Daniel B. Curtis,1,2
Bhavani Rajaram,1
Owen B. Toon,3
and Margaret A. Tolbert1
1When this research was performed, D. B. Curtis, B. Rajaram, and M. A. Tolbert were with the Cooperative Institute for Research in Environmental Science and Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309
2D. B. Curtis (daniel-curtis@uiowa.edu) is now with the Department of Physics and Astronomy and Department of Chemistry, University of Iowa, 217 IATL, Iowa City, Iowa 52242
3O. B. Toon is with the Laboratory for Atmospheric and Space Physics and Program in Atmospheric and Oceanic Science, University of Colorado, Boulder, Colorado 80309
Daniel B. Curtis, Bhavani Rajaram, Owen B. Toon, and Margaret A. Tolbert, "Measurement of the temperature-dependent optical constants of water ice in the 15–200 µm range," Appl. Opt. 44, 4102-4118 (2005)
The real and imaginary refractive indices of water ice in the far infrared (IR) are used in the satellite interpretation of cloud properties as well as to obtain information on ice throughout the solar system. However, few measurements of these values exist. We have measured the real and imaginary refractive indices of water ice in the far IR every 10 deg over the temperature range of 106–176 K. Ice films ranging from 0 to 140 µm thick were grown by the condensation of water vapor onto a cold silicon substrate, and the film transmission was measured from 650 to 50 cm−1. The thickness of the ice films was determined using optical interference from a reflected He–Ne laser (λ = 623.8 nm). The optical constants were then determined by simultaneously fitting the calculated spectra of films of varying thickness to their respective measured transmission spectra with an iterative Kramers–Kronig technique. The results are compared with previously measured data and show large discrepancies at some wavelengths while good agreement exists at others. Possible reasons for the differences are discussed. Our data clearly distinguish crystalline and amorphous ice. In addition, we note a slight shoulder in our spectra, which can be used to distinguish between cubic and hexagonal ice, although this distinction is difficult.
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Imaginary Indices of Refraction Used for the Calculation of the Real Indices Using the Kramers–Kronig Integrationa
Temperature (K)
Approximate Frequency Range (cm−1)
n at 15, 823 cm−1
52–500
500–800
800–3700
3700–7000
106
Trotta (1996), 145 K1
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K
Rajaram et al. (2001), 170 K
1.28
116
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K
Rajaram et al. (2001), 170 K
1.29
126
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K1
Rajaram et al. (2001), 170 K
1.30
136
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K
Rajaram et al. (2001), 170 K
1.310459
146
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 150 K
Rajaram et al. (2001), 170 K
1.310303
156
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 160 K
Rajaram et al. (2001), 170 K
1.310110
166
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 170 K
Rajaram et al. (2001), 170 K
1.309880
176
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 180 K
Rajaram et al. (2001), 170 K
1.309615
The last column has the temperature-dependent real index of refraction at 15, 823 cm−1 used as the anchor point for the Kramers–Kronig analysis. For T = 136 K and higher, these were calculated using the Lorentz–Lorenz equation; see Rajaram et al. (2001)26 for details. For T = 126 and lower, these values are measured values from Berland et al. (1995).34 The values of Trotta (1996)23 were used as the starting point for the iteration in the far IR in this study, while those of Toon et al. (1994),24 Clapp et al. (1995),27 and Rajaram et al. (2001)26 were used in the mid-IR and near IR.
Table 3
Groups of Films Used to Obtain the Imaginary Index of Refraction in the 50–650 cm−1 Regiona
Approximate Frequency Range (cm−1)
Group of Films
52–144
Thick
148–198
Intermediate
202–248
Thin
252–302
Intermediate
306–545
Thick
549–650
Intermediate
The thin group refers to films ≤11 µm thick. The intermediate group consists of films 12–41 µm thick, and the thick group consists of films 41–140 µm thick.
Table 4
Measured Optical Constants for Water Ice from 106 to 136 K
Frequency (cm−1)
106 K
116 K
126 K
136 K
n
k
n
k
n
k
n
k
52.069
1.713
0.0628
1.772
0.0471
1.771
0.0447
1.768
0.0381
55.927
1.695
0.0648
1.759
0.0529
1.763
0.0486
1.761
0.0449
59.785
1.693
0.0568
1.759
0.0437
1.759
0.0531
1.757
0.0469
63.643
1.693
0.0695
1.764
0.0549
1.759
0.0529
1.756
0.0483
67.501
1.689
0.0666
1.764
0.0572
1.763
0.0540
1.757
0.0468
71.360
1.690
0.0689
1.765
0.0625
1.765
0.0620
1.761
0.0480
75.218
1.689
0.0713
1.764
0.0670
1.763
0.0658
1.763
0.0538
79.076
1.689
0.0708
1.766
0.0630
1.764
0.0646
1.765
0.0516
82.934
1.691
0.0721
1.769
0.0674
1.767
0.0642
1.769
0.0548
86.792
1.693
0.0727
1.773
0.0664
1.772
0.0656
1.775
0.0539
90.650
1.695
0.0738
1.777
0.0686
1.776
0.0678
1.787
0.0548
94.508
1.698
0.0727
1.783
0.0664
1.783
0.0651
1.782
0.0852
98.366
1.705
0.0716
1.794
0.0641
1.793
0.0653
1.776
0.0604
102.224
1.716
0.0722
1.811
0.0627
1.808
0.0633
1.789
0.0570
106.082
1.728
0.0802
1.831
0.0730
1.827
0.0720
1.804
0.0534
109.940
1.738
0.0908
1.849
0.0900
1.844
0.0876
1.822
0.0585
113.798
1.747
0.106
1.862
0.110
1.858
0.107
1.840
0.0675
117.656
1.752
0.123
1.874
0.131
1.870
0.127
1.856
0.0805
121.514
1.756
0.141
1.882
0.159
1.879
0.152
1.872
0.0950
125.372
1.754
0.164
1.885
0.187
1.881
0.181
1.886
0.113
129.230
1.744
0.184
1.884
0.213
1.880
0.203
1.900
0.133
133.088
1.734
0.195
1.877
0.246
1.878
0.229
1.911
0.157
136.946
1.723
0.207
1.866
0.264
1.873
0.253
1.923
0.175
140.805
1.712
0.211
1.855
0.289
1.864
0.278
1.951
0.191
144.663
1.705
0.215
1.840
0.306
1.854
0.299
1.975
0.261
148.521
1.700
0.219
1.824
0.322
1.839
0.323
1.957
0.346
152.379
1.695
0.223
1.811
0.328
1.820
0.337
1.916
0.389
156.237
1.692
0.228
1.800
0.339
1.804
0.345
1.869
0.433
160.095
1.689
0.233
1.792
0.344
1.791
0.351
1.800
0.460
163.953
1.688
0.236
1.788
0.350
1.783
0.354
1.733
0.433
167.811
1.687
0.244
1.787
0.363
1.781
0.358
1.703
0.370
171.669
1.687
0.249
1.786
0.375
1.781
0.367
1.706
0.326
175.527
1.691
0.253
1.786
0.394
1.784
0.376
1.738
0.280
179.385
1.695
0.268
1.785
0.414
1.796
0.390
1.793
0.276
183.243
1.697
0.278
1.787
0.436
1.803
0.431
1.840
0.316
187.101
1.708
0.287
1.784
0.478
1.796
0.472
1.862
0.374
190.959
1.719
0.318
1.769
0.519
1.782
0.512
1.861
0.427
194.817
1.727
0.349
1.745
0.561
1.761
0.553
1.852
0.469
198.675
1.725
0.404
1.713
0.603
1.733
0.593
1.838
0.511
202.533
1.704
0.460
1.667
0.645
1.697
0.634
1.821
0.545
206.391
1.661
0.519
1.615
0.670
1.652
0.675
1.815
0.566
210.249
1.603
0.553
1.560
0.695
1.597
0.712
1.822
0.612
214.108
1.534
0.587
1.491
0.720
1.524
0.749
1.829
0.679
217.966
1.454
0.586
1.408
0.724
1.435
0.761
1.828
0.791
221.824
1.380
0.564
1.320
0.701
1.342
0.747
1.758
0.993
225.682
1.324
0.513
1.254
0.636
1.253
0.705
1.498
1.23
229.540
1.288
0.469
1.213
0.581
1.185
0.631
1.160
1.12
233.398
1.263
0.426
1.183
0.524
1.148
0.549
1.010
0.808
237.256
1.248
0.385
1.166
0.471
1.139
0.478
1.020
0.638
241.114
1.239
0.351
1.158
0.424
1.138
0.435
1.047
0.550
244.972
1.230
0.325
1.153
0.388
1.131
0.397
1.070
0.485
248.830
1.217
0.299
1.145
0.352
1.126
0.348
1.088
0.447
252.688
1.208
0.258
1.148
0.299
1.135
0.300
1.095
0.415
256.546
1.213
0.217
1.162
0.272
1.152
0.269
1.101
0.378
260.404
1.225
0.190
1.171
0.248
1.163
0.251
1.108
0.355
264.262
1.236
0.171
1.178
0.227
1.170
0.229
1.108
0.333
268.120
1.247
0.151
1.186
0.205
1.179
0.206
1.104
0.309
271.978
1.258
0.139
1.195
0.188
1.187
0.192
1.101
0.276
275.836
1.267
0.127
1.203
0.172
1.194
0.174
1.104
0.244
279.694
1.275
0.117
1.210
0.156
1.201
0.158
1.111
0.213
283.552
1.282
0.108
1.218
0.140
1.210
0.141
1.123
0.184
287.411
1.288
0.0991
1.227
0.128
1.219
0.129
1.137
0.164
291.269
1.294
0.0900
1.235
0.117
1.227
0.116
1.148
0.148
295.127
1.301
0.0827
1.243
0.105
1.235
0.106
1.156
0.132
298.985
1.307
0.0753
1.250
0.0953
1.242
0.0954
1.163
0.116
302.843
1.312
0.0688
1.257
0.0849
1.248
0.0849
1.168
0.0993
306.701
1.318
0.0596
1.265
0.0738
1.257
0.0703
1.181
0.0660
310.559
1.325
0.0534
1.274
0.0648
1.268
0.0620
1.202
0.0519
314.417
1.331
0.0477
1.283
0.0568
1.278
0.0536
1.221
0.0400
318.275
1.338
0.0424
1.292
0.0498
1.288
0.0462
1.240
0.0322
322.133
1.345
0.0374
1.301
0.0431
1.298
0.0402
1.257
0.0281
325.991
1.352
0.0332
1.310
0.0372
1.307
0.0349
1.271
0.0258
329.849
1.359
0.0297
1.320
0.0327
1.317
0.0312
1.284
0.0246
333.707
1.366
0.0272
1.329
0.0294
1.326
0.0285
1.295
0.0238
337.565
1.372
0.0252
1.337
0.0270
1.335
0.0267
1.305
0.0235
341.423
1.378
0.0241
1.345
0.0254
1.342
0.0253
1.313
0.0234
345.281
1.383
0.0232
1.352
0.0242
1.349
0.0244
1.321
0.0234
349.139
1.388
0.0223
1.358
0.0232
1.355
0.0235
1.328
0.0235
352.997
1.393
0.0217
1.364
0.0224
1.361
0.0227
1.334
0.0232
356.855
1.397
0.0212
1.370
0.0215
1.366
0.0220
1.339
0.0229
360.714
1.401
0.0206
1.375
0.0208
1.371
0.0213
1.344
0.0225
364.572
1.405
0.0200
1.379
0.0199
1.376
0.0204
1.349
0.0220
368.430
1.409
0.0196
1.384
0.0192
1.380
0.0196
1.353
0.0213
372.288
1.412
0.0192
1.388
0.0183
1.384
0.0188
1.358
0.0204
376.146
1.415
0.0187
1.393
0.0177
1.389
0.0180
1.362
0.0196
380.004
1.419
0.0184
1.397
0.0170
1.393
0.0173
1.366
0.0192
383.862
1.422
0.0180
1.401
0.0163
1.397
0.0165
1.369
0.0177
387.720
1.425
0.0177
1.405
0.0157
1.400
0.0159
1.373
0.0166
391.578
1.428
0.0174
1.409
0.0152
1.404
0.0152
1.377
0.0154
395.436
1.431
0.0171
1.412
0.0147
1.408
0.0145
1.381
0.0143
399.294
1.433
0.0169
1.416
0.0142
1.412
0.0139
1.385
0.0133
403.152
1.436
0.0167
1.420
0.0138
1.415
0.0135
1.389
0.0125
407.010
1.439
0.0165
1.423
0.0135
1.419
0.0129
1.393
0.0119
410.868
1.442
0.0163
1.427
0.0131
1.422
0.0126
1.396
0.0113
414.726
1.444
0.0163
1.430
0.0129
1.426
0.0123
1.400
0.0109
418.584
1.447
0.0162
1.434
0.0127
1.429
0.0120
1.404
0.0105
422.442
1.450
0.0162
1.437
0.0126
1.433
0.0119
1.407
0.0101
426.300
1.452
0.0161
1.441
0.0125
1.436
0.0117
1.410
0.00969
430.158
1.455
0.0161
1.444
0.0124
1.440
0.0116
1.414
0.00945
434.017
1.457
0.0161
1.447
0.0123
1.443
0.0116
1.417
0.00923
437.875
1.460
0.0161
1.451
0.0124
1.446
0.0115
1.420
0.00904
441.733
1.462
0.0161
1.454
0.0123
1.450
0.0116
1.423
0.00891
445.591
1.465
0.0163
1.458
0.0127
1.453
0.0117
1.426
0.00882
449.449
1.468
0.0164
1.461
0.0127
1.456
0.0119
1.429
0.00880
453.307
1.471
0.0165
1.464
0.0130
1.459
0.0121
1.432
0.00879
457.165
1.473
0.0168
1.468
0.0133
1.463
0.0123
1.435
0.00871
461.023
1.476
0.0170
1.471
0.0137
1.466
0.0126
1.438
0.00873
464.881
1.479
0.0177
1.475
0.0142
1.470
0.0130
1.441
0.00872
468.739
1.482
0.0180
1.479
0.0148
1.473
0.0135
1.444
0.00878
472.597
1.485
0.0186
1.482
0.0152
1.477
0.0138
1.447
0.00886
476.455
1.488
0.0194
1.486
0.0158
1.480
0.0145
1.450
0.00894
480.313
1.491
0.0200
1.490
0.0167
1.484
0.0152
1.453
0.00892
484.171
1.494
0.0212
1.495
0.0179
1.488
0.0160
1.456
0.00924
488.029
1.498
0.0224
1.499
0.0193
1.493
0.0172
1.459
0.00930
491.887
1.501
0.0239
1.504
0.0211
1.497
0.0186
1.462
0.00939
495.745
1.505
0.0257
1.509
0.0237
1.502
0.0207
1.465
0.00957
499.603
1.509
0.0285
1.514
0.0271
1.507
0.0235
1.468
0.00981
503.462
1.512
0.0317
1.518
0.0315
1.511
0.0273
1.471
0.0101
507.320
1.514
0.0359
1.522
0.0369
1.515
0.0321
1.474
0.0104
511.178
1.516
0.0402
1.524
0.0429
1.518
0.0370
1.477
0.0107
515.036
1.517
0.0443
1.525
0.0489
1.519
0.0425
1.481
0.0109
518.894
1.517
0.0479
1.525
0.0536
1.520
0.0473
1.484
0.0111
522.752
1.516
0.0501
1.524
0.0575
1.519
0.0512
1.489
0.0117
526.610
1.516
0.0522
1.524
0.0601
1.519
0.0533
1.493
0.0123
530.468
1.516
0.0541
1.524
0.0634
1.519
0.0557
1.498
0.0134
534.326
1.516
0.0561
1.523
0.0648
1.520
0.0585
1.504
0.0160
538.184
1.515
0.0563
1.523
0.0655
1.520
0.0600
1.508
0.0209
542.042
1.516
0.0571
1.525
0.0670
1.521
0.0608
1.511
0.0249
545.900
1.517
0.0574
1.528
0.0675
1.523
0.0626
1.515
0.0281
549.758
1.518
0.0594
1.528
0.0758
1.523
0.0678
1.515
0.0373
553.616
1.518
0.0607
1.527
0.0768
1.522
0.0696
1.513
0.0396
557.474
1.519
0.0611
1.526
0.0787
1.522
0.0701
1.513
0.0408
561.332
1.520
0.0615
1.526
0.0800
1.523
0.0715
1.513
0.0422
565.190
1.521
0.0630
1.527
0.0814
1.524
0.0728
1.514
0.0427
569.048
1.522
0.0636
1.527
0.0850
1.525
0.0750
1.515
0.0440
572.906
1.523
0.0642
1.526
0.0848
1.525
0.0769
1.516
0.0446
576.765
1.525
0.0650
1.528
0.0858
1.526
0.0777
1.517
0.0448
580.623
1.526
0.0657
1.529
0.0883
1.527
0.0784
1.519
0.0453
584.481
1.528
0.0669
1.529
0.0901
1.528
0.0803
1.521
0.0459
588.339
1.530
0.0684
1.530
0.0914
1.530
0.0821
1.523
0.0467
592.197
1.532
0.0691
1.530
0.0934
1.531
0.0842
1.526
0.0475
596.055
1.534
0.0712
1.531
0.0951
1.532
0.0863
1.528
0.0485
599.913
1.536
0.0728
1.533
0.0954
1.533
0.0878
1.531
0.0495
603.771
1.538
0.0759
1.534
0.101
1.534
0.0914
1.534
0.0508
607.629
1.537
0.0798
1.534
0.103
1.535
0.0924
1.537
0.0521
611.487
1.539
0.0769
1.531
0.109
1.537
0.0960
1.540
0.0538
615.345
1.542
0.0798
1.531
0.105
1.537
0.0992
1.542
0.0575
619.203
1.544
0.0824
1.531
0.110
1.536
0.103
1.545
0.0579
623.061
1.544
0.0887
1.531
0.108
1.534
0.105
1.548
0.0598
626.919
1.542
0.0885
1.533
0.110
1.535
0.102
1.550
0.0627
630.777
1.544
0.0869
1.534
0.115
1.536
0.107
1.553
0.0635
634.635
1.547
0.0871
1.533
0.119
1.536
0.108
1.556
0.0656
638.493
1.550
0.0923
1.530
0.122
1.537
0.111
1.560
0.0673
642.351
1.550
0.0959
1.527
0.125
1.534
0.119
1.564
0.0698
646.209
1.549
0.0992
1.520
0.129
1.530
0.117
1.568
0.0730
650.067
1.542
0.104
1.501
0.133
1.513
0.131
1.572
0.0761
Table 5
Measured Optical Constants for Water Ice from 146 to 176 K
Frequency (cm−1)
146 K
156 K
166 K
176 K
n
k
n
k
n
k
n
k
52.069
1.766
0.0406
1.769
0.0360
1.764
0.0339
1.764
0.0402
55.927
1.759
0.0392
1.765
0.0395
1.758
0.0429
1.759
0.0431
59.785
1.759
0.0395
1.761
0.0500
1.756
0.0436
1.756
0.0539
63.643
1.762
0.0427
1.760
0.0448
1.756
0.0499
1.752
0.0518
67.501
1.765
0.0470
1.763
0.0518
1.755
0.0507
1.755
0.0502
71.360
1.766
0.0523
1.763
0.0536
1.758
0.0511
1.760
0.0541
75.218
1.766
0.0538
1.762
0.0583
1.759
0.0590
1.761
0.0613
79.076
1.767
0.0555
1.763
0.0550
1.758
0.0575
1.761
0.0612
82.934
1.769
0.0548
1.767
0.0552
1.761
0.0575
1.764
0.0620
86.792
1.774
0.0542
1.771
0.0548
1.765
0.0565
1.769
0.0619
90.650
1.779
0.0546
1.779
0.0544
1.771
0.0583
1.780
0.0625
94.508
1.788
0.0498
1.784
0.0620
1.777
0.0586
1.777
0.0898
98.366
1.799
0.0581
1.789
0.0573
1.784
0.0600
1.773
0.0671
102.224
1.804
0.0629
1.798
0.0603
1.792
0.0613
1.787
0.0658
106.082
1.814
0.0594
1.810
0.0575
1.804
0.0590
1.802
0.0645
109.940
1.830
0.0620
1.827
0.0607
1.821
0.0645
1.819
0.0731
113.798
1.847
0.0713
1.844
0.0708
1.837
0.0751
1.835
0.0836
117.656
1.863
0.0825
1.860
0.0823
1.851
0.0881
1.849
0.0987
121.514
1.878
0.0969
1.876
0.0955
1.866
0.101
1.861
0.113
125.372
1.894
0.113
1.892
0.115
1.881
0.120
1.877
0.126
129.230
1.908
0.136
1.908
0.132
1.894
0.143
1.892
0.152
133.088
1.925
0.152
1.923
0.163
1.907
0.164
1.903
0.176
136.946
1.938
0.193
1.932
0.192
1.914
0.201
1.914
0.205
140.805
1.942
0.219
1.936
0.224
1.919
0.222
1.928
0.237
144.663
1.966
0.237
1.961
0.231
1.937
0.251
1.929
0.298
148.521
1.972
0.329
1.977
0.323
1.934
0.330
1.910
0.351
152.379
1.937
0.388
1.942
0.403
1.900
0.380
1.867
0.410
156.237
1.888
0.433
1.877
0.455
1.845
0.431
1.808
0.425
160.095
1.826
0.458
1.803
0.467
1.779
0.429
1.753
0.425
163.953
1.767
0.443
1.746
0.432
1.735
0.396
1.712
0.386
167.811
1.725
0.413
1.713
0.398
1.710
0.365
1.696
0.346
171.669
1.709
0.354
1.703
0.342
1.710
0.310
1.713
0.291
175.527
1.737
0.297
1.738
0.281
1.754
0.265
1.764
0.270
179.385
1.807
0.272
1.811
0.270
1.817
0.283
1.817
0.301
183.243
1.867
0.344
1.858
0.350
1.842
0.358
1.834
0.370
187.101
1.863
0.432
1.859
0.405
1.840
0.385
1.828
0.401
190.959
1.839
0.455
1.849
0.445
1.844
0.419
1.827
0.431
194.817
1.830
0.478
1.844
0.468
1.843
0.456
1.827
0.462
198.675
1.829
0.500
1.846
0.504
1.849
0.482
1.835
0.492
202.533
1.831
0.537
1.844
0.549
1.850
0.547
1.835
0.557
206.391
1.832
0.578
1.840
0.593
1.842
0.588
1.826
0.603
210.249
1.834
0.633
1.840
0.647
1.845
0.647
1.828
0.661
214.108
1.836
0.705
1.845
0.722
1.845
0.740
1.823
0.772
217.966
1.827
0.820
1.834
0.856
1.813
0.894
1.762
0.942
221.824
1.756
1.01
1.739
1.08
1.656
1.13
1.543
1.17
225.682
1.485
1.27
1.405
1.34
1.316
1.25
1.226
1.12
229.540
1.141
1.13
1.067
1.05
1.057
0.937
1.051
0.846
233.398
1.004
0.813
0.990
0.769
1.019
0.719
1.033
0.672
237.256
1.020
0.649
1.014
0.630
1.039
0.601
1.053
0.567
241.114
1.046
0.571
1.041
0.549
1.061
0.529
1.071
0.510
244.972
1.063
0.509
1.063
0.489
1.074
0.485
1.080
0.463
248.830
1.077
0.464
1.080
0.454
1.076
0.445
1.091
0.417
252.688
1.085
0.431
1.083
0.429
1.080
0.399
1.098
0.394
256.546
1.086
0.400
1.083
0.390
1.088
0.365
1.098
0.363
260.404
1.091
0.363
1.087
0.360
1.094
0.336
1.095
0.340
264.262
1.092
0.346
1.087
0.337
1.095
0.312
1.095
0.298
268.120
1.087
0.315
1.084
0.306
1.095
0.280
1.101
0.274
271.978
1.087
0.279
1.084
0.273
1.100
0.248
1.102
0.249
275.836
1.092
0.250
1.090
0.240
1.108
0.219
1.106
0.214
279.694
1.099
0.218
1.099
0.208
1.119
0.191
1.119
0.184
283.552
1.112
0.190
1.113
0.181
1.133
0.170
1.134
0.163
287.411
1.126
0.168
1.127
0.163
1.145
0.153
1.146
0.148
291.269
1.138
0.153
1.139
0.147
1.155
0.138
1.156
0.133
295.127
1.147
0.138
1.147
0.132
1.163
0.122
1.164
0.116
298.985
1.153
0.122
1.154
0.116
1.170
0.107
1.173
0.100
302.843
1.158
0.104
1.159
0.0982
1.175
0.0888
1.182
0.0821
306.701
1.170
0.0732
1.172
0.0653
1.190
0.0584
1.197
0.0573
310.559
1.190
0.0562
1.195
0.0495
1.213
0.0455
1.218
0.0456
314.417
1.210
0.0423
1.216
0.0391
1.233
0.0374
1.237
0.0393
318.275
1.230
0.0348
1.235
0.0335
1.250
0.0334
1.253
0.0357
322.133
1.247
0.0311
1.251
0.0310
1.265
0.0313
1.267
0.0337
325.991
1.262
0.0293
1.265
0.0296
1.278
0.0300
1.278
0.0325
329.849
1.275
0.0284
1.277
0.0286
1.288
0.0294
1.289
0.0316
333.707
1.286
0.0276
1.287
0.0279
1.298
0.0288
1.298
0.0312
337.565
1.295
0.0272
1.296
0.0274
1.307
0.0286
1.306
0.0309
341.423
1.304
0.0270
1.305
0.0273
1.314
0.0286
1.313
0.0310
345.281
1.311
0.0268
1.312
0.0272
1.320
0.0283
1.319
0.0308
349.139
1.318
0.0267
1.318
0.0270
1.326
0.0279
1.325
0.0303
352.997
1.324
0.0264
1.324
0.0267
1.332
0.0275
1.330
0.0298
356.855
1.330
0.0259
1.329
0.0261
1.337
0.0268
1.334
0.0290
360.714
1.335
0.0254
1.334
0.0254
1.341
0.0259
1.339
0.0280
364.572
1.340
0.0247
1.339
0.0245
1.346
0.0249
1.343
0.0269
368.430
1.344
0.0237
1.343
0.0236
1.350
0.0239
1.347
0.0257
372.288
1.348
0.0229
1.348
0.0227
1.354
0.0229
1.351
0.0246
376.146
1.352
0.0219
1.351
0.0216
1.358
0.0218
1.355
0.0233
380.004
1.357
0.0204
1.356
0.0194
1.362
0.0205
1.359
0.0220
383.862
1.361
0.0198
1.360
0.0192
1.366
0.0194
1.363
0.0207
387.720
1.364
0.0185
1.364
0.0181
1.370
0.0181
1.366
0.0195
391.578
1.368
0.0172
1.368
0.0168
1.373
0.0169
1.370
0.0184
395.436
1.372
0.0159
1.372
0.0157
1.377
0.0158
1.374
0.0172
399.294
1.376
0.0147
1.376
0.0147
1.381
0.0148
1.378
0.0162
403.152
1.380
0.0137
1.379
0.0139
1.385
0.0141
1.381
0.0153
407.010
1.384
0.0130
1.383
0.0133
1.389
0.0135
1.385
0.0144
410.868
1.388
0.0124
1.387
0.0127
1.392
0.0128
1.389
0.0136
414.726
1.392
0.0120
1.390
0.0120
1.396
0.0122
1.392
0.0129
418.584
1.395
0.0116
1.394
0.0116
1.399
0.0118
1.396
0.0125
422.442
1.399
0.0113
1.397
0.0112
1.403
0.0114
1.399
0.0121
426.300
1.402
0.0110
1.401
0.0108
1.406
0.0111
1.403
0.0118
430.158
1.405
0.0108
1.404
0.0105
1.409
0.0108
1.406
0.0116
434.017
1.408
0.0104
1.407
0.0102
1.412
0.0105
1.409
0.0116
437.875
1.411
0.0101
1.410
0.0100
1.416
0.0104
1.412
0.0114
441.733
1.415
0.00989
1.414
0.00978
1.419
0.0103
1.415
0.0114
445.591
1.418
0.00962
1.417
0.00966
1.422
0.0103
1.418
0.0114
449.449
1.421
0.00961
1.420
0.00959
1.425
0.0101
1.421
0.0114
453.307
1.424
0.00952
1.423
0.00963
1.428
0.0101
1.424
0.0114
457.165
1.427
0.00952
1.426
0.00959
1.430
0.0101
1.427
0.0115
461.023
1.430
0.00957
1.429
0.00974
1.433
0.0101
1.430
0.0114
464.881
1.432
0.00965
1.432
0.00976
1.436
0.0101
1.433
0.0115
468.739
1.435
0.00943
1.434
0.00985
1.439
0.0102
1.435
0.0115
472.597
1.438
0.00932
1.437
0.00991
1.442
0.0101
1.438
0.0116
476.455
1.441
0.00914
1.440
0.00994
1.445
0.0101
1.441
0.0116
480.313
1.444
0.00922
1.443
0.0101
1.448
0.0105
1.444
0.0118
484.171
1.447
0.00943
1.445
0.0101
1.450
0.0107
1.447
0.0120
488.029
1.450
0.00975
1.448
0.0103
1.453
0.0110
1.450
0.0123
491.887
1.453
0.0101
1.451
0.0104
1.456
0.0110
1.453
0.0127
495.745
1.456
0.0105
1.454
0.0105
1.459
0.0113
1.455
0.0128
499.603
1.458
0.0107
1.457
0.0106
1.462
0.0114
1.458
0.0130
503.462
1.461
0.0110
1.460
0.0107
1.465
0.0114
1.461
0.0133
507.320
1.464
0.0111
1.463
0.0108
1.468
0.0116
1.464
0.0133
511.178
1.467
0.0110
1.466
0.0110
1.471
0.0117
1.468
0.0134
515.036
1.470
0.0109
1.469
0.0111
1.475
0.0118
1.472
0.0137
518.894
1.474
0.0110
1.473
0.0112
1.478
0.0121
1.476
0.0141
522.752
1.478
0.0111
1.477
0.0115
1.483
0.0124
1.480
0.0148
526.610
1.482
0.0115
1.481
0.0119
1.488
0.0133
1.486
0.0167
530.468
1.487
0.0125
1.487
0.0134
1.493
0.0158
1.490
0.0205
534.326
1.492
0.0155
1.491
0.0171
1.497
0.0200
1.493
0.0248
538.184
1.496
0.0199
1.494
0.0211
1.499
0.0234
1.495
0.0283
542.042
1.498
0.0234
1.497
0.0240
1.502
0.0264
1.497
0.0309
545.900
1.501
0.0258
1.500
0.0258
1.505
0.0283
1.500
0.0336
549.758
1.502
0.0320
1.501
0.0334
1.507
0.0366
1.501
0.0405
553.616
1.502
0.0337
1.500
0.0349
1.506
0.0375
1.500
0.0428
557.474
1.502
0.0347
1.501
0.0357
1.506
0.0393
1.500
0.0438
561.332
1.503
0.0355
1.502
0.0365
1.507
0.0403
1.501
0.0450
565.190
1.504
0.0361
1.503
0.0376
1.509
0.0416
1.502
0.0459
569.048
1.506
0.0373
1.505
0.0385
1.509
0.0440
1.503
0.0476
572.906
1.508
0.0376
1.506
0.0392
1.510
0.0436
1.504
0.0475
576.765
1.510
0.0386
1.508
0.0399
1.512
0.0444
1.505
0.0484
580.623
1.512
0.0395
1.510
0.0408
1.514
0.0455
1.507
0.0495
584.481
1.514
0.0403
1.512
0.0419
1.516
0.0466
1.509
0.0502
588.339
1.517
0.0410
1.515
0.0427
1.518
0.0478
1.511
0.0513
592.197
1.519
0.0425
1.517
0.0440
1.521
0.0488
1.514
0.0528
596.055
1.522
0.0437
1.520
0.0451
1.523
0.0504
1.516
0.0538
599.913
1.524
0.0449
1.523
0.0466
1.525
0.0522
1.519
0.0558
603.771
1.527
0.0461
1.525
0.0485
1.528
0.0531
1.521
0.0580
607.629
1.530
0.0470
1.528
0.0503
1.530
0.0560
1.523
0.0592
611.487
1.533
0.0495
1.530
0.0517
1.532
0.0562
1.525
0.0606
615.345
1.535
0.0504
1.533
0.0527
1.536
0.0567
1.528
0.0635
619.203
1.538
0.0522
1.536
0.0549
1.539
0.0618
1.530
0.0658
623.061
1.542
0.0534
1.539
0.0572
1.540
0.0652
1.532
0.0682
626.919
1.545
0.0554
1.542
0.0578
1.542
0.0643
1.534
0.0710
630.777
1.548
0.0571
1.545
0.0603
1.546
0.0670
1.536
0.0717
634.635
1.552
0.0592
1.548
0.0621
1.548
0.0698
1.539
0.0755
638.493
1.556
0.0607
1.552
0.0640
1.551
0.0707
1.541
0.0770
642.351
1.561
0.0633
1.556
0.0661
1.555
0.0744
1.543
0.0806
646.209
1.566
0.0667
1.561
0.0690
1.557
0.0779
1.545
0.0826
650.067
1.573
0.0682
1.566
0.0727
1.559
0.0802
1.544
0.0879
Table 6
Peak Frequencies and Measured Absorbances of the 225 and 160 cm−1 Bands as a Function of Temperaturea
Also shown is the ratio of the peak absorbances of the 225–160 cm−1 bands. Films roughly 5.3 µm thick were chosen at the various temperatures for this table.
N/A, not applicable.
Tables (6)
Table 1
Summary of Far-IR Optical Constant Measurements Available in the Literature
Imaginary Indices of Refraction Used for the Calculation of the Real Indices Using the Kramers–Kronig Integrationa
Temperature (K)
Approximate Frequency Range (cm−1)
n at 15, 823 cm−1
52–500
500–800
800–3700
3700–7000
106
Trotta (1996), 145 K1
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K
Rajaram et al. (2001), 170 K
1.28
116
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K
Rajaram et al. (2001), 170 K
1.29
126
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K1
Rajaram et al. (2001), 170 K
1.30
136
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 130 K
Rajaram et al. (2001), 170 K
1.310459
146
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 150 K
Rajaram et al. (2001), 170 K
1.310303
156
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 160 K
Rajaram et al. (2001), 170 K
1.310110
166
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 170 K
Rajaram et al. (2001), 170 K
1.309880
176
Trotta (1996), 145 K
Toon et al. (1994), 166 K
Clapp et al. (1995), 180 K
Rajaram et al. (2001), 170 K
1.309615
The last column has the temperature-dependent real index of refraction at 15, 823 cm−1 used as the anchor point for the Kramers–Kronig analysis. For T = 136 K and higher, these were calculated using the Lorentz–Lorenz equation; see Rajaram et al. (2001)26 for details. For T = 126 and lower, these values are measured values from Berland et al. (1995).34 The values of Trotta (1996)23 were used as the starting point for the iteration in the far IR in this study, while those of Toon et al. (1994),24 Clapp et al. (1995),27 and Rajaram et al. (2001)26 were used in the mid-IR and near IR.
Table 3
Groups of Films Used to Obtain the Imaginary Index of Refraction in the 50–650 cm−1 Regiona
Approximate Frequency Range (cm−1)
Group of Films
52–144
Thick
148–198
Intermediate
202–248
Thin
252–302
Intermediate
306–545
Thick
549–650
Intermediate
The thin group refers to films ≤11 µm thick. The intermediate group consists of films 12–41 µm thick, and the thick group consists of films 41–140 µm thick.
Table 4
Measured Optical Constants for Water Ice from 106 to 136 K
Frequency (cm−1)
106 K
116 K
126 K
136 K
n
k
n
k
n
k
n
k
52.069
1.713
0.0628
1.772
0.0471
1.771
0.0447
1.768
0.0381
55.927
1.695
0.0648
1.759
0.0529
1.763
0.0486
1.761
0.0449
59.785
1.693
0.0568
1.759
0.0437
1.759
0.0531
1.757
0.0469
63.643
1.693
0.0695
1.764
0.0549
1.759
0.0529
1.756
0.0483
67.501
1.689
0.0666
1.764
0.0572
1.763
0.0540
1.757
0.0468
71.360
1.690
0.0689
1.765
0.0625
1.765
0.0620
1.761
0.0480
75.218
1.689
0.0713
1.764
0.0670
1.763
0.0658
1.763
0.0538
79.076
1.689
0.0708
1.766
0.0630
1.764
0.0646
1.765
0.0516
82.934
1.691
0.0721
1.769
0.0674
1.767
0.0642
1.769
0.0548
86.792
1.693
0.0727
1.773
0.0664
1.772
0.0656
1.775
0.0539
90.650
1.695
0.0738
1.777
0.0686
1.776
0.0678
1.787
0.0548
94.508
1.698
0.0727
1.783
0.0664
1.783
0.0651
1.782
0.0852
98.366
1.705
0.0716
1.794
0.0641
1.793
0.0653
1.776
0.0604
102.224
1.716
0.0722
1.811
0.0627
1.808
0.0633
1.789
0.0570
106.082
1.728
0.0802
1.831
0.0730
1.827
0.0720
1.804
0.0534
109.940
1.738
0.0908
1.849
0.0900
1.844
0.0876
1.822
0.0585
113.798
1.747
0.106
1.862
0.110
1.858
0.107
1.840
0.0675
117.656
1.752
0.123
1.874
0.131
1.870
0.127
1.856
0.0805
121.514
1.756
0.141
1.882
0.159
1.879
0.152
1.872
0.0950
125.372
1.754
0.164
1.885
0.187
1.881
0.181
1.886
0.113
129.230
1.744
0.184
1.884
0.213
1.880
0.203
1.900
0.133
133.088
1.734
0.195
1.877
0.246
1.878
0.229
1.911
0.157
136.946
1.723
0.207
1.866
0.264
1.873
0.253
1.923
0.175
140.805
1.712
0.211
1.855
0.289
1.864
0.278
1.951
0.191
144.663
1.705
0.215
1.840
0.306
1.854
0.299
1.975
0.261
148.521
1.700
0.219
1.824
0.322
1.839
0.323
1.957
0.346
152.379
1.695
0.223
1.811
0.328
1.820
0.337
1.916
0.389
156.237
1.692
0.228
1.800
0.339
1.804
0.345
1.869
0.433
160.095
1.689
0.233
1.792
0.344
1.791
0.351
1.800
0.460
163.953
1.688
0.236
1.788
0.350
1.783
0.354
1.733
0.433
167.811
1.687
0.244
1.787
0.363
1.781
0.358
1.703
0.370
171.669
1.687
0.249
1.786
0.375
1.781
0.367
1.706
0.326
175.527
1.691
0.253
1.786
0.394
1.784
0.376
1.738
0.280
179.385
1.695
0.268
1.785
0.414
1.796
0.390
1.793
0.276
183.243
1.697
0.278
1.787
0.436
1.803
0.431
1.840
0.316
187.101
1.708
0.287
1.784
0.478
1.796
0.472
1.862
0.374
190.959
1.719
0.318
1.769
0.519
1.782
0.512
1.861
0.427
194.817
1.727
0.349
1.745
0.561
1.761
0.553
1.852
0.469
198.675
1.725
0.404
1.713
0.603
1.733
0.593
1.838
0.511
202.533
1.704
0.460
1.667
0.645
1.697
0.634
1.821
0.545
206.391
1.661
0.519
1.615
0.670
1.652
0.675
1.815
0.566
210.249
1.603
0.553
1.560
0.695
1.597
0.712
1.822
0.612
214.108
1.534
0.587
1.491
0.720
1.524
0.749
1.829
0.679
217.966
1.454
0.586
1.408
0.724
1.435
0.761
1.828
0.791
221.824
1.380
0.564
1.320
0.701
1.342
0.747
1.758
0.993
225.682
1.324
0.513
1.254
0.636
1.253
0.705
1.498
1.23
229.540
1.288
0.469
1.213
0.581
1.185
0.631
1.160
1.12
233.398
1.263
0.426
1.183
0.524
1.148
0.549
1.010
0.808
237.256
1.248
0.385
1.166
0.471
1.139
0.478
1.020
0.638
241.114
1.239
0.351
1.158
0.424
1.138
0.435
1.047
0.550
244.972
1.230
0.325
1.153
0.388
1.131
0.397
1.070
0.485
248.830
1.217
0.299
1.145
0.352
1.126
0.348
1.088
0.447
252.688
1.208
0.258
1.148
0.299
1.135
0.300
1.095
0.415
256.546
1.213
0.217
1.162
0.272
1.152
0.269
1.101
0.378
260.404
1.225
0.190
1.171
0.248
1.163
0.251
1.108
0.355
264.262
1.236
0.171
1.178
0.227
1.170
0.229
1.108
0.333
268.120
1.247
0.151
1.186
0.205
1.179
0.206
1.104
0.309
271.978
1.258
0.139
1.195
0.188
1.187
0.192
1.101
0.276
275.836
1.267
0.127
1.203
0.172
1.194
0.174
1.104
0.244
279.694
1.275
0.117
1.210
0.156
1.201
0.158
1.111
0.213
283.552
1.282
0.108
1.218
0.140
1.210
0.141
1.123
0.184
287.411
1.288
0.0991
1.227
0.128
1.219
0.129
1.137
0.164
291.269
1.294
0.0900
1.235
0.117
1.227
0.116
1.148
0.148
295.127
1.301
0.0827
1.243
0.105
1.235
0.106
1.156
0.132
298.985
1.307
0.0753
1.250
0.0953
1.242
0.0954
1.163
0.116
302.843
1.312
0.0688
1.257
0.0849
1.248
0.0849
1.168
0.0993
306.701
1.318
0.0596
1.265
0.0738
1.257
0.0703
1.181
0.0660
310.559
1.325
0.0534
1.274
0.0648
1.268
0.0620
1.202
0.0519
314.417
1.331
0.0477
1.283
0.0568
1.278
0.0536
1.221
0.0400
318.275
1.338
0.0424
1.292
0.0498
1.288
0.0462
1.240
0.0322
322.133
1.345
0.0374
1.301
0.0431
1.298
0.0402
1.257
0.0281
325.991
1.352
0.0332
1.310
0.0372
1.307
0.0349
1.271
0.0258
329.849
1.359
0.0297
1.320
0.0327
1.317
0.0312
1.284
0.0246
333.707
1.366
0.0272
1.329
0.0294
1.326
0.0285
1.295
0.0238
337.565
1.372
0.0252
1.337
0.0270
1.335
0.0267
1.305
0.0235
341.423
1.378
0.0241
1.345
0.0254
1.342
0.0253
1.313
0.0234
345.281
1.383
0.0232
1.352
0.0242
1.349
0.0244
1.321
0.0234
349.139
1.388
0.0223
1.358
0.0232
1.355
0.0235
1.328
0.0235
352.997
1.393
0.0217
1.364
0.0224
1.361
0.0227
1.334
0.0232
356.855
1.397
0.0212
1.370
0.0215
1.366
0.0220
1.339
0.0229
360.714
1.401
0.0206
1.375
0.0208
1.371
0.0213
1.344
0.0225
364.572
1.405
0.0200
1.379
0.0199
1.376
0.0204
1.349
0.0220
368.430
1.409
0.0196
1.384
0.0192
1.380
0.0196
1.353
0.0213
372.288
1.412
0.0192
1.388
0.0183
1.384
0.0188
1.358
0.0204
376.146
1.415
0.0187
1.393
0.0177
1.389
0.0180
1.362
0.0196
380.004
1.419
0.0184
1.397
0.0170
1.393
0.0173
1.366
0.0192
383.862
1.422
0.0180
1.401
0.0163
1.397
0.0165
1.369
0.0177
387.720
1.425
0.0177
1.405
0.0157
1.400
0.0159
1.373
0.0166
391.578
1.428
0.0174
1.409
0.0152
1.404
0.0152
1.377
0.0154
395.436
1.431
0.0171
1.412
0.0147
1.408
0.0145
1.381
0.0143
399.294
1.433
0.0169
1.416
0.0142
1.412
0.0139
1.385
0.0133
403.152
1.436
0.0167
1.420
0.0138
1.415
0.0135
1.389
0.0125
407.010
1.439
0.0165
1.423
0.0135
1.419
0.0129
1.393
0.0119
410.868
1.442
0.0163
1.427
0.0131
1.422
0.0126
1.396
0.0113
414.726
1.444
0.0163
1.430
0.0129
1.426
0.0123
1.400
0.0109
418.584
1.447
0.0162
1.434
0.0127
1.429
0.0120
1.404
0.0105
422.442
1.450
0.0162
1.437
0.0126
1.433
0.0119
1.407
0.0101
426.300
1.452
0.0161
1.441
0.0125
1.436
0.0117
1.410
0.00969
430.158
1.455
0.0161
1.444
0.0124
1.440
0.0116
1.414
0.00945
434.017
1.457
0.0161
1.447
0.0123
1.443
0.0116
1.417
0.00923
437.875
1.460
0.0161
1.451
0.0124
1.446
0.0115
1.420
0.00904
441.733
1.462
0.0161
1.454
0.0123
1.450
0.0116
1.423
0.00891
445.591
1.465
0.0163
1.458
0.0127
1.453
0.0117
1.426
0.00882
449.449
1.468
0.0164
1.461
0.0127
1.456
0.0119
1.429
0.00880
453.307
1.471
0.0165
1.464
0.0130
1.459
0.0121
1.432
0.00879
457.165
1.473
0.0168
1.468
0.0133
1.463
0.0123
1.435
0.00871
461.023
1.476
0.0170
1.471
0.0137
1.466
0.0126
1.438
0.00873
464.881
1.479
0.0177
1.475
0.0142
1.470
0.0130
1.441
0.00872
468.739
1.482
0.0180
1.479
0.0148
1.473
0.0135
1.444
0.00878
472.597
1.485
0.0186
1.482
0.0152
1.477
0.0138
1.447
0.00886
476.455
1.488
0.0194
1.486
0.0158
1.480
0.0145
1.450
0.00894
480.313
1.491
0.0200
1.490
0.0167
1.484
0.0152
1.453
0.00892
484.171
1.494
0.0212
1.495
0.0179
1.488
0.0160
1.456
0.00924
488.029
1.498
0.0224
1.499
0.0193
1.493
0.0172
1.459
0.00930
491.887
1.501
0.0239
1.504
0.0211
1.497
0.0186
1.462
0.00939
495.745
1.505
0.0257
1.509
0.0237
1.502
0.0207
1.465
0.00957
499.603
1.509
0.0285
1.514
0.0271
1.507
0.0235
1.468
0.00981
503.462
1.512
0.0317
1.518
0.0315
1.511
0.0273
1.471
0.0101
507.320
1.514
0.0359
1.522
0.0369
1.515
0.0321
1.474
0.0104
511.178
1.516
0.0402
1.524
0.0429
1.518
0.0370
1.477
0.0107
515.036
1.517
0.0443
1.525
0.0489
1.519
0.0425
1.481
0.0109
518.894
1.517
0.0479
1.525
0.0536
1.520
0.0473
1.484
0.0111
522.752
1.516
0.0501
1.524
0.0575
1.519
0.0512
1.489
0.0117
526.610
1.516
0.0522
1.524
0.0601
1.519
0.0533
1.493
0.0123
530.468
1.516
0.0541
1.524
0.0634
1.519
0.0557
1.498
0.0134
534.326
1.516
0.0561
1.523
0.0648
1.520
0.0585
1.504
0.0160
538.184
1.515
0.0563
1.523
0.0655
1.520
0.0600
1.508
0.0209
542.042
1.516
0.0571
1.525
0.0670
1.521
0.0608
1.511
0.0249
545.900
1.517
0.0574
1.528
0.0675
1.523
0.0626
1.515
0.0281
549.758
1.518
0.0594
1.528
0.0758
1.523
0.0678
1.515
0.0373
553.616
1.518
0.0607
1.527
0.0768
1.522
0.0696
1.513
0.0396
557.474
1.519
0.0611
1.526
0.0787
1.522
0.0701
1.513
0.0408
561.332
1.520
0.0615
1.526
0.0800
1.523
0.0715
1.513
0.0422
565.190
1.521
0.0630
1.527
0.0814
1.524
0.0728
1.514
0.0427
569.048
1.522
0.0636
1.527
0.0850
1.525
0.0750
1.515
0.0440
572.906
1.523
0.0642
1.526
0.0848
1.525
0.0769
1.516
0.0446
576.765
1.525
0.0650
1.528
0.0858
1.526
0.0777
1.517
0.0448
580.623
1.526
0.0657
1.529
0.0883
1.527
0.0784
1.519
0.0453
584.481
1.528
0.0669
1.529
0.0901
1.528
0.0803
1.521
0.0459
588.339
1.530
0.0684
1.530
0.0914
1.530
0.0821
1.523
0.0467
592.197
1.532
0.0691
1.530
0.0934
1.531
0.0842
1.526
0.0475
596.055
1.534
0.0712
1.531
0.0951
1.532
0.0863
1.528
0.0485
599.913
1.536
0.0728
1.533
0.0954
1.533
0.0878
1.531
0.0495
603.771
1.538
0.0759
1.534
0.101
1.534
0.0914
1.534
0.0508
607.629
1.537
0.0798
1.534
0.103
1.535
0.0924
1.537
0.0521
611.487
1.539
0.0769
1.531
0.109
1.537
0.0960
1.540
0.0538
615.345
1.542
0.0798
1.531
0.105
1.537
0.0992
1.542
0.0575
619.203
1.544
0.0824
1.531
0.110
1.536
0.103
1.545
0.0579
623.061
1.544
0.0887
1.531
0.108
1.534
0.105
1.548
0.0598
626.919
1.542
0.0885
1.533
0.110
1.535
0.102
1.550
0.0627
630.777
1.544
0.0869
1.534
0.115
1.536
0.107
1.553
0.0635
634.635
1.547
0.0871
1.533
0.119
1.536
0.108
1.556
0.0656
638.493
1.550
0.0923
1.530
0.122
1.537
0.111
1.560
0.0673
642.351
1.550
0.0959
1.527
0.125
1.534
0.119
1.564
0.0698
646.209
1.549
0.0992
1.520
0.129
1.530
0.117
1.568
0.0730
650.067
1.542
0.104
1.501
0.133
1.513
0.131
1.572
0.0761
Table 5
Measured Optical Constants for Water Ice from 146 to 176 K
Frequency (cm−1)
146 K
156 K
166 K
176 K
n
k
n
k
n
k
n
k
52.069
1.766
0.0406
1.769
0.0360
1.764
0.0339
1.764
0.0402
55.927
1.759
0.0392
1.765
0.0395
1.758
0.0429
1.759
0.0431
59.785
1.759
0.0395
1.761
0.0500
1.756
0.0436
1.756
0.0539
63.643
1.762
0.0427
1.760
0.0448
1.756
0.0499
1.752
0.0518
67.501
1.765
0.0470
1.763
0.0518
1.755
0.0507
1.755
0.0502
71.360
1.766
0.0523
1.763
0.0536
1.758
0.0511
1.760
0.0541
75.218
1.766
0.0538
1.762
0.0583
1.759
0.0590
1.761
0.0613
79.076
1.767
0.0555
1.763
0.0550
1.758
0.0575
1.761
0.0612
82.934
1.769
0.0548
1.767
0.0552
1.761
0.0575
1.764
0.0620
86.792
1.774
0.0542
1.771
0.0548
1.765
0.0565
1.769
0.0619
90.650
1.779
0.0546
1.779
0.0544
1.771
0.0583
1.780
0.0625
94.508
1.788
0.0498
1.784
0.0620
1.777
0.0586
1.777
0.0898
98.366
1.799
0.0581
1.789
0.0573
1.784
0.0600
1.773
0.0671
102.224
1.804
0.0629
1.798
0.0603
1.792
0.0613
1.787
0.0658
106.082
1.814
0.0594
1.810
0.0575
1.804
0.0590
1.802
0.0645
109.940
1.830
0.0620
1.827
0.0607
1.821
0.0645
1.819
0.0731
113.798
1.847
0.0713
1.844
0.0708
1.837
0.0751
1.835
0.0836
117.656
1.863
0.0825
1.860
0.0823
1.851
0.0881
1.849
0.0987
121.514
1.878
0.0969
1.876
0.0955
1.866
0.101
1.861
0.113
125.372
1.894
0.113
1.892
0.115
1.881
0.120
1.877
0.126
129.230
1.908
0.136
1.908
0.132
1.894
0.143
1.892
0.152
133.088
1.925
0.152
1.923
0.163
1.907
0.164
1.903
0.176
136.946
1.938
0.193
1.932
0.192
1.914
0.201
1.914
0.205
140.805
1.942
0.219
1.936
0.224
1.919
0.222
1.928
0.237
144.663
1.966
0.237
1.961
0.231
1.937
0.251
1.929
0.298
148.521
1.972
0.329
1.977
0.323
1.934
0.330
1.910
0.351
152.379
1.937
0.388
1.942
0.403
1.900
0.380
1.867
0.410
156.237
1.888
0.433
1.877
0.455
1.845
0.431
1.808
0.425
160.095
1.826
0.458
1.803
0.467
1.779
0.429
1.753
0.425
163.953
1.767
0.443
1.746
0.432
1.735
0.396
1.712
0.386
167.811
1.725
0.413
1.713
0.398
1.710
0.365
1.696
0.346
171.669
1.709
0.354
1.703
0.342
1.710
0.310
1.713
0.291
175.527
1.737
0.297
1.738
0.281
1.754
0.265
1.764
0.270
179.385
1.807
0.272
1.811
0.270
1.817
0.283
1.817
0.301
183.243
1.867
0.344
1.858
0.350
1.842
0.358
1.834
0.370
187.101
1.863
0.432
1.859
0.405
1.840
0.385
1.828
0.401
190.959
1.839
0.455
1.849
0.445
1.844
0.419
1.827
0.431
194.817
1.830
0.478
1.844
0.468
1.843
0.456
1.827
0.462
198.675
1.829
0.500
1.846
0.504
1.849
0.482
1.835
0.492
202.533
1.831
0.537
1.844
0.549
1.850
0.547
1.835
0.557
206.391
1.832
0.578
1.840
0.593
1.842
0.588
1.826
0.603
210.249
1.834
0.633
1.840
0.647
1.845
0.647
1.828
0.661
214.108
1.836
0.705
1.845
0.722
1.845
0.740
1.823
0.772
217.966
1.827
0.820
1.834
0.856
1.813
0.894
1.762
0.942
221.824
1.756
1.01
1.739
1.08
1.656
1.13
1.543
1.17
225.682
1.485
1.27
1.405
1.34
1.316
1.25
1.226
1.12
229.540
1.141
1.13
1.067
1.05
1.057
0.937
1.051
0.846
233.398
1.004
0.813
0.990
0.769
1.019
0.719
1.033
0.672
237.256
1.020
0.649
1.014
0.630
1.039
0.601
1.053
0.567
241.114
1.046
0.571
1.041
0.549
1.061
0.529
1.071
0.510
244.972
1.063
0.509
1.063
0.489
1.074
0.485
1.080
0.463
248.830
1.077
0.464
1.080
0.454
1.076
0.445
1.091
0.417
252.688
1.085
0.431
1.083
0.429
1.080
0.399
1.098
0.394
256.546
1.086
0.400
1.083
0.390
1.088
0.365
1.098
0.363
260.404
1.091
0.363
1.087
0.360
1.094
0.336
1.095
0.340
264.262
1.092
0.346
1.087
0.337
1.095
0.312
1.095
0.298
268.120
1.087
0.315
1.084
0.306
1.095
0.280
1.101
0.274
271.978
1.087
0.279
1.084
0.273
1.100
0.248
1.102
0.249
275.836
1.092
0.250
1.090
0.240
1.108
0.219
1.106
0.214
279.694
1.099
0.218
1.099
0.208
1.119
0.191
1.119
0.184
283.552
1.112
0.190
1.113
0.181
1.133
0.170
1.134
0.163
287.411
1.126
0.168
1.127
0.163
1.145
0.153
1.146
0.148
291.269
1.138
0.153
1.139
0.147
1.155
0.138
1.156
0.133
295.127
1.147
0.138
1.147
0.132
1.163
0.122
1.164
0.116
298.985
1.153
0.122
1.154
0.116
1.170
0.107
1.173
0.100
302.843
1.158
0.104
1.159
0.0982
1.175
0.0888
1.182
0.0821
306.701
1.170
0.0732
1.172
0.0653
1.190
0.0584
1.197
0.0573
310.559
1.190
0.0562
1.195
0.0495
1.213
0.0455
1.218
0.0456
314.417
1.210
0.0423
1.216
0.0391
1.233
0.0374
1.237
0.0393
318.275
1.230
0.0348
1.235
0.0335
1.250
0.0334
1.253
0.0357
322.133
1.247
0.0311
1.251
0.0310
1.265
0.0313
1.267
0.0337
325.991
1.262
0.0293
1.265
0.0296
1.278
0.0300
1.278
0.0325
329.849
1.275
0.0284
1.277
0.0286
1.288
0.0294
1.289
0.0316
333.707
1.286
0.0276
1.287
0.0279
1.298
0.0288
1.298
0.0312
337.565
1.295
0.0272
1.296
0.0274
1.307
0.0286
1.306
0.0309
341.423
1.304
0.0270
1.305
0.0273
1.314
0.0286
1.313
0.0310
345.281
1.311
0.0268
1.312
0.0272
1.320
0.0283
1.319
0.0308
349.139
1.318
0.0267
1.318
0.0270
1.326
0.0279
1.325
0.0303
352.997
1.324
0.0264
1.324
0.0267
1.332
0.0275
1.330
0.0298
356.855
1.330
0.0259
1.329
0.0261
1.337
0.0268
1.334
0.0290
360.714
1.335
0.0254
1.334
0.0254
1.341
0.0259
1.339
0.0280
364.572
1.340
0.0247
1.339
0.0245
1.346
0.0249
1.343
0.0269
368.430
1.344
0.0237
1.343
0.0236
1.350
0.0239
1.347
0.0257
372.288
1.348
0.0229
1.348
0.0227
1.354
0.0229
1.351
0.0246
376.146
1.352
0.0219
1.351
0.0216
1.358
0.0218
1.355
0.0233
380.004
1.357
0.0204
1.356
0.0194
1.362
0.0205
1.359
0.0220
383.862
1.361
0.0198
1.360
0.0192
1.366
0.0194
1.363
0.0207
387.720
1.364
0.0185
1.364
0.0181
1.370
0.0181
1.366
0.0195
391.578
1.368
0.0172
1.368
0.0168
1.373
0.0169
1.370
0.0184
395.436
1.372
0.0159
1.372
0.0157
1.377
0.0158
1.374
0.0172
399.294
1.376
0.0147
1.376
0.0147
1.381
0.0148
1.378
0.0162
403.152
1.380
0.0137
1.379
0.0139
1.385
0.0141
1.381
0.0153
407.010
1.384
0.0130
1.383
0.0133
1.389
0.0135
1.385
0.0144
410.868
1.388
0.0124
1.387
0.0127
1.392
0.0128
1.389
0.0136
414.726
1.392
0.0120
1.390
0.0120
1.396
0.0122
1.392
0.0129
418.584
1.395
0.0116
1.394
0.0116
1.399
0.0118
1.396
0.0125
422.442
1.399
0.0113
1.397
0.0112
1.403
0.0114
1.399
0.0121
426.300
1.402
0.0110
1.401
0.0108
1.406
0.0111
1.403
0.0118
430.158
1.405
0.0108
1.404
0.0105
1.409
0.0108
1.406
0.0116
434.017
1.408
0.0104
1.407
0.0102
1.412
0.0105
1.409
0.0116
437.875
1.411
0.0101
1.410
0.0100
1.416
0.0104
1.412
0.0114
441.733
1.415
0.00989
1.414
0.00978
1.419
0.0103
1.415
0.0114
445.591
1.418
0.00962
1.417
0.00966
1.422
0.0103
1.418
0.0114
449.449
1.421
0.00961
1.420
0.00959
1.425
0.0101
1.421
0.0114
453.307
1.424
0.00952
1.423
0.00963
1.428
0.0101
1.424
0.0114
457.165
1.427
0.00952
1.426
0.00959
1.430
0.0101
1.427
0.0115
461.023
1.430
0.00957
1.429
0.00974
1.433
0.0101
1.430
0.0114
464.881
1.432
0.00965
1.432
0.00976
1.436
0.0101
1.433
0.0115
468.739
1.435
0.00943
1.434
0.00985
1.439
0.0102
1.435
0.0115
472.597
1.438
0.00932
1.437
0.00991
1.442
0.0101
1.438
0.0116
476.455
1.441
0.00914
1.440
0.00994
1.445
0.0101
1.441
0.0116
480.313
1.444
0.00922
1.443
0.0101
1.448
0.0105
1.444
0.0118
484.171
1.447
0.00943
1.445
0.0101
1.450
0.0107
1.447
0.0120
488.029
1.450
0.00975
1.448
0.0103
1.453
0.0110
1.450
0.0123
491.887
1.453
0.0101
1.451
0.0104
1.456
0.0110
1.453
0.0127
495.745
1.456
0.0105
1.454
0.0105
1.459
0.0113
1.455
0.0128
499.603
1.458
0.0107
1.457
0.0106
1.462
0.0114
1.458
0.0130
503.462
1.461
0.0110
1.460
0.0107
1.465
0.0114
1.461
0.0133
507.320
1.464
0.0111
1.463
0.0108
1.468
0.0116
1.464
0.0133
511.178
1.467
0.0110
1.466
0.0110
1.471
0.0117
1.468
0.0134
515.036
1.470
0.0109
1.469
0.0111
1.475
0.0118
1.472
0.0137
518.894
1.474
0.0110
1.473
0.0112
1.478
0.0121
1.476
0.0141
522.752
1.478
0.0111
1.477
0.0115
1.483
0.0124
1.480
0.0148
526.610
1.482
0.0115
1.481
0.0119
1.488
0.0133
1.486
0.0167
530.468
1.487
0.0125
1.487
0.0134
1.493
0.0158
1.490
0.0205
534.326
1.492
0.0155
1.491
0.0171
1.497
0.0200
1.493
0.0248
538.184
1.496
0.0199
1.494
0.0211
1.499
0.0234
1.495
0.0283
542.042
1.498
0.0234
1.497
0.0240
1.502
0.0264
1.497
0.0309
545.900
1.501
0.0258
1.500
0.0258
1.505
0.0283
1.500
0.0336
549.758
1.502
0.0320
1.501
0.0334
1.507
0.0366
1.501
0.0405
553.616
1.502
0.0337
1.500
0.0349
1.506
0.0375
1.500
0.0428
557.474
1.502
0.0347
1.501
0.0357
1.506
0.0393
1.500
0.0438
561.332
1.503
0.0355
1.502
0.0365
1.507
0.0403
1.501
0.0450
565.190
1.504
0.0361
1.503
0.0376
1.509
0.0416
1.502
0.0459
569.048
1.506
0.0373
1.505
0.0385
1.509
0.0440
1.503
0.0476
572.906
1.508
0.0376
1.506
0.0392
1.510
0.0436
1.504
0.0475
576.765
1.510
0.0386
1.508
0.0399
1.512
0.0444
1.505
0.0484
580.623
1.512
0.0395
1.510
0.0408
1.514
0.0455
1.507
0.0495
584.481
1.514
0.0403
1.512
0.0419
1.516
0.0466
1.509
0.0502
588.339
1.517
0.0410
1.515
0.0427
1.518
0.0478
1.511
0.0513
592.197
1.519
0.0425
1.517
0.0440
1.521
0.0488
1.514
0.0528
596.055
1.522
0.0437
1.520
0.0451
1.523
0.0504
1.516
0.0538
599.913
1.524
0.0449
1.523
0.0466
1.525
0.0522
1.519
0.0558
603.771
1.527
0.0461
1.525
0.0485
1.528
0.0531
1.521
0.0580
607.629
1.530
0.0470
1.528
0.0503
1.530
0.0560
1.523
0.0592
611.487
1.533
0.0495
1.530
0.0517
1.532
0.0562
1.525
0.0606
615.345
1.535
0.0504
1.533
0.0527
1.536
0.0567
1.528
0.0635
619.203
1.538
0.0522
1.536
0.0549
1.539
0.0618
1.530
0.0658
623.061
1.542
0.0534
1.539
0.0572
1.540
0.0652
1.532
0.0682
626.919
1.545
0.0554
1.542
0.0578
1.542
0.0643
1.534
0.0710
630.777
1.548
0.0571
1.545
0.0603
1.546
0.0670
1.536
0.0717
634.635
1.552
0.0592
1.548
0.0621
1.548
0.0698
1.539
0.0755
638.493
1.556
0.0607
1.552
0.0640
1.551
0.0707
1.541
0.0770
642.351
1.561
0.0633
1.556
0.0661
1.555
0.0744
1.543
0.0806
646.209
1.566
0.0667
1.561
0.0690
1.557
0.0779
1.545
0.0826
650.067
1.573
0.0682
1.566
0.0727
1.559
0.0802
1.544
0.0879
Table 6
Peak Frequencies and Measured Absorbances of the 225 and 160 cm−1 Bands as a Function of Temperaturea
Also shown is the ratio of the peak absorbances of the 225–160 cm−1 bands. Films roughly 5.3 µm thick were chosen at the various temperatures for this table.
N/A, not applicable.
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