# What is the significance of the transformation of the spatial vector at a point of welfare leaves during X -ray diffraction?

Fourier transformation

### 1 thought on “What is the significance of the transformation of the spatial vector at a point of welfare leaves during X -ray diffraction?”

1. The significance lies in the introduction of virtual inverted space. Called a periodic changes in the actual space of the crystal is called a positive matrix-a positive lattice, which transforms this positive grid from Fourier transformation to the periodic of the periodic. Easy to make a line). Because the interaction between the lattice and particles (such as photons, electrons, etc.) is described by the inverted space. For example, the graphic of X -ray diffraction is actually the direct image of the poured matrix of the crystal, not the direct image of the positive line of the crystal.
The dot matrix is ​​a mathematical tool that deduced fictional mathematics from a certain changes in the front matrix of the crystal. It is a set of abstract dot matrix and virtual matrix that is different from the real dot matrix. Just as the positive line describes the real space of the crystal, the ease of the dot matrix is ​​the spatial space describing the diffraction space of the diffraction pattern; this greatly simplifies the analysis and calculation of the X -ray diffraction diagram.
I. The definition of the dot matrix: The ease of the dot matrix and the positive line of the point are the relationship. (If you talk about it again, it is difficult here, because vector type, up and down, mathematics, etc. are difficult to enter correctly).
. The relationship between easy matrix and positive matrix:
1. Each point P (HKL) in the dot matrix represents a (HKL) dot matrix plane in the crystal dot matrix. The vector OP from the origin O to P (HKL) is called the inverted vector H (HKL). Easy vector H (HKL) can be decomposed in three directions:
H (HKL) = ha* kb* lc*,
h, k, l is an integer. The direction of the crystal surface (HKL) is [HKL] (Note: The vector index is placed in the square bracket; the crystal index is placed in the bracket).
2, the length of the vector H (HKL) is equal to the countdown pitch d (HKL) in the crystal line 1/d (HKL).
Summary: A dot matrix plane (HKL) in the real crystal is a point (HKL) in the upper matrix, and the h, k in the positive dot matrix is ​​the point line of the point line of the arbitrary integer ( HK0) Corresponding to a dot matrix plane (HK0) in the backset.
3. From the positive dot matrix, you can construct the inverted dot matrix
The main point: the positive line and the pseudon matrix are easy, which can be converted to the transgence of the crystal. The diffraction pattern is deemed to be a dot matrix of the diffraction space, and it is restored to the crystal positive matrix according to the law, so as to obtain the crystal structure parameters.
Pet specific methods: Select a point O as the origin in the front matrix of the crystal, and select the three bases of the crystal of the crystal as the three base lines A, BC (ABC is black body, table vector, the same below, the same below To. AB crystal surface is perpendicular to the paper on the paper surface. (000) The plane cannot be used. The projection (001) crystal of the C = 1 crystal surface in AB plane is often used to replace the crystal surface of C = 0 (001). The other two crystal surfaces with (001) crystal surfaces are straight lines, respectively, representing (100) dot matrix and (010) dot matrix surfaces.
It from the original point O (dot line 000) as a positive line (100) is also the vertical line of the crystal surface of the B -axis to form a*axis, take | OP | = 1/D (HKL), this vector OP = H (100) = a*, P point coordinates are easy to make a dot matrix 100. Its twice, 3 times, ... are 200, 300, .... From the origin (010) from the origin (010), the vertical line of the crystal surface where the A axis is located forms the B*axis. (010) |. This B*Axis first node is easy to ease 010, and the rest is expanded in turn. As a result, the dot matrix of a periodic arrangement is the poured dot matrix plane of the crystal AB crystal surface. In this backset, each dot -matrix vector is a real crystal surface, such as:  (vector from the origin to the point 110) must be perpendicular to the crystal surface (110);  must be sure It is the method of crystal (310). When analyzing the X -ray diffraction spectrum in the future, the 310 can be attributed to the contribution of the crystal surface (310). As a result, how can the HKL nodes on the matrix matrix are in the direction of the diagram of the compressed virtual facial network index (HKL) in the cell cells in the cell. The distance of the line segment is 1/d (HKL) in the medial pitch d (HKL) in the middle of the facial system. From the mellow cell surface of the unit crystal mesh, the surface is restored to the true crystal surface of the positive line, which is exactly the (HKL) crystal surface. This is why the real crystal surface is compressed to virtual to a unit crystal cell, because this is conducive to retaining the relationship between the original meaning of the diffraction index HKL and the real crystal HKL, making the analysis and belonging easily opposite.
4, the parameter relationship between the ease of the dot matrix and the positive line: (slightly)

Scroll to Top
Scroll to Top