CN116593401A - Three-dimensional orientation method of ferroelectric crystal based on optical characteristics - Google Patents

Abstract

The application discloses a three-dimensional orientation method of a ferroelectric crystal based on optical properties. The method is: obtain _the crystal plane index (h ₁ k ₁ l ₁ ) represented by the strongest diffraction peak on the cut surface of _the test wafer _; The declination angle of the crystal plane is obtained to obtain a cut plane with a crystal plane index of (h ₁ k ₁ l ₁ ); the (h ₁ k ₁ l ₁ ) crystal plane is polished, and the extinction phenomenon of the polished wafer is observed with an orthogonal polarizing microscope to determine the polished wafer The projection direction of the spontaneous polarization on the (h ₁ k ₁ l ₁ ) crystal plane; use the spontaneous polarization to determine the projection direction of the (h ₁ k ₁ l ₁ ) crystal plane (h ₂ k ₂ l ₂ ) and (h ₁ k ₁ l ₁ ) intersection line direction [uvw]; use the crystal plane (h ₁ k ₁ l ₁ ) and the intersection line direction [uvw] of two crystal planes to obtain the three-dimensional orientation of the crystal. It is solved that the three-dimensional orientation of the ferroelectric crystal can be accurately carried out without the Laue crystal orientation instrument.

Description

A 3D Orientation Method of Ferroelectric Crystals Based on Optical Properties

technical field

The application relates to a three-dimensional orientation method of a ferroelectric crystal based on optical properties, which belongs to the field of crystal technology.

Background technique

Crystal material is a solid material composed of crystalline substances, and the atoms, ions, molecules or groups contained in it have periodic regular arrangement and translational symmetry, that is, single crystal material. Single crystal materials are widely used in cutting-edge science and technology. Crystal materials include ferroelectric crystals, laser crystals, semiconductor crystals, scintillation crystals, electro-optic crystals, acousto-optic crystals, magneto-optic crystals, etc. The biggest feature of crystals is anisotropy, and the physical properties of crystals are also anisotropic, such as optical, electrical, mechanical and other physical properties are directional. Therefore, the crystal orientation must be clearly defined when the crystal is used, which requires three-dimensional orientation of the crystal.

Most lenses in use today are intraocular lenses. Artificial crystals vary according to the growth method. Many crystals have no natural growth surface. For example, the crystals grown by the pulling method and the crucible descent method are all cylindrical crystals, which brings difficulties to the three-dimensional orientation of the crystals. Orientation of cylindrical crystals, the most widely used is the Laue orientation method. The Laue crystal orientation instrument can quickly determine the three-dimensional orientation of the crystal, but the Laue crystal orientation instrument is expensive, and many research units lack relevant equipment, which is not conducive to widespread use and delays the research cycle. Followed by the X-ray orientation instrument method. The X-ray orientation instrument can measure the deviation between a known crystal plane and a certain crystal plane, but it needs to know the approximate crystal plane index of a certain crystal plane in advance, and can only perform precise one-dimensional orientation on the known crystal plane, and has no three-dimensional orientation function. Therefore, in the case of the scarcity of Laue crystal orientation instruments, a simple method for three-dimensional orientation of crystals is needed.

Contents of the invention

The purpose of the present application is to perform three-dimensional orientation of ferroelectric crystals only by their optical characteristics without using an expensive Laue crystal orientation instrument. Among many crystalline materials, ferroelectric crystals are a kind of crystalline materials with spontaneous polarization. The crossed polarizing microscope can be used to observe the extinction phenomenon in the ferroelectric crystal. The spontaneous polarization direction of the crystal can be determined through the extinction law, and the spontaneous polarization direction of the ferroelectric crystal is closely related to its crystallographic symmetry. Therefore, the optical properties of ferroelectric crystals can be utilized to three-dimensionally align ferroelectric crystals.

According to one aspect of the present application, a method for three-dimensional orientation of a ferroelectric crystal based on optical properties is provided, comprising the following steps:

1) cutting a test wafer from the ferroelectric crystal to be tested;

2) Obtain the X-ray diffraction spectrum of the cut surface of the test wafer, and determine the crystal plane index (h ₁ k ₁ l ₁ ) represented by the strongest diffraction peak in the X-ray diffraction spectrum of the test wafer;

3) Obtain the off angle between the (h ₁ k ₁ l ₁ ) crystal plane and the cut surface of the test wafer by using an X-ray orientation instrument, correct the cut surface, and obtain the crystal plane index as (h ₁ k ₁ l ₁ ) cutting surface;

4) Polish the (h ₁ k ₁ l ₁ ) crystal plane to a thickness of ≤200 μm, observe the extinction phenomenon of the polished wafer with an orthogonal polarizing microscope, and confirm that the spontaneous polarization of the polished wafer is projected on the (h ₁ k ₁ l ₁ ) crystal plane the direction of

5) Determine the intersection _{line direction [uvw] of another crystal plane (h 2 k 2 l 2 ) and} (h 1 k 1 l ₁ ) by using spontaneous polarization in the projection direction of ₍ h ₁ k ₁ l 1 );

6) Using the crystal plane (h ₁ k ₁ l ₁ ) and the intersection line direction [uvw] of the two crystal planes, the three-dimensional orientation of the crystal is obtained.

Specifically, a wafer is arbitrarily cut from the crystal to be tested; the full-spectrum X-ray diffraction pattern of the cut surface of the wafer is obtained, compared with the full-spectrum powder X-ray diffraction pattern of the crystal, and the strongest diffraction pattern in the full-spectrum X-ray diffraction pattern of the wafer is determined. The crystal plane index (h ₁ k ₁ l ₁ ) represented by the peak; the angle between the crystal plane to which the strongest diffraction peak belongs and the wafer cutting plane is determined by an ordinary X-ray orientation instrument, and the crystal plane index cut out by adjusting the cutting angle is (h ₁ k ₁ l ₁ ) wafer; grind and polish (h ₁ k ₁ l ₁ ) wafer, thickness ≤ 200 μm, observe the extinction phenomenon of the polished wafer with an orthogonal polarizing microscope, observe the extinction of the wafer with an orthogonal polarizing microscope phenomenon, determine the direction of spontaneous polarization; use the spontaneous polarization in the projection direction of (h ₁ k ₁ l ₁ ) to determine the intersection direction of another crystal plane (h ₂ k ₂ l ₂ ) and (h ₁ k ₁ l ₁ )[ uvw]; use the crystal plane (h ₁ k ₁ l ₁ ) and the intersection direction [uvw] of the two crystal planes to determine the three-dimensional direction of the crystal.

In the present application, the crystal plane index is represented by (hkl), and different crystal planes are represented by different subscripts.

Optionally, the ferroelectric crystal to be tested is a single crystal without a natural growth plane, that is, the crystal to be tested is a large single crystal without a natural growth plane, and the three-dimensional crystal orientation of the crystal cannot be visually determined through the natural growth plane. , such as cylindrical crystals grown by the pulling method and the crucible drop method.

Optionally, the ferroelectric crystal to be tested has spontaneous polarization.

Optionally, the acquisition device of the X-ray diffraction pattern is a powder X-ray diffractometer.

Optionally, the powder X-ray diffractometer includes a test crystal plane fixing device, an X-ray emitting device, a signal receiving device and an angle measuring device.

Optionally, the crossed polarizing microscope includes a polarizer, an analyzer and a stage;

The polarizer and the analyzer are in an orthogonal structure;

The stage can be rotated 360°.

Optionally, the angle δ between the crystal plane (h ₂ k ₂ l ₂ ) and the crystal plane (h ₁ k ₁ l ₁ ) satisfies:

Triclinic crystal system:

where S ₁₁ = b ² c ² sin ² α;

S ₂₂ = a ² c ² sin ² β;

S ₃₃ = a ² b ² sin ² γ;

S ₁₂ = abc ² (cosαcosβ-cosγ);

S ₂₃ =a ² bc(cosβcosγ-cosα);

S ₁₃ =ab ² c(cosαcosγ-cosβ);

Monoclinic crystal system:

Orthorhombic system:

Trigonal crystal system:

Tetragonal system:

Hexagonal system:

Cubic system:

where a, b, c, α, β, γ are unit cell parameters, d ₁ , d ₂ are the interplanar distances of crystal plane (h ₁ k ₁ l ₁ ) and crystal plane (h ₂ k ₂ l ₂ ), V is the cell volume.

Optionally, the intersection direction [uvw] of the crystal plane (h ₂ k ₂ l ₂ ) and the crystal plane (h ₁ k ₁ l ₁ ) satisfies:

u=k ₁ l ₂ -l ₁ k ₂ ;

v=l ₁ h ₂ -h ₁ l ₂ ;

w = h ₁ k ₂ -k ₁ h ₂ .

The beneficial effect that this application can produce comprises:

1) With the three-dimensional orientation method provided in this application, the three-dimensional orientation of crystals can be completed through commonly used X-ray diffractometers, ordinary X-ray orientation instruments and polarizing microscopes. This application does not require an expensive Laue crystal orientation instrument, and can also meet the requirements of three-dimensional orientation.

2) The three-dimensional orientation method provided by this application has the characteristics of simple operation, high efficiency and low crystal loss.

Description of drawings

Fig. 1 is the flowchart of the method for three-dimensional orientation of ferroelectric crystals provided in Embodiments 1 to 3 of the present application;

Fig. 2 is the powder X-ray diffraction figure of the crystal sample to be tested provided in the embodiment 1 to 3 of the present application;

Fig. 3 is the X-ray diffraction spectrum of the wafer provided in Examples 1 to 3 of the present application, wherein (a) figure is the X-ray diffraction spectrum of any cut surface obtained in Example 1, and (b) figure is the cut surface obtained in Example 1. The (111) plane X-ray diffraction spectrum after plane correction, (c) figure is the X-ray diffraction spectrum of the arbitrary cut surface that embodiment 2 obtains, (d) figure is (110) after the cut plane correction that embodiment 2 obtains Plane X-ray diffraction spectrum, (e) figure is the X-ray diffraction spectrum of arbitrary cutting surface obtained in embodiment 3, (f) figure is the (211) plane X-ray diffraction spectrum after the correction of the cut surface obtained in embodiment 3;

Fig. 4 is the polarizing microscope observation figure of the (111) wafer provided in the embodiment 1 of the present application, wherein (a) figure is the polarizing microscope observation figure of the (111) polished plate obtained in embodiment 1 without an analyzer, (b ) The figure shows the starting position of the (111) polishing sheet obtained in Example 1 under an orthogonal polarizing microscope, and the (c) figure shows the (111) polishing sheet obtained in Example 1 after being rotated 14° from the position in (b) figure Figure, (d) figure under the crossed polarizing microscope is the figure under the crossed polarizing microscope after the (111) polished sheet obtained in embodiment 1 rotates 45° from the (c) figure position;

Figure 5 is the projection of the spontaneous polarization on the crystal plane (h ₁ k ₁ l ₁ ) and the projection of the crystal planes (h ₂ k ₂ l ₂ ) and (h ₁ k ₁ l ₁ ) provided in Examples 1 to 3 of the present application. Schematic diagram of the intersection line [uvw], where (a) is the pseudocubic phase PMN-28PT single crystal spontaneous polarization direction and (111) crystal plane obtained in Example 1, and (b) is the spontaneous pole obtained in Example 1 The projection of the crystallization direction on the (111) plane, (c) is a schematic diagram of the intersection direction [01_1] of crystal planes (111) and (100) obtained in Example 1, and (d) is the pseudo Schematic diagram of the spontaneous polarization direction and (110) crystal plane of the cubic phase PMN-28PT single crystal, (e) is the projection of the spontaneous polarization direction obtained in Example 2 on the (110) plane, (f) is the projection obtained in Example 2 The schematic diagram of the intersection direction [001] of the crystal planes (110) and (100), (g) is the pseudocubic phase PMN-28PT single crystal spontaneous polarization direction obtained in Example 3 and the schematic diagram of the (211) crystal plane, Figure (h) is the projection of the spontaneous polarization direction obtained in Example 3 on the (211) plane, and Figure (i) is a schematic diagram of the intersection direction [01_1] of crystal planes (211) and (100) obtained in Example 3 ;

Fig. 6 is the X-ray diffraction diagram of the standard (100) crystal plane cut out after completing the three-dimensional orientation of the crystal provided in Examples 1-3 of the present application;

Fig. 7 is the polarizing microscope observation figure of the (110) wafer provided in the embodiment 2 of the present application, wherein (a) figure is the polarizing microscope observation figure of the (110) polished plate obtained in embodiment 2 without an analyzer, (b ) The figure shows the starting position of the (110) polishing sheet obtained in Example 2 under an orthogonal polarizing microscope, and the (c) figure shows the (110) polishing sheet obtained in Example 2 after being rotated 38° from the position of the (b) figure Figure, (d) figure under the crossed polarizing microscope is the figure under the crossed polarizing microscope after the (110) polished sheet obtained in embodiment 2 rotates 45° from the (c) figure position;

Figure 8 is a polarizing microscope observation view of the (211) crystalline wafer provided in Example 3 of the present application, wherein (a) is a polarizing microscope observation view of the (211) polished wafer obtained in Example 3 without an analyzer, (b) figure is the figure of (211) polished plate initial position obtained in embodiment 3 under the crossed polarizing microscope, (c) figure is the (211) polished plate obtained in embodiment 3 rotated 12 from (b) figure position The figure under the crossed polarizing microscope after °, (d) figure is the figure under the crossed polarizing microscope after the (211) polished sheet obtained in embodiment 3 is rotated 45° from the position of (c) figure.

Detailed ways

The present application is described in detail below in conjunction with the examples, but the present application is not limited to these examples.

In the examples of this application:

The X-ray powder diffractometer adopted is the MiniFlex 600 desktop X-ray powder diffractometer of Rigaku Company;

The X-ray orientation instrument used is the YX-2 X-ray crystal orientation instrument of Liaodong Ray Instrument Co., Ltd. The measuring range of the sample stage is 0-60°, and the measuring range of the corresponding X-ray signal receiver is 0-120°;

The crossed polarizing microscope used is Nikon LV100POL polarizing microscope. Equipped with polarizer and analyzer, 360° rotating stage.

Example 1:

The 0.72Pb(Mg _1/3 Nb _2/3 )O ₃ -0.28PbTiO ₃ (PMN-28PT) crystal grown by the crucible descent method is a cylindrical crystal without a natural crystallization plane, so the crystallization of the crystal cannot be determined by the natural growth plane. Towards. The following uses the steps of the flow chart of the crystal orientation method shown in FIG. 1 to perform three-dimensional orientation on the crystal.

Step 1. Cut a wafer arbitrarily from the PMN-28PT crystal;

Step 2: Perform powder X-ray diffraction on the cut crystal, and the obtained powder X-ray diffraction pattern is shown in Figure 2, and indexed. It should be noted that although the PMN-28PT crystal has a trigonal crystal structure, its unit cell parameter α is close to 90°, so it is also regarded as a pseudocubic phase. Therefore, in three-dimensional orientation, it can be treated as a cubic crystal system. At the same time, full-spectrum X-ray diffraction is performed on the sliced wafer, and the obtained X-ray diffraction pattern of the test wafer is shown in (a) in FIG. 3 . By comparing (a) in Fig. 2 and Fig. 3, it is found that the strongest peak of the test wafer X-ray diffraction pattern is the diffraction peak of the (111) plane;

Step 3: Fix the test wafer in step 2 on the X-ray orientation instrument, and use the X-ray orientation instrument to obtain the off angle between the crystal plane of the test wafer and the standard (111) plane. After the declination angle is obtained, the cutting surface of the crystal to be measured is corrected to obtain the cutting surface of the accurate (111) plane, as shown in (b) in Figure 3.

Step 4. Grinding and polishing the accurate (111) wafer obtained in Step 3, with a thickness of 128 μm, and placing the polished wafer on the loading stage of a polarizing microscope to observe the extinction phenomenon of the polished wafer. Fig. 4 is the observation figure of (111) polishing sheet under polarized light microscope, wherein (a) is (111) polishing sheet without adding the figure of polarizer among Fig. 4, selects its bottom edge as initial position reference edge; Fig. 4 (b) is the picture of the starting position of the (111) polished sheet under an orthogonal polarizing microscope, and (c) in Figure 4 is the image of the (111) polished sheet rotated 14° from the position of (b) in Figure 4 under the orthogonal polarizing microscope. The picture under the polarizing microscope, the field of view is darkest at this time, indicating that the direction of spontaneous polarization is consistent with that of the polarizer or analyzer. (d) in Figure 4 is the picture after the (111) polished plate is rotated 45° from the position in (c) in Figure 4. At this time, the field of view is the brightest, indicating the direction of spontaneous polarization and the direction of the polarizer or analyzer The included angle is 45°.

Step 5. In this embodiment, the crystal plane (h ₁ k ₁ l ₁ ) is the (111) plane. Figure 5(a) shows the pseudocubic phase PMN-28PT single crystal spontaneous polarization direction and (111) crystal plane, and Figure 5(b) is the projection of the spontaneous polarization direction on the (111) plane. In this embodiment, the crystal plane (h ₂ k ₂ l ₂ ) can be selected as the (100) plane, and its intersection direction [uvw] is [01_1], as shown in (c) in FIG. 5 . By comparing the projection of the spontaneous polarization direction on the (111) plane in Figure 5(b) with the projection direction of the spontaneous polarization on the (111) plane determined in Figure 4, the intersection line between the (111) plane and the (100) plane can be determined [01_1] direction, as shown in (c) in Figure 5.

Step 6. The three-dimensional direction of the crystal can be determined through the crystal plane (111) and the [01_1] crystal direction, as shown in (c) in FIG. 5 . According to the public calculation of the angle between the crystal planes, it can be seen that the angle δ between the (111) plane and the (100) plane is 54.7°. At this time, if it is necessary to cut out a single crystal element of the (100) plane, only the (111) plane needs to be rotated 54.7° around the intersection line. Fig. 6 is the X-ray diffraction pattern of the finally cut (100) plane, which is determined as the (100) plane.

Example 2

Still take the PMN-28PT crystal grown by the crucible drop method as an example. The following uses the steps of the flow chart of the crystal orientation method shown in FIG. 1 to perform three-dimensional orientation on the crystal.

Step 1. Cut a wafer arbitrarily from the PMN-28PT crystal;

Step 2: Perform powder X-ray diffraction on the cut crystal, and the obtained powder X-ray diffraction pattern is shown in Figure 2, and indexed. It should be noted that although the PMN-28PT crystal has a trigonal crystal structure, its unit cell parameter α is close to 90°, so it is also regarded as a pseudocubic phase. Therefore, in three-dimensional orientation, it can be treated as a cubic crystal system. At the same time, full-spectrum X-ray diffraction is performed on the sliced wafer, and the obtained X-ray diffraction pattern of the test wafer is shown in (c) in FIG. 3 . By comparing (c) among Fig. 2 and Fig. 3, it is found that the strongest peak of the test wafer X-ray diffraction pattern is the diffraction peak of the (110) plane;

Step 3: Fix the test wafer in step 2 on the X-ray orientation instrument, and use the X-ray orientation instrument to obtain the off angle between the crystal plane of the test wafer and the standard (110) plane. After the declination angle is obtained, the cutting surface of the crystal to be tested is corrected to obtain the cutting surface of the accurate (110) plane, as shown in (d) in Figure 3.

Step 4. Grinding and polishing the accurate (110) plane wafer obtained in Step 3, with a thickness of 145 μm, and placing the polished wafer on a loading stage of a polarizing microscope to observe the extinction phenomenon of the polished wafer. Fig. 5 is the observation figure of (110) polishing sheet under polarized light microscope, wherein (a) is the figure of (110) polishing sheet not adding polarizer among Fig. side); (b) in Fig. 7 is the figure of (110) polishing sheet starting position under the crossed polarizing microscope, and (c) in Fig. 7 is (110) polishing sheet rotating 38 from (b) figure position in Fig. 7 °After the picture under the crossed polarizing microscope, the field of view is the darkest at this time, indicating that the direction of spontaneous polarization is consistent with the direction of the polarizer or analyzer. (d) in Figure 7 is a picture of the (110) polished plate rotated 45° from the position of (c) in Figure 7 under an orthogonal polarizing microscope. At this time, the field of view is the brightest, indicating the direction of spontaneous polarization and polarization The angle between the direction of the detector or the polarizer is 45°.

Step 5. In this embodiment, the crystal plane (h ₁ k ₁ l ₁ ) is the (111) plane. Figure 5(d) shows the pseudocubic phase PMN-28PT single crystal spontaneous polarization direction and (110) crystal plane, and Figure 5(e) is the projection of the spontaneous polarization direction on the (110) plane. In this embodiment, the crystal plane (h ₂ k ₂ l ₂ ) can be selected as the (100) plane, and its intersection direction [uvw] is [001], as shown in (f) in FIG. 5 . By comparing the projection of the spontaneous polarization direction on the (110) plane in Figure 5(e) with the projection direction of the spontaneous polarization on the (110) determined in Figure 7, the intersection line between the (110) plane and the (100) plane can be determined [ 001] direction, as shown in (f) in Figure 5.

Step 6. The three-dimensional direction of the crystal can be determined through the (110) and [001] crystal orientations, as shown in (f) in FIG. 5 . According to the public calculation of the angle between the crystal planes, it can be known that the angle δ between the (110) plane and the (100) plane is 45°. At this time, if it is necessary to cut out a single crystal element of the (100) plane, it is only necessary to rotate the (110) plane by 45° around the intersection line.

Example 3:

Still take the PMN-28PT crystal grown by the crucible drop method as an example. The following uses the steps of the flow chart of the crystal orientation method shown in FIG. 1 to perform three-dimensional orientation on the crystal.

Step 1. Cut a wafer arbitrarily from the PMN-28PT crystal;

Step 2: Perform powder X-ray diffraction on the cut crystal, and the obtained powder X-ray diffraction pattern is shown in Figure 2, and indexed. It should be noted that although the PMN-28PT crystal has a trigonal crystal structure, its unit cell parameter α is close to 90°, so it is also regarded as a pseudocubic phase. Therefore, in three-dimensional orientation, it can be treated as a cubic crystal system. At the same time, full-spectrum X-ray diffraction is performed on the sliced wafer, and the obtained X-ray diffraction pattern of the test wafer is shown in (e) in FIG. 3 . By comparing (e) among Fig. 2 and Fig. 3, it is found that the strongest peak of the test wafer X-ray diffraction pattern is the diffraction peak of the (211) plane;

Step 3: Fix the test wafer in step 2 on the X-ray orientation instrument, and use the X-ray orientation instrument to obtain the off angle between the crystal plane of the test wafer and the standard (211) plane. After the declination angle is obtained, the cutting surface of the crystal to be tested is corrected to obtain the cutting surface of the accurate (211) plane, as shown in (f) in Figure 3.

Step 4. Grinding and polishing the accurate (211) wafer obtained in Step 3, with a thickness of 153 μm, and placing the polished wafer on the loading stage of a polarizing microscope to observe the extinction phenomenon of the polished wafer. Fig. 8 is the observation figure of (211) polishing sheet under polarized light microscope, wherein (a) is (211) the figure of polishing sheet not adding polarizer among Fig. side); (b) in Fig. 8 is (211) polished sheet initial figure under crossed polarizing microscope, and (c) in Fig. 8 is (211) polished sheet rotated 12 from (b) figure position among Fig. 8 °After the picture under the crossed polarizing microscope, the field of view is the darkest at this time, indicating that the direction of spontaneous polarization is consistent with the direction of the polarizer or analyzer. (d) in Figure 8 is a picture of the (211) polished plate rotated 45° from the position of (c) in Figure 8. At this time, the field of view is the brightest, indicating the direction of spontaneous polarization and the direction of the polarizer or analyzer The included angle is 45°.

Step 5. In this embodiment, the crystal plane (h ₁ k ₁ l ₁ ) is the (211) plane. Figure 5 (g) shows the pseudocubic phase PMN-28PT single crystal spontaneous polarization direction and (211) crystal plane schematic diagram, Figure 5 (h) is the projection of the spontaneous polarization direction on the (211) plane. In this embodiment, the crystal plane (h ₂ k ₂ l ₂ ) can be selected as the (100) plane, and its intersection direction [uvw] is [01_1], as shown in (i) in FIG. 5 . By comparing the projection of the spontaneous polarization direction on the (211) plane in Figure 5(h) with the projection direction of the spontaneous polarization on the (211) determined in Figure 8, the intersection line between the (211) plane and the (100) plane can be determined [01_1 ] direction, as shown in (i) in Figure 5.

Step 6. The three-dimensional direction of the crystal can be determined through the crystal plane (211) and the [01_1] crystal direction, as shown in (i) in FIG. 5 . According to the public calculation of the angle between the crystal planes, it can be known that the angle δ between the (211) plane and the (100) plane is 35.3°. At this time, if it is necessary to cut out a single crystal element of the (100) plane, only the (211) plane needs to be rotated 35.3° around the intersection line.

The above three embodiments show three typical cases of using this method to perform three-dimensional orientation of ferroelectric crystals. In actual operation, the three-dimensional orientation in other cases can also be completed according to the basic steps of orientation described in this method.

The above are only a few embodiments of the application, and do not limit the application in any form. Although the application is disclosed as above with preferred embodiments, it is not intended to limit the application. Any skilled person familiar with this field, Without departing from the scope of the technical solution of the present application, any changes or modifications made using the technical content disclosed above are equivalent to equivalent implementation cases, and all belong to the scope of the technical solution.

Claims (5)

1. A method for three-dimensional orientation of ferroelectric crystals based on optical properties, comprising the steps of:

1) Cutting a test wafer from the ferroelectric crystal to be tested;

2) Acquiring an X-ray diffraction pattern of the cutting surface of the test wafer, and determining a crystal face index (h) represented by the strongest diffraction peak in the X-ray diffraction pattern of the test wafer ₁ k ₁ l ₁ )；

3) Acquisition by means of an X-ray direction finder (h ₁ k ₁ l ₁ ) Correcting the cut surface of the test wafer by correcting the offset angle between the cut surface and the crystal plane to obtain a crystal plane index (h) ₁ k ₁ l ₁ ) Is provided;

4) Couple (h) ₁ k ₁ l ₁ ) Polishing the crystal face to a thickness of 200 μm or less, observing extinction phenomenon of the polished wafer by using an orthogonal polarization microscope, and determining spontaneous polarization of the polished wafer in (h) ₁ k ₁ l ₁ ) The direction of the crystal plane projection;

5) By spontaneous polarization in (h ₁ k ₁ l ₁ ) The projection direction determines another crystal plane (h ₂ k ₂ l ₂ ) Sum (h) ₁ k ₁ l ₁ ) Cross direction [ uvw ]]；

6) By using the crystal plane (h) ₁ k ₁ l ₁ ) And the intersection line direction of two crystal planes [ uvw ]]The three-dimensional direction of the crystal is obtained.

2. The method of claim 1, wherein the ferroelectric crystal to be measured is a single crystal without a natural growth surface.

3. The three-dimensional orientation method according to claim 1 wherein said ferroelectric crystal to be measured has spontaneous polarization.

4. The three-dimensional orientation method according to claim 1 wherein said crystal plane (h ₂ k ₂ l ₂ ) And crystal plane (h) ₁ k ₁ l ₁ ) The included angle delta of the crystal face is as follows:

triclinic system:

wherein S is ₁₁ ＝b ² c ² sin ² α；

S ₂₂ ＝a ² c ² sin ² β；

S ₃₃ ＝a ² b ² sin ² γ；

S ₁₂ ＝abc ² (cosαcosβ-cosγ)；

S ₂₃ ＝a ² bc(cosβcosγ-cosα)；

S ₁₃ ＝ab ² c(cosαcosγ-cosβ)；

Monoclinic system:

orthorhombic system:

trigonal system:

tetragonal system:

hexagonal system:

cubic system:

wherein a, b, c, alpha, beta, gamma are unit cell parameters, d ₁ 、d ₂ Is the crystal face (h) ₁ k ₁ l ₁ ) And crystal plane (h) ₂ k ₂ l ₂ ) V is the unit cell volume.

5. The three-dimensional orientation method according to claim 1, wherein said crystal plane (h ₂ k ₂ l ₂ ) And crystal plane (h) ₁ k ₁ l ₁ ) Cross direction [ uvw ]]The method meets the following conditions:

u＝k ₁ l ₂ –l ₁ k ₂ ；

v＝l ₁ h ₂ –h ₁ l ₂ ；

w＝h ₁ k ₂ –k ₁ h ₂ 。