Direct and Inverse Relations between Temperature and Pressure

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Direct and Inverse Relations between Temperature and Pressure Effects in Crystals: a Case Study on o Xylene J#drzej Marciniak, and Andrzej Katrusiak J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03543 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 11, 2017

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

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Direct and Inverse Relations between Temperature

2

and Pressure Effects in Crystals: a Case Study on

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o-Xylene

4

Jędrzej Marciniak, Andrzej Katrusiak*

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Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland.

6

ABSTRACT

7

The

8

(1,2-dimethylbenzene) are inconsistent with the rule of reverse relationship between effects of

9

pressure and temperature attributed to most crystals in general. On isobaric cooling at ambient

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pressure, the o-xylene crystal shrinks, with the strongest contraction of the unit-cell dimensions a

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and c, while during isothermal compression at ambient temperature these are the least

12

compressed directions. This direct relationship (as opposed to the 'inverse relationship' rule)

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between the compression and expansion of o-xylene has been associated with weak directional

14

CH⋅⋅⋅π interactions arranging the molecules into a 2-dimensional framework and with its distinct

15

mechanisms of distortions occurring at high-pressure and low-temperature. Single crystals of

16

o-xylene were grown in situ in isochoric and isothermal conditions in a diamond-anvil cell and

17

their structure determined by X-ray diffraction.

isothermal

compression

and

isobaric

expansion

of

crystalline

o-xylene

1 ACS Paragon Plus Environment


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INTRODUCTION

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According to the ‘inverse relationship rule’, the structural effects in the compressed and in the

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heated crystal are opposite (Figure 1).1 Recently, this rule primarily formulated for minerals, was

21

applied also for other types of crystals, such as metal-organic frameworks (MOFs), organic

22

compounds and framework materials.2–7 The only known exceptions to this rule, rutile-type

23

minerals8 and a recently reported MOF [Ag(en)NO3] (where en denotes ethylenediamine),9 both

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contain distinct frameworks adjusting to external stimuli.

25 26

Figure 1. Inverse and direct relations (red and green lines, respectively) of temperature and

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pressure effects schematically illustrated (with exaggerated changes) for a crystal plate heated

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and compressed, as indicated by black arrows. For example, the direct relationship implies the

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similar shape change of the treated sample (at the center), whereas the inverse relationship

30

differentiates the shape.

31

The flexibility of MOF crystals is often explained by the mechanic distortions of the framework

32

of cationic nodes acting as the hinges for anionic linkers.3,9–12 In such a compressed structure the

33

separated voids and channel pores usually reduce their volume in high pressure. However, a


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similar mechanism of closing voids was also proposed for molecular crystals without strong

35

interactions. For example, weakly interacting benzene molecules form CH⋅⋅⋅π bonded layers with

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small voids.13 Their collapse induces a transition and a new phase of benzene is formed.14 Thus,

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the compression of crystals can change the preferred intermolecular interactions and can cause

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molecular rearrangements, multicomponent crystallization and phase transitions.15–21 Presently

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we have investigated the effect of pressure and temperature on another molecular crystal of an

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aromatic compound; o-xylene (1,2-dimethylbenzene, melting point, m.p.= 248 K, Figure 2) is

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liquid at normal conditions, due to the absence of cohesion forces stronger than hydrogen bonds

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C-H⋅⋅⋅π.

43 44

Figure 2. o-Xylene molecule with labeled carbon atoms.

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Weak interactions involving CH groups are usually classified as hydrogen bonds C-H⋅⋅⋅π.22,23

46

Under external stimuli they yield considerably easier than electrostatic forces but harder than

47

dispersion forces. The C-H⋅⋅⋅π bonds are among the most frequent of all types of contacts in

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organic molecular crystals24 and they play an important role in the molecular aggregation, the

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packing motifs and patterns, molecular conformations, chemical reactions, selectivity and

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resolution of chiral systems, folding of proteins and nucleic acids, structural modifications and



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properties of polymers, mechanochromic and piezochromic properties, luminescence and drug

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design.25–32

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The crystal structures of m-xylene33 (1,3-dimethylbenzene, m.p. 225.5 K, space group Pbca)

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and p-xylene34(1,4-dimethylbenzene, m.p. 286.5 K, space group P21/n) were determined by

55

single-crystal X-ray and powder neutron diffraction methods in low temperature; the structure of

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o-xylene was determined only for the perdeuterated C8D10 sample, by powder neutron

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diffraction.35 Presently, we have studied intermolecular interactions in the structure of o-xylene

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as well as the correlation between the isobaric thermal expansion and isothermal compression. In

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this study we found that the strong anisotropic compression and thermal expansion of the

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o-xylene crystal cannot be reconciled with the rule of inverse effects of pressure and temperature.

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This discrepancy is particularly intriguing, given the absence of stronger directional cohesion

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forces between o-xylene molecules. In order to understand this anomalous behavior we have

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correlated the crystal compression and expansion with the changes in intermolecular contacts as a

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function of temperature and pressure.

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EXPERIMENTAL

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o-Xylene (analytical grade, from Acros Organics, m. p. 248 K) was used as delivered. All high-

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pressure diffraction experiments were performed by using a Merrill-Bassett diamond-anvil cell

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(DAC) modified by mounting the diamond anvils directly on steel supports.36 The diamond

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anvils had culets 0.7 mm in diameter. Gaskets were made of steel foil with the aperture of 0.4

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mm. Pressure was determined with an accuracy of 0.03 GPa by the ruby R1 fluorescence line

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shifts with enhanced resolution measured by a Photon Control spectrometer.37 The DAC chamber

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was filled with o-xylene and sealed; we observed that o-xylene compressed at 296 K freezes into

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a polycrystalline mass at 0.25 GPa. Pressure was further increased to 0.31 GPa and then the

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polycrystalline mass was melted by increasing the temperature to 538K with a heat gun, and a


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single crystal was grown in isochoric conditions by cooling the sample back to room temperature

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at a rate of 60 K/h. The crystal grown in this way completely filled the DAC chamber (Figure 3).

77 78

Figure 3. o-Xylene single crystal at (a) 525K; (b) 515K; (c) 490K; and (d) fully filling the

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chamber at 296K/0.31GPa. Several irregular ruby chips for pressure calibration lie around the

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chamber and most of them have been pushed to the edge of the gasket by the growing crystal.

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The high-pressure diffraction data of o-xylene collected at 0.31 GPa have been refined in the

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monoclinic space group P21/c (Table 1), consistent with the equivalent space group P21/a

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previously chosen for the perdeuterated sample.35

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In order to decrease the temperature of the subsequent crystallizations at still higher pressure we

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have mixed o-xylene with methanol (1:4 vol.); the crystals grown from this mixture in isochoric

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conditions were studied by X-ray diffraction at 0.42, 0.54, 0.80, 0.82 and 1.00 GPa. Each of these

87

crystals was in situ crystallized from a freshly prepared mixture loaded into the DAC.



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We have reduced the melting temperature again by further diluting o-xylene with methanol:

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a 1:9 (vol.) mixture was used for in situ crystallization of crystals at 1.28, 1.63, 1.96, 2.10, 2.54

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and 3.50 GPa. Again, a fresh mixture was prepared for each DAC loading.

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We have noted some systematic discrepancies in the measured unit-cell parameters, as

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exemplified in Table 1 and illustrated in Figure 4 (middle). We have attributed these

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discrepancies to the non-hydrostatic strains generated by cooling the anisotropic crystal in the

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confined rigid space of the DAC chamber.

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Table 1. Selected Crystal Data of o-Xylene at Low Temperature as well as of the High-Pressure

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Hydrostatic and Strained Sample (for details in all 0.31-3.50 GPa range see Table S1 in

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Supporting Information) low-T

98 hydrostatic strained

P(GPa)

0.0001

0.80

0.82

T(K)

240.2(5)

293(2)

293(2)

SG

P21/c

P21/c

P21/c

a(Å)

9.0350(7)

9.205(12)

9.0256(5)

b (Å)

6.1501(5)

5.714(1)

5.809(1)

c(Å)

12.8242(10) 12.439(5)

12.458(1)

β(°)

109.394(9)

110.32(9)

110.223(5)

V(Å3)

672.16(10)

613.6(9)

612.99(11)

Z

4

4

4

Dx g⋅cm3

1.049

1.149

1.15

359

578

Unique refs 1026 GOF (S)

1.079

1.077

1.089

R

0.0585

0.0639

0.0419

99


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High-pressure single-crystal diffraction data were measured on a Xcalibur Eos diffractometer

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with MoKα X-rays. The data were preliminarily reduced with CrysAlis software.38 The structure

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of o-xylene was solved by direct methods and refined with full-matrix least squares on F2's using

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Shelxs and Shelxl implemented in Olex2.39,40 The reflection intensities were accounted for the

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effects of shadowing of the beams by the gasket and absorption of X-rays by the DAC and the

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sample crystals.41 The arene hydrogen atoms were ideally positioned according to the molecular

106

geometry, while in our refinements the methyl groups were free to rotate and assumed positions

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clearly indicated by the difference Fourrier maps. For the structural-data analysis the C-H

108

distances in o-xylene were normalized to neutron data:42 arene C-H 1.083 Å and methyl C-H to

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1.059 Å.

110

Isobaric crystallizations were performed in situ on a four-circle Oxford Diffraction SuperNova

111

diffractometer equipped with a CuKα X-ray source and an Oxford Cryosystems attachment. A

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small drop of liquid o-xylene was placed in a glass capillary, 0.3 mm in diameter, and frozen at

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200 K with the cooling rate 360 K/h. The sample was then heated to 240 K and its diffraction

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data were measured. It was seen from the diffraction pattern that the sample froze in the form of

115

several crystals. The data were collected again at 220 K, 200 K and 170 K and the structures

116

determined as explained above.

117

We have performed the principal strain axis analysis using the PASCal sofware.43 The detailed

118

output of this analysis has been listed in section ‘Strain tensor analysis’ in the Supporting

119

Information.

120

RESULTS AND DISCUSSION

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All presently measured X-ray diffraction data for o-xylene at low temperature and high

122

pressure are consistent with the monoclinic structure of perdeuterated o-xylene crystal at 2K.35



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123

The crystal compression and thermal expansion are monotonic, and no anomalies indicating

124

phase transitions have been detected. The compression and thermal expansion of o-xylene crystal

125

revealed in this study are clearly inconsistent with the inverse-relationship rule. As shown in

126

Figure 4 (the central plot), the least expanding parameter b is most compressed; the expansions of

127

a and c are similar, but the compression of parameter c is intermediate between those of

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parameters a and b. In fact, the high-pressure diffraction data of the repeatedly in situ crystallized

129

samples indicate that the compression of a is negative to about 0.5 GPa. Likewise, the monoclinic

130

angle β increases with temperature and this trend also continues in high pressure up to about 1.5

131

GPa (Figure 4, the bottom plot).


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132 133

Figure 4. Thermal expansion and compression of molecular volume (top); relative changes of the

134

unit-cell parameters a; b; and c (middle); as well as changes in the monoclinic β angle (bottom).

135

Empty symbols and dashed lines indicate the non-hydrostatically compressed crystals. Dotted

136

lines connect the dimensions measured in this work for C8H10 with those of C8D10 at 2 K.35



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Herring-bone schemes of molecular aggregation exaggerate its changes upon heating and

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compression in the insets (bottom). The liquid-sample regions of isothermal compression at 296K

139

and isobaric cooling at 0.1 MPa are highlited in blue and scaled to the same width.44 The

140

crystallization pressure at 296 K is indicated by pc.

141

The principal coefficients of thermal expansion and compressibility of o-xylene (Figure 5),

142

determined using the PASCal software,43 reveal that the least thermally expanded direction [010]

143

is the most compressible.

144 145

Figure 5. Calculated (a) expansivity (in MK-1); and (b) compressibility (in TPa-1) indicatrices of

146

the o-xylene crystals viewed along direction [100].

147

At the same time the strong thermal expansion of the o-xylene crystal along a is least

148

compressible (Table 2).

149

Table 2. Themal Expansivity and Compressibility Related to Crystallographic Axes Calculated

150

for o-Xylene. Thermal expansion


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α (MK-1)

σα (MK-1)

a

Crystal directions b

X1

54.95

1.48

0.00

-1.00

0.00

X2 X3

67.62 124.36

0.76 3.15

0.80 -0.84

0.00 0.00

0.59 0.54

c 0.00 0.90 -0.01

Axes

c

Compression

K (TPa-1)

σK (TPa-1)

a

Crystal directions b

30.50 17.20 3.35

3.41 0.55 3.14

0.00 0.44 1.00

1.00 0.00 0.00

Axes

e11 e22 e33 151 152

Strong anisotropy of crystal expansion and compression is usually connected with the presence of

153

‘wine-rack’,4,5,9,11 ‘honeycomb’,3 or ‘spring’3 molecular aggregation patterns through

154

coordination bonds or hydrogen bonds and can even lead to negative linear compressibility

155

(NLC), negative area compressibility (NAC) and negative thermal expansion (NTE). The key

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structural features behind such effects in MOFs are struts and hinges of a mechanical model

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reproducing the elastic properties of the crystal. These features are absent in the molecular crystal

158

of o-xylene, but nonetheless it is strongly anisotropic and in the pressure region from 0.25 GPa to

159

0.54 GPa the crystal displays even a small NLC effect along [a]. This anisotropy of the o-xylene

160

crystal can be due to directional bonds C-H⋅⋅⋅π binding the molecules into a pattern resembling

161

the wine-rack framework, with small voids between the molecules shown in Figure 6.



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Figure 6. (a) Contacts C-H⋅⋅⋅π, blue for methyl and red for arene H-donors in o-xylene at 0.54

164

GPa; (b) a schematic representation of the pseudo wine-rack motif distortion induced by pressure

165

in o-xylene; (c) the structure viewed along the C-H⋅⋅⋅π bonded layers. Each molecule is C-H⋅⋅⋅π

166

bonded to six molecules. Green circles indicate voids 1.28 Å in diameter, and orange circles

167

indicate smaller voids (0.94 Å).

168

When pressure increases, the voids close up due to the wine-rack distortion and crystal expands

169

along [a] and shrinks along [b] – hence the strongest anisotropy along these directions. With


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170

increasing pressure the compression of weak C-H⋅⋅⋅π bonds gradually becomes more significant

171

compared to the wine-rack type distortion, and the strong anisotropic compression is notably

172

reduced around 0.5 GPa. Nonetheless, this pattern of C-H⋅⋅⋅π bonds is preserved and gradually

173

compressed up to 3.50 GPa, at least, where the shortest H⋅⋅⋅C distances are compressed from 2.90

174

Å to 2.57 Å (Figure 7).

175 176

Figure 7. Compression of the shortest C-H⋅⋅⋅π intermolecular contacts in o-xylene, based on the

177

C-H bonds normalized to the neutron data:45 the contacts involving arene H-donors are indicated

178

in red and methyl H-donors in blue. The shortest H⋅⋅⋅H contacts are shown as black squares and

179

black circles. Dotted lines connect our C8H10 data with those of C8D10 at 2 K.35 Empty symbols

180

indicate the structures with non-hydrostatic strain.

181

The layers of o-xylene molecules C-H⋅⋅⋅π bonded into the wine-rack motif extend along crystal

182

plane (001) with the molecules nearly perpendicular to this plane. Between the layers no C-H⋅⋅⋅π

183

bonds are formed and only short H⋅⋅⋅H contacts are present (Figure 6).

184

Anisotropic Stress Generated in the DAC

185

Soft o-xylene crystals become non-hydrostatically strained in the confined space of the DAC

186

chamber (Figure 3). This non-hydrostatic strain affects the unit-cell parameters (Figure 4). The



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effect of nonhydrostatic strain on o-xylene unit-cell parameters appear systematic i.e. repeatedly

188

unit-cell parameter [a] is longer and parameter [b] is shorter compared to these parameters

189

measured in hydrostatic conditions. Thus, this non-hydrostatic compression of the unit-cell

190

parameters can be plotted with smooth curves (Figure 4). The single crystals of o-xylene were

191

grown at isochoric conditions by cooling the DAC and a special care had to be taken to avoid

192

non-hydrostatic strain in the sample occuring due to its anisotropic stress generated by the

193

anisotropic thermal expansion when the temperature is changed. We noticed that when the crystal

194

filled most of the chamber volume, the unit-cell dimensions were different from those obtained

195

for the crystal grown in this way that the sample was surrounded by the hydrostatic fluid and did

196

not collide with the gasket at more than one point. In the latter case, the hydrostatic conditions

197

were secured (Figure 8).

198

199 200

Figure 8. The o-xylene crystal at 0.42 GPa/298K fully immersed in the liquid o-xylene/methanol

201

mixture. Only one side of the crystal is touching the gasket. A ruby chip lies near the upper-left

202

edge of the gasket.

203

It is characteristic that the non-hydrostatic strain enhanced the anisotropy of the crystal

204

compressibility. Thus, due to the non-hydrostatic strain the least compressible direction [100]


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205

displays a pronounced negative linear compression, and the most compressible direction [010] is

206

even more strongly compressed.

207

In order assess the magnitude of nonhydrostatic pressure in the o-xylene crystals we have

208

repeated the in situ recrystallizations and measured the pressure at various parts of the chamber

209

(Figure 9).

210 211

Figure 9. o-Xylene single crystals fully filling the DAC chamber: (a) crystal grown between

212

340-296 K with the ruby chips immersed in the crystal, and the measured pressure values in GPa;

213

(b) the same crystal after 3 hours annealing at 320 K; (c) another crystal grown between 410-296

214

K (d) this crystal after annealing at 370 K.

215

In the crystal fully filling the DAC chamber at 320 K, the pressure varied between 0.25 and

216

0.36 GPa, whereas after annealing this difference was reduced to 0.27 - 0.33 GPa. For another

217

recrystallization, when the chamber was fully filled by the o-xylene crystal at 390 K, the pressure

218

read-outs were 0.77 - 0.94 GPa, and the annealing at 370 K for three hours reduced the pressure

219

span to 0.77 - 0.85 GPa. The fluorescence of the ruby chips measured before the in situ



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220

crystallization was identical within error. The in situ recrystallization of o-xylene increased the

221

spread of pressure read-outs (Figure 9); non-hydrostatic pressure was reflected in the R1 line

222

wavelength, but no significant widening of the R fluorescence lines was noted. The sample

223

annealing relaxes some of the non-hydrostatic pressure, however, it does not eliminate it for the

224

crystal fully filling the DAC chamber. It appears that the soft crystals built of weakly interacting

225

molecules, such as o-xylene are most affected by the nonhydrostaticity in the lower range of the

226

pressure, when the crystal is still relatively soft. In o-xylene such strong effects were generated

227

about 0.8 GPa. At higher pressure the crystal becomes harder and even though the

228

nonhydrostaticity is stronger, the non-hydrostatic strain in the sample is smaller.

229

CONCLUSIONS

230

We have associated the direct relation between compression and thermal expansion of o-xylene

231

with the weak intermolecular bonds forming a wine-rack pattern and with the presence of small

232

voids in this structure. The increased temperature destbilizes this pattern of weak C-H⋅⋅⋅π bonds,

233

in the manner somewhat similar to the effect of pressure, reducing the directional character of the

234

C-H⋅⋅⋅π bonds, too, through enhanced close packing. Hence the similar effects of increased

235

temperature and pressure for the crystal expansion and compression. The direct relationship

236

observed in o-xylene can be connected in with the framework of the C-H⋅⋅⋅π bonds. It can be

237

stated that at ambient pressure the preferential directions of C-H⋅⋅⋅π bonds support the

238

arrangement of molecules within the framework, whereas at high pressure the framework folds in

239

the direction reducing the crystal volume. On the other hand the decreased temperature increases

240

the directional character of C-H⋅⋅⋅π bonds. Therefore in such structures the strain produced by

241

lowering temperature and increasing pressure can be significantly different. It may appear that

242

the observations of the direct relationships in the o-xylene crystal and in few other cases8,9 are


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243

very unusual because presently there are still very few reports on compression and thermal

244

expansion simultaneously measured for one material.46,47 Such studies are particularly relevant

245

for crystal engineering as the data collected at low-temperature and high-pressure can be used to

246

produce better piezo-responsive materials for three-dimensional pressure detectors, prototype

247

artificial muscle or shock-absorbing composites.48–50 Thus the classes of materials and effects

248

with direct and inverse relationships between changes caused by pressure and temperature can be

249

distinguished. This distinction is also important for geological studies, and provides better

250

understanding of the structural transformations of minerals subjected to high pressure and

251

temperature.

252

ASSOCIATED CONTENT

253

Supporting Information

254

Detailed crystal data, Hirshfeld surfaces of o-xylene molecules. The Supporting Information is

255

available free via the Internet at http://pubs.acs.org. Full crystal data have also been deposited in

256

the Cambridge Crystallographic Database Centre as supplementary publication numbers CCDC

257

1542572-1542586. Their copies can be obtained free of charge from http://www.ccdc.cam.ac.uk.

258

AUTHOR INFORMATION

259

Corresponding Author

260

*E-mail: [email protected],

261

Notes

262

The authors declare no competing financial interest.

263

ACKNOWLEDGEMENTS



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Page 18 of 25

264

This work was supported by the Polish National Science Center, research grant Preludium

265

2013/11/N/ST3/03793. J.M. is a recipient of a scholarship provided by the Adam Mickiewicz

266

University Foundation.

267

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Direct and Inverse Relations between Temperature and Pressure

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