Infrared modes and dielectric constants of PbFCl-type compounds

Pergamon

Materials Research Bulletin 35 (2000) 1897–1905

Infrared modes and dielectric constants of PbFCl-type compounds M. Sieskinda,*, J.-C. Bouloub, A. Fettouhia, D. Ayachoura a

CNRS, Laboratoire PHASE (UPR 292), BP 20, 67037 Strasbourg Cedex 2, France b Bruker Spectrospin, 34 Rue de l’Industrie, 67160 Wissembourg, France (Refereed) Received 23 August 1999; accepted 10 February 2000

Abstract Infrared active modes and multiphonon modes as dielectric constants of some crystals of the matlockites family have been investigated. At about 1000 K, the thermal behavior of the static dielectric constant εs// shows a sharp increase, which is imputed to an order– disorder phase transition. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Halides; D. Dielectric properties; D. Optical properties

1. Introduction Crystals of the matlockite family have been the subject of a wide range of theoretical and experimental studies. In particular, BaFCl and BaFBr crystals doped with various rare-earth elements are of considerable interest as X-ray imaging detectors [1]. A number of studies require the knowledge of some crystal properties, particularly the dielectric and elastic constants and phonon data [2–5]. It is the goal of this paper to present some information on the infrared properties of SrFCl, SrBFr, PbFCl, and PbFBr, and more precisely on their fundamental and multiphonon absorption bands and their dielectric constants. The static dielectric constants εs// measured by means of a variable frequency faradmeter have been compared with those inferred from the far-infrared spectra. On the other hand, the

* Corresponding author. Fax: ⫹33-3-88-10-62-93. 0025-5408/00/$ – see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 5 - 5 4 0 8 ( 0 0 ) 0 0 4 1 2 - 8

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Fig. 1. Ordinary reflection spectra between 50 and 500 cm⫺1 of (a) SrFCl, (b) SrFBr, (c) PbFCl, and (d) PbFBr.

difference between the static and optical dielectric constants has been assigned to the antiferroelectric character of the matlockite [6]. This hypothesis is supported by the thermal behavior of εs//, which shows an order– disorder phase transition.

2. Experimental Single crystals of MFX (M ⬅ Sr, Pb; X ⬅ Cl, Br) were grown by slowly cooling a molten mixture of carefully dehydrated MF2 and MX2 in a platinum boat, which was placed in a quartz tube filled with argon gas. The cooling rate was about 3 K/h. Typical crystal dimensions were 10 ⫻ 10 ⫻ 0.2 mm3 for SrFX and PbFX. These platelets were clear and colorless single crystals. Four modes, 2A2u and 2Eu, were IR active [7]. The two IR active modes ␯1 and ␯2 of EIR u were measured for single crystals with [001] orientation using a standard specular reflectance accessory with an angle of incidence of

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Table 1 Comparison of the observed frequencies from the absorption maxima (Kramers-Kronig analysis) Kmax and Rmax (R) of monocrystals or Tmax (T) of pressed pellets (cm⫺1) Substance EIR u (ord.)

AIR 2u (extraord.)

␯1

␯2

Kmax SrFCl

T0

再135 143 关12兴

T0

77 再114 关12兴

(T) or (R) Kmax

149 (R)

257 (R)

158 166 (R) 182 [12]

316 322 (R) 340 [12]

230 (R) 248 (T)

150 137 (T) 132 [12]

300 323 (T) 328 [12]

PbFBr

再87.9 125 关12兴 56 T 再 78–72–57 关12兴

237 255 [12]

(T) or (R) Kmax

(T) or (R)

318 110 (T) 107 (R)

L0 120 PbFCl

␯2

(T) or (R) Kmax

L0 162 SrFBr

␯1

212 235 [12] 290

T0

114 (R) 110 (T)

0

75 (R) 79 (T)

179 182 [12]

181 (T) 202 (R)

309(T) 330 [12]

152.6 179.2 (R) 156–167 [12] 165.9 (T)

285 (T) 320 [12]

Rmax and Tmax are the maxima of the reflection and transmission, respectively. The agreed values are underlined.

about 11° and a Bruker IFS113V vacuum FTIR spectrometer. For SrFCl, the two IR active modes ␯1 and ␯2 of AIR 2u were measured in the [110] direction using the same mounting. In this case, the IR beam was polarized using a gold wire grid polarizer on polyethylene for the far infrared. For the extraordinary spectrum (AIR 2u bands) of the other compounds, we examined the transmission spectrum of pressed pellets of powdered samples in polyethylene. All of the measurements were recorded with a spectral resolution of 16 cm⫺1, a TGS polyethylene window detector, and various mylar beamsplitters of 6, 25, and 50 ␮m thickness, to cover all of the far-infrared spectral range. Multiphonon bands were observed by transmission in the far-infrared using pressed pellets or single crystals with the smallest dimension along the C4 axis. Moreover, for SrFCl, two subsidiary bands were observed by reflection at the short wavelength side of the main reflectivity band. By analogy with the reflectivity spectrum of NaCl, for example, they are attributed to anharmonic interactions [8]. Let us remark that the Table 2 Effective charges e⬜* of SrFCl and SrFBr Substance

e⬜*Sr

e⬜*F

e⬜*X

SrFCl SrFBr

2.16 2.56

⫺1.08 ⫺1.28

⫺1.08 ⫺1.28

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Fig. 2. Two-phonon absorption bands of 2.1 (top) (a) SrFCl and (b) SrFBr, and 2.2 (bottom) (a) BaFCl, (b) BaFBr, and (c) BaFI.

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Table 3 Observed combination modes and their assignments Frequency (cm⫺1)

Symmetry

SrFCl ␯2(E ) ⫹ ␯l(A ) IR u

IR 2u

Ç

SrFBr

BaFCl

BaFBr

BaFI

PbFBr

Obs.

Calc. Obs.

Calc. Obs. Calc. Obs.

Calc. Obs. Calc. Obs. Calc.

380

395

362

363

353

376

338

358

331

—

440

425

433

413

395

390

385

312

501

453

463

—

405 [12]

366

—

408 [12]

T0 IR ␯1(AIR 473 2u) ⫹ ␯2(Eu )

Ç T ⫹L 0

476

470 [12]

454 455 [12]

413 [12]

0

IR ␯2(AIR 585 2u) ⫹ ␯2(Eu )

Ç

579

578 [12]

548

553

511

503

545 [12]

486

464

488 [12]

T0

density of states is almost zero below 50 cm⫺1 [9,10]. Thus, the combination of acoustic and optical modes is improbable. The samples used in the measurements of the static dielectric constant εs// were as-grown platelets of about 10 ⫻ 10 ⫻ 0.1 mm3 with the smallest dimension along the [001] direction. The crystals were inserted between two platinum paste electrodes (Leit-platin, Degussa) with a guard ring. In order to carry out the fully reproducible experiments, the samples were annealed in an electrically heated furnace at 600°C for 30 mn and then slowly cooled to room temperature during 6 h. The ambient was dry purified argon. The dielectric constants were measured from 20 to 800°C by means of a variable frequency (5 Hz to 13 MHz) faradmeter (Hewlett Packard LT 4192A) with an accuracy of 0.1 pF.

Table 4 Static and optical dielectric constants Substance

Optical measurements

Electrical measurements

⬜ ε⬁

冒冒 ε⬁

SrFCl

2.707 (5140 Å) [16]

2.645 (5140 Å) [16]

SrFBr

2.88

—

—

PbFCl

3.41 (500 cm⫺1) 4.52 (6563 Å) [15] 3.13 (500 cm⫺1) 3.24 (4000 cm⫺1)

3.97 (6563 Å) [15]

12

6.07 (50 MHz) [6] 7.15 (50 KHz) [6] 11.9 (0.8 KHz) [12] 7.57 (50 KHz) 13.2 (0.8 KHz) [12] —

—

25.2

—

PbFBr

εs⬜ (2 THz) 8.2

εs冒冒

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Fig. 3. Ordinary refractive index of (a) PbFCl and (b) PbFBr between 50 and 500 cm⫺1.

3. Results and discussion 3.1. IR active and two-phonon modes The ordinary reflection spectra (Fig. 1) of SrFX and PbFX (X ⬅ Cl, Br) were analyzed by using the Kramers-Kro¨nig method. The frequency dependent phase ␾(␯) was calculated by performing a Kramers-Kro¨nig transform (KKT) on the natural logarithm of the reflectance spectrum R(␯) between 50 and 500 cm⫺1 ␸共␯兲 ⫽ KKT 关1/ 2 Ln R共␯兲兴

(1)

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By analogy with the results from BaFCl and BaFI [11], no irregularity of reflectivity was to be expected. Thus, the reflectivity observed at 50 cm–1 was assumed to be constant between 50 and 0 cm⫺1. In the case of SrFCl and SrFBr, where the crystals are of suitable dimensions and free from mechanical stresses, the TO phonon frequencies were determined from the maxima of ε⬙(␯) and the LO phonon modes from the zero point of the positive slope of ε⬘(␯). For all of the examined crystals, the frequency of the absorption maximum Kmax was obtained from the absorption coefficient k (Table 1). Our results augment and qualify the data obtained previously by Bhat et al. [12] in the absorption of powdered samples by means of less dispersive interferometers. R IR The comparison between the modes BR 1g, Eg , and Au2u formed the subject of discussion in a previous paper [11] (R for Raman modes). The frequencies of the ␯2 (AIR 2u) modes are very close together for all the MFX (M ⬅ Sr, Ba, Pb; X ⬅ Cl, Br) compounds, with a mean ⫺1 IR value [6] (Table 1) of ␯2(AIR . It is the same for the ␯2(EIR 2u) ⬇ 300 cm u ) modes: ␯2(Eu ) ⬇ ⫺1 200 cm . It has been shown in a shell model calculation [11] that one of the eigenvalues of the 3 ⫻ IR 3 matrices ⌫7 and ⌫10 gives the ␯2(AIR 2u) and ␯2(Eu ) modes, respectively, and that for these modes the nondiagonal terms of the matrices are negligible in a first approximation. Moreover, these modes depend essentially on the mass of the F ion and on the short-range interactions between M and F. The Coulomb contributions are of the same order of magnitude for all the compounds. Finally, the most important interactions between M and F in repulsive expressions yield values that are close, but slightly higher for Sr than for Pb. These facts explain why the modes are of about the same order of magnitude, with the values for Sr being slightly higher than those for Pb. 3.2. Effective dynamical charges For SrFCl and SrFBr, the effective dynamical charges of ions have been calculated using Kurosawa’s formula [13] 4␲N

冘e */M ⫽ ε 冘冉 ␻ i

i

i

⬁

n

2 nL

2 ⫺ ␻ nT

冊

(2)

where N is the number of unit cells in a unit volume and ei* and Mi correspond to the effective charge and the mass of the ith ion, respectively. The summation on the left-hand side covers all the ions in the unit cell, and that on the right-hand side concerns all the involved vibrations (Table 2). The effective charges are of the same order of magnitude as those found for BaFX (X ⬅ Cl, Br, I) crystals [12]. 3.3. Two-phonon IR absorption The two-phonon IR transmission bands of SrFX (X ⬅ Cl, Br) and BaFX (X ⬅ Cl, Br, I) IR (Fig. 2) are tabulated in Table 3. The values of the AIR 2u and Eu modes of BaFX are given in refs. [9] and [10]. A number of combination modes have been observed by Bhat et al. [12] IR in SrFCl, SrFBr, and BaFBr. We have not observed the modes allowed to AIR 2u and Eu .

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Fig. 4. Thermal evolution of the static dielectric constant εs// of SrFCl (■) and SrFBr (F).

The selection rules [14] for absorption processes involving two phonons show that combination processes are allowed for the ⌫ point, among others. To the contrary, overtones are forbidden for this point as well as for others, such as Z, X, ⌳, and A of the Brillouin zone. Accordingly, the observed two-phonon modes are assigned to the combination modes of AIR 2u and EIR u phonons, which show a weak dispersion in the Brillouin zone [15]. The combination IR modes assigned to ␯2(EIR u ) ⫹ ␯1(Au ) were not observed in the compounds of Pb, perhaps because the crystals were of lower quality. 3.4. Dielectric constants The values of the dielectric constants of SrFCl, BaFCl, BaFBr, and BaFI have been published elsewhere [12]. To complete these previous results, we give here in Table 4 the values of the static dielectric constants εs// of SrFCl and SrFBr at 50 and 0.8 KHz at room ⬜ of PbFBr has been measured on a channeled temperature. The optical dielectric constant ε⬁ spectrum given by a crystal of 100 ␮m thickness. Fig. 3 shows the refractive index of PbFCl and PbFBr between 50 and 500 cm⫺1. Moreover, for PbFBr, regularly spaced interference fringes are observable between 500 and 4000 cm⫺1. Consequently, the ordinary refractive index shows little dispersion in this spectral region. The same constancy has been observed in the measured reflectivity for both PbFBr and PbFCl. But the difference between εs⬜ at 40 ⬜ is very high and can be assigned to an antiferroelectric cm⫺1 (on the order of 25) and ε⬁ behavior. // is probably due to More generally, the difference between the values of εs// and ε⬁ contributions of the dipolar and ionic polarizabilities. This hypothesis is confirmed by a sharp increase in the dielectric constant as the temperature is increased to about 1000 K (Fig. 4).

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There is probably an order– disorder transition involving dipoles. Around the Curie point, the inverse susceptibility ␹ can be approximated by linear functions of the temperature T.

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