PHYSICAL REVIE%' 8 VOLUME 35, NUMBER 16 1 JUNE 1987

High-pressure Raman study of the vibrational modes in A1PO4 and Si02 (a-quartz)

A. Jayaraman, D. L. Wood, and R. G. Maines, Sr.ATILT Bell Laboratories, Murray Hill, Aeu Jersey 07974

(Received 10 October 1986)

The pressure dependence of the optical-phonon frequencies in berlinite (AlPO4) and a-quartz hasbeen investigated by high-pressure Raman scattering experiments, using a diamond cell; berlinite wasstudied up to 12 GPa and u-quartz to 20 GPa. The Al soft phonon mode at 216 cm ' in AlPO4and the corresponding mode in a-quartz at 206 cm ' exhibit similar but anomalously large and non-linear pressure dependences. Further, these two modes exhibit striking decreases in their widths withincreasing pressure. These changes appear to be connected with the decoupling of the strong anhar-monic interactions of the 2 1 soft mode phonon with the two-phonon (acoustic) states in o, -quartzand with one-phonon (optical) and two-phonon (acoustic) states in AlPO4. Pressure experiments helpin distinguishing the relative strength of these interactions in the two materials. The mode-Gruneisenparameters have been obtained and, again, the 3

&soft mode has a large y;, namely, 3.45 in AlPO4

and 4.32 in a-quartz. Using refractive-index matching with o.-quartz and AlPO4, the n (P) of a 4:1methanol-ethanol mixture has been evaluated.

INTRODUCTION

Berlinite (A1PO4) is isomorphic to a-quartz (D3 ) andundergoes the same temperature-induced a-P transition asquartz near 850 K. ' Further, A1PO4 can be preparedin the other we11-known crystalline modifications ofSiOq, ' viz. , tridymite and cristobalite, by high-temperature treatment. In view of these close structuralsimilarities between A1PO4 and Si02 at ambient pres-sure, ' a close correspondence in high-pressure behaviormay also be expected for the two systems.

High-pressure Raman studies oAer a very sensitivemethod to probe phase changes as well as subtler changesin bonding induced by pressure, apart from enabling oneto collect information of interest to lat tice dynamics.Therefore, we undertook a high-pressure Raman study ofA1PO4 and have studied the optical phonons to 12 GPa.To our knowledge no high-pressure Raman investigationhas been reported for A1PO4 in the literature. We havealso investigated a-quartz (SiOq) to 20 CxPa, although thissystem has been previously studied by others. Ourpurpose was to determine the high-pressure behavior ofthe Raman modes in quartz for a close comparison withA1PO4. These results will be presented and discussed inthis paper.

EXPERIMENTS

Pressure was generated using the diamond-anvil celland calibrated using the ruby-fluorescence technique.For the pressure medium, a 4:1 methanol-ethanol mixturewas used. Raman spectra were obtained with a Spex dou-ble monochromator equipped with a conventionalphoton-counting system. For excitation the 488.0-nm linefrom an argon-ion laser was used. The laser power was inthe range of 100—200 mW.

Samples of synthetically grown A1PO4 in the form ofcrystal plates were available to us. ' Fragments from

the crystal plates were loaded into the diamond cell forrecording the Raman spectra. Since the fragments wereof unknown orientation with respect to the crystal axes,polarization measurements were not attempted. ExcellentRaman spectra, with peaks in the expected positions, "were obtained with 488-nm excitation.

In the case of quartz, platelets from a thin cross-cutquartz-crystal plate 75 pm in thickness, originallyprepared for ultrasonic generation at 40 Mc, were loadedinto the diamond cell. With 75-pm-thick platelets, wecould only go up to 60 kbar, before the diamond Hats con-tacted the quartz sample. For experiments at higher pres-sure, small fragments were obtained from a syntheticallygrown large quartz crystal. These fragments were againof random orientation, and pieces that were 20—30 pm inthickness and 50—70 pm in linear dimensions were select-ed for mounting inside the diamond cell. Gasket blanksof full hard T301 stainless steel were indented to a thick-ness of 75 —90 pm and then a 200-pm-diam hole drilled init.

RESULTS AND DISCUSSION

Although berlinite is isomorphous with quartz, its unitcell is doubled along the c axis, owing to the substitutionof Al and P ions in alternate Si sites. ' This situationbrings the q = (0, 0, vr/c ) quartz zone-boundary phononsnons into the zone center in the case of A1PO4, resultingin a richer Raman spectrum for AlPQ4 compared toquartz. Scott" has identified these features in the spec-trum of A1PO4. Group theory predicts" 8I ~ + 17I 3

Raman-active modes for A1PO4 and 4I ~+8I 3 modes forquartz. Inclusion of electrostatic split tings result in8I ~+17I 3(TO) + 17I 3(LO) modes for A1PO4 and41 ] +SI 3(TO) + SI 3(LO) for quartz. ' ' (The I

&corre-

spond to the totally symmetric 2 ~ modes and the I 3 tothe doubly degenerate E modes, in the chemical notationfor describing the mode symmetry. )

35 8316 1987 The American Physical Society

35 HIGH-PRESSURE RAMAN STUDY OF THE VIBRATIONAL. . . 8317

The pressure dependence of thee o the observed Raman peaksin 4 and n-quartz are shown in Figs. 1 and 2. Inthe case of AlPO4, we are able to follow 1e o o ow 11 Raman peaks

p aks were followed upa, while in quartz 8 ea. able I lists the observ

4 and o.- uartzv;(dv;IdP), where B is th b 1k

y;= o/o is e u modulus, v; is the h-

non frequency, and dv;/dP is its rep pe rom ow-pressure data.

It hhas been pointed out in the case ofdes h"h h bic ex i it a strong tern erature

precisel th hy ose t at show a stronp ure dependence are

ng pressure dependence;mo es in question being the ones at 128, 206, and 465

cm '. The same is true for AlPO4, and the correse, 6, and 460 cm '. Amarkable feature in Fi s. 1

pressure sensitivities exhibited by the 216-cm4 - q4 e -cm mode ofa arge initial increase in frequency with rcy wi pressure

behavior is thus hi l

n ou at ig er Dressures.s us ig ly nonlinear, as noted in the ver r-

cent pressure Raman stud oftern

s u y o quartz. Previous hi h-emperature investigation t b'

g-

shown that these modes b hs a am ient pressure' ' have

e ave anomalously as th

p ase transition is approached the h'

shapes br dey ex ibit unusual line

roa en unsymmetricall and~

y, so ten with temper-e etai ed behavior of these modes wit

ature has been int d'

erpreted in terms of anes with temper-

tion betwd of an..armonic interac-

600

E

300—V)

X

200—

ARTZ)

~ ~

~ ~ ~

I 00—

I I I

20 40 60 80 I 00 I40 I60 IBO 200PRESSURE (kbat')

FIG. 2.. 2. Pressure dependence of the hquartz.

o e phonon frequencies in e-

I I IOI I 00I 090

500

400

E

300CA

200

100

0 IO 20 30 40 50 60 70 80 9090 I 00 I IO I 20PRESSURE (kbar)

FIG. 1. PPressure dependence of the honberlinite (A1PO4).

o e phonon frequencies in

The E modes of AlPO4 at 372small ne ative sl

4 a and 382 cm ' have anegative slope and consequently have a ne

and 401 cm ' behave similarl . Butigh-frequency 3 mod f AlPO

od' t de o 04 at 1110 cm

uarz mo e at 1085 cm ' abehave diA'erently. Wh h

cm appear toy. ereas the former has an

ative slope and a broadan initial neg-

a roa minimum, the latter has a osi

uar z ecreases in fre uenctially and th

q cy with pressure ini-en increases, exhibitin a broa

odi H lo em ey. Thus, in terms of the~ I

' pe -cm mode of AlPO4 and the 1160-

cm mode of quartz seem to be the corresand not the 1085 cm

e e corresponding modese 5 cm of quartz and the 1110 cm ' of

AlPO4. At pressures above 12 Gobtain a spectrum with AlPO alth

'~

ove Pa it was im ossible

quartz there4, although in the case of

z ere was no problem in followink o20GP h.-d, (.h. ---a, t e limit of ress

e experiments were terminated at 20 GPbecause the methanol-eth l urne-e ano pressure medium turnenonhydrostatic above 20 GP

urned so

showed splittings and l - he a that the Raman peaks

g . p ittings duen ine-s ape chan es. S liress can be seen in Fig. 2 even abov

GPa; see particularly the 128-cmabove 12

a. emley has reported amorphization of uartzder pressures above 30 GPa, and aeven with Ar

a, and apparently this happensr as a pressure medium, as ud e

man spectrum of thes ju ged by the Ra-

o e sample. Because of the difficulty in

8318 A. JAYARAMAN, D. L. WOOD, AND R. G. MAINES, SR. 35

TABLE I. Observed Raman modes, and mode-Gruneisen parameter y; for AlPO4 and a-quartz.AlPO4, Bo ——287.0 kbar, calculated from the elastic constants. a-quartz, B0=371 kbar. The values inparentheses are from Ref. 6.

(cm—')

AlPO4 (berlinite)dv; /dp

(cm '/kbar) (cm ')

SiOz (quartz)d R;/dp

(cm '/kbar)

160216334460

1110

Al modes0.02.60.21.0

—0.5

03.450.170.62

—0.13

206355464

A 1 modes

2.40.050.8

4.320.050.64

(3.63)(0.03)(0.66)

105116

372382416436

E modes0.70.8

—0.1

—0.1

0.40.9

1.91.98

—0.07—0.07

0.270.59

128264394401

450

E modes

0.60.600.1

0.05

1.70.8400.09

0.04

(1.64)(0.65)

( —0.03)

(0.52)

observing any Raman peaks in AlPO4 at pressures above12 GPa, we suspected a change to a glassy state in A1PO4.However, on release of pressure the original crystallinespectrum reappeared, but somewhat reduced in intensity.Although we do not know the reason for the reduced in-tensity, the experiment weakens the argument for achange to a glassy state, in the case of A1PO4 ~

An interesting observation in connection with pressuri-zation experiments on AIPO4 and quartz in methanol-ethanol is the vanishing of the crystals in the pressuremedium due to the refractive-index matching. This is soremarkable that even the birefringence of the crystal couldbe distinguished and matched from the movement of theBecke line which gives a very good indication of the rela-tive differences in the refractive indices between the medi-um and the crystals. At room temperature the eD indexof quartz can be perfectly matched at 72 kbar and similar-ly, the eD of AIPO4 (berlinite) can be matched at 56 kbarpressure. When the quartz index is adjusted for 72 kbarusing the low-pressure data, ' we obtain n=1.59 for theindex of the 4:1 methanol-ethanol mixture at 72 kbar.

Polian et al. ' have evaluated the n (P) for 4:1methanol-ethanol mixture by first fitting the density dataof Bridgman to Tait's equation of state (EOS) and thenusing the function relating Eulerean strain to the n (p).To a very good approximation

n (p) =n (po) —0. 571[1—(popo) ] .

In Fig. 3 we show n (P), by following the same procedure,but putting the constraint that the refractive index (n) ofthe mixture should equal 1.59 at 72 kbar. This necessitat-ed using Bo——0.7 GPa and 80——10.1 in the Tait EOS tomatch the above point. We believe that the n (P) given inFig. 3 may be useful in optical measurements at highpressures.

PRESSURE AND THE A i SOFT MODE

I.7—

xDJC5

L QUARTZ

LLJ

l.5C3

l.4

I.3 '

0I I I I I I I

6 8 I 0 I 2 I 4 I6 I 8 20PR ESSURE (GPO)

FIG. 3. Refractive index of 4:1 methanol-ethanol mixture as afunction of pressure computed from n (p) relationship andBridgman's p-vs-P data. The u-quartz constraint point is shown.

The temperature dependence of the low-frequencymode in quartz has been of great interest from the stand-point of the mechanism triggering the a-/3 transition inquartz near 850 K. Raman and Nedungadi ' discoveredin 1940 that this mode underwent anomalous broadening,and decreased in frequency as the a-P quartz transitionwas approached. Since then, the connection betweensoft-mode behavior and phase transitions in crystallinesolids has received much attention, both experimentallyand theoretically. '

35 HIGH-PRESSURE RAMAN STUDY OF THE VIBRATIONAL. . . 8319

Scott investigated the temperature behavior of the softA ~ mode in quartz' as well as A1PO4 (Ref. 14) up to thea /3 -transition point and proposed that in quartzlike struc-tures there is a strong anharmonic interaction betweenone-phonon states and between one-phonon and two-phonon states. In the model for quartz, the 206-cmmode decreases in energy with increasing temperature andoverlaps a two-phonon (TA zone-edge phonon) band cen-tered around 147 cm ', interacting with it strongly. Theanharmonic coupling between the optic mode and thetwo-phonon state broadens the optic phonon anomalous-ly, by providing a relaxation mechanism for decay intoacoustic-phonon pairs. A Fermi-resonance-like interac-tion that occurs in gas molecules such as H20 has beensuggested for the anharmonic resonance between the one-phonon and the two-phonon states.

In the case of A1PO4, Scott' discovered softening ofthe 216-cm ' mode with increasing temperature andanomalous changes in line shape and linewidth, as the a-Ptransition was approached. To explain the results, he in-voked two mechanisms: a strong anharmonic coupling ofthe 216-cm ' 3

~mode with another one-phonon state

near 160 cm ' of the same symmetry, and also an anhar-monic interaction with a two-phonon (zone-boundaryacoustic-phonon) continuum. Accordingly, above 400 Ka striking anharmonic interaction between the soft modeand the 3 ~ phonon near 160 cm ' occurs which isdescribable via a Careen's-function treatment, or in termsof a Fano-type formalism. ' The interaction between theoptical phonons apparently is via the anharmonic termslinking each of the phonons to the two-phonon (acoustic)continuum. The second anharmonic coupling arises froman interaction of the same type as in quartz, between theone-phonon state at 216 cm and a two-phonon (acous-—1

tic) band centered around —140 cm '. Using a Green's-

function technique, Zawadowski and Ruvalds calculatedthe spectrum for two optic phonons interacting via anhar-

monic coupling to two acoustic phonons, and demonstrat-ed the antiresonance characteristics in the single-phonondensity of states, which is in excellent agreement with theobserved features in the first-order Raman spectrum ofA1PO4. ' In Fig. 4 the different phononic interactionsdiscussed above are shown schematically for normal pres-sure and at high pressure ( —S.5 GPa). The point torecognize here is that quartz and A1PO4 present some-

what different coupled-mode interactions and we believe

that the pressure behavior of the soft mode (216 cm ' ofA1PO4 and 206 cm ' of quartz) reffects this difference,

particularly the effect of pressure on the linewidth.

In Figs. S and 6 are shown the pressure behavior of the216-cm ' mode in A1PO4 and the corresponding mode inquartz at 20 cm ' recorded at room temperature. The206-cm ' mode in quartz sharpens somewhat and shiftsrapidly to higher frequency with increasing pressure.(Similar changes in linewidth have been noted by Deanet al. in a recent low-temperature Raman study ofquartz. They found a considerable narrowing of the 206-cm ' peak on lowering the temperature to 77 K and asmall shift to higher frequency due to thermal contractionaccompanying cooling. ) By comparison, the effect of pres-sure on the 216-cm ' peak in A1PO4 is much more strik-ing (see Fig. 5). The linewidths at half maximum aremarked on the right-hand side of the peak in Fig. 5.There appears to be also a change in the backgroundscattering continuum in the low-frequency region of thespectrums, which is also seen in Fig. 6 for quartz. Theeffect of pressure on the phonon energies is shownschematically in Fig. 4. We believe from our results thatthe anharmonic interaction between the two A ~ opticalphonons in A1PO4 is there even at room temperature and

TWOPHONON

BAND TWOPHONON

BAND

TWOPHONON

BANDTWO

PHO NONBAND

NHARMONCOUP L IN

A, R

(206A1 R280

-ZBcm '

A, RA

(-16O216 cm AM Ocm AMAN

cm-')

QUARTZ QUARTZ (HP)( DECOUPLED)

AQPOp A/PO (HP)( DECOUPLED)

280

206 RAMANPEAKS

(QUARTZ)2I6

RAMANPEAKS

(ARPO~)

FIG. 4. Phononic interactions involving the 2 1 soft mode and one- and two-phonon states in quartz and A1PO4. The eft'ect of pres-sure on the levels are shown on the right in each case and the observed linewidths at the bottom. High pressure is indicated by HP.

8320 A. JAYARAMAN, D. L. WOOD, AND R. G. MAINES, SR. 35

279

A/ F04(BERLINITE)

Sio,(a- Qu

143 158

287

142

56 kbar

CA

Z'

117 138

113

251

ts kbar

V)

LLJ

Z',

33k

16 kba

-2. kbar

l27

205

-Ikbar

100 150 200 250 300RAMAN FREQUENCY SHIFT (Cm-I)

350 100I I

I

I 50 200 250 300RAMAN FREQUENCY SHIFT (cm-1)

I

350

FIG. 5. Effect of pressure on the low-frequency phonons inAIP04. . The striking changes and shift of the soft 3 l mode (216cm ' at 1 bar) is to be noted. The half-width at half maximumis marked on the peak.

FIG. 6. Effect of pressure in the low-frequency phonons ina-quartz. Note the change in the linewidth of the 3 I mode near205 cm

this is the dominant mechanism that contributes to thelinewidth of the A~ soft mode (216 cm ') at normal pres-sure. With increasing pressure the soft A~ phonon andthe A~ phonon near 160 cm ' move rapidly away fromeach other and consequently get decoupled. Further, thiswould be true even if the two optic phonons interact viathe two-phonon continuum, since the overlap of theoptic-phonon state with the latter also rapidly decreaseswith increasing pressure (see Fig. 4). In the case ofquartz, there is no low-frequency 3

&phonon and the line

shape is mainly determined by the interaction with thetwo-phonon band. It is also to be noted here that the a-Ptransition temperature is moving farther away rapidlywith increasing pressure, since dT/dI' for the a-P phasetransition is very large and positive. The observedchanges would be quite consistent with this.

SUMMARY AND CONCLUSIONS

We conclude the following:(1j From the pressure dependence of the optical pho-

nons in A1PO4 and SiO2, it is clear that the modes whichexhibit a strong temperature dependence are also stronglypressure dependent.

(2) The pressure dependence of the soft A~ mode in

A1PO4 and in a-quartz are strikingly similar. Both showa large initial increase in frequency and rapidly flatten out

at pressures above 5 GPa. Thus, the frequency-versus-pressure behavior is highly nonlinear.

(3) Further, these two modes exhibit striking changes inwidth with increasing pressure. In AlPO4, the half-widthat half maximum decreases from about 20 to 7 cm '. o.-quartz also exhibits a large change, although not to thesame extent.

(4) Pressure decouples the strong anharmonic interac-tion of the soft A, mode with one-phonon (optic) andtwo-phonon (acoustic) states in A1PO4, and two-phonon(acoustic) states in a-quartz. However, from the morestriking changes in the observed linewidth with pressurein the case of AIPO4, we conclude that the anharmonicinteraction with the one-phonon state ( A

~ optic phonon at160 cm ') is the dominant mechanism responsible for theline broadening in AlPO4. In quartz there is no low-frequency optic phonon of the same symmetry and theonly mechanism influencing the linewidth is the anhar-monic interaction with the two-phonon (acoustic) state.Thus, pressure helps to discriminate the difference in thetwo cases.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge illuminating discussionswith Dr. Paul Fleury on the subject of phonon-phonon in-teractions and soft-mode behavior. We wish to thank Dr.G. Kourouklis for useful comments and discussions.

35 HIGH-PRESSURE RAMAN STUDY OF THE VIBRATIONAL. . . 8321

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