Nested order-disorder framework containing a crystalline matrix with self-filled amorphous-like innards

Solids can be generally categorized by their structures into crystalline and amorphous states with different interactions among atoms dictating their properties. Crystalline-amorphous hybrid structures, combining the advantages of both ordered and disordered components, present a promising opportunity to design materials with emergent collective properties. Hybridization of crystalline and amorphous structures at the sublattice level with long-range periodicity has been rarely observed. Here, we report a nested order-disorder framework (NOF) constructed by a crystalline matrix with self-filled amorphous-like innards that is obtained by using pressure to regulate the bonding hierarchy of Cu12Sb4S13. Combined in situ experimental and computational methods demonstrate the formation of disordered Cu sublattice which is embedded in the retained crystalline Cu framework. Such a NOF structure gives a low thermal conductivity (~0.24 W·m−1·K−1) and a metallic electrical conductivity (8 × 10−6 Ω·m), realizing the collaborative improvement of two competing physical properties. These findings demonstrate a category of solid-state materials to link the crystalline and amorphous forms in the sublattice-scale, which will exhibit extraordinary properties.

-> I understand that the authors performed atomistic, DFT simulations (static and molecular dynamics) to provide some insight about their structure. However, the simulations are not very convincing. The model structures are too small. How one can assess the significance of size effects on their findings? In addition, for the calculations of the MSD, the molecular-dynamics simulations are too short. How one can tell if the MSD behaviour remains unchanged if they run a little longer the MD simulation? Moreover, the authors mentioned in the text that the application of pressure is a natural choice for the design of their hybrid structure. However, they used an NVT ensemble for their MD simulations. Why not to run the simulations with an NPT ensemble and let the structure naturally to form/adjust within the framework due to the applied/target pressure? Then, the simulations would have provided a more direct argument.
-> In Table S1, the reported lattice parameters correspond to the experimental data or to the relaxed DFT structures? A comparison is needed.
-> In Figures S11 and S12, why the electronic structure at a pressure of 9.4 GPa is not presented? This value of the pressure seems to be critical from the rest of the results presented in the manuscript, hence it would have been significant to see the density of states (DOS) and investigate the behaviour of the electronic structure.
-> In Table S2, the changes of the Bader charges from 0 to 9.4 GPa pressures are insignificant. One should expect the changes in the atomic structure to be reflected on the Bader ionic charges (difference between crystal/glass).
-> In Figure S13, the three atomistic structures look, again, identical. I cannot see any difference. The figures do not provide any useful information.
Overall, I would like the authors to consider my concerns, comments, questions and suggestions. At the moment, a recommendation for publication in Nature Communications cannot be justified. Nevertheless, I would like to give them the opportunity to address all of them and respond accordingly.

0.
It is strange that there is no diffraction from the pressure-transmitting medium (Ne) on the Figures S1and Figure 1a (expected at pressures higher than 10 GPa). 1. Fig. 2c does not contain standard uncertainties of fitted parameters. One can expect significant correlations between V0 and B0 for the high-pressure phase, because V0 can not be constrained by the experiment. This information should be provided. 3. It can be noticed that the transition pressure is suspiciously close to Neon crystallization pressure (see Figure 2d). Several authors have pointed out the effect of pressure-transmitting medium incorporation into framework compounds, leading to changes of compressional behavior (e.g. Chapman et al. 10.1021/ja804079z). A proper study would require a test of different pressuretransmitting media. For example, the Authors could include some diffraction patterns from their experiments where NaCl was used as a pressure-transmitting medium.
To summarize, I am not convinced that the phenomenon, which is described in the manuscript is novel enough to warrant the publication in Nature Communications. Nevertheless, if technical flaws are properly handled, the paper will definitely fit a high-profile specialized journal (e.g. PRL, or Chem. Mater).
(Manuscript ID: NCOMMS-21-44547-T) We are very grateful to the reviewers for their time and efforts to review our manuscript.
Both reviewers' comments are encouraging and very helpful for further improving the quality of our paper. We believe that the following responses have addressed all reviewers' concerns thoroughly.

Reviewer #1
Bu Here, we would like to emphasize the unique features of the nested order-disorder framework (NOF) and its differences in comparison to the cases of 'melted' chains in highpressure metals and metal-organic or metal-inorganic frameworks. There are three unique features in this reported NOF structure, (1) the hybridization of crystalline and amorphous structure is realized within one unit cell in a single compound; (2) the retained crystalline matrix possesses long-range periodicity; (3) the structural modulation occurs at the sublattice-scale level due to the chemical-bond hierarchy.
On the one hand, the chain "melting" occurs in the metals who possess the incommensurate host-guest structure ( Figure R1a). 1-3 At certain pressure and temperature, the long-range ordering of the guest chains is lost while the host atoms remain crystalline ( Figure R1b), resulting the order-disorder hybrid structure. The melted chain in high-pressure metals is one of the most exciting discoveries in the exploration of order-disorder hybrid materials, which have been included in the revised version of Introduction (on page 2 of the revised manuscript). We agree with the reviewer that the formation of amorphous guest in a crystalline host in the melted chains in high-pressure metals is similar with the reported NOF structure. Here, we would like to state their differences from the following two aspects. (1) The NOF structure is realized within one unit cell, while the chain "melting" happens in higher dimensions and the initial unit cell does not retain. (2) The disordering of the sublattice in NOF structure takes place in three directions due to the chemical-bond hierarchy, while the order-disorder transition in the guest chains takes place in one direction caused by the incommensurate structure.
Therefore, the NOF structure reported in our work is distinguished from the melted chains in incommensurate metals.
On the other hand, metal-organic or metal-inorganic frameworks with disordered guest 3 molecules consist of two individual compounds that no chemical bonding is formed between them, 4, 5 such as gas-MOF structures ( Figure R1c); 6 while the NOF structure is realized within a single compound with chemical bonding hierarchy where the amorphous innards are self-filled in the periodically ordered crystalline matrix ( Figure R1d). The MOFrelated structures do not fit the features #1 and #3 of NOF mentioned above. Therefore, the NOF structure reported in this work is novel which is distinguished from the cases of 'melted' chains in some metals and metal-organic or metal-inorganic frameworks. We would like to express our sincere gratitude to the reviewer again for the insightful comment. Carefully considering the similarities and differences between these distinguishable hybrid systems is thus beneficial for the deeper understanding of each of them. The description of 'melted' chains in high-pressure metals and MOF structures have been included in the introduction of the revised manuscript.
On page 2: "These hybrid materials could possess advantageous properties from both crystalline and disordered units, which are increasingly attractive for potential technological applications, including black TiO2 nanomaterials for photocatalysis, 5, 6 twodimensional electron gases at crystalline-amorphous oxide interfaces for transparent conductors, 7 metal-organic frameworks (MOFs) and their composites for catalysis. 8 From the local structure point of view, hybridization has been made at the mesoscopic scale, [9][10][11] such as paracrystalline silicon, 12 intermediate crystalline metallic glass, 13 and melted chains in high-pressure metals. 14-16 " Apart from that there are several issues with the data presentation, which I would like to point out: 1. On Page 4 the Authors write that the structural softening "is related to the large atom displacement parameter of Cu2". In the experimental section the Authors write that Rietveld refinement was performed ( Figure S1). Therefore, it should be possible to track the development of the refined Cu2 ADP with pressure increase. This information should be given in the text. The corresponding description has been added in the Revised Manuscript: On pages 5 and S14: " As shown in Figure S2, the ADP values of Cu2 significantly increase from 0.01 to 0.06 Å 2 during compression, indicating the enhanced rattling vibration and the moveable Cu2 atoms under high pressures."  In the revised manuscript, in situ high-pressure X-ray absorption spectra (XAS) at Cu K- In the revised manuscript, in situ XAS results with detailed discussion have been added to address the reviewer's concern.
On pages 7 and 8: On page S5 of the Supplementary Information: "X-ray absorption spectra measurement.
In situ high-pressure X-ray absorption spectra (XAS) of Cu K-edge were collected at BL05U In order to better refine the powder XRD data using the Rietveld method, we masked the neon diffraction spots using Dioptas software. 12 That's why Figure S1, showing the Rietveld refinement results, doesn't show the diffraction from neon. We thank the reviewer for pointing out this and the information about the pressure transmitting medium for each high-pressure experiment has been included in the revised supplementary information. 10 On page S4 of Supplementary  5. Fig. 2c does not contain standard uncertainties of fitted parameters. One can expect significant correlations between V0 and B0 for the high-pressure phase, because V0 cannot be constrained by the experiment. This information should be provided.
Response: Thanks for pointing out this and the standard uncertainties of fitted 11 parameters have been included in the revised Figure 2c of the revised manuscript.
On page 6:  Figure R4c). The different behavior may be due to the different sample preparation methods. We used the solventthermal method to synthesize the single crystals at a relatively low temperature of 200 °C. 12 The lattice constant of the single crystal is determined to be a=10.31 Å using single-crystal analysis at ambient condition ( Figure R5) which is in line with the reported structure of high-quality single-crystal Cu12Sb4S13. 14 While the study by Kitagawa used a powder sample which was prepared using solid-state reactions at relatively high temperature of 900 °C, which contains a small amount of CuSbS2 as a byproduct. 13 In addition, such a high synthetic temperature may produce some Cu vacancies in Cu12Sb4S13 compound, 15,16 together with the CuSbS2 impurity, they could be responsible for the difference.  . Indexing results of the single-crystal XRD for Cu12Sb4S13 at ambient condition. 13 7. It can be noticed that the transition pressure is suspiciously close to Neon crystallization pressure (see Figure 2d). Response: We thank the reviewer for this comment. As has been stated in the response to comment 4, we used different pressure transmitting media, neon, and silicon oil, for the XRD experiments. As shown in Figure R6a, the XRD results obtained using different pressure transmitting media show the consistent compressional behavior, indicating that neon doesn't affect the structural variations. In addition, the cavity in Cu12Sb4S13 is too small (3.54 Å) for the neon molecular (4.46 Å) to incorporate in ( Figure R6b). 17   My main concern based on the results is how valid is the claim of the realization of this hybrid amorphous/crystalline material. A structure with increased disorder does not necessarily mean that it is a glassy structure. For example, the cubic (rocksalt) crystalline structure of the chalcogenide phase-change memory material, Ge2Sb2Te5, is a highlydisordered crystalline structure. Such a structure, does not have any resemblance with an amorphous, glass-like structure. Another example are the grain boundaries, where two different crystalline structures, in a polycrystalline material, form a specific defective interface.
Response: We appreciate the reviewer's very positive comments and the insightful conclusion of our work. To address the reviewer's concern, we have conducted more experiments, added two new sets of experimental data including in situ X-ray absorption spectroscopy (XAS) and scanning transmission electron microscopy (STEM). These experimental evidence and the corresponding discussion have been added to support our 15 claim in the revised manuscript.
Here, we would like to emphasize the unique features of the nested order-disorder framework (NOF) which make it different from the cases of highly-disordered crystalline structure and grain boundaries. In brief, the reported NOF structure possesses three unique features, (1)   In the revised manuscript, the in situ XAS results and the corresponding discussion have been included. 16 On pages 7 and 8: " Furthermore, in situ high-pressure X-ray absorption spectra (XAS) were  On page S5 of the Supplementary Information: "X-ray absorption spectra measurement.
In situ high-pressure X-ray absorption spectra (XAS) of Cu K-edge were collected at BL05U On page S19: Figure S6. technological applications, including black TiO2 nanomaterials for photocatalysis, 5, 6 twodimensional electron gases at crystalline-amorphous oxide interfaces for transparent conductors, 7 metal-organic frameworks (MOFs) and their composites for catalysis. 8 From the local structure point of view, hybridization has been made at the mesoscopic scale, [9][10][11] such as paracrystalline silicon, 12 intermediate crystalline metallic glass, 13 and melted chains in high-pressure metals. 14-16 " On pages 2 and 3: " Due to variable coordination conditions and valence states, copper chalcogenides have large structural variability and exhibit an intrinsic chemical-bond hierarchy, which gives a high and anisotropic tunability. [18][19][20] Besides chemical tailoring, the degree of bonding hierarchy can be tuned by applying external stimuli, including temperature, pressure, and electric field. 17,18 Recently, temperature-induced hybrid state has been reported in Cu2Se where the Cu + sublattice becomes amorphous on warming and induced liquid-like flow. 19,21 Besides, the amorphous-to-crystal transition can be triggered by electric pulses in phase-change memory material Ge2Sb2Te5 with bonding energy hierarchy. 17,22 However, strong vibration of all atoms at high temperature or electric field leads to the whole structural instability and second-phase precipitation, 19 which limits the tunability and formation of crystalline-amorphous hybrid structures. 23 As a state variable, pressure provides an effective and clean approach to adjust the atomic interactions and thus alter the bonding configuration without changing chemical compositions. [24][25][26][27] Therefore, pressure processing enables the exploration and modulation of crystalline-amorphous hybrid structures which would collaboratively optimize the competing physical properties." 2. The authors use the terminology of a void, which is a specific term in amorphous materials to define certain space. Also, certain rules (e.g. Voronoi polyhedra, and others) are typically employed to calculate and characterize voids. The term is used rather loosely in the manuscript and it needs either justification or revision.
Response: Thanks for pointing out the inappropriate use of "void". It has been changed to "space" in the revised manuscript on Page 3. Response: We thank the reviewer for such a good suggestion. The external electric field can modify the atomic structures of crystalline and amorphous materials. A well-known example is the phase-change memory material Ge2Sb2Te5 (GST). 19,20 It changes from a 20 covalently bonded amorphous phase to a resonantly bonded metastable cubic crystalline phase under electric pulses. 20 The basic principle is to take advantage of the property contrast between the crystalline and amorphous states to encode information. 19 Recent report has demonstrated that distortions in GST crystals that have a bonding energy hierarchy trigger the destruction of the subsystem of weaker bonds and subsequent collapse of the long-range order, generating the amorphous phase. 18 Such a process is similar to the forming of amorphous innards in our case. The difference is that our case forms a crystalline-amorphous hybrid NOF structure instead of a highly-disordered structure. The hybrid NOF structure combines advantages from both crystalline and amorphous subunits and realizes the collaborative improvement of two competing properties (low thermal and high electrical conductivity). In the revised introduction, we have added the corresponding description about the external electric field and state why we chose pressure to exploit the crystalline-amorphous hybrid structures.
The corresponding discussion has been added on page 2 of the revised manuscript.
"Besides chemical tailoring, the degree of bonding hierarchy can be tuned by applying external stimuli, including temperature, pressure, and electric field. 17,18 Recently, temperature-induced hybrid state has been reported in Cu2Se where the Cu + sublattice becomes amorphous on warming and induced liquid-like flow. 19,21 Besides, the amorphous-to-crystal transition can be triggered by electric pulses in phase-change memory material Ge2Sb2Te5 with bonding energy hierarchy. 17,22 However, strong vibration of all atoms at high temperature or electric field leads to the whole structural instability and second-phase precipitation, which limits the tunability and formation of crystalline-amorphous hybrid structures. 23 As a state variable, pressure provides an effective and clean approach to adjust the atomic interactions and thus alter the bonding configuration without changing chemical compositions. [24][25][26][27] Therefore, pressure processing enables the exploration and modulation of crystalline-amorphous hybrid 21 structures which would collaboratively optimize the competing physical properties." 4. The NOF structure reported in Figure 1b is it from real data (trajectory/positions) or it is a skecth/graphic? It is not clear. If it corresponds to the simulation trajectory, from the MD simulations, then the argument is more valid. In contrast, if it is a skecth I am afraid it is not enough. It is also rather blurred.
Response: Thanks for the comment. We would like to note that it is a schematic illustration to show the features of the NOF structure. To address the reviewer's concern, we have further performed atomic-resolved scanning transmission electron microscopy (STEM) and extended the first-principles simulations. In the revised version, we modified the schematic illustration (Figure 1b). Compared to the previous graphic, it is more accurate to describe the disordered Cu2 atoms diffusing within the Cu1 crystalline framework rather than in the whole crystalline structure. Such behavior can be demonstrated by both the experimental STEM results and the first-principles molecular dynamic simulations. The detailed discussion can be seen as follows.
On page 4:  Response: We thank the reviewer for the suggestion. We agree that "more compressible" should be more accurate to describe the situation of the decreased bulk modulus under high pressures. The bulk modulus B0 fitted from the Birch-Murnaghan equation can quantitatively provide the compressibility of the solids. 22 Generally, materials become hard to compress due to a decrease of the interatomic spacing, which shows higher B0 after structural transition under pressure. However, Cu12Sb4S13 shows abnormally decreased B0 from 56.5(7) to 36.9(2) GPa before and after structural transition, indicating more compressible structure due to the movable Cu2 amorphous innards in NOF.
Corresponding change has been made in the revised manuscript.
On page 5: "Such an abnormal decrease of B0 indicates the more compressible structure under high pressures". On page S17: Figure S4. Valence electron density maps at ambient pressure and at 9.4 GPa. The balland-stick models with an isosurface value of ELF = 0.94 projects onto the (101) plane. Figure 4a what is the difference between the two atomistic models? The pressure is different but the structures look identical. This figure does not provide any useful information.

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Response: We thank the reviewer for this comment. Figure 4a shows the trajectory of Cu atoms at 0 and 9.4 GPa from molecular dynamic (MD) simulations which indicates the enhanced anharmonic motion of Cu2 atoms at high pressure. We agree with the reviewer that the difference is not obvious in the large super cell we used. In the revised manuscript, we have zoomed in the trajectory of typical Cu2 atoms, which shows the enhanced anharmonic motion of Cu2 atoms more clearly (Figure 5a). Furthermore, the mean square displacement (MSD) line profiles in the time domain were obtained from the MD trajectory (Figure 5b), which indicate the MSD value of Cu2 atoms surpassing the melting threshold. Figure 4a about the MD trajectory has been modified in the revised manuscript.
On page 12: Response: Thank you for the suggestion of introducing VDOS. We have calculated and plotted the VDOS at 300 K at 0 and 9.4 GPa, as shown in Figure S17. The calculation was performed after cell relaxation using NPT ensemble and extended simulation time (10 ps).
The low-lying modes (<100 cm -1 ) of VDOS are mainly attributed to Cu2 atoms, which signify weak bonding due to their low frequencies. 23 The other atoms contribute to the higher-energy modes (>100 cm -1 ) and shift towards higher frequencies with pressure increasing, suggesting more rigid bond formation under higher pressures. 23 Whereas, the low-lying modes corresponding to Cu2 atoms still stay at the low frequencies, which indicate the retaining weak bonding under high pressures. During compression, such bonding hierarchy triggers the destruction of the sublattice with Cu2 weak bonds but the rest crystalline framework can be well-identified, generating the hybrid NOF structures.
The discussion of VDOS has been added into the revised manuscript and the VDOS results have been added in the Supplementary Information (Figure S17).
On page 11: "The vibrational density of states (VDOS) of all atoms at 0 and 9.4 GPa are shown in Figure S17. The low-lying modes (<100 cm -1 ) are mainly attributed to Cu2 atoms, which signify weak bonding duo to their low frequencies. 28 The other atoms contribute to the higher-energy modes and shift towards higher energy with pressure increasing, which suggests more rigid bond formation under pressure. 28 Whereas, the low-lying modes corresponding to Cu2 atoms still stay at the low-frequency region, which retain be respectively noted that the total number of electrons of the supercell we used is 920, which is almost at the limit of our simulation power. According to the reviewer's suggestion, we further conducted one set of MD at 0 GPa, 300 K with a double-size simulation box (232 atoms, 1840 electrons, 5000 MD steps) and the results are consistent with the more power-friendly system ( Figure R7). Figure R7. MSD results at (a) 116 atoms system and (b) double-size 232 atoms system.
We agree with the reviewer that adding an NPT step is useful to converge pressure.
Along the trajectory, we now initialize simulation with 3 ps NVT simulation for heating, follow by 5 ps NPT to the target pressure, and eventually run 10 ps NVT simulation for equilibrium (previously was 5 ps). Data reduction is taken from the equilibrium run. As shown in Figure R8, the velocity autocorrelation function shows a fully converged system at 0 GPa and 300 K. We would like to note that the updated simulation results are consistent with the previous ones. 10. In Table S1, the reported lattice parameters correspond to the experimental data or to the relaxed DFT structures? A comparison is needed.
Response: Thanks for pointing this out. The reported lattice parameters in Table S1  GPa.
According to the reviewer's suggestion, electronic structure and DOS of 9.4 GPa have been included in the revision as Figures S15 and S16, respectively. The effective masses of the electron decrease up to 0.64 m0 at 9.4 GPa, which indicates enhanced carrier mobility. However, the part-disordered structural transition occurs at above 9.4 GPa. Thus, electron scattering enhances which plays a significant role in inhibiting charge transport.
On page S12: "The effective masses of the electron decrease upon compression (1.61 m0j`Yfd F0 from 0 to 9.4 GPa), which indicates enhanced carrier mobility ( Figure S15).
Because of the rising carrier mobility, the electrical conductivity increases up to 7 GPa. 37 However, due to the part-disordered structural transition, electron scattering enhances and brings the decrease of electrical conductivity above 9.4 GPa." On page S29: Figure S15. The calculated electronic structures of Cu12Sb4S13 at 0, 5.1, 7.2, and 9.4 GPa.
On page S30: Figure S16. The calculated density of states of Cu12Sb4S13 at 0, 5.1, 7.2, and 9.4 GPa. Table S2, the changes of the Bader charges from 0 to 9.4 GPa pressures are insignificant. One should expect the changes in the atomic structure to be reflected on the Bader ionic charges (difference between crystal/glass).

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Response: We would like to note that an obvious decrease in Bader charge from 0.40 at ambient pressure to 0.30 at 11.3 GPa of Cu2 atoms can be observed (Table S3). This change is more significant in comparison to other atoms ( Figure R9). Generally, owing to the more complex coordination and weaker covalence bonding, the amorphous state has a lower average Bader charge than the one in crystalline state. [24][25][26][27] The previous studies reported a 0.110.3e difference between the crystalline and amorphous states. 24   13. In Figure S13, the three atomistic structures look, again, identical. I cannot see any difference. The figures do not provide any useful information.
Response: We thank the reviewer for pointing this out. In the revised version, we have zoomed in the trajectory of typical Cu2 atoms to clearly show the enhanced anharmonic motion of Cu2 atoms. Figure S18 about MD trajectory has been modified in the revised Supplementary Information.
On page S33: Figure S18. The trajectory of Cu atoms at selected pressures and temperatures.
The Authors have addressed all questions, which were raised by the Reviewers.
By inspecting .cif files provided by the Authors I noticed that only the ADPs of Cu2 were refined. Furthermore, there are no standard deviations of refined coordinates of Sb1 and S atoms. This leads to the question of how were these coordinates obtained and why ADPs of Cu1, Sb1, S1 and S2 left unrefined?
Until a proper Rietveld refinement is performed, the Figure S2 can not be used for the discussion in the manuscript.
Reviewer #2 (Remarks to the Author): In the response the authors considered seriously all the comments made by the reviewers. They put some significant effort to accommodate all the requests and concerns raised by the reviewers and to provide sufficient explanations.
The revised Introduction provides more content regarding the research activities in the literature and the importance of the design of such hybrid ordered-disordered structures. Moreover, the authors present in a more lucid way their choice of applying pressure in this study as means of modifying the atomic structure.
I believe the new Fig. 3 is a strong addition in the manuscript. The authors performed two new experiments, using X-ray absorption spectroscopy and scanning-transmission electron microscopy, to investigate the atomic-scale structure of the system under study before and after the application of a high pressure. The experimental data and the respective analysis presented in this figure provide a strong indication about the formation of the NOF structure.
The revised schematic illustration presented in Fig. 1b seems to be more appropriate, while the behaviour described in the new drawing can also be reflected in the (new) experimental and simulation data.
The revised Fig. 2, which includes the ELF line profile (Fig. 2f) shows clearly the different behaviour under pressure and highlights the argument of the authors about the suppression of the lone-pair electrons. In that way, it is also more clear to the readers how the volume of the isosurface is reduced (i.e. weaker localization) after the application of the external high pressure (Fig. 2e).
In addition, the authors performed new atomistic (DFT) simulations. They included a constant pressure (NPT) molecular-dynamics run in their simulation protocol, while they also extended the collection-data trajectories from 5ps to 10ps. I appreciate their efforts and I believe the new DFT simulations have increased the quality of their study. It is important to highlight that the Mean Squared Displacement (MSD) is an averaged quantity, therefore the size of the modelled system (i.e. number of atoms) and the length of the molecular-dynamics trajectory (i.e. simulation time) do play a role in the calculated MSD (the comment about the total number of electrons the authors made in their response it is not really relevant to the MSD calculation). The presentation of the results in the new Fig. 5 (and in the relevant figures in the Supplementary Information) is more clear, while also I believe that the analyses from the extended trajectories highlight better the behaviour under pressure from the quantitative point of view (better statistics), and hence strengthens the arguments. Moreover, the authors presented a new calculation for the vibrational density of states relating to their discussion about the dynamical behaviour of the atoms in the structure before and after the application of high pressure.
Also, the authors extended their calculations, analyses and discussions about the electronic structure of the system for values of higher applied pressure, as well as the same for the Bader-charges analysis.
Finally, the authors provided some raw data as Supplementary material upon request of the Reviewer #1.
Overall, I was pleased to see that the new experiments and simulations performed by the authors, together with the revisions made in the original manuscript have enhanced the validity of the arguments presented in the study and increased its quality. Therefore, I would like to recommend the publication of this revised manuscript in Nature Communications.
However, I would like to suggest an alteration in the title of the paper. I still think that the term "amorphous" does not correspond to the right description for the formation of the distorted Cu2 atoms inside the crystalline framework. Hence, I think the word should be replaced in the title accordingly. Instead of "amorphous innards", it should be "distorted innards" or (maybe) "amorphous-like innards". I think that even the authors, based on their answers in the response document, should agree with such change.