Science - USA (2019-02-15)

two isomers in coexistence with each other, the
transformation must be kinetically controlled,
and comparison to thermodynamic parameters,
such as enthalpies of mixing [which are 1000-fold
smaller ( 31 )] cannot be made. The weak temper-
ature dependence impliesthat the transformation
is predominantly enthalpic, and the mean dif-
ference inDS‡of the transformation (DS‡conversion−
DS‡reversion) of +0.52 meV K−^1 is consistent with
H-bonding entropies. As implied by Fig. 4C, the
a-Cd 37 S 20 structure becomes thermodynami-
cally unstable and converts intob-Cd 37 S 20 ,owing
to changes in the surface energy. Removal of the
surface-energy perturbation by desorption of hy-
droxyl raises the free energy ofb-Cd 37 S 20 , likewise
rendering it thermally unstable and reverting to
theaform.
A coherent transition between two clusters
implies conservation of binding coordination,
a single rate constant for the reaction, and sim-
ultaneous transformation of the entire clus-
ter rather than growth from a nucleation site
( 2 , 32 , 33 ). On the basis of the transformation
kinetics and the lack of any observable inter-
mediates, the upper bound on the lifetime of
an intermediate state must be on the order of
10 −^13 s (see supplementary materials for calcula-
tions), a time scale comparable to bond vibrations
( 33 ) and the lifetime of molecular transition
states ( 34 ); additionally, to achieve the same
rate of transformation for the MSC in an inco-
herent process, a phase boundary would need to
move at a velocity comparable to the speed of
sound of the bulk material ( 28 , 35 ). The small
atomic displacements shown from PDF analysis
indicate a structural reconfiguration without a
change in coordination number. Our experimen-
tal kinetics are thus consistent with a coherent
atomic displacement occurring in a single step
across the entire cluster, therefore bridging our
understanding of molecular isomerization and
solid-solid transformation.

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ACKNOWLEDGMENTS

The authors thank P. Ko and M. Steigerwald.Funding:This

work was supported in part by the National Science Foundation

(NSF) under award nos. CMMI-1344562 and CHE-1507753.

U.B. acknowledges funding from the European Research Council

(ERC) under the European Union’s Horizon 2020 research and

innovation program (grant no. 741767). U.B. also thanks the

Alfred & Erica Larisch memorial chair. This work also made use

of the Cornell Center for Materials Research Shared Facilities,

which are supported through the NSF MRSEC (Materials

Research Science and Engineering Centers) program (grant

DMR-1719875). This work includes research conducted at

the Cornell High Energy Synchrotron Source (CHESS), which

is supported by the NSF and the National Institutes of

Health–National Institute of General Medical Sciences under

NSF award DMR-1332208. R.D.R. thanks the U.S. Fulbright

Scholar and Hebrew University for partial funding during this

work.Author contributions:C.B.W. synthesized and prepared

samples for ultraviolet-visible absorption spectroscopy,

FTIR spectroscopy, XPS spectroscopy, and kinetic analysis.

C.B.W. and D.R.N. prepared samples for x-ray total scattering

and diffraction. C.B.W., D.R.N., and A.N. contributed to the

PDF analysis of the total scattering data. I.H. and U.B.

acquired and analyzed fluorescence spectroscopy and lifetime

measurements. All authors contributed to the interpretation of

results and preparation of manuscript.Competing interests:

None declared.Data and materials availability:All data

needed to evaluate the conclusions in the paper are present

in the paper or the supplementary materials.

SUPPLEMENTARY MATERIALS

http://www.sciencemag.org/content/363/6428/731/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S10

Tables S1 to S6

References ( 36 – 48 )

30 July 2018; resubmitted 17 September 2018

Accepted 16 January 2019

10.1126/science.aau9464

Williamsonet al.,Science 363 , 731–735 (2019) 15 February 2019 5of5

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