www.rsc.org/pccp Volume 10 | Number 42 | 14 November 2008 | Pages 6333–6456

ISSN 1463-9076

Physical Chemistry Chemical Physics

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REGULAR ARTICLE

Ashfold et al.

Near-UV photolysis of substituted phenols

REGULAR ARTICLE

Lummen and KvammeFormation of nanoparticles in supercritical water: a molecular dynamics investigation 1463-9076(2008)10:42;1-X

COVER ARTICLE

van der Spoel et al.

Structural studies of melting on the picosecond time scale

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View Online

Structural studies of melting on the picosecond time scale

David van der Spoel,*a Filipe R. N. C. Maiaa and Carl Calemanb

Received 2nd May 2008, Accepted 16th July 2008

First published as an Advance Article on the web 24th September 2008

DOI: 10.1039/b807550f

Ultrafast structural studies of laser-induced melting have demonstrated that the solid–liquid phase

transition can take place on a picosecond time scale in a variety of materials. Experimental studies

using angstrom wavelength X-rays from the sub-picosecond pulse source at Stanford (now retired)

on non-thermal melting of semi-conductors, such as indium antimonide, employed the decay of a

single Bragg-peak to measure the time component of the phase transition. These materials were

found to start melting within one picosecond after the laser pulse. Recent computer simulations

have described the thermal melting of ice induced by an infrared laser pulse. Here it was shown that

melting can happen within a few picoseconds, somewhat slower than non-thermal melting in semi-

conductors. These computer simulations are compatible with spectroscopy experiments on ice-

melting, demonstrating that simulations form a very powerful complement to experiments targeting

the process of phase-transitions. Here we present an overview of recent experimental and theoretical

studies of melting, as well as new simulations of ice-melting where the effect of the size of the

crystal on scattering is studied. Based on simulations of a near-macroscopic crystal, we predict the

decay of the most intense Bragg peaks of ice following heating by laser pulse, by modeling the

scattering from the melting sample in the simulations.

1. Introduction

Phase transitions are of fundamental importance in chemistry

and physics. Here we focus on the solid–liquid phase transi-

tion, melting, and give an overview of recent experiments and

simulations of ultra-fast melting. In addition we provide new

simulation data which predict what kind of results can be

expected in experiments of melting of ice.

Fast melting can be induced by a short, intense laser pulse.

The energy required for melting is not very high, and melting can

therefore be accomplished in a straightforward manner. Probing

of the melting process can be done in different ways, and given

that laser is used for heating the sample (pumping) it is logical to

use spectroscopic techniques for probing as well. Indeed, femto-

second spectroscopy, for which Ahmed Zewail was rewarded the

Nobel prize in chemistry in 1999, is by now a mature field and

pump–probe spectroscopy is a well-established experimental

technique to study processes in the gas-phase as well as in

solution. This technique was applied recently to study the

melting of ice using infrared spectroscopy.1–4 In these experi-

ments the challenge was to record the infrared spectrum (which

differs significantly between water and ice) as a function of time.

Another approach is to use a laser for pumping and X-ray

scattering for probing, and this has been used extensively in

materials science.5–12 Here, the time delay between pump and

probe must be measured with sufficient accuracy to describe the

aDepartment of Cell and Molecular Biology, Uppsala University, Box596, SE-75124 Uppsala, Sweden. E-mail: spoel@xray.bmc.uu.se

bPhysik-Department E17, Technische Universitat Munchen,James-Franck-Strasse, DE-85747 Garching, Germany

David van der Spoel received his Master’s degree in physics and

his PhD in chemistry (1996) from Groningen Univ. (The Nether-

lands). Currently he is a professor of biology at Uppsala Univ.

(Sweden). His main interests are in improvements in molecular

modeling techniques, both software and force fields. He is also

working on protein folding and imaging techniques using new light

sources, such as X-ray free electron lasers (XFEL).

Filipe Maia graduated in biochemistry from Oporto University,

Portugal, in 2004 and is working towards a PhD at Uppsala

University, Sweden. His main interests are diffraction imaging

and image reconstruction.

Carl Caleman holds a degree in engineering physics, and a PhD in

molecular biophysics (2007), both from Uppsala University. He

spent one year as a visiting scholar at UC Berkeley. At present he

is working at the Technical University of Munich, continuing his

work exploring the possibilities of XFEL.

David van der Spoel, Filipe Maia and Carl Caleman

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PERSPECTIVE www.rsc.org/pccp | Physical Chemistry Chemical Physics

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melting process, which was found to occur from sub-picosecond

to many picoseconds, depending on the laser intensity and

material properties. Cavalieri et al. have shown that synchro-

nisation of femtosecond X-ray pulses and a Ti : sapphire laser

pulse is possible using the sub-picosecond pulse source (SPPS)

at Stanford,13 allowing the necessary time resolution to study

the melting process. This method, called electro-optical sam-

pling, will be implemented at the linac (linear accelerator)

coherent light source (LCLS, under construction at Stanford)

as well, and in addition it should be noted that beamlines for

these kind of experiments are already available or being devel-

oped at synchrotrons around the world such as the European

synchrotron radiation facility (Grenoble, France) the Stanford

synchrotron radiation laboratory (Stanford, USA), MAX-lab

(Lund, Sweden) and the Swiss light source (Villingen,

Switzerland). Synchrotrons have orders of magnitude less

brilliance than X-ray free-electron lasers (such as LCLS) are

predicted to have,14 and synchrotrons do not have coherent

photon pulses either, but for studies of macroscopic crystals this

is not as important as the time structure of the pulses.

Finally, a new and very interesting technique was intro-

duced by Chapman et al. where photons from the free-electron

laser at Hamburg (FLASH, Germany) source were used as

pump and probe15 and the Coulomb explosion of a latex ball

could be followed with femtosecond resolution. A review of

techniques employed at new light sources was presented

recently by Gaffney and Chapman.16

The physical basis of melting depends on the way in which

melting is induced. The common form of melting is thermal

melting, where a material is heated until the motions of the

atoms (molecules) in the sample are large enough to break the

lattice constraints. Thermal melting can be induced by selec-

tively exciting vibrational frequencies,17 and hence bring the

material to resonate. The energy is thus transferred selectively

from the laser field to certain degrees of freedom, e.g. the OH

stretch frequency in the water molecule.1–4 Structural changes

in ice can be inferred from the changes in the absorption

spectra, and computer simulations may aid in the interpreta-

tion of these experiments. We have performed ice-melting

simulations using classical molecular dynamics simulations,18

and the time scale of melting that we observe in the simula-

tions is very similar to that seen in the spectroscopy experi-

ments by Laubereau and coworkers.1 We could deduce the

mechanism of energy redistribution from these simulations:

first the OH stretch is excited, this energy is transferred to

rotational motions within 2–3 ps and, after melting, is

transferred into translation motion (after 5–6 ps).

Non-thermal melting can be caused by absorption of multiple

photons from, for instance, a Ti : sapphire laser, which leads to

direct as well as indirect ionization processes (through secondary

electron cascades19–25). Quite a few studies of the different

mechanisms leading to thermal and non-thermal melting of

silicon and other semiconductors have been presented re-

cently,26–31 and similar studies for metals have been reported as

well.32–36 A theoretical model describing thermal and non-

thermal melting of metals was presented by Chen et al.37 Here,

non-thermal melting is associated with the high pressure due to

electrons being out of equilibrium with the metal lattice.37 This

points to a significant difference between the ice–water phase

transition and the melting of other solids, namely the fact that for

most liquids the density is lower than for the corresponding solid,

leading to high pressures due to melting. The high pressures in

some materials can be monitored as acoustic waves, which were

detected in germanium following non-thermal melting within

1 ps.38 Similarly, it was shown recently that laser-induced melting

of indium antimonide leads to acoustic waves which equilibrate

within 5 ps.39 Since the water density is higher than ice, a void will

be formed within the ice-lattice-bordering melting-nucleation

sites. In computer simulations18 melting of ice is accompanied

by a negative pressure, indicating that there is a tendency to

contract. Although a negative pressure is strictly non-physical, it

is an effect of the periodic boundary conditions that are typically

employed in simulations, and it means that the attractive forces

(the virial) are stronger than the kinetic pressure. In summary,

the melting of ice is very different from melting of other solids,

and this has prompted us to propose a new experiment aimed at

direct structural investigations of the process in this paper.

2. Methods

An ice crystal of 768 molecules (roughly 3 � 3 � 3 nm) was

used from the collection due to Hayward and Reimers.40

These crystals were constructed to follow the ice rules with

maximum disorder of the hydrogen positions within the

lattice.41 The procedure for melting ice crystals laid out in

our recent paper18 was used. In short, a periodic crystal was

used in which the particle-mesh Ewald method was used to

compute Coulomb interactions42 with a switch distance of 0.9

nm. Van der Waals interactions were truncated at the same

distance. The flexible TIP/4P water model due to Lawrence

and Skinner43 was used for all simulations. As previously, the

laser pulse was modeled as a fluctuating electric field:

EðtÞ ¼ E0 exp �ðt� t0Þ

2

2s2

" #

cos½oðt� t0Þ� ð1Þ

where the angular frequency o = 2pc/l, with l = 2.985 mm,

E0 = 2.5 V nm�1, s = 100 fs and t0 is the peak of the pulse.

The molecular dynamics simulations were performed using the

GROMACS software,44–47 a very powerful and efficient package

for molecular simulations. Modeling of scattering images was

done using the Hawk package, a set of libraries and programs for

computing scattering images and reconstruction of objects from

scattering data using over-sampling.48 The scattering image is

given by the Fourier transform of the atomic scattering factors fi:

Ik ¼X

N

i¼1

ffiffiffiffi

Iip

fie�ik�ri ð2Þ

Where Ii is the incoming beam intensity at atom i, k is the

scattering vector and ri is the position of atom i. To reduce the

artifacts caused by the small simulation box in the scattering

pattern a Gaussian beam was used. This smoothens out such

artifacts at the cost of somewhat blurring the patterns. The

beam was centered in the center of the simulation box. The full

width half maximum of the beam was equal to half of smallest

box edge perpendicular to the beam. The calculated scattering

images hence correspond to illuminating the box with a beam

parallel to the z axis. Due to the curvature of the Ewald sphere

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this means we obtain a projection of the Ewald sphere onto the

detector, rather than a plain in Fourier space. Apart from the

smallest box, some larger crystals (6, 9, 12 and 15 nm box

edges, corresponding to 6144, 20 736, 49 152 and 96 000 mole-

cules respectively) were built by stacking 3 nm boxes. These

were used for simulations in order to qualitatively visualize the

effect of crystal size on scattering and to monitor the decay of

scattering intensity during melting.

3. Results

3.1 Proposed melting experiment

Here we describe an ice-melting experiment inspired by the

spectroscopy work of the Laubereau group1–4 and our recent

simulations.18 The experiment is intended to give direct struc-

tural evidence of ice-melting. A schematic drawing showing

the experimental setup is given in Fig. 1. The pump pulse

comes in from the left, and is synchronized to the probe pulse

(from the bottom) with a variable time delay.13 When using

pulsed sources such as SPPS or the linac coherent light source

(note that the SPPS has been dismantled to make space for the

construction of LCLS) it is in principle possible to use a 2D

detector, given that there is enough time to read out the

results. From the scattering images a detailed picture of the

melting process can be recovered. It should be noted that in

the case of ice melting by infrared pulses the absorption depth

is comparable to the wavelength of the radiation (E3 mm).

Hence, either surface melting can be studied or, when a special

very thin container is used, bulk melting is accessible (in the

infrared spectroscopy experiments1 the sample was placed

between two CaF2 windows spaced either 1 or 2.5 mm apart).

For scattering studies it may be necessary to make sure that

single crystals are being formed.49 In addition, it may be

possible to use ionizing radiation50 in which case the difference

between thermal melting and non-thermal melting can be

studied in the same material. The expected scattering inten-

sities at different time points after the laser pulse are predicted

from simulations in the following paragraphs.

3.2 Melting and liquid scattering

Simulation of flexible TIP/4P ice illuminated with a laser pulse

displayed melting of the crystal after roughly 10 ps. Fig. 2

Fig. 1 Schematic overview of a melting experiment, with laser

(pump) and X-ray (probe) pulse hitting the sample with a short time

delay. The scattered X-rays are collected onto a 2D detector.

Fig. 2 Top: ice crystal before the pulse with instantaneous simulated scattering pattern. Bottom: water with corresponding scattering pattern.

Scattering patterns are based on a finite-size crystal (of roughly 3 � 3 � 3 nm). Note that the structures are identical to those presented in Fig. 3 of

ref. 18.

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shows the crystal before and after the pulse, along with an

instantaneous scattering image. Under experimental condi-

tions these images would show a scattering pattern integrated

over the X-ray pulse duration, which at SPPS was o100 fs.

This time resolution is sufficient to monitor the melting

process. In Fig. 2 a small, 3 � 3 � 3 nm sample was used

and the scattering patterns for both water and ice display a

large amount of residual ‘‘structure’’. The scattering image of

water in Fig. 2 lacks the familiar ring structure expected from

liquids,51–55 whereas the scattering pattern of ice in Fig. 2 does

not resemble a normal Bragg scattering pattern either. By

repeating the simulations with larger samples (Fig. 3) we can

visualize the effect of Bragg scattering, that is, cancellation of

everything in-between Bragg spots. The unit-cell of an ice Ih

crystal contains eight molecules and the largest system studied

here consists of roughly 20 � 20 � 20 unit-cells. Due to the

temperature effects as well as structural inhomogeneity within

the crystal, the ‘‘structure’’ between the Bragg spots gradually

disappears with larger crystals (Fig. 3). It should be noted that

in routine synchrotron scattering experiments very long pulses

or continuous irradiation enhance the averaging. At LCLS

experiments the short pulses (E100 fs) will imply that there is

not as much temporal averaging. This has some bearing, at

least in theory, for structural studies of molecules in nano-

crystals where the crystallographic phase problem can be

overcome by employing algorithms that simultaneously use

oversampling, as has been used for non-crystalline sam-

ples.56,57 It may be possible to combine the enhanced scatter-

ing due to Bragg scattering with oversampling in order to

reconstruct the real-space model, therefore it useful to inves-

tigate whether there is information that can be used for

phasing. From Fig. 3 it seems that in the smallest crystal

(3 nm box edge, corresponding to 6 � 6 � 6 unit cells) there

may be useful information. The amount of information is

rapidly washed out as the crystals get larger, however.

3.3 Time decay of Bragg scattering

By computing scattering images as a function of time and

monitoring a few Bragg peaks as a function of time we can

emulate what would happen in a combined laser–X-ray ex-

periment (Fig. 1). Here we have computed scattering images at

25 fs intervals for the 15 nm system. Then we measure the

intensity of two of the most intense Bragg peaks (Fig. 4). As

expected, the intensity falls off quite shortly after the laser

pulse. In the same figure the number of hydrogen bonds per

molecule is plotted as a function of time. We have previously

introduced a melting time tmelt by determining the time where

the number of hydrogen bonds is halfway between the value

for ice and that for water18 (note that in water this number is

temperature-dependent). In the current simulation (Fig. 4b)

tmelt is roughly 5 ps. Fig. 4a shows that the decay (hkl = 100)

peak is very comparable to that of the hydrogen bonding,

indicating that the melting-time definition is meaningful. On

the other hand this also indicates that we can interpret future

experiments based on this correlation, or in other words tmelt

corresponds to the time point when the intensity of the

(hkl = 100) Bragg peak is less than 50% of the maximum

intensity in ice.

4. Discussion and outlook

A new era of research into phase-transitions is opening up

with the availability of new light-sources16 as well as the

installation of femtosecond laser systems at existing synchro-

tron facilities. A crucial step to combine these is the synchro-

nization of laser and X-ray pulses.13 Recent studies combining

laser-pumping and X-ray probing include an investigation of

the interaction potential in solid bismuth,58 and the previously

mentioned melting studies on semiconductors such as

Fig. 3 Simulated scattering patterns of ice (top) and liquid water (bottom) for different sample sizes (box-edge is given). All patterns are averages

over 100 structures corresponding to 100 fs in the simulations.

Fig. 4 (a) Time decay of the largest Bragg peak in a melting

simulation of 15 � 15 � 15 nm. (b) Number of hydrogen bonds per

molecule in the simulation. Laser pulse maximum is at 1 ps.

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germanium59 or indium antimonide.8,10–12,60 Although we

have only mentioned X-rays for probing structural changes,

obviously one can use electron scattering as well, for instance

to study cooling of bismuth following laser-induced melting.61

The structure of water and ice following temperature jumps

(but not melting of ice) have been studied by X-ray scatter-

ing62–64 and neutron scattering.65 Computer simulations of

melting transitions have been reported for ice66–80 and other

materials.81–86 Indeed, new force field models and algorithms

are being developed for the study of such phase transi-

tions.87–90 Given this plethora of experimental and simulations

methods, it seems that a significant increase in structural

studies of melting can be expected in the near future.

Our angle on the study of melting is to closely follow

experiment, or in this case to predict what a future experiment

(Fig. 1) could look like.18 In this manner it is straightforward

to compare results of simulations with experimental data.

Fig. 4 shows that there is a correlation between the intensity

of scattered radiation and the number of hydrogen bonds.

This knowledge can be used to aid in the interpretation of

planned experiments of the melting of ice, initially using

synchrotron radiation, and later at LCLS.

Finally it should be noted that the picosecond timescale of

laser-induced ice melting allows for simulation studies using

more accurate models, e.g. polarizable potentials91–95 or even

quantum molecular dynamics.96–98 A first step to more accu-

rate modelling would be reproduction of the absorption

spectra for water99–101 and ice.102

Acknowledgements

The Swedish Research Foundation is acknowledged for

financial support. Paul J. van Maaren is acknowledged for

continuous reality checks.

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