CN108088773A - A kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model - Google Patents
A kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model Download PDFInfo
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Abstract
The present invention provides a kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model, the present invention is by using Fick (Fick) second law and wild (Boltzmann Matano) models of Boltzmann Yu, it studies the correlation between heat treatment temperature and time and the parameters such as diffusion velocity and concentration distribution and establishes model, the factor for improving alloying surface of low-carbon steel effect can be analyzed by model of the present invention, and pass through experiment and be modified, further improve the corrosion resistance of base material.
Description
Technical field
The present invention relates to field of material surface treatment, and in particular to a kind of surface of low-carbon steel nickel-plate alloy diffusion model
Method for building up.
Background technology
Nickel-base alloy refers to have under 650~1000 DEG C of high temperature higher intensity and certain antioxidant anticorrosive ability etc. comprehensive
Close a kind of alloy of performance.Refractoloy is subdivided into according to main performance, abros, nickel-base antiwear alloy,
Ni-based Precise Alloy and Ni-based marmem etc..Although nickel-base alloy with excellent hydrogen sulfide corrosion resistance energy,
Cost is higher, and surface of low-carbon steel electroless nickel layer, diffuses to form alloying transition zone using heat treatment, can either improve base material
Corrosion resistance, and cost can be reduced.But current surface of low-carbon steel nickel plating technology exists in diffusion process is heat-treated
Certain defect, for example, how preferably to control the phase between heat treatment temperature and diffusion velocity and diffusate concentration distribution
Mutual relation, so as to reach better alloying surface of low-carbon steel effect.
The content of the invention
In view of this, the present invention provides a kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model, described
Method can analyze the factor for improving alloying surface of low-carbon steel effect, further improve surface of low-carbon steel nickel plating technology
Effect.
The technical solution that the present invention takes is as follows：
1. a kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model, includes the following steps：
(1) gathered data
Surface of low-carbon steel is heat-treated after electronickelling is handled, by setting different temperature strips in heat treatment process
Part obtains corresponding diffusion length data (x/ μm), another one group of diffusate concentration data (C/ for gathering diffusion layer different position
kg/m3)；
(2) model is established
A. Boltzmann conversion is made on the basis of Fick's second law, it is specific as follows：
OrderThen
Wherein, C is the volumetric concentration (kg/m of diffusate3), t is diffusion time (s), and x is diffusion length (μm), and D is
Diffusion coefficient；λ represents the intermediate variable of definition；
B. using the concentration curve of Fe as research object, it is assumed that be free of in coating be free of in Fe and matrix before heat treatment
Ni takes the interface location before diffusion as coordinate origin, and it is x-axis forward direction to make along the direction of nickel coating, makes primary condition as follows：
Wherein, C1Represent the concentration of Fe, C2Represent the concentration of Ni；
Formula one is integrated, is obtained
Due toFurther obtain
Due to any timeFurther obtain
Due toFurther obtain
The position of coordinate origin x=0 is determined by formula three, and is further obtained
Wherein, m expressions meet distance of the abscissa away from origin when the section of formula three and formula four is intersected with concentration curve；
By the concentration C generation in formula two with CmIt can obtain
Wherein, CmRepresent ordinate when the section for meeting formula three and formula four is intersected with concentration curve, the concentration of curve
Value；J is diffusion flux (g/cm2)；
According to formula two, diffusion coefficient when can obtain any concentration C ˊ is
It is obtained eventually by software programming under different temperatures, the relational expression of diffusion length and concentration is：
C=a1×exp(-((x-b1)/c1)2)+a2×exp(-((x-b2)/c2)2)+a3×exp(-((x-b3)/c3)2)
+a4×exp(-((x-b4)/c4)2)+a5×exp(-((x-b5)/c5)2)+a6×exp(-((x-b6)/c6)2)
+a7×exp(-((x-b7)/c7)2)+a8×exp(-((x-b8)/c8)2)；
Wherein, C is concentration, and x is diffusion length, a1-a8, b1-b8, c1-c8Represent the coefficient obtained by programming.
Preferably, the section that formula three and formula four are met in the step (2) is Yu open countries plane.
Preferably, the formula five is obtained by following methods：
Hypothetical boundary condition meets the condition of diffusion in the big medium of one dimensional infinite, makes sample DIFFUSION TREATMENT certain time t, point
The concentration C of different position is analysed, makees concentration profile, and Yu open countries plane is found out according to formula four, obtains concentration profile and C
The area that=C1, C=C` and x=0 (Yu open countries face) are surroundedAnd at C=C` concentration profile slopeThe numerical value of D is obtained with reference to formula five, finally programming obtains diffusion coefficient in Matlab.
Preferably, programming step includes in the Matlab：
A. experimental data is stored in working space, cftool, carriage return operation are then inputted in command window；
B. variable x, y are selected, curve type of the simultaneous selection Gaussian curve as fitting provides fitting function expression formula i.e.
The relational expression of diffusion thickness and concentration, it is ensured that Adjust R-square are more than 0.99.
Preferably, data are stored or are imported from other files using matrix in the step a.
The beneficial effects of the present invention are：The present invention is wild by using Fick (Fick) second law and Boltzmann-Yu
(Boltzmann-Matano) model studies the phase between the parameters such as heat treatment temperature and time and diffusion velocity and concentration distribution
Mutual relation simultaneously establishes model, can be analyzed by model of the present invention improve alloying surface of low-carbon steel effect because
Element, and pass through experiment and be modified, further improve the corrosion resistance of base material.
Description of the drawings
Fig. 1 Boltzmann-Yu open countries method seeks diffusion coefficient schematic diagram (A is Yu open countries face, and B is index plane)；
Fe/Ni concentration profile near interface curves after Fig. 2 different heat treatments；A-c figures are followed successively by 450 DEG C, 550 DEG C and 650 DEG C
Temperature condition of heat treatment result；
Fig. 3 models fittings and verification result；A-c figures are followed successively by 450 DEG C, 550 DEG C and 650 DEG C of temperature condition of heat treatment
As a result.
Specific embodiment
The embodiment of technical solution of the present invention will be described in detail below.Following embodiment is only used for clearer
Ground illustrates technical scheme, therefore is only used as example, and is not intended to limit the protection scope of the present invention and limits the scope of the invention.
A kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model, includes the following steps：
(1) gathered data
Surface of low-carbon steel is heat-treated after electronickelling is handled, by setting different temperature strips in heat treatment process
Part obtains corresponding thickness of diffusion layer data, another one group of diffusate concentration data for gathering diffusion layer different position；At heat
Managing the thickness of diffusion layer measured under the conditions of 450 DEG C, 550 DEG C and 650 DEG C of temperature is respectively：3.51 μm, 8.55 μm and 18.59 μm,
Exemplified by invention be described in detail；The concentration of diffusion layer different position is obtained using scanning electron microscope and energy spectrum analysis, is shown in Table 1；
Diffusion lengths and diffusion concentration (%) of 1 Fe of table in Ni
(2) model is established
A. Boltzmann conversion is made on the basis of Fick's second law, it is specific as follows：
OrderThen
Wherein, C is the volumetric concentration (kg/m of diffusate3), t is diffusion time (s), and x is distance (m), and D is for diffusion
Number；λ is the intermediate variable of definition；
Therefore, solve diffusion problem and be finally attributed to the partial differential side for solving and providing under given initial and boundary condition
Journey；
B. using the concentration curve of Fe as research object, it is assumed that be free of in coating Ni is free of in Fe and matrix before heat treatment
(the Fe/Ni concentration profile near interface curves after different heat treatment are shown in Fig. 2) takes the interface location before diffusion to make edge for coordinate origin
The direction of nickel coating is positive for x-axis, makes primary condition as follows：
C1Represent the concentration of Fe, C2Represent the concentration of Ni；
Formula one is integrated, is obtained
Due toFurther obtain
Due to any timeFurther obtain
Due toFurther obtain
Formula two actually it is determined that the position of coordinate origin x=0, physical significance be x=0 both sides concentration curve with
C=C1And C=C2The area equation that two straight lines are encircled a city, i.e.,
M represents abscissa when Yu open countries plane intersects with concentration curve, the distance apart from origin；
The interface for meeting condition formula three and formula four in style is usually known as wild (Matano) planes of Yu；By formula two
In concentration C generation with CmIt can obtain
Wherein, CmRepresent ordinate when Yu open countries plane intersects with concentration curve, the concentration value of curve, J is commonly referred to as spread
Flux (g/cm2)；
Above formula shows that the integral area of Yu open countries plane side is proportional to diffusion flux of the constituent element by Yu open countries plane, thus Yu
Wild plane could also say that such a plane：Diffusion flux by its two constituent element is equal；If dispersive medium in diffusion process
Constancy of volume, i.e. lattice constant do not change with concentration, and room keeps equilibrium concentration, then Yu open countries plane and during initial sample
Soldering face overlaps；
According to formula two, diffusion coefficient when can obtain any concentration C ˊ is
Formula five is obtained by following methods：Hypothetical boundary condition meets the condition of diffusion in the big medium of one dimensional infinite, order examination
Sample DIFFUSION TREATMENT certain time t analyzes the concentration C of different position, makees concentration profile, and finds out Yu open countries according to formula four and put down
Face obtains concentration profile and C=C1, the area that C=C` and x=0 (Yu open countries face) are surroundedIt is and dense at C=C`
Spend the slope of distribution curveThe numerical value of D is obtained with reference to formula five, is programmed, is obtained not in Matlab softwares
Under synthermal, the relation between diffusion depth and diffusion concentration, Boltzmann-Yu open countries method asks diffusion coefficient schematic diagram to see Fig. 1；
Matlab soft program steps are specific as follows：
(1) fitting of curve
The experimental data of variable is stored in working space, it is specific as follows：
1) can data directly be stored with matrix, is directly inputted in command window；
2) x=[data x1, data x2 ..., data xn]；
3) y=[data y1, data y2 ..., data yn]；
When data are more, can be imported from the files such as excel, txt；
After data are stored in working space, cftool, carriage return operation are inputted in command window；
On the left side of fitting tool window, variable x, y are selected；Select curve type --- the Gaussian curve of fitting；
Fitting is automatically performed after having selected, and provides fitting function expression formula, ensures that Adjust R-square are more than
0.99；
The expression formula of its fitting function is：
C=a1×exp(-((x-b1)/c1)2)+a2×exp(-((x-b2)/c2)2)+a3×exp(-((x-b3)/c3)2)
+a4×exp(-((x-b4)/c4)2)+a5×exp(-((x-b5)/c5)2)+a6×exp(-((x-b6)/c6)2)
+a7×exp(-((x-b7)/c7)2)+a8×exp(-((x-b8)/c8)2)；
Wherein, C is concentration, and x is diffusion length, a1-a8, b1-b8, c1-c8All it is to program to obtain coefficient by Matlab.
(2) matched curve and experimental data are drawn
X=[data x1, data x2 ..., data xn]；
Y=[data y1, data y2 ..., data yn]；
plot(x,y,'r*')
hold on
X=x1:(xn-x1)/1000:xn；
C=a1×exp(-((x-b1)/c1)2)+a2×exp(-((x-b2)/c2)2)+a3×exp(-((x-b3)/c3)2)
+a4×exp(-((x-b4)/c4)2)+a5×exp(-((x-b5)/c5)2)+a6×exp(-((x-b6)/c6)2)
+a7×exp(-((x-b7)/c7)2)+a8×exp(-((x-b8)/c8)2)
plot(x,C,'go')
According to the method described above, programming obtains Boltzmann-Yu open countries method and seeks diffusion coefficient in Matlab, as shown in table 2.
At a temperature of 2 different heat treatment of table, the diffusion coefficient (unit of different position：m2/s×10-12)
Using least square method, the relation being fitted between temperature and parameters refers to table 3.
Relation between 3 temperature of table and parameters
The Fe concentration profile figures being chosen in 450 DEG C and 550 DEG C are fitted, and pass through the Fe concentration point in 650 DEG C
Cloth graph verified such as Fig. 3, and demonstrating the present invention, to establish model correct.
Finally it should be noted that：The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe is described in detail the present invention with reference to foregoing embodiments, it will be understood by those of ordinary skill in the art that：Its according to
Can so modify to the technical solution recorded in foregoing embodiments either to which part or all technical characteristic into
Row equivalent substitution；And these modifications or replacement, the essence of appropriate technical solution is not made to depart from various embodiments of the present invention technology
The scope of scheme should all cover among the claim of the present invention and the scope of specification.
Claims (5)
1. a kind of method for building up of surface of low-carbon steel nickel-plate alloy diffusion model, which is characterized in that include the following steps：
(1) gathered data
Surface of low-carbon steel is heat-treated after electronickelling is handled, by the way that different temperature conditionss is set to obtain in heat treatment process
Obtain corresponding diffusion length data (x/ μm), another one group of diffusate concentration data (C/kg/ for gathering diffusion layer different position
m3)；
(2) model is established
A. Boltzmann conversion is made on the basis of Fick's second law, it is specific as follows：
OrderThen
Wherein, C is the volumetric concentration (kg/m of diffusate3), t is diffusion time (s), and x is diffusion length (μm), and D is for diffusion
Number；λ represents the intermediate variable of definition；
B. using the concentration curve of Fe as research object, it is assumed that taken before heat treatment in coating without Ni is free of in Fe and matrix
Interface location before diffusion is coordinate origin, and it is x-axis forward direction to make along the direction of nickel coating, makes primary condition as follows：
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Wherein, C1Represent the concentration of Fe, C2Represent the concentration of Ni；
Formula one is integrated, is obtained
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Due to any timeFurther obtain
Due toFurther obtain
The position of coordinate origin x=0 is determined by formula three, and is further obtained
Wherein, m expressions meet distance of the abscissa away from origin when the section of formula three and formula four is intersected with concentration curve；
By the concentration C generation in formula two with CmIt can obtain
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Wherein, CmRepresent ordinate when the section for meeting formula three and formula four is intersected with concentration curve, the concentration value of curve；J is
Diffusion flux (g/cm2)；
According to formula two, diffusion coefficient when can obtain any concentration C ˊ is
It is obtained eventually by software programming under different temperatures, the relational expression of diffusion length and concentration is：
C=a1×exp(-((x-b1)/c1)2)+a2×exp(-((x-b2)/c2)2)+a3×exp(-((x-b3)/c3)2)
+a4×exp(-((x-b4)/c4)2)+a5×exp(-((x-b5)/c5)2)+a6×exp(-((x-b6)/c6)2)
+a7×exp(-((x-b7)/c7)2)+a8×exp(-((x-b8)/c8)2)；
Wherein, C is concentration, and x is diffusion length, a1-a8, b1-b8, c1-c8Represent the coefficient obtained by programming.
2. the method for building up of surface of low-carbon steel nickel-plate alloy diffusion model according to claim 1, which is characterized in that
The section for meeting formula three and formula four in the step (2) is Yu open countries plane.
3. the method for building up of surface of low-carbon steel nickel-plate alloy diffusion model according to claim 2, which is characterized in that
The formula five is obtained by following methods：
Hypothetical boundary condition meets the condition of diffusion in the big medium of one dimensional infinite, makes sample DIFFUSION TREATMENT certain time t, analysis is not
With the concentration C of position, make concentration profile, and Yu open countries plane is found out according to formula four, obtain concentration profile and C=
The area that C1, C=C` and x=0 (Yu open countries face) are surroundedAnd at C=C` concentration profile slopeThe numerical value of D is obtained with reference to formula five, finally programming obtains diffusion coefficient in Matlab.
4. the method for building up of surface of low-carbon steel nickel-plate alloy diffusion model according to claim 3, which is characterized in that
Programming step includes in the Matlab：
A. experimental data is stored in working space, cftool, carriage return operation are then inputted in command window；
B. variable x, y are selected, curve type of the simultaneous selection Gaussian curve as fitting provides fitting function expression formula and spread
The relational expression of thickness and concentration, it is ensured that Adjust R-square are more than 0.99.
5. the method for building up of surface of low-carbon steel nickel-plate alloy diffusion model according to claim 4, which is characterized in that
It stores data using matrix in the step a or is imported from other files.
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| CN109187610A (en) * | 2018-07-20 | 2019-01-11 | 中冶连铸技术工程有限责任公司 | Slab Microstructure Simulation method |
| CN110263292A (en) * | 2019-06-26 | 2019-09-20 | 东北大学 | A kind of calculation method for the diffusion coefficient improving Boltzmann-Matano formula |
| CN110263292B (en) * | 2019-06-26 | 2021-09-10 | 东北大学 | Calculation method for improving diffusion coefficient of Boltzmann-Matano formula |
| CN113051794A (en) * | 2021-03-12 | 2021-06-29 | 武汉理工大学 | Method and device for calculating concentration diffusion of impurity elements of quartz and storage medium |
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