Relaxation Dynamics of Orientationally Disordered ... - ACS Publications

1594

J. Phys. Chem. B 2008, 112, 1594-1603

Relaxation Dynamics of Orientationally Disordered Plastic Crystals: Effect of Dopants L. P. Singh,† S. S. N. Murthy,*,† T. Bra1 uniger,‡ and H. Zimmermann§ School of Physical Sciences, Jawaharlal Nehru UniVersity, New Delhi - 110067, India, Institute of Physics, Martin-Luther-UniVersity, Halle-Wittenberg, Friedemann-Bach-Platz 6, 06108 Halle, Germany, and Max-Planck-Institut fu¨r Medizinische Forschung, Jahnstrasse 29, 69120 Heidelberg, Germany ReceiVed: September 1, 2007; In Final Form: NoVember 13, 2007

We have examined the relaxation that occurs in the supercooled plastic crystalline phases of pentachloronitrobenzene (PCNB), dichlorotetramethylbenzene (DCTMB), trichlorotrimethylbenzene (TCTMB) along with some of their deuterated samples, and 1-cyanoadamantane (CNADM) in the presence of intentionally added dopants. The experimental techniques used in the present study are dielectric spectroscopy and differential scanning calorimetry (DSC). Only one relaxation process similar to that of the primary (or R-) relaxation characteristic of glass-forming materials is found, but there is no indication of any observable secondary relaxation within the resolution of our experimental setup. The R-process can reasonably be described by a Havriliak-Negami (HN) shape function throughout the frequency range. However, in the case of PCNB the dielectric strength (∆) of the above said R-process does not change appreciably with temperature, though interestingly, a small addition of a dopant such as pentachlorobenzene (PCB), trichlorobenzene (TCB), and chloroadamantane (CLADM) to the molten state of PCNB drastically lowers the dielectric strength by a factor of 4 to 8. Powder X-ray diffraction measurements at room temperature and DSC data do not indicate any appreciable change in the crystalline structure. It is noticed that the effect of PCB as a dopant on the magnitude of R-process of CNADM is moderate, whereas both PCB and TCB as dopants show a much reduced effect on the relaxation in DCTMB and TCTMB. It is suggested that the drastic changes in the dielectric strength of the R-process is due to the rotational hindrance caused by the presence of a small number of dopant molecules in the host crystalline lattice. In the above context, the possibility of a certain degree of antiparallel ordering of dipoles is also discussed.

1. Introduction Sometimes exceptional properties of some of the aromatic compounds are intimately associated with the disorder or shortrange order in them, i.e., their nanoscale structure.1 Quantification of disorder in such materials may aid in the design of new functional molecular materials. Hexasubstituted benzenes that belong to this class of materials have thus been subjected to in-depth study using X-ray scattering,2-9 solid-state NMR,3,4,10 and dielectric spectroscopy.11-13 In addition, some of these materials have some practical applications, for example, in agriculture as a fungicide.14 However, recently there is a growing interest among researchers working on the glass transition phenomenon to study the nature of the frozen orientational disorder in these materials.15-17 Glass transition phenomena occur when a dynamically disordered system (e.g. liquid, plastic crystal, or paramagnet) freezes as a function of external temperature (or pressure) devoid of long-range order. In this freezing process, one or more degrees of freedom of atoms or molecules continuously slow down, reaching the so-called glass transition when their dynamics has a characteristic time, generally chosen to be 102 s.18-21 Since in the liquid phase there are basically translational and orientational disorders of molecules, the glass transition of canonical glass formers is associated with the freezing of these * Author for correspondence. E-mail: [email protected]. † Jawaharlal Nehru University. ‡ Martin-Luther-University. § Max-Planck-Institut fu ¨ r Medizinische Forschung.

two degrees of freedom completely. However, a mesophase can exist between the completely ordered crystalline phase and the translationally and orientationally disordered liquid phase, the so-called plastic crystalline phase, or the orientationally disordered (OD) phase.22-31 In the plastic phase, the centers of mass of the molecules have spatial long-range order, forming a lattice that generally has high symmetry (such as cubic, quasi-cubic, or rhombohedral32) but only short-range order with respect to the orientational degrees of freedom. It is well-known that the relaxation characteristics in the supercooled plastically crystalline (PC) phase are very similar to that of supercooled liquids.22,30,31,33-37 The main relaxation process (also called the R-process) in the supercooled PC phase is found to be nonDebye in frequency dependence and non-Arrhenius in temperature (T) dependence with a steplike change in the specific heat (Cp) at the so-called glass transition temperature (Tg).38-42 Therefore, a clear understanding of the molecular relaxation in these substances, where only the orientational degrees of freedom are involved, is considered to be important to understand the glass transition phenomena in general. Among compounds forming orientational glasses, the hexasubstituted benzenes exhibit molecular relaxation in the crystalline phase where the molecular rotation is hindered43 to varying degrees,11-13 that is, free rotation of the molecules as in the true liquid phase is not possible, and hence the molecules exhibit limited rotational mobility.13,43 Most of the measurements3,4,9,10,12,13 reported so far measured dielectric relaxation over a narrow frequency range, and the T dependence of the relaxation rates is not very clear.

10.1021/jp077023l CCC: $40.75 © 2008 American Chemical Society Published on Web 01/23/2008

Relaxation Dynamics of Plastic Crystals These substances also are attractive to the researchers of glass physics, as they are composed of “rigid” non-H-bonded molecular systems and appear to lack a secondary (or β-) relaxation process,22 hitherto thought of as a characteristic feature of glass transition. A recent study17 of the relaxation of one of these substances, viz. pentachloronitrobenzene (PCNB) indicated that the dielectric strength is very sensitive to the presence of dopants, whereas this effect is not expected in a liquid glass. A recent report2 on the structure of PCNB, reiterates its structure to be rhombohedral with equal probability of finding the molecule in any one of the six possible orientations. It is noted that such a distortion of the PCNB molecules must be very uncomfortable in the average structural geometry,2 and the system surprisingly chooses to pack this way rather than find an energy minimum defining a different crystal structure. Therefore, a critical examination of the effect of a wide variety of dopants on the dielectric relaxation in PCNB and other such systems is needed to find out whether this phenomenon is of general occurrence or specific only to PCNB because of its uncomfortable structural geometry. For this purpose, we have decided to study some “rigid” non-H-bonded molecular systems with a wide variety of dopants. Here we report the results of our measurements of dielectric relaxation and differential scanning calorimetry (DSC) studies on these systems over a wide range of temperatures. 2. Experiment The samples used in the study are pentachloronitrobenzene (PCNB), 1-cyanoadamantane (CNADM), chloroadamantane (CLADM), 1,2,3-trichlorobenzene (TCB) (all with the specified purity of g99%), and pentachlorobenzene (PCB) (purity >98%) obtained from Aldrich Co., U.S.A. The other samples studied here are 1,2-dichloro-3,4,5,6-tetramethylbenzene (DCTMB), its deuterated sample DCTMB-d12, 1,2,3-trichloro-4,5,6-trimethylbenzene (TCTMB), and its deuterated sample TCTMB-d9. These four compounds were synthesized by direct chlorination of the corresponding hydrocarbons and purified by successive crystallization.3,4 The DSC measurements were performed using a PerkinElmer Sapphire DSC equipped with a quench cooling accessory. The DSC cell was calibrated for temperature using indium (melting transition ) 429.75 K) and cyclohexane (solid-solid transition ) 186.09 K) as standards. For the dielectric measurements, an HP 4284A precision LCR meter in the frequency range of 20 Hz to 1 MHz was used. For frequencies in the range of 20 Hz to 10-3 Hz, we sampled the dielectric absorption currents in the time window of 0.01-1000 s, using a digital storage oscilloscope (DSO) card DSO-2200 (Link Instruments, Inc., U.S.A.), in combination with a Keithley model no. 617 programmable electrometer. The complex permittivity was calculated by taking discrete Fourier transform (DFT) of the discharging current. But, because of a limitation set by the resolution of the DSO card in this type of measurement, we are not able to determine the complete spectral characteristic at the lower frequencies. However, the fm values measured with the help of this technique are comparable to those measured by the LCR bridge. The sample PCNB was studied using a concentric cylindrical capacitor whose empty cell capacitance, C0, is about 214 pF, and the sample is melted in vacuum to fill the capacitor plates. The sample CNADM was studied using a cylindrical capacitor with an empty cell capacitance C0 of ∼20 pF and is filled by the molten sample (in vacuum). Because of the method used in filling the capacitor, there may be an uncertainty of about 10% in the absolute values of the dielectric parameters,

J. Phys. Chem. B, Vol. 112, No. 6, 2008 1595 which, however, will not alter the general inferences. In all the other cases, because of the constraints on the sample size, a disk 2.5 cm in diameter and about 0.1 cm in thickness was made out of the sample by pressing the sample in a pressure die at a pressure of 10 kbar. Two electrodes were made independently from silver powder pressed at the same pressure. The sample disk was then pressed between the silver pallets at the same pressure to make the capacitor. This capacitor was held between two chromium-plated electrodes with the aid of a light-weight spring. The sample temperature was measured with the help of a thermocouple kept deep inside the bottom electrode. The temperature of the assembly was then controlled in the same way as before. For further details of the experimental setup and for accuracy in the measurements, the reader may consult an earlier article.17 3. Results Among the materials chosen to be added as dopants, both TCB [Tm (melting temperature) ) 326.3 K, ∆Hm (enthalpy of melting) ) 3.3 kJ/mol)] and PCB (Tm ) 358.5 K, ∆Hm ) 4.89 kJ/mol) are rigid rotator phase crystalline solids, whereas CLADM (Tm ) 439.8 K, but ∆Hm could not be measured with certainty) crystallizes to a rotator phase solid, which undergoes a first-order transition to a rigid rotator phase at a temperature of 245.4 K with an associated enthalpy (∆H) of 4.05 kJ/mol. The reason for choosing these materials is that, because of their high melting and boiling temperatures, they can readily be mixed with the samples under study in their molten state without the problem of evaporation. 3.1. Effect of Dopants on the Dielectric Behavior of PCNB. The first-order transition temperatures and the associated enthalpies15 are, for PCNB, Tm ) 417.2 K, ∆Hm ) 18.55 kJ/ mol, T1 (solid-solid transition) ) 413.4 K, and ∆H ) 0.57 kJ/mol. According to an earlier report,8 the solid phase for T1 < T < Tm (designated as SI) is triclinic in structure and is a rotator phase solid, and that for T < T1, designated as SII, is rhombohedral, which is also a rotator (plastic) phase crystalline.7,8 This plastic phase exhibits a well-defined dielectric relaxation similar to the so-called R- (or primary) relaxation process found in supercooled liquids and plastic phases and exhibits a well-defined glass transition in specific heat data at a temperature of 201 K.15,16 The spectral dependence of the R-relaxation in PCNB was reported previously.15 We have analyzed the relaxation data using the Havriliak-Negami (HN) shape function44 given by

( () )

*(f) - ∞ f ) 1+i 0 - ∞ f0

1-RHN -βHN

(1)

where f0 is the mean relaxation frequency, RHN and βHN are the spectral shape parameters, and 0 and ∞ are the limiting dielectric constants for the process under consideration. The temperature dependence of peak loss frequency (fm) is then calculated from the parameters of eq 1.45 The peak loss frequency (fm) is analyzed with the critical power law (PL)15,46 equation,

fm,R ) f0,R

( ) T - T′g T′g

r

(2)

where f0,R is a constant, T′g is the glass transition temperature at which fm,R ) 0, and r is the dynamic exponent, which can be related to the size of the cooperatively rearranging region.46 Alternatively, the data can also be described equally well by

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Figure 2. Arrhenius plot of fm of R-relaxation of PCNB with various dopants (whose concentration is expressed as a mole fraction xm). The thick line corresponds to the PL equation (eq 2) for the following parameters: log f0,R(Hz) ) 4.92, r ) 12.66, and T′g ) 166.7 K.

TABLE 1: Details of r-Process as Described by Eq 1 for Samples Shown in Figure 1 sample

Figure 1. Variation of (a) real and (b) imaginary parts of complex dielectric constant of R-relaxation with frequency at a fixed temperature of ∼281.5 K, in PCNB for various dopants (whose concentration is expressed as a mole fraction xm). The thick lines correspond to fits to eq 1 as given in Table 1.

the Vogel-Fulcher-Tammann equation47 given by

fm,R ) f0,Re(-B/(T-T0))

(3)

where T0 is the limiting temperature, and f0,R and B are constants. The above equation reduces to the Arrhenius equation,48

fm ) f0e-(E/RT)

(4)

for T0 ) 0. Since the deviation of fm values from eq 4 are not strong in some of the substances of this group, we have analyzed the data in terms of both of the equations, viz. eqs 2 and 4. The addition of a small amount of PCB, TCB, CLADM, and DCTMB as dopants brings in a drastic drop in the relaxation strength of PCNB (Figure 1). However, there is no appreciable change either in the shape of the relaxation spectra (Figure 1, where the corresponding HN parameters are given in Table 1) or in the peak loss frequency (Figure 2). We have examined the ∆ (0 - ∞) of the R-process of PCNB with PCB, TCB, CLADM, and DCTMB as dopants. In all cases, ∆ values of PCNB are lowered, interestingly even upon addition of other hexasubstituted benzenes such as DCTMB. The amount of dopant to cause the same amount of decrease varies with the nature of the dopant. For example, a 1% mole fraction of PCB, which is a pentasubstituted benzene and hence asymmetric in shape, causes a 6-fold reduction in

PCNB PCNB-PCB xm ) 0.003 PCNB-PCB xm ) 0.007 PCNB-PCB xm ) 0.012 PCNB-TCB xm ) 0.024 PCNB-CLADM xm ) 0.012 PCNB-DCTMB xm ) 0.0101

temp

RHN

βHN

f0 (Hz)

fm(Hz)

∆

281.8 0.075 0.684 6.12 × 102 0.86 × 103 1.22 281.8 0.085 0.693 8.38 × 102 1.17 × 103 0.91 281.4 0.066 0.663 6.92 × 102 0.99 × 103 0.64 281.7 0.044 0.632 8.85 × 102 1.30 × 103 0.20 281.6 0.067 0.669 7.96 × 102 1.13 × 103 0.21 281.4 0.098 0.724 9.37 × 102 1.26 × 103 0.43 281.8 0.080 0.666 9.36 × 102 1.35 × 103 0.65

the ∆ value, whereas the same mole fraction of DCTMB (a more symmetric molecule) effects a 2-fold reduction only. In order to understand the actual phase behavior of the sample, we have closely monitored the dielectric behavior of the sample during very slow heating, and the behavior is noted in small steps of temperature variation. The corresponding T variation of ∆ of the R-process is shown in Figure 3a. DSC measurements on these samples are plotted in Figure 3b. 3.2. Effect of Dopants on the Dielectric Behavior of Other Hexasubstituted Benzenes. To test whether the phenomena found in PCNB in the presence of dopants is also present among the other members in the group of hexasubstituted benzenes, we have examined two samples, viz. DCTMB and TCTMB, and their deuterated samples in the presence of dopants. The deuterated samples were originally synthesized for NMR,3,4 and as such there is some genuine interest in comparing the behavior of the purely protonated samples to that of the deuterated samples. By substituting protons for deuterons at the outer periphery of the molecule, the moment of inertia of the molecules increases slightly, which may affect the relaxation rate. Before taking the dielectric measurements, we have examined these samples for the existence of various equilibrium and nonequilibrium phases using DSC. In Figure 4, we have shown the DSC scans of both of the samples obtained at a heating rate of 10°/min, where the different transition temperatures are indicated by vertical arrows. The details of various first-order phase transition temperatures and the associated enthalpies are

Relaxation Dynamics of Plastic Crystals

Figure 3. Effect of the dopants on the behavior of PCNB. (a) The T variation of ∆. The vertical dashed lines correspond to the temperatures T1 and Tm of the pure PCNB sample. (b) The DSC curves above room temperature up to the melting temperature for a heating rate of 2 deg/ min in some of the samples shown in panel a. The curves are shifted vertically for the sake of clarity. (The sample size corresponding to the curves in order from top to bottom are 11.72 mg, 11.66 mg, 14.12 mg, and 14.40 mg.)

Figure 4. DSC curves for DCTMB (solid line, sample size 15.6 mg) and TCTMB (dotted line, sample size 16.2 mg) for a heating rate of 10 deg/min. The arrows indicates the various first-order phase transition temperatures (see Table 2). Parts of the DSC curves are magnified in the inset to show the highly diffuse transitions ending at T1 and T2.

given in Table 2. The values reported in Table 2 are an average of four runs. To give some idea of the deviations of these transition temperatures from the data of others, we have also entered the corresponding values reported in the literature. We

J. Phys. Chem. B, Vol. 112, No. 6, 2008 1597 have also examined the DSC curves in the glass transition (Tg) region of both of the samples used in this study, but we could not find any clear evidence of steplike change characteristic of glass transition within the resolution of the DSC. The samples DCTMB and TCTMB are rotator (plastic) phases at room temperature.3-6,9,10,13 The various phases present in these samples do not supercool much, and readily undergo transition to the more ordered states. The dielectric measurements are made on the compressed sample (in the form of pellet) because of the problem in filling a cylindrical capacitor associated with the high melting temperature and subsequent sublimation. However, this method gives less reliable values for the empty cell capacitance C0, and hence the corresponding dielectric parameters estimated using this C0 are approximate. Only one large dispersion is found in these samples at temperatures above 77 K, which is shown in Figure 5. It may be identified as the R-process of the plastic phase, and there is no evidence of the β-process in the sub-Tg region (or it may exist below our experimental resolution). We have analyzed the relaxation data using the HN equation, which is also demonstrated in Figure 5, and the corresponding parameters are given in Table 3. In contrast to the observations of Brot and Darmon9 (on pure samples of DCTMB and TCTMB), a clear deviation from the Debye behavior is seen in all the cases studied here, and the spectral shape is clearly non-Debye in nature. However, our fm and ∆ values are more or less in agreement with those reported by Brot and Darmon.9 The temperature dependence of the relaxation rate corresponding to the primary (R-) relaxation process is examined. The Arrhenius plots of the R-process are shown in Figure 6. In all these cases, we could not measure the dielectric loss accurately on the lower frequency range (for frequencies less than 100 Hz) because of the presence of noise. The solid lines given in Figure 6 are the critical PL fits derived from eq 2 and are not distinguishable from an Arrhenius fit for the range of fm values shown in the figure for a given phase. From the Arrhenius plot, we have found in all cases a slight shift in the T dependence of the fm value at the transition temperature T2, which corresponds to the SIII f SII phase present in these samples (see inset of Figure 6). The solid lines therein are the Arrhenius fits (eq 4) for the temperature range T2 e T e T1 and T < T2, respectively. These fitting parameters are given in Table 4. From Figure 6 and Table 4, it appears that the T dependence of the relaxation rate is Arrhenius, but a slight deviation is seen on the lower temperature side, which needs to be probed further. Shown in Figure 7 is the frequency variation of the real and imaginary parts of the dielectric constant of DCTMB with added dopant TCB. Note that the reduction in dielectric strength (∆) of the R-process is not as pronounced as that in the case of PCNB. The relaxation can be well described by the HN fit, the details of which are given in Table 5. The presence of small amounts of TCB (xm e 0.02) has no detectable effect on the relaxation in either the protonated or deuterated TCTMB samples, and the results are similar to those shown in Figure 7. Depicted in Figure 8 is the temperature variation of the dielectric strength (∆) of the R-process in (a) DCTMB, DCTMB-d12, and DCTMB-TCB with xm ) 0.02 and 0.05, and (b) TCTMB, TCTMB-d12, and TCTMB-TCB, xm ) 0.02. From this plot, a change in the T dependence of the ∆ value at the transition temperatures, T1 and T2, is observed. Thus, as we decrease the temperature below T2, the dielectric strength (∆) decreases continuously in all cases, which suggests a progressive antiparallel ordering of molecular dipoles in the crystal. According to Brot and Darmon,9 the more polar the


Singh et al.

TABLE 2: Details of Various First-Order Phase Transition Temperatures and Associated Enthalpies in DCTMB and TCTMB enthalpya (∆H) kJ/mol

transition temperature (K) sample 1,2- DCTMB (C10H12Cl2) 1,2- DCTMB-d12 (C10D12Cl2) 1,2-DCTMB-TCB, xm ) 0.02 1,2,3-TCTMB (C9H9Cl3) 1,2,3-TCTMB-d9 (C9D9Cl3) 1,2,3-TCTMB-TCB, xm ) 0.02

nature of transitionb SI f L SII f SI SIII f SII SI f L SIIfSI SIIIfSII SIfL SIIfSI SIIIfSII SIfL SIIfSI SIIIfSII SIfL SIIfSI SIIIfSII SIfL SIIfSI SIIIfSII

our work Tm T1 T2 Tm T1 T2 Tm T1 T2 Tm T1 T2 Tm T1 T2 Tm T1 T2

472.5 380.8 ( 2 164.2 ( 2 471.9 379.6 ( 2 163.7 ( 2 470.4 378.6 ( 2 162.2 ( 2 501.9 398.9 ( 2 264.5 ( 2 501.9 400.6 ( 2 266.3 ( 2 500.2 398.6 ( 2 264.0 ( 2

literature (refs 3, 4, 9)

our work

466.2 383.0 170.0 470.0 381.0 170.0

13.19 1.21 0.11 15.29 0.85 0.10 13.66 0.82 0.26 20.07 1.65 0.38 17.80 1.23 0.23 15.34 1.34 0.18

498.2, 500 401 ( 3 260 ( 3

a The ∆H values associated with transitions at T1 and T2 are approximate based on the assumption that they are first-order transitions. b S: crystalline solid; L: liquid.

TABLE 3: Details of HN Parameters for Samples Shown in Figure 5 samples

T (K)

RHN

1,2-DCTMB 170.3 0.288 (T2 < T < T1) (SII) 180.0 0.223 189.3 0.193 199.3 0.156 209.4 0.129 219.4 0.102 231.9 0.076 1,2,3-TCTMB 193.2 0.223 (T < T2) (SIII) 200.8 0.279 208.2 0.190 216.5 0.150 225.0 0.120 235.1 0.122 244.5 0.116

Figure 5. Double logarithmic plot of ′′ vs frequency for T e T1 of pure (a) DCTMB and (b) TCTMB, at different temperatures. The thick line corresponds to the HN parameters shown in Table 3.

compound, the higher the ordering temperature. It is felt that a comparison of the spectral half-width (i.e., the bandwidth at half of the maximum loss) of different hexasubstituted benzenes may be of some use to relate the departure from Arrhenius behavior with the spectral half width, and hence they are shown at different temperatures in Figure 9.

βHN

fo (Hz)

fm (Hz)

∆

1.00 0.910 0.878 0.825 0.784 0.717 0.631 0.703 0.859 0.742 0.689 0.611 0.598 0.557

5.70 × 2.79 × 103 7.96 × 103 2.21 × 104 6.15 × 104 1.58 × 105 3.91 × 105 9.95 × 102 3.98 × 103 1.86 × 104 2.42 × 104 5.71 × 104 1.57 × 105 3.57 × 105

6.92 × 3.10 × 103 9.14 × 103 2.68 × 104 7.78 × 104 2.15 × 105 5.88 × 105 1.48 × 103 4.80 × 103 1.09 × 104 3.51 × 104 9.12 × 104 2.57 × 105 6.22 × 105

5.40 5.46 5.45 5.43 5.43 5.49 5.68 0.69 0.91 1.08 1.32 1.56 1.81 2.13

102

102

3.3. Effect of Dopants on the Dielectric Behavior of CNADM. This material (CNADM), because of its large dipole moment µ ) 3.83 D, is one of the most widely studied materials in its supercooled plastic crystalline state using the dielectric relaxation technique.16,32,49-52 The first-order transition temperatures and the associated enthalpies32 are Tm (melting temperature) ) 458 K (∆H ) 15 kJ/mol) and T1 (solid-solid transition) ) 280 K (∆H ) 5.5 kJ/mol). According to an earlier report,53 the solid phase stable for T1 < T < Tm, designated as SI, is a face-centered cubic with a ) 9.81 Å (at 293 K), and is a rotator phase solid; the stable phase for T < T1, designated as SII, is monoclinic with a ) 11.278 Å, b ) 6.874 Å, and c ) 12.092 Å, and the angle β ) 101°37′ (at 240 K) is a (dielectrically) rigid rotator phase. The S1 phase can be supercooled, which exhibits53,54 a glass transition temperature Tg at 170 ( 3 K and is associated with this transition, and is a well-defined dielectric relaxation above Tg, which is similar to the R- (or primary) relaxation process found in PCNB described in the previous sections. This R- relaxation in the presence of a dopant is the subject of study here. The spectral dependence of the dielectric constant and loss are shown in Figure 10 for three concentrations of PCB as dopant. The spectral dependence of the dielectric constant and loss can be reasonably described by eq 1, and the corresponding parameters are given in Table 6. Although this reduction in ∆ value upon the addition of PCB is not as pronounced as in the


Figure 6. Arrhenius plots for (a) DCTMB, DCTMB-d12, and DCTMBTCB (xm ) 0.02) and (b) TCTMB, TCTMB-d9, and TCTMB-TCB (xm ) 0.02). The thick line corresponds to the PL equation (eq 2) for the following parameters: log f0,R(Hz) ) 2.37, r ) 12.73, T′g ) 81.3 K for pure DCTMB, and log f0,R(Hz) ) 3.81, r ) 13.14, T′g ) 101.6 K for pure TCTMB. Also shown in the inset of both panels a and b are the expended portion of the Arrhenius curve to show the diffuse discontinuity of fm at transition T2, where the thick lines correspond to Arrhenius fit (see Table 4).

case of PCNB discussed in section 3.1, still the ∆ value decreases by a factor of about 2 for a small addition of about a 5% mole fraction of PCB with some change in relaxation rate. Depicted in Figure 11 is the variation of the ∆ value during cooling and subsequent heating. These CNADM samples with PCB demonstrate considerable supercooling, which, upon subsequent heating, crystallize partially to the SII phase that melts at T1 (as shown in the corresponding DSC curves) upon further heating. However, during cooling or heating cycles, we have noticed some amount of change in the magnitude of fm value as shown in Figure 12. 4. Discussion For the sake of convenience, the results are discussed in the following sections. 4.1. Dielectric Spectra and Thermal Behavior of Neat Samples. It is observed that the behavior of the deuterated samples is essentially the same as those of the isotopically normal compound, and hence, whatever inferences we make for the neat samples is also valid for the deuterated samples, unless specified otherwise. The normal and deuterated samples of DCTMB and TCTMB show very diffuse transitions below

J. Phys. Chem. B, Vol. 112, No. 6, 2008 1599 Tm, especially the one at T1 that is spread out by about 50° (Figure 4). The dielectric relaxation could not be studied for T g T1, as the corresponding relaxation occurs at frequencies well above the range used in the present study. The corresponding ∆ variation with T (Figure 8) also does not show any drastic change at T ) T1. Moreover, no X-ray studies on Phase I have been published so far, and hence, we are not in a position to comment on the nature of Phase I. However, the dielectric characteristics change at T2: the T-dependence of ∆ and fm show changes, as revealed in Figures 6 and 8. More importantly, the ∆ value falls upon lowering the temperature and does not change upon annealing, indicating that it is an equilibrium property. This clearly testifies to the onset of ordering at T2, which continues to the lower temperature side. However, upon examination of the corresponding dielectric loss curves shown in Figure 5, it is clear that the relaxation process that reflects the orientational disorder is present even at temperatures well below T2. Upon lowering the temperature, however, there is an increase in ordering and hence a decrease in ∆ and a shift of peak loss frequency to lower and lower values until the T reaches Tg, where the relaxation gets arrested kinetically. Fourme and Renaud5,6 studied the X-ray structure of TCTMB at 173 K and found it to be triclinic, belonging to the space group P1/c. The transition from Phase I to this phase (III) involves almost no change in the position of the molecules or in the orientation of their planes; rather, the transition involves, predominantly, the setting in of orientational order. Braüniger et al.4 observed by single-crystal NMR experiments that, during heating, the transformation from triclinic to monoclinic phase is rather gradual, spanning a wide temperature range. The transition is in fact between two partially ordered phases and is consequently only weakly first order. It does not involve any major structural change of the lattice but merely a relatively small, discontinuous change in the molecular polarization. Our results shown in Figures 4, 6, and 8 testify to this. In the case of DCTMB, Braüniger et al.3 performed X-ray diffraction and deuterium NMR on DCTMB and its deuterated sample (DCTMB-d12) in Phases II and III (at 110 K) and observed that both Phase II and Phase III are monoclinic (space group P21/c), with very similar unit cell dimensions and molecular coordinates, but they differ in the nature of disorder. Phase III is “right-left” disordered, with molecular para axes that are well ordered in the crystal. Our thermal and dielectric studies shown in Figures 4, 6, and 8 support the view that there is a lot of disorder present in Phase II, that in Phase III some ordering sets in, and that this ordering increases upon lowering the temperature. However, even at temperatures well below T2, some amount of disorder is still present, as can be seen from the dielectric relaxation with peak loss frequencies at lower frequencies, whose high-frequency tail can be noticed in Figure 5a. The fact that the ∆ and fm values do not change very abruptly at T2 indicates that the corresponding transition is a weak first-order transition, as also testified from the X-ray measurements presented by Braüniger et al.3 Despite the similarity in the dipole moments55 (µ ) 2.94 D for DCTMB and 3.15 D for TCTMB) and lattice parameters of the phases present in these two systems, the ∆ value of TCTMB in Phase II is considerably lower than that of DCTMB, probably because of the greater degree of disorder in the latter sample. This is also evident from the deuterium NMR and X-ray results of Braüniger et al.4 on deuterated TCTMB, where a considerable degree of order is retained even in Phase II, reflected by a nonequal population distribution of the molecular orientation in the crystal lattice sites. Compared to this, the Phase II of DCTMB


Singh et al.

TABLE 4: Details of r-Process for Samples Shown in Figure 6 Arrhenius parameters

sample 1,2-DCTMBa 1,2-DCTMB-d12a 1,2-DCTMB-TCBa xm ) 0.02 1,2,3-TCTMBb 1,2,3-TCTMB-d9b 1,2,3-TCTMB-TCBb xm ) 0.02 a

T < T2

T2 < T < T1

HN parameters βHN

log f0 (Hz)

E (kJ/mol)

log f0 (Hz)

E (kJ/mol)

0.312-0.072 0.327-0.079 0.325-0.106

1.00-0.64 1.00-0.428 1.00-0.733

13.85 13.96 14.32

35.91 35.85 37.01

12.74 11.84 12.14

32.40 29.03 30.36

0.280-0.001 0.352-0.068 0.332-0.002

0.859-0.427 1.00-0.438 1.00-0.564

14.89 14.94 15.28

42.52 43.51 44.56

15.38 15.20 15.45

45.00 44.77 45.19

range of temp (K)

RHN

152-248 150-244 150-245 177-263 179-258 175-261

The parameters for T < T2 are approximate. b The parameters for T > T2 are approximate.

Figure 7. Variation of real and imaginary parts of relaxation in DCTMB at a fixed temperature for various concentrations of the dopant TCB. The thick line corresponds to eq 1, the details of which are given in Table 5.


temp

RHN

βHN

f0 (Hz)

fm (Hz)

∆

DCTMB 190.2 0.167 0.831 1.27 × 104 1.54 × 104 5.82 DCTMB-TCB 190.7 0.148 0.815 1.92 × 104 2.35 × 104 5.69 xm ) 0.02 DCTMB-TCB 190.3 0.226 0.999 2.43 × 104 2.44 × 104 4.04 xm ) 0.05

is much more mobile and disordered, with the molecular para axes distributed over all six local crystallographic orientations. Phases II and III do not supercool much, and hence the results presented in Figures 5-8 correspond to the equilibrium phases.

Figure 8. T variation of total dielectric strength (∆) for the samples shown in Tables 4 and 5 (and Figures 5 and 7). (For the purpose of calculation of ∆ ) 0 - ∞, the ∞ from the high-frequency limit of the R-process is extrapolated linearly toward higher temperatures). Also indicated are the different transition temperatures (shown by arrows at T1 and T2), as obtained from the DSC experiment (Figure 4) and Table 2.

The fm values for Phase II in DCTMB and Phase III in TCTMB cover about four decades of frequency (Figure 6) in which the behavior is Arrhenius. Interestingly, the corresponding f0 values shown in Table 4 are about 1-3 orders greater than the lattice vibrational frequencies, indicating some amount of cooperativity among the molecules. Upon extrapolation of the Arrhenius curves of Figure 8 to lower temperatures, we expect the fm value to be 10-3 Hz at Tg(dielectric) or Tg(D). This value is 109.5 ( 1 K in DCTMB (and its deuterated sample) and is 127.7 ( 1 K in TCTMB (and its deuterated sample). Going by the trend


J. Phys. Chem. B, Vol. 112, No. 6, 2008 1601

Figure 9. Variation of spectral half-width with temperature in the pure samples of hexasubstituted benzenes.

Figure 11. Dielectric and thermal behavior of CNADM for various concentrations of the dopant (PCB). (a) T variation of ∆ for the samples during cooling and heating cycles. The data are taken during cooling at a rate of about 0.2 deg/min down to a temperature of 77 K and then heated at the same rate. Note that the samples crystallized to a larger extent during heating to rigid rotator phase solids that subsequently undergo transformation to a rotator phase solid at the corresponding T1. (b) The corresponding DSC scans around T1 taken during heating after an initial cooling at an approximate rate of 5 deg/min down to 110 K. It may be borne in mind that the endotherm at T1 is a function of annealing time and also depends on the concentration of PCB.


temp

RHN

βHN

f0 (Hz)

fm (Hz)

∆

CNADM 234.7 0.067 0.897 9.09 × 103 9.99 × 103 4.35 CNADM-PCB 234.2 0.121 0.891 1.11 × 104 1.24 × 104 3.12 xm ) 0.02 CNADM-PCB 234.8 0.123 0.901 7.14 × 103 7.88 × 103 2.04 xm ) 0.05 Figure 10. Variation of (a) real and (b) imaginary parts of the complex dielectric constant of R-relaxation with frequency at a fixed temperature of ∼234.5 K, in the supercooled phase SI of CNADM for various concentrations of the dopant PCB, where the data are taken during cooling at a rate of about 0.2 deg/min. The thick lines are fits to eq 1, whose parameters are shown Table 6.

shown in Figures 5 and 8, the dielectric relaxation would exist even at Tg(D), but its strength ∆ must be too small in magnitude. In view of the discussion in the previous paragraph, the Tg in these systems should correspond to the kinetic onset of the order-disorder transition that is completed at T2. Regarding the dielectric spectra, Brot and Darmon9 have reported a symmetric Cole-Cole type of behavior, i.e., βHN )

1 in eq 1. As shown by us in Figures 5 and 7 and Table 3 of this study, clear deviations from this type of behavior occur, where the relaxation characteristic is highly asymmetric (i.e., βHN * 1), indicating some amount of cooperativity among the molecules. In Figure 5, the loss data of some representative example of neat samples at selected temperatures are compared with the HN fits, and the respective parameters are given in Tables 3 and 4. To compare different substances, it is better to consider the half-widths, which are well above the corresponding Debye value of 1.14 decades (Figure 9). Interestingly, we do not see a correlation between Arrhenius (or non-Arrhenius) behavior and spectral dependence. According to the “strong and fragile classification” of the glass-forming systems,33,47 devia-


Figure 12. Arrhenius plot of fm of R-relaxation of CNADM for various concentrations of the dopant (PCB) during heating. The thick line corresponds to the PL equation (eq 2) for the following parameters: log f0,R(Hz) ) 5.736, r ) 10.16, T′g ) 147.7 K.

tions from Debye behavior is accompanied by non-Arrhenius dependence of the relaxation rate, which does not appear to be the case here, especially in DCTMB and TCTMB. However, we wish to mention in this context that, the difference between eq 2 (or 3) and eq 4 is not noticeable within the experimental data given in Figure 6 (also see Table 4). Presently, it is difficult to attribute any significance to this observation. As opposed to the above two cases, in the PCNB phase II, the molecules populate equally well at all six available sites,2 resulting in high disorder, which continues to the lower temperature side. However, the ∆ values do not change appreciably upon lowering the temperature, indicating that the antiparallel ordering upon lowering the temperature, if any, is not pronounced. The dipole moment of this molecule is 2.33 D55 and is much lower than that of DCTMB and TCTMB, and this partially explains the lower ∆ value in Phase II (since, ∆ ∝ µ2). The -NO2 group in PCNB is expected to give a large steric hindrance to the rotation of the molecule about the hexad axis, leading to hindered rotation and an increase in the activation energy of rotation, which is 67 kJ/mol17 and is much larger than that of both DCTMB and TCTMB, which are given in Table 5. The activation energies obtained from the Arrhenius equation (eq 4) for T < T2 (Phase III) and T2 < T < T1 (Phase II) in the case of DCTMB are around 32.4 and 35.9 kJ/mol, and in case of TCTMB are around 45.0 and 42.5 kJ/mol, respectively (see Tables 3 and 5), which correspond closely with the values from NMR measurements for DCTMB, i.e., 33 kJ/ mol3 at 260 K, and for TCTMB.4 4.2. Effect of Dopants on the r-Process. Antiparallel alignment of dipoles is not uncommon in the supercooled liquid states of alcohols where the -OH group is sterically hindered by a neighboring radical on the same molecule. Typical is the example of 4-methyl-3-heptanol, which, upon approaching Tg from a high temperature, increasingly prefers antiparallel arrangement of the molecules in the H-bonded structure.56 The corresponding Fuoss-Kirkwood correlation factor “g” approaches zero upon lowering the temperature, which can be seen as a drastic fall in the ∆ value, and the dielectric signal is nearly absent near Tg.56 The discussion on the ∆ of DCTMB and TCTMB and the X-ray scattering studies of the same in the previous sections clearly point to a possibility of antiparallel alignment of the dipoles in a crystalline lattice without affecting the positional ordering in the crystal structure. Therefore, PCNB

Singh et al. was studied with dopants whose molecules are not too different in size and shape from those of the host PCNB and, hence, are expected to occupy the regular lattice site to form a solid solution, at least for smaller concentrations of the dopant. Interestingly, the magnitude of ∆ decreases drastically with an initial increase in the concentration of the dopant, as shown in Figures 1a and 3a, without an appreciable change in the corresponding spectral shape (Figure 1b) or relaxation rate (Figure 2) from that of the pure PCNB. This behavior is independent of the dopant, namely, PCB, TCB, CLADM, and DCTMB, although the amount of dopant added to bring about the same effect varies. Our preliminary study with DCTMB as the dopant shows that a more symmetric molecular substance may result in a smaller change in ∆. The change in ∆ also depends on the solid solubility of the dopant, which are not shown in this paper for the purpose of clarity. However, the corresponding dielectric spectra were examined at a few concentrations. Thus, this study, along with that of the PCNB-PCB system reported in one of our previous publications,17 clearly proves that the fall in ∆ values of PCNB shown in Figures 1a and 3a is effected by solid solubility (even if it is very little). This point is for smaller values of the xm of PCB in CNADM; the ∆ values change (Figures 10 and 11), although not to the extent as seen in the case of PCNB without affecting the relaxation rates (Figure 12). Somewhat similar is the case with DCTMB and TCTMB, which, in the presence of TCB, show a reduction in ∆ values (Figure 7), but not to the extent as seen in the case of PCNB or CNADM. Our dielectric measurements shown in Figure 3a for temperatures T1 < T < Tm along with the DSC results of the same shown in Figure 3b clearly reveal that, for temperatures T1 < T < Tm, the sample PCNB may consist of freely rotating molecules that get hindered below T1, and the degree of hindrance depends on the nature of the doped molecule present in the PCNB lattice. The structure above this temperature is probably triclinic with freely rotating molecules.8 According to the X-ray measurements7,8 of Phase II at room temperature, the structure is rhombohedral (space group R3h), with cell dimensions ahex ) 8.7512 Å, chex ) 11.1115 Å (from ref 7) and ahex ) 8.769 Å, chex ) 11.209 Å (from ref 8; the reader may also see the more recent ref 2). The molecular orientation is disordered in the sense that the six substituent positions around the benzene ring are indistinguishable, but free rotation of the molecules is excluded.8 A more recent study by Thomas et al.2 reveals a lack of shortrange orientational order in this phase, and the same trend is seen even at temperatures as low as 5 K. The idea that there is no structural change due to the addition of a small amount of PCB is also confirmed by us using X-ray diffractograms in one of our recent reports.17 Our preliminary X-ray diffraction study of some of the samples examined here reveal some extra lines and differing intensity. Our analysis using Cryssfire software57 of this data gives many possible structures, whereas our DSC studies presented in Figure 3b do not indicate a large structural change. Since conventional crystallography gives the average structure of the material, the orientational disorder is difficult to characterize. For this purpose, we need more sensitive X-ray studies than that used here with variable temperature arrangement. 5. Conclusions The hexasubstituted benzenes used in the study appear to lack an observable β-process within the resolution of our experimental setup, and the relaxation process in the supercooled PC phase is found to be non-Debye in frequency dependence. The

Relaxation Dynamics of Plastic Crystals relaxation rate in DCTMB and TCTMB and their deuterated samples, although appearing to be Arrhenius in temperature dependence, requires further investigation at lower frequencies than those used here to classify them as “strictly Arrhenius” in nature. Our dielectric investigation of these materials and subsequent analysis confirms the transitions at T1 and T2 to be of weak first-order in nature and are related to the antiparallel ordering. The interesting part of our study is that the lowering of ∆ of the R-process of plastic crystal is linked to the solid solubility of the dopant with the host matrix and appears to be a general feature of the non-hydrogen-bonded plastic crystals. It appears that this solid solution need not be structurally different from that of the host, but may differ in short-range orientational ordering from that of the corresponding pure phase. At this juncture, it appears that steric hindrance and antiparallel alignment of the dipoles may be interlinked. It requires detailed X-ray studies to clarify these points. Acknowledgment. L.P.S. wishes to thank CSIR, India, for Senior Research fellowship (SRF). References and Notes (1) Cole, J. M.; Wilson, C. C.; Howard, J. A. K.; Cruickshank, F. R. Acta Crystallogr., Sect. B 2000, 56, 1085. (2) Thomas, L. H.; Welberry, T. R.; Goossens, D. J.; Heerdegen, A. P.; Gutmann, M. J.; Teat, S. J.; Lee, P. L.; Wilson, C. C.; Cole, J. M. Acta Crystallogr., Sect B 2007, 63, 663. (3) Braüniger, T.; Poupko, R.; Luz, Z.; Zimmermann, H.; Haeberlen, U. J. Chem. Phys. 2001, 115, 8049. (4) Braüniger, T.; Poupko, R.; Luz, Z.; Reichert, D.; Zimmermann, H.; Schmitt, H.; Haeberlen, U. Phys. Chem. Chem. Phys. 2001, 3, 1891. (5) Fourme, R.; Renaud, M.; Andre, D. Mol. Cryst. Liq. Cryst. 1972, 17, 209. (6) Fourme, R.; Renaud, M. Mol. Cryst. Liq. Cryst. 1972, 17, 223. (7) Tanaka, I.; Iwasaki, F.; Aihara, A. Acta Crystallogr., Sect. B 1974, 30, 1546. (8) Ro¨ssell, H. J.; Scott, H. G. Mol. Cryst. Liq. Cryst. 1972, 17, 275. (9) Brot, C.; Darmon, I. J. Chem. Phys. 1970, 53, 2271. (10) Chezeau, J. M.; Strange, J. H.; Brot, C. J. Chem. Phys. 1972, 56, 1380. (11) White, A. H.; Biggs, B. S.; Morgan, S. O. J. Am. Chem. Soc. 1940, 62, 16. (12) Turney, A. Proc. IEE, II A 1953, 100, 46. (13) White, A. H.; Bishop, W. S. J. Am. Chem. Soc. 1940, 62, 8. (14) Okatman Tas, D.; Pavlostathis, S. G. J. Agric. Food Chem. 2007, 55, 5390. (15) Shahin, Md.; Murthy, S. S. N. J. Chem. Phys. 2003, 118, 7495. (16) Brand, R.; Lunkenheimer, P.; Loidl, A. J. Chem. Phys. 2002, 116, 10386. (17) Shahin, Md.; Murthy, S. S. N.; Singh, L. P. J. Phys. Chem. B 2006, 110, 18573. (18) Ediger, M. D.; Angell, C. A.; Nagel, S. R. J. Phys. Chem. 1996, 100, 13200. (19) Ngai, K. L. J. Non-Cryst. Solids 2000, 275, 7. (20) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. J. Appl. Phys. 2000, 88, 3113. (21) Williams, G. Dielectric and Related Molecular Processes, Special Periodical Report; The Chemical Society: London, 1975; Vol. 2, p 151.

J. Phys. Chem. B, Vol. 112, No. 6, 2008 1603 (22) Johari, G. P. Ann. N. Y. Acad. Sci. 1976, 279, 117. (23) Parsonage, N. G.; Staveley, L. A. K. Disorder in Crystals; Oxford University Press: Oxford, 1978. (24) Adachi, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Jpn. 1968, 41, 1073. (25) Timmermans, J. J. Phys. Chem. Solids 1961, 18, 1. (26) Brand, R.; Lunkenheimer, P.; Loidl, A. Phys. ReV. B 1997, 56, R5713. (27) Puertas, R.; Rute, M. A.; Salud, J.; Lopez, D. O.; Diez, S.; Miltenburg, J. K. V.; Pardo, L. C.; Tamarit, J. L.; Barrio, M.; Perez-Jubindo, M. A.; de la Fuente, M. R. Phys. ReV. B 2004, 69, 224202. (28) Yamamuro, O.; Yamasaki, H.; Madakoro, Y.; Tsukushi, I.; Matsuo, T. J. Phys. C: Condens. Matter 2003, 15, 5439. (29) Puertas, R.; Salud, J.; Lopez, D. O.; Rute, M. A.; Diez, S.; Tamarit, J. L.; Barrio, M.; Perez-Jubindo, M. A.; de la Fuente, M. R.; Pardo, L. C. Chem. Phys. Lett. 2005, 401, 368. (30) Tyagi, M.; Murthy, S. S. N. J. Chem. Phys. 2001, 114, 3640. (31) Murthy, S. S. N. Therm. Chem. Acta 2000, 359, 143. (32) Amoureux, J. P.; Castelain, M.; Benadda, M. D.; Bee, M.; Sauvajol, J. L. J. Phys. 1983, 44, 513. (33) Angell, C. A. J. Non-Cryst. Solids 1991, 13, 131. (34) Leslie-Pelecky, D. L.; Birge, N. O. Phys. ReV. Lett. 1994, 72, 1232. (35) Benkhof, S.; Kudlik, A.; Blockwicz, T.; Ro¨ssler, E. J. Phys. C: Condens. Matter 1998, 10, 8155. (36) Fuchs, A. H.; Virlet, J.; Andre, D.; Szwarc, H. J. Chim. Phys. Phys. Chim. Biol. 1985, 82, 293. (37) Leslie-Peleckey, D. L.; Birge, N. O. Phys. ReV. B 1994, 50, 13250. (38) Suga, H.; Seki, S. J. Non-Cryst. Solids 1974, 16, 171. (39) Sorai, M.; Seki, S. Mol. Cryst. Liq. Cryst. 1973, 23, 299. (40) Adachi, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Jpn. 1972, 45, 1960. (41) Dworkin, A.; Fuchs, A. H.; Ghelfenstein, M.; Szwarc, H. J. Phys. Lett. 1982, 43, 121. (42) Huffman, H. M.; Todd, S. S.; Oliver, G. D. J. Am. Chem. Soc. 1949, 71, 584. (43) Debye, P. Chem. ReV. 1936, 19, 171. (44) Havriliak, S.; Negami, S. J. Polym. Sci., Part C 1966, 14, 99. (45) Murthy, S. S. N. J. Phys. Chem. B 1997, 101, 6043. The exact identity between fm and f0 is fm ) f0[k′/cos(Rπ/2) - sin(Rπ/2)‚k′]1/(1-R), where k′ ) tan((1 - R)π/2(1 + β)). (46) Colby, R. H. Phys. ReV. E 2000, 61, 1783. (47) Wong, J.; Angell, C. A. Glass Structure: By Spectroscopy; Marcel Dekker: New York, 1976. (48) Hill, N. E.; Vaughan, W. E.; Price, A. H.; Davies, M. Dielectric Properties and Molecular BehaViour: Van Nostrand Reinhold: London, 1969. (49) Pathmanathan, K.; Johari, G. P. J. Phys. C: Solid State Phys. 1985, 18, 6535. (50) Murthy, S. S. N.; Tyagi, M. J. Chem. Phys. 2002, 117, 3837. (51) Carpentier, L.; Decressain, R.; Descamps, M. J. Chem. Phys. 2008, 128, 024702. (52) Decressain, R.; Carpentier, L.; Cochin, E.; Descamps, M. J. Chem. Phys. 2005, 122, 034507. (53) Foulon, M.; Amoureux, J. P.; Sauvajol, J. L.; Cavrot, J. P.; Muller, M. J. Phys. C: Solid State Phys. 1984, 17, 4213. (54) Yamamoru, O.; Ishikawa, M.; Kishimoto, I.; Pinvidic, J.; Matsuo, T. J. Phys. Soc. Jpn. 1999, 68, 2969. (55) Hall, P. G.; Horsfall, G. S. J. Chem. Soc., Faraday Trans. 2 1974, 69, 1071. (56) Murthy, S. S. N. J. Phys. Chem. 1996, 100, 8508. (57) The specific indexing program chosen for this purpose is TREOR [Werner, P. E.; Ericsson, L.; Westdahl, M. TREOR, a Semi-Exhaustive Trial-and-Error Powder Indexing Program for All Symmetries. J. Appl. Crystallogr. 1985, 18, 367.] The reader may also refer to the following: Shirley, R. The Crysfire 2002 System for Automatic Powder Indexing: User’s Manual; The Lattice Press: Surrey, England, 2002.

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