Dynamics in the ordered and disordered phases of barocaloric adamantane Bernet E. MeijeraRichard J. C. DixeyaFranz DemmelbRobin Perryc

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Dynamics in the ordered and disordered phases

of barocaloric adamantane

Bernet E. MeijeraRichard J. C. DixeyaFranz DemmelbRobin Perryc

Helen C. Walker∗bAnthony E. Phillips∗a

Keywords: barocaloric cooling; entropy; orientational dis-

order; phonons; plastic crystals

Abstract

High-entropy order-disorder phase transitions can be used

for efﬁcient and eco-friendly barocaloric solid-state cool-

ing. Here the barocaloric effect is reported in an archetypal

plastic crystal, adamantane. Adamantane has a colossal

isothermally reversible entropy change of 106 JK

−1

Extremely low hysteresis means that this can be accessed at

pressure differences less than 200 bar.

Conﬁgurational entropy can only account for about

of the total entropy change; the remainder is due to vibra-

tional effects. Using neutron spectroscopy and supercell

lattice dynamics calculations, it is found that this vibra-

tional entropy change is mainly caused by softening in the

high-entropy phase of acoustic modes that correspond to

molecular rotations. We attribute this behaviour to the con-

trast between an ‘interlocked’ state in the low-entropy phase

and sphere-like behaviour in the high-entropy phase. Al-

though adamantane is a simple van der Waals solid with

near-spherical molecules, this approach can be leveraged for

the design of more complex barocaloric molecular crystals.

Moreover, this study shows that supercell lattice dynamics

calculations can accurately map the effect of orientational

disorder on the phonon spectrum, paving the way for study-

ing the vibrational entropy, thermal conductivity, and other

thermodynamic effects in more complex materials.

School of Physics and Astronomy, Queen Mary University of London,

London E1 4NS, U.K.

ISIS Neutron and Muon Source, Rutherford Appleton Laboratory,

Didcot OX11 0QX, U.K.

Department of Physics and Astronomy, University College London,

London WC1E 6BT, U.K.

†

Electronic Supplementary Information (ESI) available. See DOI:

00.0000/00000000.

∗

Corresponding authors. E-mail addresses: a.e.phillips@qmul.ac.uk,

helen.c.walker@stfc.ac.uk

1 Introduction

With cooling and refrigeration accounting for over 25% of

global energy consumption

and 10% of emissions

, it has

become clear that innovation in this area is a key factor for

reaching our climate goals. The emissions from prevalent

vapour-compression technology are both direct and indirect:

direct emissions come from the refrigerants, that are green-

house gases commonly thousands of times more potent than

; indirect emissions originate from the electricity use,

and unfortunately the efﬁciency of vapour-compression tech-

nology is plateauing

. Improvements in sustainable cooling

will therefore lie in alternative technologies. Currently, one

of the most promising is solid-state cooling using caloric

materials: these materials do not cause direct emissions and

offer the potential of increased cooling efﬁciency.

The functional behaviour of caloric materials relies on

phase transitions with large entropy changes, induced by an

external ﬁeld. The group of barocalorics, which undergo a

pressure-induced phase transition, is especially promising.

These materials are abundant and cost-effective, and since

they are pressure-driven, their deployment does not require

a complicated refrigeration design. The remaining challenge

in this ﬁeld is to identify materials that can beat the efﬁ-

ciency of current vapour-compression technology, and that

together give us a broad range of operating temperatures that

is needed for widespread deployment.

The structure-space for barocalorics is vast, ranging from

framework materials to shape memory alloys

. A partic-

ularly promising group are the orientationally-disordered

(or ‘plastic’) crystals, which have shown giant and colossal

barocaloric effects

5–10

, and it is hoped that this group might

host many more efﬁcient barocalorics. Since the efﬁciency is

proportional to the entropy change over the phase transition,

the search for these materials must be focused on entropy as

a design principle. However, most studies only consider one

type of entropy contribution

and therefore fail to provide a

complete picture of the entropy change. A ﬁrst step towards

ﬁnding the most efﬁcient barocalorics is to unravel all con-

tributions to the entropy, their importance in plastic crystals,

arXiv:2210.13914v1 [cond-mat.mtrl-sci] 25 Oct 2022

and their corresponding molecular origins.

Here, we study the barocaloric effect and its microsopic

origins in the plastic crystal adamantane. We chose this ma-

terial for two reasons. First, adamantane is an archetypical

example of a crystal that is both orientationally disordered

and literally plastic, with a waxy consistency and high sus-

ceptibility to external stress. For these reasons, it seems

highly likely to be a barocaloric; however, despite recent

reports of barocaloric behaviour in adamantane derivatives

to our knowledge this has not previously been reported in

adamantane itself. Second, adamantane’s physical proper-

ties make it an ideal model system for plastic crystals: it has

rigid, near-spherical molecules and its intermolecular inter-

actions are dominated by van der Waals dispersion forces.

This is both encouraging for generalising our results to the

wider family of molecular barocaloric materials, and practic-

ally useful since its simplicity makes it a good test case for

the analysis of vibrational entropy that we develop here.

In this work, we reveal adamantane’s barocaloric ef-

fect through calorimetric measurements. The effect can

be classed as ‘colossal’ (following barocaloric termino-

logy

4,8,10,12

) and we predict it can be accessed with full

reversibility under pressures as low as 200 bar. We show

that more than half of adamantane’s large entropy change

can be attributed to vibrational effects, and therefore set out

to uncover the microscopic mechanisms that give rise to

the vibrational entropy change. We do this by performing

supercell lattice dynamics calculations followed by band

unfolding

13,14

, here for the ﬁrst time applied to an orienta-

tionally disordered supercell. The model is validated with

single-crystal neutron spectroscopy and further supported

by a quasi-elastic neutron scattering experiment under high

pressure. In the high-temperature phase, the acoustic modes

soften and are associated with rolling molecules, rather than

translations. This behaviour can be attributed to the change

from an interlocking structure at low temperatures to a spher-

ical close-packed structure at high temperatures. The prin-

cipal dynamical mechanism of this archetypical plastic crys-

tal is thus revealed, which can be leveraged in future barocal-

oric design.

2 Background

Adamantane is a stable hydrocarbon with formula

C10H16

which consists of a rigid tetrahedron of six-membered carbon

rings in the “armchair” conﬁguration (see ﬁgure 1). At room

temperature and atmospheric pressure, the crystal structure

is face centred cubic (

Fm¯

a=9.426 ˚

Z=4

)

15,16

. In

this phase, the molecules are randomly oriented in one of

two orientations

17,18

, and they can jump between them via

Figure 1

Relaxed conﬁguration of a disordered supercell of adam-

antane. The two different orientations are highlighted by the num-

bers and differing colours; the depth fading shows two adjacent

planes of the close-packed structure. This is a small part of an

8×8×8

supercell used in the calculations, in which the two ori-

entations are present in equal amounts.

rotation about the fourfold axes, as revealed by NMR

and

quasi-elastic neutron scattering studies

. Upon cooling to

T=208

K at ambient pressure, adamantane undergoes a

ﬁrst-order structural phase transition to the tetragonal space

group

P¯

421c

(

a=6.614 ˚

c=8.875 ˚

Z=2

)

. In this

phase there is no orientational disorder: the planes of mo-

lecules alternate down the tetragonal

axis between the two

high-temperature orientations.

Quantity Value Reference

Tt(ambient p) 208 K 16

pt(ambient T) 4.8 kbar 21–23

∆S16.2 J K−1mol−124

∆H3.38 kJ mol−124

∆VLT→HT/VHT 7.34% 16

Table 1

Thermodynamic data of adamantane’s phase trans-

ition.

∆S

∆H

∆VLT→HT

are the thermodynamic changes of

the temperature-induced phase transition at ambient pressure.

∆VLT→HTVHT

is the volume change of the unit cell from the low-

temperature (LT) to high-temperature (HT) phase as a percentage

of the high-temperature unit cell volume.

The thermodynamic data of adamantane’s phase transition

are summarised in table 1. As is hinted by the large volume

change, the phase transition can also be induced by pressure:

at ambient temperature, this happens at a pressure of

4.8

kbar

21–23

. Both the large volume change and the phase

transition temperature’s strong sensitivity to pressure are

indicators of potentially large barocaloric effects.

On top of the quasi-elastic neutron studies, inelastic neut-

ron studies have been performed in adamantane’s plastic

phase

25–27

. Here we expand upon the quasi-elastic studies

by measuring the reorientational dynamics under pressure;

the inelastic studies are extended by probing the dynamics

in both phases to reveal the phase transition mechanism.

3 Experiment

3.1 Colossal barocaloric effect

The barocaloric properties of adamantane were measured

using high-pressure differential scanning calorimetry (DSC).

Figure 2(a) and (b) show the heat ﬂow measurements and

the corresponding phase diagram. The heat ﬂow meas-

urements were performed at pressures between 900 and

1000 bar. At lower pressures, the phase transition tem-

perature is below the temperature range of the DSC so it

could not be observed. The phase diagram conﬁrms the

strong pressure-induced shift of the phase transition tem-

perature

, with

dTt/d p =18.57

K kbar

−1

on cooling and

dTt/d p =19.40

K kbar

−1

on heating. It also reveals an ex-

tremely low hysteresis up to 1.96 K at 1000 bar, which varies

very slightly with pressure. By subtracting the integral of

the heat ﬂow peaks at

p>900

bar from the integral of the

pbase =900

bar peak, we can recover the isothermal entropy

change for releasing pressure down to 900 bar (

p→900

bar)

and adding pressure starting from 900 bar (

900

bar

→p

This is shown in ﬁgure 2(c). The maximum pressure-induced

entropy change in this experiment is 116.92 J K

−1

. Fi-

nally, the reversible entropy changes are shown in ﬁgure

2(d). Starting at a pressure of 900 bar, reversible effects are

already achieved with a pressure of 50 bar to reach 950 bar.

To get an estimate of the barocaloric behaviour at low tem-

peratures and pressures, and to ﬁnd the pressure at which full

reversibility is reached, the heat ﬂow data were extrapolated

down to 0 bar. First, the phase transition temperature was

extrapolated down to 0 bar using a linear ﬁt to the data shown

in ﬁgure 2(a). Next, the 1000 bar heat ﬂow peak was trans-

lated to those phase transition temperatures: as an example,

the resulting predicted heat ﬂow data for 0 bar are shown in

ﬁgure 2(b). Using the predicted 0 bar data, the isothermal

entropy change for

p↔0

bar can be estimated; the predic-

tion for

1000 ↔0

bar is shown in ﬁgure 2(c), along with

the prediction for

200 ↔0

bar (which uses the two extrapol-

ated heatﬂow datasets of 0 and 200 bar). Further details of

behaviour at intermediate pressures is available in the sup-

plementary material. Finally, this results in the extrapolated

reversible entropy changes shown in ﬁgure 2(d). At

<200

bar full saturation is thus expected, yielding a colossal revers-

ible entropy change of 106 J K

−1

. The small operating

pressures that are necessary for adamantane’s barocaloric

exploitation are very appealing, and are likely a consequence

of the extremely small hysteresis. With the reasonable as-

sumption that the

dTt/dP

relation is linear, the hysteresis at

0 bar is estimated to have a value of only about 1.15 K, far

smaller than that of some adamantane derivatives8.

The barocaloric properties of adamantane compare favour-

ably against other caloric materials. The isothermal entropy

change far surpasses that of electrocaloric and magnetocal-

oric materials (with maximum entropy changes not greater

than

∼50

−1

−1 4,7

). Moreover, the reversible entropy

change is also among some of the largest observed in barocal-

oric plastic crystals (carboranes:

72 −97

−1

−1 10

;

1-X-adamantanes:

∼150

−1

(at 1 kbar)

; NPG:

389

−1

−1 6,7

) and crucially, due to the phase transition

temperature’s high sensitivity on pressure, adamantane’s

maximum entropy change normalised by saturation pressure

is larger than any barocaloric plastic crystal known so far,

as shown in ﬁgure 3. This means that entropy changes can

be achieved with minimal work. Although adamantane’s

low phase transition temperature makes it unsuitable for

most domestic applications, it may be an excellent candidate

for ultra-low temperature freezers used in vaccine storage

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DynamicsintheorderedanddisorderedphasesofbarocaloricadamantaneBernetE.MeijeraRichardJ.C.DixeyaFranzDemmelbRobinPerrycHelenC.WalkerbAnthonyE.PhillipsaKeywords:barocaloriccooling;entropy;orientationaldis-order;phonons;plasticcrystalsAbstractHigh-entropyorder-disorderphasetransitionscanbeusedforefci...

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Dynamics in the ordered and disordered phases of barocaloric adamantane Bernet E. MeijeraRichard J. C. DixeyaFranz DemmelbRobin Perryc

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