JP5969866B2 - How to display atomic configuration - Google Patents

Description

  The present invention relates to a method for displaying an atomic arrangement in which a three-dimensional atomic arrangement in a crystal structure is converted into a circumferential atomic arrangement for display.

  Since crystalline solids have different characteristics such as surface energy depending on crystal planes, reactivity such as catalytic reaction differs depending on which crystal plane is exposed as a surface. Thus, for example, it is recalled that a crystalline solid is cut along a crystal plane having a characteristic capable of obtaining good catalytic activity, and the crystal plane is exposed to form a surface.

  The characteristics of the crystal plane can be determined by computational science. Therefore, it is considered that characteristics of various crystal planes are obtained by computational science, and an appropriate crystal plane to be exposed as a surface is determined based on the result.

  However, calculating the characteristics of all crystal planes in the crystalline solid one by one consumes a lot of time and labor, and is not efficient. Therefore, in practice, the calculation is minimized by selecting crystal face candidates having appropriate characteristics from a plurality of crystal faces in the crystalline solid and calculating the characteristics only for the selected crystal faces. It has been proposed.

For example, Non-Patent Document 1 describes that a crystal plane represented by a small Miller index called a low index plane is selected as a calculation target for a crystal plane of divanadium pentoxide (V ₂ O ₅ ). .

J. Mater.chem, 1996, 6 (4), 653-660, Dean C. Sayle, David H. Gay, Andrew L. Rohl, C. Richard A. Catlow, John H. Harding, Marc A. Perrin and Patrice Nortier

For example, in a composite metal oxide such as lithium iron phosphate (LiFePO ₄ ), even if the Miller index is the same, the surface is not uniquely determined, and the possibility of multiple surfaces with different atomic arrangement configurations is assumed. The In this case, these characteristics are also different.

  In addition, there is a possibility that a high index surface that has been recognized as not stable in the past and has not been studied so much may have a stable and useful characteristic among the multiple surfaces as described above. There is.

  As can be understood from this, it is not sufficient to calculate only a low index plane when calculating a crystal plane having appropriate characteristics for a crystalline solid having a complex crystal structure by computational science. That is, even if the high index surface has more appropriate characteristics than the low index surface, the calculator cannot recognize that because the high index surface is not subject to calculation. After all, this is because the high index plane is not selected as the crystal plane to be exposed.

  In this way, information that can determine whether or not a crystal face can be a candidate for a crystal face to be detected by roughly estimating what characteristics the crystal face has, in other words, the crystal face to be calculated With respect to obtaining information for selecting, a means for effectively selecting a crystal plane to be calculated for a crystalline solid having a complicated crystal structure has not yet been established.

  The present invention has been made to solve the above problems, and it is easy to grasp the degree of spatial density of atoms in the crystal structure, and based on this fact, the characteristics of the crystal plane are inferred. It is an object of the present invention to provide an atomic arrangement display method that is easy to perform.

In order to achieve the above object, the present invention provides a method for displaying an atomic arrangement in which a computer is used to convert a three-dimensional atomic arrangement in a unit cell into a circumferential atomic arrangement and display it on a display .
The computing means included in the computer obtains an atomic arrangement on a straight line by projecting the position vector of each atom in the unit cell to the direction of the normal vector of the crystal plane represented by the Miller index {lmn}, and Obtaining the projected length of the position vector by normalizing the projected length of the position vector by using the distance between the origin of the unit cell and the crystal plane, respectively;
A step of displaying, on the display, the atomic arrangement on the circumference obtained by arranging the atoms in the atomic arrangement on the straight line on the circumference of the circle based on the normalized projection length by the computing means; When,
It is characterized by having.

  In this atomic arrangement display method, first, the three-dimensional atomic arrangement of each atom in the crystal structure is changed to a one-dimensional atomic arrangement with respect to the direction of the normal vector of the crystal plane represented by the Miller index {lmn} (projection direction). That is, it is converted into a linear atomic arrangement. That is, the atom arrangement on a straight line indicates the positional relationship with respect to the projection direction of each atom in the three-dimensional atom arrangement.

  Then, the projection length, which is the distance from the starting point to the position of each atom in this atomic arrangement on the straight line, is used as the distance between the origin of the unit cell and the {lmn} plane, that is, the plane spacing of the {lmn} plane. Then, standardize each to obtain the standardized projection length. The normalized projection length thus obtained is a relative length based on the repeating unit in the atom arrangement on the straight line.

  Then, based on the obtained normalized projection length, the atomic arrangement on the straight line is converted into the atomic arrangement on the circumference and displayed. For example, by arranging the starting point of atomic arrangement on a straight line on the circumference and arranging the atoms on the circumference from the starting point on the circumference for each length according to the normalized projection length of each atom. The atomic arrangement on the circumference can be displayed.

  At this time, since the standardized projection length is based on the length of the repeating unit as described above, it is possible to easily associate one round of the circle with one repeating unit. That is, in the atomic arrangement on the circumference, atoms having the same value other than the integer part of the normalized projection length are arranged at the same position on the circumference. It can be displayed adjacent to each other.

  The atoms located at both ends of the atomic arrangement on a straight line are arranged adjacent to each other between adjacent unit lattices in a crystal structure in which unit lattices are continuous. For this reason, by converting the atomic arrangement on the straight line into the atomic arrangement on the circumference and displaying it, it becomes possible to grasp the atomic arrangement relationship between successive unit cells, that is, the atomic arrangement in the crystal structure.

  As described above, the three-dimensional atomic arrangement of the crystalline solid is converted into a circular atomic arrangement and displayed, so that the distance between the atoms (rough and dense) when the crystal structure is viewed from the direction parallel to the {lmn} plane. Can be reflected in the atomic spacing in the atomic arrangement on the circumference.

  Therefore, based on this arrangement of atoms on the circumference, it is possible to give a rough idea as to what kind of atoms in the crystalline solid can be cut to obtain a crystal plane having desired characteristics. That is, it becomes possible to efficiently and accurately select a crystal plane to be calculated (a crystal plane candidate having a desired characteristic). Therefore, for example, it is possible to actually calculate the characteristics only for the crystal planes detected as candidates, and determine whether or not to expose the surfaces as the result.

  In the step of displaying the atomic arrangement on the circumference, the radius R of the circle is a length corresponding to the distance, and an angle obtained by multiplying a value other than the integer part of the normalized projection length by 2π is θ, It is preferable to display the atomic arrangement on the circumference by arranging each atom in the arrangement of atoms on a straight line on position coordinates (X, Y) represented by X = R cos θ and Y = R sin θ.

  In this case, the radius R of the circle when the atoms are arranged on the circumference is set to a length corresponding to the distance between the origin of the unit cell and the {lmn} plane (plane spacing of the {lmn} plane). Thereby, since the plane spacing in the actual crystal structure is reflected on the circumference of the circle, the correspondence between the atomic spacing in the atomic arrangement on the circumference and the atomic spacing in the crystal structure becomes clearer. That is, it is possible to display the atomic arrangement on the circumference of the crystal plane that more clearly reflects the degree of spatial density of atoms in the crystal structure on the circumference.

  Further, the plane spacing of each of the plurality of crystal planes represented by different Miller indices is a relative length obtained with reference to a common unit cell. Therefore, when obtaining a plurality of atomic arrangements on the circumference with the normal vector directions of the plurality of crystal planes as projection directions, the radius R of the circle is made to correspond to the plane spacing of the respective crystal planes. Arrangements can be directly compared. That is, it is possible to easily compare the degree of density of atoms in a crystal structure when viewed from a direction parallel to each of a plurality of crystal planes.

  Furthermore, by arranging each atom in a linear atom arrangement on the position coordinates (X, Y) based on the radius R and angle θ of the circle, the three-dimensional atom arrangement can be easily made into an atomic arrangement on the circumference. Can be displayed.

  Here, by displaying a plurality of atomic arrangements on the circumference on the same XY coordinates, the arrangements of atoms on the circumference can be arranged and displayed in a concentric manner with the respective centers aligned. For this reason, it becomes possible to easily compare a plurality of circumferential atomic arrangements.

  What is necessary is just to make it implement the above calculation automatically, for example by a calculating means. Furthermore, based on the calculation result, the atomic arrangement on the circumference can be displayed on the display.

  In this case, it is preferable that different colors are displayed for each type of atom. This makes it easy to recognize what atoms are located at the coordinates even when different atoms have the same coordinates and are displayed overlapping each other.

  Moreover, it is preferable that the displayed diameter of each atom corresponds to the atomic radius or ionic radius of each atom (hereinafter collectively referred to as “atomic radius etc.”). That is, atoms with a large atomic radius or the like may be displayed as a large circle, and small atoms may be displayed as a small circle. This also facilitates recognizing what atoms are located at the coordinates when different atoms are displayed with the same coordinates and overlapping each other. Preferably, the atomic radius or the like is similar to the displayed circle diameter.

  According to the present invention, it is possible to easily grasp the degree of spatial density of atoms in the crystal structure by displaying the atomic arrangement on the circumference, and based on the display result, the characteristics of the crystal plane can be determined. Can be easily predicted.

The unit cell of the LiFePO ₄ is a schematic diagram showing a 3-dimensional atomic arrangement. 2 is a schematic diagram showing a linear atomic arrangement obtained by projecting the position vector of each atom in the direction of the normal vector of the (100) plane in the three-dimensional atomic arrangement of FIG. This is the atomic arrangement on the circumference obtained by arranging the atomic arrangement on the straight line in FIG. 2 on the circumference. FIG. 2 is a schematic diagram showing a linear atomic arrangement obtained by projecting the position vector of each atom in the direction of the normal vector of the (010) plane with respect to the three-dimensional atomic arrangement of FIG. 1. FIG. 5 is a display diagram showing a circumferential atomic arrangement obtained by arranging the linear atomic arrangement of FIG. 4 on the circumference together with the circumferential atomic arrangement of FIG. 3. FIG. 2 is a schematic diagram showing a linear atomic arrangement obtained by projecting the position vector of each atom in the direction of the normal vector of the (201) plane with respect to the three-dimensional atomic arrangement of FIG. 1. FIG. 7 is a display diagram showing a circumferential atomic arrangement obtained by arranging the linear atomic arrangement of FIG. 6 on the circumference together with the circumferential atomic arrangement of FIG. 3.

  Hereinafter, preferred embodiments of an atomic arrangement display method according to the present invention will be described in detail with reference to the accompanying drawings.

This atomic arrangement display method can be suitably applied to all crystalline solids having a crystal structure, but is particularly suitable for a crystalline solid having a relatively complicated crystal structure such as a composite metal oxide. Can be applied. For this reason, in this embodiment, an example will be described in which the three-dimensional atomic arrangement of each atom included in the crystal structure of lithium iron phosphate (LiFePO ₄ ) is converted into a circumferential atomic arrangement and displayed.

FIG. 1 shows a unit cell formed by unit cell vectors a, b, and c with a Li atom as the origin for a LiFePO ₄ crystal. That is, FIG. 1 schematically shows an arrangement (three-dimensional atom arrangement) 10 of each atom. In addition, about a, b, and c, the arrow which means a vector is abbreviate | omitted for convenience.

The space group of such a LiFePO ₄ crystal is Pnma, and the position vector r of each atom in the unit cell is expressed by the following formula (1) based on the atomic coordinates (x, y, z). .
r = xa + yb + zc (1)

First, the position vector r of each atom is projected in the direction (projection direction) of the normal vector of the crystal plane represented by the Miller index {lmn}. At this time, the projection length p of the position vector r is expressed by the following equation (2).

  However, it is g = a * (b * c) = b * (c * a) = c * (a * b). “·” And “×” represent inner product and outer product, respectively. Similarly, b × c, c × a, and a × b in Equation (2) are outer products.

  By this projection, the three-dimensional atomic arrangement of each atom in the unit cell can be converted into a one-dimensional atomic arrangement with respect to the projection direction, that is, for example, a linear atomic arrangement shown in FIG.

Next, this projection length p is normalized by the unit distance d between the origin in the unit cell and the crystal plane represented by the Miller index {lmn}. Here, the unit distance d can be rephrased as the crystal plane spacing represented by the Miller index {lmn}. In other words, the unit distance d corresponds to the length of the repeating unit of atoms in the atom arrangement on the straight line, and is represented by the formula (3).

From the expressions (2) and (3), the standardized projection length q can be obtained by the following expression (4).
q = lx + my + nz (4)

  The standardized projection length q is a relative length based on a repeating unit of atomic arrangement on a straight line.

  As described above, the normalized projection length q can be easily calculated using the atomic coordinates (x, y, z) of each atom in the unit cell and the Miller index (lmn).

  Next, based on the normalized projection length q, the atomic arrangement on the straight line is converted into the atomic arrangement on the circumference and displayed. That is, by arranging the starting point of the atomic arrangement on a straight line on the circumference and arranging each atom on the circumference from the starting point on the circumference for each length according to the normalized projection length, It is possible to display the atomic arrangement on the circumference corresponding to one round of and one repeating unit. For example, when the linear atomic arrangement 12 shown in FIG. 2 is converted, the circumferential atomic arrangement 14 shown in FIG. 3 is obtained.

  In this atomic arrangement on the circumference, the atoms at both ends of the atomic arrangement on a straight line are adjacent to each other, and the distance between the atoms in the atomic arrangement on the circumference is the distance between the adjacent unit lattices in the crystal structure. The interval is reflected. By displaying the atomic arrangement on the circumference in this way, it is possible to grasp the relation between the atomic arrangements of successive unit cells. That is, it is possible to grasp the atomic arrangement in the crystal structure.

  In order to convert the atomic arrangement on the straight line into the atomic arrangement on the circumference for display, it is preferable to perform the following steps.

First, the radius R of the circle in which each atom in the linear atom arrangement is arranged is set to a length corresponding to the unit distance d. Further, a value H other than the integer part of the normalized projection length q is obtained by the following equation (5).
H = (lx + my + nz) mod 1 (5)

Then, an angle θ corresponding to the central angle with respect to the arc length from the origin on the circumference to each atom is obtained from the obtained product of H and 2π. Using this angle θ and radius R (unit distance d), the position coordinates (X, Y) of each atom in the atomic arrangement on the circumference are obtained from the following equations (6) and (7).
X = R cos θ (6)
Y = Rsin θ (7)

  According to the position coordinates (X, Y), by arranging each atom in a straight line atom arrangement on the XY coordinate, the atom arrangement on the circumference in which the atoms in the crystal structure are arranged on the circumference of the circle with the radius R Can be displayed.

With respect to the atomic arrangement display method according to the present embodiment based on the above, the (100) plane, the (010) plane, and the (201) plane are given as specific crystal planes in the unit cell of LiFePO ₄ . With reference to FIG. 7, each step of displaying the atomic arrangement on the circumference with the normal vector direction of these crystal planes as the projection direction will be specifically described.

As shown in FIG. 1, the (100) plane is a plane orientation that maximizes the unit distance d (plane spacing) in the unit cell. First, the case where the normal vector direction of the (100) plane is the projection direction will be described with reference to FIGS. The unit distance d ₍₁₀₀₎ of the (100) plane is 10.13172 mm.

PHYSICAL REVIEW B 77, 064414-1~12 a table main atomic coordinates shown in 1 (x, y, z) of (2008), space group of the crystal of LiFePO ₄ is because it is Pnma, the LiFePO ₄ All atomic coordinates are as shown in Table 1 below.

表１中のＯ１、Ｏ２、Ｏ３は、それぞれ、同値関係にある酸素原子を示す。具体的には、結晶内対称操作による原子座標の組が不変となる集合（同値類）ごとに区分している。なお、Ｏ１とＯ２は多重度４の酸素原子であり、Ｏ３は多重度８の酸素原子である。ここで、Ｏ１とＯ２は、多重度は同一であるが、存在位置が互いに相違する。

O1, O2, and O3 in Table 1 each represent an oxygen atom having an equivalence relationship. Specifically, the set is divided into sets (equivalence classes) in which the set of atomic coordinates by in-crystal symmetry operation is invariant. O1 and O2 are oxygen atoms having a multiplicity of 4, and O3 is an oxygen atom having a multiplicity of 8. Here, O1 and O2 have the same multiplicity but have different positions.

  From the atomic coordinates (x, y, z) in Table 1 and the equation (1), the position vector r of each atom is obtained. By projecting this position vector r in the direction of the normal vector of the crystal plane represented by the Miller index (100), the linear atomic arrangement 12 shown in FIG. 2 can be obtained.

  Then, based on the values of the atomic coordinates (x, y, z) in Table 1 and the plane index (lmn), that is, (100), the normalized projection length q of each atom is obtained from the above equation (4). Ask for each. Further, a value H other than the integer part of the normalized projection length q is obtained from Expression (5).

By substituting the angle θ obtained by multiplying H by 2π and the value of the unit distance d ₍₁₀₀₎ as the radius R into the equation (6), the value of the X coordinate of each atom on the XY coordinates is obtained. Similarly, the value of the Y coordinate is obtained from equation (7). Table 2 shows the H, X coordinate value, and Y coordinate value calculated for each atom.

表２のＸ座標値及びＹ座標値に基づいて、ＸＹ座標上に単位格子中の各原子を配置することで、図３に示す円周上原子配置１４を表示することができる。すなわち、この円周上原子配置１４では、単位格子の原点とした原子１６がシンボルとしてＸ軸上に配置され、この原子１６を始点として、各原子が、直線上原子配置１２での原子間隔に対応する原子間隔で、単位距離ｄ_{（１００）}を半径とする円の周上に配置されている。

By arranging each atom in the unit cell on the XY coordinate based on the X coordinate value and the Y coordinate value in Table 2, the circumferential atom arrangement 14 shown in FIG. 3 can be displayed. That is, in this atomic arrangement 14 on the circumference, atoms 16 that are the origins of the unit cell are arranged on the X axis as symbols, and each atom has an atomic interval in the atomic arrangement 12 on the straight line, starting from this atom 16. They are arranged on the circumference of a circle having a unit distance d ₍₁₀₀₎ as a radius at a corresponding atomic interval.

  In addition, 100 attached | subjected to the vicinity of each atom is a label for specifying that the atomic arrangement 14 on the circumference is obtained by projecting in the direction of the normal vector of the (100) plane.

  In this way, the atomic arrangement 14 on the circumference is displayed based on the standardized projection length q. Therefore, one round of the circle in which each atom is arranged and the atomic arrangement in the projection direction of the three-dimensional atomic arrangement 10 are displayed. One repeating unit corresponds. Accordingly, the atoms 16 and atoms 18 located at both ends of the linear atom arrangement 12 are arranged adjacent to each other in the circumferential atom arrangement 14, and the three-dimensional atom arrangement 10 is continuous with each other. The distance between adjacent atoms between unit lattices is reflected. Therefore, by setting the atomic arrangement 12 on the straight line to the atomic arrangement 14 on the circumference, it is possible to grasp the relation of atomic arrangement between continuous unit lattices, that is, the atomic arrangement in the crystal structure.

  From the above, the distance between atoms (degree of density) when the crystal structure is viewed from a direction parallel to the (100) plane in the unit cell can be reflected in the atomic distance of the atomic arrangement 14 on the circumference. That is, it is possible to easily grasp the degree of spatial density of atoms in the crystal structure, thereby displaying the atomic arrangement on the circumference that makes it possible to easily predict the characteristics of the crystal plane.

Furthermore, by setting the radius R of the circle when the atoms are arranged on the circumference to be a unit distance d ₍₁₀₀₎ , the spacing between the (100) planes in the three-dimensional atom arrangement 10 on the circumference of the circle is reduced. Reflected. For this reason, the correspondence between the interval of each atom in the circumferential atom arrangement 14 and the interval of each atom in the three-dimensional atom arrangement 10 becomes clearer. That is, it is possible to display the atomic arrangement 14 on the circumference that more clearly reflects the degree of spatial density of the atoms in the crystal structure on the circumference.

  For example, the above calculation may be programmed and stored in a calculation means such as a hard disk drive. When the object name or chemical formula is input to the calculation means to indicate the target substance whose atomic arrangement on the circumference is displayed, the calculation means stores the atomic coordinates (x, y) of each atom of the unit cell. , Z) is accessed to retrieve the coordinate information.

  Further, when the Miller index is input to the calculation means, the calculation means performs the calculations of the above formulas (1) to (7) and displays the atomic arrangement on the circumference on the display.

  In this case, it is preferable that different colors are displayed for each type of atom. This makes it easy to recognize what atoms are located at the coordinates even when different atoms have the same coordinates and are displayed overlapping each other.

  Moreover, it is preferable that the size of the symbol corresponding to each arranged atom in the atoms on the circumference displayed on the display corresponds to the atomic radius or ion radius (such as atomic radius) of each atom. That is, atoms with a large atomic radius or the like may be displayed as a large circle, and small atoms may be displayed as a small circle. This also facilitates recognizing what atoms are located at the coordinates when different atoms are displayed with the same coordinates and overlapping each other. Preferably, the atomic radius or the like is similar to the displayed circle diameter.

  The atomic radius or ionic radius is known. Therefore, if the calculation means accesses the database storing the atomic radii when the substance name or chemical formula is inputted, and extracts the ionic radius value, the symbol size corresponding to each atom, for example, a circle The diameter in this case can easily correspond to the atomic radius of each atom.

  In FIG. 1 to FIG. 3, for convenience, different types of atoms are shown by different line types for each type of atoms.

Next, the case where the normal vector direction of the (010) plane is the projection direction (the direction of the unit cell vector b in FIG. 1) will be described with reference to FIGS. The unit distance d ₍₀₁₀₎ of the (010) plane is 6.0096 mm.

  Similarly to the (100) plane, the position vector r of each atom is projected in the projection direction for the (010) plane. In this case, the linear atomic arrangement 20 shown in FIG. 4 can be obtained. Then, from the above equations (4) to (7), the values of the X coordinate and Y coordinate of each atom on the normalized projection lengths q, H, and XY coordinates of each atom are obtained. Of course, this calculation can also be performed by the calculation means. Table 3 shows the calculated H, X coordinate values, and Y coordinate values.

表３のＸ座標値及びＹ座標値に基づいて、ＸＹ座標上に単位格子中の各原子を配置することで、図５に示す円周上原子配置２２を表示することができる。この円周上原子配置２２に対しても、（０１０）面の法線ベクトルの方向に射影して得られたものであることを明示するラベルを付している。

By arranging each atom in the unit cell on the XY coordinate based on the X coordinate value and the Y coordinate value in Table 3, the atomic arrangement 22 on the circumference shown in FIG. 5 can be displayed. This circumferential atomic arrangement 22 is also labeled to indicate that it is obtained by projection in the direction of the normal vector of the (010) plane.

By the way, the surface intervals (unit distances d ₍₁₀₀₎ and d ₍₀₁₀₎ ) of the (100) plane and the (010) plane are relative lengths obtained with reference to a common unit cell. For this reason, by setting the radius R of the circle in the atomic arrangements 14 and 22 on the circumference as unit distances d ₍₁₀₀₎ and d ₍₀₁₀₎ as described above, the circumferences of crystal planes represented by different Miller indices are obtained. It becomes possible to directly compare the upper atom arrangements 14 and 22.

Furthermore, as shown in FIG. 5, when the circumferential atomic arrangements 14 and 22 are displayed on the same XY coordinates, the atoms are arranged on the circumferences of circles that are concentric and have different radii. That is, since the unit distance d ₍₁₀₀₎ > d ₍₀₁₀₎ , the on-circumferential atom arrangement 22 is displayed with the center aligned inside the on-circumference atom arrangement 14.

  This makes it possible to easily compare the distances between the atoms in the atomic arrangements 14 and 22 on the circumference, and easily compare the degree of atomic density in the crystal structure between different crystal planes. It becomes possible to do.

Finally, the case where the normal vector direction of the (201) plane is the projection direction will be described with reference to FIGS. The unit distance d ₍₂₀₁₎ of the (201) plane is 4.6775 mm.

  For the (201) plane, similarly to the (100) plane, by projecting the position vector r of each atom in the projection direction, the linear atomic arrangement 24 shown in FIG. 6 can be obtained. Then, from the above equations (4) to (7), the values of the X coordinate and Y coordinate of each atom on the normalized projection lengths q, H, and XY coordinates of each atom are obtained. Of course, this calculation can also be performed by the calculation means. Table 4 shows the calculated H, X coordinate values, and Y coordinate values.

表４のＸ座標値及びＹ座標値に基づいて、ＸＹ座標上に単位格子中の各原子を配置することで、図７に示す円周上原子配置２６を表示することができる。この円周上原子配置２６に対しても、（２０１）面の法線ベクトルの方向に射影して得られたものであることを明示するラベルを付している。

By arranging each atom in the unit cell on the XY coordinate based on the X coordinate value and the Y coordinate value in Table 4, the atom arrangement 26 on the circumference shown in FIG. 7 can be displayed. This circumferential atomic arrangement 26 is also labeled so as to be obtained by projecting in the direction of the normal vector of the (201) plane.

  Similar to the atomic arrangement 22 on the circumference in FIG. 5, the atomic arrangement 26 on the circumference is displayed on the same XY coordinates as the atomic arrangement 14 on the circumference in FIG. 7. This makes it possible to easily compare the intervals between the respective atoms in the circumferential atomic arrangements 14, 22, and 26.

  When the crystal structure is viewed from a direction parallel to the (100) plane, the (010) plane, and the (201) plane from the atomic spacing of the circumferential atomic arrangements 14, 22, and 26 thus obtained, The degree of spatial density of atoms can be grasped. Therefore, based on these circumferential atomic arrangements 14, 22, and 26, it is possible to give a rough idea as to what kind of atoms in the crystalline solid can be cut to obtain a crystal plane having desired characteristics. it can.

  For example, in the circumferential atomic arrangement 22 shown in FIG. 5, H = 0.25, that is, the distance between a plurality of atoms 28 arranged at an angle θ = π / 2 and adjacent atoms, and H = 0.75, The distance between a plurality of atoms 30 arranged at an angle θ = 3π / 2 and adjacent atoms is wider than the distance between other atoms. For this reason, by cutting the crystalline solid so as to expose the atoms 28 or 30, crystal surfaces having a wide interval can be used as the surface.

  As described above, since the interaction is small in the crystal planes having a wide interval, the surface energy is also expected to be small. That is, when searching for a crystal plane having a small surface energy by computational science, a crystal plane that exposes the atoms 28 or 30 can be selected as a calculation target.

  Further, for example, when detecting a crystal plane capable of increasing the symmetry of the atomic arrangement in the crystal structure after cutting the crystalline solid, the crystal plane exposing both the atoms 28 and 30 or H = 0, It is determined that a crystal plane that exposes both the atom 32 arranged at the angle θ = 0 and the atom 34 arranged at H = 0.5, that is, the angle θ = π, should be selected as a calculation target.

  Further, as shown in FIGS. 5 and 7, it can be seen that the atomic spacing is smaller in the circumferential atomic arrangement 26 than in the circumferential atomic arrangement 14 and 22. That is, when the crystal structure is viewed from the direction parallel to the (201) plane as compared to the direction viewed from the direction parallel to the (100) plane and the (010) plane, atoms in the crystal structure are more space. Dense.

  Further, when detecting a crystal plane capable of increasing the symmetry of the atomic arrangement in the crystal structure after cutting the crystalline solid, the atom 36 arranged at H = 0, that is, the angle θ = 0, and H = 0 .5, that is, a crystal plane capable of exposing both atoms 38 arranged at an angle θ = π may be selected as a calculation target.

  The present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention.

  For example, it is not essential to label each atom in the circumferential atomic arrangements 14, 22, and 26, and may be omitted. Also, the position and number of labels to be attached may be set as appropriate and are not particularly limited.

  In the above-described embodiment, the circumferential atomic arrangements 22 and 26 are displayed concentrically with respect to the circumferential atomic arrangement 14, but the circumferential atomic arrangements 14, 22, and 26 are easy to compare with each other. For example, the circumferential atomic arrangements 14, 22, and 26 may be displayed adjacent to each other.

10 ... Three-dimensional atom arrangement 12, 20, 24 ... Straight line atom arrangement 14, 22, 26 ... Circumferential atom arrangement 16, 18, 28, 30, 32, 34, 36, 38 ... atoms

Claims (3)

A method for displaying an atomic arrangement in which a computer is used to convert a three-dimensional atomic arrangement in a unit cell into a circumferential atomic arrangement and display it on a display ,
The computing means included in the computer obtains an atomic arrangement on a straight line by projecting the position vector of each atom in the unit cell to the direction of the normal vector of the crystal plane represented by the Miller index {lmn}, and Obtaining the projected length of the position vector by normalizing the projected length of the position vector by using the distance between the origin of the unit cell and the crystal plane, respectively;
A step of displaying, on the display, the atomic arrangement on the circumference obtained by arranging the atoms in the atomic arrangement on the straight line on the circumference of the circle based on the normalized projection length by the computing means; When,
A method for displaying an atomic arrangement characterized by comprising: The display method according to claim 1,
In the step of displaying the atomic arrangement on the circumference, the radius R of the circle is a length corresponding to the distance, and an angle obtained by multiplying a value other than the integer part of the normalized projection length by 2π is θ, The atomic arrangement on the circumference is displayed by arranging each atom in the arrangement of atoms on a straight line on position coordinates (X, Y) represented by X = R cos θ and Y = R sin θ. Display method. The display method according to claim 2,
An arrangement of atoms on the circumference obtained from a crystal plane represented by an arbitrary Miller index {lmn} and an arrangement of atoms on a circumference obtained from a crystal plane represented by another arbitrary Miller index {lmn} Is displayed as a concentric circle.

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