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

Abstract

The application discloses a three-dimensional orientation method of ferroelectric crystal based on optical characteristics. The method comprises the following steps: obtaining the crystal face index (h) represented by the strongest diffraction peak of the cut surface of the test wafer ₁ k ₁ l ₁ ) The method comprises the steps of carrying out a first treatment on the surface of the Acquisition by means of an X-ray direction finder (h ₁ k ₁ l ₁ ) The offset angle between the crystal plane and the cut surface of the test wafer, a crystal plane index (h) was obtained ₁ k ₁ l ₁ ) Is provided; couple (h) ₁ k ₁ l ₁ ) The crystal face was polished, and the extinction phenomenon of the polished wafer was observed by using an orthogonal polarization microscope, and the spontaneous polarization of the polished wafer was determined to be within (h ₁ k ₁ l ₁ ) The direction of the crystal plane projection; 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 ]]The method comprises the steps of carrying out a first treatment on the surface of the 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. Solves the problem that the ferroelectric crystal can be accurately oriented in three dimensions without a Laue crystal orientation instrument.

Description

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

Technical Field

The application relates to a three-dimensional orientation method of ferroelectric crystal based on optical characteristics, belonging to the technical field of crystals.

Background

The crystalline material is a solid material composed of a crystalline substance, and atoms, ions, molecules, groups, or the like contained therein have periodic regular arrangement and translational symmetry, that is, a single crystal material. Monocrystalline materials have found wide application in advanced science and technology, and crystalline materials include ferroelectric crystals, laser crystals, semiconductor crystals, scintillation crystals, electro-optic crystals, acousto-optic crystals, magneto-optic crystals, and the like. The biggest characteristic of the crystal is anisotropy, and the physical properties of the crystal are also anisotropic, such as optical, electrical, mechanical and other physical properties are directional. Thus, the crystal must be oriented clearly at the time of use, which requires three-dimensional orientation of the crystal.

The crystals used in most cases are artificial crystals. Depending on the method of growth, many crystals are not grown naturally, for example, the crystal grown by Czochralski method or the Bridgman method is cylindrical, which makes three-dimensional orientation of the crystal difficult. The orientation of the cylindrical crystals is most widely used as the laue orientation method. The Laue crystal orientation instrument can quickly determine the three-dimensional direction of the crystal, but the Laue crystal orientation instrument is high in price, and many research units lack related equipment, so that the Laue crystal orientation instrument is not beneficial to wide use and delays the research period. And then X-ray orientation method. The X-ray orientation instrument can measure the deviation between the known crystal face and a certain crystal face, but the approximate crystal face index of a certain crystal face needs to be known in advance, and the known crystal face can be precisely and unidimensionally oriented only without a three-dimensional orientation function. Thus, in the case of a laue crystal orientation apparatus which is scarce, a simple crystal three-dimensional orientation method is required.

Disclosure of Invention

The object of the application is to perform three-dimensional orientation of ferroelectric crystals by only their optical characteristics without using an expensive laue crystal orientation machine. Among the numerous crystalline materials, ferroelectric crystals are a class of crystalline materials that exhibit spontaneous polarization. The orthogonal polarization microscope can be used for observing extinction phenomenon in the ferroelectric crystal, and the spontaneous polarization direction of the crystal can be determined according to the extinction law, and the spontaneous polarization direction of the ferroelectric crystal is closely related to the crystallographic symmetry of the ferroelectric crystal. Thus, the optical properties of the ferroelectric crystal can be utilized to orient the ferroelectric crystal in three dimensions.

According to an aspect of the present application, there is provided a three-dimensional orientation method of a ferroelectric crystal based on optical characteristics, 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.

Specifically, a wafer is arbitrarily cut from a crystal to be measured; acquiring a full spectrum X-ray diffraction pattern of a cutting surface of the wafer, comparing the full spectrum X-ray diffraction pattern with the full spectrum powder X-ray diffraction pattern of the crystal, and determining a crystal face index (h) represented by the strongest diffraction peak in the full spectrum X-ray diffraction pattern of the wafer ₁ k ₁ l ₁ ) The method comprises the steps of carrying out a first treatment on the surface of the The included angle between the crystal face of the strongest diffraction peak and the cutting face of the wafer is determined by using a common X-ray orientation instrument, and the index of the crystal face is cut to be @ by adjusting the cutting angleh ₁ k ₁ l ₁ ) Is a wafer of (a); couple (h) ₁ k ₁ l ₁ ) Grinding and polishing the wafer, wherein the thickness is less than or equal to 200 mu m, observing the extinction phenomenon of the polished wafer by adopting an orthogonal polarization microscope, observing the extinction phenomenon of the wafer by adopting the orthogonal polarization microscope, and determining the spontaneous polarization direction; 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 ]]The method comprises the steps of carrying out a first treatment on the surface of the By using the crystal plane (h) ₁ k ₁ l ₁ ) And the intersection line direction of two crystal planes [ uvw ]]The three-dimensional orientation of the crystal can be determined.

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

Alternatively, the ferroelectric crystal to be measured is a single crystal without a natural growth surface, i.e. the crystal to be measured is a large single crystal without a natural growth surface, and the three-dimensional crystal orientation of the crystal cannot be intuitively determined through the natural growth surface, such as a cylindrical crystal grown by a pulling method or a crucible descent method.

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

Optionally, the device for acquiring the X-ray diffraction pattern is a powder X-ray diffractometer.

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

Optionally, the orthogonal polarization microscope comprises a polarizer, an analyzer, and a stage;

the polarizer and the analyzer are in an orthogonal structure;

the stage may be rotated 360 °.

Optionally, the 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.

Optionally, the 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 。

the application has the beneficial effects that:

1) The three-dimensional orientation method provided by the application can be used for completing the three-dimensional orientation of the crystal through a common X-ray diffractometer, a common X-ray orientation instrument and a polarized light microscope. The application can meet the three-dimensional orientation requirement without expensive Laue crystal orientation instrument.

2) The three-dimensional orientation method provided by the application has the characteristics of simplicity in operation, high efficiency and small crystal loss.

Drawings

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

FIG. 2 is a powder X-ray diffraction chart of the crystal sample to be measured provided in examples 1 to 3 of the present application;

fig. 3 is an X-ray diffraction chart of a wafer provided in examples 1 to 3 of the present application, wherein (a) is an X-ray diffraction chart of an arbitrary cut surface obtained in example 1, (b) is an (111) plane X-ray diffraction chart after correction of the cut surface obtained in example 1, (c) is an X-ray diffraction chart of an arbitrary cut surface obtained in example 2, (d) is an (110) plane X-ray diffraction chart after correction of the cut surface obtained in example 2, (e) is an X-ray diffraction chart of an arbitrary cut surface obtained in example 3, and (f) is an (211) plane X-ray diffraction chart after correction of the cut surface obtained in example 3;

fig. 4 is a view of a polarization microscope of the (111) wafer provided in example 1 of the present application, wherein (a) is a view of the (111) polished wafer obtained in example 1 under a polarization microscope without an analyzer, (b) is a view of the (111) polished wafer obtained in example 1 under a orthogonal polarization microscope, and (c) is a view of the (111) polished wafer obtained in example 1 under a orthogonal polarization microscope after being rotated by 14 ° from the (b) position, and (d) is a view of the (111) polished wafer obtained in example 1 under a orthogonal polarization microscope after being rotated by 45 ° from the (c) position;

FIG. 5 shows the spontaneous polarization in the crystal plane (h) ₁ k ₁ l ₁ ) Projection of (d) and crystal plane (h) ₂ k ₂ l ₂ ) Sum (h) ₁ k ₁ l ₁ ) Intersecting line [ uvw ]]Schematic diagram in which (a) diagram is a schematic diagram of spontaneous polarization direction and (111) crystal plane of pseudocubic PMN-28PT single crystal obtained in example 1, (b) diagram is a projection of spontaneous polarization direction on (111) plane obtained in example 1, (c) diagram is intersection line direction [01_1] of crystal planes (111) and (100) obtained in example 1]Is a schematic view of the spontaneous polarization direction and (110) plane of the pseudo-cubic PMN-28PT single crystal obtained in example 2, (d) is a schematic view of the spontaneous polarization direction and (110) plane obtained in example 2, (e) is a projection of the spontaneous polarization direction on the (110) plane, and (f) is the intersection line direction [001] of the crystal planes (110) and (100) obtained in example 2]Is a schematic diagram of the spontaneous polarization direction and (211) crystal plane of the pseudocubic PMN-28PT single crystal obtained in example 3, (g) is a schematic diagram of the spontaneous polarization direction and (211) plane obtained in example 3, (h) is a projection of the spontaneous polarization direction on the (211) plane, and (i) is the intersection line direction [01_1] of the crystal planes (211) and (100) obtained in example 3]Schematic of (2);

FIG. 6 is an X-ray diffraction chart of a standard (100) crystal plane cut after completion of three-dimensional orientation of the crystal provided in examples 1 to 3 of the present application;

fig. 7 is a view of a polarizing microscope of the (110) wafer provided in example 2 of the present application, wherein (a) is a view of the polarizing microscope obtained in example 2 in which the (110) polished sheet was not subjected to an analyzer, (b) is a view of the (110) polished sheet obtained in example 2 in which the starting position was under an orthogonal polarizing microscope, (c) is a view of the (110) polished sheet obtained in example 2 in which the (110) polished sheet was rotated by 38 ° from the position of the (b) and then under an orthogonal polarizing microscope, and (d) is a view of the (110) polished sheet obtained in example 2 in which the (110) polished sheet was rotated by 45 ° from the position of the (c) graph;

fig. 8 is a view of a polarizing microscope of the (211) wafer having a crystal orientation provided in example 3 of the present application, wherein the (a) view is a view of the polarizing microscope of the (211) polished wafer obtained in example 3 without an analyzer, (b) view is a view of the (211) polished wafer obtained in example 3 under an orthogonal polarizing microscope at a starting position thereof, (c) view is a view of the (211) polished wafer obtained in example 3 under an orthogonal polarizing microscope after being rotated 12 ° from the (b) view position, and (d) view is a view of the (211) polished wafer obtained in example 3 under an orthogonal polarizing microscope after being rotated 45 ° from the (c) view position thereof.

Detailed Description

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

In the embodiments of the present application:

the X-ray powder diffractometer adopted is a MiniFlex 600 desk type X-ray powder diffractometer of Rigaku company;

the X-ray direction finder is YX-2 type X-ray crystal direction finder of Liaodong ray instrument Co. The measuring range of the sample table is 0-60 degrees, and the corresponding measuring range of the X-ray signal receiver is 0-120 degrees;

the orthogonal polarization microscope used was LV100POL polarization microscope from Nikon. Is provided with a polarizer and an analyzer, and a 360 DEG rotary object stage.

Example 1:

0.72Pb (Mg) grown by the Bridgman method _1/3 Nb _2/3 )O ₃ -0.28PbTiO ₃ The (PMN-28 PT) crystal is a cylindrical crystal, and has no natural crystal plane, so that the crystal orientation of the crystal cannot be determined by a natural growth plane. The crystal is three-dimensionally oriented using the steps of the flow chart of the crystal orientation method shown in fig. 1.

Step one, randomly cutting a wafer from a PMN-28PT crystal;

and step two, performing powder X-ray diffraction on the cut crystal, wherein the obtained powder X-ray diffraction pattern is shown in figure 2 and is indexed. The PMN-28PT crystal has a trigonal structure, but has a unit cell parameter α of approximately 90 degrees, and is also regarded as a pseudocubic phase. Thus, in three-dimensional orientation, it can be handled as a cubic system. And simultaneously carrying out full spectrum X-ray diffraction on the cut wafer, and obtaining an X-ray diffraction pattern of the test wafer, wherein the X-ray diffraction pattern is shown in (a) of fig. 3. As a result of comparison of fig. 2 and fig. 3 (a), the strongest peak of the test wafer X-ray diffraction pattern is the diffraction peak of the (111) plane;

and thirdly, fixing the test wafer in the second step on an X-ray orientation instrument, and acquiring the deflection angles of the crystal face and the standard (111) face of the test wafer by using the X-ray orientation instrument. After obtaining the deflection angle, correcting the cutting surface of the crystal to be tested, and obtaining the cutting surface of the accurate (111) surface, which is shown in (b) of fig. 3.

And fourthly, grinding and polishing the wafer with the accurate (111) surface obtained in the third step and the thickness of 128 mu m, and placing the polished wafer on a polarizing microscope loading table to observe the extinction phenomenon of the polished wafer. FIG. 4 is an observation view of (111) a polished sheet under a polarizing microscope, wherein (a) in FIG. 4 is a view of (111) a polished sheet without an analyzer, and the bottom side thereof is selected as a reference side for the initial position; fig. 4 (b) is a view of the initial position of the (111) polishing sheet under the orthogonal polarization microscope, and fig. 4 (c) is a view of the (111) polishing sheet under the orthogonal polarization microscope after being rotated by 14 ° from the position of the (b) view in fig. 4, in which the field of view is darkest, indicating that the spontaneous polarization direction is identical to the polarizer or analyzer direction. Fig. 4 (d) is a view of the (111) polished sheet rotated 45 ° from the position of the (c) view in fig. 4, where the field of view is the brightest, indicating that the spontaneous polarization direction and the polarizer or analyzer direction have an angle of 45 °.

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

Step six, the three-dimensional direction of the crystal can be determined by the crystal planes (111) and [01_1] crystal directions, as shown in (c) of fig. 5. As is known from the crystal face angle calculation, the crystal face angle delta between the (111) plane and the (100) plane is 54.7 degrees. At this time, if it is necessary to cut out the single crystal element of the (100) face, only the (111) face needs to be rotated about the intersecting line by 54.7 °. Fig. 6 is an X-ray diffraction pattern of the (100) plane finally cut, and is determined as the (100) plane.

Example 2

PMN-28PT crystals grown by the Bridgman method are still exemplified. The crystal is three-dimensionally oriented using the steps of the flow chart of the crystal orientation method shown in fig. 1.

Step one, randomly cutting a wafer from a PMN-28PT crystal;

and step two, performing powder X-ray diffraction on the cut crystal, wherein the obtained powder X-ray diffraction pattern is shown in figure 2 and is indexed. The PMN-28PT crystal has a trigonal structure, but has a unit cell parameter α of approximately 90 degrees, and is also regarded as a pseudocubic phase. Thus, in three-dimensional orientation, it can be handled as a cubic system. And simultaneously carrying out full spectrum X-ray diffraction on the cut wafer, and obtaining an X-ray diffraction pattern of the test wafer, wherein the X-ray diffraction pattern is shown in (c) of fig. 3. As shown by comparison of fig. 2 and fig. 3 (c), the strongest peak of the X-ray diffraction pattern of the test wafer is the diffraction peak of the (110) plane;

and thirdly, fixing the test wafer in the second step on an X-ray orientation instrument, and acquiring the deflection angles of the crystal face and the standard (110) face of the test wafer by using the X-ray orientation instrument. After obtaining the deflection angle, correcting the cutting surface of the crystal to be detected, and obtaining the cutting surface of the accurate (110) surface, which is shown in (d) of fig. 3.

And fourthly, grinding and polishing the wafer with the accurate (110) surface obtained in the third step and the thickness of 145 mu m, and placing the polished wafer on a polarizing microscope loading table to observe the extinction phenomenon of the polished wafer. FIG. 5 is a view of a (110) polishing sheet under a polarizing microscope, wherein (a) in FIG. 7 is a view of the (110) polishing sheet without an analyzer, and a wafer edge is selected as a reference edge (bevel edge in the figure) of a starting position; fig. 7 (b) is a view of the initial position of the (110) polishing sheet under an orthogonal polarization microscope, and fig. 7 (c) is a view of the (110) polishing sheet under an orthogonal polarization microscope after being rotated by 38 ° from the position of the (b) polishing sheet in fig. 7, in which the field of view is darkest, indicating that the spontaneous polarization direction is coincident with the polarizer or analyzer direction. Fig. 7 (d) is a view of the (110) polished wafer under an orthogonal polarization microscope rotated 45 ° from the position of fig. 7 (c), where the field of view is the brightest, indicating that the spontaneous polarization direction is at an angle of 45 ° to the polarizer or analyzer direction.

Step five, in this embodiment, the crystal plane (h) ₁ k ₁ l ₁ ) Is a (111) plane. FIG. 5 (d) is a schematic diagram showing the spontaneous polarization direction and the (110) plane of a pseudocubic PMN-28PT single crystal, and FIG. 5 (e) is a projection of the spontaneous polarization direction on the (110) plane. In this embodiment, the crystal plane (h ₂ k ₂ l ₂ ) Is (100) plane, its intersection line direction [ uvw ]]Is [001]]Shown in fig. 5 (f). By comparing the projection of the spontaneous polarization direction on the (110) plane in FIG. 5 (e) with the projection direction of the spontaneous polarization on the (110) plane determined in FIG. 7, the intersection [001] of the (110) plane and the (100) plane can be determined]The direction is shown in fig. 5 (f).

Step six, the three-dimensional direction of the crystal can be determined by the crystal planes (110) and [001] as shown in (f) of fig. 5. As can be seen from the calculation of the crystal face angle, the crystal face angle delta between the (110) face and the (100) face is 45 degrees. At this time, if it is necessary to cut out the single crystal element of the (100) face, it is only necessary to rotate the (110) face by 45 ° around the intersecting line.

Example 3:

PMN-28PT crystals grown by the Bridgman method are still exemplified. The crystal is three-dimensionally oriented using the steps of the flow chart of the crystal orientation method shown in fig. 1.

Step one, randomly cutting a wafer from a PMN-28PT crystal;

and step two, performing powder X-ray diffraction on the cut crystal, wherein the obtained powder X-ray diffraction pattern is shown in figure 2 and is indexed. The PMN-28PT crystal has a trigonal structure, but has a unit cell parameter α of approximately 90 degrees, and is also regarded as a pseudocubic phase. Thus, in three-dimensional orientation, it can be handled as a cubic system. And simultaneously carrying out full spectrum X-ray diffraction on the cut wafer, and obtaining an X-ray diffraction pattern of the test wafer, wherein the X-ray diffraction pattern is shown in (e) of fig. 3. As shown by comparison of (e) in fig. 2 and 3, the strongest peak of the X-ray diffraction pattern of the test wafer is the diffraction peak of the (211) plane;

and thirdly, fixing the test wafer in the second step on an X-ray orientation instrument, and acquiring the deflection angles of the crystal face and the standard (211) face of the test wafer by using the X-ray orientation instrument. After obtaining the deflection angle, correcting the cutting surface of the crystal to be detected, and obtaining the cutting surface of the accurate (211) surface, which is shown in (f) of fig. 3.

And fourthly, grinding and polishing the wafer with the accurate (211) surface obtained in the third step and the thickness of 153 mu m, and placing the polished wafer on a polarizing microscope loading table to observe the extinction phenomenon of the polished wafer. FIG. 8 is a view of (211) a polished wafer under a polarizing microscope, wherein (a) in FIG. 8 is a view of (211) a polished wafer without an analyzer, and a wafer side is selected as a reference side (horizontal side in the figure) for a starting position; fig. 8 (b) is a view of the polishing sheet under an orthogonal polarization microscope, and fig. 8 (c) is a view of the polishing sheet under an orthogonal polarization microscope after 12 ° rotation of the polishing sheet from the position of fig. 8 (b), at which time the field of view is darkest, indicating that the spontaneous polarization direction coincides with the polarizer or analyzer direction. Fig. 8 (d) is a view of the polishing sheet (211) rotated 45 ° from the position of fig. 8 (c), where the field of view is the brightest, indicating that the spontaneous polarization direction is 45 ° from the polarizer or analyzer direction.

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

Step six, the three-dimensional direction of the crystal can be determined by the crystal plane (211) and the [01_1] crystal orientation, as shown in (i) of fig. 5. As is known from the crystal face angle calculation, the crystal face angle δ between the (211) plane and the (100) plane is 35.3 °. At this time, if it is necessary to cut out the single crystal element of the (100) face, it is only necessary to rotate the (211) face around the intersecting line by 35.3 °.

The three above examples illustrate three typical cases of three-dimensional orientation of ferroelectric crystals using the present method, and in practice, three-dimensional orientation may be accomplished in other cases as well, according to the basic steps of orientation described in the present method.

While the application has been described in terms of preferred embodiments, it will be understood by those skilled in the art that various changes and modifications can be made without departing from the scope of the application, and it is intended that the application is not limited to the specific embodiments disclosed.

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 。