SUPPLEMENTARY
MATERIAL
Hereafter we furnish some details about the operation we deemed as necessary to address in an
appropriate thermodynamic context the various experiments
Shelby (1976)
The experiment refer actually to dissolved noble gases (He, Ne) in silica glass, so it is only of partial
interest here. Shelby1 choose to represent the data in terms of number of dissolved atoms per cm3 of
glass. To do this he multiplied the volume V of the total system (container + gauge + valves + tubing)
expressed in cm3 by the final system pressure P in atm, by the density of He (or Ne) at room
conditions, by the density of vitreous silica, dividing by the weight of specimen in g:
C  5.42  1019
atoms
g
cm 3


atm

g ,
cm 3 cm 3
(1)
The constant 5.42×1019 is equal to the density of He (at 25 °C and 1 atm) in atoms/cm3 multiplied by
the density in g/ cm3 of vitreous silica. Dividing C by Avogadro number N° one obtains the number
of moles of He in the glass. :
5.42  1019
mol
C' 
 9.00  10 5
 atm
(2)
23
6.02  10
cm 3
The molar volume of silica glass is 27.276 cm3/mol, hence the molar fraction of gas in the liquid is
2.456×10-3 and we get LnKH,He = 6.009. Shelby1 refitted his data in form of a Langhmuir isotherm
C
K  f  V0
1  K  f 
(3)
where f is fugacity (assumed to be equal to pressure at sufficiently low pressure), K is a (Pdependent) constant and V0 is the number of atoms per cm3 of glass. The obtained values are
1.95×10-4 for He and 2.51×10-4 for Ne. Assuming these values to be true solubility constants we
would get, in terms of Henry's Law LnKH,He = 8.54 and LnKH,Ne=8.29. Probably the constants are
only operative and return the concentration in atoms. Finally, the fact that E in eq. 8 of Shelby1 is a
"binding energy" and the assumption of a vibrational contribution of the trapped gas is hard to share.
Most likely E may be assumed to correspond to the electrostatic+repulsive+dispersive interaction of
the atom with the reaction field and the gas is monatomic and unbounded, so that no vibrational
contributions are present. The values of E (-1.05 kcal/mol for He and -2.00 kcal/mol for Ne) are
roughly consistent with our PCM estimates.
Kirsten (1968)
The experiment on molten enstatite (0.5MgO-0.5SiO2) is described very carefully2. The results
obtained stemming from the observed concentration/partial pressure slope are expressed in terms of a
dimensional solubility as follows:
 cm 3STP

K He  1.2  10 4 
 atm 
g


(4.1)
1
 cm 3STP

K Ne  0.7  10 4 
 atm 
g


(4.2)
 cm 3STP

K He  0.2  10 4 
 atm 
g


(4.3)
It should be noted that the term STP (Standard Temperature and Pressure) has not an unique
significance. According to IUPAC recommendations3 in chemical thermodynamics the volume of
reduced gas must refer to 298.15 K, 10-5 Pa, while the recommended T and P in the Glossary of
Atmospheric Terms4 are 273.15 K and 10-5 Pa. In common practice however one uses sometimes
298.15 K and 1 atm (1.01325 × 10-5 Pa) and must often 273.15 K, 1 atm. The conversion constants to
obtain the reduced gas volume are respectively in the four cases 24789.560, 22710.953, 24465.402
and 22413.968. We will assume hereafter that all Authors adopted the last conversion (usually
rounded off to 22414) in retrieving their experimental results. The molar fraction of trace component
in the liquid (Xi,l) is then obtained by multiplying the number of moles per gram of substance ni/g by
the molar weight of the solvent (MW) :
X i ,l  n i g   MW
(5)
The units adopted by Kirstens2 are [(cm3 STP/g)×atm]. Assuming enstatite to be pure we have for the
liquid a molar weight pm=50.205 g, hence LnKH,He=15.130, LnKH,Ne=15.669, LnKH,Ar=16.921. In the
experiment of Kirstens the quenching procedure consisted simply in turning off the heating current,
so the nominal T of equilibration (1500°C) must be considered as a high T limit.
Shibata et al. (1998)
The experiments are well detailed and pose no interpretative problems5. Possible He loss from
samples before analyses was inferred by the authors from the large variation in He data and the high
He blank during the analysis. The high quenching rate (200°C/sec) ensure that the measured noble
element concentration in the glass corresponds to the equilibrium value in the former liquid.
However, we have seen in Shelby1 that in solid glass the departure from Henry's Law behavior are
quite immediate (see particularly figures 3 and 5 in Shelby1). The pressure range investigated by
Kirsten2 on the other hand is too limited for practical appraisals concerning silicate liquids
(maximum partial pressure = 420 Torr 0.56 bar). The data of Shibata et al.5 are in dimensional form
[(cm3 STP/g)×bar] and already scaled to 1 bar based on the calculated fugacity of the gaseous
component (see their tables 2 and 5) which is the correct procedure3. In Table A1 we report the
magnitudes adopted for calculations after conversion of the dimensional solubility into Henry's Law
constants.
Table A1: Liquid Samples in the Shibata et al.5 experiment.
_______________________________________________________________________________________________________________________
2
Magnitude
NCS1
Molar volume (cc/mol)
24.965
22.517
21.213
24.315
24.651
25.094
19.247
19.009
18.781
18.419
Molar weight (g/mol)
60.929
59.882
59.231
60.736
60.647
60.512
56.548
54.779
52.959
50.905
Density (g/cc)
2.441
2.659
2.792
2.498
2.460
2.411
2.938
2.882
2.820
2.764
Molecular volume (Å3)
41.456
37.390
35.226
40.375
40.934
41.670
31.960
31.565
31.187
30.586
(Å-3)
0.02412
0.02675
0.02839
0.02477
0.02443
0.02400
0.03129
0.03168
0.03206
0.03269
rcoll (Å)
1.489
1.438
1.410
1.476
1.482
1.491
1.365
1.359
1.354
1.345
Static polarizability (Å3)
5.610
5.457
5.283
5.807
5.668
5.481
4.818
4.602
4.380
4.135

Numeral density
NCS2
NCS3
NS1
NS2
NS3
CMS1
CMS2
CMS3
MS1
4.927
5.718
6.068
5.546
5.144
4.682
6.139
5.707
5.287
4.918
×105 K-1
7.405
8.894
9.028
9.792
8.306
6.371
8.293
7.604
6.876
6.233
'×109
-4.857
-6.851
-6.939
-8.197
-6.028
-3.653
-5.885
-5.007
-4.147
-3.428
K-2
β×106 bar-1
7.033
5.670
4.743
7.261
7.128
6.942
3.239
3.000
2.766
2.462
_______________________________________________________________________________________________________________________
Hiyagon and Ozima (1986)
The experiment was meant to investigate trace partitioning between melt and phenocrysts growing
frm the melt6. Hence the true composition of the liquid at equilibrium with the gas atmosphere could
differ appreciably from the nominal composition of the starting materials, which are two mixtures of
basalt and harzburgite (Table 1 in Hiyagon and Ozima6). Minor contamination effects with the
alumina crucible were also observed by the authors. Likely He loss from the liquid samples is also
declared by the authors. We investigated particularly the BH series results with experiments carried
out at 105 Pa. The assumed equilibrium temperature is 1300°C for the whole series. Results in the
original paper are listed as dimensional magnitudes with different scaling factors, i.e.
 cm 3STP
 cm 3STP

8


 10  for He, Ne, Ar and 
 1010  for Kr and Xe. For all the above recalled
g
g




problems we consider the data as simply qualitative at best.
Table A2: Starting compositions in the Hiyagon and Ozima
experiment6.
3
__________________________________________________
Magnitude
Mixture A
Mixture B
Molar volume (cc/mol)
20.508
19.796
Molar weight (g/mol)
60.598
58.894
Density (g/cc)
2.955
2.975
Molecular volume (Å3)
34.055
32.871
Numeral density (Å-3)
0.02936
0.03042
rcoll (Å)
1.394
1.378
Static polarizability (Å3)
4.782
4.683

5.285
5.439
×105 K-1
8.262
8.523
'×109
-5.926
-6.281
K-2
β×106 bar-1
3.791
3.462
__________________________________________________
Jambon et al. (1986)
The starting material in the experiment of Jambon et al.7 is a natural tholeiitic basalt. Experiments
were performed between 1200°C and 1600°C. No details on the quenching rate are given but a very
accurate investigation of reproducibility, dependence on grain size and time equilibration ensures a
high quality of results. There is moreover a reversal experiment carried out at 1500 °C. Results are
listed in units of
 cm 3STP 

  10 5
 g  bar 
4
Table A3: Starting compositions in the experiments of Kirstens2 and
Jambon et al.7
_____________________________________________________________
Magnitude
Kirstens (1968)
Janbon et al. (1986)
Molar volume (cc/mol)
17.947
21.280
Molar weight (g/mol)
50.190
62.494
Density (g/cc)
2.797
2.937
(Å3)
29.802
35.336
Numeral density (Å-3)
0.03355
0.02830
1.334
1.411
4.080
4.984

5.032
5.331
×105 K-1
6.554
8.410
'×109 K-2
-3.788
-6.040
Molecular volume
rcoll (Å)
Static polarizability
(Å3)
β×106 bar-1
2.258
4.353
_____________________________________________________________
Lux (1987)
The starting materials were crushed powders of natural lava8. To prevent loss of iron from the
material into the crucible a high oxygen partial pressure was maintained during equilibration. The
nominal amount of Fe2O3 thus increased during equilibration at the expenses of FeO (see Table 1 in
Lux, 1987). Quenching was obtained by electrically fusing a wire link and releasing the sample
charge into a cool zone (25-30°C). Results are given in terms of cm 3STP / g / a  10 5 here
 cm 3STP 
  10 5 .
reinterpreted as 
 g  bar 
5
Hereafter we furnish some detail relative to the SPT-PCM computation for Ar in the various media.
Table A4: SPT-PCM calculations for Ar in the media investigated by Kirsten2 and Jambon et al.7
_________________________________________________________________
Magnitude
Kirsten (1976)
Jambon et al. (1986)
mean T=1500 °C
Jambon et al. (1986)
reversal T=1500 °C
Gcav kJ/mol
24.175
21.102
20.964
Hcav kJ/mol
1.002
1.084
1.073
Scav J/(mol×K)
-77.7
-67.1
-66.7
Hint kJ/mol
-15.523
-13.096
-13.096
G°solution kJ/mol
26.577
25.507
25.370
H°solution kJ/mol
-16.952
-14.430
-14.441
S°solution J/(mol×K)
-145.997
-133.951
-133.524
-1.107
-0.429
-0.523
-5.207
-5.907
-5.816
LnKH,298.15
10.721
10.289
10.234
LnKH P,T exper.
16.920
15.616
15.568
H°f,solute kJ/mol
-26.539
-24.085
-24.096
S°solute J/(mol×K)
-0.8
11.4
11.8
V°solute J/bar
1.909
1.965
1.963
a CP solute J/(mol×K)
19.683
20.361
20.267
-5.207
-5.907
-5.816
1.390
1.458
1.456
a CP solution J/(mol×K)
J/(mol×K2)
b CP solution
b CP solute
J/(mol×K2)
rsolv at target KH (Å)
____________________________________________________________
6
Table A5: SPT-PCM calculations for Ar in the media investigated by Shibata et al.5
______________________________________________________________________________________________________________
Magnitude
NCS1-G205
NCS1-G206
NCS1-G209 NCS1-G211
NCS2-G205
NCS2-G206
NCS2-G209
NCS2-G211
NCS3-G211
Gcav kJ/mol
19.366
20.871
18.344
17.787
22.853
23.901
22.040
21.138
23.434
Hcav kJ/mol
0.876
0.981
0.811
0.777
1.309
1.402
1.244
1.172
1.360
Scav J/(mol×K)
-62.0
-66.7
-58.8
-57.1
-72.3
-75.5
-69.8
-67.0
-74.0
Hint kJ/mol
-11.171
-11.171
-11.171
-11.171
-12.385
-12.385
-12.385
-12.385
-13.138
G°solution kJ/mol
25.301
26.806
24.279
23.722
27.830
28.878
27.017
26.115
27.806
H°solution kJ/mol
-12.721
-12.616
-12.786
-12.819
-13.490
-13.398
-13.555
-13.626
-14.192
S°solution J/(mol×K)
-127.5
-132.2
-124.3
-122.6
-138.6
-141.8
-136.1
-133.3
-140.9
a CP solution J/(mol×K)
-1.835
-0.908
-2.459
-2.791
1.743
2.583
1.092
0.399
1.983
-4.790
-5.676
-4.100
-3.709
-8.444
-9.321
-7.635
-6.825
-8.447
LnKH,298.15
10.206
10.813
9.794
9.569
11.226
11.649
10.898
10.534
11.216
LnKH P,T exper.
14.745
15.279
14.481
14.374
15.875
16.236
15.692
15.472
16.280
H°f,solute kJ/mol
-19.862
-19.589
-20.812
-21.684
-20.229
-20.062
-21.271
-22.327
-22.914
S°solute J/(mol×K)
18.8
14.5
21.2
22.4
9.1
6.2
10.8
12.9
5.8
V°solute J/bar
2.039
2.072
2.017
2.005
2.047
2.067
2.032
2.016
2.013
a CP solute J/(mol×K)
18.955
19.882
18.331
17.999
22.533
23.373
21.882
21.189
22.773
-4.790
-5.676
-4.100
-3.709
-8.444
-9.321
-7.635
-6.825
-8.447
1.538
1.563
1.519
1.508
1.521
1.534
1.509
1.496
1.489
J/(mol×K2)
b CP solution
b CP solute
J/(mol×K2)
rsolv at target KH (Å)
7
Magnitude
NCS3-G211
Gcav kJ/mol
23.434
Hcav kJ/mol
Scav J/(mol×K)
NS1-G206
NS1-G209
NS1-G211
NS2-G205
NS2-G206
NS2-G209
NS2-G211
21.590
21.503
21.310
20.607
20.625
23.068
19.360
19.183
1.360
1.343
1.335
1.323
1.263
1.073
1.272
0.979
0.969
-74.0
-67.9
-67.6
-67.0
-64.9
-65.6
-73.1
-61.6
-61.1
Hint kJ/mol
-13.138
-11.464
-11.464
-11.464
-11.464
-11.339
-11.339
-11.339
-11.339
G°solution kJ/mol
27.806
27.297
27.210
27.016
26.314
26.424
28.866
25.158
24.982
H°solution kJ/mol
-14.192
-12.529
-12.538
-12.550
-12.609
-12.685
-12.486
-12.779
-12.788
S°solution J/(mol×K)
-140.9
-133.6
-133.3
-132.7
-130.5
-131.2
-138.7
-127.2
-126.7
a CP solution J/(mol×K)
1.983
2.054
1.979
1.802
1.207
-0.202
1.590
-1.094
-1.224
-8.447
-8.821
-8.741
-8.414
-7.680
-6.410
-8.227
-5.412
-5.189
LnKH,298.15
11.216
11.011
10.976
10.898
10.615
10.659
11.644
10.148
10.077
LnKH P,T exper.
16.280
15.342
15.312
15.339
15.185
15.121
15.972
14.775
14.802
H°f,solute kJ/mol
-22.914
-19.295
-19.309
-20.290
-21.358
-19.594
-19.179
-20.630
-21.503
S°solute J/(mol×K)
5.8
14.2
14.4
14.4
15.8
15.8
9.0
18.9
18.9
V°solute J/bar
2.013
2.093
2.091
2.086
2.070
2.068
2.126
2.039
2.036
a CP solute J/(mol×K)
22.773
22.844
22.769
22.592
21.997
20.588
22.380
19.696
19.566
-8.447
-8.821
-8.741
-8.414
-7.680
-6.410
-8.227
-5.412
-5.189
1.489
1.555
1.554
1.551
1.540
1.550
1.586
1.529
1.526
NS3-G209
NS3-G211
CMS1-G212
CMS1-G215
CMS2-G212
18.150
17.597
18.833
18.083
18.291
J/(mol×K2)
b CP solution
b CP solute
J/(mol×K2)
rsolv at target KH (Å)
NS1-G205
Magnitude
NS3-G205
NS3-G206
Gcav kJ/mol
19.161
20.641
CMS3-G212
18.179
MS1-G156
23.883
8
Hcav kJ/mol
0.747
0.835
0.691
0.662
0.880
0.832
0.773
0.694
0.944
Scav J/(mol×K)
-61.8
-66.4
-58.6
-56.8
-60.2
-57.9
-58.8
-58.6
-76.9
Hint kJ/mol
-11.088
-11.088
-11.088
-11.088
-14.435
-14.435
-14.644
-14.853
-15.146
G°solution kJ/mol
25.167
26.647
24.156
23.603
22.149
21.399
21.429
21.138
26.597
H°solution kJ/mol
-12.773
-12.685
-12.829
-12.858
-15.973
-16.021
-16.294
-16.587
-16.636
S°solution J/(mol×K)
-127.3
-131.9
-124.0
-122.3
-127.9
-125.5
-126.5
-126.5
-145.006
a CP solution J/(mol×K)
-2.851
-2.076
-3.380
-3.664
-2.323
-2.775
-3.167
-3.758
-1.569
-3.835
-4.539
-3.265
-2.938
-4.170
-3.698
-3.410
-2.899
-4.693
LnKH,298.15
10.152
10.749
9.744
9.521
8.934
8.632
8.644
8.527
10.729
LnKH P,T exper.
14.752
15.286
14.488
14.381
14.868
14.693
14.726
14.737
16.933
H°f,solute kJ/mol
-20.113
-19.848
-21.033
-21.878
-25.771
-26.714
-26.177
-26.560
-27.131
S°solute J/(mol×K)
18.5
14.3
21.0
22.2
16.7
18.4
17.6
17.3
-0.4
V°solute J/bar
2.032
2.065
2.011
2.000
1.900
1.893
1.889
1.882
1.917
a CP solute J/(mol×K)
17.939
18.714
17.410
17.126
18.462
18.015
17.622
17.031
19.221
-3.835
-4.539
-3.265
-2.938
-4.167
-3.697
-3.411
-2.899
-4.693
1.538
1.563
1.519
1.508
1.356
1.342
1.338
1.328
1.403
J/(mol×K2)
b CP solution
b CP solute
J/(mol×K2)
rsolv at target KH (Å)
_____________________________________________________________________________________________________________________________________
9
Table A6: SPT-PCM calculations for Ar in the media investigated by Hiyagon and Ozima6
____________________________________________________________________________________
Magnitude
BH-257
BH-258
BH-266
BH-267
BH-271
BH-275
BH-276
Gcav kJ/mol
27.579
26.299
26.845
27.338
29.609
26.798
26.245
Hcav kJ/mol
1.587
1.475
1.555
1.599
1.808
1.550
1.502
Scav J/(mol×K)
-87.2
-83.3
-84.8
-86.3
-93.2
-84.7
-83.0
Hint kJ/mol
-13.598
-13.598
-14.100
-14.100
-14.100
-14.100
-14.100
G°solution kJ/mol
31.575
30.294
30.426
30.919
33.190
30.378
29.826
H°solution kJ/mol
-14.430
-14.542
-14.963
-14.919
-14.709
-14.967
-15.016
S°solution J/(mol×K)
-154.300
-150.381
-152.234
-153.740
-160.655
-152.089
-150.401
4.143
3.128
3.758
4.159
6.071
3.720
3.278
-10.735
-9.677
-10.371
-10.791
-12.832
-10.331
-9.870
LnKH,298.15
12.737
12.220
12.273
12.472
13.388
12.254
12.031
LnKH P,T exper.
17.697
17.255
17.424
17.594
18.372
17.408
17.218
H°f,solute kJ/mol
-21.955
-22.098
-22.543
-22.490
-22.276
-22.548
-22.611
S°solute J/(mol×K)
-6.3
-2.7
-4.4
-5.7
-12.1
-4.2
-2.7
V°solute J/bar
2.026
2.009
1.996
2.002
2.031
1.995
1.988
a CP solute J/(mol×K)
24.933
23.918
24.548
24.949
26.861
24.510
24.068
-10.735
-9.677
-10.371
-10.791
-12.832
-10.331
-9.870
1.514
1.500
1.483
1.488
1.510
1.483
1.477
a CP solution J/(mol×K)
J/(mol×K2)
b CP solution
b CP solute
J/(mol×K2)
rsolv at target KH (Å)
_____________________________________________________________________________________
References
1 Shelby J.E. (1976) J. Appl. Phys.,47, 136-139
2
Kirsten T. (1968) J. Geophys. Res., 73, 2807-2810
3 Schwartz S.E. and Warneck P. (1995) Pure Appl. Chem.,67, 1377-1406
4
Calvert J.G. (1990) Pure Appl. Chem. 62, 2267-2219
6
Hiyagon H. and Ozima M. (1986) Geochim. Cosmochim. Acta, 50, 2045-2057
7
Janbon A., Weber H. and Braun O. (1986) Geochim. Cosmochim. Acta, 50, 401-408
8
Lux G. (1987) Geochim. Cosmochim. Acta, 51, 1549-1560
10