Studies on gap modes and localized modes due to BO2-, N3-, OCN-, SCN-, and SeCN- centres in KI

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Studies on gap modes and localized modes due to BO2-, N3-, OCN-, SCN-, and SeCN- centres in KI

W. Kauschke, F. Fischer

To cite this version:

W. Kauschke, F. Fischer. Studies on gap modes and localized modes due to BO2-, N3- , OCN-, SCN-, and SeCN- centres in KI. Journal de Physique, 1985, 46 (1), pp.119-128.

�10.1051/jphys:01985004601011900�. �jpa-00209940�

119

Studies on gap modes and localized modes due ^to BO-2, N-3, ^{OCN-, SCN-,}

and SeCN- centres in KI

W. Kauschke (+) ^{and F. Fischer}

Physikalisches Institut der Universität Münster, DomagkstraBe 75, ^D-4400 Münster, F.R.G.

(Reçu ^le 6 juillet 1984, révisé le 17 août, accepté ^{le 6} septembre 1984 )

Résumé. 2014 Nous avons étudié, par diffusion Raman ^et par absorption des bandes latérales vibrationnelles dans

l’infrarouge moyen, les modes de gap ^et les modes localisés au-dessus de la bande optique, modes dûs à une série de centres triatomiques ^linéaires (BO-2, N-3, OCN-, SCN-, SeCN-) dans KI. Nous comparons ^nos résultats

avec des mesures précédentes ^de l’absorption ^dans l’infrarouge lointain. Un ensemble de trois modes de gap

(A2u ~ Eu ^~ Eg ^ou A1 ~ 2 E) ^est établi par l’expérience pour chaque ^centre

^{en accord avec la théorie des}

groupes. Pour ^cette série de centres le comportement ^en fréquence ^est discuté par ^un modèle linéaire. Ce modèle

explique ^aussi l’apparition, ^{au maximum, de} quatre modes localisés transversaux (E), ^ce que ^{nous avons} pu vérifier par l’ expérience.

La comparaison ^des spectres d’absorption des bandes latérales et des spectres ^de diffusion Raman démontre que ^ces deux phénomènes ^{obéissent aux mêmes} règles de sélection et d’intensité. Ces règles peuvent ^{être déduites} théoriquement par le théorème de Wigner-Eckart ^et interprétées physiquement.

Abstract.

We have studied gap modes and localized modes above the optical ^{band due to a series of three-}

atomic linear centres (BO-2, N-3, OCN-, SCN-, SeCN-) ^{in KI} by ^Raman scattering ^and by vibrational sideband

absorption in the middle infra-red We compare ^our results with previous investigations of far infra-red absorption.

A set of three gap modes (A2u ~ Eu ^~ Eg ^{or Au ~ 2 E)} is established for each centre by experiment 2014 according

to group theory. ^The frequency behaviour within the series of centres is discussed by ^{a linear model. This model} explains also the appearance of up ^to four transverse (E) ^localized modes which are ascertained by experiment

The comparison ^{of sideband} absorption ^{and Raman} scattering spectra shows that both phenomena obey ^the

same selection and intensity ^{rules. These rules can be deduced} theoretically by ^the Wigner-Eckart theorem and

are physically interpreted

J. Physique ⁴⁶ (1985) ^{119-128 JANVIER} 1985,

Classification Physics ^Abstracts

63.20P - 78.30

78.50

1. Introduction.

Gap modes and localized modes of molecular ^centres in KI have been the subject of several investiga-

tions [1-13]. ^{Studies on molecular centres have led}

to the conclusion that

contrary ^{to monatomic} impurities

besides translational degrees ^{of free-}

dom librational degrees ^must also be involved. For the vibrational analysis, ^{there are} essentially ^three purely optical ^methods available :

-

direct far infra-red (FIR) absorption ^{at the} frequency ^{of the} gap mode (in general, ^localized

modes cannot be detected, ^{since even at} liquid ^helium temperature (LHeT) ^the optical band and the region

above are masked by the reststrahl absorption) [14],

-

first-order Raman scattering (RS) by gap modes

or localized modes (pure alkali halides do not show first order RS, ^but doping ^with impurities destroys

inversion symmetry and allows RS by ^local pho- nons) [15],

-

sideband (SB) absorption in the middle infra- red (MIR) (a binary combination of an IR active intramolecular vibration and an external mode - ^a gap mode or a localized mode - is observed in the MIR, where the crystal ^is transparent ^{at all tem-} peratures) [16].

These methods have been applied ^{to some centres} by ^different authors, particularly ^to KI: N02 [1-6].

However, they ^{have never been} performed ^under

identical experimental conditions for one centre in order to decide which modes can be observed

simultaneously ⁱⁿ RS, ^SB absorption, ^{and FIR} absorp-

tion. Furthermore, ^{there is a lack of} clarity ^{in literature} (+) ^{On leave to} Max-Planck-Institut fur Festk6rper-

forschung, HeisenbergstraBe ^{1, D-7000} Stuttgart 80, ^F.R.G.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004601011900

about selection and intensity ^rules governing ^SB spectra : whether SB of IR active internal vibrations should obey ^R selection rules and SB of IR inactive vibrations should obey ^{IR selection rules} [8, 17].

Recently Otto and Fischer [9] published ^FIR

studies on OCN-, SCN-, ^{and SeCN- centre} gap modes in KI, whereas Kauschke et al. [10] ^extended

the investigations ^{to the inversion} symmetric B02

and N3 ^{centres. These} three-atomic linear ions

are known to be embedded in 111 ) ^direction

in the KI matrix (point ^group C3v ^and D3d respective- ly) [8, 9, 16, 18]. ^The experimental results for B02

and N3 ^centres gave evidence of two IR active _gap modes each, whereas for the chalcogenocyanate

centres unequal ^{numbers of modes were found}

A comparison ^with previous investigations ^{of SB}

structure by Cundill and Sherman [7, 8] ^{was difficult}

because of a considerable difference in experimental

conditions (resolution ^and measuring temperature).

Particularly, ^{it could not be} definitively ^decided

which _gap modes were observed simultaneously

in FIR and SB spectra ^{and which} symmetry ^should be attributed to the chalcogenocyanate ^centre gap modes.

The aim of the present ^{work is to determine a} complete ^{set of} gap modes and localized modes

(symmetries ^and frequencies ^at LHeT) ^{for the} B02 , N3, OCN-, SCN-, ^{and SeCN- centre in KI} by measuring the RS and SB absorption ^and comparing

the results with the previous investigations ^{of FIR} absorption, [9,10]. Special ^{care is taken to the selection}

and intensity ^rules governing ^{the SB} absorption.

The reminder of this _paper is arranged ^{as follows.}

We will give ^some experimental details in section 2.

Section 3 is devoted to theoretical considerations :

we will predict ^the number and symmetry ^of gap modes and localized modes from _group theory,

establish SB and R selection and intensity ^rules by

the Wigner-Eckart theorem and show how to deter- mine the mode symmetry ^{for centres of} point group

C3v by ^{RS. In the} experimental part (section 4) ^we present ^the high resolution (0.1 cm-1) ^SB spectra

at LHeT. We _compare RS and SB spectra ^{of the}

same resolution (about 2 cm-1) ^and interprete ^the

similarities. Finally ^we determine the symmetry ^of the R active modes by measuring in different 900 RS geometries. ^{In section 5 we} discuss the set of _gap modes and localized modes with the aid of a linear model.

2. Experimental techniques.

2.1 SAMPLE PREPARATION.

For SB and RS measu- rements we need KI single crystals highly doped ^with B02 , ^, N3 , ⁵ OCN-, SCN-, and SeCN- centres

(concentration ranging ^{from 0.2} mol-% ^{to 2} mol-%

in the melt). ^The doped crystals ^{are grown} by ^the

same technique ^{as described in the} previous publi-

cations [9, 10], apart ^{from KI} crystals doped ^with

SCN - centres which are grown by ^the Bridgman- Stockbarger method for better drying. ^{We use cleaved} single crystals ^{with a size of 10 x 3 x 3 mm3 and}

a polished (110) face for RS. For the MIR absorption

we polish ^{or cleave} crystals ^{with a} diameter of 10 mm

and a thickness of about 2 mm. The samples doped

with borate centres are annealed at 620 °C for 10 min.

and quenched ^{to room} temperature ^before measuring,

since B02 ^{centres in KI tend to associate} slowly

at room temperature [19]. The vibration spectrum of borate associates in the MIR essentially ^consists

of broad features in the range from 700 cm -1 to 1 600 cm -1 and can be well distinguished ^{from the}

MIR spectrum of isolated B02 ^centres [20].

2.2 MIR SPECTROMETER.

The MIR spectra ^are carried out by ^a Fourier-transform spectrometer (Bruker ^{IFS 114 V)} equipped ^{with a} globar lamp

and a pyroelectric ^detector (Bames T-300 with KBr

window) working ^{at room} temperature. ^A doped

and a pure crystal ^are mounted in an optical ^helium cryostat ^{of our own} construction and measured

one after the other. The absorption spectrum ^is calculated by dividing ^{the two} transmission spectra and taking ^the logarithm.

2.3 RAMAN SPECTROMETER.

We use an argon-ion

laser (Spectra Physics type 165-03) operating ^with

0.5 W in the 514.5 nm line. The polarized light ^is

focussed on the sample mounted in an optical ^helium cryostat ^{of our own} construction. The scattered

light passes under 900 into a grating ^{double mono-}

chromator (Jarrell-Ash ^model 25-100) equipped ^with

a photodetector (RCA ^C 31034) working ^{at 260 K.}

The best resolution is about 2.3 cm-1.

To determine the mode symmetry ^{we measured} in the four different 900 RS geometries ^{for cubic} crystals [15] :

(x, ^{y, and z parallel to} the three four-fold ( ¹⁰⁰ )-

axes of the cubic crystal).

All measurements are performed ^{at LHeT} and,

for control, ^{at LNT.}

3. Theory.

3.1 NUMBER AND SYMMETRY OF GAP MODES AND LOCALIZED MODES.

We only ^{resume the results} published ^{in a} previous paper [10] ^{for a centre of} point group D3d (B02 ^and N3 ).

We identify the intramolecular vibrations :

-

A 1 g, ^symmetric stretching ^vibration v 1 (R active),

-

A2u’ antisymmetric stretching ^vibration V3 (IR

active),

121

-

Eu, bending vibration v2 (IR active);

the gap modes and localized modes each (depend- ing on whether the environment is vibrating in-phase ^or anti-phase ^{to the} impurity) :

-

A2u, longitudinal translation mode (IR active),

-

Eu, transverse translation mode (IR active),

-

Eg, transverse libration mode (R active).

Whereas for the inversion symmetric ^{centres the}

mutual exclusion rule leads to a selection of even and odd modes, modes of symmetry A 1 ^{and E should be} simultaneously ^IR and R active in the case of the

chalcogenocyanate ^centres (point group C3,)’ ^We

obtain from correlation tables [21] :

-

2 Al, stretching vibrations vl and v3 (IR, R),

-

E, bending vibration v2 (IR, R),

-

A 1, longitudinal translation _gap mode or loca- lized mode (IR, R),

-

2 E, transverse gap mode or localized mode

(IR, R).

The 2 At inner vibrations are no longer purely symmetric ^or antisymmetric. The 2 E gap modes

or localized modes do not have purely translational

or librational character.

3.2 SELECTION AND INTENSITY RULES FOR SB ABSORP- TION AND RS.

Since selection rules for two-phonon absorption ^{and RS are} well documentated [22, 23],

we give only ^a summary of main features _necessary ^to compare SB absorption ^{with RS} by ^local phonons.

As a rough simplification ^{we assume} in semiclassical

theory ^that only vibrational transitions from a

non-degenerate ground state 1 All, 1) ^{to a final}

state I y, k) ^{must be taken into account, where y}

is the irreducible representation of the final state, k ^is

a component of the irreducible representation. ^First

we consider for centres of point group D3d ^those

selection rules which arise from transformation _pro-

perties ^{of the} transition matrix clement Then we

establish intensity rules for centres of point group

C3v ^{by the} Wigner-Eckart ^theorem.

In the case of RS we have to consider the polari- sability ^{tensor P} describing the interaction of an

incident electric field E; ^{and a} scattered field E. ^{[22, 23] :} HI ⁼ E.. P. Ei. First order RS by ^{a local} (external) phonon (normal coordinate Qe) ^{arises from a term :}

(x, j8 : ^Cartesian components ^{of the} tensor).

The scalar OP,,fllDQ,, vanishes unless the coordinate

Qe transforms like P. In Placzek theory ^{P transforms}

like a symmetrized ^direct product [Dv x v] + ^{of the} polar ^vector representation ^Dv [23]. ^{This means}

in D3d : ^like A 1 g ^or Eg. Eg ^{gap modes or localized}

modes should be R active. The relative transition

probability ^is given by :

IR absorption ^can be described by the interaction of an electric dipole ^{vector M with the electric}

field E [22, 23] : HI ^{= M. E. SB} absorption ^arises

from a combination of an internal vibration (Qi)

with an external mode (Qe) :

(a : ^Cartesian component ^{of the} vector).

The scalar 02 Ma./ OQ¡ oQe vanishes unless Qi Qe

transforms like the representation ^{D v of a} polar

vector [23]. ^{The vector} representation ^{Dv of} D3d

is A2u ^Q E.. ^{In table I} the irreducible representa- tions of all products Qi Qe ^are summarized Those

products satisfying ^the upper condition are under- lined

Table I.

Irreducible representations of ^all products Qi Qe.

Hence, ^{we conclude :}

-

SB of IR active internal vibrations (A2u, EJ obey ^R selection rules (EI ^{gap modes or localized}

modes are SB active),

-

SB of IR inactive internal vibrations (All)

obey ^IR selection rules (A2u ^and E. ^{gap modes or}

localized modes are SB active).

For _group theoretical considerations it is irrelevant

as to whether the internal vibrations or the external modes give ^{rise to IR} activity. ^Our experimental

results will show that

taking ^{into account the} dynamical ^behaviour

^{SB of IR inactive vibrations}

are not observable.

The relative probability ^{of SB} absorption ^{from a} ground state Aig, ^1; A 1 g, ^{1 ) to a final state y, k ;} y’, k’ > ^is given by :

In adiabatic approximation between internal vibra- tions (600 ^{cm-1 to 2 000} cm-1) and external modes

(60 ^{cm -1 to 170} cm -1 ) the matrix elements separate into an internal and external part :

This approximation ^has already ^been proposed by

Mauring and Rebane [24] for the SB of the SH-

centre in KI.

For the chalcogenocyanate ^centres (C3v) ^similar

calculations show that A1 ^{and E} modes should be R, IR, and SB active. The relative intensities ^can be calculated by ^the Wigner-Eckart ^theorem [25, 26]

from (2) ^and (5) for RS and SB absorption. ^{Tables II}

and III summarize the result for the relative intensities of the transition matrix elements.

Table II.

Relative intensity of ^the transition matrix element for ^RS.

Table III.

Relative intensity of ^the transition matrix

element for ^SB absorption.

C Q 1,.. is the reduced matrix element of the operator

Q;,e, which results from a final state of irreducible

representation y. Whereas (2) ^and (5) ^{are still} depending

on symmetry ^and geometry properties, the reduced matrix elements depend only ^{on the} dynamical

behaviour (y ^and Qi,e)-

3.3 SYMMETRY DETERMINATION.

In order to deter- mine mode symmetry ^{we make use of the} angular dependence ^{of RS} intensity [22] :

where R is the Raman tensor of the scatterer, _{e; the} incident polarization vector, e, the scattered polari-

zation vector. We have to consider a centre of point

group C3v ^{as an isolated scatterer} oriented with equal probability along ^{the four} equivalent 111 ) ^direc-

tions. The contributions from each scatterer to the total scattering intensity ^under scattering geometries ¹

and 3 are :

where a and b are elements of the A1 ^{Raman tensor,}

c and d elements of the E Raman tensor [22].

Hence, ^two _spectra ^are sufficient to determine the mode symmetry : contributions from A1 modes have to

disappear ⁱⁿ geometry 3, ^{whereas E modes are} _present in all spectra.

4. Experimental ^results.

4.1 HIGH RESOLUTION SB SPECTRA (0.1 Cm 1 ). - Figure ^{1 shows the} transmission spectrum ^{of KI :} B02

in the region ^{of the} antisymmetric stretching ^vibration v3(A2u). ^{The two} inner vibrations at 1943.5 cm-1

(11802 ) and 2013.2 cm-1 (’OB02) arise from the boron isotopes 11 Band lOB. ^Each line is surrounded by

lines due to the 180 species [19] ^and by ^{so called}

« satellite »-lines [16] ^{due to} the interaction of neigh- bouring ^{ions. In} samples ^with high doping ^concentra-

tions SB modes can be identified at LNT as Stokes and anti-Stokes lines symmetrically ^to the central inner vibration. In samples with lower centre concentrations

we can also consider the temperature dependence ^of

the half widths : from LHeT to LNT the half width of SB modes (about ^{0.5 cm-1 for} gap modes,1.5 ^{cm - I for}

localized modes) nearly doubles while the half width of inner vibrations is lower (about ^0.2 cin- 1) ^and

remains nearly ^{constant from LHeT to LNT} (see ^f.e.

v3(OCN-) ⁱⁿ Fig. 1) ^{[27, 28].}

Fig. ^1.

Transmission spectrum ^{of KI :} B02 ^{in the} region

of the v3(A2u) antisymmetric stretching ^vibration.

For both ions, 11 BOï and 10BOï, ^{we identify a gap}

mode at 89.6 cm - I and a localized mode at 141.4 cm-1 of symmetry Eg ^{according to} section 3. The Eg ^gap

mode is also observed in combination with the weaker

bending ^vibration v2(Eu’ llBOï, ^{v = 587.3} cm-1),

123

however, ^{no SB of the R active} symmetric stretching

vibration v 1 (A 1 g) ^{is found}

Figure ² shows the absorption spectrum ^{of the}

v3(A2u) sideband for KI : N3 . The central line at 2 023.2 cm-1 corresponds ^{to zero} sideband shift. The

edge of the acoustic band (until ^{69.7 cm-1} [29]) ^{and the} optical ^band (from ^{95.6 cm-1 to 137.7 cm-1} [29]) ^are

marked by ^{bars. We} identify ^an Eg ^{gap mode at}

81.8 cm-1 and an Eg ^{localized mode at 149.2 cm-1.}

Fig. ^2.

^Sideband absorption spectrum ^{of the} v3(A2u) antisymmetric stretching vibration for KI : N3 .

The OCN- centre in KI gives ^{rise to two SB active}

gap modes and localized modes each at 78.9 cm-1

(02), ^{83.5 CM - 1} (Q3)’ ^{137.7 cm - 1} ?5), ^{and 154.8 cm 1} (S26). Figure 3 shows the SB of four inner vibrations of

Fig. ^3.

^Sideband absorption spectra ^{of the} v3(A1) ^and vl(A1) stretching vibrations and of the v2(E) ^and (2 v,) bending vibrations for KI : OCN-.

the OCN- ion : the stretching vibrations vi(A1,

1 199.5 cm-1) ^and v3(At, ^{2156.8 cm-1), the} bending

vibration v2(E, ^628.9 cm-1) and its second harmonic (2 V2) (v ^{= 1 288.6} cm-1). ^The strongest ^modes (22’

03A93, 03A96 ^{are observed} in all SB. The weaker ^resonance

mode Q. ^{at the} upper limit of the optical ^{band is} only

detectable in combination with the strongest ^inner vibration _V3 and is almost separated ^{from the} optical-

band absorption ^{at LHeT. The} gap modes and loca- lized modes _appear in all SB in the same intensity ^ratio according ^to (C’11"ICY2 )2 ^{(see Table III). The symme-}

try ^{of the} central line itself has no influence on the

shape of the SB. The ^same SB modes in different SB appear in the same ratio as the absorption strengths ^of

the central inner vibrations (CQ)’ I’ /CQ}’2’ )2. i,l i,2 ^{IR activity} seems to result from the central inner vibrations

according ^{to the reduced} matrix elements (CQi)2, ^the

frequency shift is due to the SB mode coupling by ^the

reduced matrix element (CQe)2 to the inner vibration.

In figure ^{4 we} identify ^two gap modes at 78.8 cm-1 and 83.4 cm-1 in the SB of the v3(A1, ^2065.5 cm-1) stretching vibration of the SCN- centre. We also see

the influence of the OCN- contamination. Above the

optical ^{band we} ascertain four localized modes at 145.0 cnTB ^161.6 cm - 1, ^163.9 cm - 1, ^{and 167.0 cm-1}

at LHeT. This result disagrees ^{with our} predictions ^of A ^{1 p 2 E localized modes. In section 5 a model will} explain ^the appearance of _up to four localized E modes:

Fig. ^4.

^Sideband absorption spectrum ^{of the} v3(A1) stretching vibration for KI : SCN-.

Figure ^{5 shows the} v3(A1, ^{2 070.3} cm-1) ^SB spec- trum of KI : SeCN-. The inner vibrations of the OCN- contamination are perturbing ^the spectrum. ^Never- theless we identify ^two gap modes at 69.5 cm-1 and 85.5 cm- 1. There is a weak and broad localized mode at 148 cm-1 and two stronger ^{ones at 168.4 cm-1 and} 171.2 cm-1.

4.2 COMPARISON OF SB SPECTRA WITH R SPECTRA.

We have to take into account that SB absorption ^is spatially isotropic; ^RS intensity, however, depends strongly ^{on the} scattering geometry. ^The comparison

of SB absorption ^{and RS is not} easily possible ^unless

sideband shift av cm-i>

Fig. ^5.

^Sideband absorption spectrum ^{of the} v3(A1) stretching vibration for KI : SeCN- in the gap region ^and

above the optical ^band.

-

as we will show later

only ^one kind of mode (E)

is R and SB active.

Figure ⁶ compares ^a SB spectrum of KI : OCN -

(a) ^{with a R} spectrum (b) ^of nearly ^{the same resolution} (2 ^{cm-1 and 2.3 cm-1} respectively). ^{SB and R} spectra

are very similar and they obey ^{the same} selection and

intensity rules. This result can be verified on KI : SCN-

(Fig. 7). Lower resolution of the SB spectrum ^with respect ^to figure ^{4 leads to a} broad feature at 164 cm -1 instead of the three localized modes, the weaker mode

can not be detected in RS. Nevertheless, ^{there are} also

some differences between both spectra. The SB spec-

trum is overlapped by the inner vibrations of the SCN- and OCN- ion, whereas the R spectrum still shows

Fig. ^6.

^Sideband (a) ^{and Raman} (b) spectrum ^of nearly

the same resolution (2 cm -1 ^{and 2.3 cm -1} respectively)

for KI : OCN-.

Fig. ^7.

^Sideband (a) ^{and Raman} (b) spectrum ^of nearly

the same resolution (2 ^{cm-1 and 2.3 cm-1} respectively)

for KI : SCN-.

one-phonon scattering ^{from the} perturbed host lattice where the one-phonon density ^{of states of KI is}

elevated This perturbation ^{is more} pronounced ⁱⁿ figure ^{8 for KI :} N3 which shows some aqueous inclusions from crystal growth [10]. But, also the inversion symmetric N3 ^centre satisfies the intensity

rule for local phonons. The SB modes and R modes appear in the same intensity ratio, ^since

according

to tables II and III

the same reduced matrix elements (Cy.)’ ^are describing the intensities in SB

absorption ^{and RS.}

Fig. ^8.

^Sideband (a) ^{and Raman} (b) spectrum ^{of the same}

resolution (4 cm-1) ^{for KI :} N3 .

125

4. 3 POLARIZED R SPECTRA.

Figure ⁹ and 10 show the R spectra for KI : OCN - and KI : SCN - measured under scattering geometries ^{1 and 3. In} geometry ³ A 1

modes must disappear. However, ⁱⁿ geometry ^{1 and 3} all modes are observed By ^this way E symmetry ^is ascertained for the _gap modes of the OCN- centre at 78.8 cm-1 and 83.5 cm-1 and of the SCN- centre at 78.8 cm-1 and 83.4 cm-1. Furthermore, ^{both loca-}

Fig. ^9.

Polarized Raman spectrum of KI : OCN-.

,Fig. ^10.

^{Polarized Raman spectrum} of KI : SCN-.

lized modes of the OCN- centre at 137.7 cm-1 and 154.8 em - 1 have E symmetry. ^E symmetry ^can only

be ascertained for the strongest localized mode of the SCN- centre at 163.9 cm-1. However, ^{neither a} weakening ^of scattering intensity ^{nor a} reduction of half width have been detected for this broad line.

Hence, ^{we conclude that E} symmetry may be true for the three localized modes at 161.6 cm -1,163.9 cm -1,

and 167.0 cm - I as well as for the mode at 145.0 cm - 1.

Our experiments ^suggest that all modes observed in SB absorption and RS have E symmetry, although A1 ^{modes are allowed The} matrix element CQe ^{has to}

vanish for physical (dynamical) ^reasons. A1 ^{modes as}

well as A2u modes have purely translational character,

since no librational degrees of freedom are involved in

longitudinal ^{motion. This means} for RS : the symmetric

variation of the polarisability ^tensor with the normal

coordinate vanishes. For SB absorption ^we propose the following interpretation in adiabatic approxima-

tion. IR activity arises from the high frequency ^inner

vibration with a relative intensity of (CA,,E)2 ^{The low}

frequency external mode couples by ^a coefficient

(COA,,E)2 ^to the central mode modulating ^{the inner}

vibration periodically. However, purely translational external modes can not cause any frequency ^modula- tion, since the fast inner vibration is moved adiabati-

cally. Only ^a symmetric widening and contraction of the environment of the ion causes an internal mode

frequency modulation. Whereas RS relies ^on the _sym- metric deformation of the polarizability tensor, ^SB

absorption depends ^{on the} symmetric deformation of the environment by the external mode. We conclude that SB of IR inactive internal modes must vanish for

dynamical ^reasons, since these SB modes should have

purely translational character.

5. Discussion.

Table IV _compares our results (S) for the series of centres with the previous investigations ^{of FIR} absorption (F) [9,10].

Table IV.

Wave numbers at LHeT and symmetries of gap ^modes and localized modes observed by ^FIR absorption

(F) [9, 10] ^{and RS or SB} absorption (S).

In the _gap region ^{we have} determined a complete ^set

of modes (A2u ^Q+ Eu ⁰ Eg ^{or A1 1 p 2 E). The modes of}

the inversion symmetric ^centres B02 ^and N 3 (D3d) obey the mutual exclusion rule. For the chalcogeno- cyanate ^centres (C3v) ^{all gap modes are} observable in FIR absorption (apart from the SCN- _gap mode at 78.8 cm-1 which has been masked by ^the gap mode of the OCN- contamination). ^{In RS and SB} absorption, A1 ^{gap modes} disappear, ^{but all E} gap modes ^are observed The frequency data obtained simultaneously

from FIR and SB absorption ^{at LHeT} agree well with a

precision ^{of 0.1} cm-1, whereas the absorption strengths

are different in the FIR and SB spectra (see ^also [9]).

The behaviour of the absorption strengths ^{as well as}

the frequency behaviour within the series of centres will be described by ^a simple ^model.

In the region ^{above the} optical ^{band we identified}

one localized Eg mode each for the BOZ ^and N3

centre. The only ^IR active localized modes A2u p Eu

and A 1 ^{can not} be measured by ^FIR absorption, ^since

this region ^{is masked} by ^the reststrahl absorption ^even

at LHeT. For the OCN -, SCN -, and SeCN - centre we

identify two, four, and three localized E modes _respec-

tively. ^A fourth localized E mode is expected ^{for the}

SeCN- centre. Only the result on the OCN- centre agrees with theory (A1 ^{$ 2E localized modes).}

The following ^{model of a} linear diatomic chain with

a three-atomic linear impurity (Fig. 11) ^will explain

four localized E modes by ^the interaction of the mole- cular impurity and the second nearest neighbours. ^In general, this model enables us to illustrate the modes by

« mode pictures » ^{and it} explains tendencies in the series of ^centres. Especially, ^it characterizes mode

branches. An interpretation ^{of force constants and a} complete fit of mode frequencies ^are impossible ^from

this linear model.

Fig. ^11.

Sketch of the model.

The symmetry axis of the centres is threefold, ^so any transverse vibration is doubly degenerated ^{We there-}

fore consider a two-dimensional model. The motion of the chain is described by ^two independent systems ^of linear, coupled differential equations (force ^constants

for longitudinal motion ci, for transverse motion gi).

m-l, mo and m , , ^are the ^masses of the impurity par- ticles. m - 2 and m + 2 represent ^{the six nearest} neigh-

bours (K + ions) ^of the ( 111 ) oriented ion which can

be subdivided in two classes of three ions each (being

nearest neighbours ^{to the one or} the other end of the

impurity ion), m t 3 the ^{nearest I -} ions etc. The chain is continued N-times to either side and we use periodic boundary conditions. The force constants ct 1 describe the stretching vibrations, go the bending vibration,

C:f: 2 and g t 2 ^are the coupling constants to the nearest

neighbours. ^{The force constants} of the chain

(Clil > 2 ^{=17 N/m and} glil > 2 ^{= 11} N/m) ^{are chosen so}

that

without perturbation

they ^{fit to the ideal KI}

lattice in ( 111 ) ^direction.

The equalions of motion for the diatomic chain (I i 1> 1) ^are

-

in longitudinal ^direction (elongation wi) :

-

in transverse direction (ui) :

and for the impurity ^ion

-

in longitudinal direction :

-

in transverse direction :

127

A computer program establishes the dynamical matrix, diagonalizes it and calculates the eigen- frequencies ^and elongations ^{of the} particles. ^Variable

parameters ^{are the} impurity ^masses m_ 1, mo, and m, 1, the inner force constants c:, 1, go and the coupling

force constants c±21 9±2.

Our calculations lead to « mode pictures » ^as

shown in figure ¹² a)-d) ^{for the} N3, OCN-, SCN-,

and SeCN- centre. We only present ^the best « fits » to the experimental ^{data. The « mode} pictures >> ^charac-

terize three mode branches for _gap modes and loca- lized modes each :

-

a) ^The longitudinal ^branch (A2u --+ At) ^of purely

translational character (only ^IR active). ^The frequency

behaviour of this branch can be interpreted ^{as a} pure

mass effect. Figure ^{13 shows the} frequency dependence

of the longitudinal ^mode frequency ^{from the total mass}

of the impurity. The theoretical frequency (+, ^force

constants not changed) decreases with increasing impurity ^mass and fits well to experimental ^data (e).

Fig. ^12.

« Mode Pictures ^» for the N3 (a), ^OCN- (b),

SCN- (c), ^{and SeCN-} (d) ^{centre in KI.}

Fig. ^13.

Longitudinal ^mode frequency ^{versus the total} impurity ^mass (o experimental data, ^{+ data} obtained from the model).

This mass effect is also predicted by other models for monatomic impurities [14, 30] ^which only ^consider

translational degrees ^{of freedom.}

-

b) ^The low frequency transverse branch (E. -+ E)

has purely translational character for the inversion

symmetric ^centre N3 (IR ^active). Destruction of inversion symmetry for the OCN- centre leads to an

admixture of a weak librational part ^{to the trans-} lational motion and the mode becomes slightly ^R

active (see ^{Fig. 3 and} [9]). ^{A node is} entering ^{from the}

side of the lighter particle. Finally, ^{in the case of the}

SeCN- centre only the heavier Se atom is moving.

The _gap mode frequency essentially determined by ^the

motion of the Se atom approaches ^the A1 gap mode

frequency (experimental : ^{67.7 cm-1 and 69.5} cm- l,

model : 66.7 cm-1 and 66.8 cm - 1).

-

c) ^The high frequency transverse branch (Eg -+ ^E)

has purely librational character for the inversion

symmetric N3 ^centre (R active). ^{In the case of the}

OCN- ion the librational ^{motion mixes with a little}

translational p gga and the mode becomes slightly ^IR

active (see ^{Fig. 3 and} [9]). ^{The node, situated in the}

centre of the ion before, approaches ^{the heavier atom.}

Finally, for the SeCN- centre the Se atom is at rest and only ^the lighter ^{end moves.} The increase of the

experimental ^mode frequency within the series of centres can be explained by ^an increase of force constants for the longer ^ions OCN-, SCN-, ^and

SeCN-. The force constants may be dissymmetric ^for highly dissymmetric ions like SCN - and SeCN -.

The model explains four localized modes for ions

which also perturb ^the environment of the second

nearest neighbours. ^{We have to} increase the coupling

constants g:t 2 and g+ 3. The long wavelength gap modes are not sensible to this change, whereas the short wavelength localized modes split ^{into two kinds}

of two modes each :

- modes only having ^a node between impurity ^and

the nearest neighbours (lower frequency),

-

and modes having ^a further node between the nearest and next nearest neighbours (higher frequency).

For SCN- and SeCN- centres four localized E modes are comprehensible.

Let us, at least, try ^to interprete ^the striking ^difference

in Eg ^mode frequencies ^{of the} N3 ^and B02 ^centre (81.8 ^{cm -1 to 89.6 cm -1} and 149.2 cm -1 to 141.4 cm-1). ^The high Eg ^{gap mode frequency of the} B02 ^{centre can be} explained ^{in our model} by ^{a shear}

force between the ^masses m - 2 and m+ 2. ^In reality, they

are next nearest neighbours ^to each other (K + ions)

and an interaction preferring ^a shear deformation of the octahedral environment of the impurity ^{seems to be} probable. ^A strong contribution of the environment also suggests ^a lowering for the localized Eg ^mode frequency ^{of the} B02 ^centre.

6. Conclusion

Comparing ^our results obtained from R and SB studies to previous ^FIR measurements we establish a complete

set of _gap modes for a series of three-atomic linear centres in KI. We extended the analysis ^{to localized}

modes above the optical ^band

The results of our investigations ^{are twofold :}

-

Measuring under identical experimental ^condi-

tions we were able to decide which modes are simul-

taneously R, SB, ^{and IR} active. We could _compare their intensities from the different methods. A model of a linear chain characterizes three mode branches for _gap modes and localized modes and interprets

their IR and R activity. ^The appearance of _up to four transverse localized modes can be explained by ^the

model.

-

Direct comparison of R and SB spectra ^{led to} the conclusion that both are governed by ^{the same} intensity rules. This relation seems to be general ^{and is} supported by theoretical considerations. However, ^a verification of this rule for another series of centres

(e.g. N02 , P02 , As02 ) would be desirable.

Acknowledgments.

The authors wish to express their gratitude ^{to Prof}

W. Ludwig ^{and Dr.} C. Falter for their assistance in theoretical work and to R. Arends for the growth ^of single crystals.

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