A method for three-dimensional crystal orientation and a method for crystal processing.

Abstract

This application discloses a method for three-dimensional crystal orientation and a crystal processing method. The method includes: cutting a test wafer from a crystal to be tested; obtaining an X-ray diffraction pattern of the cut surface of the test wafer, and determining the crystal plane index (h1k1l1) represented by the strongest diffraction peak in the X-ray diffraction pattern of the test wafer; obtaining the deflection angle between the crystal plane (h1k1l1) and the cut surface of the test wafer using an X-ray orientation instrument, correcting the cut surface, and obtaining a cut surface with a crystal plane index of (h1k1l1); selecting a crystal plane (h2k2l2), and determining the intersection direction [uvw] of the crystal plane (h2k2l2) and the crystal plane (h1k1l1) using an X-ray orientation instrument; and obtaining the three-dimensional orientation of the crystal using the crystal plane (h1k1l1) and the intersection direction [uvw]. This method solves the problem of quickly and accurately performing three-dimensional orientation of crystals without a Laue crystal orientation instrument.

Description

Technical Field

[0001] This application relates to a method for three-dimensional orientation of crystals and a method for processing crystals, belonging to the field of crystal technology. Background Technology

[0002] Crystalline materials are solid materials composed of crystalline substances, whose atoms, ions, molecules, or groups exhibit periodic, regular arrangements and translational symmetry; these are known as single-crystal materials. Single-crystal materials have wide applications in cutting-edge science and technology. Crystalline materials include ferroelectric crystals, laser crystals, semiconductor crystals, scintillation crystals, electro-optic crystals, acousto-optic crystals, and magneto-optic crystals. The most prominent characteristic of crystals is anisotropy; their physical properties are also anisotropic, such as optical, electrical, and mechanical properties, all of which have directionality. Therefore, the crystal orientation must be clearly defined when using crystals, which necessitates three-dimensional orientation.

[0003] Currently, most crystals used are artificial crystals. Depending on the growth method, many artificial crystals lack natural growth faces; for example, crystals grown using the Czochralski method and the crucible-lowering method are cylindrical, which poses challenges to three-dimensional orientation. The most widely used orientation method for cylindrical crystals is the Laue orientation method. The Laue crystal orientation instrument can quickly determine the three-dimensional orientation of a crystal, but it is expensive, and many research institutions lack the necessary equipment, hindering its widespread use and delaying research cycles. Other orientation methods include optical methods and X-ray orientation methods. Optical methods generally use an optical microscope to observe the morphology and interference patterns of the crystal wafer to determine the crystal plane orientation. This method requires the fabrication of wafers for optical microscopes, which is time-consuming. Furthermore, the orientation accuracy is low and the error is large. X-ray orientation instruments can measure the deviation between a known crystal plane and a specific crystal plane, but they require prior knowledge of the approximate crystal plane indices and can only perform precise one-dimensional orientation of known crystal planes, lacking three-dimensional orientation capabilities. Therefore, existing crystal orientation methods are either inefficient or expensive, necessitating a simpler three-dimensional crystal orientation method. Summary of the Invention

[0004] To address the aforementioned technical problems, this application provides a simple method, apparatus, and processing method for three-dimensional crystal orientation, which can solve the problem that existing crystal orientation instruments cannot perform three-dimensional orientation.

[0005] One aspect of this application provides a method for three-dimensional crystal orientation, the method comprising:

[0006] (1) Cut the test wafer from the crystal to be tested;

[0007] (2) Obtain the X-ray diffraction pattern of the cut surface of the test wafer and compare it with the powder X-ray diffraction pattern of the crystal to be tested to determine the crystal plane index represented by the strongest diffraction peak in the X-ray diffraction pattern of the test wafer.h 1 k 1 l 1);

[0008] (3) The crystal plane to which the strongest diffraction peak of the test wafer belongs is obtained using an X-ray diffractometer. h 1 k 1 l 1) The angle between the test wafer and the cut surface. After obtaining the angle, the cut surface of the test wafer is corrected to obtain the crystal plane index as ( h 1 k 1 l 1) The cut surface;

[0009] (4) Select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) Based on the principle that the crystal plane angle δ is relatively small, the crystal plane is determined using an X-ray orientation instrument. h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The direction of the intersection line [ uvw ];

[0010] (5) Utilizing crystal planes ( h 1 k 1 l 1) The direction of the intersection of the two crystal planes [ uvw [To obtain the three-dimensional orientation of the crystal.]

[0011] Specifically, a wafer is arbitrarily cut from the crystal to be tested; the full-spectrum X-ray diffraction pattern of the wafer cut surface is obtained and compared with the full-spectrum powder X-ray diffraction pattern of the crystal to determine the crystal plane index represented by the strongest diffraction peak in the full-spectrum X-ray diffraction pattern of the wafer. h 1 k 1 l 1); The angle between the crystal plane to which the strongest diffraction peak belongs and the wafer cutting plane is determined using a conventional X-ray orientation instrument. The crystal plane index is then cut by adjusting the cutting angle. h 1 k 1 l 1) wafer; select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h 2 k 2l 2) and crystal planes ( h 1 k 1 l 1) The principle is to minimize the included angle between crystal planes, and the crystal planes are determined using a conventional X-ray orientation instrument. h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The direction of the intersection line [ uvw ]; utilizing crystal planes ( h 1 k 1 l 1) The direction of the intersection of the two crystal planes [ uvw This allows us to determine the three-dimensional orientation of the crystal.

[0012] As one specific implementation method, the method includes:

[0013] (1) Cut a wafer arbitrarily from the crystal to be tested;

[0014] (2) Obtain the full-spectrum X-ray diffraction pattern of the wafer's cut surface and compare it with the full-spectrum powder X-ray diffraction pattern of the crystal to determine the crystal plane index represented by the strongest diffraction peak in the full-spectrum X-ray diffraction pattern of the wafer. h 1 k 1 l 1);

[0015] (3) The crystal plane to which the strongest diffraction peak belongs is obtained using a conventional X-ray diffraction instrument. h 1 k 1 l 1) The angle between the wafer and the cutting surface is adjusted by cutting the crystal plane index as follows: h 1 k 1 l 1) of the chip;

[0016] (4) Select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The principle is to minimize the included angle between crystal planes, and the crystal planes are determined using a conventional X-ray orientation instrument. h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The direction of the intersection line [ uvw ];

[0017] (5) Utilizing crystal planes ( h 1 k 1 l 1) The three-dimensional orientation of a crystal can be obtained by finding the intersection direction of the two crystal planes.

[0018] In this application, the crystal plane index is referred to as ( hkl () indicates that different crystal planes are represented by different subscripts.

[0019] Optionally, the crystal to be tested is a single crystal without a natural growth surface, that is, the crystal to be tested is a large single crystal without a natural growth surface, and the three-dimensional crystal orientation of the crystal cannot be directly determined by the natural growth surface, such as cylindrical crystals grown by the Czochralski method or the crucible lowering method.

[0020] Optionally, the crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The crystal plane angle δ satisfies:

[0021] Triclinic crystal system: S 11 h 1 h 2+ S 22 k 1 k 2+ S 33 l 1 l 2+ S 23 ( k 1 l 2 + k 2 l 1) + S 13 ( l 1 h 2+ l 2 h 1)+ S 12 ( k 1 h 2+ h 1 k 2)],

[0022] in S 11 = b 2 c 2 sin2 α ; S 22 = a 2 c 2 sin 2 β ; S 33 = a 2 b 2 sin 2 γ ; S 12 = abc 2 ( cosα cosβ - cosγ ); S 23 = a 2 bc ( cosβ cosγ - cosα ); S 13 = ab 2 c ( cosα cosγ - cosβ );

[0023] Monoclinic system: ;

[0024] Orthorhombic crystal system: ;

[0025] Trigonal crystal system: ;

[0026] Tetragonal crystal system: ;

[0027] Hexagonal crystal system: ;

[0028] Cubic crystal system: ;

[0029] Where a, b, c, α, β, and γ are unit cell parameters. d 1. d 2 is a crystal plane ( h 1 k 1 l 1) and crystal planes ( h 2 k 2 l 2) The interplanar spacing, where V is the unit cell volume;

[0030] Triclinic, monoclinic, orthorhombic, trigonal, tetragonal, hexagonal, and cubic are the crystal systems of the crystal to be tested.

[0031] Optionally, the crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The direction of the intersection line [ uvw ]satisfy:

[0032] u = k 1 l 2 – l 1 k 2;

[0033] v = l 1 h 2 – h 1 l 2;

[0034] w = h 1 k 2 – k 1 h 2.

[0035] Optionally, the crystal plane ( h 1 k 1 l 1) and crystal orientation index [ uvw This allows us to determine the three-dimensional orientation of the crystal.

[0036] Optionally, the crystal plane ( h 2 k 2 l The selection of 2) satisfies: or ;

[0037] Where θ2 is the crystal plane ( h 2 k 2 l 2) The diffraction angle;

[0038] δ is the crystal plane ( h 1 k 1 l 1) with crystal planes ( h 2 k 2 l 2) The included angle;

[0039] φ is the range of the sample rotation stage of the X-ray orientation instrument [0, φ].

[0040] Optionally, the crystal plane ( h2 k 2 l The selection of 2) satisfies:

[0041] ;

[0042] Where θ2 is the crystal plane ( h 2 k 2 l 2) The diffraction angle;

[0043] δ is the crystal plane ( h 1 k 1 l 1) with crystal planes ( h 2 k 2 l 2) The included angle;

[0044] φ is the range of the sample rotation stage of the X-ray orientation instrument [0, φ].

[0045] Specifically, the crystal plane ( h 2 k 2 l 2) The selection must satisfy the range of the X-ray orientation instrument. Let the range of the sample rotation stage of the X-ray orientation instrument be [0, φ], and the corresponding range of the signal receiver be [0, 2φ]. The crystal plane ( h 1 k 1 l 1) The diffraction angle is θ1, and the selected crystal plane ( h 2 k 2 l 2) The diffraction angle is θ2, ( h 1 k 1 l 1) face and ( h 2 k 2 l 2) If the included angle between the crystal planes is δ, then the sample stage should be positioned at θ²-δ and θ²+δ during diffraction, and this position needs to be within the range of the X-ray orientation instrument. Therefore, the selected crystal plane ( h 2 k 2 l 2) One of the following conditions must be met:

[0046]

[0047] Conversely, if the angle is too large, the X-ray orientation instrument will not be able to obtain the diffraction signal.

[0048] Optionally, the selected crystal plane ( h 2 k 2 l2) It can satisfy the above two inequalities at the same time, so that the results of the two diffraction experiments can be mutually verified, ensuring the accuracy of three-dimensional orientation.

[0049] Optionally, the selected crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The smaller the angle θ between the crystal planes, the better.

[0050] Optionally, the device for acquiring the X-ray diffraction pattern is a powder X-ray diffractometer.

[0051] Optionally, the X-ray orientation device includes: a test crystal plane fixing device, an X-ray emitting device, a signal receiving device, and an angle measuring device.

[0052] In one specific implementation, the X-ray orientation instrument is a conventional X-ray orientation instrument, equipped with a test crystal plane fixing, X-ray emission, reception, and angle measurement device. After determining a standard crystal plane that is approximately similar to the test crystal plane in advance, an X-ray diffraction experiment is conducted on the test crystal plane using the instrument to obtain the deflection angle between the test crystal plane and the standard crystal plane, thereby cutting a crystal plane that matches the standard crystal plane. This orientation instrument can only perform correction of known crystal planes and does not have the function of three-dimensional crystal orientation.

[0053] Optionally, the test crystal plane fixing device includes a 360° rotating sample stage and an orientation fixture.

[0054] As one specific implementation, the orientation device is a crystal fixing device used in conjunction with an X-ray orientation instrument. This device can not only fix the crystal to be tested, but also has a graduated rotating device that can rotate the crystal 360° around the crystal plane normal as the axis.

[0055] Another aspect of this application provides a method for processing a crystal, the method comprising: determining a target crystal plane for processing based on the three-dimensional crystal orientation of the crystal, and cutting the crystal;

[0056] The three-dimensional crystal orientation is determined according to the method described above.

[0057] The beneficial effects that this application can produce include:

[0058] The crystal orientation method provided by this invention can achieve three-dimensional orientation of crystals using a commonly used X-ray diffractometer and a conventional X-ray orientation instrument. This invention eliminates the need for expensive Laue crystal orientation instruments and avoids the cumbersome optical methods. The crystal orientation method provided by this invention features simple equipment, high efficiency, and low crystal loss. Attached Figure Description

[0059] Figure 1 This is a flowchart of the crystal orientation method provided in Embodiments 1-3 of this application;

[0060] Figure 2 These are powder X-ray diffraction patterns of the crystal samples to be tested provided in Examples 1-3 of this application;

[0061] Figure 3 These are schematic diagrams of X-ray diffraction patterns and crystal plane intersections of the wafers provided in Examples 1-3 of this application. Specifically, (a) shows the X-ray diffraction pattern of an arbitrary cut surface obtained in Example 1; (b) shows the X-ray diffraction pattern of the (111) plane after cut surface correction obtained in Example 1; (c) shows the intersection direction of the (111) and (211) planes obtained in Example 1; (d) shows the X-ray diffraction pattern of an arbitrary cut surface obtained in Example 2; (e) shows the X-ray diffraction pattern of the (211) plane after cut surface correction obtained in Example 2; (f) shows the intersection direction of the (311) and (211) planes obtained in Example 2; (g) shows the X-ray diffraction pattern of an arbitrary cut surface obtained in Example 3; (h) shows the X-ray diffraction pattern of the (110) plane after cut surface correction obtained in Example 3; and (i) shows the intersection direction of the (310) and (110) planes obtained in Example 3.

[0062] Figure 4 The crystal planes provided in Examples 1-3 of this application ( h 2 k 2 l 2) Select the schematic diagram;

[0063] Figure 5 These are schematic diagrams of the crystal orientation operation and apparatus provided in Embodiments 1-3 of this application;

[0064] Figure 6 The crystal planes provided in Examples 1-3 of this application ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) Schematic diagram of the intersection line;

[0065] Figure 7 The X-ray diffraction pattern of the standard crystal plane cut out after the three-dimensional orientation of the crystal is completed, as provided in Embodiment 1 of this application. Detailed Implementation

[0066] The present application is described in detail below with reference to the embodiments, but the present application is not limited to these embodiments.

[0067] Unless otherwise specified, the raw materials used in the embodiments of this application were all purchased through commercial channels.

[0068] In this embodiment, the X-ray powder diffractometer used is a Rigaku MiniFlex 600 benchtop X-ray powder diffractometer.

[0069] In this embodiment, the X-ray orientation instrument used is the YX-2 type X-ray crystal orientation instrument from Liaodong X-ray Instrument Co., Ltd. Its sample stage has a range of 0~60°, and the corresponding X-ray signal receiver has a range of 0~120°.

[0070] Example 1

[0071] 0.72Pb(Mg) grown by crucible descent method 1 / 3 Nb 2 / 3 O3-0.28PbTiO3 (PMN-28PT) crystals are cylindrical and lack natural crystal faces; therefore, the crystal orientation cannot be determined by the natural growth planes. The following uses... Figure 1 The steps in the crystal orientation method flowchart shown are for three-dimensional orientation of the crystal.

[0072] Step 1: Cut a wafer from the PMN-28PT crystal.

[0073] Step 2: Perform powder X-ray diffraction on the cut crystal. The resulting powder X-ray diffraction pattern is shown below. Figure 2 As shown, the values ​​were indexed. It should be noted that although PMN-28PT crystal has a trigonal crystal system, its cell parameter α is close to 90°, therefore it is also considered a pseudocubic phase. Therefore, it can be treated as a cubic crystal system during three-dimensional orientation. Simultaneously, full-spectrum X-ray diffraction was performed on the cut wafer, and the obtained X-ray diffraction pattern of the test wafer is shown below. Figure 3 As shown in Figure (a). Through Figure 2 and Figure 3 A comparison of the middle (a) figure reveals that the strongest peak in the X-ray diffraction pattern of the test wafer is the diffraction peak of the (111) plane, and the corresponding diffraction 2θ1 angle is about 39°;

[0074] Step 3: Fix the test wafer from Step 2 onto the X-ray orientation instrument and use the X-ray orientation instrument to obtain the deflection angle between the test wafer's crystal plane and the standard (111) plane. After obtaining the deflection angle, correct the cut surface of the crystal to be tested to obtain the accurate cut surface of the (111) plane. Figure 3 As shown in Figure (b).

[0075] Step 4: Select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h 2 k 2 l 2) and crystal planes ( h1 k 1 l 1) The principle is to minimize the included angle between crystal planes. Figure 4 crystal plane ( h 2 k 2 l 2) Select the schematic diagram; planes A, B, and C can all be aligned with the crystal plane ( h 1 k 1 l 1) Given that they intersect, following the principle of smaller intersecting angles between crystal planes, crystal plane A is selected as the crystal plane. h 2 k 2 l 2) is the optimal choice. In this embodiment, the crystal plane ( h 1 k 1 l 1) is the (111) plane. Calculations using the crystal plane angle formula show that the angle δ between the (111) and (100) planes is 54.7°, while the diffraction angle θ2 of the (100) plane is approximately 11°. Based on the conclusions discussed earlier regarding the range conditions of the X-ray orientation instrument, the crystal plane ( h 2 k 2 l 2) Choosing the (100) plane does not satisfy the diffraction conditions. The angle δ between the (111) and (211) planes is 19.5°, and the diffraction angle θ2 of the (211) plane is approximately 28°. θ2-δ or θ2+δ are 8.5° and 47.5° respectively, satisfying the diffraction conditions for the X-ray orientation instrument. Therefore, the (211) plane is chosen as the orientation plane. h 2 k 2 l 2). The crystal orientation index of the intersection line between plane (111) and plane (211) is [01_1]. Figure 3 As shown in Figure (c).

[0076] The crystal to be tested is fixed on the orientation fixture, which is positioned on the X-ray orientation point, such as... Figure 5 As shown. The cut surface of the crystal to be tested (111) is placed at 8.5° and 47.5° of the X-ray orientation sample position, respectively. The X-ray receiver is placed at 56° of 2θ2. The crystal is rotated 360° around the normal direction of the cut surface of the crystal to be tested (111). When the crystal is rotated to a certain angle, a diffraction signal can be received by the X-ray receiver. At this time, the direction of the intersection line between the (111) plane and the (211) plane can be determined, as shown. Figure 6 As shown.

[0077] Step 5: The three-dimensional orientation of the crystal can be determined by the crystal plane (111) and the [01_1] crystal orientation, such as... Figure 3 As shown in Figure (c). In this case, if it is necessary to cut out a single crystal element with the (100) facet, it is only necessary to rotate the (111) facet by 54.7° around the intersection line. Figure 7 The X-ray diffraction pattern of the (100) plane is determined to be the (100) plane.

[0078] Example 2

[0079] Taking PMN-28PT crystal as an example again.

[0080] Step 1: Cut a wafer from the PMN-28PT crystal.

[0081] Step 2: Perform powder X-ray diffraction on the cut crystal. The resulting powder X-ray diffraction pattern is shown below. Figure 2 As shown, the values ​​were indexed. It should be noted that although PMN-28PT crystal has a trigonal crystal system, its cell parameter α is close to 90°, therefore it is also considered a pseudocubic phase. Therefore, it can be treated as a cubic crystal system during three-dimensional orientation. Simultaneously, full-spectrum X-ray diffraction was performed on the cut wafer, and the obtained X-ray diffraction pattern of the test wafer is shown below. Figure 3 As shown in Figure (d) above. Figure 2 and Figure 3 Comparing the (d) diagram in the image, it was found that the strongest peak in the X-ray diffraction pattern of the test wafer was the diffraction peak of the (211) plane, and the corresponding diffraction 2θ1 angle was about 39°.

[0082] Step 3: Fix the test wafer from Step 2 onto the X-ray orientation instrument and use the X-ray orientation instrument to obtain the deflection angle between the test wafer's crystal plane and the standard (211) plane. After obtaining the deflection angle, correct the cut surface of the crystal to be tested to obtain an accurate cut surface of the (211) plane, such as... Figure 3 As shown in Figure (e).

[0083] Step 4: Select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The principle is to minimize the included angle of the crystal planes. In this embodiment, the crystal planes ( h 1 k 1 l 1) is the (211) plane. Calculations using the crystal plane angle formula show that the angle δ between the (311) and (211) planes is 10°, making the (311) plane a suitable choice as the crystal plane (h2k2l2). The diffraction angle θ2 of the (311) plane is approximately 39°. θ2-δ or θ2+δ are 29° and 49° respectively. The crystal orientation index of the intersection line between the (311) and (211) planes is [01_1]. Figure 3 As shown in Figure (f).

[0084] The crystal to be tested is fixed on the orientation fixture, which is then placed on the X-ray orientation instrument. Figure 5 As shown. The cut surface of the crystal to be tested (211) is placed at 29° and 49° of the X-ray orientation sample position, respectively. The X-ray receiver is placed at 78° of 2θ2, and the crystal is rotated 360° around the normal direction of the cut surface of the crystal to be tested (211). When the crystal is rotated to a certain angle, a diffraction signal can be received by the X-ray receiver. At this time, the direction of the intersection line between the (211) plane and the (311) plane can be determined, as shown. Figure 6 As shown.

[0085] Step 5: The three-dimensional orientation of the crystal can be determined by the crystal plane (211) and the [01_1] crystal orientation, such as... Figure 3 As shown in Figure (f). At this point, if it is necessary to cut out a single crystal element with the (100) facet, it is only necessary to rotate the (211) facet by 35.3° around the intersection line.

[0086] Example 3

[0087] Taking PMN-28PT crystal as an example again.

[0088] Step 1: Cut a wafer from the PMN-28PT crystal.

[0089] Step 2: Perform powder X-ray diffraction on the cut crystal. The resulting powder X-ray diffraction pattern is shown below. Figure 2 As shown, the values ​​were indexed. It should be noted that although PMN-28PT crystal has a trigonal crystal system, its cell parameter α is close to 90°, therefore it is also considered a pseudocubic phase. Therefore, it can be treated as a cubic crystal system during three-dimensional orientation. Simultaneously, full-spectrum X-ray diffraction was performed on the cut wafer, and the obtained X-ray diffraction pattern of the test wafer is shown below. Figure 3 As shown in Figure (g). Through Figure 2 and Figure 3 Comparing the (d) diagram in the image, it was found that the strongest peak in the X-ray diffraction pattern of the test wafer was the diffraction peak of the (110) plane, and the corresponding diffraction 2θ1 angle was about 31°.

[0090] Step 3: Fix the test wafer from Step 2 onto the X-ray orientation instrument and use the X-ray orientation instrument to obtain the deflection angle between the test wafer's crystal plane and the standard (110) plane. After obtaining the deflection angle, correct the cut surface of the crystal to be tested to obtain an accurate cut surface of the (110) plane, such as... Figure 3 As shown in Figure (h).

[0091] Step 4: Select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The principle is to minimize the included angle of the crystal planes. In this embodiment, the crystal planes ( h 1 k 1 l 1) is the (110) plane. Calculations using the crystal plane angle formula show that the angle δ between the (110) and (100) planes is 45°, while the diffraction angle θ2 of the (100) plane is approximately 11°. Based on the conclusions discussed earlier regarding the range conditions of the X-ray orientation instrument, the crystal plane ( h 2 k 2 l 2) Choosing the (100) plane does not satisfy the diffraction conditions. Further, considering that the angle δ between the (110) and (310) planes is 26.5°, the diffraction angle θ2 of the (310) plane is approximately 37°. θ2-δ or θ2+δ are 10.5° and 63.5° respectively, satisfying the diffraction conditions for the X-ray orientation instrument. Therefore, the (310) plane is chosen as the orientation plane. h 2 k 2 l 2). The crystal orientation index of the intersection line between plane (310) and plane (110) is

[001] . Figure 3 As shown in Figure (i).

[0092] The crystal to be tested is fixed on the orientation fixture, which is positioned on the X-ray orientation point, such as... Figure 5 As shown. The cut surface of the crystal to be tested (110) is placed at 10.5° of the X-ray orientation sample position, and the X-ray receiver is placed at 74° of 2θ2. The crystal is rotated 360° around the normal direction of the cut surface of the crystal to be tested (110). When the crystal is rotated to a certain angle, a diffraction signal can be received by the X-ray receiver. At this time, the direction of the intersection line between the (310) plane and the (110) plane can be determined, as shown. Figure 6 As shown.

[0093] Step 5: The three-dimensional orientation of the crystal can be determined by the crystal plane (110) and the

[001] crystal orientation, such as... Figure 3 As shown in Figure (i). At this point, if it is necessary to cut out a single crystal element with the (100) facet, it is only necessary to rotate the (100) facet 45° around the intersection line.

[0094] The above three embodiments demonstrate three typical cases of crystal three-dimensional orientation using this method. In actual operation, three-dimensional orientation can also be completed in other cases by following the basic orientation steps described in this method. For example, Table 1 provides orientation data for several other known (h1k1l1) planes of PMN-28PT single crystal for reference, which will not be described in detail here.

[0095] Table 1. Reference data for PMN-28PT monocrystalline orientation

[0096]

[0097] The above description is merely a few embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for three-dimensional orientation of a crystal, characterized in that, The method includes: (1) Cut the test wafer from the crystal to be tested; (2) Obtain the X-ray diffraction pattern of the cut surface of the test wafer and compare it with the powder X-ray diffraction pattern of the crystal to be tested to determine the crystal plane represented by the strongest diffraction peak in the X-ray diffraction pattern of the test wafer. h 1 k 1 l 1); (3) The crystal plane to which the strongest diffraction peak of the test wafer belongs is obtained using an X-ray diffractometer. h 1 k 1 l 1) The angle between the test wafer and the cut surface; after obtaining the angle, the cut surface of the test wafer is corrected to obtain the crystal plane ( h 1 k 1 l 1) The cut surface; (4) Select a crystal plane ( h 2 k 2 l 2), with crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) Based on the principle that the crystal plane angle δ is relatively small, the crystal plane is determined using an X-ray orientation instrument. h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The direction of the intersection line [ uvw ]; (5) Utilizing crystal planes ( h 1 k 1 l 1) The direction of the intersection of the two crystal planes [ uvw [To obtain the three-dimensional orientation of the crystal;] The crystal plane ( h 2 k 2 l The selection of 2) satisfies: or ; Where θ2 is the crystal plane ( h 2 k 2 l 2) The diffraction angle; δ is the crystal plane ( h 1 k 1 l 1) with crystal planes ( h 2 k 2 l 2) The included angle; φ is the range of the sample rotation stage of the X-ray orientation instrument [0,φ]; The crystal plane ( h 2 k 2 l The selection of 2) satisfies: ； Where θ2 is the crystal plane ( h 2 k 2 l 2) The diffraction angle; δ is the crystal plane ( h 1 k 1 l 1) with crystal planes ( h 2 k 2 l 2) The included angle; φ is the range of the sample rotation stage of the X-ray orientation instrument [0, φ].

2. The method for three-dimensional crystal orientation according to claim 1, characterized in that, The crystal to be tested is a single crystal without a natural growth surface.

3. The method for three-dimensional crystal orientation according to claim 1, characterized in that, The crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The crystal plane angle δ satisfies: Triclinic crystal system: S 11 h 1 h 2+ S 22 k 1 k 2 + S 33 l 1 l 2 + S 23 ( k 1 l 2 + k 2 l 1) + S 13 ( l 1 h 2 + l 2 h 1) + S 12 ( k 1 h 2 + h 1 k 2)], in 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 ( cosα cosβ - cos γ ); S 23 = a 2 bc ( cosβ cosγ - cosα ); S 13 = ab 2 c ( cosα cosγ - cosβ ); Monoclinic system: ; Orthorhombic crystal system: ; Trigonal crystal system: ; Tetragonal crystal system: ; Hexagonal crystal system: ; Cubic crystal system: ; Where a, b, c, α, β, and γ are unit cell parameters. d 1. d 2 is a crystal plane ( h 1 k 1 l 1) and crystal planes ( h 2 k 2 l 2) The interplanar spacing, where V is the unit cell volume; Triclinic, monoclinic, orthorhombic, trigonal, tetragonal, hexagonal, and cubic are the crystal systems of the crystal to be tested.

4. The method for three-dimensional crystal orientation according to claim 1, characterized in that, The crystal plane ( h 2 k 2 l 2) and crystal planes ( h 1 k 1 l 1) The direction of the intersection line [ uvw ]satisfy: 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。 5. The method for three-dimensional crystal orientation according to claim 1, characterized in that, The device for acquiring the X-ray diffraction pattern is a powder X-ray diffractometer.

6. The method for three-dimensional crystal orientation according to claim 1, characterized in that, The X-ray orientation instrument includes: a test crystal plane fixing device, an X-ray emitting device, a signal receiving device, and an angle measuring device.

7. The method for three-dimensional crystal orientation according to claim 6, characterized in that, The test crystal plane fixing device includes a 360° rotating sample stage and an orientation fixture.

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