|
|
The
Observed Properties of Liquid Helium
at the Saturated Vapor
Pressure
Chapter 8. Entropy
Adopted Database for µ+
Author(s) |
Key # |
Method |
Range (K) |
Barenghi, et al. |
1 |
Ion Pool |
0.2388
T
0.8462 |
Schwarz |
2 |
Drift Velocity |
0.371
T
5.18
|
Adopted
Database for µ-
Author(s) |
Key # |
Method |
Range (K) |
Barenghi,
et al. |
1 |
Ion
Pool |
0.0528
T
0.9632 |
Schwarz |
2 |
Drift
Velocity |
0.247
T
5.18
|
Comments and Key to Authors
1) Ref. 18. Uncertainties: for negative ions, > 270mK, and for positive ions, > 370mK, results are in good agreement with Ref. 14. Below these temperatures the mobilities depend on the experimental situation and the paper should be consulted for details.
2) Ref. 14. Uncertainty better than 2%.
3) The splines are fit to the log10 of the mobility.
4) To convert mobilities from m2/V×s to cm2/V×s, multiply by 104.
Table 10.1. Adopted database for the positive ion mobility.
T90 (K) |
µ+(m2/V.s) |
Key |
T90 |
µ+(m2/V.s) |
Key |
0.0255 |
2.11000E+3 |
1 |
0.3953 |
3.80000E+0 |
2 |
0.0421 |
1.73000E+3 |
1 |
0.4020
|
4.97000E+0
|
1 |
0.0459
|
1.38000E+3 |
1
|
0.4063
|
3.36000E+0 |
2 |
0.0599 |
1.32000E+3 |
1 |
0.4108
|
4.01000E+0
|
1 |
0.0656 |
1.22000E+3 |
1
|
0.4124 |
2.95000E+0
|
2 |
0.0736 |
1.05000E+3 |
1 |
0.4214 |
2.63000E+0 |
2 |
0.0836 |
1.10000E+3 |
1 |
0.4216
|
4.18000E+0
|
1 |
0.0850 |
9.13000E+2 |
1 |
0.4304 |
2.38000E+0 |
2 |
0.0922 |
9.45000E+2 |
1 |
0.4326 |
2.86000E+0 |
1 |
0.1037 |
8.46000E+2 |
1
|
0.4404
|
2.05000E+0 |
2 |
0.1052
|
7.75000E+2 |
1 |
0.4502 |
2.17000E+0 |
1 |
0.1103 |
7.70000E+2 |
1 |
0.4515 |
1.75000E+0 |
2 |
0.1250
|
5.96000E+2 |
1
|
0.4525 |
3.51000E+0 |
1 |
0.1259 |
6.51000E+2 |
1 |
0.4525 |
3.61000E+0 |
1 |
0.1259 |
5.71000E+2 |
1 |
0.4525 |
2.83000E+0 |
1 |
0.1479 |
4.21000E+2 |
1 |
0.4625 |
1.46000E+0 |
2 |
0.1505 |
4.10000E+2 |
1 |
0.4731 |
1.68000E+0
|
1 |
0.1560 |
3.95000E+2 |
1
|
0.4735 |
1.23000E+0 |
2 |
0.1636
|
2.85000E+2 |
1 |
0.4856 |
1.01000E+0 |
2 |
0.1688
|
3.06000E+2 |
1 |
0.4893
|
1.15000E+0 |
1 |
0.1740 |
2.14000E+2 |
1
|
0.4996 |
8.05000E-1 |
2 |
0.1790 |
2.07000E+2 |
1
|
0.5073 |
9.81000E-1 |
1 |
0.1865 |
1.56000E+2 |
1 |
0.5116
|
6.42000E-1 |
2 |
0.1865 |
1.82000E-+2 |
1 |
0.5253
|
7.32000E-1 |
1 |
0.1889 |
1.76000E+2 |
1
|
0.5277 |
4.86000E-1 |
2 |
0.1988 |
1.43000E+2 |
1 |
0.5310 |
6.81000E-1 |
1 |
0.2059 |
1.42000E+2 |
1
|
0.5417 |
3.73000E-1 |
2 |
0.2181 |
9.22000E+1 |
1 |
0.5470 |
5.02000E-1 |
1 |
0.2227 |
9.02000E+1 |
1 |
0.5501 |
4.86000E-1
|
1 |
0.2390
|
6.17000E+1 |
1 |
0.5568 |
2.76000E-1
|
2 |
0.2454 |
4.35000E+1 |
1 |
0.5679
|
3.45000E-1
|
1 |
0.2627 |
3.74000E+1 |
1 |
0.5718 |
3.28000E-1 |
1 |
0.2687
|
2.93000E+1 |
1 |
0.5748 |
1.98000E-1
|
2 |
0.2816 |
2.50000E+1
|
1 |
0.5883 |
2.04000E-1 |
1 |
0.3012 |
1.70000E+1 |
1 |
0.5917 |
2.19000E-1 |
1 |
0.3039 |
1.53000E+1
|
1
|
0.5918
|
2.25000E-1 |
1 |
0.3063 |
2.29000E+1 |
1 |
0.5918
|
1.41000E-1 |
2 |
0.3313 |
1.07000E+1 |
1 |
0.6115 |
1.55000E-1 |
1 |
0.3318
|
1.00000E+1 |
1 |
0.6117 |
1.32000E-1 |
1 |
0.3522 |
8.03000E+0 |
1
|
0.6119 |
9.65000E-2 |
2 |
0.3569 |
8.02000E+0 |
1
|
0.6121
|
1.49000E-2 |
1 |
0.3702
|
6.50000E+0
|
1
|
0.6218
|
1.25000E-2 |
1 |
0.3703 |
6.71000E+0
|
1
|
0.6330 |
6.60000E-2 |
2 |
0.3722 |
5.19000E+0
|
2
|
0.6340 |
8.76000E-2 |
1 |
0.3793 |
4.72000E+0 |
2
|
0.6371 |
9.54000E-2 |
1 |
0.3873 |
4.18000E+0
|
2
|
0.6440 |
8.27000E-2
|
1 |
0.3917 |
5.02000E+0
|
1 |
0.6508 |
7.48000E-2 |
1 |
Table
10.1. (Continued)
T90 (K) |
µ+(m2/V.s) |
Key |
T90 |
µ+(m2/V.s) |
Key |
0.6550
|
4.45000E-2 |
2
|
0.9788 |
8.09000E+0
|
1 |
0.6599 |
6.24000E-2 |
1 |
0.9988 |
7.15000E-4 |
2 |
0.6648 |
5.83000E-2 |
1
|
1.0026 |
6.44000E-4 |
1 |
0.6781 |
2.97000E-2 |
2 |
1.0218 |
5.60000E-4 |
1 |
0.6784 |
4.59000E-2 |
1 |
1.0509 |
4.80000E-4 |
2 |
0.6788 |
3.96000E-2 |
1 |
1.1350
|
2.57000E-4
|
2 |
0.6845 |
4.23000E-2 |
1
|
1.1991 |
1.66000E-4 |
2 |
0.6910 |
3.22000E-2 |
1 |
1.3003 |
9.16000E-5 |
2 |
0.6947
|
3.50000E-2
|
1
|
1.4015 |
5.48000E-5
|
2 |
0.6972 |
3.36000E-2 |
1 |
1.5036 |
3.53000E-5
|
2 |
0.7031
|
2.03000E-2 |
2 |
1.6057 |
2.44000E-5
|
2 |
0.7038 |
2.97000E-2 |
1 |
1.7119 |
1.80000E-5
|
2 |
0.7108
|
2.70000E-2 |
1
|
1.8161
|
1.39000E-5
|
2 |
0.7154 |
2.18000E-2 |
1 |
1.9172
|
1.09000E-5 |
2 |
0.7213
|
2.25000E-2 |
1 |
2.0203 |
8.42000E-6 |
2 |
0.7292 |
1.38000E-2 |
2
|
2.1215
|
6.22000E-6 |
2 |
0.7318 |
1.65000E-2 |
1 |
2.1365 |
5.86000E-6
|
2 |
0.7330 |
1.93000E-2 |
1 |
2.1516 |
5.55000E-6
|
2 |
0.7402 |
1.69000E-2 |
1
|
2.1676
|
5.17000E-6
|
2 |
0.7474 |
1.54000E-2 |
1 |
2.1738 |
5.04000E-6 |
2 |
0.7505 |
1.25000E-2 |
1
|
2.1788
|
4.96000E-6 |
2 |
0.7591
|
1.31000E-2
|
1
|
2.2046
|
4.72000E-6 |
2 |
0.7593 |
8.86000E-3 |
2 |
2.2647 |
4.52000E-6
|
2 |
0.7633
|
1.22000E-2 |
1 |
2.3749 |
4.30000E-6
|
2 |
0.7637 |
1.19000E-2
|
1 |
2.4951 |
4.20000E-6 |
2 |
0.7715 |
9.20000E-3 |
1 |
2.6455
|
4.13000E-6 |
2 |
0.7731 |
1.07000E-2 |
1
|
2.8260
|
4.12000E-6
|
2 |
0.7833
|
8.98000E-3
|
1
|
3.0263 |
4.16000E-6 |
2 |
0.7877
|
8.52000E=3
|
1 |
3.2567 |
4.23000E-6 |
2 |
0.7883 |
6.05000E-3
|
2
|
3.5070 |
4.35000E-2
|
2 |
0.7928
|
6.78000E-3
|
1
|
3.7771
|
4.49000E-2
|
2 |
0.8070 |
6.44000E-3 |
1 |
3.9370 |
4.60000E-2
|
2 |
0.8107
|
5.29000E-3
|
1
|
4.1671 |
4.70000E-2
|
2 |
0.8224
|
4.01000E-3 |
2 |
4.3370
|
4.80000E-2
|
2 |
0.8324 |
3.93000E-3 |
1 |
4.4570 |
4.87000E-2
|
2 |
0.8543
|
2.98000E-3 |
1
|
4.5571
|
4.98000E-2
|
2 |
0.8615
|
2.58000E-3 |
2
|
4.7073
|
4.97000E-2 |
2 |
0.8761
|
2.39000E-3
|
1
|
4.8473
|
4.92000E-6
|
2 |
0.8821
|
2.20000E-3 |
1
|
4.9673
|
4.89000E-6
|
2 |
0.8914 |
1.96000E-3 |
1
|
5.0172
|
4.83000E-6
|
2 |
0.8996
|
1.74000E-3
|
2 |
5.0571
|
4.73000E-6 |
2 |
0.9131 |
1.55000E-3 |
1
|
5.0871
|
4.62000E-6
|
2 |
0.9344 |
1.24000E-3 |
1 |
5.1270
|
4.47000E-6
|
2 |
0.9477
|
1.11000E-3 |
2
|
5.1669
|
4.01000E-6
|
2 |
0.9541
|
1.04000E-3 |
1
|
5.1868
|
3.76000E-6 |
2 |
Figure 10.1. Positive ion mobility
as a function of temperature along the saturated vapor pressure line.
Table 10.2. Knots and coefficients
for the spline fit of .
Knots |
Coefficients |
K(1)
= 2.549509E-2 |
C(1)
= 7.324336E-4 |
K(2)
= 2.549509E-2 |
C(2)
= 7.127592E-4 |
K(3)
= 2.549509E-2 |
C(3) = 6.936548E-4 |
K(4)
= 2.549509E-2 |
C(4)
= 5.173557E-4 |
K(5)
= 8.989802E-2 |
C(5)
= 4.285367E-4 |
K(6)
= 2.949869E-1 |
C(6)
= 2.823892E-4 |
K(7)
= 4.513886E-1 |
C(7)
= 2.125491E-4 |
K(8)
= 7.045304E-1 |
C(8) = 1.285926E-4 |
K(9)
= 7.577476E-1 |
C(9)
= 5.123347E-5 |
K(10)
= 7.944735E-1 |
C(10)
= -3.728677E-5 |
K(11)
= 1.062780E+0 |
C(11)
= -8.564176E-5 |
K(12)
= 1.394506E+0 |
C(12)
= -1.067754E-4 |
K(13)
= 1.791246E+0 |
C(13) = -1.321435E-4 |
K(14)
= 2.152366E+0 |
C(14)
= -1.381473E-4 |
K(15)
= 2.203504E+0 |
C(15)
= -1.396425E-4 |
K(16)
= 2.205589E+0 |
C(16)
= -1.325568E-4 |
K(17)
= 2.727358E+0 |
C(17)
= -1.292173E-4 |
K(18)
= 4.425492E+0 |
C(18)
= -1.335656E-4 |
K(19)
= 5.043800E+0 |
C(19)
= -1.409701E-4 |
K(20)
= 5.154401E+0 |
C(20)
= -1.424813E-4 |
K(21)
= 5.186798E+0 |
|
K(22)
= 5.186798E+0 |
|
K(23)
= 5.186798E+0 |
|
K(24)
= 5.186798E+0 |
|
Figure
10.2. Deviation of the database from the spline fit to .
Note : The large deviations
at low temperatures reflect a divergence in magnitudes reported in Refs.
14 and 18.
Table 10.3. Adopted database
for the negative ion mobility.
T90 (K) |
µ-(m2/V.s) |
Key |
T90 |
µ-(m2/V.s) |
Key |
0.0351
|
1.08000E+3
|
1
|
0.0884
|
8.79000E+0
|
1 |
0.0405 |
6.47000E+2 |
1 |
0.0884 |
8.89000E+0
|
1 |
0.0449 |
3.76000E+2 |
1 |
0.0903
|
7.10000E+0 |
1 |
0.0496
|
2.49000E+2
|
1
|
0.0915
|
7.49000E+0
|
1 |
0.0531
|
1.69000E+2
|
1
|
0.0921
|
7.30000E+0
|
1 |
0.0541
|
1.34000E+2 |
1 |
0.0942 |
6.59000E+0 |
1 |
0.0541 |
1.46000E+2 |
1
|
0.0946
|
5.74000E+0
|
1 |
0.0547 |
1.41000E+2 |
1
|
0.0986
|
5.44000E+0 |
1 |
0.0547 |
1.29000E+2 |
1
|
0.0987 |
4.68000E+0 |
1 |
0.0555 |
1.18000E+2 |
1 |
0.0998
|
4.91000E+0 |
1 |
0.0560 |
1.16000E+2 |
1 |
0.1002 |
5.70000E+0
|
1 |
0.0575 |
9.48000E+1 |
1
|
0.1014
|
5.00000E+0
|
1 |
0.0578 |
8.71000E+1 |
1
|
0.1015 |
4.51000E+0 |
1 |
0.0596 |
7.91000E+1 |
1 |
0.1019 |
4.81000E+0 |
1 |
0.0596 |
7.72000E+1 |
1
|
0.1019 |
4.76000E+0
|
1 |
0.0596
|
8.11000E+1
|
1
|
0.1019 |
4.79000E+0 |
1 |
0.0597
|
7.72000E+1 |
1 |
0.1036 |
4.72000E+0 |
1 |
0.0597 |
7.80000E+1 |
1
|
0.1044 |
4.33000E+0 |
1 |
0.0597 |
7.83000E+1 |
1
|
0.1048 |
3.75000E+0 |
1 |
0.0601 |
7.41000E+1 |
1 |
0.1048 |
3.98000E+0
|
1 |
0.0601 |
7.02000E+1 |
1
|
0.1064
|
3.42000E+0
|
1 |
0.0601
|
7.18000E+1
|
1
|
0.1083
|
3.41000E+0
|
1 |
0.0601 |
6.87000E+1 |
1 |
0.1084
|
3.72000E+0 |
1 |
0.0616 |
6.01000E+1 |
1
|
0.1102 |
3.49000E+0 |
1 |
0.0621 |
6.22000E+1 |
1 |
0.1125 |
3.26000E+0
|
1 |
0.0622 |
5.99000E+1 |
1
|
0.1125 |
3.22000E+0 |
1 |
0.0632 |
5.59000E+1 |
1 |
0.1142
|
2.69000E+0
|
1 |
0.0644
|
4.76000E+1
|
1
|
0.1151
|
2.67000E+0
|
1 |
0.0655 |
4.55000E+1 |
1 |
0.1164 |
2.87000E+0 |
1 |
0.0657
|
3.37000E+1 |
1
|
0.1196
|
2.31000E+0 |
1 |
0.0663 |
4.15000E+1
|
1 |
0.1206
|
2.62000E+0
|
1 |
0.0663
|
4.03000E+1 |
1 |
0.1207 |
2.55000E+0
|
1 |
0.0685 |
3.39000E+1 |
1
|
0.1209 |
2.14000E+0
|
1 |
0.0686 |
3.63000E+1 |
1 |
0.1247
|
1.96000E+0
|
1 |
0.0688
|
3.39000E+1
|
1
|
0.1295
|
1.62000E+0
|
1 |
0.0690 |
3.27000E+1
|
1
|
0.1323
|
1.59000E+0
|
1 |
0.0690 |
3.39000E+1 |
1
|
0.1387 |
1.25000E+0 |
1 |
0.0698 |
3.11000E+1 |
1
|
0.1395 |
1.29000E+0
|
1 |
0.0704 |
2.91000E+1 |
1
|
0.1411 |
1.20000E+0
|
1 |
0.0704
|
2.92000E+1 |
1 |
0.1451 |
1.09000E+0
|
1 |
0.0704
|
2.85000E+1 |
1
|
0.1464 |
1.09000E+0
|
1 |
0.0745
|
2.09000E+1
|
1
|
0.1503
|
9.61000E-1 |
1 |
0.0782 |
1.66000E+1 |
1 |
0.1510
|
9.78000E-1 |
1 |
0.0782 |
1.62000E+1 |
1
|
0.1583 |
8.07000E-1 |
1 |
0.0820 |
1.26000E+1 |
1
|
0.1600
|
8.06000E-1
|
1 |
0.0843
|
1.11000E+1
|
1
|
0.1644
|
7.10000E-1 |
1 |
0.0873
|
9.75000E+0 |
1
|
0.1673
|
6.93000E-1
|
1 |
Table
10.3. (Continued)
T90 (K) |
µ-(m2/V.s) |
Key |
T90 |
µ-(m2/V.s) |
Key |
0.1718
|
6.14000E-1
|
1
|
0.2914 |
1.20000E-1
|
1 |
0.1730
|
6.19000E-1
|
1
|
0.2920 |
1.12000E-1 |
2 |
0.1776 |
5.48000E-1
|
1
|
0.2937
|
1.21000E-1
|
1 |
0.1796
|
5.44000E-1
|
1
|
0.2965 |
1.18000E-1 |
1 |
0.1821
|
5.08000E-1
|
1
|
0.2972
|
1.13000E-1 |
1 |
0.1860 |
4.92000E-1 |
1 |
0.2990
|
1.15000E-1
|
1 |
0.1861
|
4.75000E-1 |
1 |
0.3010
|
1.02000E-1 |
2 |
0.1919
|
4.30000E-1
|
1
|
0.3017 |
1.09000E-1 |
1 |
0.1920 |
4.44000E-1 |
1
|
0.3029
|
9.99000E-2 |
1 |
0.1957
|
4.04000E-1
|
1
|
0.3072
|
1.03000E-1 |
1 |
0.1976
|
4.04000E-1 |
1 |
0.3076 |
1.06000E-1 |
1 |
0.2022 |
3.76000E-1 |
1 |
0.3111
|
9.25000E-2 |
2 |
0.2036
|
3.57000E-1
|
1
|
0.3118
|
1.02000E-1
|
1 |
0.2078
|
3.34000E-1 |
1
|
0.3132
|
9.73000E-2
|
1 |
0.2096
|
3.36000E-1 |
1
|
0.3182 |
9.62000E-2 |
1 |
0.2152
|
3.09000E-1 |
1 |
0.3202
|
9.14000E-2
|
1 |
0.2161 |
2.97000E-1 |
1 |
0.3211
|
8.35000E-2
|
2 |
0.2189
|
2.94000E-1
|
1 |
0.3231
|
9.22000E-2 |
1 |
0.2222
|
2.71000E-1 |
1 |
0.3248
|
8.78000E-2
|
1 |
0.2262
|
2.65000E-1
|
1
|
0.3292
|
8.47000E-2
|
1 |
0.2270
|
2.54000E-1
|
1
|
0.3308 |
8.60000E-2
|
1 |
0.2330
|
2.42000E-1 |
1
|
0.3331 |
7.50000E-2
|
2 |
0.2334
|
2.34000E-1 |
1 |
0.3362
|
7.96000E-2 |
1 |
0.2375 |
2.22000E-1 |
1 |
0.3377
|
6.60000E-2 |
1 |
0.2382
|
2.26000E-1
|
1
|
0.3411 |
6.42000E-2 |
1 |
0.2402
|
2.14000E-1
|
1
|
0.3424 |
7.82000E-2 |
1 |
0.2438
|
2.12000E-1
|
1
|
0.3425
|
7.55000E-2 |
1 |
0.2465 |
1.98000E-1
|
1
|
0.3446 |
6.26000E-2 |
1 |
0.2507 |
1.88000E-1 |
1
|
0.3452
|
6.70000E-2
|
2 |
0.2512
|
1.93000E-1
|
1 |
0.3463
|
7.32000E-2 |
1 |
0.2571
|
1.80000E-1
|
1
|
0.3483
|
7.44000E-2
|
1 |
0.2575
|
1.74000E-1
|
1
|
0.3494
|
6.00000E-2
|
1 |
0.2628 |
1.63000E-1
|
1
|
0.3503 |
7.10000E-2 |
1 |
0.2631
|
1.68000E-1 |
1 |
0.3529
|
7.16000E-2
|
1 |
0.2675
|
1.55000E-1 |
1
|
0.3560
|
5.69000E-2 |
1 |
0.2703
|
1.55000E-1 |
1
|
0.3582
|
6.05000E-2
|
2 |
0.2732
|
1.45000E-1 |
1 |
0.3589
|
6.83000E-2 |
1 |
0.2749
|
1.35000E-1
|
2
|
0.3634
|
6.60000E-2
|
1 |
0.2757 |
1.46000E-1 |
1 |
0.3640 |
5.33000E-2 |
1 |
0.2774 |
1.43000E-1
|
1
|
0.3711
|
5.05000E-2
|
1 |
0.2782 |
1.38000E-1 |
1 |
0.3722
|
5.40000E-2 |
2 |
0.2811
|
1.33000E-1
|
1
|
0.3741
|
6.11000E-2
|
1 |
0.2812
|
1.37000E-1
|
1
|
0.3762
|
.86000E-2
|
1 |
0.2840
|
1.23000E-1 |
2 |
0.3808 |
5.79000E-2
|
1 |
0.2879
|
1.24000E-1 |
1
|
0.3857
|
4.53000E-2
|
1 |
0.2896
|
1.26000E-1 |
1
|
0.3873
|
5.56000E-2
|
1 |
0.2898
|
1.26000E-1
|
1
|
0.3873
|
4.80000E-2
|
2 |
Table
10.3. (Continued)
T90 (K) |
µ-(m2/V.s) |
Key |
T90 |
µ-(m2/V.s) |
Key |
0.3907
|
4.37000E-2 |
1
|
0.5219
|
1.86000E-2 |
1 |
0.3933
|
5.27000E-2
|
1
|
0.5238
|
2.32000E-2 |
1 |
0.3960
|
4.20000E-2 |
1 |
0.5257 |
1.82000E-2
|
1 |
0.3999
|
5.32000E-2 |
1 |
0.5277 |
1.90000E-2
|
2 |
0.4015
|
4.04000E-2 |
1
|
0.5322
|
2.20000E-2 |
1 |
0.4063 |
4.23000E-2 |
2 |
0.5335 |
1.73000E-2
|
1 |
0.4065
|
4.82000E-2
|
1
|
0.5400
|
2.10000E-2 |
1 |
0.4087
|
3.84000E-2
|
1
|
0.5400 |
1.72000E-2 |
1 |
0.4133 |
4.61000E-2 |
1 |
0.5400 |
1.67000E-2 |
1 |
0.4178
|
3.60000E-2
|
1
|
0.5417
|
1.74000E-2
|
2 |
0.4187 |
4.43000E-2
|
1 |
0.5479
|
1.59000E-2 |
1 |
0.4214
|
3.72000E-2
|
2
|
0.5539
|
1.93000E-2 |
1 |
0.4244
|
4.27000E-2 |
1 |
0.5539 |
1.72000E-2 |
1 |
0.4263
|
3.40000E-2 |
1 |
0.5568
|
1.56000E-2
|
2 |
0.4320
|
4.05000E-2 |
1 |
0.5587 |
1.49000E-2
|
1 |
0.4321
|
3.28000E-2
|
1
|
0.5635 |
1.45000E-2 |
1 |
0.4380
|
3.90000E-2 |
1
|
0.5655 |
1.81000E-2 |
1 |
0.4381 |
3.13000E-2 |
1 |
0.5655 |
1.72000E-2
|
1 |
0.4404
|
3.27000E-2 |
2 |
0.5710 |
1.38000E-2
|
1 |
0.4465 |
3.70000E-2
|
1 |
0.5726
|
1.72000E-2
|
1 |
0.4468 |
2.97000E-2 |
1
|
0.5748
|
1.41000E-2 |
2 |
0.4533
|
3.54000E-2 |
1
|
0.5789 |
1.31000E-2
|
1 |
0.4542
|
2.83000E-2
|
1
|
0.5820 |
1.64000E-2 |
1 |
0.4598 |
3.95000E-2
|
|
0.5836
|
1.27000E-2 |
1 |
0.4617
|
2.69000E-2 |
1 |
0.5912 |
1.21000E-2 |
1 |
0.4625
|
2.84000E-2
|
2
|
0.5918
|
1.25000E-2 |
2 |
0.4653 |
3.29000E-2 |
1
|
0.5936 |
1.51000E-2 |
1 |
0.4694
|
2.57000E-2 |
1 |
0.6048 |
11000E-2
|
1 |
0.4714 |
3.17000E-2 |
1
|
0.6052 |
1.40000E-2 |
1 |
0.4717
|
2.44000E-2
|
1
|
0.6052 |
1.64000E-2
|
1 |
0.4794 |
3.01000E-2 |
1 |
0.6102 |
1.34000E-2 |
1 |
0.4805
|
2.39000E-2
|
1
|
0.6102 |
1.07000E-2 |
1 |
0.4845
|
2.95000E-2
|
1
|
0.6119
|
1.09000E-2 |
2 |
0.4856 |
2.45000E-2 |
2
|
0.6152
|
1.31000E-2 |
1 |
0.4908
|
2.81000E-2
|
1
|
0.6189
|
1.01000E-2
|
1 |
0.4921 |
2.23000E-2 |
1
|
0.6242
|
9.69000E-3
|
1 |
0.4951 |
2.19000E-2 |
1
|
0.6278 |
1.20000E-2 |
1 |
0.4986 |
2.68000E-2
|
1
|
0.6278
|
1.31000E-2
|
1 |
0.4996 |
2.25000E-2 |
2 |
0.6330 |
9.29000E-3
|
2 |
0.5016
|
2.64000E-2
|
1 |
0.6340 |
9.10000E-3 |
1 |
0.5062
|
2.57000E-2 |
1 |
0.6347 |
1.14000E-2
|
1 |
0.5070 |
2.03000E-2 |
1
|
0.6416 |
8.76000E-3
|
1 |
0.5111
|
1.99000E-2
|
1
|
0.6419
|
1.08000E-2
|
1 |
0.5116
|
2.09000E-2
|
2
|
0.6464
|
1.04000E-2
|
1 |
0.5126 |
2.47000E-2
|
1
|
0.6468 |
8.87000E-3 |
1 |
0.5126 |
2.20000E-2 |
1 |
0.6529
|
8.45000E-3
|
1 |
0.5162 |
2.06000E-2
|
1
|
0.6532
|
7.85000E-3
|
1 |
Table
10.3. (Continued)
T90 (K) |
µ-(m2/V.s) |
Key |
T90 |
µ-(m2/V.s) |
Key |
0.6543
|
9.79000E-3
|
1
|
0.8132 |
1.90000E-3 |
1 |
0.6550
|
7.86000E-3 |
2
|
0.8224
|
1.71000E-3 |
2 |
0.6588
|
7.30000E-3 |
1 |
0.8229
|
1.74000E-3 |
1 |
0.6595 |
7.98000E-3
|
1
|
0.8357
|
1.51000E-3 |
1 |
0.6637
|
7.69000E-3 |
1 |
0.8417 |
1.44000E-3 |
1 |
0.6644 |
9.01000E-3
|
1 |
0.8421 |
1.37000E-3 |
1 |
0.6662
|
7.07000E-3
|
1
|
0.8450
|
1.32000E-3
|
1 |
0.6712
|
7.23000E-3 |
1 |
0.8526 |
1.22000E-3 |
1 |
0.6763 |
6.50000E-3 |
1
|
0.8606
|
1.66000E-3
|
1 |
0.6766 |
6.93000E-3 |
1
|
0.8615
|
1.19000E-3 |
2 |
0.6781
|
6.50000E-3
|
2
|
0.8713
|
1.00000E-3
|
1 |
0.6824
|
6.18000E-3 |
1 |
0.8834 |
8.83000E-4 |
1 |
0.6831 |
6.55000E-3 |
1 |
0.8996
|
8.40000E-4
|
2 |
0.6889
|
5.86000E-3
|
1
|
0.9144
|
6.28000E-4
|
1 |
0.6932
|
5.99000E-3
|
1 |
0.9257
|
5.74000E-4
|
1 |
0.6958 |
5.54000E-3 |
1 |
0.9321 |
5.50000E-4 |
1 |
0.7023 |
5.73000E-3 |
1 |
0.9394 |
7.53000E-4 |
1 |
0.7031 |
5.25000E-3 |
2 |
0.9412
|
5.03000E-4
|
1 |
0.7038
|
5.14000E-3 |
1 |
0.9453 |
4.95000E-4
|
1 |
0.7108 |
5.17000E-3 |
1 |
0.9477 |
5.63000E-4 |
2 |
0.7116 |
5.28000E-3 |
1
|
0.9578
|
4.32000E-4
|
1 |
0.7123
|
5.06000E-3 |
1 |
0.9578 |
4.40000E-4
|
1 |
0.7135 |
4.70000E-3 |
1
|
0.9689
|
4.08000E-4 |
1 |
0.7165
|
4.90000E-3 |
1 |
0.9736
|
3.77000E-4
|
1 |
0.7206 |
4.68000E-3 |
1
|
0.9945
|
3.14000E-4
|
1 |
0.7217
|
4.36000E-3 |
1
|
0.9988
|
3.77000E-4 |
2 |
0.7262
|
4.43000E-3 |
1 |
1.0098 |
2.75000E-4
|
1 |
0.7292
|
4.11000E-3 |
2
|
1.0098 |
2.90000E-4
|
1 |
0.7296 |
4.06000E-3
|
1 |
1.0198 |
2.75000E-4 |
1 |
0.7364
|
4.04000E-3 |
1 |
1.0308
|
2.35000E-4
|
1 |
0.7368
|
3.96000E-3 |
1 |
1.0358
|
2.35000E-4
|
1 |
0.7440
|
3.75000E-3
|
1
|
.0509
|
2.04000E-4 |
1 |
0.7455
|
3.51000E-3 |
1 |
1.0509
|
2.04000E-4
|
1 |
0.7505 |
3.53000E-3 |
1
|
1.0509 |
2.60000E-4 |
2 |
0.7532 |
3.23000E-3 |
1
|
1.1350 |
2.51000E-4 |
2 |
0.7564 |
3.15000E-3 |
1 |
1.1991 |
1.00000E-5 |
2 |
0.7593 |
3.09000E-3
|
2
|
1.3003 |
5.76000E-5 |
2 |
0.7676 |
2.99000E-3
|
1 |
1.4015
|
3.60000E-5
|
2 |
0.7743
|
2.78000E-3 |
1 |
1.5036 |
2.42000E-5 |
2 |
0.7774
|
2.67000E-3
|
1
|
1.6057
|
1.74000E-5
|
2 |
0.7802
|
2.56000E-3
|
1
|
1.7119
|
1.33000E-5 |
2 |
0.7841
|
2.46000E-3 |
1 |
1.8161 |
1.05000E-5 |
2 |
0.7881 |
2.35000E-3 |
1
|
1.9172
|
8.42000E-6
|
2 |
0.7883
|
2.35000E-3
|
2
|
2.0203 |
6.47000E-6 |
2 |
0.7964 |
2.18000E-3 |
1
|
2.1215
|
4.61000E-6 |
2 |
0.7964 |
2.24000E-3 |
1 |
2.1365 |
4.37000E-6 |
2 |
0.8054
|
2.06000E-3
|
1
|
2.1516
|
4.05000E-6 |
2 |
2.1676
|
3.68000E-6
|
2
|
4.1671
|
4.96000E-6
|
2 |
2.1738
|
3.56000E-6
|
2
|
4.3370
|
1.91000E-6 |
2 |
2.1788
|
3.46000E-6 |
2
|
4.4570 |
1.87000E-6 |
2 |
2.2046 |
3.26000E-6 |
2
|
4.5571
|
1.86000E-6 |
2 |
2.2647 |
3.01000E-6 |
2 |
4.7073
|
1.80000E-6 |
2 |
2.3749 |
2.78000E-2 |
2
|
4.8473
|
1.76000E-6
|
2 |
2.4951
|
2.61000E-6
|
2
|
4.9673 |
1.72000E-6 |
2 |
2.6455
|
2.47000E-6 |
2 |
5.0172
|
1.69000E-6
|
2 |
2.8260 |
2.34000E-6 |
2 |
5.0571
|
1.67000E-6 |
2 |
3.0263
|
2.26000E-6
|
2
|
5.0871
|
1.65000E-6
|
2 |
3.2567 |
2.18000E-6 |
2
|
5.1270
|
1.61000E-6
|
2 |
3.5070
|
2.11000E-6
|
2
|
5.1669
|
1.58000E-6 |
2 |
3.7771
|
2.03000E-6 |
2 |
5.1868
|
1.57000E-6 |
2 |
3.9370
|
2.01000E-6 |
2 |
|
|
|
Figure 10.3. The recommended
values of the negative ion mobility as a function of temperature at saturated
vapor pressure.
Table
10.4. Knots and coefficients for the spline fit of . .
Knots |
Coefficients |
K(1)
= 3.513060E-2 |
C(1)
= 7.033374E-4 |
K(2)
= 3.513060E-2 |
C(2)
= 6.736553E-4 |
K(3)
= 3.513060E-2 |
C(3)
= 5.158198E-4 |
K(4)
= 3.513060E-2 |
C(4)
= 4.508211E-4 |
K(5)
= 5.875667E-2 |
C(5) = 4.002894E-4 |
K(6)
= 1.179363E-1 |
C(6)
= 2.552750E-4 |
K(7)
= 1.537502E-1 |
C(7)
= 2.496965E-4 |
K(8)
= 1.649872E-1 |
C(8)
= 1.466750E-4 |
K(9)
= 6.623561E-1 |
C(9)
= 1.088565E-4 |
K(10)
= 8.008330E-1 |
C(10)
= 4.892824E-5 |
K(11)
= 8.281207E-1 |
C(11)
= 1.064366E-5 |
K(12)
= 9.599097E-1 |
C(12) = -4.138096E-5 |
K(13)
= 1.152959E+0 |
C(13)
= -8.747069E-5 |
K(14)
= 1.351840E+0 |
C(14)
= -1.058640E-4 |
K(15)
= 1.607292E+0 |
C(15)
= -1.326369E-4 |
K(16)
= 2.021290E+0 |
C(16) = -1.474489E-4 |
K(17)
= 2.176597E+0 |
C(17)
= -1.522085E-4 |
K(18)
= 2.186372E+0 |
C(18)
= -1.603564E-4 |
K(19)
= 2.189764E+0 |
C(19) = -1.681873E-4 |
K(20)
= 2.374662E+0 |
C(20)
= -1.700160E-4 |
K(21)
= 3.014612E+0 |
C(21)
= -1.756753E-4 |
K(22)
= 4.660651E+0 |
C(22)
= -1.768276E-4 |
K(23)
= 4.838042E+0 |
C(23)
= -1.801619E-4 |
K(24)
= 5.105466E+0 |
C(24)
= -1.804100E-4 |
K(25)
= 5.186798E+0 |
|
K(26)
= 5.186798E+0 |
|
K(27)
= 5.186798E+0 |
|
K(28)
= 5.186798E+0 |
|
Figure 10.4. The fractional
deviation of values of the adopted database from the recommended values
for the in liquid 4He expressed in percent.
Table
10.5. Recommended values of the positive ion mobility in liquid 4He.
T90
(K) |
µ+(m2/V.s) |
T90
(K) |
µ+(m2/V.s) |
0.1000
|
8.577E+2
|
2.1765 |
5.017E-6 |
0.1500 |
3.902E+2
|
2.1766
|
5.015E-6 |
0.2000
|
1.403E+2 |
2.1767 |
5.013E-6 |
0.2500
|
4.723E+1
|
2.1768 |
5.012E-6 |
0.3000
|
1.765E+1 |
2.1769 |
5.010E-6 |
0.3500 |
8.127E+0 |
2.1770
|
5.008E-6 |
0.4000 |
4.202E+0
|
2.2000
|
4.733E-6 |
0.4500 |
2.146E+0 |
2.2500
|
4.571E-6 |
0.5000 |
9.786E-1
|
2.3000
|
4.447E-6 |
0.5500 |
4.069E-1
|
2.3500 |
4.349E-6 |
0.6000
|
1.627E-1
|
2.4000
|
4.274E-6 |
0.6500 |
6.605E-2 |
2.4500
|
4.218E-6 |
0.7000
|
2.870E-2
|
2.5000 |
4.178E-6 |
0.7500
|
1.359E-2
|
2.5500
|
4.151E-6 |
0.8000 |
6.271E-3 |
2.6000 |
4.135E-6 |
0.8500 |
3.148E-3
|
2.6500 |
4.127E-6 |
0.9000
|
1.756E-3 |
2.7000 |
4.124E-6 |
0.9500 |
1.066E-3 |
2.7500 |
4.125E-6 |
1.0000
|
6.906E-4
|
2.8000 |
4.128E-6 |
1.0500 |
4.676E-4 |
2.8500 |
4.133E-6 |
1.1000 |
3.247E-4
|
2.9000 |
4.140E-6 |
1.1500 |
2.299E-4
|
2.9500
|
4.148E-6 |
1.2000 |
1.659E-4 |
3.0000
|
4.158E-6 |
1.2500
|
1.221E-4
|
3.0500 |
4.170E-6 |
1.3000 |
9.174E-5
|
3.1000
|
4.184E-6 |
1.3500
|
7.033E-5
|
3.1500 |
4.198E-6 |
1.4000
|
5.505E-5
|
3.2000
|
4.215E-6 |
1.4500 |
4.398E-5
|
3.2500 |
4.233E-6 |
1.5000 |
3.583E-5 |
3.3000 |
4.252E-6 |
1.5500 |
2.971E-5 |
3.3500 |
4.272E-6 |
1.6000 |
2.503E-5 |
3.4000 |
4.293E-6 |
1.6500
|
2.139E-5
|
3.4500 |
4.316E-6 |
1.7000 |
1.852E-5 |
3.5000 |
4.339E-6 |
1.7500
|
1.622E-5
|
3.5500
|
4.364E-6 |
1.8000 |
1.434E-5 |
3.6000 |
4.389E-6 |
1.8500
|
1.277E-5 |
3.6500 |
4.416E-6 |
1.9000 |
1.140E-5
|
3.7000 |
4.443E-6 |
1.9500 |
1.014E-5
|
3.7500
|
4.470E-6 |
2.0000
|
8.945E-6
|
3.8000
|
4.499E-6 |
2.0500
|
7.787E-6
|
3.8500 |
4.528E-6 |
2.1000
|
6.653E-6 |
3.9000
|
4.557E-6 |
2.1500
|
5.550E-6
|
3.9500 |
4.586E-6 |
2.1760 |
5.025E-6
|
4.0000
|
4.616E-6 |
2.1761 |
5.024E-6
|
4.0500
|
4.646E-6 |
2.1762
|
5.022E-6
|
4.1000 |
4.677E-6 |
2.1763
|
5.020E-6
|
4.1500
|
4.707E-6 |
2.1764
|
5.019E-6
|
4.2000
|
4.737E-6 |
4.2500
|
4.767E-6
|
4.6500
|
4.969E-6 |
4.3000 |
4.797E-6 |
4.7000 |
4.978E-6 |
4.3500 |
4.826E-6
|
4.7500
|
4.979E-6 |
4.4000
|
4.855E-6
|
4.8000 |
4.970E-6 |
4.4500
|
4.883E-6
|
4.8500
|
4.951E-6 |
4.5000 |
4.910E-6 |
4.9000 |
4.921E-6 |
4.5500
|
4.934E-6
|
4.9500
|
4.878E-6 |
4.6000
|
4.954E-6
|
5.0000
|
4.822E-6 |
Table
10.6. Recommended values of the negative ion mobility of liquid 4He.
T90
(K) |
µ-(m2/V.s) |
T90
(K) |
µ-(m2/V.s) |
0.1000 |
5.012E+0 |
2.1765 |
3.513E-6 |
0.1500
|
9.560E-1
|
2.1766
|
3.511E-6 |
0.2000
|
3.913E-1 |
2.1767
|
3.509E-6 |
0.2500 |
1.924E-1 |
2.1768
|
3.507E-6 |
0.3000
|
1.079E-1
|
2.1769 |
3.505E-6 |
0.3500
|
6.729E-2
|
2.1770
|
3.503E-6 |
0.4000 |
4.546E-2 |
2.2000 |
3.269E-6 |
0.4500 |
3.244E-2 |
2.2500 |
3.062E-6 |
0.5000
|
2.383E-2
|
2.3000
|
2.921E-6 |
0.5500
|
1.757E-2 |
2.2500 |
3.062E-6 |
0.6000 |
1.267E-2
|
2.3000
|
2.921E-6 |
0.6500 |
8.707E-3 |
2.3500 |
2.821E-6 |
0.7000
|
5.592E-3
|
2.4000 |
2.740E-6 |
0.7500
|
3.444E-3 |
2.4500 |
2.670E-6 |
0.8000
|
2.138E-3
|
2.5000
|
2.607E-6 |
0.8500 |
1.342E-3
|
2.5500
|
2.552E-6 |
0.9000
|
8.006E-4
|
2.6000 |
2.504E-6 |
0.9500 |
4.844E-4 |
2.6500 |
2.461E-6 |
1.0000 |
3.173E-4 |
2.7000 |
2.423E-6 |
1.0500
|
2.253E-4
|
2.7500
|
2.390E-6 |
1.1000 |
1.685E-4 |
2.8000
|
2.360E-6 |
1.1500
|
1.290E-4 |
2.8500
|
2.334E-6 |
1.2000 |
9.880E-5
|
2.9000
|
2.309E-6 |
1.2500 |
7.567E-5 |
2.9500 |
2.287E-6 |
1.3000
|
5.836E-5
|
3.0000
|
2.267E-6 |
1.3500
|
4.562E-5
|
3.0500
|
2.248E-6 |
1.4000 |
3.636E-5 |
3.1000 |
2.229E-6 |
1.4500 |
2.956E-5 |
3.1500 |
2.212E-6 |
1.5000
|
2.449E-5
|
3.2000
|
2.195E-6 |
1.5500 |
2.066E-5 |
3.2500 |
2.180E-6 |
1.6000 |
1.772E-5
|
3.3000 |
2.164E-6 |
1.6500
|
1.545E-5 |
3.3500
|
2.150E-6 |
1.7000
|
1.363E-5
|
3.4000 |
2.136E-6 |
1.7500
|
1.214E-5
|
3.4500
|
2.122E-6 |
1.8000 |
1.088E-5 |
3.5000 |
2.109E-6 |
1.8500 |
9.757E-6 |
3.5500 |
2.097E-6 |
1.9000 |
8.736E-6 |
3.6000 |
2.084E-6 |
1.9500 |
7.779E-6
|
3.6500 |
2.072E-6 |
2.0000 |
6.862E-6 |
3.7000 |
2.060E-6 |
2.0500 |
5.971E-6 |
3.7500 |
2.049E-6 |
2.1000 |
5.052E-6 |
3.8000 |
2.037E-6 |
2.1500 |
4.060E-6 |
3.8500 |
2.026E-6 |
2.1760 |
3.523E-6 |
3.9000 |
2.015E-6 |
2.1761
|
3.521E-6
|
3.9500 |
2.003E-6 |
2.1762 |
3.519E-6 |
4.0000 |
1.992E-6 |
2.1763 |
3.517E-6 |
4.0500 |
1.980E-6 |
2.1764 |
3.515E-6 |
4.1000 |
1.969E-6 |
4.1500 |
1.957E-6 |
4.6000 |
1.837E-6 |
4.2000 |
1.945E-6 |
4.6500 |
1.822E-6 |
4.2500 |
1.933E-6
|
4.7000
|
1.806E-6 |
4.3000 |
1.920E-6 |
4.7500 |
1.790E-6 |
4.3500 |
1.907E-6 |
4.8000 |
1.774E-6 |
4.4000 |
1.894E-6 |
4.8500 |
1.759E-6 |
4.4500
|
1.881E-6 |
4.9000 |
1.743E-6 |
4.5000 |
1.867E-6 |
4.9500
|
1.726E-6 |
4.5500 |
1.852E-6 |
5.0000 |
1.703E-6 |
Chronological Bibliography for Ion Mobilities
1 |
R. L. Williams, "Ionic Mobilities in Argon and Liquid Helium," Can.
J. Phys. 35, 134-146 (1957). |
2 |
G.
Careri, F. Scaramuzzi, and J. O. Thomson, “Heat Flush and Mobility
of Electric Charges in Liquid Helium,” Nuovo Cimento 13, 186-196
(1958). |
3 |
L.
Meyer and F. Reif, “Mobility of He Ions in Liquid Helium,”
Phys. Rev. 110, 279-280 (1958). |
4 |
R.
G. Arkhipov and A. I. Shalnikov, “On the Problem of the Motion
of Charges in Liquid Helium,” Sov. Phys. JETP 37, 888-890 (1960). |
5 |
G.
Careri, U. Fasoli, and F. S. Gaeta, “Experimental Behavior of
Ionic Structures in Liquid Helium II,” Nuovo Cimento 15, 774-783
(1960). |
6 |
F.
Reif and L. Meyer, “Study of Superfluidity in Liquid He by Ion
Motion,” Phys. Rev. 119, 1164-1173 (1960). |
7 |
L.
Meyer and F. Reif, “Ion Motion in Superfluid Liquid Helium Under
Pressure,” Phys. Rev. 123, 727-731 (1961). |
8 |
L.
Meyer, H. T. Davis, S. A. Rice, and R. J. Donnelly, “Mobility
of Ions in Liquid 4He I and 3He as a Function of Temperature and Pressure,”
Phys. Rev. 126, 1927-1934 (1962). |
9 |
B.
E. Springett and R. J. Donnelly, “Pressure Dependence of the
Radius of the Negative Ion in Helium II,” Phys. Rev. Lett. 17,
364-367 (1966). |
10 |
K.
W. Schwarz and S. R. W., “Scattering of Positive Ions by Elementary
Excitations in Superfluid Helium,” Phys. Rev. Lett. 22, 1278-1280
(1969). |
11 |
D.
M. Sitton and F. Moss, “Free Ion Mobility in Helium II using
Field Emission Points,” Phys. Lett. 34, 159-160 (1971). |
12 |
G.
Ahlers and G. Gamota, “Ion Mobilities in 4He Near the Superfluid
Transition and the Melting Line,” Phys. Lett. A 38, 65-66 (1972). |
13 |
R.
M. Ostermeier and K. W. Schwarz, “Motion of Charge Carriers
in Normal 4He,” Phys. Rev. A 5, 2510-2519 (1972). |
14 |
K.
W. Schwarz, “Charge Carrier Mobilities in Liquid Helium at the
Vapor Pressure,” Phys. Rev. A 6, 837-844 (1972). |
15 |
K.
W. Schwarz, “Mobilities of Charge Carriers in Superfluid Helium,”
in Advances in Chemical Physics (John Wiley and Sons, Inc., 1975),
Vol. 33. |
16 |
C.
F. Barenghi, C. J. Mellor, C. M. Muirhead, and W. F. Vinen, “Experiments
on Ions Trapped Below the Surface of Superfluid 4He,” J. Phys.
C: Solid State Phys. 19, 1135-1144 (1986). |
17 |
C.
J. Mellor, C. M. Muirhead, J. Traverse, and W. F. Vinen, “Proceedings
of the 18th International Conference on Low Temperature Physics,”
J. Appl. Phys. 26, 383-384 (1987). |
18 |
C.
F. Barenghi, C. J. Mellor, J. Meredith, C. M. Muirhead, P. K. H. Sommerfeld,
and W. F. Vinen, “Ions Trapped Below the Surface of Superfluid
Helium I. The Observation of Plasma Resonances, and the Measurement
of Effective Masses and Ionic Mobilities,” Phil. Trans. R. Soc.
Lond. A 331, 139-172 (1991) |
|
|