ABSTRACT

LASER EXCITED FLUORESCENCE OF I RAMAN SPECTRA OF PERIODATE CRYSTALS,

2’
AND RAMAN SPECTRA OF CRYSTALLINE ACETYLENE AND DEUTERATED ACETYLENE

By
9}“.<

Douglas Avaatzenbuhler

Three independent projects were performed. In the first,
the laser excited (Ar+ 5145 A and HeNe 6328 A) fluorescence spectra
of iodine vapor were studied. It was found that the Ar+ 5145 A
laser excited primarily the 43-0 P (12) and 43-0 R (14) transitions
(with approximately equal intensity) with a small amount from a v"=l
state with a high rotational level (J'RIOO). The HeNe 6328 A
laser excited primarily the 6-3 P (33) transition along with a small
amount of the 11-5 R (127) transition. After these levels were laser
resonance excited, a large number of additional excited states were
generated by collisional processes before fluorescence. These appear
to account for essentially all other features of the spectra.

In the study of the Raman Spectra of periodate crystals,
sodium, potassium, rubidium, silver and ammonium periodate powder

crystals of the Scheelite (C64h) structure were studied. NaIO single

4
crystals were analyzed for symmetry assignments which were carried to
the other compounds by analogy. All samples were studied both at
room temperature and 377°K. The shifts in periodate fundamentals

were found to be dominated by an electrostatic (site) interaction

potential. Five of the six Raman active lattice modes were observed

and symmetries assigned; however it appears that translations of

both cations and anions as well as the librations of the anions are

mixed (within symmetry blocks). Splittings on the two bending NH:
ion fundamentals plus two additional lattice modes (NH+ librations)

4

+
verify that the NH4 group does not rotate freely.
The Raman spectra of crystalline CZHZ and C2D2 were
obtained to aid in the determination of the crystal structure of

the lower temperature phase. In general, the D factor group with

2h
two molecules per primitive cell on C2h (12 sites interprets all
spectral features,except v4 of C2D2 which has two additional unpredicted
components. Mixed crystal spectra were also obtained where one

isotope was matrix isolated in a host lattice of the other isotope.

The spectral splittings were interpreted in terms of site and factor
group terms, and intensity calculations were performed using the

"oriental gas" model. The intensity calculations support an angle

m
of m45° between the molecular axis and the crystallographic z axis.

LASER EXCITED FLUORESCENCE OF I RAMAN SPECTRA OF PERIODATE CRYSTALS,

2’
AND RAMAN SPECTRA OF CRYSTALLINE ACETYLENE AND DEUTERATED ACETYLENE

BX<

<
(0‘2.
Douglas A\ Hatzenbuhler

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirement
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1970

/ /
\rfl

7.291

ACKNOWLEDGMENTS

I would like to thank Professor George E. Leroi for the
time and effort he has spent contributing to my education. Also,
the interest and helpful discussions of many of the faculty at
Michigan State University is greatly appreciated.

The entire molecular Spectrosc0py group has provided a
friendly and relaxed atmosphere which has made research much more
enjoyable than it otherwise might have been.

Financial support from Michigan State University and the
Office of Naval Research is appreciated.

I would also like to thank Mrs. Naomi Hack for the

excellent translation of my handwriting into a well-typed manuscript.

ii

Chapter I

Chapter II

Chapter III

TABLE OF CONTENTS

LASER EXCITED RESONANCE FLUORESCENCE OF
MOLECULAR IODINE

Introduction
Interpretation
Experimental

Results and Discussion
Conclusions

Appendix I

Appendix II

RAMAN SPECTRA OF PERIODATE CRYSTALS
OF THE SCHEELITE STRUCTURE

Introduction
Interpretation
Experimental
Results and Discussion
Assignment of Symmetry
Powder Spectra
Interpretation of Intermolecular
Forces
Conclusions

Appendix III

RAMAN SPECTRA OF PURE AND MIXED CRYSTALS
OF ACETYLENE AND DEUTERATED ACETYLENE

Introduction
Interpretation
Experimental

Results and Discussion
Conclusions

REFERENCES

iii

35

35
35
45
48
48
54

66
78

80

86

86
87
91
92
117

118

III

IV

VI

VII

VIII

IX

XI

XII

XIII

XIV

XV

10

22

24

31

32

37

50

51

61

62

63

64

67

68

LIST OF TABLES

Title

0
12 fluroescence data (5145 A excited).
Transitions with energy coincident with either
HeNe 6328 A or Ar+ 5145A laser excitation.

Franck-Condon factors calculated by Zare.14

O 0
Observed intensities of 6328 A and 5145 A laser
excited fluorescence spectra of 12.

+

Potential constants for ground (12 ) and first
excited (3HO+) electronic states of 12.

u
Calculated energies associated with transitions
of I2 near Ar+ 5145 A laser exciting line.
Correlation diagram for crystals of the Scheelite
structure.

Predicted intensities for polarized Raman spectra
of NaIO4 single crystal.

Depolarization ratios (intensity_l[ intensity II)
for two orientations of an NaIO4 single crystal
at 81° K.

Lattice modes of periodate crystals at T = 293°K.

Raman active lattice modes of periodate crystals
near liquid N2 temperature.

Fundamental vibrations of solid periodates at
T = 293 °K.

Raman active fundamentals of periodates near
liquid N2 temperature.

+
Fundamental frequencies of the NBA group in solid

NH4I04.

Unit cell dimensions and cation electronegativities
of periodate crystals with the Scheelite structure.

iv

XVII

XVIII

XIX

XXII

XXIII

XXIV

XXV

XXVI

69

71

88

95

106

107

109

111

112

114

116

Distances of first three sets of nearest neighbors
(anions and cations) for the periodates of
Scheelite structure.

Linear least squares plots of v (A ) and v
(E8 and B8) for periodates of Scheélite structure.

Correlation diagrams for the two temperature phases
(a and B) of crystalline acetylene.

Frequencies and intensities of a—C H and d-C D
o 2 2 2 2
at 30 K.

Frequencies and intensities of higher temperature

phase of C2H2 and CZDZ'

Mixed crystal frequencies of C and C D at 50°K.

2H2 2 2

. . 62,63
Gas phase polarizability data for C2H2'
Total scattering activities observed and calculated
for C2H2 and CZDZ.

Eigenvectors and ratios of total Raman intensities
of v1 and v2 of C2H2 and C2D2.

Relative scattering activities of the components

of v4 and the librations.

Calculated and observed ratios of scattering
activities of the factor group components of

v1 and v2 C2H2.

10.

ll.

12.

11

13

15

16

l8

19

21

26

27

34

38

LIST OF FIGURES

Title

The effect of anharmonicity on the 12 fluorescence
Spectrum (schematic).

0
First Stokes fluorescence component of Ar+ 5145 A
laser excited Spectrum of 12.

Boltzmann distribution of rotational energy levels
of the ground electronic State of I2 at 300°K
and 700°K.

O
Eighteenth Stokes component of Ar+ 5145 A laser

excited fluorescence of 12.

0
First anti-Stokes component of 5145 A Ar+ laser

excited fluorescence of 12.

0

First two Stokes components of HeNe 6328 A laser
excited fluorescence of 12.
First anti—Stokes, sixth and ninth Stokes components
of the 6328 A laser excited fluorescence Spectrum
of I .

2
Boltzmann distribution of vibrational energy
levels of the ground electronic state of 12 at
300°K and 700°K.

First anti-Stokes and first two Stokes components
of Ar+ 5145 A laser excited fluorescence of 12

at 21°, 0° and -23°C.
First anti-Stokes and first two Stokes components
of Ar+ 5145 A laser excited fluorescence of 12

at 21°C with 180 microns of He gas added.

Intensity calibration of laser—Raman spectrometer.

Crystallographic unit cell for Scheelite structure.

vi

13.

14.

15.

l6.

17.
18.
19.
20.
21.

22.

23.

24.
25.A.
25.B.
26.
27.
28.

29.

30.

31.

39

47

52

53

55

56

57

58

59

6O

74

75

93

93

94

96

98

99

100

101

4

Unsilvered dewar for Raman Spectra of solid samples.

Symmetry coordinates for tetrahedral 10 group.

Raman spectrum of NaIO single crystal in
"orientation 1" at 83° .

Raman Spectrum of NaIO single crystal in
"orientation 2” at 97° .

Raman Spectrum of NaIO4 powder at 293°K and 81°K.

Raman Spectrum of K IO4 powder at 293°K and 100°K.

Raman spectrum of RbIO4 powder at 293°K and 80°K.

Raman spectrum of AgIO4 powder at 293°K and 80°K.

Raman Spectrum of NH4104 powder at 293°K and 81°K.

+
Raman spectrum of NH4 fundamentals of NH4104 powder
at 293°K and 89°K.
Plot of frequency vl(Ag) versus electronegativity/

r . . .
anion-cation

Plot of frequency vl(ag) versus Ranion-anion'

Spray—on cell for Malaker refrigerator.
Closed sample head for Malaker refrigerator.

Raman spectrum of a—CZH2 (30°K).

Raman spectrum of a—C2D2 (30°K).

Raman spectrum of v C2D2 (a phase at 30°K).

4

Raman Spectrum of 5% C H isolated in C D
o 2 2 2 2
at 50 K.

v of Raman Spectrum of 5% C H isolated in C D
o 2 2 2 2
at 50 K.

Raman spectrum of 5% and 1.5% C2D2 isolated in

C2H2.

vii

32.

33.

34.

35.

102

104

105

113

v of Raman spectrum of 5% and 1.5% C2D2

isolate

d in C2H2 at 50 K.

Raman spectrum of higher temperature (8) phase

of C2H2

at 175°K.

Raman spectrum of higher temperature (8) phase

of C2D2

Primiti

at 160°K.

ve unit cell of halogen structure (a-CZHZ)

Showing crystal axes (Y,Z) and molecular axes

(y ,2)
DU 0

. X and x0 are coincident and directed
plane of paper.

viii

LASER EXCITED RESONANCE FLUORESCENCE OF MOLECULAR IODINE

Introduction

 

The visible fluorescence spectrum of iodine vapor has been
studied for more than fifty years.1 This work has led to the accurate
evaluation of the ground electronic state (12;) vibration-rotation
constants by Rank and Rao2 and the first excited electronic state's
(3H0d+) vibration-rotation constants by Steinfeld, g£_§l,3 In
addition to these Studies, iodine has been used several times4 for
the study of energy transfer processes in gases. To perform these

studies, it was necessary to monochromatically excite the I vapor,

2
which was normally "quenched" by addition of a foreign gas. The
development of the laser provided an ideal excitation source for such
experiments.

Laser excited fluorescence has been reported for diatomic
potasium5 and sodium,6 from which the vibration-rotation constants
were determined to higher accuracy than were previously available.
Concurrent with our study, the observation and identification of

O
krypton ion (5682 A) laser excited fluorescence of I was reported,

8,9,10

2

O
as well as observation of Ar+ (5145 A) laser excitation.

0
A130, 6328 A HeNe laser excited I fluorescence was reported11

2

and identified,12 in complete agreement with our work. More recently,
0

an analysis of the 5145 A Ar+ laser excited Spectrum (and HeNe

9
6328 A again) has been presented.13 However, it appears that one of

the Ar+ laser excited transitions has been mislabeled, and the weak
"anti-Stokes" one was not observed.

This work was originally initiated to study the Raman
Spectrum of ICN (and the series of cyanogen halides). However,
irradiation of ICN with approximately 800 mwatts of 5145 A laser
radiation caused the solid ICN sample to decompose, forming gaseous
iodine as one of the decomposition products. This iodine then
absorbed the 5145 A laser radiation, undergoing the transition
from the 12; ground state to the 3H0u+ excited electronic State,

and the more intense fluorescence spectrum of the I vapor was

2
recorded instead of the Raman Spectrum of ICN. In the present Study
the first high resolution analyses of the 5145 A Ar+ and 6328 A HeNe
laser excited fluorescence Spectra of 12 were performed.
Interpretation

The expected fluorescence Spectrum from monochromatically
excited I2 would consist of almost equally Spaced doublets separated
from each other by the ground State vibrational energy level spacings.
The P-R doublet spacing (resulting from the AJail selection rule
for the fluorescence) would depend on the rotational quantum number J,
the larger the J value the greater the separation. For a given J, the
doublet's Spacing would slowly decrease at higher vibrational quantum
numbers v" as a result of the vibration-rotation interaction terms in B3.

If, as is the case for 12, there are several transitions that overlap

the excitation energy of the (nearly) monochromatic source, then

there will be a P-R doublet for each of these transitions; however,
one component of each doublet will coincide at each vibrational
level, for this will be the transition that overlapped the laser's
energy for excitation and then fluoresced giving~no overall change
in rotational quantum number J. This results from the fact that
the selection rule AJ=il applies both upon excitation and fluorescence
back to the ground state. Therefore the total AJ will be either 0
and +2 (for R excitation) or 0 and -2 (for P excitation). In either
case, the AJTotal=o transition will be allowed, and at each vibrational
level of the fluorescence Spectrum these components will again overlap
since the energy differences involved are identical.

If, however, the two excitation transitions initiated in
different vibrational levels of the ground State, when they fluoresce
back to vibrational levels separated by the same difference in v"

the AJ =0 transitions will not be precisely overlapping, but

Total
rather will be separated by the anharmonicity of the ground state.
Furthermore, as one progresses to higher and higher vibrational
components of the fluorescence spectrum, this separation of the

AJ =0 components increases, since the separation of the two

Total
transitions being excited remains the same, while at each higher
vibrational energy level the anharmonicity causes the energy difference
upon fluorescence to become smaller. Thus the AJTotal=O transitions
initiating in vibrational levels only one (or a few) quantum numbers
apart will almost completely overlap in the first few vibrationally

shifted components of the fluorescence Spectrum, but will become

completely resolved in the more highly Shifted components.

This effect can most easily be visualized by viewing
Figure l which shows two transitions (labeled a and b) being
excited by the monochromatic source. a1 and b1 then represent
the fluorescence back to the ground state with one vibrational quantum
more in energy than the initial ground state. [This will in the
future be referred to as the "lat Stokes" component.] Analogously,
the SR and bk represent the "kth Stokes" component ,or fluorescence
back to the kth vibrational level above the level from which it was
represent the

excited. And the fluorescences labeled a_ and b_

1 1
first "anti-Stokes" component of the spectrum. These definitions
of "Stokes" and "anti-Stokes" are not rigorously correct; however,
they carry the same Significance as in Raman spectroscopy and will
Simplify the remainder of the discussion. From Figure 1, one can

clearly see that the AJ =0 transitions of the first Stokes

Total
components of a and b will be nearly superimposed, while the kth
Stokes components will now be quite different in energy. Also, as

one progresses to higher and higher Stokes components, the AJ 0

Total=
fluorescence that was excited from the higher ground vibrational

level will Shift to higher energies (shorter wavelengths) relative
to the fluorescence excited from the lower ground vibrational level,

while as one goes to higher and higher anti-Stokes components,

the reverse happens.

Figure 1

The effect of anharmonicity on the I fluorescence spectrum.

2

(schematic)

Figure l

fluorescence
31

 

 

 

excitations

‘ b 3-1 °-1 ak bk

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The final factor to consider in the interpretation of
the 12 spectra is the intensity of the various vibrational components
of the fluorescence series. The intensities of the fluorescence from
a particular vibrational level of the excited molecule to the various
vibrational levels of the ground state are given by the Franck—Condon
factors. These are just the overlap integrals of the vibrational
wave functions for the respective ground and excited State vibrational
energy levels. The Franck-Condon factors of interest for this analysis
were calculated by the method developed by Zare14 and supplied to us
15

by Prof. J. I. Steinfeld.

Experimental

 

Reagent grade iodine (from Matheson, Coleman, and Bell)
was used without further purification. The sample cell used was a
small glass tube with flat (90°) windows and a Side-arm U-tube that
contained the solid iodine. The U-tube could be placed in an
appropriate Slush bath for temperature control. Initially the sample
cell was fitted with a stopcock so that the cell could be evacuated
(through a liquid N2 trap) and then Simply shut off. However, when
the background pressure became of more importance, the cell was
pumped down as before (only now to a background pressure of NS x 10-6
mm Hg) and sealed off under these conditions. Precise quantities of
foreign gas could be admitted prior to seal-off, if desired.

16
The instrument used was a laser-Raman spectrometer

consisting of: either a Spectra-Physics Model 125 HeNe laser (providing

m100 mwatts 6328 A radiation) or a Spectra-Physics Model 140 Ar+
laser excitation source (providing, at optimum moments, nearly 1 watt
of either 5145 A or 4880 A radiation); Spex 1400 double monochromator;
ITT FW-l30 "Startracker" selected grade S-20 photomultiplier tube;
Victoreen VTE-l D.C. amplifier; and Hewlett—Packard Moseley 7100 B
strip chart recorder. In the final experiments, the Spectra-Physics
Ar+ laser was replaced by a Coherent Radiation Model 52 Ar+ laser
with essentially the same power output. The laser beam was focused
into the sample by a lens (focal-length 10 cm) and then reflected
by a concave mirror placed below the cell, thus approximately
doubling the effective laser power. The fluorescence was collected
at 90° from the laser's incident direction and focused on the
monochromator entrance Slit.
Results and Discussion

Table I lists the wavelength (in vacuum) of the central

0 0
maximum (AJ =0) of each vibrational level of the 5145 A (m5146.77 A

Total
in vacuum) Ar+ laser excited fluorescence Spectrum that was obtained.
Also listed are the total Shifts in energy (Avcm-l) from the exciting
line and the separation of adjacent central maxima A(Avcm—1), along
with the change in vibrational quantum number Av" and a literature
value for A(Avcm-l).17 From this table it is clear that our instrumen—
tation and hence our data aHBIKI of high enough accuracy to improve

the quality of the already available constants for 12. However,

for the purpose of assigning the observed resonance fluorescence,

enough accuracy was obtained to determine the most probable vibronic

transitions occurring in our Spectra.

 

 

Table I
12 fluorescence data (5145 A excited)
A(vac) Xa Av(cm—l) A(Av)(cm_l) Av" LitA(Av)b(cm-l)
5204.08 213.99 213.99 1 213.31
5262.55 428.52 214.53 2 212.05
5321.25 637.10 208.58 3 210.80
5381.26 846.66 209.56 4 209.66
5442.60 1056.08 209.42 5 208.50
5504.26 1261.92 205.84 6 207.20
5567.30 1467.63 205.71 7 205.80
5631.53 1672.49 204.86 8 204.55
5696.76 1875.93 203.44 9 203.18
5763.14 2078.02 202.09 10 201.93
5830.20 2277.59 199.57 11 200.68
5898.75 2478.12 200.53 12 199.30
5968.30 2674.49 196.37 13 198.05
6039.60 2872.29 197.80 14 196.73
6111.60 3067.34 195.05 15 195.36
6184.75 3260.87 193.53 16 194.06
6259.50 3453.95 193.08 17 192.73

 

a. R.m.s. error on 38 readings for first 3 vibrational levels is
O _ O
:o.3o A + :1.1 cm 1 at 5145 A.

b. Reference 17.

The possible transitions with energy approximately the
same as either the 5145 A Ar+ or 6328 A HeNe laser lines are listed
in Table II. This table is excerpted from Steinfeld, gt al.'s
paper.18 (It Should be noted that more recent work19 indicates
an error in assignment of the 57-2 band as the 49—1 band. Therefore,
the new, more accurate constants reported in ref. 18 are not an
improvement over those of ref. 3. The earlier constants were used
in our calculations.) The J" values for the 45—0 and 50-1 transitions,
in Table II were increased by one from those reported by Steinfeld,
g£_§1, This was determined by a computer fit of the vibration-

rotation constantsz’3

for the transitions of interest. See Appendix I
for details of these calculations and the results.

Figure 2 shows the highest resolution we could obtain for

 

laser fluorescence
H i ' > v" + l)

the "first Stokes" component (i.e. v
-——— excit.

O
of the 5145 A Ar+ laser excited Spectrum. The central peak (labeled

a) corresponds to the rotationally unshifted (AJ =0) component of

Total
each transition initiating in the v"=0 ground state. The two other
largest peaks (labeled b and c) correspond to the rotationally Shifted
components of the transitions 43-0 P(12) and 43—0 R(l4) reSpectively.
The peak labeled d could correspond to the rotationally shifted
component of the 45-0 P(65) series. However, since it is comparable
in Size to the other small peaks further from the central peak which
have been ascribed to a collisional process changing the energy level

of the excited State of the molecule prior to fluorescence (see next

paragraph),peak d is probably primarily one of these peaks. This has

10

Table II

0
Transitions with energy coincidence with either HeNe 6328 A or

+ o , a
Ar 5145 A laser exc1tation.

 

v v J" A(in air) associated
with transition

 

Near 6328.16 A (HeNe) 6 3 P(33) 6328.19 A
6 3 R(39) 6328.13
9 4 P(1l9) 6328.11
Near 5145.36 A (Ar+) 43 0 P(12) 5145.379 A
43 0 R(l4) 5145.384
45 0 P(65) 5145.35
49 1 R(l8) 5145.43
50 l P(40) 5145.39

 

a. From reference 18, corrected as noted in text.

11

Figure 2
0
First Stokes fluorescence component of Ar+ 5145 A laser excited

spectrum of 12.

 

 

 

0ro R

0‘09

12

been confirmed by a later experiment [see Figure 9] which shows
the I2 fluorescence observed at-23°C where the vapor pressure is
so low that the collisional background is much less intense.
Positions labeled e and f correspond to the expected positions of
the 50-1 P(40) doublet (e being separated from a by the anharmonicity
of the ground state potential well).

An alternate explanation for some of the side peaks
involves collisions while I is in the excited state.4 Analogous to

2

ortho and para hydrogen, an individual I molecule possesses only

2

’all even or all odd J valued rotational levels. Also, the molecules
in the prOper ground state for 5145 A resonance excitation are very
"poor" in rotational energy as can be seen from Figure 3. The
requisite rotational quantum number J"=12 or 14, and the most probable
J" value at room temperature is >50. (Since 3' < B", Jmax will be

) The actual temperature of the I that is fluorescing is

H
>Jmax' 2

probably considerably higher than room temperature, since Holzer et al.9
found that bromine under similar experimental conditions absorbed so
much energy from the laser beam that the temperature appeared to be
approximately 700°K. This would change the rotational pOpulation to
a distribution more like the dotted line of Figure 3, where Jmax is
even higher.

Under these conditions, the most probable result of a

collision yielding a minimal change in energy of an excited molecule

will be to increase the rotational quantum number by two.4 Thus,

13

Figure 3
Boltzmann distribution of rotational energy levels of the ground

electronic state of 12 at 300°K and 700°K.

Figure 3

'01 o: pazxtemaou

sararsuaau; antistau

 

20'0

l4

assuming this series of events: v"J" i3§§§+ v'J' 22999398§ v'
(J'+2) fluorescence v" (J'+1) and v" (J'+3), we obtain the

 

transitions labeled g, h and i in Figure 2 by using v"J" as 0" 12"
and 0" 14" respectively.

Confirmation of this assignment can be made by observing
Figure 4, which shows the eighteenth Stokes component. At this
point in the fluorescence series, the difference in separation between
the 0 - lst vibrational quantum levels and the 18 - l9 ones (see
Figure 1) will be >20 cm-l, so that both components of a doublet
initiating in v”=l would be Shifted to more than 20 cm.1 higher in
energy than the fluorescence excited from v"=0. We see that the small
peaks are Still in the same relative position to the larger ones of
the series as they were in the first Stokes Spectrum (Figure 2);
therefore they must all have initiated from the same (v"=0) level.
There are no other nearby transitions initiating from the v"=0 level
which coincide with the laser's energy, with appropriate doublet
separation, so we conclude that a collision of the molecule while
it was in the excited State must have occurred.

One can also separate the excitations starting in the
v">0 level from those Starting in the v"=0 level by looking at
the first anti-Stokes band(v"+*+v"-l), which has no analogous
component in the series Starting in v"=0. Figure 5 Shows a scan of
this region of the 5145 A laser excited fluorescence spectrum, which
consists of a widely spaced doublet. The wide Splitting of this
doublet implies a high rotational quantum number (J”>%100), and to

fit this with the laser's energy requires a transition to such

15

Figure 4
O
Eighteenth Stokes component of Ar+ 5145 A laser excited

fluorescence of 12.

16

Figure 5
0
First anti-Stokes component of 5145 A Ar+ laser excited fluroescence

of 12.

 

 

 

 

 

 

17

a high vibrational level in the excited state that the experimental
constants determined for low v' cannot be applied to determine

the precise transition that occurred. This can be seen from the
limits placed on the constants in ref. 18. The two transitions
Starting in v"=l and the 45-0 transition listed in Table II, are not
observed in our fluorescence Spectra.

The HeNe 6328 A laser excited Spectrum consists predominantly
of one transition, which, based upon its fit in energy, the rotational
Splitting of the doublets, and the order of magnitude of the corres-
ponding Franck-Condon factors must be the 6-3 P(33) transition of
Table II. Figure 6 shows the first two components of this series.

At approximately 6447 A and 6456 A there are sudden increases in
the non-resonance (collisionally shifted) fluorescence background.
These are ascribed to collisions involving excited 12 molecules
that result in a loss of a vibrational quantum of energy before
fluorescence. The first discontinuity arises from v'=6-%~+v'=5.
The second, less intense of these results from a much weaker fluor-
escence series, which is barely observable in the second Stokes
component (near 6500 A) in this region of the resonance spectrum.
This weaker transition is clearly visible in Figure 7, which shows
the lst anti-Stokes, and 6th and 9th Stokes components of the
fluorescence. This transition, although not listed in Table II, is
best assigned as 11-5 R(127) as reported by Hanes and Dahlstrom.12
A total of 5 anti-Stokes components were observed for this transition

thus confirming that the excitation initiated in at least the 5th

18

Figure 6

0

First two Stokes components of HeNe 6328 A laser excited

fluorescence of 12.

19

Figure 7
First anti-Stokes, sixth and ninth Stokes components of

0
the 6328 A laser excited fluorescence Spectrum of 12.

20

vibrational level of the ground state. Again it appears highly

likely that the I is heated by the laser radiation. As can be

2
seen in Figure 8, the population of the higher vibrational levels
is significantly greater at higher temperatures. Unfortunately
the potential constants for the excited state are not well enough
known to calculate a vibrational temperature from the observed
relative intensities of the v"=3 and v"=5 fluorescence series.
The relevant Franck-Condon factors for the fluorescence
transitions observed in this work are listed in Table 11174’15
It should be noted that there is a significantly greater change in
the magnitude of the individual v" Franck-Condon factors for v'=6
fluorescence (6328 A excitation) than for the v'm43 range (5145 A
excitation). This larger, order of magnitude difference in the
overlap integrals is reproduced in the observed intensities (Table IV);
however even in this region the agreement is not excellent. All
experimental intensities have been corrected for instrumental
sensitivity (see Appendix II). In the higher (v'm43) region,
the calculated Franck-Condon factors are rather independent of v"
(see Table III), showing only a small parity dependence and no order
of magnitude change over a large number of ground vibrational energy
levels. Since even in the lower (6328 A excited) region, the Franck-
Condon factors are not accurate enough to predict more than the order

of magnitude of the intensities, it appears that the Franck-Condon

factors are too insensitive to predict the relative intensities of

21

Figure 8
Boltzmann distribution of vibrational energy levels of the ground

electronic state of 12 at 300°K and 700°K.

 

 

9 BJHSIJ

22

mHNoo. mwmoo. Ammoo. enmoo. HHmoo. NNNOO. NNHoo. nmmmo. ma
cmooo. mmooo. mHooo. Hmooo. wNHoo. nmmoo. cameo. mumooo. ma
omNoo. mmNoo. memoo. mmmoo. mmmoo.. meoo. Hoaoo. mHmNoo. NH
mmooo. qwooo. omooo. quoo. moaoo.r womoo. ommoo. mmmmo. 0H
mmmoo. mamoo. Nomoo. naqoo. womoo. omNoo. quoo. mono. ma
mmooo. wqooo. maooo. wmooo. Hoaoo. moaoo. momoo. mwoao. «a
mamoo. wmmoo. wmmoo. mqqoo. Hoqoo. «mmoo. oqmoo. mooooo. ma
ooooo. Hmooo. moooo. oqooo. noaoo. omaoo. womoo. moomo. NH
ammoo. mmmoo. quoo. onqoo. mmqoo. Nomoo. ammoo. omomo. HH
wmooo. maooo. Hoooo. moooo. mNHoo. wHNoo. wNmoo. HNHNO. OH
mmmoo. mmqoo. Hoqoo. omqoo. quoo. Humoo. «mNoo. cooaoo. m
moooo. mooooo. moooo. Noaoo. Omaoo. mmmoo. Romeo. mwcmoo. w
nmmoo. wmqoo. mmqoo. mmqoo. moqoo. mmmoo. mwmoo. Hmnmo. N
000000. moooo. Hmooo. «maoo. ANNoo. namoo. mmqoo. mmmmo. o
quoo. Hoqoo. quoo. mmqoo. mumoo. onoo. comes. quqo. m
mNooo. Hmooc. owooc. oqmoo. ammoo. Haeoo. cameo. mmqmo. q
Noqoo. ommoo. moqoo. nwmoo. Romeo. womoo. wNmoo. mwmoo. qmmoo. «mace. qumoo. m
Nomoo. mmmoo. wwmoo. wmmoo. waqoo. nwmoo. muqoo. ommoo. nwooo. mmwoo. commoo. N
mNmoo. cameo. qamoo. mwmoo. comoo. qmqoo. comoo. momoo. quoo. HNHoo. oqmooo. H
wwwoo. anco. quao. oHHHo. mmHHo. owoao. mmoao. mmnao. wmwao. mNmHo. «Noooo. o

 

 

 

om mq wq mq we mq «q mq Ne

ma.pammcfimum .H .h .woum an voaaaasm .vonuma qam.mumN ma umumasoamo muouomm covaoonxoamum

HHH waan

23

mNNoo.
mmooo.
MNNoo.
omooo.
HNNoo.
mmooo.

mmNoo.
nqooo.
mmNoo.
Hmooo.
HaNoo.
mmooo.

memoo.
Haooo.
oqmoo.
«Hooo.
quoo.
Naooo.

cameo.
moaoo.
Hemoo.
mwooo.
Hemoo.
ooooo.

OHNoo.
NHNoo.
HmNoo.
qwaoo.
«wNoo.
qmaoo.

Noaoo.
nqmoo.
oqaoo.
oomoo.
owaoo.
NNNoo.

oNooo.
moqoo.
mqooo.
omqoo.
qmooo.
Noqoo.

Hmmao. mN
omnmo. «N
NHmNo. MN
NHNNoo. NN
mommoo. HN
mmomo. ON

 

A.uaoov HHH «Hams

24

Table IV

' o 0
Observed intensities of 6328 A and 5145 A laser excited fluorescence

spectra of 12.

 

 

 

1'; 5145 X Intensity}! 6328 X Intensityb

O coincident with laser unobserved (<0.000)
1 .00305 unobserved (<0.000)
2 .00564 .00251

3 .00351 coincident with laser
4 .00337 .02455

5 .00300 .04115

6 .00154 .05074

7 .00259 .04516

8 .000967 .00550

9 .00293

10 .000846

11 .00217

12 .000792

13 .00178

14 .000604

15 .00143

16 .000565

17 .00134

18 .000435

19 .000891

20 .000426

21 .000536

22 .000344

23 .000350

24 .000421

25 .000273

 

l Franck-Condon factor of Table III.
4 Franck-Condon factor of Table III.

a. Normalized tO‘V"

b. Normalized to v"

25

the transitions excited by the 5145 A radiation. Thus our
measured intensities (Table IV) probably give the relative Franck-
Condon factors more accurately than those in Table III, which are
calculated values.

Additional interesting information that can be obtained
from our spectra concerns quenching. To quantitatively study the
energy transfer peaks, better resolution than we are able to get of
each multiplet is needed. However, an approximate estimate of
collisional transfer probabilities can be obtained by studying the
12 fluorescence as a function of temperature. Figure 9 shows the
one anti-Stokes and first two Stokes components of the 5145 A
excited spectrum run at three different temperatures (21°C, 0°C
and -23°C). The vapor pressure of 12 at 20°C is 198.8 microns
and at 0°C is 29.81 microns, while at -23°C extrapolation of Gerry
and Gillespie's20 data shows it to be not more than a few microns.
The instrumental gain was varied for the different temperatures, but
for one temperature the intensities were recorded at the same
sensitivity. Figure 10 shows the quenching effect of 180 microns of
He added to the cell with 12 at room temperature. A definite
increase in the intensities of post-collision fluorescence is observed.
This aspect of our study was not pursued further, since it was felt
to lie outside the immediate research interests of our group. However,
these last spectra (Figures 9 and 10) along with a number of others
have been supplied to Prof. J. I. Steinfeld for further investigation

and analysis which will, hopefully, provide a better understanding

of iodine quenching.

26

Figure 9
0
First anti-Stokes and first two Stokes components of Ar+ 5145 A

laser excited fluorescence of 12 at 21°, 0° and —23°C.

Guam .

 

Same—«n . 8

 

iiiéj_,,_xz§
‘5‘

‘

 

 

 

‘I’ '0'}

Dean 1,

I -s Sill/NJ!!!

N. «H

 

27

Figure 10
First anti-Stokes and first two Stokes components of Ar+ 5145 A
laser excited fluorescence of 12 at 21°C with 180 microns of
He gas added.

V ‘1

.\\l./\)I\Ja\\. -
(.

 

A0: 323:. 02¢

oo_w

owun.

28

Conclusions

 

We find almost all of the Ar+ (5145 A) laser resonance-
excited fluorescence of 12 to be due to the 43+0 excitation. Of
this W472 is in the P(12) line auiN63z in the R(l4) transition.

The remaining small contribution (<W3Z total fluorescence intensity),
is due to an unidentified excitation from a J">%100, v"=1 level.

Each of these excited states then gives rise to a whole series of
other excited states by means of collisions before the molecule
fluoresces. The other transitions of Table II which appear to match
the laser's frequency were not excited with any observable intensity.
The HeNe 6328 A laser line resonance-excited primarily (>W9OZ) the
6-3 P(33) transition, with the remainder being the 11-5 R(127)
transition. The other calculated fits were not observed. The Ar+
5017 A laser line appeared to excite some transitions to even higher
vibrational levels (v') than the 5145 A line; however, this resonance
excitation was not pursued since the published constants for the excited
electronic state are not accurate enough to predict which specific
transition was being excited.

The Franck-Condon factors calculated by late14 appear to work
well in the HeNe 6328 A case, where the intensities vary by more than
an order of magnitude over just a few vibrational levels. However,
they do not appear accurate enough at levels as high as v'=43 to
predict the intensities of the fluorescence components. This is due
in part to the small changes in the values of the Franck-Condom factors

over a rather extended number of vibrational levels and also to the

inaccuracies in the parameters used to obtain the Franck-Condon factors.

Appendices I and II

29

APPENDIX I

Calculation of the Transition Energies of I2

Following the respective conventions of references 2

(" state) and 3 (' state), one can write

II II _ Ill II "l2 II "l3
G (v ) - wg(v + 2)+xewe(v + 2) +yewe(v + 2)
II II_1_4 N "l5
+ zewe(v + 2) +tewe(v + 2)
I I _ I I l _ I I 1:2 I I _1_3 I I l4
G (v ) - we(v + 2) wexe(v + 2) +weye(v + 2) +weze(v + 2)

F"(J"-1) = [132mg (v"+ -%-)+‘yg(v"+ %)2+62(v"+ %)3
+¢2(V"+ %)4]Jll (JII_1)

+[ng+sg(v"+ %) 1 (3")2 (J"2-l)

F' (J') = [Bé-aé(v'+ -%-)+y;(v'+ %-)2+6;(v'+ -:—)3]J' (J'+1)

' I | l q 2 ' 2
-[De+se<v + 2)](J > (J +1)

where G"(v") is the vibrational energy of the ground(122) electronic
state; v" the ground vibrational quantum number; 6' (v') the vibrational
energy of the first excited (3H0u+) electronic state; v' the excited
state's vibrational quantum number; F"(J"-l) the rotational energy

of the molecule in the ground electronic state and in the J"el

rotational level [note that F"(J"-l) is also a function of v"]; and

30

F'(J') the rotational energy of the molecule in the excited electronic
state in the J' rotational level [also a function of v']. The two
electronic potential minima are separated in energy by the value Te.

The potential constants are then given in Table V. The
energy difference for a transition between the two electronic states
is then given by

E = Te + G'(V') _ G"(v") + F!(Jl) _ F"(J").

The selection rule AJ=il applies, so J'=J"il.

A computer fit was performed for transitions near those
listed for 5145 A excitation in Table II, using these equations and
the constants given in Table V. The results are listed in Table VI.
No additional fit was obtained to accurately assign the one anti-Stokes
transition observed; however, this requires extending the potential
constants for the excited electronic state beyond their accuracy limits,

and it appears they were not applicable in this region.

31

Table V

Potential constants for ground (12;) and first excited (3H0u+)

electronic states of 12. (all units are cmfl)

 

Te - 15770.59b

 

Constant Ground (") Statea Excited (') Stateb
we 214.51886 125.273

xcn -0.60738 0.7016

e e ' -3 -3
yéwe -l.307x10 -S.67x10
zewe -5 .04xlO-6 +3. 2x10'5
tewe -l . 6x10.-7

B 0.037389 0.028969

e _4 —4
ae -l.210x10 1.562x10
ye 1.90::10'8 -4.0x10’7
ae 8.57x10-11 -3.5x10’8
¢e -1.86x10'10

0 -4.54x10'9 3.51.10"9

e -11 -10
Be -1.20x10 3.9x10

 

a. Reference 2.

b. Reference 3.

32

Table VI

Calculated energies associated with transitions of I
O
Ar+ 5145 A laser exciting line.

near
2

 

Laser Line Energy = 19429.66 cm.-1 (mlcmfll wide)

 

 

 

 

 

v"=0 - v'=43 P transitions v"=0 - v'=43 R transitions
J" AE J" AE
10 19430.35 12 19430.40
11 19429.92 13 19429.96
12 19429.44 14 19429.49
13 19428.93 15 19428.98
14 19428.38 16 19428.44
v"=0 - v'=45 P transitions v"=1 - v'=50 P transitions
J" AE J" AB

37 19434.40
63 19434.74 38 19432.78
64 19432.27 39 19431.13
65 19429.76 40 19429.43
66 19427.21 41 19427.70
v"=1 - v'=49 R transitions
J" AB
16 , 19431.20
17 19430.54
18 19429.84
19 19429.10
20 19428.32

21 19427.50

33

APPENDIX II

Intensity Calibration

 

The procedure for intensity calibration of the monochromator

follows directly from the article by Stair, et al.21 The only

 

difference in our calibration lamp's circuit from that of Figure 3
of ref. 21 is that a 0.60 ohm resistor was used in place of the
ammeter so that one simply has to measure the voltage drop across
the resistor to determine the current (0.60 volts/amp). A General
Electric (GE) Model 6.6A/T4/CL ZOO-watt quartz-iodine lamp was used
as recommended in ref. 21. Operating the lamp at 6.50 amps provided
a filament color temperature measured to be 3060°K as expected.
The temperature was measured using an optical pyrometer loaned to us
by Dr. Eick's research group.

Figure 11 gives the intensity calibration obtained between
4800 A and 8000 A. This is a plot of sensitivity factor :3.

wavelength (A). The sensitivity factor is defined so that:

sensitivity factor X measured intensity = true relative intensity.

34

Figure 11

Intensity calibration of laser-Raman spectrometer.

3 was»:

I an

Jonas; Aatatnysuss

RAMAN SPECTRA OF PERIODATE CRYSTALS OF THE SCHEELITE STRUCTURE

Introduction

 

In the study of vibrational Spectrosc0py of crystals,
the two principal goals are to determine crystal structures (where
they are difficult to determine from diffraction experiments) from
group theoretical analyses of the vibrational degrees of freedom,
and to determine the nature of the intermolecular forces that
dominate in the crystal. With the aid of single crystals unambiguous
assignment of the symmetry of each vibrational motion observed can
be made. By studying a series of similar compounds, one can hope
to correlate the differences in the observed spectra with the differences
in the forces in the corresponding crystals.

In this project, sodium, potassium, rubidium, silver and
ammonium periodate powders were studied at room temperatures and

cooled to approximately liquid N temperatures. Also, several single

2

crystals of NaIO were studied. From the data obtained we assign

4
the spectra, interpret the dominant intermolecular forces in these

crystals, and also provide information to aid in the interpretation
of the temperature dependence of their nuclear quadrupole resonance

spectra.

Interpretation

 

The group theoretical treatment of the vibrational motions

22,23

in crystals has been thoroughly developed. This is the so-called

35

36

"factor group" analysis, which first considers the isolated molecular
(or ionic) point group in order to assign symmetries to the internal
vibrational degrees of freedom and also to define the symmetries of
the translations (Tx’Ty and T2) and rotations (Rx’Ry and R2) of the
molecule as a whole. Then the point symmetry of the crystallographic
site on which the molecule (or ion) is located is used to determine
to which irreducible representations of this site group the symmetry
coordinates of the molecule (molecular point group) belong. One can
thus see if any molecular degeneracy is lifted at the site. (The
site is usually of lower symmetry than the molecule.) Finally, these
symmetry coordinates of the site are coupled to the other equivalent
symmetry coordinates of the remaining sites of the primitive unit
cell to form the symmetry coordinates of the factor group (unit cell
group). From this we are able to predict the number of components
of each of the internal vibrational fundamentals as well as the number
of external (translational and librational) motions that will be active
in both infrared and Raman spectroscopy. A more detailed explanation
of the factor group analysis is included in Appendix III.

The appropriate factor group analysis for the periodates
of the Scheelite structure is shown in Table VII. The crystallographic
unit cell for the Scheelite structure is shown in Figure 12. Symmetry
coordinate representations of the internal degrees of freedom of
the tetrahedral 10; group are given in Figure 13.24 Scheelite has
the C6 (I41/a) Space group with two molecules per primitive unit cell,

4h

with both cations and anions on SA sites.25 We then expect the Raman

spectrum to consist of: 1(Ag) component of 01,

2(Ag and Bg) components

37

Table VII

Correlation diagram for crystals of the Scheelite structure.

 

 

 

 

 

 

 

 

Molecular Site Factor Group Activity
(anion) group A Symmetry Symmetry
19. 31 3411
2 2 2
+
V1 A1 A \ Ag x y ,z
. B inactive
u
V2 E B\Bg X2-y2,xy
A z (1 acoustic)
u
T
(Rx’Ry’Rz)anion

 

E E (XZ,YZ)
\ 8
EU

(x,y) (l acoustic)

“3’V4’ 2

(Tx’Ty’Tz)anion

(Tx’Ty’lz)cationa

 

a Although the cations are not of symmetry Td (except for NHZ), they
are on identical symmetry sites (S4) and therefore their translational

degrees of freedom behave identically to those of the anion.

38

Figure 12

Crystallographic unit cell for Scheelite structure.

 

 

39

Figure 13

Symmetry coordinates for tetrahedral I0; group. F2 = T2-

 

 

 

40

3 and v4, and two librational

(Ag and E8) and four translational (2 B8 and 2 E8) lattice modes.

of 02, 2(Bg and E8) components each of v

The infrared spectrum would consist of: 1 (Au) component of v2,

2(Au and Eu) components each of v and v4, and one librational (Eu)

3
and two translational (Au and En) lattice modes.

The frequencies of the various components of the internal
degrees of freedom of the 10; group will differ through the series of
periodate crystals studied in this work because of the different
interionic distances and forces. For example, V1(Ag) of the 10; ion
is found to vary in frequency from a low of 753 cm“1 in AgIO4 to a
high of 797 cm.-1 in RbIO4. If one can determine the general form
of the interaction which dominates (if indeed one does dominate),
then there should be a correlation between the frequency of the respective
fundamentals and the relative magnitude of the interacting force for
the different crystals.

Two basic models have been proposed for the interaction

26,27 26

forces in crystals of the Scheelite structure. J. F. Scott

treated Ca++, Sr++ and Ba++W0:, which had been subject to earlier

28’29’30 and predicted the Spectrum of

spectroscopic investigation,
ZnWO4 by using a van der Waals' interaction force between nearest
neighbor anions. This model is an extension of the multipole inter-
action model developed by Decius31 from the work of Mandel and Mazur72’33
For the Raman spectrum, Scott26 suggests that the dominant interaction

term in the potential function between adjacent anions is the van der

Waals' term which varies as R-6

. . . If one assumes that this
anion-anion

41

perturbing potential affects the internal force constants of the
34
isolated periodate anion in the manner fcrystal— fisolated anion
+ f'(V(R)) where f' is the perturbation of the force constant due
to the potential V(R), and then assumes f'(V(R)) = k-V(R) + ...,

$33,, the leading term in the perturbing force constant is proportional

to the perturbing potential, we find that a plot of the square of the

internal vibrational frequency vs. R
-—- anion-anion

would be expected to
give a straight line. A similar plot (however, of frequency instead
of frequency squared) for the tungstates was performed by Scott

in ref. 26. It should be noted that if we separate the crystalline

35’36 the site effect

intermolecular interactions into two categories:
due to electrostatic interactions in the crystal and factor group
coupling due to resonance interactions of adjacent identical molecular
(or ionic) groups in the crystal, Scott's model is based on the
assumption that the perturbing potential causing the shift in internal
frequency for the anion in the different crystals is due primarily to
the change in the factor group coupling (Davydov Splitting) strength
between the various crystals in the series.

An alternative model for predicting the shift in fundamental
frequency based on the change in magnitude of the site interaction in
the series of crystals has been used by Ulbricht and Kriegsmann27
for analysis of the perrhenates of the Scheelite structure. In this
model, the perturbation potential is assumed to be ionic and thus

depend on r An additional parameter is necessary to

anion—cation'

Specify the degree of ionic character of the crystal, which will vary

42

from cation to cation. A measure of the amount of ionic character
can be obtained from the difference in electronegativity between the
anion and cation. Unfortunately, the electronegativity of the 10;
is not known. If it were, one could take the difference in electro-
negativity between the cation and anion, square it to get a value
proportional to the positive—negative ionic charge interaction, and

divide by r to obtain the relative perturbing potential

anion-cation
functions. Since the electronegativity of the ReOZ ion was also not
known, Ulbricht and Kriegsman simply used the electronegativity of

the cation as a measure of the ionic character of the crystal..

Also, instead of assuming the force constant f to be dependent upon

the perturbing potential according to the functional form f'(V(r)) =

k V(r) as Scott had done, they plotted the frequency versus the first
derivative (force) of the potential. It has also been suggested by

L. C. Kravitz37 that the second derivative of the potential should be
proportional to the shift in frequency of the fundamental. This is

in analogy to calculating the harmonic force constant for a potential
function. We are uncertain which of these plots (frequency Xi

zeroth, first or second derivative of the potential function) should
give a linear relationship even if the assumed potential function is

the correct one, and literature can be cited to support each.26’27’34’37
We would also suggest that one should plot the square of the frequency
g§_some form of the potential function, since a perturbation on the

force constant perturbs the square of the frequency; however, none

of the above references does this. The limited data points that

43

we have obtained and the crudeness of both models make it impossible
for us to determine experimentally which is correct. All types of
plots mentioned above will be discussed in the Results and Discussion
section, and it is clear that there exists enough difference between
the two potential function forms to distinguish which type of potential
dominates.

The external lattice vibrations are rather hard to classify
beyond symmetry, Since there are three degrees of freedom forming Eg
symmetry modes [(Rx’Ry) of anion, (Tx’Ty) of anion and cation] and two
of B8 symmetry (T2 of anion and cation). Only the Ag (R2 of anion)
mode is of a unique symmetry. As a result, the normal coordinates of
E8 and B8 symmetry can be an arbitrary mixture of the different degrees

of freedom of the same symmetry. In addition, the lowest-lying

v4,
fundamental of the 10; group is so close in frequency to the external
lattice frequencies that the normally-assumed separation of internal
from external vibrations is likely also not to be valid.29’30’38’39
However, a knowledge of which particular frequency might best represent
the libration of the 10; group about the x and y axes (Rx’Ry) would be
of particular interest for interpreting the temperature dependence
of the NQR spectra of the periodate crystals.

If we can make some approximate assignment of the lattice
modes, it would have to be by comparison of the frequency dependence
in the series of crystals. If the vibrational mode is translational

in origin and the translations of the cations and anions are independent

of each other, the frequency of one E8 and one Bg motion should vary in

44

proportion to the inverse square root of the mass of the cation,

and Similarly one E8 and one Bg mode Should be independent of the
cation mass. At the other extreme, the Born-Von Karman model, if

the cation and anion translations are totally coupled, there should
be two E8 and two Bg modes whose frequencies vary as the reduced mass
of the two ions. A mass dependence between these two could result
from any partial mixture of the proper symmetry motions of the anions
and cations. The dependence of the frequency on the dimensions of

the unit cell [3333, E8 proportional to a2 (the x and y dimension),
and B8 proportional to c (the z dimension)] is not as straightforward,
since the cause of the change in unit cell size will be the change in
cation which will be accompanied by a corresponding change in cationic
radius. Therefore, the full effect of the change in the unit cell
size will not be felt by the periodate group.

The librational motions of the periodate groups, if
unmixed with the translational modes, should be relatively independent
of the cationic mass, but depend on the cation electronegativity
(i333, covalent character). The Rz (A8) motion is symmetrically unique,
and it has been suggested that the other librational motion (Eg)
be the E8 mode lying closest to the Ag mode,40 since in cubic symmetry
they would become degenerate.

Considerable work has been done on the study of

rotational degrees of freedom of the NH: group in crystals, and

45

+
the phase transitions associated with the NRA motions.4l’42’43’44

It has been concludedz‘l’42 that rotational motion occurs in the

warmer phases of the ammonium halide crystals; however, the exact
nature of this motion is not completely understood.43 For this
reason we were interested in observing the fundamentals of the NH:
group in NH4IO4. If both site and factor group couplings are

+

observed for the NH4 fundamentals then it must not rotate, since

+
the NH4 must maintain one configuration long enough so that the
environment does not average out during the molecular vibration.
Furthermore the adjacent NH:

tion with respect to each other for factor group coupling to occur.

ions must remain in one specific orienta-

However, in our case, (Td ion on S4 Site in 04h factor group) all
the fundamentals that are expected to give more than one component
(v2, v3 and v4) are already split by the site. Therefore restricted
rotational motion (as long as it is not free rotation that would
average the site effect out entirely) can still occur even with
observation of Splitting of the NH+ fundamentals.

4
Experimental

 

Sodium, potassium, silver and ammonium periodate
powders were obtained by Mr. Richard A. Johnson from Prof. M. T.

Rogers and used without further purification. RbIO4 was synthesized

by Mr. Johnson from rubidium hydroxide and periodic acid, and the

final product provided a white powder with sharp Raman spectra

(completely analogous IO4

fundamentals) and no unpredicted peaks.

46

The Single crystals of NaIO4 were grown by Mr. Johnson
by recrystallization from saturated aqueous solution by the procedure
recommended by Kirkpatrick and Dickinson.45

The Raman Spectrometer used was that described in the
previous chapter (see 12 Fluorescence Experimental). Powdered
samples were placed in bent capillary tubes which were mounted in an
unsilvered dewar cell, as depicted in Figure 14. Nitrogen gas was
passed through coils immersed in a liquid nitrogen reservoir and
blown into the sample dewar for cooling. The flow rate of the N2 gas,
which could be accurately controlled, determined the temperature,
which was measured by a Copper-Constantan thermocouple placed in a
water-filled tube adjacent to the sample capillary. The single
crystals of NaIO4 were mounted on a goniometer in a glove box for
room temperature spectra and attached by means of some clay to the
end of a glass rod and placed in the dewar used for powder samples
(Figure 14) for low temperature spectra.

Attempts were made to first determine the unique axis of
the single crystals by means of optical polarization data (polarizing
microscope) and it was found that the unique axis did not lie
perpendicular to any of the crystal faces. Interfacial angles were
then measured (using an optical microscope) and attempts were made to
determine the unique axis from these; however, grinding and poliShing
the crystal to form a surface perpendicular to its c-axis resulted in

loss of polarization of the Raman spectra and no significant increase

in extinction under the polarizing microscope. As a result, the best

47

Figure 14

Unsilvered dewar for Raman spectra of solid samples.

a. Inlet for cold N2 from dewar.

b. Insulated with 1/2" foam rubber tubing.
c. Fitted cork steppers.

d. Window for laser exciting light.

e. Evacuated glass jacket.

f.' Window for Raman scattered light.

g. Bent capillary sample holder.

h. Thermocouple.

i. H20

j. Glass tube

k. N2 outlet.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/

 

 

 

 

 

 

 

 

 

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

48

depolarization ratios (ratio of intensity of Raman scattering with
polarization perpendicular to incident beam over intensity of Raman
scattering with polarization parallel to incident beam) were obtained
on two approximately perpendicular orientations of a crystal with
uncut, unpolished surfaces. It might be noted that these NaIO4
crystals were "home-grown" and as a result not as perfect and pure

as professionally grown and oriented single crystals might be.
Although the observed depolarization ratios are not numerically
exactly in agreement with group theoretical predictions, enough
accuracy was obtained to enable assignment of the symmetries of all

the observed peaks in the NaIO spectra. Assignment was carried to

4
the other crystals by analogy.

Results and Discussion

 

 

Assigpment of Symmetry

The frequencies of the internal I04 vibrations in aqueous

solution are known to be:46

_ -1
01(A1)— 793 cm

v2(E) = 272 cm-1

854 cm‘1

v3(T2)
v4(T2) = 310 cm-1

From these frequencies and the correlation diagram for

the Scheelite structure (Table VII), it is clear that with V1(Ag)
and the two components of v3 (B3 and E8) identified, the symmetries
of the components of all the other vibrations in the crystal can be

identified by comparison with the depolarization ratios of these

three frequencies.

49

For C4h symmetry, the following polarizability derivative

matrices govern the Raman active intensities:47

 

 

C4h Symmetry Polarizability derivatives
= O, 0 =
Ag OLxx o‘yy,é zz’aik O
B a = -a a ;a =0
8 xx W" X)! 12
E a..=a =O;a =0
8 11 xy yz xz

From these values, we see that the following spectra would be
predicted: (See Table VIII). All other configurations simply
reproduce these values.

With two approximately perpendicular orientations of a
single crystal of NaIO4 we were able to obtain (at=80°K) the depolar-
ization ratios listed in Table IX. Figures 15 and 16 show the Raman
spectra of the NaIO4 single crystal in orientations l and 2 respectively.
The small peak at =100 cm-l seen in Figure 15 in the "unanalyzed"
portion of the spectrum on the low frequency shoulder of the second
Eg lattice mode is a grating ghost.

Even with essentially perfect crystals, problems of internal
reflection, birefringence, convergence and refraction limit the
Iquality of polarization measurements so that the measured depolarization
:ratios are useful primarily to qualitatively assign symmetries.

Thus, since we were able to accomplish the assignment of symmetries
Imith.our spectra, little could have been gained by the use of more
perfect crystals. From our data (Table IX) it appears clear that

orientation 1 was principally some mixture of orientations l and 3

50

 

 

 

 

w Nx
m a x o N N x m
mm o x o N N x m
w NN
< o x a N N x m
mm o x o N N x N
mm axd x xxd m h x N
w< o x xxs A m x N
w Nu
m a N o x x N H
m xx
m o N a x x N H
w xx
< o N a x x N H

1H1 __mmmm mem

ON poucmHuo coHumNHNmHom wson wcHuouco
muuoaamm qumcmucH NonHms< muHmsmuaH uonHms< ucovHosH uanH mGOHumuGMHuo

 

 

.Hmumxuu mech 1NOHNz mo muuomam amsmm meHNNHoa now mmHuHmamuaH wouonmum
HHH> oHan

51

Table IX
Depolarization Ratios (intensityl/intensityll) for two orientations

of an NaIO4 single crystal at 81°K.

 

 

 

 

 

 

Assignment Frequency (cm-l) Orientation l Orientation 2

Lattice Bg 97.7 1.04 1.92

Eg 111.2 3.33 1.00

E8 153.1 4.17 1.43

Ag 169.4 0.27 0.28

E8 1 218.3 4.55 1.03

v2 A 292.0 0.35 0.26
8

Bg 301.5 0.35 1.47

v E 358.6 3.70 1.15
4 8

B8 377.0 1.27 2.13

v1 A 783.9 0.22 0.30
8

v3 E 832.3 5.00 1.01
8

B 848.2 0.30 1.92

 

52

Figure 15

Raman spectrum of NaIO single crystal in "orientation 1" at 83°K.

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

53

Figure 16

Raman Spectrum of NaIO4 single crystal in "orientation 2" at 97°K.

54

of the predicted intensities (Table VIII), while orientation 2
of Table IX is primarily orientation 2 of Table VIII.

Powder Spectra

 

+ + + -
The Raman spectra of Na+, K , Rb , Ag and NHZIO4 at

room temperature and approximately liquid nitrogen temperature are
shown in Figures 17, 18, 19, 20 and 21 respectively, with the NH:
fundamentals of NH4IO4 shown separately in Figure 22. Table X lists
the Raman frequencies observed in this work, along with the infrared
frequencies of reference 39 for the lattice region of the periodates
at room temperature. Table XI lists the Raman lattice frequencies

of the periodate crystals at approximately liquid nitrogen temperature.
At most, five of the six predicted lattice modes were observed with
certainty, with one Bg translational mode missing from all the spectra.
Tables XII and XIII list the corresponding fundamental frequencies

of the I02 group at room and liquid nitrogen temperatures. The NaIO4
(Figure 17) and RbIO4 (Figure 19) Spectra Show no additional features
than Tables X to XIII, except that RbIO4 was later run under higher

gain to Show the highest frequency lattice mode. The KIO Spectrum

4
(Figure 18) shows in addition to the data in Tables X to XIII, two
weak, relatively broad peaks at N737 cm.1 and 753 cm-1, slightly lower

in frequency (and less intense) than the 018 component of v These

1.
might be assigned as combination bands of the infrared region of v4
(398 + 338 or 314 cm_1, or 2 x 398 cm-l);36 however, this would require

rather large phonon dispersion curves. They are more likely impurity

peaks, since the most probable impurity, 10’, has Raman bands

Figure 17

Raman spectrum of NaIO4 powder at 293° and 81°K.

56

Figure 18

Raman Spectrum of KIO powder at 293° and 100°K.

4

57

Figure 19

Raman Spectrum of RbIO4 powder at 293° and 80°K.

 

 

 

 

58

Figure 20

Raman Spectrum of AgIO4 powder at 293° and 80°K.

Peaks labelled G

F

grating ghosts

laser fluorescence lines

 

 

:IIU.

8.. _ _ . .
-JwayfillllJfilll
11..” 1
1111.1 ... .
1.1
11’: .1: M
1 .1. 1
11 1. 1:
.11 111 11.1
1..” 1.. :
1 1w 11
1. 11 .1
.... 1 . 1
1 1
1
11
_ . _ . . .

.c“
-.
r

1
... _’

1.. 2a
:1. a...

016

 

.~~‘
..-.....—.._.__-~-‘_~_

----. - ..._ .. 1

‘f". --

59

Figure 21

Raman spectrum of NH powder at 293° and 81°K.

4104

60

Figure 22

+ O 0
Raman Spectrum of NH fundamentals of NH powder at 293 and 90 K.

4 4I04

61

Table X

Lattice modes of periodate crystals at T =0293°K (cm-l)

 

 

Symmetry Na+ K+ Rb+ Ag+ NH:
88 95.5 69.6 54.0 65.1 63.6
Hg 107.4 87.6 68.7 ——-— 82.7
Aua 126. 98. --- --- 88.
Hg 147.3 116.4 84.6 --— 129.0
Agb 162.8 132.8 113.9 159.1(2) 201.8
Eua 162 140. 76. 86. 190.
Eg 210.7 ---- l48.9(?)--- ---

 

 

 

 

 

 

3. Infrared active (u subscripted) modes from ref. 39.
b. Incorrectly assigned as E8 in ref. 39.

(?) Implies symmetry assignment by analogy from NaIO is speculative.

4

62

Table XI

Raman active lattice modes of periodate crystals near liquid N2

temperature (in cm-l).

 

 

 

 

 

 

 

 

T(°K)81° 97° 80° 80° 81°

Symmetry Na+ K+ Rb+ Ag+ NH:

88 97.7 72.2 ‘ 55.5 68.6 64.8

E 111.2 93.2 73.9 71.3(2) 89.5

3 113.7(2)

E8 153.1 122.0 90.0 118.2 140.6(2)
A 169.4 145.4 128.3 164.8 148.6(2)
8 195.3(?)
B 218.3 178.8 153.2(2) 217.9 216.2(?)
8 240.7(2)

 

(?) Implies symmetry assignment by analogy from NaIO is speculative.

4

63

Table XII

Fundamental vibrations of solid periodates at T =~293°K (cm—l)a

 

 

 

Fundamental Symmetry Na+ K+ Rb+ Ag+ NH:
v1 Ag 784.2 795.6 797.0 753.1 796.5
v 018(Raman) 768.2 779.3 779.1 739.1 779.6
v1 B b 791 796 793 795 792
u
v2 Ag 290.2 278.0 273.8 288.7C 277.3e
02 B8 300.4 292.7 286.7 290.5
v2 Au 264 264 268 250 262
v3 Eg 831.7 844.1 845.7 800.5 842.2
v3 Bg 847.3 856.9 853.3 814.3 851.7
v3 Eu 850 881 848C 848 845
v3 Au 831 870 863 862
v3 018(Raman) 826.5
04 E8 356.6 336.6 326.9 342.4 290.5(2)e
v4 Bg 374.1 346.4 336.4 357.9 337.3
04 Eu 368 398 398 394 39
v4 Au 322 338 370 346 372
314 306 308 316
3. Infrared active modes from ref. 39.
b. Bu is inactive, but leu is still seen weakly in I.R. (ref. 39).
Second component expected in this region apparently not resolved.
d. Apparently one Eu lattice mode also mixes with v4. The assignments
were not distinguished in ref. 39.
e. Resolved only at low temperatures.

Raman active fundamentals of

temperature (in cm-l).

64

Table XIII

solid periodates near liquid nitrogen

 

 

T(°K)

Fundamental Symmetry

81° 97° 80° 80° 81°

Na K Rb Ag NH

 

v1 Ag
18
v1 0
v2 Ag
v2 B8
03 Eg
v3 Bg
v3 018
v4 Eg
v4 Bg

 

783.9 797.5 798.3 754.0 796.3
768.4 780.2 780.0 739.8 777.9
292.0 278.0 274.2 259.7

289.98
301.5 295.1 287.8 285.7

832.3 845.9 847.1 801.7 841.7
848.2 858.3 858.1 817.4 849.0

829.4 783.7

358.6 337.7 328.0 342.9 298.0

377.0 349.3 338.4 360.1 339.1

 

 

 

 

 

a. Second component of v2 apparently not resolved.

b. These two bands are not resolved at room temperature and are

assigned only by relative position.

65

in aqueous solution48 at 780, 793 and 826 cm—1. Two similar small

peaks were observed in the AgIO Spectra (Figure 20) and are again

4

best assigned as impurity bands. Also, in the AgIO spectrum the

4

second Raman-active component of v was not resolved, even at low

2
temperatures, and it is possible that the sixth lattice mode (Bg)

may have been observed as a shoulder on the E8 (118.2 cmfl) band, but
this peak is more probably a grating ghost. The lower quality of

the AgIO4 Spectra results from the fact that the powder sample was
yellow, and even the Kr+ 5682 A laser line burned the sample, so

the spectra were recorded using the weaker HeNe 6328 A laser line.

The NH4104 Spectra are not expected to be completely

analogous to the Spectra of the other periodates, since the ammonium
ion would be expected to have librational degrees of freedom (an E8
and an Ag mode being Raman active), and there are in addition the same

internal vibrational degrees of freedom for the NH: ion as in the 102

+
ion. Since the NH is also on an S site, the group theoretical

4 4

predictions for the NH: vibrations are completely equivalent to the

4.

Shows two additional high frequency peaks. However, since the

correlation diagram (Table VII) for IO The lattice region (at 81°K)

assignment can no longer be made in analogy with the N3104 single

crystal data, we cannot assign the symmetries in this region of the

NH4IO4 Spectra. Also, the bending (v2 and v4) region of the 104 of

NH4I04 shows only three components at room temperature, although upon

cooling the expected fourth component becomes resolved.

II 1.1! I llllllll
ll
‘
.Ilulllll

 

66

+

The NH4 fundamental regions are shown in Figure 22 with

the peak frequencies listed in Table XIV. Also observable on this

spectrum (Figure 22) is a weak, broad peak at W1709 cm_1 which is

either 2v3 of IO4 or an impurity, and a small structureless peak at
W2833 cm"1 that shows multiplet structure at 91°K, which is assigned
as an impurity. The other sharp features (on the sides of the high

gain scan of v and v at 293°K and one on either side of the 91°K

1 3

scan of v and 03) are laser fluorescence lines that were not filtered

1

in order to obtain maximum intensity.

Interpretation of Intermolecular Forces

 

With this data we will attempt to interpret the shifts
in frequency of the internal modes of the I02 ion in the various
crystals in terms of the intermolecular potentials described earlier,
and to assign the external lattice modes to principally one symmetry
coordinate whenever possible.

25’45 and cation electronegativities49

The lattice constants
for the periodates of interest are listed in Table XV. As noted
earlier, there are various methods of interpreting the intermolecular
forces in the Scheelite crystals. Because of the large number of
possible graphs that could be drawn to test the various models, only
least squares fits to the majority of the plots will be included,
with only the graphs of plots Specifically discussed included.

Table XVI lists the apprOpriate values for the distances

of the first three nearest neighbor anions and cations for each of

the periodates. From Figure 12 it can be determined that the first

67

Table XIV

Fundamental frequencies of the NH: group in solid NH4IO4 (cm-1).

 

 

 

 

 

Literature frequencya Raman active 293°K 91°K
factor group Frequency Frequency
components

3033 V A A 3170.6 3146.5

1 l g
1685 02 E Ag 1679.8 1649.0
B 1656.6
8
3134 v T E 3236.5 3206.9
3 2 g
B
8
1397 v T E 1429.4 1433.8
4 2 g
B 1449.9
8

 

a. From reference 24.

68

Table XV

. . . a . . . . b .
Unit cell dimen81ons and cation electronegat1v1t1es of periodate

crystals with the Scheelite structure.

 

 

 

 

 

 

Compound aO(A) cO(A) Cation Electronegativity
NaIO4 5.32 ' 11.93 1.01
KIO4 5.75 12.63 0.91
RbIO4 5.921 13.052 0.89
AgIOa 5.374 12.094 1.42
NH4IO4 5.938 12.790 --—-

 

a. References 38 and 42.

b. Reference 43.

69

Table XVI

Distances of first three sets of nearest neighbors (anions and cations)

O

for the periodates of Scheelite structure (in A).

 

 

 

 

 

 

 

 

 

 

Crystal nearest neighbor M+IOZ(4)a 2nd nearest (4) 3rd nearest (2)
NaIO4 3.76 4.99 5.96
KIO4 4.07 5.31 6.32
RbIO4 4.19 5.48 6.53
AgIO4 3.80 5.05 6.05
NH4IO4 4.20 5.41 6.40
Crystal nearest neighbor IOZIOZ(4) 2nd nearest (4) 3rd nearest (4)
NaIO4 4.00 5.32 7.52
K104 4.27 5.75 8.13
RbIO4 4.41 5.92 8.37
AgIO4 4.04 5.37 7.60
NH4IO4 4.36 5.94 8.40

 

a. Number in parentheses indicates the number

equivalent neighbors at this distance.

of symmetrically

70

three nearest neighbor anion-cation distances are —§-a, (%—a2 +
1 2 1/2 1 . . . .
-§ c ) and i-c respectively, and that the first three anion-cation

2 1/2

, a, and /2'a respectively. From

distances are [(é—a)2 + (%C) 1

Table XVI it is clear that the assumption that nearest neighbor

interaction is the only one of significance (in either model) is a

4

group is not known, the next nearest neighbor (another anion) cannot

poor approximation. However, since the electronegativity of the 10

be included in the ionic (Ulbricht and Kriegsmann) model,27 while
in Scott's model26 it would appear to be incorrect to include the
anions at a distance of a A, while at the same time ignoring a
cation at —%—a A away. Thus the calculations were performed using

only nearest neighbor distances.

50,51 for

Table XVII lists the linear least squares fits
v1 (Ag) and the two Raman—active components of v3 (B8 and Eg) for the
plots of frequency and frequency squared versus the zeroth, first
and second derivatives of the two potential functions. The two
potential function forms used were V(r) a E- for the ionic model,
where e is the cationic electronegativity and r the cation-anion
nearest neighbor distance from Table XVI, and V(R) a 16 for the
van der Waals' model where R is the anion—anion neare:t neighbor
distance from Table XVI.

It is clear from Table XVII that there is more accuracy
(nearly an order of magnitude) in the ionic model, since the uncertainty

in frequency (y variance) is much greater in the plots for the van der

Waals' (anion-anion interaction) model. That is, the dominant factor

71

Table XVII

Parameters in linear least squares fits of v

(A ) and v3 (E and B ) for
periodate crystals of the Scheelite structure. g g g

 

 

e = electronegativity (cation); r =

r . ' r .
cation-anion’ anion-anion

 

y = mx+b

X 35 _1 g 2 b y variance Vb—

vl er.2 -2.771x102 857.2 1.4

v1 er-3 —9.357x103 846.9 6

01 8:6 -3.191x105 838.7 5.3

01 _7 -2.736x105 835.5 18.0

v1 -3 -9.763x106 828.2 18.1

v1 -3.552x10 822.8 18.1

(01)2 er"l -4.295x105 7.284x105 2.025x103 853.5
(01)2 er“2 -l.451x106 7.125x105 5.374x103 844.1
(91)2 er'3 -4.948x106 6.998x10S 7.945x103 836.5
(91)2 8’6 -4.264x108 6.952x10S 2.773x104 833.8
(91)2 '7 -1.522x109 6.839x10S 2.780x104 827.0
(91)2 8‘81 -5.537x109 6.754x105 2.787x104 821.8
033g er-Z —2.849x10: 907.3 1.1

V3Eg er_3 -9.634x103 896.8 3.3

v3Eg e36 -3.289x105 888.5 5.0

v3Eg -7 -2.863x106 886.0 18.2

v3Eg _8 -1.022x106 878.4 18.2

v3Eg 2 _1 -3.718x105 872.7 5 18.3 3

(038g)2 er-z -4.688x106 8.165x105 1.563x103 903.6
(9388)2 er_3 -1.586x106 7.993x105 5.104x103 894.0
(9383)2 e36 -5.417x108 7.855x105 7.906x104 886.3
(V3Eg)2 R-7 -4.738x109 7.819x10S 2.970x10S 884.3
(V3Eg)2 R-8 -l.69lx109 7.693x105 2.977x105 877.1
(9383) R -6.153x10 7.599x10 2.985x10 871.7

Table XVII (continued)

 

-1

.604x102

.697x102

.942x103

.267x10S

.094x105

.946x106

.346x105

.452x106

.914x106

.799x108

.356x109

.937x109

72

913.1

902.9

894.8

886.9

880.9

876.4

8.280x10

8.109x10

7.975x10

7.845x10

7.744x10

7.669x10

19.

19.

19

7

l

1.

3

3

3

.1

.695x103

.079x104

318x104

.179x104

.182x104

.187x104

909.9

900.5

893.0

885.7

880.0

875.7

 

73

controlling the shift in internal stretching frequencies in the
periodate crystals is the electrostatic site interaction rather than
the factor group resonance coupling. Similar results, but with the
opposite trend in frequencies occurred for the bending (v2 and v4)
modes. It should also be noted that in all cases, the y variance
increases with the higher derivatives of the potential function (the
straight line is less accurately followed) while the intercepts (which
should give the frequency at r = m, 3,3, isolated) Show exactly the
opposite effect, approaching more and more closely the solution
frequencies with the higher order derivatives of the potential function.
However, since the gaseous (truly isolated) vibrational frequencies are
not available, the error in intercept is most likely due to solvent
effects. Also, in the ionic model, where the nearest neighbor

cations lie in the xy plane and the B8 motions involve motion along

the unique (z) axis there is noticeably less accuracy in the least
squares plots, while for the van der Waals' model, where the nearest
neighbor anions are not in the xy plane, the B8 modes are approximately
the same in accuracy (y variance approximately the same).

Figures 23 and 24 Show plots of v1 versus er—1 and v1
versus R.6 respectively. The plots of v1 are given instead of (v1)2
since the percent variance of the square of the frequency is slightly
larger than that of the first power of the frequency. It is clear
from Figures 23 and 24 that the important difference in the two models
comes from the inclusion of the electronegativity of the cation. This

. . + + . .
is not very noticeable for Na , K and Rb+ where there is JUSt a small

74

Figure 23

Plot of fre en A ’ ' .
qu cy vl( g) versus e1ectronegat1v1ty/ranion_cation

Frequency (cm-l)

800 _
0
r
- G
750
I I I I I I I I I I ' I I I I I I I I I I I
.20 . 30 .40

ElectroncgativILy/r (rclntlvc units)

75

Figure 24

Plot of frequency vl(Ag) versus Rcation-anion'

' Frequency (cm-1)

800

775 _

750 -

.13

.15

R-6 (relative units)

.20

.25

76

change in electronegativity (see Table XV); however the Ag+ ion
makes the effect much clearer. The frequencies of the A3104 modes
appear to be much too low compared to the other periodate salts
without inclusion of the significantly higher electronegativity of
silver. Thus, the most important factor in determining the Shifts
in the frequencies of an internal mode in these crystals appears to
be the strength of the ionic interaction between cations and anions.
As the ionic character increases, the stretching frequencies shift
to higher values, or conversely, as the covalency increases in the
crystals, the internal anionic stretching frequencies decrease.

The changes in the accuracy of the plots as a function of potential
derivatives (and frequency or frequency squared) are small enough

so that although the best fit results from plotting frequency versus
potential function in all cases, it would be unreasonable to exclude
the validity of the other plots on the basis of our data alone.
Considerably more eXperimental data or rather extensive theoretical
calculations would be necessary to conclude which plots are rigorously
correct.

The Raman—active lattice modes of the periodates (Table X
and XI) can only be approximately assigned to particular symmetry
coordinates within a given symmetry block. However the Similarity
in frequency shifts between the various crystals for the highest
frequency Eg lattice mode and the Ag(Rz) periodate libration leads us
to conclude that this is the E8 mode principally of librational

character. It should be noted that even the frequency of the Ag

77

librational mode (purely a motion of the periodate ion) varied
considerably through the series of crystals.

The translations of the cations and anions appear to
be mixed, but not just to the extent of being dependent on the reduced
mass of the cation-anion pair. No linear plot was obtained for the
E8 lattice modes [plotting frequency and frequency squared versus
a. l/u (u = the cation-anion reduced mass), b. ll/E , c. a2 (a = the
xy lattice constant), d. a2//E , e. eaZ/u (e = the cation eleCtro-
negativity), f. eazl/E , g. 1//E (m = the cation mass), h. az/m, i.
eazl/Efl, and thus we cannot confirm the above assignment of the
librational Eg mode as being the one of highest frequency. It is
important to note that the Silver periodate lattice modes were the
furthest from any of the linear plots, implying that again the greatest
shortcoming of our attempts at obtaining a correlation of the frequencies
in the different cyrstals is our inability to properly compensate for
the change in ionic character of the crystals.

Although this outline of the assignment for the lattice
modes is extremely qualitative, it is felt that further assignment
would be too Speculative without a detailed normal coordinate analysis
calculation, which requires many unknown force constants, and is thus
unfeasible at the present time.

The ammonium fundamentals (much weaker than the periodates
in the Raman Spectrum) were observed (at 81°K) to show Splitting on

two (v2 and 04) of the three expected to be Split on the basis of

78

+
the correlation diagram. At room temperature all of the NH4

fundamentals were much too broad to show similar splittings. Since
these splittings are predicted to occur at the site (even before
factor group coupling is considered), we can conclude from this only

+

that the NH4 does not rotate freely. In addition to this, two

additional high-frequency lattice modes (the number predicted for

+
NH4 librations), which were not observed in any of the other periodate
crystals, are most probably the NH: librations. However, these also

were not observed at room temperature.

Conclusions

 

All of the Raman-active fundamentals of the periodate
crystals of the Scheelite structure have been identified and assigned

symmetries with the exception of one component of v in AgIO

4.

We find the potential form that appears to dominate in determining

2

the frequency shifts of the internal modes is of the ionic (site
effect) form. This is in agreement with Ulbricht and Kriegsmann's
analysis of the perrhenate spectra,27 but does not agree with Scott's
analysis of the tungstates.26 However Scott did not study cations
with greatly differing electronegativities. More recently, Kravitz37

has reported that PbWO also does not follow Scott's predictions,

4

and this is expected since Pb has a considerably higher electronegativity
than the cations Scott studied.

+
In NH4104 splittings on the NH4 fundamentals and additional

lattice modes imply the NH+

4 ion does not rotate freely; however,

these observations do not exclude some type of one-dimensional rotation.

79

+ o
The very wide half—widths of the NH4 fundamentals (particularly at 298 K)
are indicative of rather extensive motion of the NH+ ion.

4

In the lattice region, all but one (Bg translational)
mode was observed and assigned symmetry. However, there was no clear
distinction between the librational and the translational motions of
the same symmetry, and the observed normal modes are apparently mixtures
of the two types of motions of the anion as well as translations of
the cation. It is also probable that the low frequency (bending)
internal modes of the periodate mix to an appreciable extent with

the external modes.

Appendix III

80

APPENDIX III

 

Construction of a Correlation Diagram.

 

Although the group theoretical basis for the factor
group analysis of crystals is accurately presented in references 22
and 23, and correlation diagrams are also listed in Molecular

Vibrations by Wilson, Decius and Cross,52 it is rather difficult to

 

draw directly from these references the insight into the factor
group analysis. This appendix in no way replaces the above references,
but rather is designed to present a simpler, more physically oriented
explanation of the factor group analysis, and then to construct the
factor group used in the analysis of the Scheelite structure.
NaIO4 is of the Scheelite structure, which has the Cih
space group with two molecules per primitive unit cell. Both the
cations and anions are on sites of 84 symmetry. These are the necessary
x—ray data for the analysis. If this information is not available (as
is often the case for molecular compounds and for hydrogen-containing
compounds) then the limited data available are used in conjunction
with all possible factor groups to generate the various possible spectral
predictions, and under favorable circumstances the crystal symmetry
may be inferred from the spectroscopic results.
After the degrees of freedom of the free molecule (or ion)
have been assigned to their reSpective symmetry classes (including
external translations Tx’ Ty, and TZ and rotations Rx’ Ry, and R2)

using the isolated molecular point group, one considers how these

are affected by the crystallographic site.

81

The site group is a point group that is a subgroup of
the crystal space group. It consists of all symmetry operations
which leave the site invariant. Thus all site group operations are
point Operations and screw axes and glide planes cannot belong to a
site group. Any point has some site group associated with it (at
least Cl), and tabulation of types and numbers of equivalent sites
are given in Halford's paper22 and the International Tables for
X—ray Crystallography.53 The effect of the site group on the molecular
vibrations is to rename the irreducible representations of the molecular
point group to correlate with irreducible representations of the site
group. In the usual case that the site is of lower symmetry than
the molecule, the site may lift degeneracies present in the molecular
point group, creating closely spaced vibrational components from one
isolated molecular vibration.

The final step in the analysis is the coupling of the
site symmetry modes in the factor group. The factor group is defined
as the crystallographic space group minus all pure translational
operations. Thus the factor group is a finite subgroup of the Space
group and has the physical significance of having the symmetry of
the primitive unit cell where one treats all translations that transform
one unit cell into another translationally equivalent unit as being
the identity operation. By using this rule, screw axes and glide
planes will just become point operations (rotations and reflections)
beamsezthe associated motion is just a translation. Thus the factor

group is isomorphous with a point group. That is, if one looks

 

82

at a three dimensional picture of a unit cell, some of the point
group operations of the factor group will ng£_be present. However,
corresponding space group operations will be present and the trans-
formation properties of the two groups will be the same, so that one
can predict the spectra from the point group isomorphous with the
factor group.

In order to see how the irreducible representations of
the site groups transform under the symmetry of the factor group one
uses the equation:

bi‘ = Z x§(R) Xian/hr

R

where bir is an integer denoting how many times the i£h_irreducible
representation of the r£h_site group appears in the K£h_irreducible
representation of the factor group p. The summation is over all
symmetry elements (R) of the site group (note: site group a subgroup
of the factor group, therefore all elements are also present in the
factor group); XX(R) and x:(R) are the correSponding traces (1,3,,
elements of the corresponding character tables) and hr is the order of
the r£h_site group. Physically, this means that coupling the identical
motions of the equivalent occupied sites in the unit cell will, in
general, create a reducible representation of the factor group which
can be decomposed by the equation above into the various irreducible
representations of the factor group. Infrared or Raman activity
is then obtained by observing which irreducible representations
of the factor group transform as vectors (IR) or tensor components

(Raman).

83

We shall now consider NaIO4 and construct the Scheelite

correlation diagram (Table VII). The 102 group is tetrahedral in
solution, and although this is not necessarily so in the crystal,

the perturbation on the T symmetry will be assumed small enough

d

that the internal modes of the anion group can be assigned symmetries

under the Td point group. The internal coordinates for a tetrahedron

are depicted in Figure 13 along with their appropriate symmetries.
One finds from any character table that the translations (Tx’ Ty and T2)

of the tetrahedron form a basis for the T1 irreducible representation

and the rotations (Rx’ Ry and R2) a basis for T Therefore we see

2.

we have one internal mode (v1) of A symmetry, one of E symmetry (V2),

1

one external mode (translational) of T symmetry, and 2 internal

1
vibrations (v3 and v4) and one external (rotational) mode of T2
symmetry. We shall now carry the v2(E) mode through in detail. The
other symmetries may be treated in analogous fashion.

First from the character tables24 for the molecular

(ionic) point group (Td) and site group 34 we find:

 

 

 

3
Td E 8C3 3C2 684(or 84) 60d
E 2 -l 2 0 0
3
S4 E 84 C2 S4
A l 1 l l
B l —l l -l
E 1 i —1 -1
l —i —l 1
(Note:
A+B 2 0 2 O )

 

84

We see that to obtain the characters of the E irreducible representation

of Td symmetry we must add one each of the A and B irreducible

representations of the S4 group. The elements of the molecular group
Td that are not in the site group S4 are ignored.

Now from the C4h character table we find the bér. As an example

A

we will calculate the bKS4's. That is, to which (K) irreducible

representations of the factor group C4h does the A irreducible

representation of the S4 site go?

AS R4 C S

4 4h 4
b -- Z x (8.) x (R.)/4
K R1 K 1 A 1 \A\dimension of S4

elements of S4

AS C S C S
4 _ 4h , 4 4h 4 .
8 8 g
c 3 C411 S

4h 4 3 4 3
+ xAg (C2) xA (C2) + xAg (84)xA (S4)]/4

= 1

AS AS AS AS AS
. . . 4 _ 4 _ 4 _ 4 _ 4 _
Similarly. bB - l and bE - bA — bB - bE - O.
u g u g u

Thus we see that v2(E) of the Td 10; ion has its two-fold degeneracy
lifted at the Site, creating one A and one B symmetry mode under

the S4 site. Furthermore, the A mode of the S4 site is coupled with
the A mode of the other molecule in the primitive unit cell to form

one mode of Ag and one of Bu symmetry in the factor group C4h'

A similar procedure for all other symmetries leads to the Table VII.

85

Tables (with occasional errors) of these correlation diagrams
are listed in references 22 and 52; however it is convenient to be
able to reconstruct fimse data for the cases of interest to insure

accuracy.

RAMAN SPECTRA OF PURE AND MIXED CRYSTALS OF ACETYLENE AND DEUTERATED

ACETYLENE

Introduction

 

The vibrational Spectrum of solid acetylene has been of

interest for a number of years.54-58 X-ray crystallographic studiessg’6O

have yielded the space group T:

unit cell on 86 sites for the higher temperature (8) phase (analogous

with four molecules per primitive

to C02). However, cooling through the phase transition (133°K

for C2H2)59 shatters Single crystals, and the resulting X-ray powder

data hawabeen able to determine only that an orthorhombic structure

is formed.56

Through previous spectroscopic studies,54-58 it has been

proposed that the lower temperature (a) phase has Space group D2h

(analogous to the halogens), with two molecules per primitive unit

cell on C2h sites (with the C

molecular axis).

2 axis of the site perpendicular to the
This study was initiated to provide a complete, temperature

dependent study of the Raman Spectra of the crystalline phases of

acetylene to confirm the crystal structure predictions and provide

data on intermolecular forces in these crystals. Both phases of

CZHZ and C2D2 were studied as a function of temperature and in the'

lower temperature phase, mixed crystals (from 1.5 to 5% of one isotope

doped into the other) were studied.

86

87

Interpretation

 

The correlation tables for the two phases of acetylene are
drawn in Table XVIII. (See Appendix III for method of construction.)
From Table XVIII, we see that for the lower temperature

4.
phase, the two 28 vibrations ( v and v2) of C H are coupled in

1 2 2

the factor group (Davydov Split) into an Ag and B3 mode; and the

8
Hg(v4) bending mode is Site split (into Ag and Bg modes) and then
each of these modes is factor group coupled giving four nondegenerate

unit cell modes (Ag’ B , B and B ). The lattice librations would

18 28 38
similarly give rise to four one-dimensional modes, while the translations

and the other internal vibrations (v and v5) are infrared and not

3
Raman active. The higher temperature (8) phase Raman spectrum would
be expected to have two components (Ag and T8) for the symmetric
stretching vibrations (v1 and v2) and three (2Tg and E8) for the “g
bend and also for the lattice librations. The lattice translations
and v3 and v5 would again be infrared and not Raman active.

Following Dow's development35 we see that the isolated

frequencies are affected by two interaction terms in the crystal:

2
l

C
II

2
- |¢p¢rl } Vpr dr

E f {IIPII
M = T E' 362 30Lb f(¢p¢r)* vPr(¢p¢;) dr

where the ¢i represent the vibrational states of the isolated molecule

(a prime (') indicates that molecule is vibrationally excited), Vpr

88

Table XVIII

Correlation diagram for the lower temperature (a) phase of

 

 

 

 

 

 

 

 

 

 

 

 

 

crystalline C2H2.
Molecular Site Factor
point group Dooh group C2h£L2 group D2h Activity
+ 2 2 2
Vl’vz £8 A8\Ag x ’y ’z
,/////////r B38 yz
B28 xz
I].
V3’Tz 2“ Bu‘§\“\\\\~\\\\\~Blu z
B2u y
v5,(Tx,Ty) Hu Au‘-~§‘~‘§‘\\‘\‘Au inactive
B3u ' x

 

Correlation diagram for the higher temperature (8) phase of crystalline

 

 

 

 

 

 

 

 

 

 

C2H2.
Molecular Site Factor Activity
point group Dooh group S6 group Th
+ 2 2 2
Vl’VZ 28 Ag Ag x ,y ,2
T8 (xy.y2.ZX)
2 2 2 2 2
V4’(RX’Ry) Hg E8 E8 (X +y Z ,X ”y )
fi+
V3(Tz) Lu . Au Au
T (x,y.2)

 

 

V5!(Tx,Ty) ”U E E

 

89

is an interaction (perturbation) potential assumed to be the Sum of
pairwise molecule interactions, the B matrix is the unitary matrix

that converts from internal (unperturbed molecular normal coordinates)
to symmetry (factor group) coordinates, and T counts the number of
equivalent sites the molecules occupy per primitive unit cell. The
summations are over all molecules (r) other than p. The D term,
analogous to a valence bond coulomb integral, is the (site) effect

of the static crystal field. The M term, analogous to a valence

bond exchange integral, results from the exchange of energy between

two molecules (p and r ) in the crystal. If the two molecules (p and r)
are translationally equivalent, M gives rise to a shift in the frequency
of the fundamental, while if p and r are translationally inequivalent
the M term will give rise to (factor group or Davydov) Splitting of

the fundamental. Thus, in the pure crystal, the isolated molecule's
frequencies are shifted by the D term (site effect) and then both
shifted and split by factor group (M term) coupling.

Isotopically substituted material which has significantly
different vibrational frequencies (as is the case for substitution of
deuterium for hydrogen) will exhibit the same total effect on the
fundamentals of the pure crystal. In addition, by taking spectra of
dilute mixtures of one of the isotopes mixed in the other, we can
separate the D and M terms. If we assume the crystal structures and

interaction potentials are the same, the D (Site) term will remain

the same regardless of whether the molecule is isolated in an isotopically

90

different crystal or if the surrounding molecules are the same isotope.
However, if the surrounding molecules are isotopically different

(to the extent that the vibrational modes are not nearly the same
frequency) the M term will not exist, since the one vibrating molecule
can no longer exchange its vibrational energy directly with a
neighboring molecule. If we also assume harmonic coupling, the splitting
due to the M term will be symmetric, therefore the shift of the isolated
peak from the center of the pure crystal peaks will give a measure

of the part of the M term that gives rise to a shift in frequency.

Thus, the shift from the gaseous frequency to the isolated crystalline
frequency gives a measure of the site (D) effect. Then the pure
crystalspectra show the magnitude of M; the splitting giving M due to
translationally inequivalent molecules, and the difference of the mean
frequency of the Split components from the isolated (mixed crystal)
frequency measures M due to translationally equivalent molecules.

The relative intensities of the vibrational modes can be
calculated by use of the "oriented gas" model based on the assumption
of no molecular interactions.61 What'needs to be done is take the
Raman absolute intensity and depolarization ratio measurements of the
gaseous molecule62 and determine from these the mean value (3') and
anisotropy (y') of the polarizability derivative matrix for each
internal vibration. It is then assumed that these quantities are not
changed upon crystallization. For the librational lattice modes, one
uses the molecular polarizability anisotropy measured by Bridge and
Buckingham63 and again assumes no change in this value and the moment

of inertia upon crystallization for the calculation of the intensities.

91

and v2)

+
For the two 2g symmetric stretching modes of C2H2(vl

there is the additional consequence of the change in composition of
the normal modes upon deuteration. The "C-H" stretching (v1) normal

. mode has much less CEC bond stretching force constant involved in it
than the corresponding "C—D" v1 stretch of C2D2. Since a unit stretch
of the CEC triple bond has associated with it a much larger polariz-
ability change than the C—H bond, this additional mixing of the two

2+ symmetry modes must be considered before comparing the relative

8

intensities of v1 to v2

this, the gas phase bond polarizabilities62 are multiplied by the

in the two different isotopic species. To do

coefficients of the eigenvectors of the normal coordinates obtained
by a conventional "normal coordinate" analysis.64 We will try to

interpret the acetylene spectra by use of these models.

 

Experimental
C2H2 was obtained from the Matheson Co. and purified by
repeated trap to trap (77°K to 193°K) vacuum distillation. The C D

2 2
(99.5%D) was obtained from the Stohler Isotope Chemical Corp. and

was used without further purification. However, the vacuum manifold
used for handling the sample was first treated with D20. The laser-
Raman spectrometer was again the same as previously described (see

the chapter on I fluorescence-Experimental section). Three sampling

2
techniques were used. For the higher temperature phase, a closed cell
cooled by cold N2 gas flow was used. The same dewar drawn in Figure 14
was fitted with a small sample tube passing through the cork stoppers

and fitted with a stopcock for connection to a vacuum line. For the

colder Spectra (77°K to 30°K) a Malaker Corp. Cryomite Mark VII—C

92

was
closed cycle helium refrigerator/fitted first with a spray-on sample

head (Figure 25A) and later (for all data shown) with a closed sample
head (Figure 25B). The closed cell design was developed so that the
sample could be slowly annealed from above the phase tranSition down
to W30°K. As soon as the spray-on style head was allowed to warm up
to N100°K the C2H2 sublimed away from the end surface of the c0pper
block back to the colder portions of the cell and away from the useful
sample area. In the smaller closed cell, a larger sample was sublimed
into the head (ml c.c.) until the sample inlet sidearm was sealed off
with the sample. In this way, the annealing process could be carried
out with only a relatively small loss of sample. The annealing
noticeably reduced linewidths so that at 30°K all fundamentals were
only ml cm.1 (the inherent laser exciting line width) wide.
Results and Discussion

The Raman spectrum of the low-temperature (a) phase of
crystalline CZHZ is shown in Figure 26 and the frequencies and relative
intensities are listed in Table XIX. The spectrum (Figure 26) consists
of three lattice bands (4 are expected on the basis of the correlation
diagram, Table XVIII), three components of 04 (4 expected), three bands
in the 02 region (two are expected; the small, low frequency band is

due to C13), and three bands in the 0 region (two expected, the weak

1

one again being C13). Figure 27 shows the corresponding C Spectrum.

2D2
There are two small grating ghosts (W49 cm.1 and 58 cm-1 respectively)

and again 3 lattice modes, 3 components of v and 3 components of v1

2

with the two factor group Split components barely resolved. The v4 band

93

Figure 25A

Spray-on cell for Malaker refrigerator.a

Figure 25B

Closed sample head for Malaker refrigerator.a

Both sample cells were contained inside a 2-inch outer vacuum
jacket.

Attached to Malaker cold head. ('

l" Kovar seal.

Spray-on nozzle.

Remainder same as design B.

Silver soldered.

1/2" Kovar seal.

1/8" Kovar seal.

1/16" thin-walled stainless steel tubing coil.

1/2” outside vacuum jacket spacer with 1/16” tubing feed-thru.

94

Figure 26

Raman spectrum of a C H2 (30°K).

2

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Table XIX
Frequencies and intensities of a-C2H2 and o—CZD2 at 30°K.
C H C D
2 2 Width at Width 2 2
Assignment Frequency 1/2 Inten- Fre- at l/2 Intensity
-1 height sity a quency height
(cm ) -1
(cm )
Lattice 83.6 2.0 43.5 71.1 3.0 43.7
87.4 1.5 56.5 74.1 2.0 56.3
174.9 5.5 8.7 152.1 6.0 15.5
01 3311.5 1.0 6.2 2671.0C 1.5 4.6
3320.6 1.0 5.8
13 '
02(C ) 1925.3 1.0 0.8 1724.6 1.0 1.9
1950.4 1.0 25.7 1733.7 1.0 35.7
1959.3 1.0 3.9 1744.6 1.0 7.7
522.7 1.0 2.3
v4 628.3 1.0 2.7 523.7 1.0 3.9
531.1 1.0 2.3
638.2 1.0 6.1 532.5 1.0 9.4
658.3 1.0 1.7 536.3 1.0 4.3
540.9 1.0 0.3

 

a. Normalized to first two intensities = 100.

. -l . .
b. Instrumental resolution = 1.0 cm (laser linew1dth).
c. Two components not resolved well enough to list

separately.

96

Figure 27

Raman spectrum of a C2D2 (30°K).

 

OJON

IIIJ

1.51

1

 

 

AYJON

 

 

 

Opu—

goon
Na0

 

 

 

 

 

 

 

 

97

of C2D2 is shown under high resolution in Figure 28. Instead of
the predicted four components of v4 (three were observed in C2H2)

there are now six components; however the highest frequency one may

be due to v4 of CZHD.54 Figure 29 shows the matrix isolated spectrum

of C2H2 in C2D2, again showing the lattice region (essentially unchanged

from pure C2D2), 92 of C2D2 showing three components as before,

v2 of CZHZ now isolated and unsplit (not factor group coupled),
v1 of C2D2 as before except now (at 50°K) the two factor group

components are less resolved, and the isolated unsplit v1 of C2H2.

Figure 30 has the v4 of C2D2 (eXpanded on t0p line) essentially

unchanged from pure C2D2 except for a small low frequency shoulder,
and the isolated v4 of C2H2 now split into an approximate doublet,
demonstrating the site effect (D term) without the factor group coupling

(M term). Figure 31 shows two different concentrations of C2D2 (5%

and 1.5%) isolated in C2H2. The lattice region is unchanged from

pure C2H2, v2 of C2D2 is now an isolated singlet, v2 of C2H2 again

shows the three components as when pure, v1 of C2D2 is an isolated

singlet and is the doublet (plus C13) as in the pure solid.

V1 C2H2

Figure 32 has v4 (at 5% and 1.5% of C2D2) for both C D and CZH

2 2 2'

v4 of C2D2 now Shows four components (the weak one at highest

frequency is again assigned as v4 of C HD) instead of the expected

2

two, and v4 of C2H2 has the three components as in the pure solid.

98

Figure 28

Raman Spectrum of v4 C2D2 (a phase at 30°K).

 

 

 

 

 

 

 

 

 

555555555

99

Figure 29

D at 50°K.

Raman spectrum of 5% C H isolated in C2 2

2 2

 

 

 

V4

100

Figure 30

of Raman spectrum of 5% C2H2

isolated in C2D

2

at 50°K.

 

101

Figure 31

Raman spectra of 5% and 1.5% C

2

D

2

isolated in C2H2'

 

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102

Figure 32

v4 of Raman spectrum of 5% and 1.5% C

O
2D2 isolated in 02H2 at 50 K.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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WW $148

103

Figure 33 Shows the higher temperature (above 133°K)

8 phase spectrum of pure C showing two lattice modes (of the three

2H2
expected), two (of the expected three) components of v4 (three including
the asymmetry of the larger lower frequency mode), three components of

v2 (the two predicted plus C13), and the two predicted components of

v1. Figure 34 shows the analogous warmer phase of pure CZD The

2.
sharp features at approximately 20, 30 and 50 cm"1 are grating ghosts

superimposed on the two broad lattice modes, and v is not Split as

1

before (it was only barely resolvable in a CZDZ)’ the v and v4 regions

2

are completely analogous to those of CZH Table XX lists the peak

2.
frequencies, widths at half height and intensities of the warmer

temperature phase of C H and C D . Table XXI lists the peak frequencies

2 2 2 2
of the mixed crystal Spectra of C2H2 and C2D2°
From Table XXI we see that v1 isolated of C2H2 lies within

experimental error (:1.0 cmfl) of the midpoint of the pure crystal

peaks (ignoring 013 of course). The gaseous frequency of v is 3373.7

1
cm-l.24 Thus at the site of the crystal (plus any temperature effect)

the frequency of v is shifted down to 3317.1 cmfl. Similarly for

l

0202 01 shifts from 2700.5 in the gas to 2671.1 cm'1 at the crystal

site. Then factor group coupling (the M term in the Interpretation

section) splits the vibration symmetrically about this site frequency

by 9.2 cm-1 in CZHZ and :1J0cm51 in C D

2 2. The symmetric splitting

would come from the (harmonic) part of M that deals with exchange of

vibrational energy with non-translationally equivalent nearest neighbors

104

Figure 33

Raman Spectrum of higher temperature (8) Phase of C2H2 at 175°K.

 

 

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105

Figure 34

Raman Spectrum of higher temperature (8) phase of C

2132

at 160°K

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Table XX
Frequencies and intensities of higher temperature phase of CZHZ
and C2D2°
02H2 (T8166 K) 02D2 (T2=168 K)
Assignment Frequency Half-widtha Intensitberequency Half- IntenE
-l (cm'l) width sity
(cm )
Lattice 30.7 ~35. 25.1 m25
66.8 c 59.7 c
v1 3327.6 N5.5 6.9 2681.0 1.5 10.
3332.8 m4.5 3.1
v2 1928.4 1.5 2.5 1732.3 1.0 15.7
1954.7 1.0 74.8 1743.2 1.0 89.0
1960.2 1.0 7.7 1750.1 1.5 48.0
v4 624.8 3.5 7.7 524.9 3.5 85.7
647.0 c 0.3 535.9 6 5.3

 

a. Instrumental resolution = 1.0 cm_1.

b. Normalized to v1 = 10.0

c. Wide

Mixed crystal frequencies of C

107

Table XXI

2 2 2 2

H and C D at 50°K.

 

 

 

 

Cznz C2D2
Assigpment Host Isolated Gasa Host Isolated Gasa
Lattice I 83.0 71.9
87.4 75.2
174.0 155.1
b
v1 3305.4
3312.8 3317.1 3373.7 2671.9 2671.7 2700.5
3322.0
02 1926.0b 1724.9b
1950.8' 1957.0 1973.8 ,1734.6 1742.2 1762.4
1959.2 1745.6
v4 628.8 523.0
645.8 611.8 524.3 521.4
638.5
653.9 531.1 530.6 505.
657.8 532.5 538.4

535.6

540.6c 547.8c

 

a. Room temperature data from ref. 24.

b. C13 isotope peak.

c. Tentatively assigned as v of C HD (see ref. 54).

4 2

108

while any asymmetry to the splitting (in this case very small)

would come from exchange of vibrational energy with translationally
equivalent (non-nearest) neighbors. The large (order of magnitude)
change in the magnitude of the factor group Splitting between C2H2
and C2D2 can be explained best by the fact that it appears for hydrogenic
modes the dominant form of the perturbing potential is a hydrogen-
hydrogen repulsion term.65 With this type of potential, the factor
group Splitting is controlled by the amplitude of the C-H vibration.
This amplitude will be smaller in the deuterated case both because of
the Significant increase in mass of the deuterium and because of

the additional mixing of CEO character into the C-D stretching normal
mode of CZDZ (see the following discussion of intensities for the
normal coordinate eigenvectors). Thus it is reasonable for the coupling
to be much smaller in the deuterated case. Unfortunately, v2 does
not follow the predictions of this model as well. The isolated v2 of
CZHZ occurs at 2.0 cm.-1 above the midpoint of the two factor group
coupled modes which are themselves only 8.4 cm"1 apart. Similarly v2
of C2D2 isolated is 2.1 cm.1 above the average of the two factor
group coupled modes which are 11.0 cm.-1 apart. This would indicate
Significantly larger contribution from the non-nearest neighbors
(frequency shifting) part of M. Since we do not know the form of

the perturbing potential that would be appropriate for this mode,

we cannot conclude whether this is reasonable or not. However, one

would expect the contributions of non-nearest neighbors (translationally

109

equivalent) to be greater for a mode such as v , Since v2 is not as likely

2
to be dominated by the repulsive part of the interaction potential.

However, it iS likely that the assumption of a center-center pertur-

bation potential is not very meaningful in this type of crystal,

and that electronic overlap between molecules is Significant, and

under these conditions the model would not be useful. The v4 splittings

cannot be Successfully interpreted for either isotOpe, since in C2H2

one of the four predicted modes is not observed, and in C2D2 both

the pure crystal and the isolated molecule shows at least one unpredicted

band. In the isolated v4 of CZHZ however, we do clearly see the two-

fold degeneracy lifted by the Site by approximately 8 cm-l.
Table XXII lists the experimental (gas phase) values for

the squares of the mean values [(87)2] and anisotropies [(Y')2] of

the polarizability derivative matrix associated with v

1
62 63
C2H2 and the magnitude of (all-El), that is the absolute value

and v2 of

of the difference between the polarizability parallel to the (linear)

molecular axis and the polarizability perpendicular to the molecular

 

 

 

 

 

 

 

 

axis.
Table XXII
‘ 62,63

Gas phase polarizability data for C2H2

- 2 cm - 2 cm °3
Band ' -——- ' -——— - A

an > (Y)(L) (6111M)
v1 0.88 2.61
v2 2.48 1.20
Lattice 0.0 1.45 1.86

Librations

110

The expression for the intensity of a Raman transition is

given by66
K' (vo -v)4 g

’ v[l-:xp(-hv/kT)] [4 5(a')2 + (Y )2 1

 

where K' is a constant, v0 the frequency of incident exciting radiation,
v the frequency of the transition, h Planck's constant, k the Boltzmann
constant, and T the temperature (°K). g is the degeneracy of the
transition, 3“ and y' are the mean value and anisotropy of the
polarizability derivative matrix, and g[4.5(§')2 + (y')2] is called
the scattering activity. This equation assumes Placzek's polariz-
ability theory is valid,66 and that we are irradiating a polycrystalline
sample with polarized light.67

With the gas phase data, and the moment of inertia of the.
molecule, one can calculate the relative and total intensities of
the various fundamental components and librational modes by calculating
the scattering activity [g[4.5(8")2 + (y')2]] of the various modes.
For the internal modes, the total scattering activity comes directly
from the above data, while for the librational modes, Cahill67 has
develOped the general expressions for the relative scattering
activities as well as their total intensities. These are calculated
by construction of unit cell symmetry coordinates and differentation
of the unit cell polarizability (assumed to be the sum of the gaseous
molecular polarizabilities contained in the unit cell) with respect
to each of the unit cell symmetry coordinates. Since this procedure

57 67

has already been written up in complete detail ’ for the crystal

structure of interest, I will include only the results.

111

The total scattering activities (calculated and observed)

are listed in Table XXIII.

Table XXIII

Total scattering activities observed and calculated for C H and C D .
cm4
Scattering activities (~E-0

 

 

 

 

Band calculated observed C H observed C D

 

 

 

 

2 2 2 2

 

2 2 2 2
v1 6.58 11.79 2.40
v2 12.36 12.36 12.36
v4 1.00 1.44
Librations 1.45 1.42 1.08

 

The change in observed total scattering activity of v1
compared to v2 (see Table XXIII) for the deuterated compound was
anticipated as a result of different amounts of mixing of the internal
coordinates that comprise these normal modes. This was borne out

by the calculated eigenvectors listed in Table XXIV; however use of
these eigenvector coefficients along with the gas phase bond polariz-

abilities62 predict a much greater change than observed (see Table

XXIV).

112

Table XXIV

Eigenvectors and ratios of total Raman intensities of v1 and v2

of C2H2 and CZDZ'

—;
_7

 

 

 

 

 

q1 = q2 = C-H internal coordinates; q3 = CEC internal coordinate
eigenvectors ratios of scattering
activities v /v
1 2
v1 v2 calculated observed
C2H2 0.7221(q1+q2) 0.1278(ql+q2) 0.61 0.95
-0.1802 q3 +0.3663 q3
C2D2 0.4869(q1+q2) 0.2299(q1+q2) 0.012 0.19

-0.3012 q3_ +0.2756 q3

 

Our errors in predicting the magnitude of this change in
relative intensity of vllv2 upon deuteration are probably due both
to the inherent assumptions of the "bond polarizability"68 concept
and to the fact that the transformation from internal
coordinates to normal coordinates is not an orthogonal one.69

In the Structure appropriate for the lower temperature (a)
phase of C2H2’ (D2h factor group analogous to the halogens), there is
an unknown parameter, 6 in Figure 35 which can vary from 0 to 90°
without changing the crystal structure. The relative scattering

activity of the various modes will depend upon the value of the angle 6.

Table XXV lists the relative scattering activity for 04 and the librations

113

Figure 35

Primitive unit cell of halogen structure (a-CZHZ) showing crystal
axes (Y,Z) and molecular axes (yo,zo). X and x0 are coincident

and directed out of plane of paper for molecule at origin.

 

 

 

—>N

 

 

 

 

114

Table XXV

Relative scattering activities of the components of v4 and the

 

 

 

 

 

librations.
Calculated relative scattering activities
(degrees) AS 5181_ B28 B3g
0 0. 1. 0. 1. r
10 .117 .970 .030 .884
20 .413 .884 .117 .589
30 .750 .750 .250 .250
35 .881 .670 .329 .116
40 .970 .587 .413 .030 '
45 1 .500 .500 0 :
50 .970 .413 .587 .030
55 .881 .329 .670 .116
60 .750 .250 .750 .250
70 .413 .117 .884 .589
80 .117 .030 .970 .884
90 0. 0. 1. 1-
Observed
Lattice C2H2 (87.4) (83.6) (174 9) (emfl)
1.00 0.74 0.31
0202 (74.1) (71.1) (152.1) (cm-1)
1.00 0.74 0.57
04 0282 (638.2) (628.3) (658.3) (cm-l)
1.00 0.43 0.29
”4 C2D2 (i523T7) (253215) (536'3) (cm-1)

1.0 0.52 0.37

 

115

as a function of 6, and also the experimentally observed values.
Table XXVI lists the ratio of scattering activities for the B38
and A8 symmetry modes of the symmetric stretching (v1 and v2)
fundamentals as a function of 6 along with the observed experimental
values.

From Table XXV we see that the experimental data appear
to best fit an angle 6 of 45°, although Ito's assignment58 of the
highest frequency lattice mode as being 2x A8 would also fit C2H2

reasonably well if 6 = 0°. However, the increase in the highest

 

frequency lattice mode intensity in C2D2 and the relative intensities

of the components of v4 lead us to conclude an angle of 45° is more
probable. This conclusion is supported by Table XXVI, where although
no angle predicts the correct ratio of observed intensities of the

factor group components of the v1 and v2 modes, they are closest to

the predictions of an angle of 45°.

We thus feel that we have at least qualitatively explained
all of the Raman Spectral features observed with the exception of
v4 of C2D2. A different crystal structure appears unlikely because
of the large amount of (infrared and Raman) spectroscopic data that
is well explained by the present structure. No impurities, other

than approximately 3% C HD were found in a mass spectroscopic analysis

2

of the sample used. The possibility of CZHD affecting the C2D2 spectra

to cause the extra peaks (by site splitting but not factor group

coupling with C2D2) also seems unlikely, since the unexplained peaks

Table XXVI

116

Calculated and observed ratios of scattering activities of the factor

group components of v and v of a-acetylene.

1 2

 

 

 

Observed
ratio 6(degrees) 0 10 20 30 40 45 C2H2 C2D2
B /A v 0 .0375 .145 .303 .428 .446 0.818 7
3g 3 1 i
B /A v 0 .0080 .029 .054 .070 .072 0.103 0.123
3g g 2

 

 

 

 

117

did not grow in relative intensity upon addition of 5% CZHZ to
the sample.

One possible, but rather unlikely explanation of the extra
components of v4 involves the naturally abundant 013 acetylene v4
modes which might "borrow" intensity (as in Fermi resonance) from v4
bands of adjacent C D molecules.

2 2

Conclusions

 

The Raman spectra of both crystalline phases of C2H2 and

C2D2 have been recorded and interpreted by the corresponding "factor

group" correlation diagrams. In the lower temperature phase, mixed

 

crystal Spectra of one isotope isolated in the other have been obtained
and intepreted in terms of the site effect without factor group coupling.

In the lower temperature phase, where the crystal Structure
55,56,58
is not certain, our data agrees well with the proposed structure

in all places except v4 of C2D2. The two unexpected additional

components of v4 of C2D2 have not yet been adequately explained.

10.

11.

12.

l3.

14.

15.

l6.

17.

18.

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