answer:| Modification | Explanation | | --- | --- | | Replaced "extrinsic" with "external" | "Extrinsic" can be seen as a more technical term that may not be easily understood by readers unfamiliar with the subject. | | Changed sentence structure | The original sentence was a bit convoluted and difficult to understand. By reorganizing the wording, the sentence is more clear and concise. | | Replaced "material" with "substrate" | In an academic context, it is more appropriate to use specific terminology when referring to a certain type of material. In this case, "substrate" is more specific and appropriate. | | Replaced "deformations or distortions" with "plastic deformation" | This is a more specific way of describing the type of deformation being referred to. | | Changed wording of "describes its resistance" to "refers to its ability" | This phrasing is more concise and clearer. | The mechanical stability of a substrate refers to its ability to withstand plastic deformation in the presence of external strain.

answer:| Modification | Explanation | | --- | --- | | Added an introductory phrase | The original sentence lacked context and did not clearly introduce the topic being discussed. By adding an introductory phrase, the sentence is more clear and provides necessary background. | | Changed "near their equilibrium position" to "from equilibrium" | This phrasing is more concise and clearer. | | Replaced "Thus" with "This means that" | "Thus" is less common in academic writing and can be seen as less formal. | | Added "of the crystal" after "structural" | Adding "of the crystal" is more specific and appropriate in an academic context. | | Reorganized sentence structure | The original sentence was a bit convoluted and difficult to understand. By reorganizing the wording, the sentence is more clear and concise. | | Changed wording of "whether the crystal structure is at a local potential minimum" to "if the crystal structure is in a state of local potential minimum" | This phrasing is more concise and clearer. | | Clarified "DFT" to "density functional theory" | DFT is a technical term that may not be understood by all readers, so spelling it out is necessary. | This means that the dynamic stability of the crystal reflects its structural tolerance against small atomic displacements from equilibrium. To determine if the crystal structure is in a state of local potential minimum, one can check if the phonon dispersions calculated through density functional theory have imaginary-frequency modes.

answer:| Modification | Explanation | | --- | --- | | Reorganized sentence structure | The original sentence was a bit convoluted and difficult to understand. By reorganizing the wording, the sentence is more clear and concise. | | Changed "poor convergence" to "inadequate convergence" | "Poor" is less specific than "inadequate", which better describes the issue at hand. | | Changed "supercell size" to "size of the supercell" | This phrasing is more clear and concise. | | Replaced "2D materials" with "two-dimensional materials" | In an academic context, it is more appropriate to use the full wording for clarity. | Imaginary frequencies that are observed during phonon dispersion calculations may be the result of either inadequate convergence due to limited cutoff energy, k-points, or size of the supercell, or may indicate lattice dynamical instability towards large wave undulations of two-dimensional materials.

answer:| Modification | Explanation | | --- | --- | | Reorganized sentence structure | The original sentence was a bit convoluted and difficult to understand. By reorganizing the wording, the sentence is more clear and concise. | | Replaced "about" with "approximately" | "Approximately" is more specific and appropriate in an academic context. | | Changed "energy eigenvalues" to "eigenenergies" | "Eigenenergies" is a more precise and widely used term in physics and engineering. | | Replaced "the other" with "the remaining" | "The remaining" is a more precise and specific way of referring to the energy eigenvalue that is not specified in the sentence. | | Clarified "EF" to "Fermi level" | "EF" is a technical term that may not be understood by all readers, so spelling it out is necessary. | To compute the average value of SOC splitting, we calculated the eigenenergies on a regular grid of approximately 7000 k-points, sampling the primitive cell in reciprocal space. To obtain the representative value around the Fermi level, we imposed a condition such that one of the eigenenergies is below and the remaining one is above the Fermi level.