2 thoughts on “(X -ray) The farther the crystal diffraction point is, the smaller the corresponding space size (inverted space).”

Amber

The farther the original point of the crystal X -ray diffraction point is farther, the smaller the space size of the crystal! When the diffraction angle (2θ) increases, the surface spacing of the crystal surface must be reduced to meet the diffraction conditions 2dsinθ = n λ. That is, the farther the original point of the crystal X -ray diffraction point, the smaller the space corresponding to the crystal! The most important application of Easy Subcer is to use the Evald reflection ball diagram and elaborate the diffraction principle. From the first level of Prague formula 2dsinθ = λ, sinθ = (1/d)/(2/λ), that is, the 1/d and 2/λ of the 1/d and 2/λ of the sine relationship with θ, respectively. side. FIG. 1 is the famous EWALD reflection ball. This centered on sample location C, 1/λ as the radius as the garden ball, and the two points of the X -ray ACO (diameter) A and O are on the equatorial garden. The crystal surface (HKL) forms a diffraction CG to the equatorial garden at G, then AG⊥OG. ΘOag = θ, oG = 1/d. The G point is the diffraction spots that meet the Prague equation (HKL) crystal surface, and the G point must be on this sphere. This ball is called Evald's reflex. CG is the diffraction direction, and ∠OCG = 2θ is the diffraction angle. The G point can also be regarded as a point in the direction of the diffraction surface (HKL) of point O as the origin (HKL). The length of the method of this method is equal to the count of the crystal surface spacing D (HKL) of the diffraction surface (HKL) series! In this way, the elements of the poured matrix are linked to the size of the actual crystal cells. o point is the original point of Easy to make matrix! Please note that the point O, point G, and OG rotating diffraction surfaces here are composed of crystal crystal compartments as a positive line. O point is the original point of this ups and dot matrix. OG is an easy vector HHKL [H is a black body, black body represents vector].

The meaning of the ease of matrix lies in the introduction of virtual inverted space. Calcified grids that are constituted by the actual space of the crystal are called a positive matrix-the positive lattice; the Fourier transforms this positive lattice-the positive matrix change into a periodic inverted space (inverted lattice- 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 image pattern 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 can be derived from the front line of the crystal. The transformation is a kind of mathematical tool that deduced from a certain change from the front matrix of the crystal: "inverted" is the countdown, "easy" is the countdown, "easy" means Change! Easy to matrix is a set of abstract dot matrix and virtual matrix different from the real dot matrix. Just as the positive line describes the real space of the crystal, it is easy to easily describe the diffraction space of the diffraction pattern; there is a corresponding relationship between each other, which greatly simplifies the identification and analysis of the X -ray diffraction diagram spectrum. The calculation of the pattern cells. 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 put it in detail, it is difficult here, because vector type, up and down bidding, mathematical expression, etc. are difficult to correctly enter here). . 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. Vector OP from origin o to P (HKL) is called inverted vector H (HKL), [OG in the Evald reflection ball diagram mentioned above is OP here] ) Vector, the method of (HKL) crystal surface. [Understand the crystal surface index HKL as the crystal parameter of the real crystal, and the volatile vector H (HKL) in the dot matrix is perpendicular to the (HKL) vector, which is the real (HKL) crystal surface method. 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: HKL placed in the square bracket is the vector index; HKL placed in the parentheses is the crystal surface index. The ingenuity of the easy line is here: the number is unchanged! It has different meaning when appearing in the right line and the ease of matrix! ] 2, the length of the vector H (HKL) is equal to the countdown of the crystal pitch d (HKL) in the crystal matrix 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. [Note: The number of matrix is reduced by one level than the dimension of the positive matrix! 】 3, the plenty of matrix can be constructed from the positive line. The diffraction pattern is deemed to be a dot matrix of the diffraction space, and it is restored to the crystal positive line 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. The as a positive line (100) from the origin O (point line 000) is also the vertical line of the crystal surface where the B axis is located. OP | = 1/D (HKL), this vector OP = h (100) = a*, P point coordinates are easy to ease. 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: [110] (vector from the origin to the point 110) must be perpendicular to the crystal surface (110); [310] 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, the HKL nodes on the ease of the dot matrix are all on 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 cell 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 attribution of the belonging operation easily reverse. 4, the parameter relationship between the ease of the dot matrix and the positive line: (here it is difficult to enter the expression, the submission, the bidding, etc., so it can be found on the textbook.)

According to the Prague equation 2dsinθ = λ The diffraction angle increased. Under certain situations of the wavelength, the spacing of the crystal surface was relatively small to the diffraction. The smaller the D value, the larger the one/d in the inverted space ball. The original point is the original point of the upper matrix, and the diffraction point is the point corresponding to the corresponding point in the dotted matrix

AmberThe farther the original point of the crystal X -ray diffraction point is farther, the smaller the space size of the crystal!

When the diffraction angle (2θ) increases, the surface spacing of the crystal surface must be reduced to meet the diffraction conditions 2dsinθ = n λ. That is, the farther the original point of the crystal X -ray diffraction point, the smaller the space corresponding to the crystal!

The most important application of Easy Subcer is to use the Evald reflection ball diagram and elaborate the diffraction principle. From the first level of Prague formula 2dsinθ = λ, sinθ = (1/d)/(2/λ), that is, the 1/d and 2/λ of the 1/d and 2/λ of the sine relationship with θ, respectively. side.

FIG. 1 is the famous EWALD reflection ball.

This centered on sample location C, 1/λ as the radius as the garden ball, and the two points of the X -ray ACO (diameter) A and O are on the equatorial garden. The crystal surface (HKL) forms a diffraction CG to the equatorial garden at G, then AG⊥OG. ΘOag = θ, oG = 1/d. The G point is the diffraction spots that meet the Prague equation (HKL) crystal surface, and the G point must be on this sphere. This ball is called Evald's reflex. CG is the diffraction direction, and ∠OCG = 2θ is the diffraction angle. The G point can also be regarded as a point in the direction of the diffraction surface (HKL) of point O as the origin (HKL). The length of the method of this method is equal to the count of the crystal surface spacing D (HKL) of the diffraction surface (HKL) series! In this way, the elements of the poured matrix are linked to the size of the actual crystal cells.

o point is the original point of Easy to make matrix!

Please note that the point O, point G, and OG rotating diffraction surfaces here are composed of crystal crystal compartments as a positive line. O point is the original point of this ups and dot matrix. OG is an easy vector HHKL [H is a black body, black body represents vector].

The meaning of the ease of matrix lies in the introduction of virtual inverted space. Calcified grids that are constituted by the actual space of the crystal are called a positive matrix-the positive lattice; the Fourier transforms this positive lattice-the positive matrix change into a periodic inverted space (inverted lattice- 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 image pattern 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 can be derived from the front line of the crystal. The transformation is a kind of mathematical tool that deduced from a certain change from the front matrix of the crystal: "inverted" is the countdown, "easy" is the countdown, "easy" means Change! Easy to matrix is a set of abstract dot matrix and virtual matrix different from the real dot matrix. Just as the positive line describes the real space of the crystal, it is easy to easily describe the diffraction space of the diffraction pattern; there is a corresponding relationship between each other, which greatly simplifies the identification and analysis of the X -ray diffraction diagram spectrum. The calculation of the pattern cells.

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 put it in detail, it is difficult here, because vector type, up and down bidding, mathematical expression, etc. are difficult to correctly enter here).

. 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. Vector OP from origin o to P (HKL) is called inverted vector H (HKL), [OG in the Evald reflection ball diagram mentioned above is OP here] ) Vector, the method of (HKL) crystal surface. [Understand the crystal surface index HKL as the crystal parameter of the real crystal, and the volatile vector H (HKL) in the dot matrix is perpendicular to the (HKL) vector, which is the real (HKL) crystal surface method. 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: HKL placed in the square bracket is the vector index; HKL placed in the parentheses is the crystal surface index. The ingenuity of the easy line is here: the number is unchanged! It has different meaning when appearing in the right line and the ease of matrix! ]

2, the length of the vector H (HKL) is equal to the countdown of the crystal pitch d (HKL) in the crystal matrix 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. [Note: The number of matrix is reduced by one level than the dimension of the positive matrix! 】

3, the plenty of matrix can be constructed from the positive line. The diffraction pattern is deemed to be a dot matrix of the diffraction space, and it is restored to the crystal positive line 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.

The as a positive line (100) from the origin O (point line 000) is also the vertical line of the crystal surface where the B axis is located. OP | = 1/D (HKL), this vector OP = h (100) = a*, P point coordinates are easy to ease. 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: [110] (vector from the origin to the point 110) must be perpendicular to the crystal surface (110); [310] 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, the HKL nodes on the ease of the dot matrix are all on 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 cell 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 attribution of the belonging operation easily reverse.

4, the parameter relationship between the ease of the dot matrix and the positive line: (here it is difficult to enter the expression, the submission, the bidding, etc., so it can be found on the textbook.)

PattiAccording to the Prague equation 2dsinθ = λ

The diffraction angle increased. Under certain situations of the wavelength, the spacing of the crystal surface was relatively small to the diffraction.

The smaller the D value, the larger the one/d in the inverted space ball. The original point is the original point of the upper matrix, and the diffraction point is the point corresponding to the corresponding point in the dotted matrix