
25
15
25
25
50
100
25
25
25
25
100
"
"
52.612
-168
-161.04
Reference
-76.248
467.6
389.61
water-ice
-76.248
64.55
794.84
a
24.844
0
13
1158.8
24.844
2.408
-1620.1
103lna
C
11
76
10953246
19.3
20.6
20.6
127
949
1249
1325
749
884
20
22
27
858
-15
164
156
9.3
9.1
9.4
3.1
2.8
14.7
40.1
30.6
12.5
"
18O
B
6
O'Neil (1968)
Arnason (1969)
Suzuoki and Kumura (1973)
Majzoub (1971) plus Arnason (1969)
Suess (1949)
100°-200°
Bottinga (1969) calculated
0°-600°
Bottinga (1969) plus Majzoub (1971)
Horibe and Craig (1975) written communication, in Friedman
Bottinga (1969) calculated
0-700
Bottinga (1969a) calculated
0°-700°
Bottinga (regressed)
10-250
Bottinga (1969a) plus Majzoub (1971)
0°-100°
Galley et al. (1972)
25°-200°
Gonfiantini and Fontes (1967)
Suzuoki and Epstein (1976)
450°-850°
Suzuoki and Epstein (1976)
450°-850°
Majzoub (1971)
Bottinga and Craig (1969)
Kakiuchi and Matsuo, 1979
10°-40°
O'Neil (1968)
Suzuoki and Kumura (1973)
Majzoub (1971) plus O'Neil (1968)
Bottinga (1968)
0-100
O'Neil, Clayton and Mayeda (1969)
0°-500°
Bottinga, 1968
0°-600°
200°-800°
100°-650°
0°-500°
110°-200°
100°-575°
5°-125°
5°-125°
5°-125°
<100°
<100°
<100°
<100°
<100°
0-280
200-700
0-700
1.000198 Ohmoto and Rye (1979)
<600°
25.0
24.3
1.025354 Bottinga, (1969)
1.024602 Richet et al. (1977)
0-700
400°-1300°
SO42--SO2(g)
25
-1
9.2667
-7.4213
12.4
1.012487 Sakai (1968)
SO42--H2S (aq)
25
3
14.009
-11.197
69.5
1.072008 Sakai (1968)
SO42--H2S (aq)
25
5.07
0
6.33
63.4
1.065411 Robinson (1973)
SO42--HS -(aq)
25
3
15.67
-13.592
72.7
1.075418 Sakai (1968)
25°- ~250°