# Microscopic Mechanism of the Thermal Amorphization of ZIF-4 and Melting of
ZIF-zni Revealed via Molecular Dynamics and Machine Learning Techniques

Emilio Mendez  Rocio Semino<EMAIL_ADDRESS>Sorbonne
Université, CNRS, Physico-chimie des Electrolytes et Nanosystèmes
Interfaciaux, PHENIX, F-75005 Paris, France

###### Abstract

We investigate the microscopic mechanism of the thermally induced ambient
pressure ordered–disordered phase transitions of two zeolitic imidazolate
frameworks of formula Zn(C3H3N2)2: a porous (ZIF-4) and a dense, non-porous
(ZIF-zni) polymorph via a combination of data science and computer simulation
approaches. Molecular dynamics simulations are carried out at the atomistic
level through the nb-ZIF-FF force field that incorporates ligand–metal
reactivity and relies on dummy atoms to reproduce the correct tetrahedral
topology around Zn^2+ centres. The force field is capable of reproducing the
structure of ZIF-4, ZIF-zni and the amorphous (ZIF$\\_$a) and liquid
(ZIF$\\_$liq) phases that respectively result when these crystalline materials
are heated. Symmetry functions computed over a database of structures of the
four phases, are used as inputs to train a neural network that predicts the
probabilities of belonging to each of the four phases at the local Zn^2+ level
with 90% accuracy. We apply this methodology to follow the time-evolution of
the amorphization of ZIF-4 and the melting of ZIF-zni along a series of
molecular dynamics trajectories. We first computed the transition temperature
and determined associated thermodynamic state functions. Subsequently, we
studied the mechanisms. Both processes consist of two steps: (i) for ZIF-4, a
low-density amorphous phase is first formed, followed by the final ZIF$\\_$a
phase while (ii) for ZIF-zni, a ZIF$\\_$a-like phase precedes the formation of
the liquid phase. These processes involve connectivity changes in the first
neighbour ligands around the central Zn^2+ cations. We find that the
amorphization of ZIF-4 is a non-isotropic processes and we trace back the
origins of this anisotropic behaviour to density and lability of coordination
bonds.

##  I INTRODUCTION

Amorphous Metal-Organic Frameworks (MOFs) have been long known, but only very
recently they have attracted attention of the research community. Horike  _et
al._ (2020) Indeed, since amorphous MOFs may conserve building blocks and
practically all connectivity from their crystalline counterparts, they combine
attractive properties such as intrinsic porosity and high surface areas
Thornton  _et al._ (2016) of crystalline phases with mechanical robustness and
the presence of multiple defects that can act as catalytic centres typical of
amorphous phases. Ma and Horike (2022) Amorphous MOFs can be synthesised as
such, but they are mostly obtained from their parent crystalline structures by
exerting an external stimulus on them. Fonseca  _et al._ (2021) Since these
ordered–disordered transitions are reversible, guests within the pores of the
crystalline phases can become trapped when the structure becomes amorphous to
be later released by forcing the MOF to return to its crystalline state. This
principle makes these materials attractive for important industrial and
environmental applications including water purification, Zhang  _et al._
(2019) drug delivery Orellana-Tavra  _et al._ (2016, 2020), capture of
radioactive species Sava  _et al._ (2011); Chapman  _et al._ (2011) and
catalysis Yu, Hou, and Gong (2017); Duan  _et al._ (2019) among others.
Moreover, it is easier to adequately shape amorphous materials for
applications (for example as pellets, extrudates or sprays) without
compromising their porosity or chemical properties. Bazer-Bachi  _et al._
(2014)

Zeolitic Imidazolate Frameworks (ZIFs) conform an exceptionally stable family
of MOFs with potential applications to many societal challenging processes.
These MOFs have the particularity that their distribution of
metal–ligand–metal angles is analogous that of Si–O–Si angles in zeolites, but
since their bonds are longer, their porosities are larger. This offers some
advantages in terms of potential guest-host-based applications, but it also
gives ZIFs more flexibility (i.e. their elastic moduli are at least one order
of magnitude lower than those of zeolites), Tan, Bennett, and Cheetham (2010)
as coordination bonds are weaker than covalent bonds. In addition,
amorphization of ZIFs occurs at milder conditions (for example, lower
temperatures) than for their zeolite analogues, Greaves  _et al._ (2003);
Peral and Íñiguez (2006) as deforming the metal-ligand4 tetrahedron involves
reorganising much weaker bonds than it does for the SiO4 case.

Many ZIFs exhibit ordered–disordered phase transitions. These may be induced
by changes in temperature, Bennett  _et al._ (2010, 2011a) pressure, Bennett
_et al._ (2011b) mechanical grinding, Bennett  _et al._ (2011c) interaction
with X-rays, Widmer  _et al._ (2019a) or even eliminating water from their
structures. Weiß and Henke (2023) Heat-induced amorphization was observed in a
number of MOFs, Masciocchi  _et al._ (2001); Ohara  _et al._ (2009); Ma and
Horike (2022); León-Alcaide  _et al._ (2023) in this work we will concentrate
our efforts on ZIF-4. This MOF is well-known for its applications to
separating alkenes from alkanes among other gas mixtures Hartmann  _et al._
(2015) and its synthesis has been scaled-up. Hovestadt  _et al._ (2017) It is
one of the many existing polymorphs of chemical formula Zn(C3H3N2) and it
exhibits a cag topology with connected cages of a diameter of 4.9 Å. Park  _et
al._ (2006) ZIF-4 has a complex phase diagram, consisting of a series of
amorphous and crystalline phases. Widmer  _et al._ (2019b) At ambient
pressure, the following phase transitions have been experimentally detected:

ZIF-4 $\xrightarrow{\text{ 1 }}$ ZIF$\\_$a $\xrightarrow{\text{ 2 }}$ ZIF-zni
$\xrightarrow{\text{ 3 }}$ ZIF$\\_$liq

_Transition 1_ is an amorphization phase transition from the crystalline
porous ZIF-4 to ZIF$\\_$a, an amorphous phase that has a continuous random
network structure similar to amorphous silica. Bennett  _et al._ (2010) This
transition occurs at T1=589 K. Bennett  _et al._ (2016) Further heating leads
to _transition 2_ : a recrystallization of ZIF$\\_$a into the crystalline
dense ZIF-zni solid, which happens at T2=773 K. It is interesting to note that
other Zn(C3H3N2) polymorphs, including ZIF-1 (crb topology), ZIF-3 (dft
topology) and ZIF-6 (gis topology) also yield the same amorphous phase upon
heating that subsequently crystallises into ZIF-zni. Bennett  _et al._ (2011a)
Finally, _transition 3_ involves the melting of ZIF-zni at T3=863 K to give a
liquid MOF (ZIF$\\_$liq). Beake  _et al._ (2013) Bennett and coworkers have
shown that heating ZIF-4 first leads to the formation of a low density phase
before reaching the high density amorphous phase that transforms into ZIF-zni
upon further increasing the temperature. Bennett  _et al._ (2015)

Neutron total diffraction data revealed that the Zn-centred tetrahedron
remains quite rigid during the amorphization, although an out-of-the-plane
ligand motion can act slightly reducing the total connectivity of the
amorphous phase with respect to the full connectivity of ZIF-4. Beake  _et
al._ (2013) High field 13C and 15N NMR measurements can help differentiate
ZIF-4 from ZIF-zni and show that there is an important structural similarity
between ZIF$\\_$a and both crystalline phases, albeit a signal broadening for
the amorphous material. This confirms that the amorphous phases obtained by
thermal annealing starting from ZIF-4 or ZIF-zni are identical. Baxter  _et
al._ (2015) In situ far infra-red spectroscopy proved that the ligand does not
significantly strain during the amorphization process and that collective
modes involving deformation of the ZnN4 tetrahedron are the main contributors
to the amorphization. Ryder  _et al._ (2017) From a computational standpoint,
Gaillac and coworkers have studied the melting mechanism of ZIF-4 via ab
initio molecular dynamics simulations. Gaillac  _et al._ (2017); Gaillac,
Pullumbi, and Coudert (2018) In these works, ZIF-4 is considered as a starting
point, since treating representative sections of ZIF$\\_$a and ZIF-zni would
yield too large systems to subject them to ab initio molecular dynamics while
spanning reasonable timescales to get correct simulation averages. Very high
temperatures, of the order of 1000 K or more, are explored in order to get
enough statistics, so the intermediate states between ZIF-4 and ZIF$\\_$liq
are ignored. The authors reach a good agreement between the structural
characteristics of their model and the experimental PDFs, they find that
under-coordinated Zn centres act as "seeds" for the melting process to occur
and they propose a molecular mechanism for the melting involving first-
neighbours exchanges. Despite this wealth of information, many questions
remain unanswered, including: what is the mechanism of the amorphization of
ZIF-4? What is the mechanism of the melting of ZIF-zni? What happens beyond
first-neighbours distances in these transformations? In order to answer these
questions we need larger simulation cells, thus, it is necessary to rely on a
computational model where electronic degrees of freedom are averaged following
the Born-Oppenheimer approximation. However, including reactivity, in
particular, metal–ligand reactivity, is essential to model these kinds of
ordered–disordered phase transitions. A popular reactive force field, ReaxFF,
has been tested for this task, but the modelling community has not yet reached
a consensus on whether this force field is adequate to model amorphous
ZIFs.Yang  _et al._ (2018); Castel and Coudert (2022)

In this contribution, we rely on nb-ZIF-FF (non-bonded ZIF-FF) Balestra and
Semino (2022) to study the ordered–disordered _transitions 1_ and _3_ cited
above. This force field, originally developed by Balestra and Semino with the
purpose of modelling the self-assembly of ZIFs, features metal–ligand
reactivity by means of Morse potentials to treat coordination bonds. We found
that it captures structural, mechanical and thermodynamic properties of the
amorphous and liquid phases as well as of the crystalline ones. We circumvent
the inherent difficulty of differentiating multiple ordered and disordered
phases through the training of a neural network sorting algorithm that
identifies the correct phase at the local, atomic level with high accuracy.
This data science augmented molecular dynamics approach allows us to reach
molecular detail in the study of the mechanisms of these ordered–disordered
transformations and to answer the above raised questions. We observe the
formation of a phase recognised as liquid-like prior to the formation of
ZIF$\\_$a upon heating ZIF-4 at a temperature T>T1, which can be associated
with experimental observations. Bennett  _et al._ (2015) For ZIF-zni, we found
the opposite: the density decreases monotonically, going from an amorphous-
classified state into the liquid. Both processes occur in an anisotropic
fashion, which can be correlated to the local density and labilities of
coordination bonds within the materials.

This work is structured as follows. Sec. II details the systems of study, the
algorithm applied to generate disordered structures, the development of our
neural network sorting algorithm and the molecular dynamics simulations
details. We then present and discuss our results in Sec. III and summarise
them in Sec. IV.

##  II METHODS

###  II.1 Systems of Study

We focus on two crystalline MOFs within the Zn(C3H3N2)2 series of polymorphs:
Park  _et al._ (2006) ZIF-4 and ZIF-zni, a porous and a dense phase
respectively. We analyse the phase transitions that transform ZIF-4 into
ZIF$\\_$a and ZIF-zni into a melt: ZIF$\\_$liq (_transition 1_ and _transition
3_ , see Sec. I). Widmer  _et al._ (2019b) These two are ordered–disordered
transitions, so we can adequately sample them by just increasing the
temperature (to increase the kinetic energy) of the materials. Studying
_transition 2_ is a much more complicated problem, since it would involve
using more sophisticated enhanced sampling simulation methods, to correctly
sample the collection of rare events that lead from a disordered to an ordered
phase.

Figure 1:  Structure of (a) ZIF-4, (b) ZIF-zni, (c) ZIF$\\_$a, (d)
ZIF$\\_$liq. Color code: Zn (silver), N (blue), C (grey). For clarity
purposes, H atoms are ignored and the snapshots have been scaled up to the
same size.

Fig. 1 illustrates the structure of the four studied systems. ZIF-4 and ZIF-
zni initial structures were obtained from the Cambridge Structural
Database.Groom  _et al._ (2016) ZIF$\\_$a configurations were generated by
simulated annealing of these two crystalline phases via the procedure that we
detail below, in Sec. II.2. ZIF$\\_$liq is obtained by heating ZIF-zni or
ZIF-4 to T = 700 K. All materials were modelled at the atomistic level through
the nb-ZIF-FF force field.Balestra and Semino (2022) This force field
partially includes reactivity, by allowing the metal–ligand bond to break and
form throughout classical molecular dynamics simulations. This is the only
kind of reactivity needed to model amorphization of ZIF-4, since the integrity
of the ligands along the process was confirmed experimentally.Ryder  _et al._
(2017) The metal–ligand bond is modelled through a Morse potential, which
yields zero pairwise forces at long metal–ligand distances. The correct
tetrahedral local symmetry around Zn^2+ cations is enforced by distributing
part of the cation’s charge into the four vertices of a flexible tetrahedron
that holds it in its centre (cationic dummy atom model). This force field has
been carefully validated for reproducing structural and mechanical properties
of a series of ZIFs, including ZIF-4 and ZIF-zni. For more details concerning
the nb-ZIF-FF force field, the reader is referred to Ref. Balestra and Semino,
2022.

###  II.2 Generation of the Amorphous Structures

To generate ZIF$\\_$a, we started either from ZIF-4 or from ZIF-zni. The
crystalline structures were subjected to a temperature ramp through which the
material is heated from 300 to 900 K, then a short constant T=900 K run is
performed and finally a second temperature ramp brings the system back to 300
K. We tested ramps of 1 K ps-1 and 4.8 K ps-1, which comply with the less-
than-5 K ps-1 rule proposed by Castel and Coudert to avoid damaging the full
coordination of the Zn^2+ centres in the crystalline form.Castel and Coudert
(2022) We note that these ramps are orders of magnitude higher than those
experimentally achievable (on the order of 5-100 K min-1)Bennett  _et al._
(2015). We compared radial distribution functions (RDFs) of the amorphous
materials generated with these two temperature ramp values and found no
significant differences. Constraints were added on the 900 K constant
temperature simulation so that the final materials have approximately a cubic
shape.

To sample the diversity of glass configurations, we generated three
independent runs starting from ZIF-4 and three starting from ZIF-zni, that
differ in the total time span of the 900 K constant temperature section: 250,
500 or 750 ps. The calculated properties of the glass correspond to an average
of the six independent structures obtained after the annealing. During the
heating ramp, the volume of the system suffers from an abrupt change that can
be distinguished from the expected fluctuations, signalling the phase
transition. Even though at the end of the simulation experiment the
temperature is brought back to its initial value of 300 K, the final volume
differs from the initial one, thus demonstrating that the phase transition has
taken place and has not reverted.

ZIF$\\_$a configurations generated from ZIF-4 or from ZIF-zni are
indistinguishable, and they describe quite well the experimentally
characterised amorphous material in terms of density, typical neighbour
distances and angles and of its bulk modulus, as shown in Tab. 1. The bulk
modulus $K$ was calculated from the volume fluctuations in the NPT ensemble:

$\langle(\Delta V)^{2}\rangle=\frac{k_{b}T}{K}$ (1)

Table 1:

Density, bulk modulus, Zn–Zn and Zn–N average neighbours distances and N–Zn–N
average angle computed via nb-ZIF-FF along with reference values.
$\rho(gcm^{-3})$ K (GPa) $\langle d_{Zn-Zn}\rangle$ (Å) $\langle
d_{Zn-N}\rangle$ (Å) $\langle\theta_{N-Zn-N}\rangle$ (°) nb-ZIF-FF 1.57 3.9
5.81 1.86 109 Reference 1.63111Ref. Bennett  _et al._ , 2016. 4.3222Ref.
Castel and Coudert, 2023. 5.95333Ref. Gaillac  _et al._ , 2017. 1.99333Ref.
Gaillac  _et al._ , 2017. 104444Ref. Beake  _et al._ , 2013.

Besides correctly capturing average distance and angle values, nb-ZIF-FF also
passes an even more difficult test: it yields correct distributions for these
properties. To the best of our knowledge, the angles distributions have up to
date only been correctly predicted by ab initio molecular dynamics, this is
the first time that an atomistic force field incorporating reactivity allows
to accomplish this challenging task, particularly for the N–Zn–N angle
distribution that is known to slightly widen in the amorphous phase. Beake
_et al._ (2013) Indeed, as pointed out by Castel and Coudert, Castel and
Coudert (2023) the most widely used reactive force field, ReaX-FF Yang  _et
al._ (2018), fails to reproduce the N–Zn–N angle distribution. Fig. S1 in the
Supplementary Material shows that nb-ZIF-FF is capable of predicting the
subtle widening of the angle distribution, that is due to the presence of a
small proportion of tri-coordinated Zn cations in ZIF$\\_$a.

The subtle under coordination of the Zn^2+ centres in the amorphous material
can be appreciated in Fig. 2. The left panel shows the Zn–N radial
distribution function for the four phases studied. Even though all structures
are quite similar and difficult to distinguish experimentally, Baxter  _et
al._ (2015) we can already see some subtle differences in their RDFs. Indeed
the peaks for the liquid are broader than those from the amorphous solid and
those are, in turn, broader than for the crystals. In the inset of the left
panel, we can see that the RDF does no go to zero between the first two peaks
nor for ZIF$\\_$a nor for ZIF$\\_$liq, which indicates nitrogen exchanges in
the first coordination sphere of the zinc cations and is in agreement with
previous findings. Gaillac, Pullumbi, and Coudert (2018) The right panel of
Fig. 2 shows the integral of the Zn–N RDF for the four phases, which gives us
information on the number of N that can be found on average around a Zn^2+
centre as a function of the distance. The curves for ZIF-4 and ZIF-zni reach
the value of four at 2.3 Å indicating the expected perfect tetrahedral
coordination in their first neighbours sphere. On the other hand, the curve
corresponding to ZIF$\\_$a shows a loss in the average Zn–N coordination for
the same distance, which is even more pronounced in the case of ZIF$\\_$liq.
This indicates that both disordered phases typically contain a small
proportion of tri-coordinated Zn^2+ centres, as a result of the increased
flexibility of ligand motions, as found experimentally. Ryder  _et al._ (2017)

Figure 2:  Zn–N radial distribution (left panel) and its integral (right
panel) for ZIF-4, ZIF-zni, ZIF$\\_$a and ZIF$\\_$liq obtained by molecular
dynamics simulations employing nb-ZIF-FF as a force field.

The excellent performance of the combination of nb-ZIF-FF with our simulated
annealing method in yielding ZIF$\\_$a configurations in good agreement with
several experimentally measured properties make us confident in our model for
this glassy material.

###  II.3 Machine Learning Methods

To succeed in our goal of studying the mechanism of the ZIF-4 and ZIF-zni
ordered–disordered phase transitions, we first need to define a metric that
allows us to distinguish between these crystalline phases and their disordered
counterparts at the local, atomic environment level. Such a local metric would
allow us to track the evolution of the amorphization and melting processes
throughout a simulation, to observe their progression from the deformation of
the local structure around a single Zn^2+ centre (i.e. distortions in the
tetrahedral spacial arrangement of the first ligand neighbours) to the
generation of larger disordered domains within the crystal and how these
domains propagate or merge until they take over and the phase transformation
reaches its end.

Amorphous materials have traditionally been characterised via en extensive
exploration of structural properties, including RDFs, structure factors and
pore size distribution. Sapnik  _et al._ (2023) These ways of describing
amorphous materials, albeit useful, rely on preconceived ideas of the
underlying chemistry of these materials. Machine learning methods based in
agnostic descriptors have been developed to automatically identify,
differentiate and classify long-range ordered materials in an unbiased way,
free of preconceptions. The task becomes more daunting when the collection of
objects to be classified includes amorphous materials, due to the inherent
lack of translational symmetry which makes both the choice of appropriate
descriptors as well as the sampling of structural diversity, harder. A number
of methods have been proposed to deal with this difficult task. Karayiannis,
Foteinopoulou, and Laso (2009); Pietrucci and Martoňák (2015); Caro  _et al._
(2018); Swanson  _et al._ (2020); Banik  _et al._ (2023); Rogal, Schneider,
and Tuckerman (2019) Here, we test the performance of Behler-Parrinello
Symmetry Functions (BPSF) Behler (2011) as unbiased generic descriptors that
act at the atomic environment level, to inform the degree of ZIF$\\_$a-ness,
ZIF-4-ness, ZIF-zni-ness and ZIF$\\_$liq-ness of a given Zn^2+-centred
environment. These functions fulfil the basic criteria for being well-behaved
chemical descriptors, that is, they yield the same value for two
configurations that are related in that one of them is the result of a
translation, rotation or same-element-atom permutation operation applied over
the other. These atom-centred many-body functions can be classified into two
types: _radial_ and _angular_. The former ones are given by the sum over two-
body terms and are related to the connectivity of the central atom, while in
the latter ones, three-body terms are considered. We tested twelve symmetry
functions of the type:

$\displaystyle G_{i}^{rad}=\sum_{j\neq i}e^{-\eta(R_{ij}-R_{s})^{2}}\cdot
f_{c}(R_{ij})$ (2)

$\displaystyle
G_{i}^{ang}=2^{1-\zeta}\sum_{i,j,k}(1-\lambda\cos{\theta_{ijk}})^{\zeta}\cdot
e^{-\eta(R_{ij}^{2}+R_{ik}^{2}+R_{jk}^{2})}$ $\displaystyle\cdot
f_{c}(R_{ij})\cdot f_{c}(R_{ik})\cdot f_{c}(R_{jk})$ (3)

Where $f_{c}$ is a cutoff function that decays to zero at a distance $R_{c}$.
Each of the $n_{Zn^{2+}}$ cations in a given configuration will be thus
characterised through 12 symmetry functions, each of them centred on the
tagged Zn^2+ cation, 4 of them radial and 8 angular. Only Zn–Zn correlations
were considered. Further details, including the parameters that were
considered for defining the symmetry functions can be found in the
Supplementary Material.

Before analysing our trajectories through the lens of our chosen descriptors,
we sought to verify their aptitude in recognising the four systems studied. To
this end, we built a database comprising 30000 configurations in total, out of
which 3000, 3000, 12000 and 12000 correspond to ZIF-4, ZIF-zni, ZIF$\\_$a and
ZIF$\\_$liq respectively, each of them comprising 64 atomic Zn^2+-centred
environments. The amount of non-crystalline structures is higher to improve
the classification, since the differentiation between these two groups will be
the most challenging task for the algorithm. The configurations correspond to
microstates obtained from MD simulations at temperatures spanning the whole
stability range in the case of crystalline structures, while for ZIF$\\_$a the
sampling was made at temperatures between 300 K and 500 K. As mentioned above,
liquid state configurations were sampled at 700 K. We justify this criterion
by the change of slope at $\sim 600K$ observed in the curve of mean potential
energy vs. temperature (see Fig. S2) associated with the jump in $Cp$ that
occurs at the glass transition temperature (ZIF$\\_$a $\xrightarrow{}$
ZIF$\\_$liq). We then computed the symmetry functions described by eqs. 2 and
3 for each of their Zn^2+-centred environments via the RuNNer code Behler
(2015) and plotted their values distributions for all structures together as
box plots in R,R Core Team (2022) the resulting graph is shown in Fig. S3. We
can see from the plot that none of the symmetry functions alone suffices to
distinguish between the four phases. We thus used them as features to feed
into a neural network that was trained to output the probabilities that the
Zn^2+-centred environment belongs to a ZIF-4, ZIF$\\_$a, ZIF$\\_$liq or ZIF-
zni phase (four output values). In order to train the neural network, we
divided our database, composed by 1920000 Zn^2+-centred environments (64x30000
structures) into train and test sets in a 80:20 proportion. The neural network
architecture was composed by an input layer of 12 nodes, corresponding to the
symmetry functions, a single hidden layer comprising 6 nodes, and a output
layer of 4 nodes, each one representing the probability of an environment to
be classified as one of the reference structures (see Fig. 3). Further details
can be found in the Supplementary Material. If we assign the environment to
the class that has the highest associated probability to obtain a clear-cut
sorting, our neural network yields 90.3% accuracy in the classification
exercise for the test set.

Figure 3:  Schematics of our neural network trained over atom-centred symmetry
functions of ZIF-4, ZIF$\\_$a, ZIF-zni and ZIF$\\_$liq microstates that allows
to classify Zn^2-centred environments (left and right hand illustrations:
before and after the classification.

In table 2 we show the confusion matrix obtained for the test set (which is
composed of structures that were not used in the training process). This table
indicates the fractions of environments of each type (rows) classified as each
of the possible structures (columns). The diagonal elements correspond to the
fraction of correct classifications. As expected, the highest source of error
($\sim$10%) was obtained from the miss-classification of ZIF$\\_$a and
ZIF$\\_$liq structures, Schoenholz  _et al._ (2016) while the classification
of crystalline structures was satisfactory in 95% of the cases. Indeed, by
simple visual inspection both disordered phases seem to be indistinguishable
(see Fig. 1). A hint that the classification was possible was given by the
fact that the Zn–N radial distribution functions for ZIF$\\_$a and ZIF$\\_$liq
differ, as shown above in Fig. 2a. It is however quite remarkable that the
neural network manages to distinguish them with such low error despite their
important structural similarity. The accuracy of the classification is even
more impressive if we take into account that it was made based on structural
information only, as it is well-known that the main difference between glasses
and their parent crystalline structures lie in their dynamics rather than in
their structures. Incorporating dynamics information into the features for a
neural network distinguishing amorphous materials would most likely further
improve the accuracy.

Table 2:

Confusion Matrix. The diagonal elements are highlighted in bold and the
predicted classes in italics.  ZIF-4 ZIF-zni ZIF$\\_$a ZIF$\\_$liq ZIF-4 0.951
0.000 0.004 0.045 ZIF-zni 0.000 0.946 0.044 0.010 ZIF$\\_$a 0.000 0.019 0.895
0.086 ZIF$\\_$liq 0.012 0.002 0.098 0.888

Fig. 3 shows an example of how our neural network can be applied to follow the
time evolution of an amorphization process. In the left part, we can see a
material that exhibits coexisting ordered and disordered domains. By applying
our neural network, we can distinguish between ZIF-4-, ZIF-zni-, ZIF$\\_$a-
and ZIF$\\_$liq-like environments. Finally, to check that the classification
of the amorphous phases is meaningful, we plotted the fraction of disordered-
like centres that are classified as being ZIF$\\_$liq-like instead of
ZIF$\\_$a-like as a function of temperature (see Fig. S4). We can see from
this plot that there is a clear temperature dependence on the labelling, which
is consistent to what is expected for the thermodynamic stability of these two
distinct disordered states (see Fig. S2).

###  II.4 Molecular Dynamics Simulations

Classical molecular dynamics simulations were carried out through the LAMMPS
open source simulation packageThompson  _et al._ (2022) with nb-ZIF-FF as a
force field.Balestra and Semino (2022) The integration of equations of motion
was performed in the NPT ensemble, with Nose-Hoover thermostats and barostats.
The damping parameters were set to 100 time steps for the thermostat and 1000
time steps for the barostat. Unless the contrary is specified, the barostat
alters the box sizes in a isotropic way. In all cases the pressure was set to
1 bar. The time step was set to 0.5 fs except for simulations with temperature
over 700 K, in which a time step of 0.25 fs was used. For generating
configurations for the neural network training set, systems of 64 Zn atoms
where used, which corresponds to a 2x2x1 supercell of ZIF-4 or a ZIF-zni unit
cell (1600 particles in total, including both crystallographic and dummy
atoms) while for production runs, the number of Zn atoms was 1024, which
corresponds to a 4x4x4 and a 2x2x4 supercell for ZIF-4 and ZIF-zni
respectively.

##  III RESULTS AND DISCUSSION

###  III.1 Thermodynamic Analyses

We start our study of ZIF-4 $\xrightarrow{}$ ZIF$\\_$a (amorphization,
_transition 1_) and ZIF-zni $\xrightarrow{}$ ZIF$\\_$liq (melting, _transition
3_) by determining their equilibrium temperatures. We could be tempted to
extract the transition temperature from the simulations that we performed to
generate the amorphous structures (see Sec. II.2) as the temperature that
matches the drastic volume change of the system, which signals that the
amorphization process has taken place. However, this would be misleading: the
temperature ramp is so fast that the system cannot reach thermal equilibrium
at each temperature. The false transition temperature we see when we apply a
temperature ramp to heat the system has to be higher than the thermodynamic
transition temperature. In order to find the equilibrium temperature for
_transitions 1_ and _3_ , we need to find conditions in which both phases are
equally stable. Govers  _et al._ (2008) We first generated a simulation box
where ZIF$\\_$a and ZIF-4 coexist and occupy approximately the same volume
each by running a short simulation at the temperature in which we observed the
phase transition in the simulated annealing (T=550 K). Subsequently, we
started a series of molecular dynamics simulations at the NPT ensemble, each
with different target constant temperature. We let the system evolve, and then
we assessed whether the number of amorphous sites had increased, decreased or
remained stable. The temperature for which the two phases coexist without one
of them gaining terrain over the other is the equilibrium temperature. We
followed the same procedure to determine the ZIF-zni melting temperature. Fig.
S5 shows the time evolution of the number of liquid-like Zn^2+ centres for
ZIF-zni at different temperatures. We can see that the number of liquid-like
centres fluctuates around a constant value at T = 625 K. Through this
procedure we found $T\\_{amorphization}=T_{1}=420K$ and
$T\\_{melting}=T_{3}=625K$. The experimental counterparts are around 520 K and
860 K respectively. Widmer  _et al._ (2019b)

We can also obtain the amorphization and melting entropies ($\Delta S_{1}$ and
$\Delta S_{3}$) from these simulations. At the temperature in which the phases
coexist, their chemical potentials are equal and $\Delta G=0$, so the entropy
can be readily obtained from the enthalpy by diving it by $T$. The enthalpy is
given by the internal energy coming from the force field plus the pressure-
volume term. In addition, we can obtain free energy differences at temperature
$T$ by integration of the Gibbs-Helmholtz equation:

$\Delta G(T)=-T\int_{T_{eq}}^{T}\frac{\langle\Delta H\rangle(T)}{T^{2}}dT$ (4)

Where $T_{eq}$ is the equilibrium temperature obtained before. This allows us
to compute $\Delta G$ of both reactions at 298K. Then, since we have a common
reference state, i.e. the glass, we can extract information about the relative
stability of ZIF-4 with respect to ZIF-zni. These results, along with
reference values, are presented in Tab. 3.

Our computed enthalpies are in good agreement with the reference experimental
and ab initio values. From the free energy difference we obtain the correct
thermodynamic stability trend: ZIF-4 is in fact metastable at ambient
temperature and pressure. Entropies can be rationalized in terms of structural
properties. Indeed, the disordered phases have higher entropies than the
ordered ones, and if we compare the entropies associated to the crystalline
phases, we can see that is higher for ZIF-4 than for ZIF-zni. This is a
consequence of the lower density (higher porosity) of ZIF-4, which confers it
the possibility of adopting many more equivalent microstates than its high
density counterpart can. We note that our equilibrium temperatures are
deviated from the experimental values. Even though we cannot predict the right
values, the tendencies are reproduced. Experimental values should also be
carefully considered, since it has been proven that the amorphization
temperature is very sensible to the temperature ramp used to trigger it.
Bennett  _et al._ (2015)

Table 3:

Thermodynamic properties of the different transitions studied. For ZIF-4
$\xrightarrow{}$ ZIF$\\_$a and ZIF-zni $\xrightarrow{}$ ZIF$\\_$liq
transitions, the values correspond to the calculated equilibrium temperatures,
while the ZIF-4 $\xrightarrow{}$ ZIF-zni values correspond to ambient
conditions. Reference values from experiments (111Ref. Bennett  _et al._ ,
2015.) and ab initio calculations (222Ref. Widmer  _et al._ , 2019b.) are
shown between parenthesis.  $T$ $\Delta G$ $\Delta H$ $\Delta S$ $(K)$
$(kJmol^{-1})$ $(kJmol^{-1})$ $(JK^{-1}mol^{-1})$ ZIF-4 $\xrightarrow{}$
ZIF$\\_$a 420 (589)111Ref. Bennett  _et al._ , 2015. 0.0 3.6 8.7 ZIF-zni
$\xrightarrow{}$ ZIF$\\_$liq 625 (863)111Ref. Bennett  _et al._ , 2015. 0.0
16.3 (9.8)111Ref. Bennett  _et al._ , 2015. 26.0 ZIF-4 $\xrightarrow{}$ ZIF-
zni 298 -6.5 -12.4 (-14.0)222Ref. Widmer  _et al._ , 2019b. -19.6

###  III.2 Mechanisms of the phase transitions

We continue our study by simulating the amorphization and melting processes at
the NPT ensemble at P=1 bar and T=550 K for ZIF-4 and T=700 K for ZIF-zni.
These temperatures are higher than the respective transition temperatures, to
guarantee thermodynamic feasibility and reasonably fast kinetics. At the end
of these simulations, we reach the corresponding disordered phase (glass from
ZIF-4 and liquid from ZIF-zni). We also run the same simulations for ZIF-4 and
ZIF-zni but with a box consisting of 3x3x3 unit cells to verify whether the
size of the simulation box was large enough to avoid unphysical effects that
could happen if the process was favoured by an early artificial percolation of
the new phase in a small simulation box. The average times needed for the
amorphization to occur for the smaller systems are very close to those we
obtained for the larger ones, so we can confirm that our boxes are large
enough to adequately treat the two processes. We run four independent systems
for each transition in order to take into consideration their stochastic
character, the results presented below come from an average of these four
independent simulation experiments.

Figure 4:  A–D: Representative snapshots of a ZIF-4 amorphization simulation
at (A) 0, (B) 1.1, (C) 1.7 and (D) 4.5 ns. E–H: Representative snapshots of a
ZIF-zni melting simulation at (E) 0, (F) 0.5, (G) 0.8 and (H) 1.25 ns.
ZIF$\\_$liq- and ZIF$\\_$a-like environments are shown in orange and green
respectively. For clarity purposes, Zn^2+ centres classified as belonging to a
ZIF-4 and ZIF-zni phases are not coloured.

A series of snapshots of the system throughout the simulation is shown in Fig.
4. Panel A shows the initial configuration, which corresponds to a ZIF-4
crystal. As expected, and confirming the validity of our neural network, the
amount of environments classified as ZIF-zni-like remains negligible during
the whole simulation. We first observe the generation of a liquid-like phase
(coloured in orange, panel B). Subsequently, the amorphous ZIF$\\_$a phase is
formed from within this lower density phase (coloured in green, panel C) and
gradually expands until it takes over the whole system (panel D, final
configuration). The amorphization process thus consists of two steps: a first
step in which the Zn–N connectivity slightly drops to yield a more disordered,
low density state, followed by a second stage that gives rise to ZIF$\\_$a.
The intermediate liquid-like phase that is first formed could be associated to
the experimentally identified low density non-crystalline phase. Bennett  _et
al._ (2015) Indeed, this phase is less dense than ZIF$\\_$a in about $\sim$
10% which is comparable to the experimentally obtained density difference
between the low density and high density amorphous phases. Bennett  _et al._
(2015) The liquid phase, in turn, is more dense than the porous ZIF-4 crystal.
Note that we did not explicitly include the experimentally found low density
phase in the training of the neural network, but the algorithm identified it
as a liquid-like phase probably due to the correlation between local density
and the symmetry functions values. Furthermore, since the classification is
done only by structural information, the fact that the intermediate phase is
assigned to be a liquid does not imply that the dynamics are faster than those
associated to the amorphous final phase.

For ZIF-zni (Fig. 4, panels E-H), the situation is inverted: from the crystal
(panel E), the connectivity starts gradually diminishing to yield an
amorphous-like phase at a first stage (panel F), which then continues to
increase its density to reach the final ZIF$\\_$liq state (panel G). The
liquid phase grows inside the amorphous phase until it takes over the whole
simulation box. This suggests that both transitions are thus two-step
processes, in what they have in common is that the intermediate phase that is
formed in the first step has intermediate density between that of the initial
and the final phases ($\rho_{ZIF-4}$ < $\rho_{ZIF\\_liq}$ < $\rho_{ZIF\\_a}$ <
$\rho_{ZIF-zni}$).

In all simulation experiments, we observed that the disordered phases grow as
a single cluster that expands and reorganises in terms of the Zn–N
connectivity, instead of forming a series of disordered micro-domains that
subsequently aggregate. The formation of the higher density amorphous phase
does not seem to occur at the interface between crystalline and liquid
environments: on the contrary, it is generated at the bulk liquid and
propagates until practically all environments are ZIF$\\_$a-like. For the
melting of ZIF-zni, we also observe that the final phase is formed within the
bulk of the intermediate disordered phase.

The time-evolution of the the fraction of Zn^2+ centres $X_{Zn}$ that
correspond to ZIF-4-, amorphous- and liquid-like states is plotted in Fig. 5
and in Fig. S6 for _transition 1_ and _3_ respectively. From these plots we
can first confirm the two above mentioned stages for both processes. We can
also see in Fig. 5 that once the amorphous cluster is formed, it grows until
it takes over the whole simulation box .

Figure 5:  Time evolution of the fraction of disordered (amorphous-, green,
and liquid-like, orange) and crystalline (ZIF-4-like, black) Zn^2+ centres for
an amorphization simulation starting from a ZIF-4 crystal (ZIF-4
$\xrightarrow{}$ ZIF$\\_$a). A,B,C and D mark the points of the trajectory
from which we obtained the snapshots for Fig. 4. The vertical dotted line
indicates the occurrence of a change in connectivity of the type shown in Fig.
6. The number of 3 membered rings formed by neighbour Zn^2+ centres per unit
cell is shown in cyan, the scale is given in the right side y axis.

To unveil the microscopic processes that trigger the initial steps of the
amorphization, we performed a simulation starting from ZIF-4 at a slightly
lower temperature than the above described (T=540 K) in which no amorphization
is observed during the whole simulation time span, due to the fact that this
is a slow activated process. Indeed, the classification algorithm only
identifies a small fraction ($\sim$ 2%) of non-crystalline Zn^2+ centres,
which corresponds to low-lifetime random fluctuations of the network. The
presence of tricoordinated Zn^2+ is observed in both cases, and these
represent $\sim$ 2% of the metallic cations. These unstable defects are
generated by breaking Zn–N bonds, and have an average lifetime of $\sim$3 ps,
meaning that the process is reversible. This indicates that bond breaking
events leading to undercoordinated Zn^2+ centres are not sufficient to trigger
the amorphization process.

By monitoring the connectivity of the Zn–N network over time we can observe
all possible pathways to restore the tetrahedric coordination of a defect
site. Three different mechanisms can be identified: (i) the broken Zn–N bond
is restored, leading to exactly the same connectivity as before the defect
formation; (ii) the tricoordinated Zn^2+ binds to the other nitrogen that
belongs to the same ligand moiety, i.e. a rotation of the imidazolate restores
the original connectivity; or (iii) a new bond is formed between the Zn^2+ and
a different ligand molecule, leading to a change in the connectivity of the
system. This latter mechanism is illustrated in Fig. 6. The first two
mechanisms were observed in both T = 540 K and T = 550 K simulations, but the
last one only took place in significant amounts in the high temperature
system, which exhibits an amorphization. In the 540 K simulation, just a few
(13) events of this kind were registered along the simulation, and every one
of them finally reverted to the original connectivity after a short period of
time. These may be considered as failed initial attempts of the new phase to
nucleate. This scenario suggests that the first steps of the amorphization are
related to the formation of Zn–N bonds that change the original connectivity
of the network. This kind of events are much more infrequent than simple bond
breaks or than the formation of tricoordinated sites. Processes of type (iii)
typically occur for the first time in a simulation at about t=100 ps, while
type (ii) processes rotations take place each 1.5 ps on average and simple
bond breaking are observed each 0.1 ps. These results are averages over four
independent runs at T=550 K. In figure 5 we include a dotted line indicating
the time of occurrence of a type (iii) event. We can see that the process is
accompanied by a sudden jump in the number of liquid-like environments
recognised by the neural network, thus triggering the amorphization
transition.

Figure 6:  Typical stages of a process of type (iii) described in the main
text. a) A Zn–N bond breaks in an initially tatracoordinated Zn^2+. b) A
tricoordinated Zn defect is formed. c) A new metal–ligand bond is formed
between the original Zn and a different imidazolate moiety, leading to a
change in the connectivity of the system. For clarity purposes only Zn and N
atoms are shown in the figure.

The same analysis was done for the melting of ZIF-zni, by comparing
simulations performed at T=700 K and T=670 K, in which no melting was
observed, leading to a similar classification of timescales. In this case,
since we are at a higher temperature, the characteristic times are reduced to
$\sim$50 ps for the first type (iii) event to occur, while type (ii) rotations
take place each 0.5 ps on average and bond breakings occur each 0.02 ps.

We complement the microscopic description of the amorphization process by
studying the evolution of the number of 3 membered rings formed by neighbour
Zn^2+ centres (here we count only the Zn^2+, in fact the rings are formed by
alternating metals and ligands, as the (Si–O)n rings in zeolites). These kind
of structures are known to be present in the glass state but not in the
crystal, which exhibits rings of 4, 6 and 8 members.Castel and Coudert (2022)
We can see in Fig. 5 that the number of 3 membered rings in the early stage
correlates with the growth of the intermediate low density phase, thus
suggesting that the formation of this kind of structures could be an important
step in the amorphization process. The correspondence seems to be amplified in
the stage of formation of the final glass structure. This indicates that the
final configurations are richer in 3 membered rings patterns, while the
intermediate phase preserves more of the topological features of ZIF-4.

To gain further microscopic insight into the propagation of the disordered
phases during these ordered–disordered transitions, we plotted the average
disordered (amorphous- and liquid-like) cluster size projected into the three
Cartesian axes as a function of the number of disordered Zn^2+ centres
$N_{Zn}$ in Fig. 7. A similar plot for _transition 3_ can be found in Fig. S7.
We can see from the curves in Fig. 7 that the growth of the disordered phase
is anisotropic: it occurs faster in the $x$ direction than in the other two.
This behaviour is reproduced in all the independent simulations we run and can
be observed both for the first disordered liquid-like low density phase as
well as for the final ZIF$\\_$a amorphous phase. In the case of _transition 3_
, ZIF-zni melting, no preferential direction can be clearly distinguished
during the whole interval of cluster sizes.

Figure 7:  Top: Average length in each of the three cartesian axes directions
as a function of $N_{Zn}$, the number of Zn^2+ centres in the ZIF$\\_$liq
cluster along ZIF-4 amorphization. The inset shows a snapshot of the unit cell
in the XY plane. Each ligand is coloured according to its tendency for bond
breaking. The colour scale is related to the average time associated to the
bond breaking process: from red (less stable bonds) to blue (more stable)
passing through white (intermediate reactivity bonds). Only N and Zn^2+ atoms
(grey) are shown. Bottom: atomic density as a function of position in each
direction for the crystalline ZIF-4 supercell. The colour code is the same as
in the top figure.

Anisotropy in the formation of amorphous domains has also been experimentally
hypothesised for ZIF-4 systems. Widmer  _et al._ (2019a) Fig. 7b depicts local
density histograms for ZIF-4 projected into the three Cartesian axes. We can
see that the local density stays more or less constant when projected onto the
$x$ axis, thus facilitating the connectivity exchange events that drive
amorphization, as discussed above. Indeed, the porosity along this direction
is more connected than in the other two, which show jumps in the local density
that are associated to cage changes. We complement this analysis by adding
information about the lower temperature simulations made at T=540 K and T=670
K that exhibit bond breaking and formation while preserving the original
crystalline structures for ZIF-4 and ZIF-zni respectively. We associated each
bond breaking event to a ligand position in the unit cell, in order to check
if there are ligand sites that are more labile than others. We found that in
the case of ZIF-4, the 32 ligand sites of the unit cell are divided as
follows: 8 of them present a high stability, breaking at a rate of
approximately once each 4 ps; 8 of them present the highest tendency to break
(once each 2.5 ps), while the others lie in an intermediate reactivity. In the
inset of the top panel of Fig. 7 we show a plot of the XY plane of the unit
cell with the ligands coloured as blue for the first kind, red for the second,
and white for the last one. We can observe that bonds oriented in the X
direction are the most labile, while the ones pointing in Y or Z are more
stable, in agreement with our previous results. The origin of the difference
in stability may be found in the participation of each ligand in different
rings. The most stable bonds are those that are part of a four Zn membered
ring, while the most labile are only part of 6 membered rings.

In the case of ZIF-zni at T= 670 K, the classification of the 128 ligand
positions results in 32 members that are more stable than the others, each
breaking their coordination bonds each 4.5 ps on average. The others present
mean breaking times spanning the interval between 1.9 and 2.7 ps. In this
case, members of four Zn membered rings present an intermediate stability. It
is found that the most and least labile bonds have important projections in
the $z$ direction, this can be observed in the colouring in the inset of Fig.
S7.

##  IV CONCLUSIONS

We have studied the molecular mechanisms and thermodynamic properties of a
series of phase transformations that link two crystalline polymorph ZIFs
(ZIF-4 and ZIF-zni), with two disordered phases, a lower density, liquid-like
one (ZIF$\\_$liq) and a higher density, amorphous solid (ZIF$\\_$a). To this
end, we have modelled these states via a force field that incorporates
reactivity in the coordination bonds. We validate our model by successfully
comparing structural and mechanical properties computed from it with reference
experimental and ab initio data. We have augmented our molecular dynamics
method with a phase sorting algorithm based on a neural network that can
assign Zn^2+ centred environments to their parent state with high accuracy.
The accuracy is quite astounding taking into account that the algorithm has
only been fed structural features as inputs and that it can even distinguish
between disordered phases.

Our molecular dynamics simulations allowed us to determine thermodynamic state
functions of the ZIF-4 $\xrightarrow{}$ ZIF$\\_$a and ZIF-zni $\xrightarrow{}$
ZIF$\\_$liq transitions as well as for ZIF$\\_$a $\xrightarrow{}$ ZIF$\\_$liq
via thermodynamic integration. Specially relevant are those state functions
related to the transition between the two crystalline polymorphs that are
difficult to measure experimentally. Our results are in good agreement with
reference values, and those that were not previously measured can be
rationalized in terms of the disorder and porosity of the different phases.

We have furthermore followed the amorphization of ZIF-4 and the melting of
ZIF-zni processes and obtained mechanistic details at the microscopic level.
We identified two stages in both processes. Density changes monotonically in
both cases, as does the connectivity. These processes occur via changes in the
identity of the first neighbour ligand moieties that are coordinatively bonded
to the Zn^2+ centres. Kinetics of the amorphization of ZIF-4 are faster in a
preferential direction. We have rationalised this through the analysis of
local densities projected onto the three Cartesian axes and the study of the
lability if the coordination bonds.

This work sheds light on the mechanism of important phase transformations for
materials that are excellent candidates for solving pressing environmental and
industrial issues. More specifically, our results help better understand the
process of generation of amorphous MOFs, which have have been suggested to be
key in bridging the gap between research laboratory and real-world application
of these promising and versatile porous materials. We also hope that the
methods that we developed and deployed are useful to other researchers in this
and other fields to study the amorphization of other families of materials or
even more broadly to study other kinds of reactive processes.

###### Acknowledgements.

This work was funded by the European Union ERC Starting grant MAGNIFY, grant
number 101042514. This work was granted access to the HPC resources of CINES
under the allocation A0130911989 made by GENCI and to the HPC resources of the
MeSU platform at Sorbonne-Université.

## Data Availability Statement

The data that support the findings of this study are available within the
article and its supplementary material.

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