- Email: [email protected]
Angular dependent raman scattering studies of KH2PO4
Vplume 35, ilurnb; 2
1 September
CHEMICAL PHYSICS LETTSRS
Received 25 April 1975 Re-f&d mannujcript received
1975
16 May 1975
km-tan scattering spectra of a KH2P04 single crystal were mez.sured at vuious crystal orientations rebtive to the tincident and sntteredlight propagatior! directions. It has been found that the contribution of thelong-rangee!e Jrostatic interaciion is less th;m 10% of the total scattering effitiency of the E(x) and B,(s) modes in WP. Alow freqzency mode, previously predicted by group. theory, was aLso observed for the first time.
1. Introduction Vc have recently
reported
[l]
experimental
re-
sults on the angulu deiyendence of the intensity of the phonons and internal modes of the KH2P04(KDP) single crystal. In ref. [ 11, Raman spectra of A, and B, modes of KDP single crystal were taken by keeping the direction of the incident and the scattered wave vectors fmed at 90” to en& other while the orientation of the cIystalLognphic axes were rotated relative to the light propagating directions. It was found th2t the sc2tterir:g intensities of Al and B, modes exhibited an angular variation by rotating the crystal as described above. These experimental resuits lvere nor consistent with the polarization selection rules for the first order Raman process. We report in this paper the angular vviation of the intensity of the E and B, modes in KDP crystal. The &man spectra were ta!!en with the same scattering geometry [l] but v&h the incident light polarized non-& to and the scattered light polarized partiel to .the plane of scatterti,g. Our experimental results show that thpUangular variations of the intensity of the E and BZ modes agree with that predicted by the We acknowledge tile Oitice of
N2v2i Research and the Petroleum Reseuch Fund. administered by the American Chemistry Society, for tk.e support of this r&arch. ** Alfred P..Sloan Foundation Research Fellow. l
..
polarization selection rule. We 2lso report the observ2tion of a lower frequency optical mode in KDP. Aevious attempts lo locate this mode by She et al. [2] were unsuccessful due to its weak titensity a5d its close proximity to the laser line. Moreover, we have also found that this lowest frequency optical mode exhibits a noticeable shift in the p& frequency as the crystal is rotated with respect to the fied directions of the incident and the sattered light vectors. The experimental results and the discussion are described below.
2. Experimental
results 2nd discussion
The experimental set up 2nd the details of the scattering geometry for Raman spectra were described elsewhere [I ] _Aq oriented s+$e crystal of KDP was cut and po!ished in the form of 2 cylinder of 2.5 cm length and 2.5 cm diameter witi the cylinder 2xis paraYe to one of the crystiogs2p~~c axes (t&en as they axis). The optical axis, Z, is normd to the cylinder axis. The incident and the sattered light vectors ki and .& respectively, are orthogonal to each other. 4 is the angle between the oFtip 2xis 2nd the vector kj (see fig. 1). The ticident light was polarized normal to the plane of scattering while the s-ccattered light was polarized in ;he plane of scattering. T&us for Q = 0 and 90°, the ntretig
cctigurations
correspond
I September 1975
CHEhIiCAL PHYSICS LETTERS
Volume 35, number 2
Assignment of the observeii Raman active modes in KHzPOs
Mode
Symntetry species
frequency (cm-' j
R2man tensor
Fig I. Rzman sur:ering geometry.
The scrtttern~ng confiiuration .Foran intermediate -saiue of Q is the combination c,f .rcVz)~ and xtj~x)z. Raman spe&ra of the phortons and the interns1 modes of KDP at various values of Q are showa in SJGJ. 2, The spectra t&en with 9 = O” consist of E modesat c:II~~, 113 cm-l, 185 cm-l, and lo z(.yt>v and zt’~x)z, respectively.
and 531 cm-l *, and with 4 = 90” the spectra consist of A, modes at 367 cm-l, 915 cm-l; a B, mode at 473 cm-r, and a B2 mode at 391 cm-r. A broad
continuous band extending from 0” to 100 cm-l in the xQx]z scattering configuration (0 = 90°) is associated
with the law frequency
optical
phonon.
This
band is the well-known overdamped soft mode of B2 type, which is closely related to the phase transition of KDP [3,43.
The assignmenis of the observed modes and their Reman tensor components, as determined from group theoretical considerations, are @en in table I _Modes of E symmetry transform as o,* and cyzXRaman iensor componeilts. They are in close egreement with the observed modes in the spectrum taken with 9 = 0”, corresponding to the z&z)x con~guratio~. Sinrilarly, the group ‘&xx-y allows only B, modes to be present i? the spectra taken with the .~tyx)z ~on~~uration.
However, the spectrum taken at q5= 90° exhibit the presence of A, and B1 modes in addition to the B, modes. Tfle presence of A, modes at 923 cm-r, 367 cm-l
and a BI mode at 437 cm-l is anomalous are not expected to be present in +Ae
as these modes
configuration. Scrutiny of the experimental set up inilicates t&t the presence of these modes is
X(JJY)Z
Frequency
Shif tkm-1)
Fe. 2. Raman spectra of XDP t&en at vxrious vdues of+. The an@, $3,is between the ciystz!logaphic axis and the incident wake vecior. For @ = 0” and 90”, the scztterins co& figurations are zcyY)* anbr(~~)z, p_spectivel~.
not due to the polar&&ion !e&tage. The anomalous polarization behavior of the 915 cm-1 mode has also been observed C-51earlier and has been exphined as being due to the asymmetric ‘~c~ystal f%!d” surrounding the PO:- ion in the KHzP04 crystal. The 9 15 cm-l mode is associated with the breathh,o motion of the PO:- ran ’ perturbed by tie O-H-0 hydrogen bond in the E(Ii2F04 c&Xzi. The A1 mode at 367 ‘.
265 :.
Volume
cm -’
35,l?umber
CHEMICAL
2
and B1 mode at 473 cm-’
with FOG- ion in the KH,FO,
PHYSICS
are also associated
[2j _The asymmetric
“c~iystal field” could introduce the poki&ation anomalies for the mode at 915 cm-l as well 2.s for the mcdes at 367 cm-l and 473 cm-l. As a rssult, the depolarization of t:he scattering from the internal vibration with Al and B, symmetry may occur. This consideration can zlso be used to explain the presence of AI modes at 915 and 367 cm-l and the B, mode at 473 cm-l in the _ycyX)z configuration. According to tijudon [6], the scattering efficienm cy, S, of the &man and infrared active modes in the uniaxial crystal is given by:
(1)
i September
LEl-iERS
process be confined to the xz plane and the scattered light to be approximately irannsverse. The scattering intensities of E and B2 modes in the direction of KS can be evaluated as follows: Consider the E(x) mode in the scattering geometry of fig. 1. The’mode is polarized in the x direction but propagating at an angle of (n/4 - I$) with respect to the x axis. Thus the E(x) mode can be resolved in twc components; a quasilongitudinal component along the #s direction and a quad-transverse component normal to the KS. The scattering efficiency can then be written by the use of eq. (1). We obtain, for the E(x) mode, $
= (a +8)2(~)2(~)2.2cos2(,/4 = (3 cp)2(,:~~)2,2,0,2(,/4-
s; = a2 (e#)’ where R, is an element of the Raman tensor, and ep and ec are the components of the unit vectors along the principal axes, u and p_ [ is the unit vector in the direction of the lattice displacement which dictates the deformation potenti scattering and K is the unit vector in the direction of the electric field which induces the polar scattering. Q and B are the cons+ants of proportionality. (Yis proportional to the lattice displacement uld /3 is proportiona! to the eleciric field strength [6] . In KDP crystsl, the ionic electrostatic forces predominate over the anisotropy in the short range interatomic forces, and there exist quasilongitudinal extraordinary phonons for which the electric t
Bz(z)_
where X, y. or z ii parentheses repreants the mechtica! polariition of‘ the phonon. Let the scattering 266
”
1975
- f$) 9) co&,
(2)
2 Sk? (n/4 - @) co2 $I.
(3)
The subscript II on S means the scattered light is polarized in the scattering plane; the superscripts P and t represent the quasi-longitudinal and the quasitransverse compor.ents, respectively. e1 and e” are the components perpendicu!ar and parallel to the plane of scattering. (The incident and the scattered Ii&t waves are taken as transverse.) In eq. (3), fl= 0 because the quasi-transverse part of the extraordinary phonon has a negi$ible electric field. The total scattering efficiency, S;,, due to the E(x) phonon is the sum of eqs. (2) and (3): Sn = (etei)2
e2 Y3 [( 1 •t O/a)2 cos’(aj4
+ sin2(IT14-@)]
- @)
cos2@.
(4)
Similarly, the scattering efficiency of the B2(z) vibration of KDP crystal can be evaluated. We obtain S, = (e:e:)2d2c2
[(I
+/3/a)*COS~(T/~+Q)
f sin’(7i/4+@)] sin29
(5)
for the B(z) mode. For imulstig crystals, like KH2P0,, the po!ar scattering due to long range e!ectric field effects is small compared to the deformation potential scattering. Namely, in eqs. (4) and (5), ij/(~ < 1. Therefore, we expect that the scatieiing efficiencies of the E(x) and B2(z) modes should exhibit COST@and the sin29 dependences, respectively. Ir? Gg. 3 we have shown the theoretica! curves from eqs. (4) and (5) for different values ofP/~y as a
Volume 35, number Z
I September 1975
CHEhfiCALPHYSICSLETTERS
at 98 cm-’ was taken 2s 5 cm -’ _Our experimental resuIts show “&at for The B~{z) and E(x) modes in KDP the retio ,8/a Is Less than 0.1~ indicating that -the polar scattering mechanism contributed less than t 0% of the total scattering efficiency.
3. Lowest fr2quency optical mode
Fig. 3. Comparison of the theoredcaJ md experiments values for the relative integatcci intensities. Solid curves are tt;eoretiwJ values. All values are normalized to unity for the dat3 at Q = JSO.(al Data for the B?(z) mode at 391 cm-‘. (b) Data for the E(x) mode at 98 cm-‘. Seeeqs. (4) and (5) and the &?Xffor detail.%
function OFthe angle 0. The scattering efEciencies are normalized for the value at 4 = 4SQ such tit2t: S(@ = 45’)
= 1
There is a low frequency optical phonon of B1 symmetry in KDP crystd which has not yet been observed [Z] . This mode is weak and close to the laser excitation line. The low frequency (below 200 cm-l) specrra in fig. 2 exhibit a definite spectral chulge as the ori~nt~tiorl of the crystal is varied from Q = 0” r_o 45’. Spectra taken with higher resolution (0.5 cm-‘) and twenty times higher gain than the spectra of fig. 2 are shown in fig. 4 at + = O”, 12.5”. 15’, 18” and 30”. The presence of a weak mode at 35 cm-l is quite evident in the spectra taken with 4 = 0”. The peak frcquency of the mode shifts towards lower values with
for all values of fi/cr_
Fig_ 3a shows the theoretical curves hcl experimental data points for the B,(Z) modes at 391 cm-l _ The integrated intensity of the 391 cm-l mode was measured from the R;iman spectra of fig. 2. The measured integrated intensities at the various values of Q were also normalized to give unit integrated intensity at # = 45”. This normalization of the integrated &tensity helped compare the experimental values with the theoreticd results obtrtined from eq. (5). Similarly, fig. 3b shows the normalized theoretical curves and
:
I
IO<
Frequency
Skift(cm”)
Fig. 4. Low frequency Razzan spectra of KDP exhibiting the presence of an optical mode below 20 CR>-~. Thz spectr;? in this figure are k!en at twenty times hi&w gain r&&e to the spectra of fii. 3.
267
Volume 3.5,numkd2i 2
1 September
CHEBIICALPHYS~CSLE~ERS
the rotation of the crystal to smaller 13vdues. Ai # = 30" this mode.& overlapped by the stiong E(x) mode at 98 cm- t _This is the first eTrider.cereported of the lowest frequency optital phonon mode (> 20 cmWi) in the KDP crystal. This optical Iattice -mode (> 20 ~rn-~)need not be confused with th B, mode at 80 cmvi, as obrakenai I$= 909 corresponding The spectra in fig. 2 show that the lowest frequency optical lattice mode is present for @= 0” to 30”. The spectra taken at Q = 75” and 90° exhibit the B2(z) mode at SO cm-t. According to She et al. [2], the low frequency opiical phonon has BL symmetry and is thus only Raman active. The large anomalous frequency shift (see fig. 4) of this mode with respect to the change of 4 indicates that the lcng-rxrge dipole-dipole interaction may dictate the behavior of this mode. Since the long-range &polar interaction is more dominant at a small scatteri:l?g angle, it would be of great interest to examine the low frequency spectra as a function of $5for small scattering angles. served in the spectra
to thax~x)z configuration.
4. Conc:usions
By studying the angnlar dependent Ramnn scattering spectra, it has been shown that the contribution
I975
of the long-range electrostatic interaction is less than 10% of the scatter@ efficiency of the E(x) and Bz(z) inodes in KDP. We have q&o found, for the first time, a low frequency optic4 phonon in K.DP,which was previously predicted theoretically. Thislow frequency mode shows an anomalous freq.uency shift towards smaller vdues as the angie between the optical axis relative to the incident light propagation direction is decreased_ It is suggested that an experiment carried out at a small scattering angle. should show enhanced anomalous behavior.
References [I] h1.K. Srivastava and C.H. W’ang, Breakdown of Selection Rules
in
the
Ra.mul Spectra of KDP, J. Chem. Phys., to
be published.
[Z) C.Y. She, T.W. Brobsq and D.F. Edwards, Phys. Rev. B4 (1971) 1580. (31 LP. Kaminotv and T.C: Damen, Phys. Rev. Letters 20 (1968) 1105. [4] C.M. Wilson and HJ. Cummins, in: Proceedings of the Second International Cortference on Light Slztterine in SoLids,ed. kf:. Balkanski (Flammarion, Paris, 1971) p. 420. [S] hi.K. Srivastava, R.W. Grow and C.H. Wang, C&em. Phys. L&rers 26 (1974) 157. [6] R. Loxdon, Advan. Phys. 13 (1964) 423. [7] A.S. Barker Jr. ami K. Loudon, Rev. Mod. Phys. 44 (1,072) 18.
1 September
CHEMICAL PHYSICS LETTSRS
Received 25 April 1975 Re-f&d mannujcript received
1975
16 May 1975
km-tan scattering spectra of a KH2P04 single crystal were mez.sured at vuious crystal orientations rebtive to the tincident and sntteredlight propagatior! directions. It has been found that the contribution of thelong-rangee!e Jrostatic interaciion is less th;m 10% of the total scattering effitiency of the E(x) and B,(s) modes in WP. Alow freqzency mode, previously predicted by group. theory, was aLso observed for the first time.
1. Introduction Vc have recently
reported
[l]
experimental
re-
sults on the angulu deiyendence of the intensity of the phonons and internal modes of the KH2P04(KDP) single crystal. In ref. [ 11, Raman spectra of A, and B, modes of KDP single crystal were taken by keeping the direction of the incident and the scattered wave vectors fmed at 90” to en& other while the orientation of the cIystalLognphic axes were rotated relative to the light propagating directions. It was found th2t the sc2tterir:g intensities of Al and B, modes exhibited an angular variation by rotating the crystal as described above. These experimental resuits lvere nor consistent with the polarization selection rules for the first order Raman process. We report in this paper the angular vviation of the intensity of the E and B, modes in KDP crystal. The &man spectra were ta!!en with the same scattering geometry [l] but v&h the incident light polarized non-& to and the scattered light polarized partiel to .the plane of scatterti,g. Our experimental results show that thpUangular variations of the intensity of the E and BZ modes agree with that predicted by the We acknowledge tile Oitice of
N2v2i Research and the Petroleum Reseuch Fund. administered by the American Chemistry Society, for tk.e support of this r&arch. ** Alfred P..Sloan Foundation Research Fellow. l
..
polarization selection rule. We 2lso report the observ2tion of a lower frequency optical mode in KDP. Aevious attempts lo locate this mode by She et al. [2] were unsuccessful due to its weak titensity a5d its close proximity to the laser line. Moreover, we have also found that this lowest frequency optical mode exhibits a noticeable shift in the p& frequency as the crystal is rotated with respect to the fied directions of the incident and the sattered light vectors. The experimental results and the discussion are described below.
2. Experimental
results 2nd discussion
The experimental set up 2nd the details of the scattering geometry for Raman spectra were described elsewhere [I ] _Aq oriented s+$e crystal of KDP was cut and po!ished in the form of 2 cylinder of 2.5 cm length and 2.5 cm diameter witi the cylinder 2xis paraYe to one of the crystiogs2p~~c axes (t&en as they axis). The optical axis, Z, is normd to the cylinder axis. The incident and the sattered light vectors ki and .& respectively, are orthogonal to each other. 4 is the angle between the oFtip 2xis 2nd the vector kj (see fig. 1). The ticident light was polarized normal to the plane of scattering while the s-ccattered light was polarized in ;he plane of scattering. T&us for Q = 0 and 90°, the ntretig
cctigurations
correspond
I September 1975
CHEhIiCAL PHYSICS LETTERS
Volume 35, number 2
Assignment of the observeii Raman active modes in KHzPOs
Mode
Symntetry species
frequency (cm-' j
R2man tensor
Fig I. Rzman sur:ering geometry.
The scrtttern~ng confiiuration .Foran intermediate -saiue of Q is the combination c,f .rcVz)~ and xtj~x)z. Raman spe&ra of the phortons and the interns1 modes of KDP at various values of Q are showa in SJGJ. 2, The spectra t&en with 9 = O” consist of E modesat c:II~~, 113 cm-l, 185 cm-l, and lo z(.yt>v and zt’~x)z, respectively.
and 531 cm-l *, and with 4 = 90” the spectra consist of A, modes at 367 cm-l, 915 cm-l; a B, mode at 473 cm-r, and a B2 mode at 391 cm-r. A broad
continuous band extending from 0” to 100 cm-l in the xQx]z scattering configuration (0 = 90°) is associated
with the law frequency
optical
phonon.
This
band is the well-known overdamped soft mode of B2 type, which is closely related to the phase transition of KDP [3,43.
The assignmenis of the observed modes and their Reman tensor components, as determined from group theoretical considerations, are @en in table I _Modes of E symmetry transform as o,* and cyzXRaman iensor componeilts. They are in close egreement with the observed modes in the spectrum taken with 9 = 0”, corresponding to the z&z)x con~guratio~. Sinrilarly, the group ‘&xx-y allows only B, modes to be present i? the spectra taken with the .~tyx)z ~on~~uration.
However, the spectrum taken at q5= 90° exhibit the presence of A, and B1 modes in addition to the B, modes. Tfle presence of A, modes at 923 cm-r, 367 cm-l
and a BI mode at 437 cm-l is anomalous are not expected to be present in +Ae
as these modes
configuration. Scrutiny of the experimental set up inilicates t&t the presence of these modes is
X(JJY)Z
Frequency
Shif tkm-1)
Fe. 2. Raman spectra of XDP t&en at vxrious vdues of+. The an@, $3,is between the ciystz!logaphic axis and the incident wake vecior. For @ = 0” and 90”, the scztterins co& figurations are zcyY)* anbr(~~)z, p_spectivel~.
not due to the polar&&ion !e&tage. The anomalous polarization behavior of the 915 cm-1 mode has also been observed C-51earlier and has been exphined as being due to the asymmetric ‘~c~ystal f%!d” surrounding the PO:- ion in the KHzP04 crystal. The 9 15 cm-l mode is associated with the breathh,o motion of the PO:- ran ’ perturbed by tie O-H-0 hydrogen bond in the E(Ii2F04 c&Xzi. The A1 mode at 367 ‘.
265 :.
Volume
cm -’
35,l?umber
CHEMICAL
2
and B1 mode at 473 cm-’
with FOG- ion in the KH,FO,
PHYSICS
are also associated
[2j _The asymmetric
“c~iystal field” could introduce the poki&ation anomalies for the mode at 915 cm-l as well 2.s for the mcdes at 367 cm-l and 473 cm-l. As a rssult, the depolarization of t:he scattering from the internal vibration with Al and B, symmetry may occur. This consideration can zlso be used to explain the presence of AI modes at 915 and 367 cm-l and the B, mode at 473 cm-l in the _ycyX)z configuration. According to tijudon [6], the scattering efficienm cy, S, of the &man and infrared active modes in the uniaxial crystal is given by:
(1)
i September
LEl-iERS
process be confined to the xz plane and the scattered light to be approximately irannsverse. The scattering intensities of E and B2 modes in the direction of KS can be evaluated as follows: Consider the E(x) mode in the scattering geometry of fig. 1. The’mode is polarized in the x direction but propagating at an angle of (n/4 - I$) with respect to the x axis. Thus the E(x) mode can be resolved in twc components; a quasilongitudinal component along the #s direction and a quad-transverse component normal to the KS. The scattering efficiency can then be written by the use of eq. (1). We obtain, for the E(x) mode, $
= (a +8)2(~)2(~)2.2cos2(,/4 = (3 cp)2(,:~~)2,2,0,2(,/4-
s; = a2 (e#)’ where R, is an element of the Raman tensor, and ep and ec are the components of the unit vectors along the principal axes, u and p_ [ is the unit vector in the direction of the lattice displacement which dictates the deformation potenti scattering and K is the unit vector in the direction of the electric field which induces the polar scattering. Q and B are the cons+ants of proportionality. (Yis proportional to the lattice displacement uld /3 is proportiona! to the eleciric field strength [6] . In KDP crystsl, the ionic electrostatic forces predominate over the anisotropy in the short range interatomic forces, and there exist quasilongitudinal extraordinary phonons for which the electric t
Bz(z)_
where X, y. or z ii parentheses repreants the mechtica! polariition of‘ the phonon. Let the scattering 266
”
1975
- f$) 9) co&,
(2)
2 Sk? (n/4 - @) co2 $I.
(3)
The subscript II on S means the scattered light is polarized in the scattering plane; the superscripts P and t represent the quasi-longitudinal and the quasitransverse compor.ents, respectively. e1 and e” are the components perpendicu!ar and parallel to the plane of scattering. (The incident and the scattered Ii&t waves are taken as transverse.) In eq. (3), fl= 0 because the quasi-transverse part of the extraordinary phonon has a negi$ible electric field. The total scattering efficiency, S;,, due to the E(x) phonon is the sum of eqs. (2) and (3): Sn = (etei)2
e2 Y3 [( 1 •t O/a)2 cos’(aj4
+ sin2(IT14-@)]
- @)
cos2@.
(4)
Similarly, the scattering efficiency of the B2(z) vibration of KDP crystal can be evaluated. We obtain S, = (e:e:)2d2c2
[(I
+/3/a)*COS~(T/~+Q)
f sin’(7i/4+@)] sin29
(5)
for the B(z) mode. For imulstig crystals, like KH2P0,, the po!ar scattering due to long range e!ectric field effects is small compared to the deformation potential scattering. Namely, in eqs. (4) and (5), ij/(~ < 1. Therefore, we expect that the scatieiing efficiencies of the E(x) and B2(z) modes should exhibit COST@and the sin29 dependences, respectively. Ir? Gg. 3 we have shown the theoretica! curves from eqs. (4) and (5) for different values ofP/~y as a
Volume 35, number Z
I September 1975
CHEhfiCALPHYSICSLETTERS
at 98 cm-’ was taken 2s 5 cm -’ _Our experimental resuIts show “&at for The B~{z) and E(x) modes in KDP the retio ,8/a Is Less than 0.1~ indicating that -the polar scattering mechanism contributed less than t 0% of the total scattering efficiency.
3. Lowest fr2quency optical mode
Fig. 3. Comparison of the theoredcaJ md experiments values for the relative integatcci intensities. Solid curves are tt;eoretiwJ values. All values are normalized to unity for the dat3 at Q = JSO.(al Data for the B?(z) mode at 391 cm-‘. (b) Data for the E(x) mode at 98 cm-‘. Seeeqs. (4) and (5) and the &?Xffor detail.%
function OFthe angle 0. The scattering efEciencies are normalized for the value at 4 = 4SQ such tit2t: S(@ = 45’)
= 1
There is a low frequency optical phonon of B1 symmetry in KDP crystd which has not yet been observed [Z] . This mode is weak and close to the laser excitation line. The low frequency (below 200 cm-l) specrra in fig. 2 exhibit a definite spectral chulge as the ori~nt~tiorl of the crystal is varied from Q = 0” r_o 45’. Spectra taken with higher resolution (0.5 cm-‘) and twenty times higher gain than the spectra of fig. 2 are shown in fig. 4 at + = O”, 12.5”. 15’, 18” and 30”. The presence of a weak mode at 35 cm-l is quite evident in the spectra taken with 4 = 0”. The peak frcquency of the mode shifts towards lower values with
for all values of fi/cr_
Fig_ 3a shows the theoretical curves hcl experimental data points for the B,(Z) modes at 391 cm-l _ The integrated intensity of the 391 cm-l mode was measured from the R;iman spectra of fig. 2. The measured integrated intensities at the various values of Q were also normalized to give unit integrated intensity at # = 45”. This normalization of the integrated &tensity helped compare the experimental values with the theoreticd results obtrtined from eq. (5). Similarly, fig. 3b shows the normalized theoretical curves and
:
I
IO<
Frequency
Skift(cm”)
Fig. 4. Low frequency Razzan spectra of KDP exhibiting the presence of an optical mode below 20 CR>-~. Thz spectr;? in this figure are k!en at twenty times hi&w gain r&&e to the spectra of fii. 3.
267
Volume 3.5,numkd2i 2
1 September
CHEBIICALPHYS~CSLE~ERS
the rotation of the crystal to smaller 13vdues. Ai # = 30" this mode.& overlapped by the stiong E(x) mode at 98 cm- t _This is the first eTrider.cereported of the lowest frequency optital phonon mode (> 20 cmWi) in the KDP crystal. This optical Iattice -mode (> 20 ~rn-~)need not be confused with th B, mode at 80 cmvi, as obrakenai I$= 909 corresponding The spectra in fig. 2 show that the lowest frequency optical lattice mode is present for @= 0” to 30”. The spectra taken at Q = 75” and 90° exhibit the B2(z) mode at SO cm-t. According to She et al. [2], the low frequency opiical phonon has BL symmetry and is thus only Raman active. The large anomalous frequency shift (see fig. 4) of this mode with respect to the change of 4 indicates that the lcng-rxrge dipole-dipole interaction may dictate the behavior of this mode. Since the long-range &polar interaction is more dominant at a small scatteri:l?g angle, it would be of great interest to examine the low frequency spectra as a function of $5for small scattering angles. served in the spectra
to thax~x)z configuration.
4. Conc:usions
By studying the angnlar dependent Ramnn scattering spectra, it has been shown that the contribution
I975
of the long-range electrostatic interaction is less than 10% of the scatter@ efficiency of the E(x) and Bz(z) inodes in KDP. We have q&o found, for the first time, a low frequency optic4 phonon in K.DP,which was previously predicted theoretically. Thislow frequency mode shows an anomalous freq.uency shift towards smaller vdues as the angie between the optical axis relative to the incident light propagation direction is decreased_ It is suggested that an experiment carried out at a small scattering angle. should show enhanced anomalous behavior.
References [I] h1.K. Srivastava and C.H. W’ang, Breakdown of Selection Rules
in
the
Ra.mul Spectra of KDP, J. Chem. Phys., to
be published.
[Z) C.Y. She, T.W. Brobsq and D.F. Edwards, Phys. Rev. B4 (1971) 1580. (31 LP. Kaminotv and T.C: Damen, Phys. Rev. Letters 20 (1968) 1105. [4] C.M. Wilson and HJ. Cummins, in: Proceedings of the Second International Cortference on Light Slztterine in SoLids,ed. kf:. Balkanski (Flammarion, Paris, 1971) p. 420. [S] hi.K. Srivastava, R.W. Grow and C.H. Wang, C&em. Phys. L&rers 26 (1974) 157. [6] R. Loxdon, Advan. Phys. 13 (1964) 423. [7] A.S. Barker Jr. ami K. Loudon, Rev. Mod. Phys. 44 (1,072) 18.