Atomic Displacements Research Articles

Giant Modulation of Refractive Index from Picoscale Atomic Displacements.

It is shown that structural disorder-in the form of anisotropic, picoscale atomic displacements-modulates the refractive index tensor and results in the giant optical anisotropy observed in BaTiS3, a quasi-1D hexagonal chalcogenide. Single-crystal X-ray diffraction studies reveal the presence of antipolar displacements of Ti atoms within adjacent TiS6 chains along the c-axis, and threefold degenerate Ti displacements in the a-b plane. 47/49Ti solid-state NMR provides additional evidence for those Ti displacements in the form of a three-horned NMR lineshape resulting from a low symmetry local environment around Ti atoms. Scanning transmission electron microscopy is used to directly observe the globally disordered Ti a-b plane displacements and find them to be ordered locally over a few unit cells. First-principles calculations show that the Ti a-b plane displacements selectively reduce the refractive index along the ab-plane, while having minimal impact on the refractive index along the chain direction, thus resulting in a giant enhancement in the optical anisotropy. By showing a strong connection between structural disorder with picoscale displacements and the optical response in BaTiS3, this study opens a pathway for designing optical materials with high refractive index and functionalities such as large optical anisotropy and nonlinearity.

Atomic displacement threshold energies and defect generation in GaN, AlN, and AlGaN: A high-throughput molecular dynamics investigation

Gallium nitride, aluminum nitride, and their ternary alloys form an important class of wide-bandgap semiconductors employed in a variety of applications, including radiation-hard electronics. To better understand the effects of irradiation in these materials, molecular dynamics simulations were employed to determine the threshold recoil energies to permanently displace atoms from crystalline sites. Threshold displacement energies were calculated with the lattices at 0 K. Thermal effects are found to lower the threshold energies by ∼1 eV. The threshold energy knockout events observed result in Frenkel pair defects. The electronic structure and dynamics of these Frenkel pair defects are analyzed and the consequences for device operation are discussed.

Electrochemical Reduction of Perfluorooctanoic Acid (PFOA): An Experimental and Theoretical Approach.

Perfluorooctanoic acid (PFOA) is an artificial chemical of global concern due to its high environmental persistence and potential human health risk. Electrochemical methods are promising technologies for water treatment because they are efficient, cheap, and scalable. The electrochemical reduction of PFOA is one of the current methodologies. This process leads to defluorination of the carbon chain to hydrogenated products. Here, we describe a mechanistic study of the electrochemical reduction of PFOA in gold electrodes. By using linear sweep voltammetry (LSV), an E0' of -1.80 V vs Ag/AgCl was estimated. Using a scan rate diagnosis, we determined an electron-transfer coefficient (αexp) of 0.37, corresponding to a concerted mechanism. The strong adsorption of PFOA into the gold surface is confirmed by the Langmuir-like isotherm in the absence (KA = 1.89 × 1012 cm3 mol-1) and presence of a negative potential (KA = 3.94 × 107 cm3 mol-1, at -1.40 V vs Ag/AgCl). Based on Marcus-Hush's theory, calculations show a solvent reorganization energy (λ0) of 0.9 eV, suggesting a large electrostatic repulsion between the perfluorinated chain and water. The estimated free energy of the transition state of the electron transfer (ΔG‡ = 2.42 eV) suggests that it is thermodynamically the reaction-limiting step. 19F - 1H NMR, UV-vis, and mass spectrometry studies confirm the displacement of fluorine atoms by hydrogen. Density functional theory (DFT) calculations also support the concerted mechanism for the reductive defluorination of PFOA, in agreement with the experimental values.

Origin of discrete donor–acceptor pair transitions in 2D Ruddlesden–Popper perovskites

Two-dimensional (2D) van der Waals nanomaterials have attracted considerable attention for potential use in photonic and light–matter applications at the nanoscale. Thanks to their excitonic properties, 2D perovskites are also promising active materials to be included in devices working at room temperature. In this work, we study the presence of very narrow and spatially localized optical transitions in 2D lead halide perovskites by μ-photoluminescence and time-decay measurements. These discrete optical transitions are characterized by sub-millielectronvolt linewidths (≃120μeV) and long decay times (5–8 ns). X-ray photoemission and density-functional theory calculations have been employed to investigate the chemical origin of electronic states responsible of these transitions. The association of phenethylammonium with methylammonium cations into 2D Ruddlesden–Popper perovskites, (PEA)2(MA)n−1PbnI3n+1, particularly in phases with n≥2, has been identified as a mechanism of donor–acceptor pair (DAP) formation, corresponding to the displacement of lead atoms and their replacement by methylammonium. Ionized DAP recombination is identified as the most likely physical source of the observed discrete optical emission lines. The analysis of the experimental data with a simple model, which evaluates the Coulombic interaction between ionized acceptors and donors, returns a donor in Bohr radius of the order of ≃10 nm. The analysis of the spectral and electronic characteristics of these single donor–acceptor states in 2D perovskites is of particular importance both from the point of view of fundamental research, as well as to be able to link the emission of these states with new optoelectronic applications that require long-range optically controllable interactions.

An Investigation of the Effect of Wide Range Gamma Radiation from Nanoindentation of the SAC305 Solder Alloy

This study utilises nanoindentation testing to investigate the impact of varying gamma radiation doses on the micromechanical properties of Sn-Ag-Cu (SAC) alloy. Specifically, the focus is on evaluating changes in hardness, reduced modulus, and creep behaviour. The stencil-printed method and reflow soldering process were employed to apply the SAC solder paste and create solder joints on the surface of the printed circuit board. The soldered samples underwent exposure to gamma radiation at different doses, specifically 5, 50, 500, 5000, and 50000 Gy. The solder received in its original state was used as the control sample. Subsequently, the samples were subjected to a nanoindentation test in order to ascertain the correlation between load and depth, depth and dwell time, when exposed to radiation. The load-depth curve results indicate that there is a transition in the behaviour of solder joint materials from elastic to plastic deformation as the radiation dose increases. A finding has been made indicating that exposure to gamma radiation has the potential to induce a transition in the behaviour of SAC from an elastic state to a plastic state. The exposure to radiation doses has been found to induce changes in the atomic arrangement and structural properties of materials, leading to an increase in their hardness values. Nevertheless, it was observed that with increasing radiation doses up to 500 Gy, there was a noticeable decrease in the hardness value, which can be attributed to the occurrence of softening behaviour. Exposure to a high dose exceeding 5000 Gy leads to atomic displacement and transmutation products, subsequently resulting in plastic deformation. The stress exponent value signifies the occurrence of the deformation mechanism in solder material when exposed to gamma radiation. The study revealed that there was a shift in the deformation mechanism from grain boundary sliding to dislocation climb as the radiation dose increased from low to high levels.

Toward an Understanding of the Anisotropy in Hcp Zinc Metal: Total Scattering Structural Study Using Synchrotron-Based, Temperature-Dependent, X-Ray Pair Distribution Function Analysis

Abstract: Among hexagonal close packing (hcp) metals, zinc has a non-ideal hcp structure due to a significantly increased axial ratio c/a. We studied the behavior of the ratio of lattice constants c/a and the ratio of thermal displacement parameters (U_33 / U_11) in the temperature range of 100-300 K, using the X-ray total scattering atomic pair distribution function (PDF) analysis over different refinement r-ranges. The temperature-dependent PDF analysis confirmed that the crystal structure of zinc has significant static distortion along the c-direction. The measured value of atomic displacement parameters of zinc showed a notable anisotropy as expressed by the ratio U_33 / U_11 of ≈ 2.2 at 100 K. The lattice parameter ratio c/a was slightly reduced at low temperatures but remained unusually large. The extrapolated value of the ratio c/a reached 1.832 at 0 K. The PDF refinements using the crystallographic model revealed that there are some local structure features in zinc that are not captured by the crystallographic model. On the other hand, our local structure refinement indicated a presence of local bond distortion along the z-direction that averaged out over wider r-range refinements with a large U_33 value. Keywords: Hcp anisotropy, Zinc metal, Total scattering, X-ray scattering, Pair distribution function. PACs numbers: 61.46.Df, 61.10.-i, 78.66.Hf, 61.46.-w.

Three-Fold Coordination of Copper in Sulfides: A Blockade for Hole Carrier Delocalization but a Driving Force for Ultralow Thermal Conductivity.

Copper-rich sulfides are very promising for energy conversion applications due to their environmental compatibility, cost effectiveness, and earth abundance. Based on a comparative analysis of the structural and transport properties of Cu3BiS3 with those of tetrahedrite (Cu12Sb4S13) and other Cu-rich sulfides, we highlight the role of the cationic coordination types and networks on the electrical and thermal properties. By precession-assisted 3D electron diffraction analysis, we find very high anisotropic thermal vibration of copper attributed to its 3-fold coordination, with an anisotropic atomic displacement parameter up to 0.09 Å2. Density functional theory calculations reveal that these Cu atoms are weakly bonded and give rise to low-energy Einstein-like vibrational modes that strongly scatter heat-carrying acoustic phonons, leading to ultralow thermal conductivity. Importantly, we demonstrate that the 3-fold coordination of copper in Cu3BiS3 and in other copper-rich sulfides constituted of interconnected CuS3 networks causes a hole blockade. This phenomenon hinders the possibility of optimizing the carrier concentration and electronic properties through mixed valency Cu+/Cu2+, differently from tetrahedrite and most other copper-rich chalcogenides, where the main interconnected Cu-S network is built of CuS4 tetrahedra. The comparison with various copper-rich sulfides demonstrates that seeking for frameworks characterized by the coexistence of tetrahedral and 3-fold coordinated copper is very attractive for the discovery of efficient thermoelectric copper-rich sulfides. Considering that lattice vibrations and carrier concentration are key factors for engineering transport phenomena (electronic, phonon, ionic, etc.) in copper-rich chalcogenides for various types of applications, our findings improve the guidelines for the design of materials enabling sustainable energy solutions with wide-ranging applications.

Effect of water activity on the mechanical glass transition and dynamical transition of bacteria-solute systems

This study examined the mechanical glass transition and dynamical transition of bacteria (Cronobacter sakazakii)-solute (glycerol and glucose) systems. From the effect of water activity (aw) on the mechanical relaxation, the aw at which mechanical glass transition occurs at 25 °C (a typical ambient temperature) was determined as 0.225 for the glycerol-added sample and 0.540 for the glucose-added sample. These values were lower than that (0.667) reported previously for non-added sample. The effect of temperature on the mean square displacement of atoms within the samples was investigated by incoherent elastic neutron scattering. The aw at which dynamical transition occurs at 25 °C was determined as 0.156 for the glycerol-added sample and 0.475 for the glucose-added sample. These values were lower than that (0.675) reported previously for non-added sample. According to the Couchman-Karasz model, the Tg for the bacteria plasticized by the additive and that for the bulk additive were obtained.

Effect and Regulation Mechanism of Post-deposition Annealing on the Ferroelectric Properties of AlScN Thin Films.

Integrating ferroelectric AlScN with III-N semiconductors to enhance the performance and tunability of nitride devices requires high-quality AlScN films. This work focuses on the effect and regulation mechanism of post-annealing in pure N2 on the crystal quality and ferroelectric properties of AlScN films. It is found that the crystal quality improves with increasing annealing temperatures. Remarkably, the leakage current of AlScN films caused by grain boundaries could be reduced by four orders of magnitude after annealing at 400 °C. The crystal growth dynamics simulations and band structure calculations indicate that the energy supplied by the temperature facilitates the evolution of abnormally oriented grains to have a better c-axis orientation, resulting in the defect states at the Fermi-level disappearing, which is mainly the reason for the leakage current decrease. More interestingly, the reduction of leakage current leads to the previously leaking region exhibiting ferroelectric properties, which is of great significance to improve the ferroelectricity of AlScN and ensure the uniformity of devices. Furthermore, annealing enhances the tensile strain on the film, which flattens the energy landscape of ferroelectric switching and reduces the coercive field. However, the risk of incorporation of oxygen will also be increased if the annealing temperatures are higher than 400 °C, which will not only reduce the relative displacement of metal atoms and nitrogen atoms in AlScN but also enhance the ferroelectric depolarization field, leading to the remnant polarization decreasing dramatically. These discoveries facilitate a deeper understanding of the influencing mechanism on the ferroelectric properties of AlScN films and provide a direction for obtaining high-quality AlScN.

High‐Performance CaMg2Bi2‐Based Thermoelectric Materials Driven by Lattice Softening and Orbital Alignment via Cadmium Doping

AbstractZintl compounds such as n‐type Mg3(Sb,Bi)2 show promising thermoelectric applications benefiting from their high valley degeneracy and low lattice thermal conductivity. However, the heavier p‐type AMg2X2 (A = Ca, and Yb; X = Bi and Sb) Zintl counterparts even exhibit a higher κlat due to strong chemical bonding. Reducing κlat of AMg2X2 is an important route for improving thermoelectric performance. Herein, it is found that Cd doping at the Mg site in CaMg2Bi2 can weaken intralayer covalent bonds and soften acoustic phonons, as well as fill the optical phonon gap. These effects result in large atomic displacement, low phonon group velocity, and strong lattice vibration anharmonicity. Doping 10% Cd leads to a reduction of 56% in the κlat of CaMg2Bi2. Moreover, Cd doping promotes orbital alignment and thus increases the density‐of‐states effective mass and Seebeck coefficient. Eventually, in conjunction with carrier concentration optimization by Na doping and band structure engineering by Ba doping, a high ZT of ≈1.3 at 873 K in (Ca0.85Ba0.15)0.995Na0.005Mg1.85Cd0.15Bi2 sample is realized. This work highlights the significant role of manipulating chemical bonding in suppressing phonon propagation of semiconductors.

Dynamical refinement with multipolar electron scattering factors.

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

Static and dynamic disorder in ion-implanted silica glass

Structural disorder in solid-state materials has a direct impact on the complex of its physicochemical properties and functional characteristics of developed devices. The purpose of this work is to establish the influence of ion irradiation of SiO2 glass on static and dynamic disorder separately. Silica glasses implanted with carbon ions were studied using optical absorption spectroscopy and Raman spectroscopy. The temperature behavior of the fundamental absorption edge was considered in terms of the Urbach rule. The dose dependences of the root-mean-square atomic displacements caused by static and dynamic disorder were obtained. Analysis of Raman spectra confirmed the optical spectroscopy data and revealed a decrease in the medium-range order size along with topological changes in the SiO2 structure after ion implantation. The described step-by-step technique for quantitatively assessing the degree of static and dynamic disorder is universal and can be used to analyze other materials.

Capturing interference variations of atomic motion in vibrational modes by non-resonant Raman images

Non-resonant Raman imaging associated with vibrational modes provides an optical means to structure and function characterisation for a single molecule, where the interference between atomic motions in a vibrational mode plays an important role. Taking the [18]annulene as a proof-of-the-concept molecule, we present here a comprehensive study on the dependence of non-resonant Raman images on interference variations involving the phase and amplitude of atomic displacements in vibrational modes. Calculations demonstrate that constructive and destructive phase interferences contribute to the characteristic merging and repulsion of Raman patterns, respectively, which should be attributed to the same/opposite signs of Raman polarisability. In addition, the imaging characteristic by constructive and destructive interferences become more significant with the increase of plasmonic size. Moreover, Raman images are highly sensitive to the subtle variations of interference induced by molecular symmetry and element substitution, highlighting the importance of amplitude variations of interference in modes for Raman images to monitor molecular structure changes. Our findings propose the capability of Raman images toward capturing interference variations in modes, serving as good references for Raman imaging to characterise various molecules and their corresponding structure changes by analysing interference effects in vibrational modes.

Rotational phase transitions in antifluorite-type osmate and iridate compounds

We present temperature-dependent single-crystal diffraction results on seven antifluorite-type A2MeX6 compounds with Me = Os or Ir: K2OsCl6, A 2OsBr6 with A = K, Rb, Cs and NH4, and K2IrX 6 with X = Cl and Br. The structural transitions in this family arise from MeX 6 octahedron rotations that generate a rich variety of symmetries depending on the rotation axis and stacking schemes. In order to search for local distortions in the high-symmetry phase we perform refinements of anharmonic atomic displacement parameters with comprehensive data sets. Even at temperatures close to the onset of structural distortions, these refinements only yield a small improvement indicating only small anharmonic effects. The phase transitions in these antifluorites are essentially of displacive character. However, some harmonic displacement parameters are very large reflecting soft phonon modes with the softening covering large parts of the Brillouin zone. The occurrence of the rotational transitions in the antifluorite-type family can be remarkably well analyzed in terms of a tolerance factor of ionic radii.

Temperature-Dependent Structural and Elastic Properties of CdS, CdSe, and CdTe Compounds Studied by Statistical Moment Method

The statistical moment method has been applied to investigate the temperature effects on the lattice parameters and elastic properties of the zinc-blende CdX (X = S, Se, Te) compounds. The analytical expressions of thermal-induced atomic displacement, lattice constant, elastic moduli (Young’s modulus, bulk modulus and shear modulus) and elastic constants (including C11,C12 and C44) of the zinc-blende compounds have been derived. We have pointed out that the temperature effects on the elastic properties of CdS and CdSe are almost the same. And the elastic quantities of CdS and CdSe are more strongly dependent on temperature than those of CdTe semiconductor. This phenomenon is caused by the weaker coupling force of Cd-Te bonds compared to those of Cd-S and Cd-Se bonds. Furthermore, from the calculated Debye temperatures of CdX (X = S, Se, Te) compounds we conclude that CdS has higher phonon thermal conductivity and is therefore more thermally conductive among the three semiconductor compounds. The calculations of present work can be used as an appropriate reference for the experiments in future.

Qualitative ab initio theory of magnetic and atomic ordering in FeNi

Magnetic and atomic ordering in equiatomic FeNi alloy is studied by different techniques and methods based on density functional theory in order to clarify the main driving forces and their interplay behind these transitions and possibility of their accurate description within standard density functional theory calculations. The Curie temperature is obtained in Monte Carlo simulations using magnetic exchange interactions obtained by applying the magnetic force theorem within multiple scattering theory for different magnetic and atomic configurational states, including account for the thermal atomic displacements and exchange-correlation potential. The calculations show a very strong sensitivity of the results upon exchange-correlation potential, atomic order, and thermal atomic displacements. The calculated Curie temperature of a completely random alloy with the account of thermal lattice displacement is at least about 200 K below the known experimental data (780–800 K) depending on the above mentioned factors. The atomic order-disorder transition temperature is determined from effective chemical interactions, which apart from the chemical contribution (on the ideal fcc lattice) include contributions from lattice thermal vibrations and local lattice relaxations. The effective chemical interactions are strongly affected by the magnetic state, so the order-disorder transition temperature changes between 1000 and 140 K in the fully ordered ferromagnetic and paramagnetic states, respectively. For the reduced magnetization 0.7 (close to the experimental order-disorder transition temperature at 600 K), the order-disorder transition temperature varies between 550 and 700 K depending mostly on the exchange-correlation potential. The latter effect is the uncertainty in the choice of the exchange-correlation approximation in density functional theory calculations. Published by the American Physical Society 2024

Femtosecond Electron Diffraction Reveals Local Disorder and Local Anharmonicity in Thermoelectric SnSe.

In addition to long-range periodicity, local disorder, with local structures deviating from the average lattice structure, dominates the physical properties of phonons, electrons, and spin subsystems in crystalline functional materials. Experimentally characterizing the 3D atomic configuration of such a local disorder and correlating it with advanced functions remains challenging. Using a combination of femtosecond electron diffraction, structure factor calculations, and time-dependent density functional theory molecular dynamics simulations, the static local disorder and its local anharmonicity in thermoelectric SnSe are identified exclusively. The ultrafast structural dynamics reveal that the crystalline SnSe is composed of multiple locally correlated configurations dominated by the static off-symmetry displacements of Sn (≈0.4 Å) and such a set of locally correlated structures is termed local disorder. Moreover, the anharmonicity of this local disorder induces an ultrafast atomic displacement within 100 fs, indicating the signature of probable THz Einstein oscillators. The identified local disorder and local anharmonicity suggest a glass-like thermal transport channel, which updates the fundamental insight into the long-debated ultralow thermal conductivity of SnSe. The method of revealing the 3D local disorder and the locally correlated interactions by ultrafast structural dynamics will inspire broad interest in the construction of structure-property relationships in material science.

Micromechanical study of nano-cutting metal-ceramic WC/Cu by diamond tools

In this paper, the effect of the distribution of ceramic particles WC in Cu matrix on the nano-cutting behavior was investigated using molecular dynamics, and the cutting force, friction coefficient, machined surface quality, sub-surface damage depth, atomic displacement and internal defects were systematically studied, and the performance comparison at different cutting speeds was also investigated. It was found that due to the location of the WC phase, the overall removal of the material by the tool can be divided into the following three ways: When WC particles are above the cutting plane, there is less fluctuation in cutting forces and friction coefficients, and less impact on machined surface and subsurface damage; When the WC particles are below the cutting plane, the fluctuation of cutting force and friction coefficient is slow. Meanwhile, shallow craters are produced at the WC location; When the center of mass of WC particles is on the same level as the cutting plane, the cutting force and friction coefficient fluctuate drastically, the quality of the machined surface deteriorates sharply, and at the same time the hard particles pulled out by the tool remain on the machined surface. It was also found that the WC particles underwent different degrees of counterclockwise deflection in the three stages and caused a diversion of the atomic displacement in front of the tool. In addition, different degrees of dislocation plugging are formed between the WC and the tool at different positions, and the density of dislocation lines increases, which makes the substrate near the WC particles strengthened.

Optimizing Thermoelectric Properties through Compositional Engineering in Ag-Deficient AgSbTe2 Synthesized by Arc Melting.

Thermoelectric materials offer a promising avenue for energy management, directly converting heat into electrical energy. Among them, AgSbTe2 has gained significant attention and continues to be a subject of research at further improving its thermoelectric performance and expanding its practical applications. This study focuses on Ag-deficient Ag0.7Sb1.12Te2 and Ag0.7Sb1.12Te1.95Se0.05 materials, examining the impact of compositional engineering within the AgSbTe2 thermoelectric system. These materials have been rapidly synthesized using an arc-melting technique, resulting in the production of dense nanostructured pellets. Detailed analysis through scanning electron microscopy (SEM) reveals the presence of a layered nanostructure, which significantly influences the thermoelectric properties of these materials. Synchrotron X-ray diffraction reveals significant changes in the lattice parameters and atomic displacement parameters (ADPs) that suggest a weakening of bond order in the structure. The thermoelectric characterization highlights the enhanced power factor of Ag-deficient materials that, combined with the low glass-like thermal conductivity, results in a significant improvement in the figure of merit, achieving zT values of 1.25 in Ag0.7Sb1.12Te2 and 1.01 in Ag0.7Sb1.12Te1.95Se0.05 at 750 K.

Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and Efficient Cubic-Scaling Density Functional Perturbation Theory Calculations within Plane Waves.

Density functional perturbation theory (DFPT) is a crucial tool for accurately describing lattice dynamics. The adaptively compressed polarizability (ACP) method reduces the computational complexity of DFPT calculations from O(N4) to O(N3) by combining the interpolative separable density fitting (ISDF) algorithm. However, the conventional QR factorization with column pivoting (QRCP) algorithm, used for selecting the interpolation points in ISDF, not only incurs a high cubic-scaling computational cost, O(N3), but also leads to suboptimal convergence. This convergence issue is particularly pronounced when considering the complex interplay between the external potential and atomic displacement in ACP-based DFPT calculations. Here, we present a machine learning K-means clustering algorithm to select the interpolation points in ISDF, which offers a more efficient quadratic-scaling O(N2) alternative to the computationally intensive cubic-scaling O(N3) QRCP algorithm. We implement this efficient K-means-based ISDF algorithm to accelerate plane-wave DFPT calculations in KSSOLV, which is a MATLAB toolbox for performing Kohn-Sham density functional theory calculations within plane waves. We demonstrate that this K-means algorithm not only offers comparable accuracy to QRCP in ISDF but also achieves better convergence for ACP-based DFPT calculations. In particular, K-means can remarkably reduce the computational cost of selecting the interpolation points by nearly 2 orders of magnitude compared to QRCP in ISDF.