Novel perovskite type ferrodielectric material search method

Abstract

To provide a search method for searching a perovskite type crystal structure ferrodielectric material which may become a ferrodielectric material using first principle calculation.SOLUTION: A novel perovskite type ferrodielectric search method comprises: a known material data calculation procedure for calculating a phonon dispersion curve which is obtained by executing phonon calculation based on first principle calculation by a cubic perovskite structure, for multiple known dielectric materials comprising a perovskite structure, the perovskite structure having one or more ferrodielectric materials; an unknown material data calculation procedure for calculating a phonon dispersion curve of an unknown dielectric material having a perovskite structure; a clustering procedure for analyzing the phonon dispersion curves calculated in the known material data calculation procedure and the unknown material data calculation procedure for grouping; and a determination procedure for determining that the known ferrodielectric material is a ferrodielectric material candidate, according to a distance from a position of the known ferrodielectric material to a position of the unknown dielectric material obtained in the clustering procedure.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a search method for searching for candidates for ferroelectric materials having a perovskite crystal structure that can become ferroelectric materials, using first-principles calculations and clustering. [Background technology]

[0002] Ferroelectric materials such as lead zirconate titanate (PZT) have been widely used in non-volatile ferroelectric memories, and filters and actuators in mobile phones and personal computers, but lead has been used in many of these materials. In recent years, due to environmental concerns, there has been active research and development into lead-free ferroelectric materials, but many of the high-performance ferroelectric materials have a perovskite-type crystal structure consisting of oxygen octahedra or a similar structure. On the other hand, there are many materials that do not become ferroelectric even though they have a perovskite crystal structure, and efficient methods for searching for such materials are needed. [Prior art documents] [Patent documents]

[0003] [Non-Patent Document 1] Moriwaki, "Application of first-principles calculations to ferroelectric / dielectric research", Japan Institute of Metals, Material, Vol. 59, No. 2 (2020), pp. 78-83 Summary of the Invention [Problem to be solved by the invention]

[0004] It is known that by calculating phonon dispersion using first-principles calculations for known dielectric materials, it is possible to quantitatively calculate the presence or absence of a soft mode that undergoes a phase transition to a ferroelectric, the crystal structure after the phase transition, the energy sequence, and spontaneous polarization, etc. (see Non-Patent Document 1). For example, when examining the phonon dispersion curve obtained by calculating the phonon dispersion, it is known that ferroelectrics have a soft mode in which the frequency is a negative imaginary value. However, even if a dielectric material has a soft mode in its phonon dispersion curve, it is not necessarily a ferroelectric. The inventors have discovered that by solving the problem that dielectric materials having a soft mode contain non-ferroelectric materials, phonon calculations based on the above-mentioned first-principles calculations can be used to search for new perovskite-type ferroelectrics, and as a result of examining the search method in detail, they have established a search method for new perovskite-type ferroelectrics that selects ferroelectric materials by phonon calculations. The present invention has been made in view of the above-mentioned circumstances, and has an object to provide a method for searching for a ferroelectric material having a perovskite crystal structure that can serve as a ferroelectric material. [Means for solving the problem]

[0005] The present invention is as follows. 1. A known material data calculation procedure for calculating phonon dispersion curves obtained by performing phonon calculations based on first-principles calculations on a cubic perovskite structure for a plurality of known dielectric materials having a perovskite structure including at least one ferroelectric material; An unknown material data calculation procedure for calculating a phonon dispersion curve obtained by performing a phonon calculation based on a first-principles calculation on a cubic perovskite structure for an unknown dielectric material having one or more perovskite structures; a clustering step of analyzing and grouping the phonon dispersion curve calculated in the known material data calculation step and the phonon dispersion curve calculated in the unknown material data calculation step; a determination step of determining that the unknown dielectric material is a ferroelectric material candidate when a distance from the position of the known ferroelectric material obtained by the clustering step to a position of the unknown dielectric material is within a predetermined distance; A method for searching for a new perovskite-type ferroelectric material, comprising: 2. The method for searching for new perovskite-type ferroelectrics according to 1. above, wherein the clustering step performs the grouping by hierarchical clustering. 3. The method for searching for new perovskite-type ferroelectrics according to 1 or 2 above, wherein the clustering step uses vector data of a plurality of points on each of the phonon dispersion curves for grouping. 4. The method for searching for new perovskite-type ferroelectrics according to 3. above, wherein the vector data consists of phonon frequencies at a plurality of points where the wave vectors on the phonon dispersion curve are equally spaced. 5. The method for searching for new perovskite-type ferroelectrics according to 4 above, wherein one code selected from the group consisting of Phonopy code and Phonon code is used for the phonon calculation. Effect of the Invention

[0006] The method for searching for perovskite-type crystal structure ferroelectric materials of the present invention includes a known material data calculation procedure, an unknown material data calculation procedure, a clustering procedure, and a judgment procedure. Therefore, it is possible to determine whether a material is a candidate for a ferroelectric material based only on the perovskite-type crystal structure without performing a soft mode search by phonon calculation for each phase that has undergone a structural phase transition, and it is possible to determine candidate ferroelectric materials with less calculation effort and time.

[0007] When the clustering procedure performs the grouping by hierarchical clustering, the results can be easily output in a format in which the inter-cluster distances between dielectric materials are highly interpretable, and candidate ferroelectric materials can be determined more accurately. When the clustering procedure uses vector data of a plurality of points on each of the phonon dispersion curves for grouping, the data can be made to exhibit the characteristics of the phonon dispersion curves required for clustering, and candidate ferroelectric materials can be determined more accurately. When the vector data consists of phonon frequencies at multiple points where the wave vectors on the phonon dispersion curve are equally spaced, the characteristics of the phonon dispersion curve are more easily expressed with a smaller amount of data, making it possible to more accurately determine candidate ferroelectric materials. When one code selected from the group consisting of Phonopy code and Phonon code is used for the phonon calculation, the phonon state can be grasped with the accuracy of first-principles calculation, and candidates for ferroelectric materials can be determined. [Brief description of the drawings]

[0008] The invention will be further explained by the following detailed description, giving non-limiting examples of exemplary embodiments according to the invention, with reference to the mentioned drawings, in which: [Figure 1] FIG. 1 is a tree diagram showing the results of clustering 64 types of cubic perovskite crystals. [Diagram 2] This is an enlarged view of the tree diagram of the 31 types of cubic perovskite crystals shown on the left side of FIG. [Diagram 3] This is an enlarged view of the tree diagram of the 33 types of cubic perovskite crystals shown on the right side of FIG. [Figure 4] This is a phonon dispersion curve diagram for CaZrO3 in a cubic perovskite structure. [Diagram 5] This is a phonon dispersion curve diagram for LaAlO3 in a cubic perovskite structure. [Figure 6] This is a phonon dispersion curve diagram for NaTaO3 in a cubic perovskite structure. [Figure 7] This is a phonon dispersion curve diagram for KTaO3 in a cubic perovskite structure. [Figure 8] This is a phonon dispersion curve diagram for BaTiO3 in a cubic perovskite structure. [Figure 9] This is a phonon dispersion curve diagram for AgNbO3 in a cubic perovskite structure. [Figure 10] FIG. 13 is a diagram showing a portion of vector data for BaTiO3. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] The present invention will now be described in detail with reference to the accompanying drawings. The matters shown herein are illustrative and are intended to exemplify the embodiments of the present invention, and are described for the purpose of providing what is believed to be the most effective and easily understandable explanation of the principles and conceptual features of the present invention. In this respect, it is not intended to show structural details of the present invention beyond the extent necessary for a fundamental understanding of the present invention, and the description in conjunction with the drawings will make it clear to those skilled in the art how some forms of the present invention can be actually embodied.

[0010] By calculating the phonon dispersion for known dielectric materials using first-principles calculations, it is possible to quantitatively calculate the presence or absence of a soft mode that undergoes a phase transition to a ferroelectric, the crystal structure after the phase transition, the energy sequence, and spontaneous polarization, etc., and therefore it can be inferred that by calculating the phonon dispersion for unknown dielectric materials, it is possible to determine the presence or absence of a low-temperature phase in which spontaneous dielectric polarization occurs, and to determine whether or not the material is a ferroelectric. However, to determine whether a material is a ferroelectric, it is necessary to confirm the crystal structure after the phase transition and whether spontaneous dielectric polarization occurs, and therefore it is necessary to calculate whether a soft mode exists or not and whether spontaneous polarization occurs for the phase after the phase transition until the phase where spontaneous dielectric polarization occurs, which requires a large amount of calculation and time. Furthermore, finding a ferroelectric material from a large number of unknown dielectric materials requires a huge amount of calculation and time, making it difficult to implement.

[0011] The inventors therefore speculated that an unknown ferroelectric material, whose phonon dispersion curve is similar to the phonon dispersion curve in the cubic perovskite structure of a known ferroelectric material, can undergo a phase transition similar to that of the known ferroelectric material and reach a phase in which spontaneous dielectric polarization occurs, and that non-ferroelectric materials in which the phonon dispersion curve of the cubic perovskite structure has a soft mode can be excluded from the candidates. They then discovered that instead of finding ferroelectrics by calculating the phonon dispersion of each phase for all unknown dielectric materials, it is possible to search for candidate ferroelectric materials in a shorter time by using clustering, a type of machine learning, to determine the similarity of the phonon dispersion curves in the cubic perovskite structures of unknown and known dielectric materials. They also discovered a method to convert the phonon dispersion curves of known and unknown ferroelectric materials, which are necessary for clustering, into data necessary for machine learning.

[0012] The novel perovskite ferroelectric material searching method based on the above-mentioned discoveries is characterized by comprising a known material data calculation step, an unknown material data calculation step, a clustering step, and a judgment step.

[0013] 1. Procedure for calculating data for known materials The known material data calculation procedure is a procedure for calculating phonon dispersion curves obtained by performing phonon calculations based on first-principles calculations on a cubic perovskite structure for a plurality of known dielectric materials having a perovskite structure including at least one ferroelectric material. The known dielectric material may be any known compound having a cubic perovskite structure, and may be, for example, a dielectric material having a perovskite structure included in the International Crystal Structure Database, such as BiScO3, CaZrO3, MgTiO3, TmCrO3, YCrO3, LaScO3, BaSiO3, NdAlO3, PrAlO3, LaAlO3, NaTaO3, SrSiO3, BaSnO3, SrVO3, BaZrO3, KTaO3, BaTiO3, KNbO3, PbTiO3, NaVO3, AgNbO3, NaNbO3, CeCrO3, LiUO3, RbUO3, NdVO3, LaCoO3, and SrCrO3.

[0014] In order to improve the search accuracy, it is preferable that the known dielectric materials include a uniform variety of dielectric materials with different ferroelectric properties. For this reason, it is necessary to include at least one ferroelectric material and at least one paraelectric material. It is also possible to include pyroelectric materials excluding ferroelectric materials and piezoelectric materials excluding ferroelectric materials and pyroelectric materials. The number of known dielectric materials is appropriately set depending on the required search accuracy, but can be set to, for example, 50 or more (more specifically, 60 or more).

[0015] Known ferroelectric materials are known compounds with a perovskite structure and in which spontaneous dielectric polarization occurs in the low temperature phase. Examples of such materials include BaTiO3, (Ba,Sr)TiO3, PbTiO3, Pb(Zr,Ti)O3, (Pb,La)(Zr,Ti)O3, LiNbO3K(Ta,Nb)O3, and Pb(Mg 1 / 3 Nb 2 / 3 )O3 can be mentioned.

[0016] The calculation method of the phonon dispersion curve by the phonon calculation based on the first-principles calculation can be performed by a known method. For example, as the first-principles calculation, a pseudopotential method using a plane wave as a basis function and a projector augmented wave (PAW) method based on density functional theory can be used. In addition, as a specific code for calculating the phonon dispersion curve, the vasp code, castep code, quantum espresso code, pwscf code, PHASE code, STATE-SENRI code, QMAS code, ABINIT code, etc. can be used. The phonon calculation method may be the frozen phonon method, etc. Furthermore, the Phonopy code or the Phonon code may be used as a specific code for performing the phonon calculation. Since the phonon dispersion curves of these calculation methods change depending on the material system, calculation conditions such as the type of functional and +U correction to the 3d electron system are set appropriately. For example, the general gradient approximation (GGA-PBA sol) can be used as the functional. This is because the general gradient approximation is suitable for solid materials.

[0017] In first-principles calculations, the cutoff energy can be set to 400 eV or more. The cutoff energy is set to 400 eV or more in order to shorten the calculation time while ensuring sufficient calculation accuracy (energy, force, structure). In addition, the k-point density is set to 0.5 / (10 -10 m) or less. This is because sufficient calculation accuracy (energy, force, structure) cannot be ensured with a k-point density exceeding this limit. Furthermore, the force applied to atoms at the end of the structure optimization is set to 0.1 eV / (10 -10 m) or less, because if this is exceeded, sufficient calculation accuracy (energy, force, structure) cannot be ensured.

[0018] The phonon dispersion curve obtained by the known material data calculation procedure is the phonon dispersion curve of a cubic perovskite structure, and 15 branches are obtained by performing phonon calculations based on first-principles calculations on known dielectric materials. In addition, the calculated phonon dispersion curve is a curve that represents the phonon vibration frequency (frequency) for wave vectors from R to g(Γ) in all branches.

[0019] 2. Procedure for calculating unknown material data The unknown material data calculation procedure is a procedure for calculating a phonon dispersion curve obtained by performing a phonon calculation based on first-principles calculation on a cubic perovskite structure for an unknown dielectric material having one or more perovskite structures. The unknown dielectric material is a hypothetical perovskite structure compound (e.g., CsTaO3, SnTiO3, InTaO3, KPaO3, AgPaO3, SmGaO3, YbGeO3, DyInO3, ErGaO3, and HgHfO3) that is not known to be a ferroelectric material. The means for calculating the phonon dispersion curve of an unknown dielectric material is the same as the means for calculating the phonon dispersion curve of a known dielectric material except for the calculation target, so the explanation will be omitted. In addition, the means for calculating the phonon dispersion curve of an unknown dielectric material may be the same as the means for calculating the phonon dispersion curve of a known dielectric material.

[0020] 3. Clustering Procedure The clustering step is a means for analyzing and grouping the phonon dispersion curve calculated in the known material data calculation step and the phonon dispersion curve calculated in the unknown material data calculation step. The grouping method is clustering, which is a type of machine learning, and known hierarchical or non-hierarchical clustering can be used. Among these, hierarchical clustering is preferable because it can easily output results in a format in which the distance between clusters of dielectric materials is more easily interpretable than non-hierarchical clustering, and it can more accurately determine candidates for ferroelectric materials.

[0021] The specific method of hierarchical clustering is not particularly limited, and agglomerative hierarchical clustering such as Ward's method (minimum variance method), the centroid method, the shortest (longest) distance method, and the group average method can be used, or variance hierarchical clustering can be used. Of these, Ward's method is a good example. There is no particular limitation on the specific method of non-hierarchical clustering, and examples thereof include the k-means method, the k-means++ method, the x-means method, and a mixed normal distribution method.

[0022] The data used for clustering may be any data that represents the characteristics of the phonon dispersion curve obtained by the analysis of the phonon dispersion curve, and the form of the data is not particularly limited. For example, a plurality of points on each curve (each branch) of the phonon dispersion curve may be vector data. More specifically, the angular frequency (frequency) of the phonon at each point on each curve (each branch) where the wave number vector is equally spaced may be vector data (see, for example, FIG. 10). The data used for clustering is not limited to the angular frequency (frequency) of the phonons, but may be, for example, the slope of a curve corresponding to a wave vector at a fixed interval. Furthermore, the phonon dispersion curve may be visualized and the brightness of each pixel may be used as data. The clusters typically contain one dielectric material per cluster.

[0023] 4. Judgment Procedure The judgment procedure is a procedure for judging that the unknown dielectric material is a candidate ferroelectric material when the distance from the position of the known ferroelectric material obtained by the clustering procedure to the position of the unknown dielectric material is within a predetermined distance. The position represents the position of the cluster of each of the dielectric materials when the clustering is performed, and the distance is the distance from the cluster of the ferroelectric material to the cluster of the unknown dielectric material when the clustering is performed. The distance between the clusters can be, for example, the distance when performing a hierarchical cluster analysis. The "predetermined" in the predetermined distance can be set appropriately. For example, the distance where there is no noise, which is a cluster containing dielectrics other than ferroelectrics, can be set as the predetermined distance. The predetermined distance can also be defined by the number and / or ratio of the noise. For example, the distance where the number of noises is 2 or less and / or the ratio of noises is 30% or less can be obtained from the result of clustering. By shortening the distance, noise that is dielectrics other than ferroelectrics is reduced, and the effect of the novel perovskite-type ferroelectric search method that can determine ferroelectric material candidates in terms of calculation amount and time is enhanced. On the other hand, since there is a risk of candidates being overlooked when the distance is shortened, the predetermined distance can be determined taking into consideration the calculation amount and time required to verify ferroelectric material candidates.

[0024] In addition, when there are a plurality of known ferroelectric materials, if the ferroelectric material closest to the unknown dielectric material is within the specified distance, the unknown dielectric material can be determined to be a candidate ferroelectric material. Furthermore, when there are a plurality of unknown ferroelectric materials, the distances to all of the known ferroelectric materials are obtained for each unknown ferroelectric material, and each is determined to be a candidate for the ferroelectric material.

[0025] Furthermore, the predetermined distance can be set by a method other than the distance between clusters. For example, the distance can be set so that the clusters of the ferroelectric material and the unknown dielectric material are adjacent to each other, without any clusters of a known non-ferroelectric dielectric material in between. Also, the distance can be set so that an appropriately set number of clusters of a known non-ferroelectric dielectric material, such as one, is included between the clusters of the ferroelectric material and the unknown dielectric material. Furthermore, the distance can be set so that the clusters are close to a group of multiple known dielectric materials (known dielectric materials that are close to each other).

[0026] 5. Working Example In order to verify whether this new method for searching for perovskite-type ferroelectrics is effective, a search was conducted using this new method for searching for perovskite-type ferroelectrics by treating known ferroelectric materials as unknown dielectric materials and carrying out the following steps (1) to (5) in sequence.

[0027] (1) As a procedure for calculating data on known materials, a total of 64 perovskite-type compounds, including the ferroelectric BaTiO3, KNbO3, PbTiO3, and SrTiO3, were listed as known dielectric materials, as shown in Figures 1 to 3. These dielectric materials are compounds registered in the International Crystal Structure Database, and their dielectric constants and crystal structures are known. In addition, BaTiO3, a known ferroelectric material, was excluded from the known dielectric materials as an unknown dielectric material.

[0028] (2) As a procedure for calculating data for known materials, the phonon dispersion curves of the cubic perovskite structure were calculated for the 63 known dielectric materials. The VASP code using the PAW method was used for the first-principles calculations. In addition, the general gradient approximation (GGA-PBA sol) optimized for solid-state materials was used for the exchange-correlation functional. The Phonon code using the frozen phonon method was used for the phonon calculations. As examples of the obtained phonon dispersion curves, the phonon dispersion curves of CaZrO3 (Figure 4), LaAlO3 (Figure 5), NaTaO3 (Figure 6), KTaO3 (Figure 7), and AgNbO3 (Figure 8) are shown below. (3) As a procedure for calculating unknown material data, the phonon dispersion curve of the cubic perovskite structure of BaTiO3 was calculated. The calculation method of the phonon dispersion curve was the same as that in (2) above.

[0029] (4) As a clustering procedure, vector data of each phonon dispersion curve calculated by the known material data calculation procedure and the unknown material data calculation procedure was prepared, and clustering was performed by Ward's method using Euclidean distance as the distance function. The results of the clustering are shown in tree diagrams in Figures 1 to 3. The vector data used for clustering was the angular frequency, which is the y-axis value of the phonon dispersion curve. In detail, as shown in Fig. 10, 101 points were obtained in the range of wave vector R to g(Γ) in each branch using equal wave vectors, and the frequency values ​​were used as vector data. Therefore, in this embodiment, the frequency values ​​of 101 points x 15 branches = 1515 points are used as vector data for one dielectric material.

[0030] (5) As a judgment procedure, the distance between clusters of BaTiO3, which is treated as an unknown dielectric material, was compared with that of other ferroelectric materials KNbO3, PbTiO3, and SrTiO3. If the distance between clusters shown in Figures 1 and 3 was within 13, it was determined to be a candidate for a ferroelectric material. As a result, BaTiO3 was determined to be a candidate for a ferroelectric material because the inter-cluster distance with KNbO3 was 4, and the inter-cluster distance with PbTiO3 and SrTiO3 was 7. The reason why the Euclidean distance is set to 13 or less (more preferably 10 or less, and particularly preferably 4 or less) is that, if the distance is within 13, noise of dielectrics other than ferroelectrics is reduced, and the effect of the novel perovskite-type ferroelectric searching method, that is, the ability to determine ferroelectric material candidates in terms of the amount of calculation and time, is enhanced. In addition, BaTiO3, KNbO3, PbTiO3, and SrTiO3, which show ferroelectric phase transitions, are classified as being close in distance (within 13), and it can be seen that the characteristics of their phonon dispersion curves are similar. In contrast, BaZrO3 and KTaO3, which have no soft mode in their cubic perovskite structure and do not show a ferroelectric phase transition, are farther away (distance 15) and therefore are excluded from the list of ferroelectric material candidates. This means that there is no need to separately confirm the presence or absence of these low-temperature phases, and it can be seen that the reduction in calculation amount and time, which is an effect of this new perovskite-type ferroelectric search method, is effective.

[0031] The present invention is not limited to the above-described embodiment, but may be modified in various ways within the scope of the present invention depending on the purpose and application. [Industrial Applicability]

[0032] The search method of the present invention makes it possible to determine candidates for unknown ferroelectric materials with less computational effort and time.

Claims

1. A known material data calculation procedure for calculating phonon dispersion curves obtained by performing phonon calculations based on first-principles calculations on a cubic perovskite structure for a plurality of known dielectric materials having a perovskite structure including at least one ferroelectric material; An unknown material data calculation procedure for calculating a phonon dispersion curve obtained by performing a phonon calculation based on a first-principles calculation on a cubic perovskite structure for an unknown dielectric material having one or more perovskite structures; a clustering step of analyzing and grouping the phonon dispersion curve calculated in the known material data calculation step and the phonon dispersion curve calculated in the unknown material data calculation step; a determination step of determining that the unknown dielectric material is a candidate ferroelectric material when a distance from the position of the known ferroelectric material obtained by the clustering step to a position of the unknown dielectric material is within a predetermined distance; A method for searching for a new perovskite-type ferroelectric material, comprising:

2. 2. The method for searching for novel perovskite-type ferroelectrics according to claim 1, wherein the clustering step performs the grouping by hierarchical clustering.

3. 3. The method for searching for novel perovskite-type ferroelectrics according to claim 1, wherein the clustering step uses vector data of a plurality of points on each of the phonon dispersion curves for grouping.

4. 4. The method for searching for novel perovskite-type ferroelectrics according to claim 3, wherein the vector data is made up of phonon frequencies at a plurality of points on the phonon dispersion curve where the wave vectors are equally spaced.

5. The method for searching for new perovskite-type ferroelectrics according to claim 4, wherein one code selected from the group consisting of Phonopy code and Phonon code is used for the phonon calculation.

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