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Spectroscopic investigations of phase transitions in complex solids
Journal of Moiecular Structure, 292 (1993) 229-254 Elsevier Science Publishers B.V.. Amsterdam
Spectroscopic complex solids
investigations
229
of
phase
transitions
in
C.N.R. Rao, Solid State & Structural Chemistry Unit and CSIR Centre of Excellence in Chemistry, Indian Institute of Science, Bangalore 560012, India
Abstract Spectroscopic methods have provided information of seminal importance in understanding phase transitions in solids. After briefly examining some fundamental concepts related to phase transitions, we shall discuss several case studies particularly involving the use of vibrational (IR and Raman) spectroscopy. Examples will include both order-disorder and displacive transitions. Under the former are included transitions in nitrates, ammonium halides, alkylammonium salts, plastic state of C6U and superionic conductors (specially CsHSOq). In addition, we shall discuss some aspects of incommensurate phase transitions, the glass transition and electronic phase transitions. Transitions of phosphonitrilic halide tetramers and alkane dicarboxylic acids are also examined.
1.
INTRODUCTION
The topic of phase transitions is one of vital interest to scientists working in diverse areas from theoretical materials techphysics to few nology 111. In the past variety of phase decades, a have been investransitions resulting in major tigated advances in the understanding of the phenomena associated transitions with phase the systems. Phase of diverse and transitions in solids associated structural changes first-order can occur in a a reconstructive fashion by mechanism or by means of a slight distortion of the 0022-2860/93/$06.00
0 1993 Elsevier Science Publishers B.V.
lattice through small displacements or ordering of the constituent atoms or molecules. Even during ordering there can be a displacive component just as there can be an ordering component in a displacive transition. The main types of structural phase transitions are the following: Order-disorder, e.g. molecular reorientation (NaN021, tunnelling of protons in Hbonds (KDP) Displacive, e.g. ferro-, anti-ferrodistortive and ferroelastic transitions
Electronic, All rights reserved.
e.g.,
spin-
230
wave charge-density state, transimetal-insulator and tions. Many of the molecular cryscrystals well as tals as ions molecular containing tranundergo order-disorder displacive with a sitions g-triazine, component (e.g. There are ammonium halides). several cases where the hightemperature phase of a solid is orientationally disordered and ordering results in rotation-translation coupling with both displacive or/and orderFerrodisorder regimes. distortive transitions involve displacements corresponding to optic length a long-wave phonon (hence z = z') while distorantiferrodistortive tions involve zone boundary ferphonons (hence z +nz); roelastic transitions involve acoustic phonons. Some of the ferroelectric solids show the first two types of transitions. Spectroscopic investigations transitions in of phase the solids generally involve temperature measurement of or pressure dependent changes features in a certain of spectrum characteristic of at phases the one of least Speca transition. across provide methods troscopic information on static as well processes occuras dynamic a transition, during ring complementary information on the former being provided by While diffraction methods. magnetic resonance methods, by and large, are more appropriate to study local dynamics,
inelastic scattering and IR absorption methods are useful to examine collective dynamics [2,31. The vibrational spectroscopic techniques employed are light scattering, inelasand tic neutron scattering IR absorption. Light scattering techniques include elastic scattering, Bril(Rayleigh) scattering louin (by sound waves close to the frequency and photon) of the incident scattering. Inelastic Raman suffers scattering neutron from disadvantages such as volume, poor sample large long measurement resolution, Optical spectroscopy time. disadvantages have methods such as selection rule remore are but strictions, readily used for the study of valuphase transitions and the on information able structural and mechanistic transitions aspects of phase has been obtained by these techniques. this presentation, we In examine spectroscopic shall important some studies of phase structural cases of involving disortransitions der-order as well as displaBecause of cive mechanisms. subthe the vast scope of the choice of systems ject, had necessarily to be subjective reflecting the speaker's personal interests. We shall not deal with transitions in superconductors and ferroelecbe these will since tries dealt with in detail by other in special lectures speakers shall devoted to them. We however examine phase transitions of Buckminsterfullerene,
231
'6 I which has become a molecu Pe of great excitement in recent months. We shall also explore some cases of electronic transitions and certain phase transitions of chemical discussing Before interest. the various phase transitions we shall ~briefly review some important concepts related to phase transitions. 2. SOME IMPORTANT CONCEPTS phase Thermodynamically, transitions are classified as order desecond first or the whether pending first derivzive of the Gibbs' disconvaries free energy continuously tinuously or The across the transition. used to parameter important characterize a .transition is the order parameter, 5, which observable usually an is of the system (e.g. property mode frequency). vibrational order parameter varies The differently with the thermodynamic variable (T, P) depending on whether the transition order. second is first or provides the Landau's theory under conditions symmetry which structural phase transithe latoccur. From tions tice dynamical point of view, an important aspect of structransitions is phase tural that of the soft mode wherein a vibration mode goes to zero frequency at T, : w=
w,(T-Tc)l"
(1)
Note that the order parameter also varies similarly. 5 =
cJTc-T)1'2
Eqn (1) represents the soft mode behaviour of a displaIf one incive transition. cludes anharmonic terms the mode behaviour is given soft by, 02 = AT + A(T-T,)
(3)
The anharmonic contribution becomes large in the orderthe where limit, disorder atomic displacements are also large. and light Both neutron have measurements scattering phase certain that shown only not are transitions associated with an inelastic due to the soft component phonon but also a quasi-elastic component whose intensity and dominates grows as T+T, around scattering the TE’ , componen The quasi-elastic called the central peak, has been explained based on varmodels theoretical ious mode (coupling of the soft thermal relaxation, imputo rity or surface effect, inassociated property trisic with clusters of the new phase in the old phase. of An interesting aspect phase tranmany structural sitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational In Jahnor libration modes. Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is strain (acouswith coupled antiferro In tic phonon).
232
distortive transitions, a zone boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). transitions phase Many (generally of second order) are characterized by a critibehaviour cal point and the point is critical at the expocritical described by nents. All macroscopic properties are then expressed as a function of [(T-T,)/T,l raised the critito some power. In flucregion correlated cal the order paramtuations of eter cause a break-down of theory. mean-field Landau's been major theohave There underadvances in retical phenomena critical standing the concepts include which and universality of scaling and the use of renormalization group theory. There is a special class of structural phase transitions where the distortion (primary cannot be order parameter) fracexpressed as a simple latreciprocal tion of the Such an incomtice vector. mensurate phase has no translation symmetry and becomes dynamically disordered at high In systems with temperatures. quasi one- or two-dimensional charge density waves, modulation of the charge density at the Fermi wavevector forms an incommensurate CDW which couples to the lattice to produce Such periodic distortion. a associated are transitions change from metallic -with a to insulator behaviour (e.g. Peierls transition).
3, ORDER-DISORDER TRANSITIONS transitions Order-disorder motions molecular involving investigated by have been methods, typiNMR and NQR and cal examples being NaNO etra2 layered alkylammonium the chlorides of type (' H2n+lN!$2~t~on~l =s~~;t~~; Mnf. have been studies scopic of carried out on a variety crystals such as KCN, NaCN, perovskite nitrates, metal etc. The compounds layer transitions of NaCN and KCN (at 288K and 168K respectively) involve the orientational and ions disorder of CNexhibit a large decrease in elastic constant at T, the C t41, ii4emonstrating the softening of the long wavelength transverse acoustic phonon 151 Coupling as shown in Fig. 1. (strain) between translation parameter order the and ions) (reorientation of the the orientational influences the CNamong interaction ions. 3.1 Nitrates: Optical spectroscopic studtransitions in ies of phase metal nitrates have yielded results. RbN03 interesting undergoes several phase tranorientathe sitions where tional order and dynamics of the orientational state of NOT play a crucial role. Thus, in the Raman spectrum of RbN03, raised as the temperature is above 3OOK, the libration mode the decreases as frequency line width increases, just as in NaN02 [61. The linewidth
233
Thus the V-IV transiture. the 255R removes tion at splitting of the v3 Raman band transition V-VI The 181 with the is associated softening of the NO. tion mode at 112 fm-lli';'s;Based on the Raman bands of NH3D diluted isotopically different species in phases, the point group symmeconsidered try of NH; is to be C2v in IV and III and Infrared C3v in I101 changes spectra [f7: show these findings which support symmetry and suggest a Td high temNHd in the for perature phase I at u400Kt In (< 255K), degeneraphase V ties of the \I.+(T) and vi (T) modes of N4 4 as well as of the V (E') and V4 (E') lifted in modes of N% - are the infrare d ; even the+ v; are vi bands of NH and found in the IR spec% rum of In the IR spectrum of V. weak the v4 band becomes II, while the copbination bands involvin_f NH4 libration (vi z 400 m 1 present in V disppear even in IV. In the IR spectra of ,I, v4 v1 and weak are very bands of NO3 suggesting a nearly D3h symmetry for the anion. l
l
T-T,(K)
FOE. 1 Plot of the square of2the TA phonon frequencyof NaCN, w (llO), obtainedfrom Brillouinscattering against(T-Tc) (afterSatijaand Wang [51) i.s,stven by, r_= a+bT+CT/(l+ where T is the orientatime: the tional relaxation actixation barrier is u 39 kJ mol . IR spectra show changes on going from 300K through the IV-III and higher temperaFor ture transitions [71. example, the splitting of the modes disappear and V v3 across the f V-III transition suggesting a change in point symmetry from C2v to group NH NO undergoes several c. associated pil Xse t!aniitions with the orientations of NH; bonding hydrogen and NO;, between the two ions playing a role depending on the tempera-
3.2 Ammonium halides: NH Cl and NH4Br undergo order-disorder firs f-order transitions around 240K involving the flipping of NH4f tetrahedra' between two orientations related by an inversion. There is no external these with associated mode libr tion The transitions. mode of NH4Br varies as w 8= A+
234
In the IR spectra, strong peaks some of the high-tempedisappear in the disordered phase. rature Interestingly, the strength of libration mode BE El11
l
indeed interesting. NQR iita on these halides have obtain also been employed to information on the temperature the dependence of order parameter. Alkylammonium salts: 3.3 Alkylammonium tetrachlorides of the type (CnHZn+lNH3)2MClq containetc.), (M = Cd, Mn (with ing perovskite layers
"1
the alkylammonium groups occusites and the pying the A M ions the B sites) exhibit structural phase transitions which have attracted considerable attention of both magnetic resonance and optical spectroscopists. Interlayer interaction is weak in these halides. The parent phase stable at high temperature is tetragonal with the Il/mmm-D 7 space group and orienta!?ional disorder of the alkylammonium group is necessary to get the hightemperature tetragonal structure. There is increasing ordering at low temperatures. Thus the temperature-dependence of 35C1 NQR measurements
=n2= n3=n4= i/4 ---
n,>n2=
n4’n3
-----_-_-
_
Tc,=484K(Cd) -1
-Tc2= 279 K (Cd) nl = n2> n3=n4
-------_--
pq Tc,= 163 K (Cd)
n,=l n2=n3=n4=0
)-Eq
Fig.2 Model for the orientational disorder of CH,Nq groups in (CH NH ) CdCl (afterKind et al [14]. In the-tetEagonal high of the C-N bond are equally tem~erAx&e pl+ase,the orientations distributedamong four energetically equivalentorientations (n1 =n 2 = n3 = n4 = *)
235
[I21 onth~H~~~~%~_*~d~&l tf;;w
phase of (CH3NH3)2MC14. Dis;f;der in these compounds fects not the organic only part, but also the inorganic part by means of coupling due to N-H... .Cl hydrogen bonds which give rise to shortrange ordering. Infrared spectroscopic studies of the phase transitions of alkylammonium halides, RNH3X, as well as of (RNH3) MX4 where x= Cl or Br have %Ieen carried out 1161. The hightemperature phase (> 264K) of CH3NH3C1 where disorder occurs because the C-N bond coincides with the 4-fold axis of the crystal does indeed show an infrared spectrum characteristic of undistorted CH3NHi(C ,); besides the various mo a e splittings, the low-temperature phase shows t e C-N torsion mode at 480 cm- P . Undistorted CH3NH; ions, as evidenced
that sition around 394K is related to the change in the asymmetry of the motion of the CH3NH3 the difference in the group: frequencies between the NQR phases shows a critical two behaviour. Disorder dynamics C-N bond directions in the across the transition in KHaNH3) 2CdC14 has been examine by proton-nitrogen double resonance measurements: proton second moment and Tl measurehave also thrown light ments on the transitions of these compounds 1133. In Fig. 2 we show the model accounting for orientational the disorder Extensive Raman studies Cl41 have been carried out on these alkylammonium chlorides 1151. Pressure experiments show that a displacive mechanism due to a shear mode is operative in the high pressure l
--I
.
cm 1600 1500 I I
(a)CJ
,, ,
1600 I
1500 I
(b) Mn
,, ,
1600 I
1500 I
(c)Cu
Fig. 3 Infraredspectraof (CH3NH3)2MC14 (afterRao et al [16])
236
L
,.
I
1
I
1
1200
1600
3500 3000
’
I
I
I
I
800
400
300
200
loo
1
Wavenumber (cm-‘)
Fig. 4 Infrared spectra of (CH3NH3)2Sb2Clq (after Varma et al (171)
I
I
100
Roman shift Fig.
I
I
200
300 (cm-‘)
Anion modes in the Raman spectra of [(CH3),NHl,Sb,C19 (after Varma et al [171) 5
from the IR spectra, are also seen in the high-temperature phases of (CH3NH31MC14 (Fig. Alkylammonium bromides 3). and the corresponding alkylammonium tetrabromometallates show IR spectra reflecting phase transitions characteristics similar to those of the chlorides [16]. Infrared and Raman spectroscopic investigations have been carried out recently on the interesting phase transitions of methylammonium haloantimonates of the type [N(CH3) _ Hn13Sb2X9 where n = O-3 an$1 = Cl or Br 1171. It has been shown that the vibration modes due to CH3 deformation as well as those involving theNH (n= 1, 2 and 3) groups sg ow significant changes across the phase transitions besides those due anion (Figs. The anion modes differ with the number of CH groups since the nature of thi anion itself changes, the free anion being present only in the quarternary compound. High-temperature phases of the chloroantimonates seem to involve random orientations of the methylamino groups. A new phase transition is predicted in all the chloroantimonates below 15OK, based on the changes in the anion bands at low-temperatures (see Fig. 5 and also the lowfrequency region in Fig. 4). Changes in the infrared and Raman spectra accompanying the phase transitions of (CH3NH3j3 Sb2Brg and (CH3NHf13Bi2Brg are similar and in t e high-temperature phase of these com-
pounds the (CH3NH3)+ cations are oriented randomly, possiwith point bly group c3v symmetry. 3.4 Plastic state of C6 : Many molecular crysta Ps of globular molecules exhibit an orientationally disordered or a plastic state close to the melting temperature. The rotational motion is generally hindered and the molecule has to overcome a potential barrier during reorientation. In the low-temperature orientationally ordered phase, molecules librate. IR and Raman spectroscopy as well as magnetic resonance methods have been employed to investigate the plastic state in several systems. Dielectric spectra due to the rotational and librational motion have also been studied. We shall examine here the plastic to crystalline transition exhibited by buckminsterfullerene C60. X-ray diffraction, differen'al scanning calorimetry and $3C NMR reveal a first-order phase transition from the fee (space group Pm31 phase to a simple cubic (SC) P2 /a3 phase around 250K 1181. B 0th x-ray and NMR studies suggest that this transition is related to orientational ordering of the molecules in the SC phase. %: molecules rotate ‘60 freely In the fee phase whereas in the SC phase, they perform jump-diffusion between nearly degenerate orientations separated by a potential barrier. This barrier has been determined to be u 260 meV from the temperature and time-dependence of the
238
thermal conductivity as well as from the frequency-dependence of sound velocity and This value of attenuation. the barrier is close to the theoretical estimte of m 300 meV obtained from a simple free-energy model incorporating the intermolecular interaction in the form of the Lennard-Jones potential as well as the Coulomb interaction. The latter takes into account the charge-transfer between the electron-excess "double" bonds (bond-length .~1.40A’) and the electrondeficient "single" bonds (bond-length u 1.45 A? of neighbouring molecules. Maximization o "to the shortCoulomb interaction range to appears to lead the orientationally ordered phase where a pentagon consisting of five single bonds of a C faces the doub ?: molecule bonds of the neighbouring With a potential molecules. barrier of -300 meV, thermally transition rates activated local potential between the minima slow down at low teman peratures leading to orientational glassy behaviour with a T of ~90-130K [I91 similar tQ that found in the The (KBr) _ (KCN), system. transition orien tr a ional increases temperature, T,, markedly with pressure at a rate of around llK/kbar. This is understandable since presthe increase would sure intermolecular strength of the hence interactions and barrier governing rotational molecular reorientations.
Raman experiments have been carried out as a function of temperature across the orderdisorder phase transition of The observed modeC6 1201. spP itting and appearance of new Raman modes are consistent with the fee (SC) symmetry of the high (low) temperature phase. The Raman frequencies show a discontinuous juyp (increase of 2 to 10 cm 1 from the fee to the SC phase. This has been explained in terms of the smaller unit cell volume ( ~2.5%) of the SC structure. The line-widths also show discontinuous jumps value in the (smaller SC
r
I
I
I
I
1568 1564 h
‘E v -
0
1463
3
7
706 492' 0
772
I
-*.__ I 100
ri
I 200
I 300
T(K)
Fig. 6 Temperaturedependence of Raman frequenciesof C60 across the fee-sctransition (aftervan Loosdrecht et al [20])
239
phase) esting modes the T,
-1 from softening of -10 cm disordered to ordered the to be phase is considered mainly due to charge-transfer effects, the volume change small. The being fairly the increase in linewidth found by us in c60 is similar to that in the pressure-inof inorduced amorphization ganic crystals such as Sn14 [221 and Pb2z;z$$7 't";;.Ram;; Fig. 8 we Sn14 indicating data on amorphization at high pressures. Pressure-induced amorphization is associated with of down slowing the
at T,. Another interobservation is that the soften on approaching from above (Fig. 6).
We have found [211 pressure-induced orientational ordering in single crystals of Raman spectroscopy. %g by double-bond stretching pentagonal pinch vibration shows considerable softening across a transition around 3.5 kbar (Fig. 7). The linewidths increase considerably at higher pressures indicating an orientationally glassy state (Fig. 7). The mode
I
1450’ 0
I
I
I 80
40 Pressure
I
I
120
(k bar)
Fig.7 Pressuredependence of the peak frequency, w, of C and of the half-widthat halfmaximum, l? (afterChandrabhas et al [5?])
240
Sn 1, :
---In
9.0 (x90)
I
I
I
I
t
200
100 Raman
shift
300 (cm’)
Fig. 8 Pressure-dependence of Raman spectrum of Sn14 (from Sugai [23]) orientational kinetics of molecular units like NbO octahedra in Pb2Ntz07 an8 Snf tetrahedra Sn14. We & elieve that the observed increase in the line-width of the intramolecular mode of solid '60 is a signature of the orientational glassy phase high pressures in '60 at analogous to the glassy phase proposed below 1OOK atmospheric pressure 1191. 1,' the pressure increases, the barriers separating energy the orientational states of increase resulting in CO sPower dynamics even at room temperature. The line-width would be large in the glassy
because phase the environment of the C o molecules will be different grom one another giving rise to a inhomogeneous broadening of the Raman Some contribution to line. the increased line-width can also come from the enhanced vibrational-rotational coupling as the orientational relaxation time increases with increased pressure. Our experiments also show that the Raman intensity decreases with increasing pressure. This can be understood as due to the increase in the electrical conductivity of c6 resulting from pressure-in8 uced decrease of the band gap. A decrease in band gap reduces the penetration depth (and therefore the scattering volume) of the incident laser. 3.5 Superionic conductors: Superionic conductors such as AgI and B-alumina show phase transitions associated with the melting or disordering of one sub-lattice. NMR relaxation measurements have provided useful information on an ionic motion; motional effects have also been detected by EPR experiments The static melt-like 1241. disorder is reflected in the Raman spectra (often broad and structureless) and dynamics of ionic motion are directly seen in the lowfrequency relaxation modes. Light scattering in superionic conductors has been reviewed In addition to a wide 1251. variety of studies, such
241
temperature dependence of the far IR dynamical conductivity has been measured. We shall examine one system here to indicate the kind of from obtained information spectrosinfrared and Raman COPY [261. CsHSOq is reported trantwo phase to undergo 320 (III-II) around sitions and 420K (11-I) with the highI showing temperature phase conductivity. protonic high studies Temperature-dependent widths of IR show large and Raman bands in this phase.
The main bands showing changes are the HSO libration modes, stretch ing bending and the modes of the S-OH unit, and Omode. 0 stretching The third the first show and frequency or decrease in high temperadisappear at tures. The changes in spectra reflect the increase in disorder as well as changes in hydrogen bonding with increase in temperature. Typical spectra are shown in Figures 9 and 10 to illustra e the changes. of the 470 cm- f band The sulfate unit as well as the 6 CS,_, Ll”HS0,
Noo
3000
2000
lOa Wavenumber
” 500
400
300
200
100
(cm-‘)
(b)
i
I
,
,
850
300 Roman
*naft
I
,
1400 (cm-‘)
Fig. 9 Infrared and Raman spectra of CsHS04 at different temperatures (from Varma and Rao, unpublished results)
Fig. 10 Infrared and Raman spectra of Li substituted CsHS04 (from Varma and Rao, unpublished results)
242
(SO) around 600 cm-1 disappear around 390K accompanied by a marked change in the FWHM of the v(SO) bands indicating another phase between II and I. The superionic-conducting phase is associated with less hydrogen bonding and greater orientational freedom for the HSO4 ion. Substitution of Li for Cs in CsHSO4 brings about interesting changes. With 30% substitution, the phase transitions are eliminated and the room temperature phase looks like the high-temperature superionic-conducting phase of CsHSO4. IR and Raman spectra nicely bring out these features. 4. TRANSITIONS CIVE LIMIT
IN THE DISPLA-
Displacive transitions in a variety of crystals have been investigated by optical and magnetic resonance spectroscopies [2,31. In crystals such as benzil, anomalies in the elastic properties result from bilinear coupling between an optic mode (microscopic order parameter) and the macroscopic strain. Such transitions are different from those where the strain component is the parameter order and an acoustic phonon softens (e.g. ferroelastic transitions, transitions of s-triazine and Critical effects in NaN3). transitions have displacive been examined in detail by NMR, NQR and relaxation experof the iments, perovskites formula ABX3 being most notable among the systems studied. In perovskites, the are structural transitions
associated with small distortions from the ideal cubic structure, involving one or more tilts of the octahedra around the symmetry axis, often accompanied by distortions of the octahedra. The a-8 transformation of quartz, Si02, occurring at 846K is a truly displacive (non-ferroelectric) transition with the order parameter at the centre of the Brillouin This was the first zone. phase transition in which soft behaviour was observed mode by Raman and Nedungadi more than four decades ago and Scott reviewed this in 1974. Two A2 modes and three E(TO) modes disappear the above transition temperature. There is a critical increase of damping of all the IR modes around the transition. The pressure-induced transitions of K2Hg(CN4) in the O-5 kbar accompanied by the range, splitting of the v(CN) band, shift of the C-Hg-C bendband and softening of ing the 44 cm" band, seem to arise frorq- the distortion of the Hg(CNj4 tetrahedra [271. Chloranil shows a secondtransition at order phase 90.3K which is associated with mode. underdamped soft an The transition occurs through rotation staggered of a the molecules about the axis moleperpendicular to the cular planes: there is also a rotation about the molecular In Fig. 11, we O-O axis. softening mode show Raman associated with the molecular rotation. Pressure shifts the
243
4130bar
6
Temperature(K) Fig. 11 Pressure-dependence of Raman mode softeningin chloranil
l
In s-triazine, the phase transition (not strictly of second order) at 198.8K is not associated with the softening of a Raman optical lattice mode (unlike in benzil). There is however splitting of the
the transition is probably associated with a soft acoustic mode Based on 1321. the temperature dependence of spinthe spin-lattice and spin relaxation rates, molecuthe lar reorientation of been molecule have characterized. Elastic anomalies accompanying structural phase transitions are best understood in terms of the symmetry of the order parameter and of the elastic strain. Accordingly, anomalies in the phase transition of (NH41 SO4 around 234K have been exp3s. ained in terms of the coupling between the two. No underdamped soft mode has been observed for the transition, but the libration and SO$- ions modes of NH: are considered to be the soft
244
modes. The distortion of the SOiion accounts for the change in the linewidth and the frequency of the v3 band. NMR spectroscopy provides not only the reorientational frequencies of the NH: and the activation energies, but also information on the distortion of the tetrahedra and the mechanism of the transition. We have found somewhat changes in the distortions of the component ions in the phase transitions of hydrazonium sulfate, N H SO4 [33] similar to those o the free state, N$i$4::d.S+ :t;;ec;\$elyand Ilfd symme;;;;~ . the temperature phase, I, above 483K, both these ions attai ?+ the free-ion symmetries, N H6 becoming ethane-like withou $ a torsional barrier. AccordinglYL1 the torsion band at 517 cm in the room-temperature phase, II, along with the vl and v2 IR bands of sojdisappear completely after the II-I transition (Fig. 12). The Raman spectrum of I has a greater number of bands and the modes of bending N*H; manifest themselves in t is phase. Both the ions greatly distorted in the are low-temperature phase III, hydrogen bonding between the ions being more dominant in this phase. 5. INCOMMENSURATE PHASE SITIONS
TRAN-
The phase transitions discussed earlier were, by and soft large, associated with modes at the centre or
N2H6S04
Wavmnbers(Cni’)
Fig. 12 Temperaturedependence the torsionalband of N H2+ in N2H6S04 (afterVarma at?d'Rao[3 the boundary of the BrilloL zone. In transitions invol ing incommensurate phase as K2SeC4, the soft mode located neither at the zc at the boundar centre nor Raman scattering combined wi studi Brillouin scattering have thrown much light understanding these trz sitions. Another example involvj transitions phase whc phases incommensurate Raman studies have been mc useful is that of halides Layer the type Rb2ZnCl . as Z sue% chalcogenides
245
cules become strongly IRactive due to coupling 134, 351 as shown in Fig. 13.
charge-transfer and TaSe3 the of salts type exhibit phase (TMTSFjZRe04 CDW involving transitions excitation [131. Incommensurate modulation leads to the soft phonon splitting of the amplitudon and into branch Accordcomponents. phason Raman ingly, th;fAlg 2q;_dT:#B, show bands splitting into two components which low temperatures at soften as the temperature is increased through the second where the order transitions disappears. CDW state (TMTSFj2Re04 shows electronphonon activated IR absorption state. TCNQ CDW in the IRsalts exhibit strongly chargeelectronic active (polarized modes transfer along the stretching axis) in the near or mid-IR region. Totally symmetric IR-inactive vibrations of isolated mole-
6.
THE GLASS
TRANSITION
Glasses belong to a class of amorphous solids prepared by melt quenching and are distinguished by the glass transition that they exhibit The first derivatives [361. of the free energy vary continuously across the glass transition temperature, T,, and the second derivativzs show more or less discontinuous changes; the glass transition cannot be strictly considered to be a secondorder transition. Across the glass transition, diffusive motion of particles sets in, accompanied by a coupling of vibrational modes to other modes. The transition exhibits relaxational features and
Cs-TCNQ
Rb-TCNQ(I) -1
o
1583cm
A
1186cm-’
o
724
i t
o
1583
cm’
A
1186
cm’
crri’
I-
200
250 T/K -
300
)-
T/K -
Fig. 13 Temperature-variation of the intensities of the vibronicbands
of TCNQ salts (afterRao et al [35])
246
have dielectric loss peaks been found in glasses near Tg due to the so-called B-relaxation: such relaxation seems have little to do with to long-range order. Raman bandhave and bandshapes widths been employed to understand glass transition 1371. the bands The depolarized Raman greater changes across show (Fig. 14) compared to the T such bands p%larized and be due to changes could thermal expansivichanging ties. Molecular glasses show
0,-0-0---c /
Is (b) 0-o--0--0 1 \ \ P 8.0\ \
suga marked change in gesting that rotationa9 modes are possibly excited at T are small Pn Changes in rr ionic glasses while those in due -cV are larger, possibly coupling. mode complex to ESR measurements on organic spin with doped glasses probes [38] show that the spin sharply correlation time, ‘cc, (Fig. 15). above T drops In2Tganic gv+ss%s doped with show an anomaor Fe Mn intensity decrease in lous Mijssbauer 57Fe above Tg. spectra of Fe-doped glasses the decrease in show a recoil-free fraction around T Such changes have bee!! 1391 used to understand the nature transition. All of the glass that suggest these studies can transition glass the be associated with the emergence of degrees of freedom liquid in the supercooled the inactive in are that Some of the spectroglass. scopic data also point to the relevance of the cluster model for glasses. l
7.ELECTRONIC PEASE TRANSITIONS
transitions Metal-nonmetal and such as VO in oxides o\\o NO---_o ? have been inves igated V2O &A_-A--LL&A primarily I , by 1 R spectroscopy 250 150 to find out whether the order electronic T/K parameter is of Magnon lattice origin. or Fig. 14 (a) Variation in t_y FWHM such oxides Raman spectra of of Raman band at 2963 cm of have helped to understand the methylsalicylate across T ; (b) interacmagnetic nature of Variation of the orientatikal (cirthe with associated tions cles) and vibrational (triangles) In complex oxides transitions. relaxation times of methyl salicylate such as Lal~~Srx~~O~;OLaMnl_x across T g (after Ganguly et al [37]) N1,03 or 23. Y 4 ET;;gence of meta 1c1ty
247
I
I
I
0.6
0.9
I
1
12
I
1.5
T, IT
Variation of log T (from ESR spin probe measurements) with A, glycerol; B, Ckoluidine; C, methyl salicylate; D, propylene c&bonate;- E, dimethylphthalate (after Parthasarathy et al [%8])
Fig. T-,,::
increase in x is characteristically accompanied by disappearance of certain infrared absorption bands. We shall not discuss metalnonmetal transitions in oxides here, but examine an interesting pressure-induced electronic phase transition in buckminsterfullerene, found by us recently %% luminescence spectroscopic studies 1401. High pressure luminescence studies show that the photoluminescence maximum (marked E in Fig. to l%wer shifts ener16) gies with increase in pressure is and not detectable beyond 3GPa. In the inset of Fig. 16 we show the pressure dependence of Eg ’ the low-pressure region. 12
is found that the disappearance of E.g. is accompanied a stri ing colour change by from red to black. Interestingly, electrical resistivity measurements have shown a pressure-dependent band gap in These observations have t6 B earing on the mechanism of superconductivity in doped fullerenes. l
Insights into the viability of the electron-phonon mechanism of T in doped G60 can be obtaine 3 from an analysis of the lattice constant dependence of T,. Ignoring simplicity for the coulomb pseudopotential u*, using the weak coupling approximation for T, and keeping the lattice constant dependence
248
theoretical predicted by studies. We note that such a electron-phonon conventional mechanism for T, would imply = 3.6, the values of 2 UKBT, BCS value. The real situation however may be more complex. 7.1 Spin-state transitions: complexes show Many Fe(II) ransitions from the low-spin 1Al high-spin (L,) to the 5T2 (H) state or vice versa on variation of temperature or Some of the pressure 1411. transitions are accompanied by structural changes as in the case of Fe(Phen) (NCSj2 which undergoes a firs $-order tranOn partial sition at 150K. of Fe(II) by substitution Mn(I1) the transition graduto secondtransforms ally negative because of order Such spinpressure effect. 11.5 12.5 13.5 14.5 state transitions have been 103cm-' Massbauer specstudied by Infrared spectrostroscopy. Fig. 16 Room-tempertureluminiscence copy useful in is equally spectraof a singlecrystalof C transicharacterizing such at differentpressures. Insetsl%3s tions, the H states and L the pressure-variation of the peak show characteristic bands as position(afterSood et al [401) Effect Fig. 17. shown in Mn substitution is to of ony of N d(ln )/d(lna)= of the proportion increase -AidlnN /d(%a)zX' T 8(lnW)/ high-spin state at low the bandd(lna) %here W is the temperatures. The nature of band. A therefore width of the t transition the simple interpre 6aUtion of the changes with Mn substitution The the dependence of pressure Fig. 18. as shown in peak, tophotoluminescence nature coupling of the spin gether with the value W z 0.5 state of the transition metal translates to d(lnW)/ ion to the lattice in these eh Assuming that d(lna) = 12. transitions has not yet been holds for this same value fully understood. measand using the z:g" value for d(lnTc)/d(lna) 8. OTHER TRANSITIONS of +40.2, we estimate a X value of 0.3, which is in Over a period of years many values the agreement with interesting solid state phase
L
249
transitions have been invesspectroscopic tigated by methods and there is no way much of the work can be reviewed here. However, before closing, I would like to some studies that we mention have carried out in recent that could be of years chemical interconsiderable The first one I would est. like to mention would be the conformational polymorphisim octahalo-cyclophosphazine in tetramers, P4N X8 (X = Cl or F). P4N C$ undergoes a first-order ph ase transition at 336K accompanied by a change in molecular conformation from a low-temperature skew-tub (S4) phase to a high-temperature skew-chair (Ci or C2 ) base. Vibrational assignmen k s of both the phases have been made [42]. Vibra-
700
600
500
tional. assignments of P4 across its phase transiYfZ at 199K have also been made 1421; there appears to be par ial softening of the 105 cm- i external mode. Alkane dicarboxylic (or alkanedioic) acids, especially those with an odd number of carbon atoms, exhibit phase transitions 1351. In the case of malonic acid, CH2(100HJ2 a high-temperature transition is found at 37OK. In this acid the low-temperature P phase consists of orthogoacid dimeric units which nal are not equivalent. Raman and infrared studies show units that the two dimer equivalent in become the high-temperature a phase [43, 441. The largest discontinuities in the transition are
400
300 cm
200
100
-1
Fig. 17 Infraredspectraof Fe (Phen)2(NCS)2at differenttemperatures (from the author'slaboratory)
250
80-
Fe, Mnl_x(Phen)2(NCS)Z 0 x = 1.00 0 x = 0.75 m x = 0.25
20lo-+ 0. 0
I
I
50
100
I 150 Temp
I 200
1 250
300
(K)
Fig. 18 Variation of the spin-state population of FexMnlx(phen)2(NCS)2 with composition (from the author's laboratory)
(a)
P
L
Fig. 19 IR and Raman spectra of the a and #3 phases of malonic acid (after Ganguly et al [43] and de Villepin et al [44])
251
found in the v(C=O), 5(OH), V(C-0) and skeletal bending the In modes (Fig. 19). tw region, low-frequency Raman bands at 86 and 52 cm -P due to external modes drop_tt and 32 cm . T to 73 that These changes indicate phase transithe during reorientation of the tion, c-axis the about molecules the gets strongly coupled to torsional low-frequency librational and (yOH...O) The space group of the modes. to be a phase is suggested
- c2 C4 comp$e&;os,',',ii; tak B pha%e. show the equivalence clearly two carboxylic dimer of the units in the a-phase by giving a single line in the spectrum [451 as shown in Fig. 20. Unlike malonic acid, the other odd-member dioic acids seem to have a low-temperature phase identical with carboxylic dimeric units and inequivalent dimeric units in the high-temperature phase. These fea res have been confirmed fr C NMR spectra [45]. by Acknowledgement:
354K -
340K
-
358K -
I would like to thank my students and other coworkers who have collaborated with me in the area of phase transitions over the past several years. Thanks are also due to the various funding agencies, especially the CSIR (India), University Grants Commission and the Department of Science and Technology, Government of India.
357K -
292K 1 180 175 PPM
Fig. 20 l3C NMR spectrum of malonic acid in the carboxyl region (after Jagannathanand Rao [45])
REFERENCES 1. C.N.R. Rao and R.J. Rao, Phase Transitions ’ Solids, Mc-Graw Hill, Nai York, 1978. 2. F.J. Owens, C.P. Poole Jr. and H.A. Farach, Magnetic Resonance of Phase Transitions, Academic Press, New York, 1979. 3. 2. Iqbal and F.J. Owens, Vibrational spectroscopy Of Phase Transitions, Academic Press, New York, 1984.
252
Solid State 4. S. Hanssuhl, Commun. 13 (1973) 147. 5. S.K. Satija and C.H. Wang, J. Chem. Phys. 66 (1977) 2221. Chem. Phys. 6. F.J. Owens, (1979) 116. Lett. 64 7. J.R. Fernandes, S. Ganguly Spectroand C.N.R. Rao, (1979) 35A Acta, chim. 1013. 8. H.C. Tang and B.H. Torrie, Solids, Chem. J. Phys. 39 (1978) 845. 9. 2. Iqbal and C.W. ChrisFerroelectrics 12 toe, (1976) 177. S.F.A. Kearley, 10. G.J. I.A. Oxton, and Kettle 36A Acta Spectrochim. (1980) 419. 11. H. Buhay, J.B. Sokoloff and C.H. Prerry, J. Chem. Phys. 68 (1978) 5139; L. Petzelt, and J. Novak Commun. 19 State Solid (1976) 947. 12. R. Kind and J. Roos, Phys. Rev. B13 (1976) 45. 13. J. Seliger, R. Blinc, H. 2. Kind, Arend and R. R. Phys. 825 (1976) 189; Blinc, J. Chem. Phys. 66 (1977) 278. 14. R. Kind, R. Blinc and B. B19 Rev. Phys. Zeks, (1979) 3743. in Vibrational 15. M. Couzi, structure, and spectra Vol. 17A, Elsevier, Amsterdam, 1989. 16. C.N.R. Rao, S. Ganguly, H.R. Swamy and I.A. Oxton, J. Chem. Sot. Faraday 2, 77 (1981) 1825. 17. V. Varma, R. Bhattacharand Vasan jee, H.N. Rao, Spectrochim. C.N.R. Acta (in Press).
18. See reviews by H.R. KrishSood and A.K. namurthy 31 A&B [Ind. J. Chem. (1992) F64] as well as F.D.D.S. R.D. Johnson, Bethure and C.S. Yannoni [Act. Chem. Res. 25 (1992) 1691. 19. J. P. Lu, X.P. Li and R.M. Phys. Rev. Lett. Martin, 68 (1992) 1551. Loosdrecht, van 20. P.H.M. P.J.M. van Bentum and G. Phys. Rev. Lett. Meijer, 68 (1992) 1176. 21. N. Chandrabhas, M.N. ShaMuthu, D.V.S. shikala, A.K. Sood and C.N.R. Rao, Chem. Phys. Lett. 1992, in print. J. Phys. C 18 22. S. Sugai, (1985) 799. Kou23. A. Jayaraman, G.A. rouklis, A.S. Cooper and J. Phys. G.P. Espinosa, (1990) 1091. Chem. 94 in SupeRichards 24. P.M. ted. Conductors rionic SpringerSalmon), M.B. Verlag, 1979. 25. M.J. Delaney and S. Ushioda in Superionic Conductors ted. M.B. Salmon), Springer-Verlag, 1979. Ph. Colom26. M. Pham-Thi, and R. Novak ban, A. J. Raman, Spectr. Blinc, 18 (1987) 185; Also V. C.N.R. Rao, Varma and unpublished results. 27. P.T.T. Wong, Phys. Rev. B23 (1981) 375. 28. A. Girard, Y. Delugeard, H. and C. Ecolivet Cailleau, J. Phys. C, 15 (1982) 2127. Solid State 29. C. Ecolivet, Commun. 40 (1981) 503.
253 30.
31. 32. 33. 34. 35. 36. 37.
38.
A. Yoshihara, W.D. Wilker, E.R. Bernstein and J.C. Raich, J. Chem. Phys. 76 (1982) 2064. J.C. Raich and E.R. Bern73 stein, J. Chem. Phys. (1980) 1955. A. Zussman and M. Oron, J. Chem. Phys. 66 (1977) 743. V. Varma and C.N.R. Rao, J. Mol. Strut. 268 (1992) 1. R. Bozo and C. Pecile, J. 67 (1977) Chem. Phys. 3864. C.N.R. Rao, S. Ganguly and Swamy, Croat. Chem. H.R. Acta 55 (1982) 207. R. Parthasarathy, R.J. Rao Chem. and C.N.R. Rao, Sot. Rev. 12 (1983) 361. S. Ganguly, R. ParthasaraC.N.R. thy, K.J. Rao and Rao, J. Chem. Sot. Faraday 1395. 2, 80 (1984) R. Parthasarathy, K.J. Rao J. Phys. and C.N.R. Rao, Chem. 85 (1981) 3085.
39. S. Bharati, R. ParthasaraC.N.R. thy, K.J. Rao and Solid State Commun. Rao, 46 (1983) 457. 40. A.K. Sood, N. Chandrabhas, D.V.S. Muthu, A. Jayaraman, N. Kumar, H.R. Krishnamurthy, T. Pradeeg and C.N.R. Rao, Solid State Commun. 81 (1992) 89. Int. Rev. Rao, 41. C.N.R. 1 (1985) 19. Phys. Chem. Fernandes 42. V. Varma, J.R. J. Mol. and C.N.R. Rao, Strut. 198 (1989) 403. 43. s. Ganguly, J.R. Fernandes, G.R. Desiraju and Chem. Phys. C.N.R. Rao, Lett. 69 (1980) 227. 44. J. de Villepin, M.H.Limage, A. Novak, N. Tougry, M. LePostollec, H. Poulet, S. Ganguly and C.N.R. Rao, J. Raman Sec. 15 (1984) 41. and Jagannathan 45. N.R. Chem. Phys. C.N.R. Rao, Lett. 140 (1987) 46.
Spectroscopic complex solids
investigations
229
of
phase
transitions
in
C.N.R. Rao, Solid State & Structural Chemistry Unit and CSIR Centre of Excellence in Chemistry, Indian Institute of Science, Bangalore 560012, India
Abstract Spectroscopic methods have provided information of seminal importance in understanding phase transitions in solids. After briefly examining some fundamental concepts related to phase transitions, we shall discuss several case studies particularly involving the use of vibrational (IR and Raman) spectroscopy. Examples will include both order-disorder and displacive transitions. Under the former are included transitions in nitrates, ammonium halides, alkylammonium salts, plastic state of C6U and superionic conductors (specially CsHSOq). In addition, we shall discuss some aspects of incommensurate phase transitions, the glass transition and electronic phase transitions. Transitions of phosphonitrilic halide tetramers and alkane dicarboxylic acids are also examined.
1.
INTRODUCTION
The topic of phase transitions is one of vital interest to scientists working in diverse areas from theoretical materials techphysics to few nology 111. In the past variety of phase decades, a have been investransitions resulting in major tigated advances in the understanding of the phenomena associated transitions with phase the systems. Phase of diverse and transitions in solids associated structural changes first-order can occur in a a reconstructive fashion by mechanism or by means of a slight distortion of the 0022-2860/93/$06.00
0 1993 Elsevier Science Publishers B.V.
lattice through small displacements or ordering of the constituent atoms or molecules. Even during ordering there can be a displacive component just as there can be an ordering component in a displacive transition. The main types of structural phase transitions are the following: Order-disorder, e.g. molecular reorientation (NaN021, tunnelling of protons in Hbonds (KDP) Displacive, e.g. ferro-, anti-ferrodistortive and ferroelastic transitions
Electronic, All rights reserved.
e.g.,
spin-
230
wave charge-density state, transimetal-insulator and tions. Many of the molecular cryscrystals well as tals as ions molecular containing tranundergo order-disorder displacive with a sitions g-triazine, component (e.g. There are ammonium halides). several cases where the hightemperature phase of a solid is orientationally disordered and ordering results in rotation-translation coupling with both displacive or/and orderFerrodisorder regimes. distortive transitions involve displacements corresponding to optic length a long-wave phonon (hence z = z') while distorantiferrodistortive tions involve zone boundary ferphonons (hence z +nz); roelastic transitions involve acoustic phonons. Some of the ferroelectric solids show the first two types of transitions. Spectroscopic investigations transitions in of phase the solids generally involve temperature measurement of or pressure dependent changes features in a certain of spectrum characteristic of at phases the one of least Speca transition. across provide methods troscopic information on static as well processes occuras dynamic a transition, during ring complementary information on the former being provided by While diffraction methods. magnetic resonance methods, by and large, are more appropriate to study local dynamics,
inelastic scattering and IR absorption methods are useful to examine collective dynamics [2,31. The vibrational spectroscopic techniques employed are light scattering, inelasand tic neutron scattering IR absorption. Light scattering techniques include elastic scattering, Bril(Rayleigh) scattering louin (by sound waves close to the frequency and photon) of the incident scattering. Inelastic Raman suffers scattering neutron from disadvantages such as volume, poor sample large long measurement resolution, Optical spectroscopy time. disadvantages have methods such as selection rule remore are but strictions, readily used for the study of valuphase transitions and the on information able structural and mechanistic transitions aspects of phase has been obtained by these techniques. this presentation, we In examine spectroscopic shall important some studies of phase structural cases of involving disortransitions der-order as well as displaBecause of cive mechanisms. subthe the vast scope of the choice of systems ject, had necessarily to be subjective reflecting the speaker's personal interests. We shall not deal with transitions in superconductors and ferroelecbe these will since tries dealt with in detail by other in special lectures speakers shall devoted to them. We however examine phase transitions of Buckminsterfullerene,
231
'6 I which has become a molecu Pe of great excitement in recent months. We shall also explore some cases of electronic transitions and certain phase transitions of chemical discussing Before interest. the various phase transitions we shall ~briefly review some important concepts related to phase transitions. 2. SOME IMPORTANT CONCEPTS phase Thermodynamically, transitions are classified as order desecond first or the whether pending first derivzive of the Gibbs' disconvaries free energy continuously tinuously or The across the transition. used to parameter important characterize a .transition is the order parameter, 5, which observable usually an is of the system (e.g. property mode frequency). vibrational order parameter varies The differently with the thermodynamic variable (T, P) depending on whether the transition order. second is first or provides the Landau's theory under conditions symmetry which structural phase transithe latoccur. From tions tice dynamical point of view, an important aspect of structransitions is phase tural that of the soft mode wherein a vibration mode goes to zero frequency at T, : w=
w,(T-Tc)l"
(1)
Note that the order parameter also varies similarly. 5 =
cJTc-T)1'2
Eqn (1) represents the soft mode behaviour of a displaIf one incive transition. cludes anharmonic terms the mode behaviour is given soft by, 02 = AT + A(T-T,)
(3)
The anharmonic contribution becomes large in the orderthe where limit, disorder atomic displacements are also large. and light Both neutron have measurements scattering phase certain that shown only not are transitions associated with an inelastic due to the soft component phonon but also a quasi-elastic component whose intensity and dominates grows as T+T, around scattering the TE’ , componen The quasi-elastic called the central peak, has been explained based on varmodels theoretical ious mode (coupling of the soft thermal relaxation, imputo rity or surface effect, inassociated property trisic with clusters of the new phase in the old phase. of An interesting aspect phase tranmany structural sitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational In Jahnor libration modes. Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is strain (acouswith coupled antiferro In tic phonon).
232
distortive transitions, a zone boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). transitions phase Many (generally of second order) are characterized by a critibehaviour cal point and the point is critical at the expocritical described by nents. All macroscopic properties are then expressed as a function of [(T-T,)/T,l raised the critito some power. In flucregion correlated cal the order paramtuations of eter cause a break-down of theory. mean-field Landau's been major theohave There underadvances in retical phenomena critical standing the concepts include which and universality of scaling and the use of renormalization group theory. There is a special class of structural phase transitions where the distortion (primary cannot be order parameter) fracexpressed as a simple latreciprocal tion of the Such an incomtice vector. mensurate phase has no translation symmetry and becomes dynamically disordered at high In systems with temperatures. quasi one- or two-dimensional charge density waves, modulation of the charge density at the Fermi wavevector forms an incommensurate CDW which couples to the lattice to produce Such periodic distortion. a associated are transitions change from metallic -with a to insulator behaviour (e.g. Peierls transition).
3, ORDER-DISORDER TRANSITIONS transitions Order-disorder motions molecular involving investigated by have been methods, typiNMR and NQR and cal examples being NaNO etra2 layered alkylammonium the chlorides of type (' H2n+lN!$2~t~on~l =s~~;t~~; Mnf. have been studies scopic of carried out on a variety crystals such as KCN, NaCN, perovskite nitrates, metal etc. The compounds layer transitions of NaCN and KCN (at 288K and 168K respectively) involve the orientational and ions disorder of CNexhibit a large decrease in elastic constant at T, the C t41, ii4emonstrating the softening of the long wavelength transverse acoustic phonon 151 Coupling as shown in Fig. 1. (strain) between translation parameter order the and ions) (reorientation of the the orientational influences the CNamong interaction ions. 3.1 Nitrates: Optical spectroscopic studtransitions in ies of phase metal nitrates have yielded results. RbN03 interesting undergoes several phase tranorientathe sitions where tional order and dynamics of the orientational state of NOT play a crucial role. Thus, in the Raman spectrum of RbN03, raised as the temperature is above 3OOK, the libration mode the decreases as frequency line width increases, just as in NaN02 [61. The linewidth
233
Thus the V-IV transiture. the 255R removes tion at splitting of the v3 Raman band transition V-VI The 181 with the is associated softening of the NO. tion mode at 112 fm-lli';'s;Based on the Raman bands of NH3D diluted isotopically different species in phases, the point group symmeconsidered try of NH; is to be C2v in IV and III and Infrared C3v in I101 changes spectra [f7: show these findings which support symmetry and suggest a Td high temNHd in the for perature phase I at u400Kt In (< 255K), degeneraphase V ties of the \I.+(T) and vi (T) modes of N4 4 as well as of the V (E') and V4 (E') lifted in modes of N% - are the infrare d ; even the+ v; are vi bands of NH and found in the IR spec% rum of In the IR spectrum of V. weak the v4 band becomes II, while the copbination bands involvin_f NH4 libration (vi z 400 m 1 present in V disppear even in IV. In the IR spectra of ,I, v4 v1 and weak are very bands of NO3 suggesting a nearly D3h symmetry for the anion. l
l
T-T,(K)
FOE. 1 Plot of the square of2the TA phonon frequencyof NaCN, w (llO), obtainedfrom Brillouinscattering against(T-Tc) (afterSatijaand Wang [51) i.s,stven by, r_= a+bT+CT/(l+ where T is the orientatime: the tional relaxation actixation barrier is u 39 kJ mol . IR spectra show changes on going from 300K through the IV-III and higher temperaFor ture transitions [71. example, the splitting of the modes disappear and V v3 across the f V-III transition suggesting a change in point symmetry from C2v to group NH NO undergoes several c. associated pil Xse t!aniitions with the orientations of NH; bonding hydrogen and NO;, between the two ions playing a role depending on the tempera-
3.2 Ammonium halides: NH Cl and NH4Br undergo order-disorder firs f-order transitions around 240K involving the flipping of NH4f tetrahedra' between two orientations related by an inversion. There is no external these with associated mode libr tion The transitions. mode of NH4Br varies as w 8= A+
234
In the IR spectra, strong peaks some of the high-tempedisappear in the disordered phase. rature Interestingly, the strength of libration mode BE El11
l
indeed interesting. NQR iita on these halides have obtain also been employed to information on the temperature the dependence of order parameter. Alkylammonium salts: 3.3 Alkylammonium tetrachlorides of the type (CnHZn+lNH3)2MClq containetc.), (M = Cd, Mn (with ing perovskite layers
"1
the alkylammonium groups occusites and the pying the A M ions the B sites) exhibit structural phase transitions which have attracted considerable attention of both magnetic resonance and optical spectroscopists. Interlayer interaction is weak in these halides. The parent phase stable at high temperature is tetragonal with the Il/mmm-D 7 space group and orienta!?ional disorder of the alkylammonium group is necessary to get the hightemperature tetragonal structure. There is increasing ordering at low temperatures. Thus the temperature-dependence of 35C1 NQR measurements
=n2= n3=n4= i/4 ---
n,>n2=
n4’n3
-----_-_-
_
Tc,=484K(Cd) -1
-Tc2= 279 K (Cd) nl = n2> n3=n4
-------_--
pq Tc,= 163 K (Cd)
n,=l n2=n3=n4=0
)-Eq
Fig.2 Model for the orientational disorder of CH,Nq groups in (CH NH ) CdCl (afterKind et al [14]. In the-tetEagonal high of the C-N bond are equally tem~erAx&e pl+ase,the orientations distributedamong four energetically equivalentorientations (n1 =n 2 = n3 = n4 = *)
235
[I21 onth~H~~~~%~_*~d~&l tf;;w
phase of (CH3NH3)2MC14. Dis;f;der in these compounds fects not the organic only part, but also the inorganic part by means of coupling due to N-H... .Cl hydrogen bonds which give rise to shortrange ordering. Infrared spectroscopic studies of the phase transitions of alkylammonium halides, RNH3X, as well as of (RNH3) MX4 where x= Cl or Br have %Ieen carried out 1161. The hightemperature phase (> 264K) of CH3NH3C1 where disorder occurs because the C-N bond coincides with the 4-fold axis of the crystal does indeed show an infrared spectrum characteristic of undistorted CH3NHi(C ,); besides the various mo a e splittings, the low-temperature phase shows t e C-N torsion mode at 480 cm- P . Undistorted CH3NH; ions, as evidenced
that sition around 394K is related to the change in the asymmetry of the motion of the CH3NH3 the difference in the group: frequencies between the NQR phases shows a critical two behaviour. Disorder dynamics C-N bond directions in the across the transition in KHaNH3) 2CdC14 has been examine by proton-nitrogen double resonance measurements: proton second moment and Tl measurehave also thrown light ments on the transitions of these compounds 1133. In Fig. 2 we show the model accounting for orientational the disorder Extensive Raman studies Cl41 have been carried out on these alkylammonium chlorides 1151. Pressure experiments show that a displacive mechanism due to a shear mode is operative in the high pressure l
--I
.
cm 1600 1500 I I
(a)CJ
,, ,
1600 I
1500 I
(b) Mn
,, ,
1600 I
1500 I
(c)Cu
Fig. 3 Infraredspectraof (CH3NH3)2MC14 (afterRao et al [16])
236
L
,.
I
1
I
1
1200
1600
3500 3000
’
I
I
I
I
800
400
300
200
loo
1
Wavenumber (cm-‘)
Fig. 4 Infrared spectra of (CH3NH3)2Sb2Clq (after Varma et al (171)
I
I
100
Roman shift Fig.
I
I
200
300 (cm-‘)
Anion modes in the Raman spectra of [(CH3),NHl,Sb,C19 (after Varma et al [171) 5
from the IR spectra, are also seen in the high-temperature phases of (CH3NH31MC14 (Fig. Alkylammonium bromides 3). and the corresponding alkylammonium tetrabromometallates show IR spectra reflecting phase transitions characteristics similar to those of the chlorides [16]. Infrared and Raman spectroscopic investigations have been carried out recently on the interesting phase transitions of methylammonium haloantimonates of the type [N(CH3) _ Hn13Sb2X9 where n = O-3 an$1 = Cl or Br 1171. It has been shown that the vibration modes due to CH3 deformation as well as those involving theNH (n= 1, 2 and 3) groups sg ow significant changes across the phase transitions besides those due anion (Figs. The anion modes differ with the number of CH groups since the nature of thi anion itself changes, the free anion being present only in the quarternary compound. High-temperature phases of the chloroantimonates seem to involve random orientations of the methylamino groups. A new phase transition is predicted in all the chloroantimonates below 15OK, based on the changes in the anion bands at low-temperatures (see Fig. 5 and also the lowfrequency region in Fig. 4). Changes in the infrared and Raman spectra accompanying the phase transitions of (CH3NH3j3 Sb2Brg and (CH3NHf13Bi2Brg are similar and in t e high-temperature phase of these com-
pounds the (CH3NH3)+ cations are oriented randomly, possiwith point bly group c3v symmetry. 3.4 Plastic state of C6 : Many molecular crysta Ps of globular molecules exhibit an orientationally disordered or a plastic state close to the melting temperature. The rotational motion is generally hindered and the molecule has to overcome a potential barrier during reorientation. In the low-temperature orientationally ordered phase, molecules librate. IR and Raman spectroscopy as well as magnetic resonance methods have been employed to investigate the plastic state in several systems. Dielectric spectra due to the rotational and librational motion have also been studied. We shall examine here the plastic to crystalline transition exhibited by buckminsterfullerene C60. X-ray diffraction, differen'al scanning calorimetry and $3C NMR reveal a first-order phase transition from the fee (space group Pm31 phase to a simple cubic (SC) P2 /a3 phase around 250K 1181. B 0th x-ray and NMR studies suggest that this transition is related to orientational ordering of the molecules in the SC phase. %: molecules rotate ‘60 freely In the fee phase whereas in the SC phase, they perform jump-diffusion between nearly degenerate orientations separated by a potential barrier. This barrier has been determined to be u 260 meV from the temperature and time-dependence of the
238
thermal conductivity as well as from the frequency-dependence of sound velocity and This value of attenuation. the barrier is close to the theoretical estimte of m 300 meV obtained from a simple free-energy model incorporating the intermolecular interaction in the form of the Lennard-Jones potential as well as the Coulomb interaction. The latter takes into account the charge-transfer between the electron-excess "double" bonds (bond-length .~1.40A’) and the electrondeficient "single" bonds (bond-length u 1.45 A? of neighbouring molecules. Maximization o "to the shortCoulomb interaction range to appears to lead the orientationally ordered phase where a pentagon consisting of five single bonds of a C faces the doub ?: molecule bonds of the neighbouring With a potential molecules. barrier of -300 meV, thermally transition rates activated local potential between the minima slow down at low teman peratures leading to orientational glassy behaviour with a T of ~90-130K [I91 similar tQ that found in the The (KBr) _ (KCN), system. transition orien tr a ional increases temperature, T,, markedly with pressure at a rate of around llK/kbar. This is understandable since presthe increase would sure intermolecular strength of the hence interactions and barrier governing rotational molecular reorientations.
Raman experiments have been carried out as a function of temperature across the orderdisorder phase transition of The observed modeC6 1201. spP itting and appearance of new Raman modes are consistent with the fee (SC) symmetry of the high (low) temperature phase. The Raman frequencies show a discontinuous juyp (increase of 2 to 10 cm 1 from the fee to the SC phase. This has been explained in terms of the smaller unit cell volume ( ~2.5%) of the SC structure. The line-widths also show discontinuous jumps value in the (smaller SC
r
I
I
I
I
1568 1564 h
‘E v -
0
1463
3
7
706 492' 0
772
I
-*.__ I 100
ri
I 200
I 300
T(K)
Fig. 6 Temperaturedependence of Raman frequenciesof C60 across the fee-sctransition (aftervan Loosdrecht et al [20])
239
phase) esting modes the T,
-1 from softening of -10 cm disordered to ordered the to be phase is considered mainly due to charge-transfer effects, the volume change small. The being fairly the increase in linewidth found by us in c60 is similar to that in the pressure-inof inorduced amorphization ganic crystals such as Sn14 [221 and Pb2z;z$$7 't";;.Ram;; Fig. 8 we Sn14 indicating data on amorphization at high pressures. Pressure-induced amorphization is associated with of down slowing the
at T,. Another interobservation is that the soften on approaching from above (Fig. 6).
We have found [211 pressure-induced orientational ordering in single crystals of Raman spectroscopy. %g by double-bond stretching pentagonal pinch vibration shows considerable softening across a transition around 3.5 kbar (Fig. 7). The linewidths increase considerably at higher pressures indicating an orientationally glassy state (Fig. 7). The mode
I
1450’ 0
I
I
I 80
40 Pressure
I
I
120
(k bar)
Fig.7 Pressuredependence of the peak frequency, w, of C and of the half-widthat halfmaximum, l? (afterChandrabhas et al [5?])
240
Sn 1, :
---In
9.0 (x90)
I
I
I
I
t
200
100 Raman
shift
300 (cm’)
Fig. 8 Pressure-dependence of Raman spectrum of Sn14 (from Sugai [23]) orientational kinetics of molecular units like NbO octahedra in Pb2Ntz07 an8 Snf tetrahedra Sn14. We & elieve that the observed increase in the line-width of the intramolecular mode of solid '60 is a signature of the orientational glassy phase high pressures in '60 at analogous to the glassy phase proposed below 1OOK atmospheric pressure 1191. 1,' the pressure increases, the barriers separating energy the orientational states of increase resulting in CO sPower dynamics even at room temperature. The line-width would be large in the glassy
because phase the environment of the C o molecules will be different grom one another giving rise to a inhomogeneous broadening of the Raman Some contribution to line. the increased line-width can also come from the enhanced vibrational-rotational coupling as the orientational relaxation time increases with increased pressure. Our experiments also show that the Raman intensity decreases with increasing pressure. This can be understood as due to the increase in the electrical conductivity of c6 resulting from pressure-in8 uced decrease of the band gap. A decrease in band gap reduces the penetration depth (and therefore the scattering volume) of the incident laser. 3.5 Superionic conductors: Superionic conductors such as AgI and B-alumina show phase transitions associated with the melting or disordering of one sub-lattice. NMR relaxation measurements have provided useful information on an ionic motion; motional effects have also been detected by EPR experiments The static melt-like 1241. disorder is reflected in the Raman spectra (often broad and structureless) and dynamics of ionic motion are directly seen in the lowfrequency relaxation modes. Light scattering in superionic conductors has been reviewed In addition to a wide 1251. variety of studies, such
241
temperature dependence of the far IR dynamical conductivity has been measured. We shall examine one system here to indicate the kind of from obtained information spectrosinfrared and Raman COPY [261. CsHSOq is reported trantwo phase to undergo 320 (III-II) around sitions and 420K (11-I) with the highI showing temperature phase conductivity. protonic high studies Temperature-dependent widths of IR show large and Raman bands in this phase.
The main bands showing changes are the HSO libration modes, stretch ing bending and the modes of the S-OH unit, and Omode. 0 stretching The third the first show and frequency or decrease in high temperadisappear at tures. The changes in spectra reflect the increase in disorder as well as changes in hydrogen bonding with increase in temperature. Typical spectra are shown in Figures 9 and 10 to illustra e the changes. of the 470 cm- f band The sulfate unit as well as the 6 CS,_, Ll”HS0,
Noo
3000
2000
lOa Wavenumber
” 500
400
300
200
100
(cm-‘)
(b)
i
I
,
,
850
300 Roman
*naft
I
,
1400 (cm-‘)
Fig. 9 Infrared and Raman spectra of CsHS04 at different temperatures (from Varma and Rao, unpublished results)
Fig. 10 Infrared and Raman spectra of Li substituted CsHS04 (from Varma and Rao, unpublished results)
242
(SO) around 600 cm-1 disappear around 390K accompanied by a marked change in the FWHM of the v(SO) bands indicating another phase between II and I. The superionic-conducting phase is associated with less hydrogen bonding and greater orientational freedom for the HSO4 ion. Substitution of Li for Cs in CsHSO4 brings about interesting changes. With 30% substitution, the phase transitions are eliminated and the room temperature phase looks like the high-temperature superionic-conducting phase of CsHSO4. IR and Raman spectra nicely bring out these features. 4. TRANSITIONS CIVE LIMIT
IN THE DISPLA-
Displacive transitions in a variety of crystals have been investigated by optical and magnetic resonance spectroscopies [2,31. In crystals such as benzil, anomalies in the elastic properties result from bilinear coupling between an optic mode (microscopic order parameter) and the macroscopic strain. Such transitions are different from those where the strain component is the parameter order and an acoustic phonon softens (e.g. ferroelastic transitions, transitions of s-triazine and Critical effects in NaN3). transitions have displacive been examined in detail by NMR, NQR and relaxation experof the iments, perovskites formula ABX3 being most notable among the systems studied. In perovskites, the are structural transitions
associated with small distortions from the ideal cubic structure, involving one or more tilts of the octahedra around the symmetry axis, often accompanied by distortions of the octahedra. The a-8 transformation of quartz, Si02, occurring at 846K is a truly displacive (non-ferroelectric) transition with the order parameter at the centre of the Brillouin This was the first zone. phase transition in which soft behaviour was observed mode by Raman and Nedungadi more than four decades ago and Scott reviewed this in 1974. Two A2 modes and three E(TO) modes disappear the above transition temperature. There is a critical increase of damping of all the IR modes around the transition. The pressure-induced transitions of K2Hg(CN4) in the O-5 kbar accompanied by the range, splitting of the v(CN) band, shift of the C-Hg-C bendband and softening of ing the 44 cm" band, seem to arise frorq- the distortion of the Hg(CNj4 tetrahedra [271. Chloranil shows a secondtransition at order phase 90.3K which is associated with mode. underdamped soft an The transition occurs through rotation staggered of a the molecules about the axis moleperpendicular to the cular planes: there is also a rotation about the molecular In Fig. 11, we O-O axis. softening mode show Raman associated with the molecular rotation. Pressure shifts the
243
4130bar
6
Temperature(K) Fig. 11 Pressure-dependence of Raman mode softeningin chloranil
l
In s-triazine, the phase transition (not strictly of second order) at 198.8K is not associated with the softening of a Raman optical lattice mode (unlike in benzil). There is however splitting of the
the transition is probably associated with a soft acoustic mode Based on 1321. the temperature dependence of spinthe spin-lattice and spin relaxation rates, molecuthe lar reorientation of been molecule have characterized. Elastic anomalies accompanying structural phase transitions are best understood in terms of the symmetry of the order parameter and of the elastic strain. Accordingly, anomalies in the phase transition of (NH41 SO4 around 234K have been exp3s. ained in terms of the coupling between the two. No underdamped soft mode has been observed for the transition, but the libration and SO$- ions modes of NH: are considered to be the soft
244
modes. The distortion of the SOiion accounts for the change in the linewidth and the frequency of the v3 band. NMR spectroscopy provides not only the reorientational frequencies of the NH: and the activation energies, but also information on the distortion of the tetrahedra and the mechanism of the transition. We have found somewhat changes in the distortions of the component ions in the phase transitions of hydrazonium sulfate, N H SO4 [33] similar to those o the free state, N$i$4::d.S+ :t;;ec;\$elyand Ilfd symme;;;;~ . the temperature phase, I, above 483K, both these ions attai ?+ the free-ion symmetries, N H6 becoming ethane-like withou $ a torsional barrier. AccordinglYL1 the torsion band at 517 cm in the room-temperature phase, II, along with the vl and v2 IR bands of sojdisappear completely after the II-I transition (Fig. 12). The Raman spectrum of I has a greater number of bands and the modes of bending N*H; manifest themselves in t is phase. Both the ions greatly distorted in the are low-temperature phase III, hydrogen bonding between the ions being more dominant in this phase. 5. INCOMMENSURATE PHASE SITIONS
TRAN-
The phase transitions discussed earlier were, by and soft large, associated with modes at the centre or
N2H6S04
Wavmnbers(Cni’)
Fig. 12 Temperaturedependence the torsionalband of N H2+ in N2H6S04 (afterVarma at?d'Rao[3 the boundary of the BrilloL zone. In transitions invol ing incommensurate phase as K2SeC4, the soft mode located neither at the zc at the boundar centre nor Raman scattering combined wi studi Brillouin scattering have thrown much light understanding these trz sitions. Another example involvj transitions phase whc phases incommensurate Raman studies have been mc useful is that of halides Layer the type Rb2ZnCl . as Z sue% chalcogenides
245
cules become strongly IRactive due to coupling 134, 351 as shown in Fig. 13.
charge-transfer and TaSe3 the of salts type exhibit phase (TMTSFjZRe04 CDW involving transitions excitation [131. Incommensurate modulation leads to the soft phonon splitting of the amplitudon and into branch Accordcomponents. phason Raman ingly, th;fAlg 2q;_dT:#B, show bands splitting into two components which low temperatures at soften as the temperature is increased through the second where the order transitions disappears. CDW state (TMTSFj2Re04 shows electronphonon activated IR absorption state. TCNQ CDW in the IRsalts exhibit strongly chargeelectronic active (polarized modes transfer along the stretching axis) in the near or mid-IR region. Totally symmetric IR-inactive vibrations of isolated mole-
6.
THE GLASS
TRANSITION
Glasses belong to a class of amorphous solids prepared by melt quenching and are distinguished by the glass transition that they exhibit The first derivatives [361. of the free energy vary continuously across the glass transition temperature, T,, and the second derivativzs show more or less discontinuous changes; the glass transition cannot be strictly considered to be a secondorder transition. Across the glass transition, diffusive motion of particles sets in, accompanied by a coupling of vibrational modes to other modes. The transition exhibits relaxational features and
Cs-TCNQ
Rb-TCNQ(I) -1
o
1583cm
A
1186cm-’
o
724
i t
o
1583
cm’
A
1186
cm’
crri’
I-
200
250 T/K -
300
)-
T/K -
Fig. 13 Temperature-variation of the intensities of the vibronicbands
of TCNQ salts (afterRao et al [35])
246
have dielectric loss peaks been found in glasses near Tg due to the so-called B-relaxation: such relaxation seems have little to do with to long-range order. Raman bandhave and bandshapes widths been employed to understand glass transition 1371. the bands The depolarized Raman greater changes across show (Fig. 14) compared to the T such bands p%larized and be due to changes could thermal expansivichanging ties. Molecular glasses show
0,-0-0---c /
Is (b) 0-o--0--0 1 \ \ P 8.0\ \
suga marked change in gesting that rotationa9 modes are possibly excited at T are small Pn Changes in rr ionic glasses while those in due -cV are larger, possibly coupling. mode complex to ESR measurements on organic spin with doped glasses probes [38] show that the spin sharply correlation time, ‘cc, (Fig. 15). above T drops In2Tganic gv+ss%s doped with show an anomaor Fe Mn intensity decrease in lous Mijssbauer 57Fe above Tg. spectra of Fe-doped glasses the decrease in show a recoil-free fraction around T Such changes have bee!! 1391 used to understand the nature transition. All of the glass that suggest these studies can transition glass the be associated with the emergence of degrees of freedom liquid in the supercooled the inactive in are that Some of the spectroglass. scopic data also point to the relevance of the cluster model for glasses. l
7.ELECTRONIC PEASE TRANSITIONS
transitions Metal-nonmetal and such as VO in oxides o\\o NO---_o ? have been inves igated V2O &A_-A--LL&A primarily I , by 1 R spectroscopy 250 150 to find out whether the order electronic T/K parameter is of Magnon lattice origin. or Fig. 14 (a) Variation in t_y FWHM such oxides Raman spectra of of Raman band at 2963 cm of have helped to understand the methylsalicylate across T ; (b) interacmagnetic nature of Variation of the orientatikal (cirthe with associated tions cles) and vibrational (triangles) In complex oxides transitions. relaxation times of methyl salicylate such as Lal~~Srx~~O~;OLaMnl_x across T g (after Ganguly et al [37]) N1,03 or 23. Y 4 ET;;gence of meta 1c1ty
247
I
I
I
0.6
0.9
I
1
12
I
1.5
T, IT
Variation of log T (from ESR spin probe measurements) with A, glycerol; B, Ckoluidine; C, methyl salicylate; D, propylene c&bonate;- E, dimethylphthalate (after Parthasarathy et al [%8])
Fig. T-,,::
increase in x is characteristically accompanied by disappearance of certain infrared absorption bands. We shall not discuss metalnonmetal transitions in oxides here, but examine an interesting pressure-induced electronic phase transition in buckminsterfullerene, found by us recently %% luminescence spectroscopic studies 1401. High pressure luminescence studies show that the photoluminescence maximum (marked E in Fig. to l%wer shifts ener16) gies with increase in pressure is and not detectable beyond 3GPa. In the inset of Fig. 16 we show the pressure dependence of Eg ’ the low-pressure region. 12
is found that the disappearance of E.g. is accompanied a stri ing colour change by from red to black. Interestingly, electrical resistivity measurements have shown a pressure-dependent band gap in These observations have t6 B earing on the mechanism of superconductivity in doped fullerenes. l
Insights into the viability of the electron-phonon mechanism of T in doped G60 can be obtaine 3 from an analysis of the lattice constant dependence of T,. Ignoring simplicity for the coulomb pseudopotential u*, using the weak coupling approximation for T, and keeping the lattice constant dependence
248
theoretical predicted by studies. We note that such a electron-phonon conventional mechanism for T, would imply = 3.6, the values of 2 UKBT, BCS value. The real situation however may be more complex. 7.1 Spin-state transitions: complexes show Many Fe(II) ransitions from the low-spin 1Al high-spin (L,) to the 5T2 (H) state or vice versa on variation of temperature or Some of the pressure 1411. transitions are accompanied by structural changes as in the case of Fe(Phen) (NCSj2 which undergoes a firs $-order tranOn partial sition at 150K. of Fe(II) by substitution Mn(I1) the transition graduto secondtransforms ally negative because of order Such spinpressure effect. 11.5 12.5 13.5 14.5 state transitions have been 103cm-' Massbauer specstudied by Infrared spectrostroscopy. Fig. 16 Room-tempertureluminiscence copy useful in is equally spectraof a singlecrystalof C transicharacterizing such at differentpressures. Insetsl%3s tions, the H states and L the pressure-variation of the peak show characteristic bands as position(afterSood et al [401) Effect Fig. 17. shown in Mn substitution is to of ony of N d(ln )/d(lna)= of the proportion increase -AidlnN /d(%a)zX' T 8(lnW)/ high-spin state at low the bandd(lna) %here W is the temperatures. The nature of band. A therefore width of the t transition the simple interpre 6aUtion of the changes with Mn substitution The the dependence of pressure Fig. 18. as shown in peak, tophotoluminescence nature coupling of the spin gether with the value W z 0.5 state of the transition metal translates to d(lnW)/ ion to the lattice in these eh Assuming that d(lna) = 12. transitions has not yet been holds for this same value fully understood. measand using the z:g" value for d(lnTc)/d(lna) 8. OTHER TRANSITIONS of +40.2, we estimate a X value of 0.3, which is in Over a period of years many values the agreement with interesting solid state phase
L
249
transitions have been invesspectroscopic tigated by methods and there is no way much of the work can be reviewed here. However, before closing, I would like to some studies that we mention have carried out in recent that could be of years chemical interconsiderable The first one I would est. like to mention would be the conformational polymorphisim octahalo-cyclophosphazine in tetramers, P4N X8 (X = Cl or F). P4N C$ undergoes a first-order ph ase transition at 336K accompanied by a change in molecular conformation from a low-temperature skew-tub (S4) phase to a high-temperature skew-chair (Ci or C2 ) base. Vibrational assignmen k s of both the phases have been made [42]. Vibra-
700
600
500
tional. assignments of P4 across its phase transiYfZ at 199K have also been made 1421; there appears to be par ial softening of the 105 cm- i external mode. Alkane dicarboxylic (or alkanedioic) acids, especially those with an odd number of carbon atoms, exhibit phase transitions 1351. In the case of malonic acid, CH2(100HJ2 a high-temperature transition is found at 37OK. In this acid the low-temperature P phase consists of orthogoacid dimeric units which nal are not equivalent. Raman and infrared studies show units that the two dimer equivalent in become the high-temperature a phase [43, 441. The largest discontinuities in the transition are
400
300 cm
200
100
-1
Fig. 17 Infraredspectraof Fe (Phen)2(NCS)2at differenttemperatures (from the author'slaboratory)
250
80-
Fe, Mnl_x(Phen)2(NCS)Z 0 x = 1.00 0 x = 0.75 m x = 0.25
20lo-+ 0. 0
I
I
50
100
I 150 Temp
I 200
1 250
300
(K)
Fig. 18 Variation of the spin-state population of FexMnlx(phen)2(NCS)2 with composition (from the author's laboratory)
(a)
P
L
Fig. 19 IR and Raman spectra of the a and #3 phases of malonic acid (after Ganguly et al [43] and de Villepin et al [44])
251
found in the v(C=O), 5(OH), V(C-0) and skeletal bending the In modes (Fig. 19). tw region, low-frequency Raman bands at 86 and 52 cm -P due to external modes drop_tt and 32 cm . T to 73 that These changes indicate phase transithe during reorientation of the tion, c-axis the about molecules the gets strongly coupled to torsional low-frequency librational and (yOH...O) The space group of the modes. to be a phase is suggested
- c2 C4 comp$e&;os,',',ii; tak B pha%e. show the equivalence clearly two carboxylic dimer of the units in the a-phase by giving a single line in the spectrum [451 as shown in Fig. 20. Unlike malonic acid, the other odd-member dioic acids seem to have a low-temperature phase identical with carboxylic dimeric units and inequivalent dimeric units in the high-temperature phase. These fea res have been confirmed fr C NMR spectra [45]. by Acknowledgement:
354K -
340K
-
358K -
I would like to thank my students and other coworkers who have collaborated with me in the area of phase transitions over the past several years. Thanks are also due to the various funding agencies, especially the CSIR (India), University Grants Commission and the Department of Science and Technology, Government of India.
357K -
292K 1 180 175 PPM
Fig. 20 l3C NMR spectrum of malonic acid in the carboxyl region (after Jagannathanand Rao [45])
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252
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31. 32. 33. 34. 35. 36. 37.
38.
A. Yoshihara, W.D. Wilker, E.R. Bernstein and J.C. Raich, J. Chem. Phys. 76 (1982) 2064. J.C. Raich and E.R. Bern73 stein, J. Chem. Phys. (1980) 1955. A. Zussman and M. Oron, J. Chem. Phys. 66 (1977) 743. V. Varma and C.N.R. Rao, J. Mol. Strut. 268 (1992) 1. R. Bozo and C. Pecile, J. 67 (1977) Chem. Phys. 3864. C.N.R. Rao, S. Ganguly and Swamy, Croat. Chem. H.R. Acta 55 (1982) 207. R. Parthasarathy, R.J. Rao Chem. and C.N.R. Rao, Sot. Rev. 12 (1983) 361. S. Ganguly, R. ParthasaraC.N.R. thy, K.J. Rao and Rao, J. Chem. Sot. Faraday 1395. 2, 80 (1984) R. Parthasarathy, K.J. Rao J. Phys. and C.N.R. Rao, Chem. 85 (1981) 3085.
39. S. Bharati, R. ParthasaraC.N.R. thy, K.J. Rao and Solid State Commun. Rao, 46 (1983) 457. 40. A.K. Sood, N. Chandrabhas, D.V.S. Muthu, A. Jayaraman, N. Kumar, H.R. Krishnamurthy, T. Pradeeg and C.N.R. Rao, Solid State Commun. 81 (1992) 89. Int. Rev. Rao, 41. C.N.R. 1 (1985) 19. Phys. Chem. Fernandes 42. V. Varma, J.R. J. Mol. and C.N.R. Rao, Strut. 198 (1989) 403. 43. s. Ganguly, J.R. Fernandes, G.R. Desiraju and Chem. Phys. C.N.R. Rao, Lett. 69 (1980) 227. 44. J. de Villepin, M.H.Limage, A. Novak, N. Tougry, M. LePostollec, H. Poulet, S. Ganguly and C.N.R. Rao, J. Raman Sec. 15 (1984) 41. and Jagannathan 45. N.R. Chem. Phys. C.N.R. Rao, Lett. 140 (1987) 46.