A real-space moiré fringe inversion method

Abstract

The present invention proposes a real-space moiré fringing inversion method that utilizes a binary image of the moiré region, along with the specimen grating planes and reference grating directions obtained after analyzing the moiré region, to invert the moiré region. This method verifies the moiré region parameters and further calculates other parameters of the moiré region, extending the TEM moiré inversion method. While validating the moiré region parameters obtained by the TEM moiré inversion method, the present invention also calculates other parameters present in the moiré region, significantly enriching full-field measurement methods for moiré regions. In the field of photomechanics, this method further develops parameter calculation methods for newly generated small grains.

Description

Technical Field

[0001] The present invention relates to an inversion method for real-space moiré fringes, and in particular to an inversion method for obtaining a sample lattice structure by utilizing a binary image of a moiré region and analyzing the image, and belongs to the field of photomechanics. Background Art

[0002] Moire patterns are a common phenomenon in TEM or STEM experiments. Moire regions are often considered to be formed by the superposition of two distinct lattice layers along the observation direction, differing in lattice constant, lattice angle, or atomic layer orientation relative to the observation direction. The formation of moire patterns can reveal smaller transformation processes within the crystal. Since 3D full-field measurements of moire patterns require rotating the crystal zone axis to observe images of the same location in different directions, 3D full-field measurements of moire patterns are relatively rare in existing research, and corresponding methods are also rare. To date, only TEM moire inversion can invert the interplanar spacing of newly generated small grains in the moire region, but this method lacks a closed-loop verification of the inversion parameters of the moire region. Therefore, a real-space moire pattern inversion method has been developed. This method, combined with the TEM moire inversion method without rotating the crystal zone axis, verifies the data obtained by the TEM moire inversion method, thus forming a closed-loop calculation and deriving other parameters of the moire region. Summary of the Invention

[0003] The purpose of the present invention is to propose a real-space moiré fringes inversion method, which brings the existing binary image of the moiré area and the data obtained in the moiré inversion method into the real space and generates a moiré area without deformation.

[0004] The inversion method of real-space moiré fringes proposed in the present invention comprises the following steps:

[0005] (1) Input the binary image of the moiré region and give the assumed number of atomic layers, i.e., height H;

[0006] (2) Using the binary image of the moiré region to obtain the edge of the moiré, and obtaining the maximum width max(dx) and the maximum height max(dy) from it, and at the same time obtaining the width a and length b of the binary image;

[0007] (3) Using the obtained edge of the moiré region and the given height H, the outer frame of the moiré region specimen grid line can be obtained. At the same time, the height H is combined with the width a and length b of the binary image to obtain the outer frame of the moiré region reference grid, that is, a cubic region.

[0008] (4) Construct a cubic crystal array based on the obtained r and R as edge lengths. The formulas for r and R are as follows:

[0009]

[0010]

[0011] (5) Rotate the two obtained cubic crystal arrays around the x-axis, y-axis, and z-axis to the angles calculated using the TEM moiré inversion method;

[0012] (6) Using the outer frame obtained in (3) to intercept the cubic crystal array in (4), a specimen grid and a reference grid are obtained;

[0013] (7) Use the specimen grid and the reference grid to perform spatial superposition, adjust the direction of the specimen grid line, and update the data in (4), (5) and (6) to obtain the moiré grid line.

[0014] The present invention proposes a real-space moiré fringing inversion method that utilizes a binary image of the moiré region, along with the specimen grating planes and reference grating directions obtained after analyzing the moiré region, to invert the moiré region. This method verifies the moiré region parameters and further calculates other parameters of the moiré region, extending the TEM moiré inversion method. While verifying the moiré region parameters calculated by the TEM moiré inversion method, the present invention also calculates other parameters of the moiré region, further enriching the full-field measurement methods for moiré regions. In the field of photomechanics, this method represents a new breakthrough in the parameter calculation methods for newly generated small grains. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Flowchart of a real-space moiré fringe inversion method.

[0016] Figure 2 2 is a moiré pattern obtained by inversion using this method in an embodiment.

[0017] Figure 3 In the embodiment, the image of the moiré region needs to be inverted.

[0018] Figure 4 4 is a graph of the inversion results of the moiré region obtained using this method in the embodiment. DETAILED DESCRIPTION

[0019] The present invention proposes a real-space moiré fringe inversion method, comprising the following steps:

[0020] (1) Input the binary image of the moiré region and give the assumed number of atomic layers, i.e., height H;

[0021] (2) Using the binary image of the moiré region to obtain the edge of the moiré, and obtaining the maximum width max(dx) and the maximum height max(dy) from it, and at the same time obtaining the width a and length b of the binary image;

[0022] (3) Using the obtained edge of the moiré region and the given height H, the outer frame of the moiré region specimen grid line can be obtained. At the same time, the height H is combined with the width a and length b of the binary image to obtain the outer frame of the moiré region reference grid, that is, a cubic region.

[0023] (4) Construct a cubic crystal array based on the obtained r and R as edge lengths. The formulas for r and R are as follows:

[0024]

[0025]

[0026] (5) rotating the two obtained cubic crystal arrays around the x-axis, y-axis, and z-axis to a given angle;

[0027] (6) Using the outer frame obtained in (3) to intercept the cubic crystal array in (4), a specimen grid and a reference grid are obtained;

[0028] (7) Use the specimen grid and the reference grid to perform spatial superposition, adjust the direction of the specimen grid line, and update the data in (4), (5) and (6) to obtain the moiré grid line.

[0029] The specific embodiments of the present invention will now be further described.

[0030] In one embodiment of the method of the present invention, when inverting a moiré region, the reference grid line of the moiré region is a lattice with a crystal orientation of <001> , the crystal plane of the lattice obtained by the moiré inversion method is {111}. The binary image of the moiré area is used as input, and the width a and length b of the binary image, the boundary of the moiré area, and the max(dx) and max(dy) of the moiré area are obtained respectively. Since the crystal orientation of the reference grid line is <001> , which is the positive direction in three-dimensional space and does not need to be rotated, then the width a, length b and height H of the binary image are directly used to generate a lattice structure to form a reference grid lattice; the boundary of the moiré area is combined with the height H to obtain the assumed outer frame of the moiré boundary; R is calculated using the obtained moiré area max(dx), max(dy) and height H, and a regular cube lattice is generated with R as the side length, and is placed in a rectangular coordinate system and rotated around the x-axis, y-axis and z-axis respectively. Since the crystal plane of the specimen grid line here is {111}, the regular cube lattice needs to be rotated to <111> ; Use the outer frame of the moiré boundary obtained above and the regular cube lattice rotated to the 111 crystal direction to take the intersection, so as to obtain the specimen grid line lattice structure of the moiré area, and spatially superimpose the specimen grid lines and the reference grid lines to form a moiré area. Finally, let the specimen grid lines rotate around the normal direction of {111}, and repeat the superposition of the specimen grid lines and the reference grid lines to form the final simulated image of the moiré area. At the same time, several possibilities of the crystal direction of the specimen grid lines in the moiré area can also be obtained.

Claims

1. A real-space moiré fringe inversion method, characterized in that The method comprises the following steps: (1) Input the binary image of the moiré region and give the assumed number of atomic layers, i.e., height H; (2) Using the binary image of the moiré region to obtain the edge of the moiré, and obtaining the maximum width dx and the maximum height dy from it, and at the same time obtaining the width a and length b of the binary image; (3) Using the obtained edge of the moiré region and the given height H, the outer frame of the moiré region specimen grid line can be obtained. At the same time, the height H is combined with the width a and length b of the binary image to obtain the outer frame of the moiré region reference grid; (4) Construct a cubic crystal array based on the obtained r and R as edge lengths. The formulas for r and R are as follows: (5) rotating the two obtained cubic crystal arrays around the x-axis, y-axis, and z-axis to a given angle; (6) Using the outer frame obtained in step (3) to intercept the cubic crystal array in step (4), a specimen grid and a reference grid are obtained; (7) Use the specimen grid and the reference grid to perform spatial superposition, adjust the direction of the specimen grid line, and update the data in steps (4), (5) and (6) to obtain the moiré grid line.

Images