Thermally Promoted Cation Exchange at the Solid State in the Transmission Electron Microscope: How It Actually Works

Cation exchange offers a strong postsynthetic tool for nanoparticles that are unachievable via direct synthesis, but its velocity makes observing the onset of the reaction in the liquid state almost impossible. After successfully proving that cation exchange reactions can be triggered, performed, and followed live at the solid state by an in situ transmission electron microscopy approach, we studied the deep mechanisms ruling the onset of cation exchange reactions, i.e., the adsorption, penetration, and diffusion of cations in the host matrices of two crystal phases of CdSe. Exploiting an in situ scanning transmission electron microscopy approach with a latest generation heating holder, we were able to trigger, freeze, and image the initial stages of cation exchange with much higher detail. Also, we found a connection between the crystal structure of CdSe, the starting temperature, and the route of the cation exchange reaction. All the experimental results were further reviewed by molecular dynamics simulations of the whole cation exchange reaction divided in subsequent steps. The simulations highlighted how the cation exchange mechanism and the activation energies change with the host crystal structures. Furthermore, the simulative results strongly corroborated the activation temperatures and the cation exchange rates obtained experimentally, providing a deeper understanding of its phenomenology and mechanism at the atomic scale.

2 Figure SI_1.Averaged intensity profiles recorded along the width (i.e., the direction perpendicular to the length of each NW) of the non-exchanged zones of CdSe NWs.The panel at the top refers to an EELS map also presented in Figure 1B for a wz CdSe NW, the panel at the bottom refers to a closeup of an EDS map also presented in Figure 2 for a zb NW.The pale blue rectangles indicated the portions of NWs used to collect each profile.

MD Simulations performed to investigate the evolution (formation and possible disappearance) of the Cu2Se domains during the thermal increase in the zb CdSe nanowires
We investigated the following systems: Model system 1 (MS1): zb CdSe NW (with total length LTOT=5 nm and radius r=5 nm where a small (LR=1 nm) Cu2Se region (see Fig. SI_7, left) was centrally inserted.
Model system 2 (MS2): zb CdSe NW with total length LTOT=10 nm and radius r=5 nm where a large (LR=6 nm) Cu2Se region (see Fig. SI_7, middle) was inserted.After optimizing the geometry by a combination of steepest-descent and conjugate-gradients algorithms, we performed 25 ns-long MD simulations at T=750 K.The choice of such a temperature, larger than the experimental one, was made for accelerating the actual CE kinetics, without largely affecting the system stability (we stress that in this case we did not aim at calculating rates; rather, we simply focused on atomic-scale structural evolution).As well, to reduce the complexity of the simulated systems, we did not consider any external Cu atom positioned around the nanowire as well as the presence of Cd vacancies in the nanowire.The outcome of the MD simulations of the three systems can be rationalized as follows.The stability or the disappearance of Cu2Se domains within the CdSe phase can be explained in terms of capillarity effects.The mechanism driving the formation and growth of an a-phase crystal within a b-phase matrix can be described through the following thermodynamic equation:

MS1. To investigate the diffusion of
In this equation, P is the thermodynamics pressure acting at the a-c boundary, dV is the transformed volume, gab represents the free energy difference between the a and b phases, while γab describes the free energy associated with the surface reconstruction of the b-phase crystal within the a-phase matrix.Significantly, a specific b-seed can be considered stable when the value of P is greater than zero (P > 0).Thus, the threshold conditions for the stability vs. disappearance of such a seed can be defined by determining the specific values of dS and dV that result in P = 0.
When a b-seed is stable, its size undergoes growth at a rate that eventually reaches a constant value determined by gab, namely the free energy difference between the a-and b-phases, along with a mobility factor dictated by various material parameters.However, if local thermodynamics is such that the b-seed is not stable, it will tend to diminish and convert back into an a-phase.
Based on the preset model, it is possible to estimate the the minimum radius R* of a stable bseed inside the a-phase matrix: R*=R|P=0=2γab/gab.
The values for gab and γab are not easy to calculate or measure experimentally, and unfortunately, there is no literature available on these values for a Cu2Se seed growing in a CdSe matrix.However, we can make an initial assumption that the energy required for the surface reconstruction of a Cu2Se surface in CdSe is the same as the energy required for a Cu2Se surface in a vacuum.
Using this assumption, we can estimate the free energy associated with surface reconstruction at 13 T=673 K to be γab,673 K= 0.320 eV/Å 2 .
Additionally, based on Ref.
[18], we can estimate the free energy difference gab between wz CdSe and a Cu2Se crystal at T=673K to be ΔGab,673 K= 0.0219 eV/Å 3 .
Using these values, we can estimate the minimum radius a Cu2Se-seed needs to be energetically stable at T=673 K to be R*=R|P=0=2γab/gab=2.9 nm.This estimate is consistent with both the experimental results and the MD simulations.

Figure SI_2 .
Figure SI_2.Representative HRTEM images collected along the length of a zb CdSe NW.

Figure SI_3 .
Figure SI_3.Average energy landscape corresponding to a straight diffusion path from the initial

Figure SI_4 .
Figure SI_4.Diffusion coefficient D(T) estimated for the Cu interstitial defect in a wz (left) and

Figure SI_5 .
Figure SI_5.Average energy landscape corresponding to a straight path of a single Cu atom from

Figure SI_6 .
Figure SI_6.Average energy landscape corresponding to a straight diffusion path from the initial MS3): zb CdSe NW with total length LTOT=15 nm and radius r=5 nm where both small and a large Cu2Se (with size LR1=1 and lR2=4 nm, respectively) were inserted (see Fig.SI_7, right).

Figure SI_7 .
Figure SI_7.Representation of the three CdSe/Cu2Se models systems investigated by classical Cu and Cd atoms during the whole 25 ns dynamics of the MS1, we estimated the atomic radial distribution (i.e., the number of atoms divided by corresponding ring surface area with radius R) in the NW (see Fig. SI_8, left panel) at time t=0, 12.5 and 25 ns.While the Cd radial distribution appeared almost unaffected during the dynamics, we observed a significant variation in the case of Cu: we observed a clear evolution from an initially almost flat distribution towards a final distribution characterized by two peaks at Rcoordinate ~0 and 4.5 nm.

Figure SI_8 .
Figure SI_8.MS1(left panel): starting and following evolution of Cu (blue atoms) and Cd (red

Figure SI_9 .
Figure SI_9.Top row: top view of the NW evolution in MS1 during the 25 ns dynamics.Bottom

Figure SI_10 .
Figure SI_10.MS2 (left panel): starting and following evolution of Cu (blue atoms) and Cd (red

Figure SI_11 .
Figure SI_11.MS3 (left panel): starting and following evolution of Cu (blue atoms) and Cd (red

Figure SI_12 .
Figure SI_12.Attraction basin for a Cu atom close to a CdSe NW.Left panel corresponds to the

Figure SI_13 .
Figure SI_13.Cd vacancy formation energy as a function of the computational cell size estimated