CN1284965C - Method for measuring phase content of Ni-base superalloy - Google Patents

Abstract

The present invention discloses a method for measuring the phase content of Ni-base high temperature alloy. The method comprises the following steps: (1), the observation surfaces of samples to be measured are burnished and polished; (2), base phases, the mixed regions of base phases with precipitated phases in a sequence structure, and the integral chemical components of test samples are respectively measured by an electronic probe; (3), statistic average values are respectively calculated for the measured data of all phases; (4), target functions of stress strain relations, which are caused by the concentration of the sub-lattice elements of the separated phases in a sequence structure and atom replacement between all elements are established; (5), constraint conditions are established; (6), a calculation program is programmed by the objective functions and the constraint conditions which are established; (7), the content of the separated phases in a sequence structure is reduced into the actual content of all phases in an alloy sample; (8), the content of carbon phases is calculated by the results. The result of the present invention is consistent to the result of a conventional chemical phase analysis method. The method largely saves time used by analysis. The present invention can be used for the important fields of the design, the technical control, the phase analysis, etc. of high temperature alloy.

Description

A kind of method of measuring nickel base high temperature alloy phase content

Technical field

The microstructure that the present invention relates to high temperature alloy is measured, and specifically, relates to the method for measuring nickel base high temperature alloy phase content.

Background technology

High temperature alloy is to make aeromotor parts and heating power and nuclear power generation part of appliance metal material the most widely.Character, form, content and distribution that the microstructure of alloy is promptly respectively formed phase have determined its mechanical behavior under high temperature and operation life.Wherein, each content of forming phase is the important microstructure parameter that alloy designs and its moulding and Technology for Heating Processing institute must considerations, is the indispensable important component part of the pairing microstructure state of best usability.Therefore, high temperature alloy design and development and use department attach great importance to mensuration and assessment to its phase content for a long time.Existing the high temperature alloy phase content is carried out assay method mainly comprise: chemical analysis, electrochemical methods and electron probing analysis method.Carry out phase content mensuration with chemistry and electrochemical methods and all relate to determining of loaded down with trivial details process of the test and test parameter, and the required test duration is longer; When using the electron probing analysis method to carry out phase constituent mensuration, though it is comparatively easy that process realizes, but maximum problem is, electron beam is beaten on tested phase particle and excite the characteristic X-ray zone around it, often comprise precipitated phase and matrix in this zone mutually, measurement result comprise simultaneously precipitated phase with its around matrix composition information mutually, therefore can't accurately obtain the composition information of tested precipitated phase in this way, thereby also can't obtain the information of tested phase content.How utilizing the electron probe process to realize easy these characteristics, is that this unfavorable factor of chemical constitution script in precipitated phase and territory, matrix phase mixture changes favorable factor into measured result, is a key of the present invention.

Summary of the invention

The object of the present invention is to provide a kind of assay method of high temperature alloy phase content, the operation of this method and calculate easy, the result is accurate.

The object of the present invention is achieved like this: at first utilize the backscattered electron imaging technique of electron probe to obtain sample ordered structure precipitated phase and matrix phase mixture territory pattern and it is carried out chemical constitution (atomic percentage of each displaced type alloying element) measure, atom body strain minimum principle when replacing between the element that proposes according to the present invention then, by setting up in two sublattices of ordered structure precipitated phase, the objective function of the caused atom body strain of displacement behavior minimum between element, and set up two contained separately constituent contents of sublattice (being sublattice concentration) sum and be 100% constraint condition respectively, in 1～100% scope, with percentage is unit, getting double figures behind the radix point is step-length, the matrix phase content is set one by one, by the programming line search computing of going forward side by side, acquisition makes objective function have the matrix phase content of minimum value, thereby can obtain the content and the pairing phase constituent of ordered structure precipitated phase in the Mixed Zone; By different ordered structure precipitated phases are carried out the measuring and calculating of said method, and carry out the conversion Calculation that alternate Mixed Zone is reduced to sample integral body, can obtain the actual content of whole each the ordered structure precipitated phase of alloy sample; In addition, according to M ₂₃C ₆Characteristics with contained metallic element kind in the MC carbonide, the matrix phase that utilization has been calculated and the content and the concentration thereof of ordered structure precipitated phase, and, can obtain the content of each carbonide phase by setting up and finding the solution the simultaneous equations that relate to above-mentioned carbide content and alloy element concentration thereof.

Technical process of the present invention and characteristics thereof:

1. specimen preparation

It is energy spectrum analysis that the present invention adopts the backscattered electron imaging pattern to carry out electron probe, before the analysis, only the metallographic sample preparation mode is polished tested sample, polish routinely, but not carrying out the reagent to sightingpiston that the microexamination of conventional secondary electron imaging pattern must carry out corrodes (concerning many alloy samples, erosion to its polished surface is a very time-consuming process, because how erosion effect directly influences the image quality of secondary electron).If corrode sample before analyzing, can influence the accuracy of composition measurement on the contrary, because the backscattered electron imaging is not to be etched difference of height (the secondary electron imaging is by this) between the tissue by sample, but lean on the component difference of its macroscopic view and microstructure.This shows that the high temperature alloy sample that is used to carry out quantitative measurement must special preparation.

2. composition measurement

With electron probe is that energy spectrometer is measured high temperature alloy ordered structure precipitated phase and the matrix Mixed Zone mutually and the average assay of sample, realizes easily also obtaining enough accuracys.

The size of ordered structure precipitated phase (as γ ' etc.) usually tens in the range scale of hundreds of nanometers, even therefore under electron microscope, can observe this class precipitated phase, but because the divergence range of the characteristic X-ray that electron beam is excited below the sample observation point (several micron) has substantially exceeded the range scale of precipitated phase particle, therefore can't accurately record the composition of this phase, the gained composition is the ordered structure precipitated phase and the matrix composition of two-phase Mixed Zone mutually, and this is the difficulty that conventional electrical probe or energy spectrum analysis can't overcome.The present invention utilizes this to put just and obtains two phase mixture compositions, while is according to the characteristics (rich Ni, Co, Fe etc. in high temperature alloy) of matrix phase constituent, on the sample sightingpiston, avoid precipitated phase and find position to carry out multiple spot and count composition measurement, to determine the average assay of matrix phase with matrix phase constituent feature.Expansion to the range of observation of sample, is carried out composition measurement to sample integral body under electron microscope, the measuring point number is got the average assay that its mean value promptly gets sample more than 3; Ordered structure precipitated phase and matrix phase mixture territory composition and matrix phase constituent have been arranged,, the ordered structure precipitated phase can have been come with matrix component separating mutually according to the following optimization measuring method of being introduced in 3.; Carbonide in the alloy sample is (as M ₂₃C ₆, MC etc.) composition need not measure, can calculate according to the following analytical method of introducing in 4., so also avoided the indeterminacy problem that is caused of dispersing owing to characteristic X-ray; Because the atom of metallic element is generally lack of alignment in the carbonide, therefore can not adopt ordered structure precipitated phase and the matrix composition method of determining and calculating of two-phase Mixed Zone mutually, and analytical algorithm has just in time solved this class problem.

3. the optimization measuring and calculating of ordered structure precipitated phase (γ ', μ) content

The ordered structure precipitated phase that obtains according to method in 2. (γ ', μ) and matrix be the compositional data of (γ) Mixed Zone and the compositional data of matrix phase (γ) mutually, realize the composition of ordered structure precipitated phase (γ ', μ) and the measuring and calculating of phase content thereof easily by optimization method of determining and calculating of the present invention, and can objectively respond the authenticity of its content, this is core of the present invention place.

Electron probe or energy spectrum analysis are mainly used to survey the chemical constitution of domain of dependence in the alloy sample usually.The present invention proposes, record two-phase Mixed Zone and matrix alloy element concentration mutually, utilize in two sublattices of ordered structure precipitated phase (γ ', μ), the caused atom body strain of displacement behavior should minimum principle between different elements, and each concentration of element sum is 100% constraint condition in the objective function of setting up corresponding atom body strain minimum and the different sublattices; According to lever law, by the content of certain step-size change matrix phase (γ), find the optimum solution that can satisfy objective function and constraint condition in the 1-100% scope, promptly get the alloy element concentration and the content thereof of ordered structure precipitated phase (γ ', μ).According to above step, no matter how various the alloying element kind is, and how complicated its character is, all can make things convenient for, calculate faithfully the content of each ordered structure precipitated phase in the alloy.

Computing method:

The optimization measuring and calculating of ordered structure precipitated phase γ ' phase content:

The γ ' that records according to electron probe and matrix be the alloy element concentration C of (γ) Mixed Zone mutually _{γ '+γ}And the alloy element concentration C of matrix phase _γ' by lever law, have

$C_{{\mathrm{\γ}}^{\′}}=\frac{C_{{\mathrm{\γ}}^{\′}+\mathrm{\γ}}-V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}}{1-V_{\mathrm{\γ}}}$

In the formula, C _{γ '}Be the alloy element concentration of γ ' phase, V _γContent for the matrix phase.Obviously, recording C _{γ '+γ}And C _γAfter, V _γBe still unknownly, but we know that a V is arranged _γ, just corresponding C _{γ '}The very corn of a subject is, works as V _γWhen why being worth, gained C _{γ '}Can make in two sublattices of the γ ' phase unit cell drift angle and the center of area, displacement center of area Ni atom and the caused atom body strain of drift angle Al atom minimum can obtain stable γ ' phase (high temperature alloy can obtain stable γ ' phase after standard solid solution+timeliness thermal treatment).Around this principle, the concentration of element of establishing the γ ' phase structure cell center of area (Ni position) and two sublattices of drift angle (Al position) is respectively (X _{γ '}) _2i-1(X _{γ '}) _2i, the body strain that atomic substitutions causes between each element is respectively ε _I-NiAnd ε _I-Al, then objective function is arranged mutually for γ ':

$f_{{\mathrm{\γ}}^{\′}}={[\frac{3}{4}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i=1}\·{\mathrm{\ϵ}}_{i-\mathrm{Ni}}+\frac{1}{4}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i}\·e_{i-\mathrm{Al}}]}^2\⇒\min$

In the formula, ${\mathrm{\ϵ}}_{i-\mathrm{Ni}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}{\mathrm{\π}\·r}_{\mathrm{Ni}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Ni}}^3}=\frac{r_i^3-r_{\mathrm{Ni}}^3}{r_{\mathrm{Ni}}^3},{\mathrm{\ϵ}}_{i-\mathrm{Al}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Ali}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Al}}^3}=\frac{r_i^3-r_{\mathrm{Al}}^3}{r_{\mathrm{Al}}^3},$

γ _iAtomic radius for element i.The middle mutually sublattice concentration of element (X of γ ' _{γ '}) _2iWith this mutually each concentration of element be phase constituent C _{γ '}The pass be:

${\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i}=[4C_{{\mathrm{\γ}}^{\′}}^T-3{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i-1}]$

In the formula, C _{γ '} ^TBe C _{γ '}Transposed matrix.

The optimization measuring and calculating of ordered structure precipitated phase μ phase content:

Contain the μ phase time in nickel base superalloy to be determined, similar with γ ' situation mutually, the μ that records according to electron probe and matrix be the alloy element concentration C of (γ) Mixed Zone mutually _μ+γAnd the alloy element concentration C of matrix phase _γ,, have by lever law

$C_{\mathrm{\μ}}=\frac{C_{\mathrm{\μ}+\mathrm{\γ}}-V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}}{1-V_{\mathrm{\γ}}}$

Objective function about the μ phase is:

$f_{\mathrm{\μ}}={[\frac{7}{13}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{\mathrm{\μ}}\right)}_{2i=1}\·{\mathrm{\ϵ}}_{i-\mathrm{Fe}}+\frac{6}{13}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{\mathrm{\μ}}\right)}_{2i}\·e_{i-\mathrm{Mo}}]}^2\⇒\min$

ε in the formula _I-FeAnd ε _I-MoRepresent in middle mutually Fe position of μ and the Mo position sublattice different element i atomic substitutions Fe and the caused body strain of displacement Mo atom respectively:

${\mathrm{\ϵ}}_{i-\mathrm{Fe}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}{\mathrm{\π}\·r}_{\mathrm{Fe}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Fe}}^3}=\frac{r_i^3-r_{\mathrm{Fe}}^3}{r_{\mathrm{Fe}}^3},{\mathrm{\ϵ}}_{i-\mathrm{Mo}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Mo}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Mo}}^3}=\frac{r_i^3-r_{\mathrm{Mo}}^3}{r_{\mathrm{Mo}}^3}$

In the formula, γ _iAtomic radius for element i.The middle mutually sublattice concentration of element (X of μ _μ) _2iWith this mutually each concentration of element be phase constituent C _μThe pass be:

${\left(X_{\mathrm{\μ}}\right)}_{2i}=[\frac{13}{6}\·C_{\mathrm{\μ}}^T-\frac{7}{6}{\·\left(X_{\mathrm{\μ}}\right)}_{2i-1}]$

In the formula, C _μ ^TBe C _μTransposed matrix.

Constraint condition: the sublattice concentration of element sum of each ordered structure precipitated phase is 100% in above-mentioned objective function; The concentration change scope of every kind of element between 0～100%, that is, and 0≤X _2i-1, X _2i≤ 100%.

Computation process: objective function (f) and the constraint condition (Constr) set up are compiled into calculation procedure, with each ordered structure precipitated phase in the sample that obtains of measuring and calculating as stated above (γ ', μ etc.) and the matrix chemical constitution mean value C of (γ) mixed zone mutually _{J+ γ}(C _{J+ γ}Subscript represent different ordered structure precipitated phase j and the matrix mixed zone that constitutes of γ mutually, wherein j represents γ ' or μ phase) with the matrix chemical constitution (C of (γ) mutually _γ) operation program of substitution correspondence respectively; For the satisfied score value that respectively coordinates of result of calculation is reached with percentage is unit, keeps double-digit precision behind the radix point, and successively setting unit is 1%, 0.1% and 0.01% matrix phase content variable (V _γ) step-length, promptly change V in the calculation procedure in proper order by above step-length _γValue finds the V that can make objective function (f) reach minimum value in calculating process _γBe worth, promptly get the concentration (X of two sublattices in the precipitated phase _2i-1, X _2i), and the actual chemical constitution (C of acquisition ordered structure precipitated phase _{γ '}, C _μ) and the mixed zone in the content (100%-V of precipitated phase _γ).

Be two-phase content separately in the ordered structure precipitated phase that records under the electron probe and the territory, matrix phase mixture by above-mentioned measuring method gained, need calculate by following reduction and make them become the actual content of above-mentioned each phase in the alloy sample:

(V _γ′) _real＝(V _γ′) _calc.·(V _γ′+γ)，

(V _μ) _real＝(V _μ) _calc.·(V _μ+γ)

In the following formula, (V _{γ '}) _Real(V _μ) _RealBe respectively γ ' and μ actual content mutually in the sample; (V _{γ '}) _Calc.(V _μ) _Calc.Be respectively and calculate γ ' and μ content mutually in the gained mixed zone; (V _{γ '+γ}) and (V _μ+γ) be respectively the experiment the γ ' that surveys with γ mixed zone and μ and γ mixed zone shared separately content in alloy sample.

4. carbonide (M ₂₃C ₆, MC) analytical Calculation of phase content

If carbonide only is M in the alloy ₂₃C ₆Or MC, then deduct ordered structure precipitated phase through preceding method measuring and calculating gained (γ ', μ) and matrix (γ) content (V mutually with 100% _{γ '}, V _μAnd V _γ), all the other are M ₂₃C ₆Or the content (V of MC _M23C6Or V _MC); If carbonide comprises M simultaneously in the alloy ₂₃C ₆And MC, then earlier according to the composition characteristic of MC carbonide, calculate its content (V _MC), then with the 100% content (V that deducts all known phases _{γ '}, V _μ, V _γ, V _MC), surplus is M ₂₃C ₆Content, its algorithm main points are as follows: because M ₂₃C ₆In do not contain Ti and Nb, therefore in the simultaneous equations that contain Ti and Nb, do not relate to M ₂₃C ₆Carbonide; The composition characteristic of MC carbonide is, metallic element M is Ti or Nb, or Ti and Nb coexistence, on whether containing Ti in the alloy and Nb decides; When containing Ti or Nb element in the alloy, its concentration is C ^M, for carbonide MC, its concentration is C _MC ^M, M represents Ti or Nb, because when using lever law to calculate each phase content, every kind of element is the calculating formula of a corresponding lever law all, and then only containing a known variables is carbide content (V _MC) equation, promptly

$C^M=V_{{\mathrm{\γ}}^{\′}}{C}_{{\mathrm{\γ}}^{\′}}^M+V_{\mathrm{\μ}}\·C_{\mathrm{\μ}}^M+V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}^M+V_{\mathrm{MC}}{\·C}_{\mathrm{MC}}^M$

In the formula $C_{\mathrm{MC}}^M=1,$ So:

$V_{\mathrm{MC}}=C^M-V_{{\mathrm{\γ}}^{\′}}\·C_{{\mathrm{\γ}}^{\′}}^M-V_{\mathrm{\μ}}\·C_{\mathrm{\μ}}^M-V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}^M$

Because the ordered structure precipitated phase (γ ', μ) and matrix mutually the content and the concentration (composition) thereof of (γ) be known, therefore, will can try to achieve the content (V of carbonide MC after the known quantity substitution _MC ^M), then, by the method that 4. begins to introduce promptly can be regarded as M ₂₃C ₆Content V _M23C6When containing Ti and Nb simultaneously in the alloy, then have the simultaneous equations of two lever laws and Ti and Nb percentage composition and expression formula, can obtain the percentage composition (V of this carbonide (MC) by the group of solving an equation _MC), then, by the method that 4. begins to introduce promptly can be regarded as M ₂₃C ₆Content V _M23C6

Embodiment

Method of the present invention may further comprise the steps:

1. the metallographic sample preparation mode is polished the tested sample sightingpiston, polish routinely;

2. under electron probe, select the backscattered electron imaging pattern, survey matrix phase and the chemical constitution of matrix respectively with ordered structure precipitated phase Mixed Zone and sample integral body, matrix mutually respectively is no less than 5 (as 10) with the measuring point number of matrix and ordered structure precipitated phase Mixed Zone, the measuring point number of sample integral body is no less than 3 (in theory, many more its results of measuring point number are accurate more);

3. above-mentioned matrix phase, matrix are carried out statistical average respectively with the determination data of ordered structure precipitated phase Mixed Zone and sample integral body, obtain matrix phase and the assembly average (as mathematics mean value) of matrix respectively with each ordered structure precipitated phase Mixed Zone and sample overall chemical composition;

4. set up the sublattice concentration of element (X that relates to the ordered structure precipitated phase _2i+1, X _2i) and each element between the objective function (f) of the body strain relation that causes of atomic substitutions:

Objective function about γ ' phase: $f_{{\mathrm{\γ}}^{\′}}={[\frac{3}{4}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i=1}\·{\mathrm{\ϵ}}_{i-\mathrm{Ni}}+\frac{1}{4}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i}\·e_{i-\mathrm{Al}}]}^2\⇒\min$

In the formula, (X _{γ '}) _2i-1, (X _{γ '}) _2i, ε _I-NiAnd ε _I-AlAs described above;

All contain orderly structure precipitated phase γ ' phase in all nickel base superalloys, what have also contains the μ phase, and what have does not contain the μ phase.In nickel base superalloy to be determined, contain the μ phase time, about the objective function of μ phase:

$f_{\mathrm{\μ}}={(\frac{7}{13}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{\mathrm{\μ}}\right)}_{2i-1}\·{\mathrm{\ϵ}}_{i-\mathrm{Fe}}+\frac{6}{13}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{\mathrm{\μ}}\right)}_{2i}\·{\mathrm{\ϵ}}_{i-\mathrm{Mo}})}^2\⇒\min$

(X in the formula _{γ '}) _2i-1, (X _{γ '}) _2i, ε _I-FeAnd ε _I-MoAs described above;

5. constraint condition: the sublattice concentration of element sum of each ordered structure precipitated phase is 100% in above-mentioned objective function; The concentration change scope of every kind of element between 0～100%, that is, and 0≤X _2i-1, X _2i≤ 100%;

6. utilize the optimization toolbox programming of general-purpose computations software Matlab 6.0, objective function (f) and the constraint condition set up are compiled into calculation procedure, and each ordered structure precipitated phase in the sample that will obtain by above-mentioned steps (γ ', μ) and matrix be the chemical constitution mean value C of (γ) mixed zone mutually _{J+ γ}With the matrix chemical constitution (C of (γ) mutually _γ) operation program of substitution correspondence respectively; Elder generation's setting unit is 1% matrix phase content variable (V _γ) step-length, change the V in the calculation procedure _γValue promptly gets 1%, 2%, 3% respectively ... 99%, find the V that can make objective function (f) reach minimum value by above-mentioned formula _γValue; Press this method again at this V _γOn the value basis again setting unit be that the step-length of 0.1% matrix phase content variable is (for example, if the V that obtains by previous step _γValue is 5%, then gets 4.1%, 4.2% respectively ... 4.9%, 5.1%, 5.2% ... 5.9%), finds the V that can make objective function (f) reach minimum value _γValue (promptly is accurate to this V _γBehind the radix point of percentage of value the 1st); At last, by this method V of the 1st after this is accurate to radix point _γOn value (is unit with the percentage) basis again setting unit be the step-length of 0.01% matrix phase content variable, find the 2nd the V of being accurate to behind the radix point that can make objective function (f) reach minimum value _γValue (is unit with percentage); So promptly get the concentration (X of two sublattices in the precipitated phase _2i-1, X _2i), and the actual chemical constitution (C of acquisition ordered structure precipitated phase _{γ '}, C _μ) and the mixed zone in the content (100%-V of precipitated phase _γ);

7. the reduction of ordered structure precipitated phase content is calculated: calculating to make to reduce by two-phase content separately in the ordered structure precipitated phase that records under the above-mentioned steps gained electron probe and the territory, matrix phase mixture by following reduction becomes above-mentioned each actual content mutually in the alloy sample:

(V _γ′) _real＝(V _γ′) _calc.·(V _γ′+γ)，

(V _μ) _real＝(V _μ) _calc.·(V _μ+γ)

In the following formula, (V _{γ '}) _Real, (V _μ) _Real, (V _{γ '+γ}) and (V _μ+γ) as described above;

8. carbonide (M ₂₃C ₆, MC) analytical Calculation of phase content:

If carbonide only is M in the alloy to be measured ₂₃C ₆Or MC, then with 100% ordered structure precipitated phase and the matrix phase content that deducts through preceding method measuring and calculating gained, all the other are M ₂₃C ₆Or the content of MC;

If carbonide comprises M simultaneously in the alloy to be measured ₂₃C ₆And MC, utilize M ₂₃C ₆Generally do not contain the characteristics of Ti, Nb in the carbonide, and the characteristics (only need consider during calculating that metallic element gets final product) that generally only contain Ti and/or Nb (here " or " Ti and Nb in the expression alloy have only one) in the MC carbonide; If contain Ti and Nb in the alloy simultaneously, then use lever law:

$C^{\mathrm{Ti}}=V_{{\mathrm{\γ}}^{\′}}\·C_{{\mathrm{\γ}}^{\′}}^{\mathrm{Ti}}+V_{\mathrm{\μ}}{C}_{\mathrm{\μi}}^{\mathrm{Ti}}+V_{\mathrm{MC}}\·(1-C_{\mathrm{MC}}^{\mathrm{Nb}})+V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}^{\mathrm{Ti}}$

$C^{\mathrm{Nb}}=V_{{\mathrm{\γ}}^{\′}}\·C_{{\mathrm{\γ}}^{\′}}^{\mathrm{Nb}}+V_{\mathrm{\μ}}{C}_{\mathrm{\μi}}^{\mathrm{Nb}}+V_{\mathrm{MC}}\·C_{\mathrm{MC}}^{\mathrm{Nb}}+V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}^{\mathrm{Nb}}$

In the following formula, C ^TiAnd C ^NbThe concentration (for known quantity) of representing Ti and Nb in the alloy respectively, $1-C_{\mathrm{MC}}^{\mathrm{Nb}}=C_{\mathrm{MC}}^{\mathrm{Ti}},$ Oneself amount of knowing (V with other _{γ '}C _{γ '} ^Ti, C _{γ '} ^Nb, V _μ, C _μ ^Nb, C _μ ^Nb, V _γ, C _γ ^TiAnd C _γ ^Nb) the above-mentioned Simultaneous Equations of substitution, can try to achieve the content V of MC carbonide _MC(M among the MC can be Ti and Nb, or Ti or Nb, on whether having Ti and/or Nb in the alloy decides), then, with the 100% content (V that deducts all known phases _{γ '}, V _μ, V _γAnd V _MC), promptly get M ₂₃C ₆Content V _M23C6

If Ti in the alloy and Nb have only one, the equation of lever law is arranged then:

$C^M=V_{{\mathrm{\γ}}^{\′}}\·C_{{\mathrm{\γ}}^{\′}}^M+V_{\mathrm{\μ}}\·C_{\mathrm{\μ}}^M+V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}^M+V_{\mathrm{MC}}\·C_{\mathrm{MC}}^M$

In the formula, C ^MBe the concentration of Ti in the alloy or Nb, M represents Ti or Nb, $C_{\mathrm{MC}}^M=1$ (be among the MC metallic element have only Ti or Nb), so, $V_{\mathrm{MC}}=C^M-V_{{\mathrm{\γ}}^{\′}}\·C_{{\mathrm{\γ}}^{\′}}^M-V_{\mathrm{\μ}}\·C_{\mathrm{\μ}}^M-V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}^M$

Because the ordered structure precipitated phase (γ ', μ) and matrix mutually the content and the concentration (composition) thereof of (γ) be known, therefore, will promptly try to achieve the content (V of carbonide MC after the known quantity substitution _MC ^M), then, with the 100% content (V that deducts all known phases _{γ '}, V _μ, V _γAnd V _MC), promptly get M ₂₃C ₆Content V _M23C6

Example:

Be example with the used nickel-base high-temperature alloy material GH163 of aeroengine components, GH150 and GH652 respectively, the result who the inventive method and chemofacies analytical approach is carried out the phase content analysis compares.This example is chemofacies to be analyzed measured ordered structure precipitated phase content and matrix phase content carry out arithmetic and mix (concrete mode: (V _j) _{J+ γ}=V _j/ (V _j+ V _γ)), and with chemofacies analyze in the measured ordered structure precipitated phase each concentration of element (chemical constitution) and matrix mutually in each concentration of element (chemical constitution) mix (concrete mode: $C_{j+\mathrm{\γ}}^i={\left(V_j\right)}_{j+\mathrm{\γ}}\·C_j^i+[1-{\left(V_j\right)}_{j+\mathrm{\γ}}]\·C_{\mathrm{\γ}}^i,$ Be lever law), so obtain ordered structure precipitated phase j (γ ', μ) and the matrix phase content (V of ordered structure precipitated phase j in (γ) Mixed Zone (γ ', μ) mutually respectively _j) _{J+ γ}And the concentration C of element i in the Mixed Zone _{J+ γ} ⁱ(this promptly be equivalent to electron probe following two phase contents of each ordered structure precipitated phase and matrix phase mixture of surveying and the troubled water of composition thereof), 4.～7. carrying out the ordered structure precipitated phase by embodiment then calculates with matrix calculating and reduction mutually, and 8. carrying out the analytical Calculation of carbonide phase by embodiment, its result lists in the table 1.

Example is 1.: chemofacies the analysis showed that, contains γ ', M in the GH163 alloy ₂₃C ₆And γ.According to GH163 alloy sample chemical analysis gained γ ' in the table 1 and γ phase content (being measured value) and mutually and the alloy sample chemical constitution according to the GH163 alloy sample chemical analysis gained γ ' in the table 2 and γ, carry out mixing of γ ' and γ two-phase phase content and phase constituent thereof by the concrete mode of first section description of example, carry out the calculating and the reduction calculating of γ ' and γ phase phase content then by embodiment step 4.～7., promptly obtain the actual content of this two-phase, and 8. carry out carbonide phase M by embodiment ₂₃C ₆Analytical Calculation, be about to 100% and deduct reduction and calculate gained γ ' and γ actual phase content mutually, its surplus is M ₂₃C ₆Content.Table 1 has been listed the measuring and calculating value of each phase content of GH163 alloy sample, and measuring and calculating value as can be seen and measured value have well identical.

Table 1 GH163 alloy sample phase content chemofacies is analyzed the measuring and calculating value of measured value and the inventive method

The GH163 alloy sample	Data Source	Phase content, %
					γ′	M 23C 6	γ
		1	The actual measurement measuring and calculating	9.08 9.13				0.74 0.74	90.18 90.13
2	The actual measurement measuring and calculating				9.22 9.24	0.73 0.74	90.04 90.02
		3	The actual measurement measuring and calculating	7.81 7.84				0.76 0.76	91.43 91.40

Table 2 GH163 alloy sample and each phase chemistry composition (concentration of element) thereof

Sample	Measurand	Chemical constitution, atomic percentage %
									Ni	Co	Cr	Ti	Mo	Al	Si
		1	Alloy (C M) γ′(C γ′) M 23C 6 (C M23C6) γ(C γ)	50.77 65.98 6.47 49.60	19.77 8.27 6.77 21.04	17.61 10.24 43.48 18.14	1.82 10.06 15.95 0.87	9.76 4.16 27.33 10.18								0.19 1.28 0.00 0.08	0.08 0.00 0.00 0.08
2	Alloy (C M) γ′(C γ′) M 23C 6 (C M23C6) γ(C γ)								50.77 66.29 4.34 49.56	19.77 8.20 5.58 21.08	17.61 9.40 51.02 18.18	1.82 10.83 9.83 0.83	9.76 4.02 29.24 10.19	0.19 1.25 0.00 0.09	0.08 0.00 0.00 0.08
		3	Alloy (C M) γ′(C γ′) M 23C 6 (C M23C6) γ(C γ)	50.77 66.34 4.85 49.82	19.77 8.60 5.52 20.85	17.61 9.10 53.37 18.04	1.82 10.92 8.86 0.98	9.76 3.71 27.40 10.13								0.19 1.33 0.00 0.10	0.08 0.00 0.00 0.08

Example is 2.: chemofacies the analysis showed that, contains γ ', MC, μ and γ in the GH150 alloy mutually.According to GH150 alloy sample chemical analysis gained γ ' in the table 3, μ and γ phase content (being measured value), and according to the GH150 alloy sample chemical analysis gained γ ' in the table 4, μ and γ are mutually and the chemical constitution of alloy sample integral body, carry out γ ' and γ phase content by the concrete mode of first section description of example, μ and γ phase content, and γ ' and γ phase constituent mutually, μ and the γ mixing of phase constituent mutually, carry out the calculating and the reduction calculating of ordered structure precipitated phase phase content then by embodiment step 4.～7., obtain γ ', the actual content of μ and γ phase, and 8. carry out the analytical Calculation of carbonide phase MC content by embodiment, be about to 100% and deduct reduction calculating gained γ ', the actual phase content of μ and γ phase, its surplus is the content of MC.Table 3 has been listed the measuring and calculating value of each phase content of GH150 alloy sample, and measuring and calculating value as can be seen and measured value have good coincideing.

Table 3 GH150 alloy sample phase content chemofacies is analyzed the measuring and calculating value of measured value and the inventive method

The GH150 alloy sample	Data Source	Phase content, %
						γ′	MC	μ	γ
		1	The actual measurement measuring and calculating	12.46 11.77	0.24 0.22					0.15 0.17	87.15 87.84
2	The actual measurement measuring and calculating					6.33 5.60	0.24 0.99	2.23 2.48	91.19 90.93
		3	The actual measurement measuring and calculating	5.85 5.40	0.24 0.41					2.77 3.09	91.13 91.10

Table 4 GH150 alloy sample and each phase chemistry composition (concentration of element) thereof

Sample	Measurand	Chemical constitution, atomic percentage %
										Al	Ti	Nb	W	Mo	Ni	Cr	Fe
		1	Alloy (C M) γ′(C γ′) MC (C MC) μ(C μ) γ(C γ)	2.06 8.89 0.00 0.00 1.09	2.49 13.61 71.96 0.00 0.71	0.59 0.46 6.95 0.00 0.60	0.94 0.44 0.00 18.70 0.99	3.08 0.19 7.48 21.99 3.44	47.98 73.24 2.04 21.96 44.54									16.04 1.31 0.00 24.05 18.18	26.81 1.86 11.57 13.30 30.44
2	Alloy (C M) γ′(C γ′) MC (C MC) μ(C μ) γ(C γ)									2.06 7.60 0.00 0.00 1.72	2.49 14.16 63.00 1.10 1.55	0.59 0.71 9.35 0.00 0.58	0.94 0.35 0.00 11.67 0.73	3.08 0.32 5.28 26.41 2.69	47.98 69.95 10.28 14.98 47.37	16.04 1.98 0.00 21.50 16.93	26.81 4.95 12.09 24.33 28.43
		3	Alloy (C M) γ′(C γ′) MC (C MC) μ(C μ) γ(C γ)	2.06 7.36 0.00 0.00 1.79	2.49 14.98 71.79 1.01 1.55	0.59 0.73 7.71 0.00 0.58	0.94 0.37 0.00 11.98 0.65	3.08 0.24 4.23 23.30 2.64	47.98 71.11 7.73 17.55 47.53									16.04 1.31 0.00 21.19 16.88	26.81 3.90 8.55 24.97 28.39

Example is 3.: chemofacies the analysis showed that, contains γ ', MC, M in the GH652 alloy ₂₃C ₆With γ mutually.According to GH652 alloy sample chemical analysis gained γ ' in the table 5 and γ phase content (being measured value), and mutually and alloy sample overall chemical composition according to the GH652 alloy sample chemical analysis gained γ ' in the table 6 and γ, carry out γ ' and γ phase content and γ ' and γ mixing of phase constituent mutually by the concrete mode of first section description of example, 4.～7. carrying out γ ' by embodiment then calculates and reduction calculating with γ phase content mutually, obtain γ ' and γ actual content mutually, and by embodiment 8. calculate respectively carbonide phase MC and M ₂₃C ₆Content, its process is: utilize only to contain Ti and Nb among the MC, and other metallic element concentration is zero characteristics, use the 8. middle method of introducing of separating Simultaneous Equations of embodiment, try to achieve the MC phase content, with 100% content that deducts γ ', γ and MC phase, its surplus is M then ₂₃C ₆Content, listed the measuring and calculating value of each phase content of GH652 alloy sample in the table 5, measuring and calculating value as can be seen and measured value have good coincideing.

Table 5 GH652 alloy sample phase content chemofacies is analyzed the measuring and calculating value of measured value and the inventive method

The GH652 alloy sample	Data Source	Phase content, %
						γ′	MC	M 23C 6	γ
		1	The actual measurement measuring and calculating	13.76 10.84	0.04 0.04					1.08 1.09	85.11 88.03
2	The actual measurement measuring and calculating					14.53 11.57	0.04 0.04	1.14 1.14	84.29 87.25
		3	The actual measurement measuring and calculating	15.31 12.11	0.05 0.04					1.12 1.12	83.53 86.73

Table 6 GH652 alloy sample and each phase chemistry composition (concentration of element) thereof

Sample	Measurand	Chemical constitution, atomic percentage %
							Al	Ti	Cr	Ni	Nb
		1	Alloy (C M) γ′(C γ′) MC(C MC) M 23C 6 (C M23C6) γ.(.C γ)	7.09 17.68 0.00 0.00 5.47	0.34 1.73 64.09 0.00 0.09	28.66 10.16 0.00 95.00 30.82						63.79 69.97 0.00 5.00 63.57	0.12 0.47 35.91 0.00 0.04
2	Alloy (C M) γ′(C γ′) MC(C MC) M 23C 6 (C M23C6) γ(C γ)						7.09 17.94 0 0 5.32	0.34 1.65 59 0 0.09	28.66 9.96 0 94.85 31	63.79 70.05 0 5.15 63.54	0.12 0.4 41 0 0.05
		3	Alloy (C M) γ′(C γ′) MC(C MC) M 23C 6 (C M23C6) γ(C γ)	7.09 17.94 0 0 5.2	0.34 1.56 59.54 0 0.09	28.66 10.06 0 94.84 31.2						63.79 70.06 0 5.16 63.46	0.12 0.38 40.46 0 0.05

The present invention has the following advantages and good effect:

1. the present invention utilizes electron probe to be difficult to the independent precipitated phase composition measurement that realizes and is in fact precipitated phase and this objective present situation of matrix phase Mixed Zone composition measurement, the atom body strain minimum principle that causes when proposing element phase double replacement in the ordered structure precipitated phase sublattice, set up corresponding optimization object function and the constraints of elemental concentration in sublattice, institute is surveyed two phase mixture compositions and the substitution of matrix phase composition, carry out optimization computation by the setting that changes matrix phase content, thereby obtain composition and the corresponding content thereof of the ordered structure precipitated phase of surveying, the method be for electron probe when ordered structure precipitated phase composition is measured in the high temperature alloy sample, its fructufy solves this problem for these these characteristics of blending constituent with matrix phase;

2. the present invention carries out the zone with electron probe backscattered electron mode and the matrix phase composition measurement does not need the special preparation sample, and process implementation is simple, convenient, save time;

3. the present invention programmes with common software Matlab and is optimized calculating, and program is simple, computational speed is fast, and results of measuring is accurate;

4. the inventive method can be used for the phase constituent of other all kinds of alloys that contain the ordered structure precipitated phase and the measuring and calculating of content thereof, has broad application prospect.

In a word, there is no at present with electron probe the high temperature alloy sample is measured respectively ordered structure precipitated phase and matrix phase Mixed Zone composition and matrix phase composition, thereby and then measured result is optimized method and the technology that calculate to obtain ordered structure precipitated phase, Carbide Phases and matrix phase composition and content thereof. The present invention will provide a kind of scientific method and instrument for the impact that high temperature alloy development, technology controlling and process, analysis alloy structure change its mechanical property. Carry out composition measurement with the method, make things convenient for, save time, be easy to realize; Computational process is simple, quick, can realize that under common software Matlab its results of measuring is accurate, has solved the problem of electron probe original " indeterminacy ", and more simple than existing chemical Phase Analysis Method. The method can be widely used in all kinds of alloy phase analyses with ordered structure precipitated phase.

Claims (1)

1. a method of measuring nickel base high temperature alloy phase content is characterized in that, may further comprise the steps:

1. the metallographic sample preparation mode is polished the tested sample sightingpiston, polish routinely;

2. under electron probe, select the backscattered electron imaging pattern, survey matrix phase and the chemical constitution of matrix respectively with ordered structure precipitated phase Mixed Zone and sample integral body, matrix mutually respectively is no less than 5 with the measuring point number of matrix and ordered structure precipitated phase Mixed Zone, and the measuring point number of sample integral body is no less than 3;

3. above-mentioned matrix phase, matrix are carried out statistical average respectively with the determination data of ordered structure precipitated phase Mixed Zone and sample integral body, obtain matrix phase and the assembly average of matrix respectively with each ordered structure precipitated phase Mixed Zone and sample overall chemical composition;

4. set up the sublattice concentration of element (X that relates to the ordered structure precipitated phase _2i-1, X _2i) and each element between the objective function (f) of the body strain relation that causes of atomic substitutions:

Objective function about γ ' phase: $f_{{\mathrm{\γ}}^{\′}}={[\frac{3}{4}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i-1}\·{\mathrm{\ϵ}}_{i-\mathrm{Ni}}+\frac{1}{4}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i}\·{\mathrm{\ϵ}}_{i-\mathrm{Al}}]}^2\⇒\min$

In the formula, (X _{γ '}) _2i-1(X _{γ '}) _2iThe concentration of representing element in middle mutually Ni position of γ ' and the Al position sublattice respectively; ε _I-NiAnd ε _I-AlRepresent in Ni position and the Al position sublattice atomic substitutions Ni of different element i and the caused body strain of displacement Al atom respectively:

${\mathrm{\ϵ}}_{i-\mathrm{Ni}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Ni}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Ni}}^3}=\frac{r_i^3-r_{\mathrm{Ni}}^3}{r_{\mathrm{Ni}}^3},$ ${\mathrm{\ϵ}}_{i-\mathrm{Al}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Ali}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Al}}^3}=\frac{r_i^3-r_{\mathrm{Al}}^3}{r_{\mathrm{Al}}^3}$

In the formula, r _iAtomic radius for element i; The middle mutually sublattice concentration of element (X of γ ' _{γ '}) _2iWith this mutually each concentration of element be composition C _{γ '}The pass be:

${\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i}=[4\·C_{{\mathrm{\γ}}^{\′}}^T-3\·{\left(X_{{\mathrm{\γ}}^{\′}}\right)}_{2i-1}]$

In the formula, C _{γ '} ^TBe C _{γ '}Transposed matrix,

$C_{{\mathrm{\γ}}^{\′}}=\frac{C_{{\mathrm{\γ}}^{\′}+\mathrm{\γ}}-V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}}{1-V_{\mathrm{\γ}}}$

C _{γ '+γ}For previous experiments is surveyed precipitated phase γ ' and the matrix composition or the concentration of γ Mixed Zone mutually;

In nickel base superalloy to be determined, contain the μ phase time, about the objective function of μ phase:

$f_{\mathrm{\μ}}={[\frac{7}{13}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{\mathrm{\μ}}\right)}_{2i-1}\·{\mathrm{\ϵ}}_{i-\mathrm{Fe}}+\frac{6}{13}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_{\mathrm{\μ}}\right)}_{2i}\·{\mathrm{\ϵ}}_{i-\mathrm{Mo}}]}^2\⇒\min$

ε in the formula _I-FeAnd ε _I-MoRepresent in middle mutually Fe position of μ and the Mo position sublattice different element i atomic substitutions Fe and the caused body strain of displacement Mo atom respectively:

${\mathrm{\ϵ}}_{i-\mathrm{Fe}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Fe}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Fe}}^3}=\frac{r_i^3-r_{\mathrm{Fe}}^3}{r_{\mathrm{Fe}}^3},$ ${\mathrm{\ϵ}}_{i-\mathrm{Mo}}=\frac{\frac{4}{3}\mathrm{\π}\·r_i^3-\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Mo}}^3}{\frac{4}{3}\mathrm{\π}\·r_{\mathrm{Mo}}^3}=\frac{r_i^3-r_{\mathrm{Mo}}^3}{r_{\mathrm{Mo}}^3}$

In the formula, r _iAtomic radius for element i; The middle mutually sublattice concentration of element (X of μ _μ) _2iWith this mutually each concentration of element be composition C _μThe pass be:

${\left(X_{\mathrm{\μ}}\right)}_{2i}=[\frac{13}{6}\·C_{\mathrm{\μ}}^T-\frac{7}{6}\·{\left(X_{\mathrm{\μ}}\right)}_{2i-1}]$

In the formula, C _μ ^TBe C _μTransposed matrix,

$C_{\mathrm{\μ}}=\frac{C_{\mathrm{\μ}+\mathrm{\γ}}-V_{\mathrm{\γ}}\·C_{\mathrm{\γ}}}{1-V_{\mathrm{\γ}}}$

C _μ+γBe composition or the concentration of μ that abovementioned steps is surveyed with territory, γ phase mixture;

5. set up constraint condition: the sublattice concentration of element sum of each ordered structure precipitated phase is 100% in above-mentioned objective function; The concentration change scope of every kind of element between 0～100%, that is, and 0≤X _2i-1, X _2i≤ 100%;

6. objective function (f) and the constraint condition of being set up is compiled into calculation procedure, each ordered structure precipitated phase in the sample that will obtain by above-mentioned steps (γ ', μ) and matrix be the chemical constitution mean value C of (γ) mixed zone mutually _{J+ γ}With the matrix chemical constitution (C of (γ) mutually _γ) operation program of substitution correspondence respectively, C _{J+ γ}Subscript represent different ordered structure precipitated phase j and the matrix mixed zone that constitutes of γ mutually, wherein j represents γ ' or μ phase; Successively setting unit is 1%, 0.1% and 0.01% matrix phase content variable (V _γ) step-length, change the V in the calculation procedure _γValue finds the V that can make objective function (f) reach minimum value _γValue is so promptly get the concentration (X of two sublattices in the precipitated phase _2i-1, X _2i), and the actual chemical constitution (C of acquisition ordered structure precipitated phase _{γ '}, C _μ) and the mixed zone in the content (100%-V of precipitated phase _γ);

7. the reduction of ordered structure precipitated phase content is calculated: calculating to make to reduce by two-phase content separately in the ordered structure precipitated phase that records under the above-mentioned steps gained electron probe and the territory, matrix phase mixture by following reduction becomes above-mentioned each actual content mutually in the alloy sample:

(V _γ′) _real＝(V _γ′) _calc.·(V _γ′+γ)，

(V _μ) _real＝(V _μ) _calc.·(V _μ+γ)

In the following formula, (V _{γ '}) _Real(V _μ) _RealBe respectively γ ' and μ actual content mutually in the sample; (V _{γ '}) _Calc.(V _μ) _Calc.Be respectively and calculate γ ' and μ content mutually in the gained mixed zone; (V _{γ '+γ}) and (V _μ+γ) be respectively the experiment the γ ' that surveys with γ mixed zone and μ and γ mixed zone shared separately content in alloy sample;

8. carbonide (M ₂₃C ₆, MC) analytical Calculation of phase content:

If carbonide only is M in the alloy to be measured ₂₃C ₆Or MC, then with 100% ordered structure precipitated phase and the matrix phase content that deducts through preceding method measuring and calculating gained, all the other are M ₂₃C ₆Or the content of MC;

If carbonide comprises M simultaneously in the alloy to be measured ₂₃C ₆And MC, when only containing Ti or Nb element in the alloy, use lever law, will can try to achieve the content of carbonide after the known quantity substitution; When containing Ti and Nb simultaneously in the alloy, use lever law and Ti and Nb percentage composition and expression formula, organize the percentage composition that obtains this carbonide respectively by solving an equation, with 100% content that deducts all known phases, obtain M then ₂₃C ₆Content.