CN113916866A - Alloy material crystal structure detection method based on Raman spectrum analysis - Google Patents
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Abstract
The invention discloses an alloy material crystal structure detection method based on Raman spectrum analysis, which starts from the relationship between Raman frequency shift and doping concentration, carries out quantitative analysis on the Raman frequency shift of an alloy material under different doping concentrations according to a bond relaxation theory and a local bond average approximation theory, and establishes the relationship between the doping concentration of the alloy and coordination number, bond length and bond energy. The invention can be used for quantitatively monitoring the crystal structure in the alloy doping material; the obtained crystal structure information can be used for further researching the relation between doping concentration and physical quantities such as stress strain, forbidden bandwidth, thermal expansion coefficient and the like.
Description
Technical Field
The invention belongs to the field of material physics, and particularly relates to a method for detecting a crystal structure of an alloy material based on Raman spectrum analysis.
Background
The current methods for determining crystal structure can be divided into two major categories, direct methods and model methods. The direct method, namely directly obtaining the X-ray intensity from experiments, deducing the phase angle of a structural factor by utilizing a series of mathematical treatments, realizes the direct and automatic determination of the crystal structure, and becomes the current mainstream method for determining the small and medium molecular structures. The model method is that the symmetry, other properties and structural rules of the crystal are utilized to put forward a reasonable model for the structure to be researched, then the diffraction intensity of the crystal is calculated theoretically, the calculated value is compared with the experimental value, and the model is corrected for many times, so that the calculated value and the experimental value are as consistent as possible.
The method for mainly obtaining the structural parameters of the crystal material comprises the following steps: x-ray diffraction, electron diffraction, raman spectroscopy, and the like. When X-rays having a certain wavelength are irradiated onto a crystalline substance, the X-rays are scattered by encountering regularly arranged atoms or ions within the crystal, and the phase of the scattered X-rays is enhanced in some directions, thereby exhibiting a characteristic diffraction phenomenon corresponding to the crystal structure. An X-ray diffractometer (XRD) performs structural analysis using the Bragg equation, i.e. 2dsin θ ═ n λ, where λ is the incident ray wavelength, d is the interplanar spacing, and θ is the diffraction angle. However, the X-ray diffraction technique has a limitation on the size of the crystals to be analyzed, and even if a synchrotron radiation light source is applied, only crystals larger than a micron level can be analyzed, and the structure of the nanocrystals cannot be analyzed. The electron diffraction analysis method is based on the fluctuation of electrons. The incident electrons are elastically scattered by each atom in the sample, and the electrons (beams) elastically scattered by each atom interfere with each other and are uniformly intensified in some directions, i.e., electron diffraction waves (beams) of the sample are formed. However, electron diffraction analysis is a two-dimensional plane projection image of a three-dimensional object, and is not used for three-dimensional lattice study of materials, but is only used for determination of surface lattices. Raman spectroscopy is a scattering spectrum. The raman effect originates from molecular vibrations (and lattice vibrations) and rotations. The empirical relationship between bond distance and raman stretching frequency was demonstrated using diatomic approximation, an exponential least squares fit to correlate the measured raman frequency with the reported crystallographic bond length. But only one or a few of the bond lengths and the physical quantities associated therewith can be determined with large error.
At present, a Raman spectrum unscrambling method adopts a selection method of a pulse amplitude discriminator threshold value, a method of acquiring spectral lines with very different intensities in a segmented manner, a method of processing data in a logarithmic manner and the like to obtain a Raman spectrogram with obvious intensity contrast, and adopts calculation software to theoretically calculate the Raman spectrogram of a sample.
The technology or the method can only determine the crystal structure of a certain type of material, and the application range is narrow; moreover, these techniques or methods are only capable of determining one or a few physical quantities among the structural parameters of the crystalline material; the calculation process is complex, time-consuming and error-prone. The invention carries out spectrum decomposition on the Raman spectrum, and systematically and quantitatively analyzes the lattice structure of the alloy material under different concentrations.
Disclosure of Invention
The invention aims to provide a method for detecting a crystal structure of an alloy material based on Raman spectrum analysis, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
a Raman spectrum analysis-based alloy material crystal structure detection method is characterized in that a relationship between doping concentration and coordination number, bond length and bond energy is established by performing spectrum decomposition on a Raman phononic spectrum of an alloy material.
As a further scheme of the invention: establishing the relationship between the doping concentration and the coordination number, the bond length and the bond energy comprises the following steps:
the method comprises the following steps: expanding the Hamilton quantity corresponding to the main vibration mode in the whole phonon vibration system by a Taylor series to obtain a function relation expression delta omega of the vibration frequency shift and key parameters of the simple harmonic vibration systemx(z,dz,EzMu), comparing the third term of the Taylor series with the vibration energy, neglecting the high-order term to obtain,
can be obtained by the analysis of the dimension,
term is proportional to Ez/d2To do so
Step two: detecting the Raman frequency shift of the alloy material under different concentrations through experiments, and calculating bond parameters (coordination number, bond length and bond energy) under the corresponding Raman frequency shift through theory to obtain crystal structure parameters of the alloy material under different concentrations;
measured raman vibration frequency: omegax＝ωx(1)+Δωx(x is the doping concentration); (3)
ωx(1) as a reference point vibration frequency, the Raman frequency shift is Δ ωxCombining equations (2) and (3), the Raman frequency shift ωx(z) is related to the effective coordination number (z) as follows,
wherein,
in the formula, ωx(1) For the vibration frequency, omega, of the reference point at different concentrationsx(z) is the corresponding Raman frequency shift under different effective coordination numbers, according to the relation of coordination numbers, bond lengths and bond energies in the bond relaxation theory, as follows,
subscripts z and b represent the values for the effective coordination number and bulk value, respectively, of the nearest neighbor atoms, and the bond contraction coefficient CZRelating only to the effective coordination number, a function of the coordination number, EcohRepresents an atomic bonding energy; m represents a bond property parameter determined by the chemical bond type of the substance;
and calculating coordination numbers, bond lengths and bond energies of the alloy materials under different Raman frequency shifts according to the Raman frequency shifts under different concentrations obtained by experiments and theories, so as to obtain bond parameters of the alloy materials under different concentrations.
As a further scheme of the invention: the method comprises the following steps of carrying out quantitative analysis on the Raman spectrum to obtain alloy crystal structure parameters under different concentrations:
step A: measuring a Raman spectrum doping concentration effect diagram of the alloy material through experiments;
and B: calculating and obtaining coordination numbers under different Raman frequency shifts according to a relational expression of the Raman frequency shifts and the coordination numbers;
and C: and (3) taking a chemical bond Raman characteristic vibration mode as a bridge to obtain coordination numbers, bond lengths and bond energies under different doping concentrations.
Compared with the prior art, the invention has the beneficial effects that: the invention starts from the relation between the Raman frequency shift and the doping concentration, carries out quantitative analysis on the Raman frequency shift of the alloy material under different doping concentrations according to a bond relaxation theory and a local bond average approximate theory, and establishes the relation between the doping concentration of the alloy and the coordination number, the bond length and the bond energy.
Drawings
FIG. 1 is a graph of Sn concentration (x) versus coordination number for Ge1-xSnx doping in accordance with the present invention.
FIG. 2 is a graph of Sn concentration (x) versus bond length for Ge1-xSnx doping in accordance with the present invention.
FIG. 3 is a graph showing the relationship between Sn concentration (x) and Ge-Ge bond energy in Ge1-xSnx doping.
FIG. 4 is a graph of Si-Si bond concentration (x) versus coordination number for Ge1-xSix doping in accordance with the present invention.
FIG. 5 is a graph of Ge-Ge bond concentration (x) versus coordination number for Ge1-xSix doping in accordance with the present invention.
FIG. 6 is a graph of Si-Si bond concentration (x) versus bond length for Ge1-xSix doping in accordance with the present invention.
FIG. 7 is a graph of Ge-Ge bond concentration (x) versus bond length for Ge1-xSix doping in accordance with the present invention.
FIG. 8 is a graph of Si-Si bond concentration (x) versus bond energy for Ge1-xSix doping in accordance with the present invention.
FIG. 9 is a graph of the concentration (x) of Ge-Ge bonds versus bond energy for Ge1-xSix doping in accordance with the present invention.
FIG. 10 is a graph showing the relationship between the Zn-O concentration (x) and the coordination number in Zn1-xMnxO in the present invention.
FIG. 11 is a graph showing the relationship between the Zn1-xMnxO concentration (x) and the bond length in the present invention.
FIG. 12 is a graph showing the relationship between the Zn1-xMnxO concentration (x) and the bond energy in the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
Referring to fig. 1 to 12, in an embodiment of the present invention, a method for detecting a crystal structure of an alloy material based on raman spectroscopy establishes a relationship between the crystal structure of the alloy material and coordination number, bond length, and bond energy through raman frequency shift.
Further improvement is carried out to obtain a functional relation formula between doping concentration, Raman spectrum and bond parameter. And detecting the alloy material under different concentrations through a Raman scattering experiment to obtain corresponding Raman frequency shift. And establishing a functional relation between the Raman frequency shift and the key parameter through a key relaxation theory.
Typically, the measured raman vibration frequency consists of two parts:
ωx＝ωx(1)+Δωx (3)
x represents the doping concentration of the alloy material, omegax(1) For diatomic vibration frequencies (i.e., reference point frequencies) at different concentrations, Δ ωxIs the raman shift caused by doping.
Expanding interatomic action potential by using Taylor series to obtain a functional relation expression delta omega of the vibration frequency shift and the key parameter of the simple harmonic vibration systemx(z,dz,Ezμ). Comparing the third term of the Taylor series with the vibration energy, neglecting the high-order term
Can be obtained by the analysis of the dimension,
term is proportional to Ez/d2. While
Reference point frequency shift omegax(1) Effective coordination number and Raman frequency shift ωxThe functional relationship of (z) is as follows,
wherein,
in the formula, ωx(1) For the vibration frequency, omega, of the reference point at different concentrationsx(z) is the experimental value of Raman frequency shift at different concentrations.
In a further improvement, the Raman frequency shift is in a functional relation with the bond length and the bond energy by combining the bond relaxation theory with the equation (1). Effective coordination number (Z) using bulk materialb12) as a known parameter, in combination with the relation of effective coordination number and bond length. The bond relaxation (BOLS) theory is needed to establish the relationship between the doping concentration, the raman shift and the bond length:
subscripts z and b represent the values for the effective coordination number and bulk value, respectively, of the nearest neighbor atom. Coefficient of bond shrinkage CZIs a function of the effective coordination number only. EcohRepresents an atomic bonding energy; m represents a bond property parameter determined by the chemical bond type of the substance.
Carrying out quantitative analysis on the Raman spectrum to obtain alloy crystal structure parameters under different concentrations, and specifically comprising the following steps:
firstly, measuring a Raman spectrum doping concentration effect diagram of an alloy material through an experiment;
step two, according to a relation between the Raman frequency shift and the coordination number:
ω (1) + (ω (b) - ω (1)) × ((2 × (1+ exp ((12-z)/(8 × z))) (1)) × (1- (z-12)/12)) ═ ω (x), and effective coordination numbers at different raman shifts were calculated. And the doping concentration and the coordination number under the same Raman frequency shift are mutually corresponding; and calculating and obtaining the bond length and the bond energy under different concentrations according to the relationship between the bond relaxation theory and the coordination number.
And step three, taking the chemical bond Raman characteristic vibration mode as a bridge to obtain coordination numbers, bond lengths and bond energies under different doping concentrations.
The formula derivation process of the invention is as follows:
1. effective coordination number versus bond parameter
Key to bond relaxation theory (BOLS): the bond length (d) of the chemical bond of the low coordinating atom (z) will shrink spontaneously to be shorter and the bond energy will be stronger. The mathematical expression is as follows:
subscripts z and b represent the nearest neighbor effective coordination number and bulk number, respectively. Coefficient of bond shrinkage CZIs a function of the effective coordination number only. EcohRepresents an atomic bonding energy; m represents a chemical bond of a substanceBond property parameter of type determination.
2. Relationship between Raman spectrum and key parameter
And expanding the Hamilton quantity corresponding to the main vibration mode in the whole phonon vibration system by Fourier multiple series. Typically, the measured raman vibration frequency is:
ωx＝ωx(1)+Δωx(x is doping concentration) (3)
Omega (1) is the vibration frequency of the reference point, and the Raman frequency shift is delta omegax。
Under the condition of considering effective coordination number z, the interatomic action potential is expanded by using Taylor series, and then the functional relation between the vibration frequency shift and the bond parameter of the simple harmonic vibration system can be obtainedx(z,dz,Ezμ). Comparing the third term of the Taylor series with the vibration energy, neglecting the high-order term to obtain,
can be obtained by the analysis of the dimension,
term is proportional to Ez/d2. While
Since no chemisorption occurs, the reduced mass μm1m2/(m1+m2) Remains unchanged and is constant.
Combining equations (2) and (6), and using the bulk material effective coordination number Zb as a known parameter, one can obtain the relative Raman shifts of all Raman vibration modes, the reference point shift ωx(1) Effective coordination number and frequency shift ωx(z) the relationship between (a) and (z),
wherein
In the formula of omegax(1) For the vibration frequency, omega, of the reference point at different concentrationsx(z) is the corresponding experimental value of Raman frequency shift under different effective coordination numbers.
First, measuring Ge under different doping concentrations through experiments1-xSnxA Raman frequency shift, wherein when x is 0, the Raman frequency shift and the bond length of the Ge-Ge bond are respectively; db＝2.436nm,ω＝302cm-1And when x is 0.1, the Ge-Ge bond raman shifts to ω0.1＝293.97cm-1Bond length of d0.12.449 nm. The optimal value m of the bond property parameter of the Ge-Ge bond is 6. The effective coordination number of the bulk material is set to 12.
Second, calculating Ge under different doping concentrations1-xSnxAnd key parameters corresponding to the Raman frequency shift.
When the concentration x becomes 0.1 according to the formula (6),
Ci(z)＝2/{1+exp[(12-z)/8z]}＝d0.1/db＝2.449/2.346＝1.00534
effective coordination number: z is a radical of0.113.1211. According to the formula (2), the following results are obtained,
then, ωx(z)＝232.1071+(302-232.1071)Ax(z,zb)(cm-1)
And calculating to obtain Ge-Ge bond parameters (coordination number, bond length and bond energy) corresponding to the Raman characteristic modes at different concentrations.
And thirdly, drawing a relation graph of coordination number, bond length and bond energy of the Ge-Ge bond under Sn doping concentration by taking the Raman characteristic model of the Ge-Ge bond as a bridge, as shown in figures 1 to 3.
Method 2
First, test Ge1-xSixAnd (3) carrying out Raman frequency shift on the alloy, and obtaining the Raman frequency shift, the effective coordination number and the bond contraction coefficient when the Si concentration is 0, 0.59 and 1.
When x is 0, the Raman frequency shift, the effective coordination number and the bond contraction coefficient of the Si-Si bond are respectively; omegaSi-Si＝528.6cm-1，CNSi-Si＝12，Ci(Si-Si)＝1。
When x is 1, the Raman frequency shift, the effective coordination number and the bond contraction coefficient of the Ge-Ge bond are respectively; omegaGe-Ge＝307.1cm-1，CNGe-Ge＝12，Ci(Ge-Ge)＝1。
When x is 0.59, the Si — Si bond raman shifts to ωSi-Si(0.59)＝501.8cm-1Effective coordination number of CNSi-Si(0.59) ═ 7.277526, bond shrinkage factor Ci(Si-Si,0.59) ═ 0.95947; raman frequency shift of Ge-Ge bond to omegaGe-Ge(0.59)＝294.7cm-1Effective coordination number of CNGe-Ge(0.59) ═ 4.97344, bond shrinkage factor Ci(Ge-Ge,0.59) ═ 0.91193. The most preferable value of the bond property parameter of the Si — Si bond is m 4.8, and the most preferable value of the bond property parameter of the Ge — Ge bond is m 6. The effective coordination number of the bulk material is set to 12.
And step two, taking the experimental data of the step one as an input parameter, and substituting the input parameter into equation (2) to obtain:
by substituting the obtained ASi-Si and AGe-Ge values into equation (4), the raman reference shifts for the Si-Si and Ge-Ge bonds can be calculated:
the relation of effective coordination numbers corresponding to different Raman frequency shifts is as follows:
and calculating bond parameters (coordination number, bond length and bond energy) of the Ge-Ge bond and the Si-Si bond corresponding to the Raman characteristic modes under different concentrations.
And thirdly, drawing a relation graph of coordination numbers, bond lengths and bond energies of the Ge-Ge bond and the Si-Si bond under the Si doping concentration by taking the Raman characteristic model of the Ge-Ge bond and the Si-Si bond as a bridge, as shown in figures 4 to 9.
Method 3
First, measuring Zn under different doping concentrations through experiments1-xMnxO raman shift, wherein when x is 0, the average bond length d of Zn — O bond is 0.194nm, raman shift ω is 437cm-1, and effective coordination number CN is 12; when x is 0.09, the average bond length of the Zn — O bond is d (0.09) 0.1973nm, and the raman shift is ω (0.09) 425cm-1And the coordination number is CN (0.09) ═ 16.4841. The optimum value m of the bond property parameter of the Zn-O bond is 2.4. The effective coordination number of the bulk material is set to 12.
Second, calculating Zn under different doping concentrations1-xMnxAnd O key parameters corresponding to the Raman frequency shift.
When the concentration of 0.09 is obtained according to the formula (2),
by substituting the obtained AZn-O value into equation (4), the Raman reference shift of the Zn-O bond can be calculated:
wherein,
ωZn-O(z)＝ωZn-O(1)+[ω(zb)-ωZn-O(1)]AZn-O(z,zb)
＝406.735+(437-406.735)×AZn-O(z,zb)(cm-1)
and calculating Zn-O bond parameters (coordination number, bond length and bond energy) corresponding to the Raman characteristic modes at different concentrations.
And thirdly, drawing a relation graph of coordination number, bond length and bond energy of the Zn-O bond under the Mn doping concentration by taking the Raman characteristic model of the Zn-O bond as a bridge, as shown in the figures 5 to 12.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof.
Claims (3)
1. A method for detecting a crystal structure of an alloy material based on Raman spectrum analysis is characterized in that the relationship between doping concentration and coordination number, bond length and bond energy is established by performing spectrum decomposition on a Raman phonon spectrum of the alloy material.
2. The method for detecting the crystal structure of the alloy material based on the Raman spectrum analysis according to claim 1, wherein the establishing of the relation between the doping concentration and the coordination number, the bond length and the bond energy comprises the following steps:
the method comprises the following steps: expanding the Hamilton quantity corresponding to the main vibration mode in the whole phonon vibration system by a Taylor series to obtain a function relation expression delta omega of the vibration frequency shift and key parameters of the simple harmonic vibration systemx(z，dz，EzMu), comparing the third term of the Taylor series with the vibration energy, neglecting the high-order term to obtain,
can be obtained by the analysis of the dimension,
term is proportional to Ez/d2To do so
Step two: detecting the Raman frequency shift of the alloy material under different concentrations through experiments, and calculating bond parameters (coordination number, bond length and bond energy) under the corresponding Raman frequency shift through theory to obtain crystal structure parameters of the alloy material under different concentrations;
measured raman vibration frequency: omegax＝ωx(1)+Δωx(x is the doping concentration); (3)
ωx(1) as a reference point vibration frequency, the Raman frequency shift is Δ ωxCombining equations (2) and (3), the Raman frequency shift ωx(z) is related to the effective coordination number (z) as follows,
wherein,
in the formula, ωx(1) For the vibration frequency, omega, of the reference point at different concentrationsx(z) is the corresponding Raman frequency shift under different effective coordination numbers, according to the relation of coordination numbers, bond lengths and bond energies in the bond relaxation theory, as follows,
subscripts z and b represent the values for the effective coordination number and bulk value, respectively, of the nearest neighbor atoms, and the bond contraction coefficient CZRelating only to the effective coordination number, a function of the coordination number, EcohRepresents an atomic bonding energy; m generationThe table is a bond property parameter determined by the chemical bond type of the substance;
according to the Raman frequency shift obtained by experiments under different concentrations and the coordination numbers, bond lengths and bond energies obtained by theoretical calculation under different Raman frequency shifts, the key parameters of the alloy material under different concentrations can be obtained by taking the Raman frequency shift as a bridge according to the characteristics of the Raman frequency shift (the same Raman frequency shift corresponds to the same crystal structure).
3. The alloy material crystal structure detection method based on Raman spectrum analysis according to claim 2, wherein the Raman spectrum is quantitatively analyzed to obtain alloy crystal structure parameters at different concentrations, and the specific steps are as follows:
step A: measuring a Raman spectrum doping concentration effect diagram of the alloy material through experiments;
and B: calculating and obtaining coordination numbers under different Raman frequency shifts according to a relational expression of the Raman frequency shifts and the coordination numbers; calculating and obtaining bond length and bond energy under different concentrations according to the relationship between the bond relaxation theory and the coordination number;
and C: and (3) taking a chemical bond Raman characteristic vibration mode as a bridge to obtain coordination numbers, bond lengths and bond energies under different doping concentrations.
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