PHYSICAL REVIEW 8 VOLUME 31, NUMBER 7 1 APRIL 1985

Existence of an isotropic point and birefringence dispersion studyin (C2H5NH3)2CuClq crystal near its thermochromic phase transition

I

J. FernandezCatedra de Fisica, Escuela Superior de lngenieros Industriales, Universidad de/ Pais Vasco, Bilbao, Spain

A. Gomez Cuevas, M. A. Arriandiaga, C. Socias, and M. J. TelloDepartamento de Fisica, Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, Bilbao, Spain

(Received 6 July 1984)

The anomalous optical dispersion and the existence of an isotropic point in the organic-inorganicdouble-halide (C2H5NH3)2CuC14 crystal (in short EACuC) around its thermochromic low-

temperature phase transition were investigated by means of birefringence, thermal expansion, andcalorimetric measurements as well as by direct conoscopic and orthoscopic observations under polar-ized light. The birefringence dispersion data are analyzed using a simple two-oscillator model basedon the optical band structure of EACuC. The model adjustable parameters are related with the os-cillator strength and average positions, respectively. The thermal behavior of the involved parame-ters is compatible with the existence of the isotropic point below the thermochromic phase transi-tion. These results, together with the optical extinction measurements and the domain pattern ob-

servations, suggest a complicated structural phase-transition sequence which is also discussed.

I. INTRODUCTION

n-ethyl ammonium copper chloride is a ferroelasticcrystal which belongs to the (C„Hq„+~NH3)2MX4 familywhere low-temperature magnetic order, structural phase-transition sequences and long-chain conformationalchanges have been thoroughly investigated (see Refs. 1—5and references therein). This interest was recently rein-forced by the discovery of new properties related to thestructural changes. For instance, two singular incom-mensurate phases, reached by a lock-in transition with aflipping modulation vector and a reentrant one, ' werefound in his-propyl ammonium manganese chloride crys-tals. A pure and proper gyrotropic phase was detected inhis-penthyl ammonium zinc chlori. de, " and more recentlythe existence of an isotropic point together with a highoptical dispersion which occurs in long-chain zinc com-pounds' was found. These last properties open new pos-sibilities for this interesting family as a function of M, X,and n.

The high-temperature phase transition of the(C2HsNH3)2CuC14 (in short EACuC) was extensivelystudied in a previous paper. ' A short qualitative descrip-tion of the low-temperature thermochromic anomaly wasalso included. More recently, Kleeman et al. ' have re-viewed the whole structural phase-transition sequencewith very interesting crystal-optical results below roomtemperature. Both papers show the existence of a broadlow-temperature region where large birefringence varia-tions and some other diffuse anomalies occur. Up to nowthese effects have been associated with the existence of theso-called thermochromic transition (TCT) around 233 Kwhich, as Willet proposed' is mainly induced by a changein the copper-ion coordination geometry which in turnmust be associated with overall changes of the interaction

strengths in the crystal as the temperature varies. Thus,sometimes, phase transitions may be favored by the onsetof new dynamic modes of motion in the crystal struc-ture.

Three facts have led us to undertake the study ofbirefringence dispersion in EACuC over a broad tempera-ture region around 233 K. First, birefringence drops tozero far below the TCT; second, a noticeable color disper-sion is observed -in the conoscopic pattern; and finally,EACuC exhibits a complicated domain pattern belowroom temperature. The aim of this paper is to give a fur-ther insight on the optical and thermal behavior of thiscompound near the TCT and to show the existence of anisotropic point.

The general features of the optical band structure arepresented in Sec. II and will support the two-oscillatormodel proposed in Sec. III to account for thebirefringence dispersion. The experimental results areshown in Sec. IV, and their discussion is presented in Sec.V. As we shall see, the existence of an isotropic point isrevealed by the birefringence behavior below the TCT.The adjustable parameters used for the birefringenceparametrization have proved to be of great importance,not only because of the good experimental fitting of thetwo-oscillator model but also because they are involved inthe structural behavior of the crystal. In Sec. VI the finalconclusions. are presented.

II. GENERAL FEATURES OF THE OPTICALBAND STRUCTURE

EACuC has a pronounced two-dimensional structure ofnearly isolated layers of corner-sharing CuC16 octahedra.The cavities between octhaedra contain alkylammoniumR groups with the carbon chains slightly deviated from

31 4562 1985 The American Physical Society

31 EXISTENCE OF AN ISOTROPIC POINT AND. . . 4563

the perpendicular to the octahedral plane. ' ' The organ-ic chains are joined by weak hydrogen bonds from theNH3 groups to the Cl ions, and the interlayer bonding isachieved by van der Waals forces between the ends of thecarbon chains as well as long-range Coulomb forces.These facts support the principal role played by the CuC16octahedra in the main characteristics of the energy-bandstructure in EACuC. In fact, the energy-absorption bandsobserved in this compound by means of optical and pho-toacoustic spectroscopy (Fig. 1) in the near-visible rangehave the same features as those found in the analogousmethyl compound (MACuC). '9 This means that the elec-tronic transitions responsible for these bands come chieflyfrom the CuC16 units.

The two bands observed at the violet edge of the pho-toacoustic spectra in EACuC between 2.5 and 5 eV, showbroad peaks around 350 and 475 nm at room temperature,with a somewhat lower energy than those in MACuC.Their nature can be related to the ligand-to-metal charge-transfer transitions from the two broad zp-like and a@-like filled ligand orbitals to the half-filled antibonding b&x(o") d-like metal level ( h v~ and h v2 transitions). As canbe seen in Fig. 2, transitions to the remaining d-like con-duction levels will be missing whenever the antibondingorbitals are filled as in the Cu + case. Because of therelatively large overlap of the pd orbitals, the d-like con-duction bands are about 1 to 2 eV broad.

At long wavelengths MACuC presents, at 300 K,another broad absorption peak (at about 825 nm) withsimilar characteristics, to those found in EACuC. ' It cor-responds to interband transitions between antibonding lev-els belonging to the same electronic d-like metal configu-ration. Those transitions, as well as probably some of thecharge-transfer ones, are Laporte forbidden. However ifthe symmetry of the system is either slightly distorted bythe presence of a weak low-symmetry field of an odd pari-ty, or, instantaneously distorted by an appropriate oddelectron-phonon interaction mode, the selection rule canbe slightly relaxed. '

The observed mixing of the eg and t2g orbitals closelycorresponds to the spl'itting of the 3d metal orbitals due tothe tetragonally distorted octahedral CuC16 complex,mainly promoted by a Jahn-Teller effect which leads to alower energy and degeneracy. For the CuC16 complex theEz mode reduces the symmetry of the system to D4I, . Aswe shall see below, the anomalous expansion of the crystalfavors a progressive withdrawing of the two Cl atoms ly-ing in the b axis until a nearly-square four-coordinateddistortion of the CuC16 group is achieved.

III. OSCILLATOR DESCRIPTIONOF THE BIREFRING ENCE DISPERSION

As stated above, we are looking for a formulation of thebirefringence dispersion which also explains the dispersionbehavior observed in EACuC as temperature variesaround the TCT. Let us suppose the frequency of the in-cident light is far from any of the resonance frequencies,and the absorption is not too large. Then, simple-dispersion theory approximately gives for the index ofrefraction

PAS (arb. units)

COO

OA S (orb. uni f s )

FIG. I. (a) and (b) Optical-absorption spectra (OAS)EACuC at room temperature and 79 K, respectively. (c) Pho-toacoustic spectra (PAS) at room temperature.

n (co) 1=—gCO —CO

where summation covers the significant individual dipoleoscillator contributions from the selected optical barids,and co;,f; are their resonance frequency and strength,respectiveIy.

In terms of the wavelength this relation can be expand-ed for resonances lying in the longer (red) or shorter (vio-let) wavelength regions giving

&„(S„,A,„) C„(S„,A,„)n =1+2„(S„A,„)+A,

2

. . —B„(S„,A,„)A, —C„(S„A,„)A, —.. .

where S„, is some renormalized oscillator strength andA,„„the oscillator position. As this relation is unnecessari-ly complicated for our purposes, and taking account ofthe band model presented in the foregoing section, weshall select a somewhat shorter relation which only in-cludes two significative oscillators (violet and red).

Moreover, on cooling, the absorption edge of the violetpdm lower energy band shows very strong thermochromiceffects, with a large violet s'hift =—1.22)& 10 eV/deg,which are made possible by an anomalously lattice expan-sion on cooling [Fig. 5(a)j. This distortion is compatiblewith the E2g symmetry mode which shifts the hv2 bandto higher energies as a consequence of changes in the Cl-Cu spacing. The pdo. overlapping is expected to be muchless sensitive to Cl-Cu displacements giving no perceivableeffects on the position of the hVj band. These facts to-gether with the bare shape of the experimental bands lead

J. FERNANDEZ et al. 31

b) g(o*)I ]4

II

l

j/

&l

1

fig q 2A,„S,AX„AS„A,2n 1 —(A „/A, ) 1 —(A, /&, )

(4)

where A, is the wavelength of the incident light, withNow, let nb and n, be the refraction indices

relative to the indicatrix section parallel to the light vectorE in a biaxial crystal. The birefringence dispersion for-mula which can be obtained from (3) is

/

] bt g(m'

I/ & J]p(tT' )

1 y3d I'.e„+ tgg)1~ g„{vr*)

h

\

\

where n, A.„, and A,, are average values over axes b and c,and AA,„—=k„—A, '„and AS, —=S, —S,' are the main parame-ters describing the field-induced shifts in the oscillator po-sition and strength along both axes. AS, was not takeninto account due to the insensibility of the absorptionband to different polarizations. As 2,„ is supposed to betemperature independent and is higher than A,„, its varia-tion from axis b to c was also neglected. As we shall seein Sec. V the temperature dependence of the parameters informula (4) plays a very important role in order to under-stand the optical behavior of EACuC around its isotropicpoint.

IV. EXPERIMENTAL RESULTS

FIG. 2. A simplified qualitative diagram showing the expect-ed ligand-metal charge transfer h v~ and hv2, and the intrametalh v3 transitions for a limiting four-coordinated distortion of theoctahedral CuC16 complex.

A. Experimental procedure

Very-high-quality crystals of ferroelastic EACuC wereprepared by the methods described by Arend et al.Calorimetric and thermal-expansion techniques were pre-viously described. ' Birefringence measurements werecarried out on monodomain samples with a fringe-countmethod and a slow dynamic temperature regime. Thelight source was a 900 W xenon lamp with a 0.25-m focalmonochromator. It was also used for conoscopic andorthoscopic observations with the aid of a microscope setup on an optical bench. The photoacoustic spectra wereobtained with the same basic equipment but a piezoelec-tric detector and a lock-in technique were used. The uvand ir spectra were obtained with a standard Cary spec-trometer.

B. Birefringence dispersion

S„A,„1 —(A,„/A, )

S„A,

1 —(A, /k„)(3)

us to choose for the violet side one average electronic os-cillator with a temperature-independent strength S„and atemperature-dependent average position A,

The two-oscillator model is now completed by a secondred average oscillator which accounts for the vibronicallyallowed d-d transitions between the split levels of theCu + ion (hv3 transition). The band area shows a largeenhancement with rising temperature and keeps approxi-mately its average position. However, the persistence ofthe absorption at lower temperatures suggests that thetransitions are partly electronically allowed. So, we shallkeep the average position X„constant and instead allowfor a temperature-dependent renormalized oscillatorstrength.

The resulting optical index is then given by the expres-sion

Figure 3 shows the temperature and wavelength depen-dence of the birefringence in the, temperature range from160 to 235 K with no expansion corrections, as measuredin the (b, c) cleavage plane. The b and c axes correspondto the extinction directions for the orthorhombic roomtemperature Dzi, phase. ' In agreement with Kleeman re-sults, ' the extinction directions in the (100) plane showweak deviations from their positions at room temperature.So, the assumption of a symmetry lower than theorthorhombic one, below TCT, has no perceivable influ-ence on the birefringence measurements. The wavelengthstep between curves is 10 nm, and the measuring rangecovers the transport region of EACuC in the temperatureinterval explored. For the sake of clarity, a limited tem-perature region is shown in Fig. 3. The complete curveshows that dispersion tends to be weaker as the TCT isapproached.

As can be observed, birefringence passes smoothly fromnegative to positive values with increasing temperature.

31 EXISTENCE OF AN ISOTROPIC POINT AND. . . 4565

-100

Ec

C

I

180I

200T (K)

l.220

FIG. 3. Temperature and wavelength dependence of thelinear birefringence of EACuC along the [1,0,0] direction.

510 540A Cnm)

570 600

The isotropic point shows a spectral dependence and cov-ers a temperature interval which is about 8' broad for thescanned wavelengths. As we shall later see this opticalanomaly is present as well in other members of this familyof compounds with different cations and chain lengths. '

In Fig. 4 the birefringence dispersion is shown forseveral temperatures between 165 and 205 K. Each curveshows the best fit of the experimental points to formula(4) with three free parameters P& ——2S,EA,„P2——X„, andP3 ——b,S„and average values of 825 nm, for X„and 1.66for n. The thermal behavior and physical meaning ofthese parameters will be discussed in Sec. V. The chosenwavelength range corresponds to the most transparent re-gion in EACuC. Shorter and longer wavelengths are notpresented because damping starts to be significant andtheir corresponding factor was neglected in thebirefringence formula.

The upper limiting temperature was chosen for tworeasons. On one side, dispersion noticeably decreases withincreasing temperature and the measuring error increases.Qn the other, the width of the transparent region de-creases for higher temperatures and damping factors needto be considered as we have first pointed out.

FIG. 4. Birefringence dispersion of EACuC between 165 and205 K. , experimental values. Solid lines show the best fits ofexperimental points to formula (4}for each temperature.

were performed between 180 K and room temperature.The experimental results are shown in Fig. 5 whereseveral overlapping effects can be seen. Figure 5(a) showsthe thermal expansion of a (b, c) crystal plate along the adirection. Figure 5(b) shows the intensity curve as a func-tion of temperature for a (b, c) crystal plate in the extinc-tion position between crossed polarizers at room tempera-ture. The signal has been strongly magnified in order toappreciate the small effects observed along the tempera-ture scanning. In Fig. 5(c) the differential-scanning-calorirnetry therrnograms around the TCT are presented.Finally, Fig. 5(d) displays the main features observed byconoscopic and orthoscopic optical techniques, one ofwhich is the existence of a uniaxial conoscopic pattern at195 K related with the isotropic point.

V. DISCUSSION

C. Optical and thermal behavior

In order to investigate the thermochromic behavior ofEACuC, thermal expansion, calorimetric measurements,and optical (conoscopic and orthoscopic) observations

A. Birefringence dispersion and isotropic point

The values obtained for parameters P~ and P3 from thefit of the experimental points are shown in Fig. 6 as afunction of temperature. As can be seen, both parameters

4566 J. FERNANDEZ et al. 31

0— —-3x)0

—-Qx )p

pO

(b)

—-5xfP

-1.5—

$50 375 200T(KiFIG. 6. Temperature dependence of the adjustable parame-

ters P~ ——2S„AA,„and P3 ——AS„used in the two-oscillator model[Eq. (4) in text]. ~, P„.6, P, .

+5 44)I

$90

(3)+I

210T (K)

I230

(2)+I

+I

250

FIG. 5. Thermal and optical behavior of EACuC. (a)Thermal expansion along [1,0,0] direction. (b) Light intensityversus temperature of a (b,c}plate placed in extinction positionat room temperature between crossed polars. (c) Differential-scanning calorimetric curve. {d) Orthoscopic and conoscopic op-tic observations in white light along the [1,0,0] direction: (1)vanishing of some domain walls, and transitory fading of theconoscopic pattern; (2) noticeable color change and no domainspresent, new domains appear below (2); (3) some domain wallsvanish again, ' (4) isotropic point, no domains and uniaxial cono-scopic pattern; (a), (y), and (P) are conoscopic patterns above,below, and at the isotropic point, respectively.

drop to zero in a narrow temperature interval around 200K, which closely coincides with the temperature spread ofthe isotropic point observed by birefringence and cono-scopic measurements [Figs. 3 and 5(d)]. This fact con-firms the interpretation given for AA, , and AS„ in thebirefringence-phenomenological model.

Now, let Eb and E, be the violet optical-oscillator ener-gies along the b and c crystal axes for waves propagatingwith their wave vector perpendicular to the (b, c) sectionof the optical indicatrix. It can then be easily shown thatAA, , is liriearly related with AE, =Eb —E, at the shortwave edge of the optical-oscillator model. From thelinear dependence of hA, , with temperature (Fig. 6), asimilar law is found for the hE, temperature dependence.

If the ferroelastic nature of EACuC is taken into ac-count, we may suppose that below the isotropic point thespontaneous elastic energy arising from the crystal distor-tion is linearly related with the optical anisotropy (AE„).It would then be possible to have a direct measurement ofthe order parameter associated to the second-order phasetransition which leads the crystal to the isotropic point.The I'q parameter which was not plotted in Fig. 6 gives aviolet shift for the mean position of the violet oscillator ofthe same order than the violet shift of the observed ab-sorption edge.

g. Structural aspects around the TC&

From a crystallochernical point of view, the microscop-ic mechanism of the thermochromic phase transitionshould involve (as stated in many other cases' ) a rein-forcement of the N —H . Cl hydrogen bond network asthe temperature is lowered from room temperature. Theelectron density is drawn away from the chlorine axialions favoring a square-planar geometry which may lowerthe overall free energy. Before a complete planar configu-ration is achieved, the progressive increase of the electro-static energy in the (b, c) plane is compensated by a de-crease of the elastic energy promoted by the observedanomalous expansion of the crystal along the b axis [Fig.5(a)]. The experimental results shown in Figs. 5(a)—5(d),reveal a fairly complicated behavior around the TCT. Ascan be seen, several overlapping effects appear in the tem-perature interval between 180 and 260 K, suggesting morethan one crystallographic phase transformation.

In agreement with previous measurements, ' the ob-

31 EXISTENCE OF AN ISOTROPIC POINT AND. . . 4567

served change in the extinction directions (relative toroom temperature) below 2SO K and especially below 233K (the TCT temperature) points to the possibility of anonorthogonal symmetry phase. Besides, the peak in theenthalpy-versus-temperature curve [Fig. 5(c)] is smearedout over a wide temperature range. This behavior can beinterpreted as a decrease in the disorder of the organicchains and N—H . . Cl hydrogen bonds as temperature islowered.

The expected continuous monoclinic-monoclinic phasetransition allowed by the existence of an isotropic "pointphase" could be driven by energy-minimum requirementsbetween two monoclinic crystal structures with close lat-tice energy values. This would be a rather new situationwhere two low-symmetry phases are connected by an iso-tropic point phase.

This interpretation is also supported by the observationof a diffuse conoscopic pattern in a narrow temperaturerange around 250 K which may be produced by the fluc-tuations in the directions of the ethyl chains from theNH3 groups. As the temperature is lowered below theTCT, the 45' biaxial conoscopic pattern with a wave vec-tor normal to the (b, c) plate shows a progressive decreaseof the apparent 2E optic angle which finally drops to zeroat about 195 K for white light. On further cooling, thecrystal becomes biaxial once again with its optical planerotated 90' around the acute bisectrix [Fig. S(d)]. Thisbehavior is also found at higher temperatures in relatedRZnC14 and RZnC12Br2 compounds. '

Measurements performed with monochromatic light ex-hibit the same behavior but the isotropic temperatureranges from about 180 to 200 K in agreement with thetemperature interval at which birefringence goes to zero(Fig. 3). These facts, together with the extinction mea-surements [Fig. 5(b)] and the orthoscopic domain observa-tions [schematically shown in Fig. 5(d)] support the hy-pothesis of monoclinic phases above and below the isotro-pic point.

In EACuC, the possibility of energy interchanges be-tween the CuC16 sublattice (electrostatic) and the 8 sub-lattice (elastic, or dynamic) favors the coupling betweenthe motions of the R groups and CuC16 octahedrathrough the N—H. Cl hydrogen bonds. These compet-

ing interactions should explain the complicated behaviorof EACuC around the TCT, allowing for the continuity atthe border of the various phases. A more detailed crystal-lographic study is necessary in order to clarify the natureof the physical processes involved throughout the wholelow-temperature phase transition sequence.

VI. CONCLUSIONS

From the above discussion the following conclusionscan be reached:

(i) We have shown that the two-oscillator model withthree adjustable parameters proposed, appropriately de-scribes the birefringence dispersion found in EACuCbelow its thermochromic phase.

(ii) The agreement between the two-oscillatorbirefringence model and the experimental results supportsthe main features of the optical band structure discussed.

(iii) The physical meaning of the adjustable parametersinvolved is confirmed by their thermal behavior: (a) Thevariation of P& and P3 with temperature reveals the ex-istence of an isotropic point below the thermochromicphase transition. (b) P2 gives a violet shift for the energyposition of the violet oscillator in agreement with the ex-perimentally observed value.

(iv) The existence of an isotropic point is confirmed byconoscopic measurements in monochromatic light.

(v) The extinction and domain patterns exhibited byEACuC together with the above conclusions suggest acomplicated crystallographic phase sequence which, forthe first time in this kind of compounds, would include acontinuous orthogonal to monoclinic phase transition.

ACKNOWLEDGMENTS

We wish to thank Dr. F. Agullo Lopez and Dr. Zaldofrom Universidad Aut6noma de Madrid for their assis-tance in optical-absorption measurements. We are alsograteful to J. Etxebarria for helpful comments. Finally,the authors wish to thank Dr. J. Manas for his encourage-ment and help throughout this and previous works. Thiswork was sponsored by the Comision Asesora de Investi-gacion Cientifica y Tecnica of the Spanish Government.

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