Temperature-dependent neutron diffraction on TiI3

Z. Kristallogr. 226 (2011) 640–645 / DOI 10.1524/zkri.2011.1370 # by Oldenbourg Wissenschaftsverlag, Mu¨nchen

Temperature-dependent neutron diffraction on TiI3 Joachim Angelkort*, I, Anatoliy SenyshynII, Andreas Scho¨nleberI and Sander van SmaalenI I II

Lehrstuhl fu¨r Kristallographie, Universita¨t Bayreuth, Universita¨tsstraße 30, 95447 Bayreuth, Germany FRM II-TUM, Lichtenbergstraße 1, 85747 Garching, Germany

In memoriam Professor Dr. Dr. h.c. mult. Hans Georg von Schnering Received December 17, 2010; accepted April 7, 2011

Titanium-titanium bonding / Linear thermal expansion coefficient / First-order phase transition Abstract. Crystal structures of TiI3 were determined and refined at selected temperatures between 4 and 340 K against neutron powder diffraction data. On heating, thermal expansion is found to increase abruptly at the phase transition at Tc ¼ 323 K. Most prominently, linear thermal expansion is highly anisotropic and small along ~ c (i.e. along chains of Ti atoms) in the low-temperature phase, c. An order parawhile above Tc it is much larger along ~ meter is defined by the ratio between the long and the short Ti––Ti distances on the metal chains. The temperature dependence of the order parameter indicates the transition to be of first order.

1. Introduction The average crystal structure of TiI3 consists of a hexagonal densest packing of iodine atoms in which the titanium atoms are accommodated in one third of the octahedral vacancies and form metal chains parallel to the hexagonal axis [1]. The hexagonal high-temperature phase with space group P63 =mcm and lattice parameters ˚ at T ¼ 326 K a ¼ b ¼ 7:1416ð5Þ and c ¼ 6:5102ð4Þ A transforms on cooling at Tc ¼ 323 K into an orthorhombic low-temperature phase with space group Pmnm and lattice parameters a ¼ 12.3609(7), b ¼ 7.1365(5) and ˚ at T ¼ 273 K [2]. In the high-temperature c ¼ 6.5083(4) A structure the metal chains are uniform, while they are dimerised in the low-temperature structure. The dimerisation is caused by a Peierls or a spin-Peierls pairing of the d1 Ti3þ ions. Unlike the phase transitions of the compounds TiOCl [3, 4] and TiOBr [5] the transition of TiI3 is not accompanied with a formation of an antiferromagnetic low-temperature phase. The magnetic susceptibility of the high- and low-temperature phases of TiI3 measured by * Correspondence author (e-mail: [email protected])

Klemm [6] is anomalously low and is suspected to result from a superposition of a ferro- and antiferromagnetic coupling of the magnetic moments to a so-called mesomagnetic state. Indeed, DFT-calculations of Sementa [7] performed for isostructural b-TiCl3 suggest that a mesomagnetic ordering of the magnetic moments would establish the most stable state. In [8] the structural phase transition of TiI3 was claimed to possess a second-order character. Here we present experimental evidence that the phase transition is a first-order phase transition as already proposed in [2].

2. Experimental A polycrystalline sample of TiI3 was synthesised from a stoichiometric mixture of titanium and iodine in evacuated quartz glass ampoules employing the vapor transport method. The reaction was governed by heating the ampoules for 5 days in a temperature gradient with a temperature of 863 K at the educt side and a temperature of 763 K at the product side of the ampoules. The reaction product consisted of needle-shaped crystals of TiI3 embedded in a red film of TiI4 . After cooling to room-temperature TiI4 was sublimated from the TiI3 -crystals by reheating the product side of the ampoules for some hours at a temperature of 588 K. For the neutron diffraction experiment 5 g of TiI3 were synthesized. To reduce effects resulting from texture, the crystals were cut to lengths of 5–10 mm. The sample was filled into a sample container of vanadium possessing a diameter of 13 mm. A neutron powder diffraction experiment was carried out at instrument SPODI [9] at FRM II (Forschungs-Neutronenquelle Heinz Maier-Leibnitz, Garching) employing ˚ . Scattered neutrons neutrons of a wavelength of 1.54828 A were detected up to a maximal scattering angle 2q of 150 deg. The temperature of the sample was adjusted in the temperature range between room-temperature to 4 K by the application of a cryostat. In a temperature range between room-temperature and 370 K the sample was heated by means of an electrical oven obliging the experimental setup to be modified and a remounting of the sample. At the temperatures of 300 K and 320 K measure-

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640

Table 1. Experimental and crystallographic data for measurements (long exposure) at four different temperatures. Temperature (K)

4

100

300

340

Formula weight (g/mol)

428.60

428.60

428.60

428.60

Crystal system Space group ˚) a (A

orthorhombic Pmnm

orthorhombic Pmnm

orthorhombic Pmnm

hexagonal P63 =mcm

12.2249(2)

12.2523(3)

12.3391(5)

7.1446(1)

˚) b (A ˚ c (A)

7.0695(1) 6.47052(7)

7.0849(1) 6.47571(7)

7.1330(2) 6.49842(9)

7.1446 6.5099(1)

˚ 3) Volume (A

559.21(2)

562.13(2)

571.96(3)

287.785(7)

Z Calculated density (g/cm3 )

4 5.089

4 5.062

4 4.976

2 4.944

Detector distance (mm) ˚) Wavelength (A

300

300

300

300

1.54828 0.01512

1.54828 0.01504

1.54828 0.01478

1.54828 0.01469

2qmax (deg)

150

150

148

148

Number of all reflections Number of observed reflections

653 627

654 619

655 607

121 110

Absorption coefficient (mm1 )

Number of refined parameters

14

14

14

7

Rp (observed) RF (observed)

0.0383 0.0454

0.0317 0.0430

0.0256 0.0462

0.0262 0.0517

GoF (observed) ˚ 3) Drmax (e/A ˚ Drmin (e/A3 )

5.21

4.30

2.62

4.14

0.446 0.684

0.308 0.534

0.237 0.257

0.290 0.284

ments were carried out with both the low- and the hightemperature setups. Diffraction patterns were measured over 24 h each at the temperatures 4, 100, 300 and 340 K to allow for a structure refinement against the measured data (long exposure; Table 1). Diffractograms measured over 2 h (short exposure) were used to determine the lattice parameters. For the low-temperature measurements the sample temperatures were adjusted via the cryostat to 4 K and to temperatures ranging from 25 K to 300 K employing temperature increments of 25 K. The high-temperature measurements were performed for temperatures ranging from 300 K to 370 K increasing the temperature by 10 K between consecutive measurements. In the diffraction patterns no peaks of impurities were found and no magnetic reflections were observed at any temperature. The majority of the peaks in the diffractograms could be assigned to TiI3 . Some peaks, however, were found to be caused by the scattering of the vanadium of the sample container, of the aluminium heat shielding or by the scattering of the niobium foil used as heater depending on the experimental setup used for the measurement. Regions where strong reflections of vanadium and niobium or reflections of vanadium and aluminium occurred were neither used for the profile fitting nor for structure refinements. From the data reduction of the diffraction profiles measured with the high-temperature experimental setup the 2q-regions 38–39, 42–42.7, 54.5– 55.2 and 68.8–69.5 were excluded while the excluded regions of the diffraction profiles measured with the low-temperature setup were 39.15–39.75, 42–42.7 and 45–46.1 . Profile fitting and structure refinement were performed by using the computer program Jana2006 [10]. The lattice parameters were determined from Le Bail fits of the data (Table 2). Crystal structures were determined through Riet-

Table 2. Lattice parameters and volumes of the unit cells in the lowand the high-temperature phases at various temperatures, obtained from Le Bail fits to data measured with short exposures. Standard uncertainties are in parenthesis. T [K]

˚] a [A

˚] b [A

˚] c [A

˚ 3] V [A

Low-temperature phase 4l

12.22231(15)

7.06956(7)

6.46989(5)

559.040(10)

25l 50l

12.22541(15) 12.23492(16)

7.07030(7) 7.07335(8)

6.47013(5) 6.47135(5)

559.260(10) 560.043(10)

75l

12.24383(16)

7.07826(8)

6.47330(5)

561.009(10)

100l 125l

12.25360(18) 12.26257(20)

7.08303(9) 7.08868(9)

6.47551(6) 6.47789(7)

562.027(10) 563.093(11)

150l

12.27221(22)

7.09425(11)

6.48036(7)

564.194(12)

l

175 200l

12.28230(24) 12.29271(28)

7.10057(10) 7.10861(13)

6.48295(7) 6.48523(10)

565.387(12) 566.706(16)

225l

12.30327(24)

7.11435(13)

6.48824(9)

567.914(14)

250l 275l

12.31531(24) 12.32711(25)

7.12273(15) 7.12988(15)

6.49123(9) 6.49443(10)

569.402(16) 570.801(18)

300l

12.33672(27)

7.13490(14)

6.49788(11)

571.951(19)

300h 310h

12.34058(22) 12.34555(27)

7.13615(14) 7.13892(15)

6.49782(8) 6.50013(11)

572.225(10) 572.881(17)

320l

12.34612(29)

7.13854(13)

6.50109(11)

572.962(18)

320h

12.35437(26)

7.14206(14)

6.50417(10)

573.900(16)

High-temperature phase 330h 340h

7.14129(10) 7.14446(10)

7.14129 7.14446

6.50737(11) 6.50999(11)

287.402(7) 287.773(7)

350h

7.14750(13)

7.14750

6.51285(14)

288.144(9)

360h 370h

7.15112(11) 7.15441(11)

7.15112 7.15441

6.51528(12) 6.51755(13)

288.544(7) 288.910(8)

Sample temperatures were attained by employing a low-temperature (l) or a high-temperature (h) experimental setup.

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641

Temperature-dependent neutron diffraction on TiI3

J. Angelkort, A. Senyshyn, A. Scho¨nleber et al. Table 3. Linear thermal expansion coefficients in the low- and hightemperature phases. ba , bb and bc were determined parallel to a, b and c of the low-temperature phase and the equivalent lattice directions ð2a1 þ a2 Þ, a2 and c in the hexagonal high-temperature structure. Standard uncertainties are in parenthesis.

1.0

T = 300 K

relative intensity

0.8

P mnm 0.6

T 1 [K]; T 2 [K] 0.4

0.2

0.0 0.0

20.0

40.0

60.0

80.0

2q (deg)

100.0

120.0

140.0

Fig. 1. Rietveld plot of the diffraction data at 300 K (long exposure). Data points are represented by black dots. The light grey curve constitutes the calculated profile resulting from a Rietveld refinement of the low-temperature structure. Grey shaded regions in the pattern were not used for the structure refinement. The calculated reflection positions are indicated by vertical bars. The difference between calculated and observed diffraction profiles is given by the bottom trace.

veld refinements against data measured by long exposures1 . The fit to the data is good, as evidenced by the low R values (Table 1) and good match between observed and calculated intensity profiles (Fig. 1). The starting values of the lattice parameters and the starting model for the structure refinements were taken from [2].

3. Results Linear thermal expansion coefficients were determined for different temperatures from temperature-dependent changes of the lattice parameters. The values found for the high- and the low-temperature phases were averaged separately (Table 3). The relative changes of the lattice parameters as functions of temperature are depicted in Fig. 2. For a comparison of the temperature-dependent changes the lattice parameters of the low-temperature phase were normalised to the values determined for a temperature of 4 K and the lattice parameters of the high-temperature phase were normalised to pseudo-hexagonal lattice parameters calculated from the orthorhombic lattice parameters rffiffiffiffiffiffiffiffiffi ao bo pffiffiffi and ch ¼ co ; at 4 K through the relation: ah ¼ 3 where ah and ch represent the hexagonal lattice parameters and ao , bo and co stand for the orthorhombic lattice parameters. The lattice parameters of the high-temperature phase increase linearly with temperature. For the lattice parameters of the low-temperature phase, however, a small but evident deviation from linearity is found (Fig. 2). In the low-temperature phase the averaged linear thermal expansion coefficients along the lattice directions a, b and c were determined as 3.4  105 K1 , 3.5  105 K1 and 1.8  105 K1 . In the high-temperature phase the line1 Supplementary data of the crystal structure refinements can be found at the database of the Fachinformationszentrum Karlsruhe (FIZ) under the CSD numbers 42286-422871.

ba [105 K1 ]

Low-temperature phase 2.92(12) 100l ; 125l 3.14(14) 125l ; 150l l l 150 ; 175 3.29(15) 3.39(17) 175l ; 200l 3.44(17) 200l ; 225l 3.91(16) 225l ; 250l 250l ; 275l 3.83(16) 3.19(17) 275l ; 300l 3.81(23) 300l ; 320l 3.44(33) averagel High-temperature phase 330h ; 340h 4.44(16) 4.25(19) 340h ; 350h 350h ; 360h 5.08(19) 4.59(18) 360h ; 370h 4.59(20) averageh

bb [105 K1 ]

bc [105 K1 ]

3.19(9) 3.14(11) 3.57(12) 4.53(13) 3.23(15) 4.71(16) 4.02(16) 2.81(14) 2.55(15) 3.53(70)

1.47(8) 1.53(8) 1.60(9) 1.41(10) 1.85(11) 1.85(11) 1.97(12) 2.12(13) 1.98(15) 1.75(24)

4.43(28) 4.25(32) 5.08(34) 4.59(31) 4.59(20)

4.02(34) 4.39(38) 3.74(40) 3.48(38) 3.91(22)

Sample temperatures were adjusted using a low-temperature (l) or a high-temperature (h) experimental setup.

ar expansion coefficients along the directions a and c are 4.6  105 K1 and 3.9  105 K1 , respectively (Table 3). Thus, the linear thermal expansion coefficient is in the

Fig. 2. Relative changes of the lattice parameters (‘T /‘T0 ) and of the volume of the unit cell (VT /VT0 ) in the high- and the low-temperature phases as functions of temperature. The lattice parameters were determined by a profile fitting using data measured with a low-temperature experimental setup (open symbols) or data measured with a high-temperature experimental setup (filled symbols). The grey shaded area marks a part of the stability range of the high-temperature phase. The volumes of the unit cells were normalised to the volume determined at 4 K. The description concerning the normalisation of the lattice parameters is given in the text.

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642

I2

I2

I4

˚ ) and bond angles (deg) at different Table 4. Interatomic distances (A temperatures. 4K

Ti

I1

I3

I1

Ti

c

I2 a

I2

I4

b

Fig. 3. Section of the TiI3 -structure at T ¼ 300 K showing a dimer of titanium atoms coordinated by iodine atoms. Ellipsoids indicate the atomic displacements for a probability of 50 percent to encounter the atoms at the predicted positions.

low-temperature phase remarkably smaller along the c-direction than along the a- or b-directions and possesses in the high-temperature phase almost equal values for the directions parallel and perpendicular to c (Table 3 and Fig. 2). The transition into the low-temperature phase is accompanied with a dimerisation of the titanium atoms on the metal chains (Fig. 3 and Table 4). Because of the stiff nature of the covalent bond between the d 1 Ti3þ ions and the coincidence of the bonding axis with the metal chain axis a dilatation of the lattice along the chain axis is less favorable than a dilatation perpendicular to c. The alternation of titanium dimers of adjacent metal chains along the c-direction causes a decrease of the compressibility of the whole framework parallel to c allowing for the considerable decrease of the linear thermal expansion coefficient along this direction. The transition into the high-temperature phase is accompanied by a vanishing of the dimerisation and an increase of the linear thermal expansion coefficient predominantly along c. With the vanishing of the covalent titanium-titanium bond the direction-dependence of the linear thermal expansion coefficient decreases notably. In the low-temperature structure the anisotropy of the atomic displacement parameters (ADPs) increase with the approach of the phase transition temperature (Table 5 and Fig. 3). The high anisotropy of the ADPs of titanium at T ¼ 300 K reflects the competition of the thermal motion with the covalent titanium-titanium bond in the vicinity of the phase transition. Indeed, the equivalent isotropic ADPs for titanium and iodine possess higher values in the hightemperature phase than in the low-temperature phase (Table 6). At a temperature of 300 K, however, the titanium atom possesses along the c-direction an ADP larger than the average value in the high-temperature structure. The axis of the elongated displacement ellipsoid of the tita-

100 K

300 K

340 K

Intrachain distances Ti-Ti 3.507(6) 2.963(6) Ti-I1 (2) 2.776(5) Ti-I2 (2) 2.796(5) Ti-I3 2.666(7) Ti-I4 2.908(7) I1-I1 4.066(3) I1-I2 (2) 3.948(3) I1-I3 (2) 3.988(6) I1-I4 (2) 3.953(3) I2-I2 3.841(6) I2-I3 (2) 3.946(3) I2-I4 (2) 3.858(7)

3.518(7) 2.958(7) 2.765(5) 2.802(5) 2.687(8) 2.887(9) 4.077(4) 3.944(4) 3.992(6) 3.953(3) 3.836(6) 3.952(3) 3.840(8)

3.399(17) 3.099(17) 2.712(9) 2.847(10) 2.825(14) 2.778(13) 4.172(5) 3.954(5) 3.933(10) 3.969(4) 3.875(10) 3.955(5) 3.919(9)

3.25497(11) 3.25497(11) 2.7886(8) 2.7886(8) 2.7886(8) 2.7886(8) 3.9222(14) 3.9652(8) 3.9222(14) 3.9652(8) 3.9222(14) 3.9652(8) 3.9222(14)

Interchain distances I1-I1 4.066(3) I1-I2 4.145(6) I1-I2 4.177(6) I1-I3 (2) 4.132(6) I1-I4 (2) 4.119(4) I2-I2 4.158(4) I2-I3 4.193(5) I2-I4 (2) 4.189(5) I3-I4 (2) 4.109(5)

4.077(4) 4.151(6) 4.201(6) 4.141(6) 4.134(4) 4.180(4) 4.210(4) 4.219(9) 4.123(6)

4.172(5) 4.262(9) 4.189(9) 4.213(10) 4.209(6) 4.175(6) 4.233(7) 4.200(9) 4.145(7)

4.1757(10) 4.2300(10) 4.2300(10) 4.2300(10) 4.2300(10) 4.1757(10) 4.2300(10) 4.2300(10) 4.1757(10)

Bond angles I1-Ti-I1 I1-Ti-I2 (2) I1-Ti-I3 (2) I1-Ti-I4 (2) I2-Ti-I2 I2-Ti-I3 (2) I2-Ti-I4 (2) Ti-I1-Ti (2) Ti-I2-Ti (2) Ti-I3-Ti Ti-I4-Ti

91.97(18) 90.23(10) 94.21(14) 88.10(17) 86.77(17) 92.48(18) 85.10(14) 64.51(15) 77.68(16) 67.5(2) 74.2(2)

92.5(2) 90.23(10) 94.13(16) 88.7(2) 86.40(19) 92.1(2) 84.90(17) 64.66(16) 77.79(17) 66.8(2) 75.1(3)

92.9(4) 90.65(15) 90.5(3) 92.6(3) 85.8(4) 88.4(4) 88.3(4) 69.7(3) 73.3(3) 66.5(4) 75.4(4)

89.375(14) 90.625(14) 89.375(14) 90.625(14) 89.375(14) 90.625(14) 89.375(14) 71.41(3) 71.41(3) 71.41(3) 71.41(3)

nium atom points at this temperature between the bonded titanium atom and atom I3. The iodine atom closest to the titanium atom (I1 in Table 4 and Fig. 3) exhibits an elongation of the displacement ellipsoid in the c-direction while the elongation axis of the displacement ellipsoids of the other iodine atoms are oriented perpendicular to the cdirection (Table 5 and Fig. 3). At temperatures above Tc the energy of the thermal motion apparently exceeds the bonding energy of the titanium-titanium bond resulting in only slightly anisotropic ADPs of the titanium atom. The order parameter of the phase transition was calculated as a function of temperature from the titanium–titanium distances in the low-temperature structure (Table 4) according to:  h¼

dlong dshort

 1

ð1Þ

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643

Temperature-dependent neutron diffraction on TiI3

J. Angelkort, A. Senyshyn, A. Scho¨nleber et al.

Table 5. Anisotropic atomic displacement parameters of iodine and titanium at different temperatures. T (K)

U11

U22

U33

U12

U13

4

0.0091(18)

0.0027(19)

0.0074(15)

0

0

––0.0131(22)

100 300

0.0138(19) 0.0234(30)

0.0069(21) 0.0273(32)

0.0156(17) 0.0418(24)

0 0

0 0

––0.0111(11) 0.0162(42)

340 I1*

0.0317 (9)

0.0317(15)

0.0392(15)

0.0159

0

0

4

0.0088(18)

0.0092(6)

0.0077(21)

0.0019(12)

0

0

100

0.0106(19)

0.0137(16)

0.0188(19)

0.0023(13)

0

0

300 I2*

0.0232(31)

0.0191(22)

0.0554(30)

0.0057(22)

0

0

4

0.0146(23)

0.0092(0)

0.0075(19)

0.0001(12)

0

0

100 300 I3*

0.0157(22) 0.0483(39)

0.0148(17) 0.0407(34)

0.0174(20) 0.0145(22)

0.0047(14) 0.0081(28)

0 0

0 0

U23

Ti

4

0.0075(27)

0.0092(0)

0.0117(40)

0

0

0

100 300 I4*

0.0196(29) 0.0272(45)

0.0012(23) 0.0350(41)

0.0116(31) 0.0212(40)

0 0

0 0

0 0

4 100

0.0055(25) 0.0116(27)

0.0092(0) 0.0348(34)

0.0168(41) 0.0019(25)

0 0

0 0

0 0

300

0.0873(67)

0.0006(23)

0.0151(33)

0

0

0

* The atomic displacement parameters for the symmetry independent single iodine atom at T ¼ 340 K are in the high-temperature structure: 0.0388(4) 0.0529(7) 0.0300(4) 0.0265 0 0. Table 6. Relative atomic coordinates and equivalent isotropic atomic ˚ 2 ) for the low- and high-temperature strucdisplacement parameters (A tures at different temperatures. Atomic coordinates in the low-temperature structure refer to the orthorhombic lattice with the origin of Pmnm at m2=nm and atomic coordinates for the high-temperature structure refer to the hexagonal lattice. y

z

Ueq

4K Ti

0

––0.2366(9)

I1

0.1633(3)

––0.4113(5)

0

0.0086(9)

I2 I3

0.6571(4) 0

0.0913(5) 0.0770(8)

0 0

0.0104(10) 0.0095(16)

I4

0.5

0.5647(8)

0

0.0105(16)

––0.22898(67)

0.0064(10)

100 K ––0.2397(10) ––0.4110(6)

Ti I1

0 0.1630(3)

I2

0.6565(4)

0.0932(7)

0

0.0160(12)

I3 I4

0 0.5

0.0769(7) 0.5628(12)

0 0

0.0108(16) 0.0161(17)

300 K Ti 0

––0.2585(16)

I1

0.1593(5)

––0.4049(8)

I2 I3

0.6570(6) 0

I4

––0.2286(7) 0

––0.23844(18)

0.0121(11) 0.0144(10)

0.0308(17)

0

0.0325(16)

0.0890(10) 0.0727(12)

0 0

0.0345(19) 0.0278(24)

0.5

0.5666(9)

0

0.0344(26)

0 0.3170(2)

0 0

0 0.25

0.0342(6) 0.0390(4)

340 K Ti I

0.2

h = (dlong/ dshort) - 1

x

with dlong and dshort representing the long and the short titanium–titanium distances, respectively. A plot of the calculated values against the temperature is depicted in

0.1

0 0

100

200

300

T (K)

400

Fig. 4. The order parameter h determined from the ratio of the longer Ti––Ti distance (dlong ) and the shorter Ti–Ti distance (dshort ) on a metal chain in the low-temperature crystal structure for different temperatures. The crystal structures were determined in structure refinements against reflection data measured in neutron (open circles) or Xray diffraction (squares) experiments. The solid curve is a fit to the data points using Eq. (2). For temperatures above Tc ¼ 323 K (grey shaded area) the high-temperature phase is stable.

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644

Fig. 4 together with values of the order parameter determined from structural data published in [2] and obtained by structure refinements using single-crystal X-ray diffraction data. As can be seen from the graph in Fig. 4 the order parameter possesses an almost constant value of 0.19 for temperatures below T ¼ 273 K and decreases abruptly in the temperature range between 273 K to Tc ¼ 323 K. The change of the order parameter was fitted using the power function:   Tc  T b : ð2Þ h¼a Tc The fit converged to the parameters a ¼ 0.194(9), Tc ¼ 300.0(3) K and b ¼ 0.05(4). The value found for the exponent shows a clear discrepancy to the value of 1=3 expected for a second-order phase transition. The deviation of the curve of the fit function from the data points in Fig. 4 indicates that a power function as given by Eq. (2) cannot well describe the experimental points. The use of such a function is therefore actually not suitable to fit the discontinuous behavior of the order parameter confirming the proposal in [2] that the phase transition of TiI3 is a first-order phase transition. The present results contrast the proposal of Meyer et al. [8] of a second-order phase transition. As the hexagonal symmetry of the high-temperature phase allows exactly one Ti––Ti distance along the chains, the two different Ti––Ti distances in the range 330––370 K, as reported in [8], cannot be explained by the proposed phase transition at Tc ¼ 323 K.

4. Conclusions The change of the order parameter determined from structural parameters as a function of temperature corroborates the occurrence of a first-order phase transition at Tc ¼ 323 K. In the high-temperature phase the linear thermal expansion coefficient is almost equal for all directions. The transition into the low-temperature phase is associated with a larger decrease of the linear thermal expansion coefficient parallel to the c-direction than for directions perpendicular to c. The formation of covalently bonded d 1 Ti3þ ion pairs along the metal chains is sought

responsible for the occurrence of an anisotropy of the linear thermal expansion coefficient in the low-temperature phase. The dimerisation causes a decrease of the compressibility of the TiI3 framework along c resulting in the decrease of the linear thermal expansion coefficient along this direction. Conversely, the sudden increase of the linear thermal expansion coefficient parallel to c indicates a loss of the structural blockage by the vanishing of the titanium-titanium bonding at the transition into the high-temperature phase. The highly anisotropic ADPs of titanium at a temperature of 20 K below Tc provide evidence of the competition of the thermal motion of the atoms with the covalent Ti––Ti bond resulting in the destruction of the covalent bond at Tc . Acknowledgment. We thank Alfred Suttner for synthesizing crystals of TiI3 .

References [1] von Schnering, H.-G.: Zur Struktur des Titan(III)-jodids. Naturwissenschaften 53 (1966) 359–360. [2] Angelkort, J.; Scho¨nleber, A.; van Smaalen, S: Low- and hightemperature structures of TiI3 . J. Solid State Chem. 182(3) (2009) 525–531. [3] Seidel, A.; Marianetti, C.-A.; Chou, F.-C.; Ceder, G.; Lee, P. A.: S ¼ 1=2 chains and spin-Peierls transition in TiOCl. Phys. Rev. B 67 (2003) 020405(R). [4] Scho¨nleber, A.; van Smaalen, S.; Palatinus, L.: Structure of the incommensurate phase of the quantum magnet TiOCl. Phys. Rev. B 73 (2006) 214410. [5] van Smaalen, S.; Palatinus, L.; Scho¨nleber, A.: Incommensurate interactions and nonconventional spin-Peierls transition in TiOBr. Phys. Rev. B 72 (2005) 020105(R). [6] Klemm, W.; Krose, E.: Das magnetische Verhalten der Titantrihalogenide. Z. Anorg. Allg. Chem. 253 (1947) 209–217. [7] Sementa, L.; D’Amore, M.; Barone, V.; Busico, V.; Causa, M.: A quantum mechanical study of TiCl3 a, b and g crystal phases: geometry, electronic structure and magnetism. Phys. Chem. Chem. Phys. 11 (2009) 11264–11275. [8] Meyer, G.; Gloger, T.; Beekhuizen, J.: Halides of titanium in lower oxidation states. Z. Anorg. Allg. Chem. 635 (2009) 1497–1509. [9] Hoelzel, M.; Senyshyn, A.; Gilles, R.; Boysen, H.; Fuess, H.: Scientific Review: The structure powder diffractometer SPODI. Neutron News 18(4) (2007) 23–26. [10] Petricek, V.; Dusek, M.; Palatinus, L.: Jana2006. The crystallographic computing system. Institute of Physics, Praha, Czech Republic (2006).

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Temperature-dependent neutron diffraction on TiI3