- Email: [email protected]
High-resolution measurements on the infrared absorption 3 ← 0 band of deuterium chloride
(1977)
JOUBNALOPhCOLECULARSPECTROSCOPY65,388-394
High-Resolution Measurements on the Infrared 3+0 Band of Deuterium Chloride
Absorption
P. NIAY, C. COQUANT, P. BERNAGE, AND H. BOCQUET Laborattire de Spectroscopic Mokulaire, Epuipe associee au CNRS (E.R.A. UniversitC des Sciences et Techniques de Litle, Boite Postale 36 59650 Villeneuve d’ilscp, France
303),
High-resolution measurements of the wave numbers of the 3 + 0 band lines are reported for the two isotopic species Ds6Cl and DsrCl. Molecular constants are given, which best reproduce all the available data. By comparing experimental I’ij constants to the calculated ones obtained from Hs6C1, we have deduced the TCl I’ii constants. We have also computed a new dipole moment series expansion for DCl.
Thirty-three lines of the 330 band of D3U, and 30 lines for the D3’C1 variety, were recorded with a S. I. S. A. M. spectrometer (1) having a theoretical resolving power of 0.028 cm-r. A multipath White type absorption cell, 2 m long, with an absorption path length varying from 24 to 224 m (depending on the intensities of lines) was filled at a pressure of 50 or 100 Torr, according to the linewidth (2). The lines were measured relative to atomic lines of thorium and to fringes obtained with a Fabry-Perot interferometer, in the manner described by Bernage et al. (3). In order to reduce random errors introduced by noise, each line was measured at least five times. Average values for the observed wavenumbers (in cm-l) of the lines are listed in Table I. The experimental uncertainties were estimated to be less than 0.010 cm-’ for most lines. Previous measurements (4) of the 3-O band were obtained from low-resolution spectra and a systematic discrepancy ranging from 0.25 to 0.55 cm-l appears. A set of equilibrium molecular constants was determined for each isotopic molecule by using all the available accurate measurements (5, 6) and fitting them to a least squares routine applied to the following term value expression (1) in the direct approach method (7) : T(zJ, J) = YlO(V + +> + Yzo(v + 3)” + Y30(11+ +
(J)(J
+
+ J2(J+
1)CYOl + 1)2[Yo2 +
Yll(V
+
Y12(a +
Each measurement in the infrared factor proportional to the inverse of In order to increase the accuracy Y22, Y31, Yo3 constants of DC1 from
and the of the
3) + $1 +
+>3 + YZl(V + Y22(v +
Y,o(u 3)” +
$)“I
+
$1” Y31(u +
4)“l
+J3(J+
u3p031.
(1)
microwave regions was included with a weight square of its uncertainty. the computation, we have calculated the Y~o, H35C1 data, by using high-precision ratios PN~ 388
Copyright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN OOZE2852
INFRARED
between
molecular
nuclear
ABSORPTION
OF DC1
389
reduced masses PN, and the approximate Y'ij/Yi
j =
isotopic relations :
(2)
[pN/pNI](1+2j)/2,
where the index I is connected with an isotopic variety of DCl. The procedure employed in the calculation was to correct the T(v, J) values for the terms in (e + +)“, J2(J + l)“(r + 3)?, (v + PJ(J + I), and J3(J + l)e by means of constants calculated from the isotope relations. The molecular constants of each isotopic molecule are given in Table II, together with the D35C1 ones deduced from H35C1 constants and together with D37C1 constants TABLE I,
Wavenumbers
(vacuum cm-l) of observed transitions 3+0
infrared band of DC2
in the
NIAY ET AL.
390
TABLE II, Molecular
DC@
2142.001
0.08263 x
4.6600
I12802
x10-6
I.29 -5.392
x 10-5(b) * 1O-9(b)
2.35
10-S
1.3 x
10-7 10-7
2141.99
10-k
-2.278
x lO-5(b)
-1.408
x
x 10-6
-5.44
x IO-*(b)
I x 2.5
x
10-7 10-8
x
10-3
-3.227 x to-3 5.447644
5.432769
10-S
-0.112801
7 x 10-s
10-r
1.362
x
0.08274
0.0824
I x 10-S 2.2
2144.871 -27.1632
-27.089
-3.209
5.448804
2.37
from 0: N
6 x 10-4
-0.113290 x
.alculated
lct_~~ with
10-3 10-a
* lo-x(b)
4.6680
1.8 x
3 x
0.08179
3 x 10-s
x IO-‘(b)
-2.*62x.,0-5(b) -1.396 x 10-r
5.5 x
2145.164
-3.200
for DCL
DCi’7 AYij
-27.16656
1.8 x 10-s
2.6 x
constants
Ice35
10-2
10-36)
5.432777 -0.
1.6 x
(a)
I x 10-z
-27.0967
-3.181
AYij
equilibrium
x
-0.11327
10-4
2145.155 -27.1704 0.0828
-3.228 x 10-j 3.449087 -0.11331
4.686 x 10-4
4.688 x IO-'
-2.262
x 10-s
-2.278x 10-s
-2.279 x 10-5
-1.398
x
10-r
-1.406 x lo-'
-1.406 x IO-'
x 10-6
1.367X IO-6
1.367x 10y6
4.660
I.357
x IO-‘(b)
me-
2142.060
We
-
2145.187
I.+
=
2142.028
q, - 2144.913
2145.197
8.
5.432848
8.
-
5.448849
8.
-
5.432814
Be - 5.447689
5.449132
-
,
I
a1
-
-2.36425
cc:)
a2 = 3.66281Cc)
(cl a3 * -4.70624
a* - 5.2131
(15- -5.5269 (cl
06 - 8.3664 ('I
Cc)
calculated from Da5Cl experimental data, in Dunham framework (using the pN2 values given in Table II). On account of the Yij accuracy, no really significant disagreement appears when we compare the observed D3’C1 Yij to the calculated ones. In this case, we can conclude that the measurement precision and the number of observed bands are not suflicient to show a significant breakdown of the B. 0. approximation. The situation is somewhat different when we compare the observed Da5Cl Yij to the calculated ones from H35C1, since a strong discrepancy appears between the observed YOUand Yro values and the calculated ones. The other Yii constants agree to within experimental error. If, in Dunham framework, we use the pan ratio between molecular atomic reduced masses pat instead of the nuclear reduced masses, we obtain a set of equilibrium constants in which the Y~o value is now in good agreement with the observed one. On the other hand, the disagreement between the Yol values, although substantially reduced, does remain. Bunker (8) has shown that the adiabatic and nonadiabatic corrections resulting from the breakdown of the B. 0. approximation have the same order of magnitude as the Dunham corrections, and this author has obtained (9) the following relations by
INFRARED
neglecting
terms involving
l+z i
higher powers of Be2/co,2:
15 + 14% - 9~ + 15~~ - 23&a,! + :
Yol = bleat
I l,,=~c
3Yl
ABSORPTION OF DC1
95lIlll3 25a4-------2 4wt [
67a2” 4
459al’a? +_-_ 8 + 8kr -
1
(a? + a?) + 8K1
1155 aP 64 12alkl -
32aoR,‘A.
II , (4)
where gJ is the rotational 9 factor defined in terms of nuclear magneton, m, and mp are, respectively, the electron and proton mass, B, and we are the usual spectroscopic coefficients, k1 and kz are the second and third coefficients of the potential energy correction series expansion defined by van Vleck (IO), Beat involving the atomic reduced mass. Bunker has assumed that PNgJ and A, are isotopically independent, and the effect of the breakdown on the B.O. approximation on the ai values has been estimated to be very small by Tipping and Herman (1 I). Watson has shown that pg., is isotopically dependent (12) but this effect is very small (2%) and can be neglected against the gJ determination accuracy. Accordingly, in the way described by Bunker, we have transformed the relations (3) and (4) into the simplified ones (13) ~*‘Yol = PNB~ + (~,‘PN)COI,
(5)
PNfYlO = Pi&& + (l/PN)CIO,
(6)
where ~NB~, C’OI,PN*W,, and CIO are isotopically Co1 =
independent 21(a? + al”)
15 + 14aI - 9az + 1Sar - 23ala, + 2
+ 8kl
1
0,s
MN’~
2w,?
+ w’Be
I14r g.,, m,,
95aIa3 Cl0 =
25a4 - -
2
67ai2 - ~4
1155
459 + s
a1:a2 -
- 64
aI4 + 8k, -
12a,kl - 32aoR,?A,
1 1
B,2
x P?vJ-- . [
40,
Hy plotting ~“~Yol for H3jCl, D3Q and T35Cl vs PN-‘, Bunker (13) has computed @NH
NIAY
392
ET AL.
TABLE III, equilibrium constants for TCL35
Molecular
Molecule
u;2Ylo
UN1 (u-1)
HC.e"
2959.476
Xl""
2959.906
0.525238912
TC('5
2960.049(a)
0.360224349 i
Cl0
p1'2 w e
1.02135049 -8.6669 x 10-l
2960.361
YlO = 1776.583 (2) Yzo = -18.636
(b)
yjo = 0.047
(b)
y,,,, = -0.152 x lO-2 (b) yol = 3.737206 (c) yil
=
-0.064
yzl
=
‘0.022x IO-i (b)
(b)
Y 'I = -0.089 A IO"
(b)
yoL = -0.066 Y 10-l (b) y;; = j =
0.053 Y lO-5 (b) 0.0074 Y
10-7
(b)
Bunker and the present one, we have only computed I.CN& and Cl0 by using the same method and then we have deduced the Y~ovalue for T35C1. These values are displayed in Table III, together with the other T35C1 Yij values calculated by Webb (5) in the Dunham framework. As part of our program, we have attempted to record the 4 + 0 band DC1 lines. We were unsuccessful, however, and in order to explain this, we have computed the 3X(0,4,0) “rotationless” matrix element by using the HCl dipole moment series expansion given by Tipping and Ogilvie and by calculating the matrix elements (0 1xi] 4) in the way described by these authors (15) : ,mO,4,0) =
where x = (R - R,)/R,.
go Mi(Old
4),
INFRARED
ABSORPTION
OF DC1
393
TABLE IV.
MOMENT
DIPOLE
EXPANSION
FOX
HCC
and
DC(
(all
values in ______
Debye)
DCC
HCC
The ~R(o,~,o, value was computed equal to 9.72 X lo_5 D. On account of the experi mental 31z(0,3,0) value (3.08 X 10-4 D) (16) and of the intensity of the lines in our O-3 band experiments [for instance, a 50% absorption peak with a 24 m path length for R(3)], we have calculated that a 12 m path length should be enough to obtain a 5% peak for the 04 band R(3). We cannot explain this strong discrepancy, unless the Mq value is wrong. To obtain an absorption peak inferior to 5% with a 400 m absorption path length, the :~E(o,~,o)value is to be below 1.8 X lO+ D. Consequently, we have computed a new dipole moment series expansion for DCl, by using the experimental zz (o,~,O)values (16) (a = 1, 2, and 3) together with a ~TZ(O,~,~) value chosen lower than 1.8 X 1O-5 D. The Mi values we obtained are displayed in Table IV, together with the HCl ones given by Tipping and Ogilvie. We note a disagreement between the different determinations of M, values; but the other Mi are in good agreement when taking into account experimental 37Z(o,n,oj determinations. RECEIVED :
November
8, 1976 REFERENCES
I. I’. CONNES,Thtse, Paris, 1957; J. VERGES,Thbe, Orsay, 1969. 2. P. RERNAGEAND P. NIAY, Nom Reo. Opt. 7, 159 (1976). 3. P. RERNAGE,R. HOUDART,AND P. XIAY, Spect. Acta B 26, 261 (1971); P. BERNAGE,P. NIAY, 1. Mol. Spectrosc., to appear.
394 4. 5. 6. 17. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
NIAY ET AL.
B. H. VAN HORNE AND C. D. HAUSE, J. C/rem. Phys. 25, 56 (1956). D. U. WEBB, Ph.D. Dissertation, Ohio State University, 1967. F. C. DELUCIA,P. HELYINGER,ANDW. GORDY, Phys. Rev. A 3, 1849 (1971). N. &LUND, J. Mbl. Speclrosc. 50, 424 (1974). P. R. BUNKER,J. Mol. Spectrosc. 28,422 (1968). P. R. BUNKER,J. Mol. Speclrosc. 35, 306 (1970). J. H. VAN VLECK, J. Chem. Phys. 4,327 (1936). R. H. TIPPING AND R. M. HERMAN,J. Chem. Phys. 44,3112 (1966). J. K. G. WATSON, J. Mol. Spectrosc. 45, 99 (1973). P. BERNACE AND P. NIAY, Etude comparCe des constantes de HBr et DBr, Cunad. J. Phys. to appear. P. R. BUNKER,J. Mol. Speclrosc. 39, 90 (1971). R. H. TIPPING ANDJ. F. OGILVIE,J. Mol. St7uct. 35, 1 (1976). W. S. BENEDICT,R. HERMAN, G. E. MOORE, AND S. SILVERMAN,J. Chew. Phys. 26, 1671 (1957). E. W. KAISER, J. Chem. Phys. 53, 1686 (1970). F. G. SMITH,J. Quad Spectrosc. Rad. Transfer 13, 717 (1973).
JOUBNALOPhCOLECULARSPECTROSCOPY65,388-394
High-Resolution Measurements on the Infrared 3+0 Band of Deuterium Chloride
Absorption
P. NIAY, C. COQUANT, P. BERNAGE, AND H. BOCQUET Laborattire de Spectroscopic Mokulaire, Epuipe associee au CNRS (E.R.A. UniversitC des Sciences et Techniques de Litle, Boite Postale 36 59650 Villeneuve d’ilscp, France
303),
High-resolution measurements of the wave numbers of the 3 + 0 band lines are reported for the two isotopic species Ds6Cl and DsrCl. Molecular constants are given, which best reproduce all the available data. By comparing experimental I’ij constants to the calculated ones obtained from Hs6C1, we have deduced the TCl I’ii constants. We have also computed a new dipole moment series expansion for DCl.
Thirty-three lines of the 330 band of D3U, and 30 lines for the D3’C1 variety, were recorded with a S. I. S. A. M. spectrometer (1) having a theoretical resolving power of 0.028 cm-r. A multipath White type absorption cell, 2 m long, with an absorption path length varying from 24 to 224 m (depending on the intensities of lines) was filled at a pressure of 50 or 100 Torr, according to the linewidth (2). The lines were measured relative to atomic lines of thorium and to fringes obtained with a Fabry-Perot interferometer, in the manner described by Bernage et al. (3). In order to reduce random errors introduced by noise, each line was measured at least five times. Average values for the observed wavenumbers (in cm-l) of the lines are listed in Table I. The experimental uncertainties were estimated to be less than 0.010 cm-’ for most lines. Previous measurements (4) of the 3-O band were obtained from low-resolution spectra and a systematic discrepancy ranging from 0.25 to 0.55 cm-l appears. A set of equilibrium molecular constants was determined for each isotopic molecule by using all the available accurate measurements (5, 6) and fitting them to a least squares routine applied to the following term value expression (1) in the direct approach method (7) : T(zJ, J) = YlO(V + +> + Yzo(v + 3)” + Y30(11+ +
(J)(J
+
+ J2(J+
1)CYOl + 1)2[Yo2 +
Yll(V
+
Y12(a +
Each measurement in the infrared factor proportional to the inverse of In order to increase the accuracy Y22, Y31, Yo3 constants of DC1 from
and the of the
3) + $1 +
+>3 + YZl(V + Y22(v +
Y,o(u 3)” +
$)“I
+
$1” Y31(u +
4)“l
+J3(J+
u3p031.
(1)
microwave regions was included with a weight square of its uncertainty. the computation, we have calculated the Y~o, H35C1 data, by using high-precision ratios PN~ 388
Copyright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN OOZE2852
INFRARED
between
molecular
nuclear
ABSORPTION
OF DC1
389
reduced masses PN, and the approximate Y'ij/Yi
j =
isotopic relations :
(2)
[pN/pNI](1+2j)/2,
where the index I is connected with an isotopic variety of DCl. The procedure employed in the calculation was to correct the T(v, J) values for the terms in (e + +)“, J2(J + l)“(r + 3)?, (v + PJ(J + I), and J3(J + l)e by means of constants calculated from the isotope relations. The molecular constants of each isotopic molecule are given in Table II, together with the D35C1 ones deduced from H35C1 constants and together with D37C1 constants TABLE I,
Wavenumbers
(vacuum cm-l) of observed transitions 3+0
infrared band of DC2
in the
NIAY ET AL.
390
TABLE II, Molecular
DC@
2142.001
0.08263 x
4.6600
I12802
x10-6
I.29 -5.392
x 10-5(b) * 1O-9(b)
2.35
10-S
1.3 x
10-7 10-7
2141.99
10-k
-2.278
x lO-5(b)
-1.408
x
x 10-6
-5.44
x IO-*(b)
I x 2.5
x
10-7 10-8
x
10-3
-3.227 x to-3 5.447644
5.432769
10-S
-0.112801
7 x 10-s
10-r
1.362
x
0.08274
0.0824
I x 10-S 2.2
2144.871 -27.1632
-27.089
-3.209
5.448804
2.37
from 0: N
6 x 10-4
-0.113290 x
.alculated
lct_~~ with
10-3 10-a
* lo-x(b)
4.6680
1.8 x
3 x
0.08179
3 x 10-s
x IO-‘(b)
-2.*62x.,0-5(b) -1.396 x 10-r
5.5 x
2145.164
-3.200
for DCL
DCi’7 AYij
-27.16656
1.8 x 10-s
2.6 x
constants
Ice35
10-2
10-36)
5.432777 -0.
1.6 x
(a)
I x 10-z
-27.0967
-3.181
AYij
equilibrium
x
-0.11327
10-4
2145.155 -27.1704 0.0828
-3.228 x 10-j 3.449087 -0.11331
4.686 x 10-4
4.688 x IO-'
-2.262
x 10-s
-2.278x 10-s
-2.279 x 10-5
-1.398
x
10-r
-1.406 x lo-'
-1.406 x IO-'
x 10-6
1.367X IO-6
1.367x 10y6
4.660
I.357
x IO-‘(b)
me-
2142.060
We
-
2145.187
I.+
=
2142.028
q, - 2144.913
2145.197
8.
5.432848
8.
-
5.448849
8.
-
5.432814
Be - 5.447689
5.449132
-
,
I
a1
-
-2.36425
cc:)
a2 = 3.66281Cc)
(cl a3 * -4.70624
a* - 5.2131
(15- -5.5269 (cl
06 - 8.3664 ('I
Cc)
calculated from Da5Cl experimental data, in Dunham framework (using the pN2 values given in Table II). On account of the Yij accuracy, no really significant disagreement appears when we compare the observed D3’C1 Yij to the calculated ones. In this case, we can conclude that the measurement precision and the number of observed bands are not suflicient to show a significant breakdown of the B. 0. approximation. The situation is somewhat different when we compare the observed Da5Cl Yij to the calculated ones from H35C1, since a strong discrepancy appears between the observed YOUand Yro values and the calculated ones. The other Yii constants agree to within experimental error. If, in Dunham framework, we use the pan ratio between molecular atomic reduced masses pat instead of the nuclear reduced masses, we obtain a set of equilibrium constants in which the Y~o value is now in good agreement with the observed one. On the other hand, the disagreement between the Yol values, although substantially reduced, does remain. Bunker (8) has shown that the adiabatic and nonadiabatic corrections resulting from the breakdown of the B. 0. approximation have the same order of magnitude as the Dunham corrections, and this author has obtained (9) the following relations by
INFRARED
neglecting
terms involving
l+z i
higher powers of Be2/co,2:
15 + 14% - 9~ + 15~~ - 23&a,! + :
Yol = bleat
I l,,=~c
3Yl
ABSORPTION OF DC1
95lIlll3 25a4-------2 4wt [
67a2” 4
459al’a? +_-_ 8 + 8kr -
1
(a? + a?) + 8K1
1155 aP 64 12alkl -
32aoR,‘A.
II , (4)
where gJ is the rotational 9 factor defined in terms of nuclear magneton, m, and mp are, respectively, the electron and proton mass, B, and we are the usual spectroscopic coefficients, k1 and kz are the second and third coefficients of the potential energy correction series expansion defined by van Vleck (IO), Beat involving the atomic reduced mass. Bunker has assumed that PNgJ and A, are isotopically independent, and the effect of the breakdown on the B.O. approximation on the ai values has been estimated to be very small by Tipping and Herman (1 I). Watson has shown that pg., is isotopically dependent (12) but this effect is very small (2%) and can be neglected against the gJ determination accuracy. Accordingly, in the way described by Bunker, we have transformed the relations (3) and (4) into the simplified ones (13) ~*‘Yol = PNB~ + (~,‘PN)COI,
(5)
PNfYlO = Pi&& + (l/PN)CIO,
(6)
where ~NB~, C’OI,PN*W,, and CIO are isotopically Co1 =
independent 21(a? + al”)
15 + 14aI - 9az + 1Sar - 23ala, + 2
+ 8kl
1
0,s
MN’~
2w,?
+ w’Be
I14r g.,, m,,
95aIa3 Cl0 =
25a4 - -
2
67ai2 - ~4
1155
459 + s
a1:a2 -
- 64
aI4 + 8k, -
12a,kl - 32aoR,?A,
1 1
B,2
x P?vJ-- . [
40,
Hy plotting ~“~Yol for H3jCl, D3Q and T35Cl vs PN-‘, Bunker (13) has computed @NH
NIAY
392
ET AL.
TABLE III, equilibrium constants for TCL35
Molecular
Molecule
u;2Ylo
UN1 (u-1)
HC.e"
2959.476
Xl""
2959.906
0.525238912
TC('5
2960.049(a)
0.360224349 i
Cl0
p1'2 w e
1.02135049 -8.6669 x 10-l
2960.361
YlO = 1776.583 (2) Yzo = -18.636
(b)
yjo = 0.047
(b)
y,,,, = -0.152 x lO-2 (b) yol = 3.737206 (c) yil
=
-0.064
yzl
=
‘0.022x IO-i (b)
(b)
Y 'I = -0.089 A IO"
(b)
yoL = -0.066 Y 10-l (b) y;; = j =
0.053 Y lO-5 (b) 0.0074 Y
10-7
(b)
Bunker and the present one, we have only computed I.CN& and Cl0 by using the same method and then we have deduced the Y~ovalue for T35C1. These values are displayed in Table III, together with the other T35C1 Yij values calculated by Webb (5) in the Dunham framework. As part of our program, we have attempted to record the 4 + 0 band DC1 lines. We were unsuccessful, however, and in order to explain this, we have computed the 3X(0,4,0) “rotationless” matrix element by using the HCl dipole moment series expansion given by Tipping and Ogilvie and by calculating the matrix elements (0 1xi] 4) in the way described by these authors (15) : ,mO,4,0) =
where x = (R - R,)/R,.
go Mi(Old
4),
INFRARED
ABSORPTION
OF DC1
393
TABLE IV.
MOMENT
DIPOLE
EXPANSION
FOX
HCC
and
DC(
(all
values in ______
Debye)
DCC
HCC
The ~R(o,~,o, value was computed equal to 9.72 X lo_5 D. On account of the experi mental 31z(0,3,0) value (3.08 X 10-4 D) (16) and of the intensity of the lines in our O-3 band experiments [for instance, a 50% absorption peak with a 24 m path length for R(3)], we have calculated that a 12 m path length should be enough to obtain a 5% peak for the 04 band R(3). We cannot explain this strong discrepancy, unless the Mq value is wrong. To obtain an absorption peak inferior to 5% with a 400 m absorption path length, the :~E(o,~,o)value is to be below 1.8 X lO+ D. Consequently, we have computed a new dipole moment series expansion for DCl, by using the experimental zz (o,~,O)values (16) (a = 1, 2, and 3) together with a ~TZ(O,~,~) value chosen lower than 1.8 X 1O-5 D. The Mi values we obtained are displayed in Table IV, together with the HCl ones given by Tipping and Ogilvie. We note a disagreement between the different determinations of M, values; but the other Mi are in good agreement when taking into account experimental 37Z(o,n,oj determinations. RECEIVED :
November
8, 1976 REFERENCES
I. I’. CONNES,Thtse, Paris, 1957; J. VERGES,Thbe, Orsay, 1969. 2. P. RERNAGEAND P. NIAY, Nom Reo. Opt. 7, 159 (1976). 3. P. RERNAGE,R. HOUDART,AND P. XIAY, Spect. Acta B 26, 261 (1971); P. BERNAGE,P. NIAY, 1. Mol. Spectrosc., to appear.
394 4. 5. 6. 17. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
NIAY ET AL.
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