Multi-scale simulation method for segregation defect of multi-component alloy, product, medium and equipment

Abstract

The invention discloses a multi-scale simulation method, a product, a medium and equipment for segregation defects of a multi-component alloy, and belongs to the technical field of metallurgy. The method comprises the following steps: S1, constructing a macroscopic heat and mass flow model; comprising a momentum equation which is used for describing alloy melt flow behaviors and revealing the influence of convection on solute distribution; the temperature equation is used for depicting temperature field evolution in the solidification process; the concentration equation is used for describing migration and distribution of solute in the solidification process; the pressure Poisson equation is used for correcting the velocity field; s2, constructing a microscopic phase field model by adopting a mode of combining a phase field method and a lattice Boltzmann method; s3, performing space-time discretization on the momentum equation, the temperature equation and the concentration equation by adopting a finite difference method; s4, performing multi-scale numerical simulation coupling on the macrosegregation and the microsegregation; and S5, the alloy segregation behavior and segregation zone dendritic crystal morphology are visualized. According to the method, macro and micro multi-scale accurate simulation of the multi-component alloy segregation phenomenon can be realized.

Description

Technical Field

[0001] The present invention belongs to the field of metallurgy technology, and in particular relates to a multi-scale simulation method, product, medium and equipment for segregation defects in multicomponent alloys. Background Art

[0002] Industrial alloys generally include multiple elements. During the solidification process of multi-component alloys, segregation defects will occur due to the large difference in the specific gravity of the various elements in the alloy and the uneven distribution of components. Alloy segregation defects can be divided into two categories: microsegregation and macrosegregation. Macrosegregation is the uneven distribution of alloy elements on a macroscopic scale caused by the relative movement between the solute-poor solid phase and the solute-rich liquid phase during the solidification process. Macrosegregation is difficult to eliminate through subsequent processing and directly affects the performance of parts. Microsegregation on the microscale is manifested as the competitive distribution behavior of various solute elements at the solid-liquid interface during the evolution of the dendrite morphology of multi-component alloys. Microsegregation will lead to a decrease in the impact toughness and plasticity of alloy castings, an increase in the tendency to hot cracking, and a shortened casting life.

[0003] With the rapid development of computers, numerical simulation has made rapid progress in the field of materials science. Combining it with experiments can simplify solidification experiments and reduce R&D costs. Solidification numerical simulation technology has evolved from simple temperature field simulation to a complex process involving temperature, solute, flow, and phase transition coupling; from macroscopic heat transfer, mass transfer, and flow in liquid metals to microscopic structural evolution.

[0004] Currently, the most mature method for macro-scale numerical simulation of alloys is the finite element method, while the main methods for micro-scale numerical simulation include Monte Carlo, cellular automata, and phase field methods. However, most of these methods are for simple alloys with a single component.

[0005] Existing patent 1 (A method and device for predicting defect tendencies in aluminum alloy semi-continuous castings, patent number: CN111104763A) provides a method and device for predicting defect tendencies in aluminum alloy semi-continuous castings based on the high-throughput finite element method. This method and device can accurately predict the defect tendencies of aluminum alloy semi-continuous castings. Through high-throughput finite element numerical simulation, the maximum element segregation, the maximum Niyama value (shrinkage criterion), and the maximum hot cracking index of the aluminum alloy semi-continuous castings under various process conditions are obtained. The defect tendencies of the aluminum alloy semi-continuous castings are predicted based on the obtained maximum element segregation, the maximum Niyama value (shrinkage criterion), and the maximum hot cracking index.

[0006] Existing patent 2 (a three-dimensional prediction method for dendrite growth and segregation during steel solidification, patent number: CN113127988A) uses the phase field method to introduce mechanisms such as nucleation, growth, and solute diffusion into numerical simulation. It can not only realistically reproduce the microscopic morphology of competitive grain growth during molten steel solidification, but also accurately predict the solute redistribution phenomenon during the competitive grain growth process, thereby improving the accuracy of the prediction of competitive grain growth during molten steel solidification.

[0007] Traditional numerical simulation methods mostly focus on single-scale studies of macrosegregation or microsegregation. However, there are currently few studies on the coupling of multi-scale macrosegregation and microdendritic segregation caused by solute transport and redistribution at the solidification front, and there is a lack of in-depth exploration of the internal connection between macrosegregation and microsegregation. Summary of the Invention

[0008] The present invention aims to solve one of the technical problems in the above-mentioned related art at least to a certain extent.

[0009] To this end, the purpose of the present invention is to provide a multi-scale simulation method, product, medium and equipment for multi-component alloy segregation defects, which can achieve accurate macro-micro multi-scale simulation of multi-component alloy segregation phenomena.

[0010] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0011] An embodiment of the present invention provides a multi-scale simulation method for segregation defects in multicomponent alloys, the method comprising:

[0012] S1. Constructing a macroscopic heat and mass flow model; the macroscopic heat and mass flow model includes:

[0013] The momentum equation is used to describe the flow behavior of alloy melts and reveals the effect of convection on solute distribution;

[0014] Temperature equation, which is used to describe the evolution of the temperature field during solidification, thereby regulating the solidification rate and phase change;

[0015] Concentration equations, used to couple convection and diffusion mechanisms to describe the migration and distribution of polyvalent solutes during solidification;

[0016] Poisson's equation for pressure, used to correct the velocity field and ensure flow continuity;

[0017] S2. Construct a microscopic phase field model by combining the phase field method and the lattice Boltzmann method;

[0018] S3. Use the finite difference method to perform spatial and temporal discretization on the momentum equation, temperature equation, and concentration equation;

[0019] S4. Couple multi-scale numerical simulations of macrosegregation and microsegregation;

[0020] S5. Obtain the alloy segregation behavior and dendrite morphology in the segregation zone through visualization processing.

[0021] In addition, the multi-scale simulation method for multi-component alloy segregation defects according to the present invention may also have the following additional technical features:

[0022] In some embodiments, in step S1, the momentum equation is based on the Navier-Strokes equation, taking into account the density, velocity, pressure, viscosity, gravity, temperature and concentration gradient of the fluid;

[0023] The temperature equation includes heat conduction, specific heat capacity and latent heat effect caused by phase change;

[0024] The concentration equation considers both convection and diffusion mechanisms based on Fick's law of diffusion. The convection term describes the transport of substances due to liquid flow, and the diffusion term describes the transport of substances due to concentration gradients.

[0025] In some embodiments, when the momentum equation is discretized in time and space in step S3, the convection term is processed using central difference and the viscosity term is processed using second-order central difference to improve the accuracy and stability of the solution.

[0026] In some embodiments, when the temperature equation is discretized in time and space in step S3, the convection term uses a first-order central difference format, and the diffusion term uses a second-order central difference format.

[0027] In some embodiments, when the concentration equation is discretized in time and space in step S3, the heat source term caused by phase change is directly added to the local temperature change, and the solute redistribution term is directly added to the concentration change.

[0028] In some embodiments, in step S2, a phase field method is used as a diffusion interface method, and a lattice Boltzmann model is used to calculate the microscopic flow around the dendrite, thereby simulating the growth of the microscopic dendrite;

[0029] The phase field method is derived from the free energy density function; the lattice Boltzmann model describes fluid motion through a two-step evolution of repeated collision and flow;

[0030] The temperature distribution and flow velocity distribution are calculated by the equations in S1 and used as boundary conditions for phase field simulation to characterize the microscopic dendrites under macroscopic conditions.

[0031] In some embodiments, the microscopic phase field model in S2 is discretized using the finite difference method; wherein, the time discretization is discretized using the forward difference approximate derivative, and the space discretization is discretized using the central difference approximate derivative.

[0032] An embodiment of the present invention further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the multi-scale simulation method for segregation defects in multicomponent alloys as described in any one of the above items.

[0033] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the multi-scale simulation method for segregation defects of multicomponent alloys as described in any one of the above items.

[0034] An embodiment of the present invention also provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the multi-scale simulation method of segregation defects in multicomponent alloys as described in any one of the above items.

[0035] Compared with the prior art, the present invention has at least the following beneficial effects:

[0036] In an embodiment of the present invention, a multi-scale simulation method for multi-component alloy segregation defects is provided. This method uses a macroscopic heat and mass flow model and a microscopic phase field model to perform multi-scale multi-component alloy segregation simulation. Based on numerical simulations of fluid mechanics and heat and mass transfer theory, the method simulates the evolution of multi-physical fields by visualizing physical quantities that are difficult to measure in multi-component alloys, making it suitable for predicting macroscopic segregation. Macroscopic flow and temperature conditions are used as input variables in the microscopic phase field model to simulate the dendrite morphology characteristics at corresponding locations. Based on the determined physical property parameters of the multi-component alloy, this method achieves macroscopic and microscopic multi-scale simulation of the multi-component alloy segregation phenomenon.

[0037] In the embodiments of the present invention, a multi-scale simulation method for segregation defects in multicomponent alloys is provided. To address the problem of multi-scale segregation coupling in the solidification of multicomponent alloys, a multi-scale numerical simulation method based on multi-component heat and mass flow-phase field coupling is proposed. The method reveals the influence of macroscopic heat and mass flow on microscopic dendrite morphology in the multicomponent system, breaks through the dimensional limitations of the single-scale traditional binary model, and provides a new numerical simulation method for multi-scale segregation simulation of multicomponent systems.

[0038] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flowchart of a multi-scale simulation method for segregation defects in multicomponent alloys disclosed in one embodiment of the present invention;

[0040] Figure 2Multi-scale segregation diagrams of different elements in the Mg-9wt%Al-1wt%Zn alloy disclosed in one embodiment of the present invention: (a) macrosegregation of Al element; (b) concentration distribution of Al element on the vertical line; (c) microsegregation and dendrite morphology of Al element; (d) macrosegregation of Zn element; (e) concentration distribution of Zn element on the vertical line; (f) microsegregation and dendrite morphology of Zn element. DETAILED DESCRIPTION

[0041] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0042] The embodiments of the present invention are described in detail below through specific embodiments and application scenarios with reference to the accompanying drawings.

[0043] The present invention addresses the technical deficiencies of traditional solidification simulation technology in multicomponent alloy systems and proposes a multiscale numerical simulation method for multicomponent alloys, focusing on resolving the key issue that existing technologies (such as Patent 1 which only focuses on macroscopic defect criteria and Patent 2 which is limited to microscopic solute redistribution) cannot effectively resolve the multiscale segregation coupling mechanism of multicomponent alloys. By coupling the macroscopic heat and mass flow model of multicomponent alloys with the multicomponent phase field model, the present method realizes the coupled numerical simulation of macroscopic melt convection, multisolute cross-diffusion, microscopic dendrite competitive growth and multicomponent solute redistribution. In particular, in view of the unique solute interaction characteristics of multicomponent alloys, a solute transport model that couples the multicomponent mass conservation equation with thermodynamics is established at the macroscale, multicomponent phase field theory is used to characterize the multicomponent interface distribution dynamics at the microscale, and a cross-scale numerical simulation mechanism is established through a multi-physical field (temperature field, flow field) coupling algorithm. This multi-scale simulation technology not only breaks through the limitations of traditional single-element / binary models in their insufficient adaptability to multicomponent systems, but can also quantitatively reveal the impact of macro-segregation on micro-solute distribution and dendrite growth in multi-component systems, providing innovative solutions for the prediction and regulation of multi-scale segregation defects during the solidification process of multi-component alloys.

[0044] See also Figure 1 As shown, in some embodiments of the present invention, a multi-scale simulation method for segregation defects in multicomponent alloys is provided, the steps comprising:

[0045] Step 1: Establish a macroscopic heat and mass flow model

[0046] In some embodiments of the present invention, in simulating the macrosegregation of a multicomponent alloy, it is first necessary to establish accurate control equations, including a momentum equation, a temperature equation, and a concentration equation.

[0047] In the above examples, the momentum equation describes the flow behavior during alloy solidification. This equation, based on the Navier-Strokes equations, accounts for factors such as fluid density, velocity, pressure, viscosity, gravity, temperature, and concentration gradients. During the alloy casting process, the momentum equation helps predict how metal flow affects solute flow distribution and the formation of macrosegregation.

[0048]

[0049] Where ρ is density, u is velocity vector, p is pressure, μ is dynamic viscosity, and F T is the thermal buoyancy, F S is the solute buoyancy, and the Boussinesq approximation is used to determine these two buoyancy forces:

[0050] F T =ρgβ T (TT ref ) (2)

[0051]

[0052] Where, β T is the coefficient of thermal expansion, β i S is the solute expansion coefficient of each alloying element, g is the acceleration due to gravity, T is the temperature, and T ref is the reference temperature, C i is the macroscopic solute concentration of element i, C i ref is the reference concentration of element i.

[0053] In some embodiments of the present invention, the temperature equation describes and predicts how the temperature field varies over time and space. During alloy solidification, the temperature distribution directly affects the solidification rate and phase transformation, which are key factors in the formation of macrosegregation. The temperature equation includes heat conduction, specific heat capacity, and the latent heat effect caused by phase transformation, all of which affect the temperature distribution in macrosegregation.

[0054]

[0055] Where c p is the specific heat capacity, λ is the thermal conductivity, L is the latent heat, and f is the liquid fraction.

[0056] In some embodiments of the present invention, a concentration equation is used to describe and predict the concentration distribution of elements in an alloy based on Fick's diffusion law. This equation accounts for both convection and diffusion, which together determine how solute elements migrate and distribute during solidification. Convection describes the transport of substances due to liquid flow, while diffusion describes the transport of substances due to concentration gradients:

[0057]

[0058] Where D i is the diffusion coefficient of element i, k pi is the equilibrium distribution coefficient of element i, f s is the solid phase fraction.

[0059] Furthermore, to ensure the continuity of the velocity field, the pressure Poisson equation is used to correct the velocity field and ensure that the passive condition is met. This equation is crucial to maintaining the physical consistency of the model.

[0060]

[0061] Step 2: Establish a microscopic phase-field model

[0062] In some embodiments of the present invention, the phase field method is used as a diffusion interface method on the microscale model, and the lattice Boltzmann model (LBM) is used to calculate the microscopic flow around the dendrite to simulate the growth of microscopic dendrites. The phase field method is derived from the free energy density function, and the LBM is a method based on mesoscopic dynamics that describes fluid motion through a two-step evolution of repeated collisions and flows. The temperature and flow velocity distributions calculated by the above-mentioned macroscopic heat and mass flow equations are used as boundary conditions for the phase field simulation of multi-element alloy dendrites, thereby characterizing the microscopic dendrites under macroscopic conditions:

[0063]

[0064] Where φ∈(0,1) is the phase field variable, φ=0 is the liquid phase, φ=1 is the solid phase, and the region 0<φ<1 is the solid-liquid interface. M is the interface mobility, σ is the interface energy, η is the interface width, and V m is the molar volume, ΔG sl is the thermodynamic driving force of phase change related to supercooling, c l i (c s i ) represents the microscopic solute concentration of component i in the l(s) phase, u is the velocity vector, D i is the solute diffusion coefficient of component i. i (r,t) is the particle distribution function, τ LBM is the single relaxation time, f ieq (r,t) is the equilibrium distribution function.

[0065] Step 3: Discretize the physical equations using the finite difference method

[0066] In some embodiments of the present invention, in the discretization of the momentum equation, central difference processing is used for the convection term, and second-order central difference is used for the viscosity term to improve the accuracy and stability of the solution:

[0067]

[0068] Similarly, the macroscopic temperature and concentration equations are solved using finite differences, with first-order central differences used for the convection term and second-order central differences used for the diffusion term. The heat source term due to phase change is added directly to the local temperature change, and the solute redistribution term is added directly to the concentration change.

[0069]

[0070] The finite difference method is used to discretize equations (7) and (8). The time discretization is discretized by the forward difference approximate differential, and the space discretization is discretized by the central difference approximate differential:

[0071]

[0072] Where Δt and Δx are the time step and space step, and (i, j) is the node coordinate.

[0073] Step 4: Coupling the multi-scale numerical simulation of macrosegregation and microsegregation

[0074] In some embodiments of the present invention, a specific solid-liquid phase transition location is selected at the midpoint of macrosegregation, and the macroscopic flow field and temperature distributions at that location are extracted to calculate the degree of undercooling. The flow field velocity and undercooling are then used as microscopic dendrite growth conditions and input into a microscopic phase-field model to determine the microscopic dendrite morphology in the region of solute redistribution caused by the specific macroscopic solid-liquid phase transition, thereby achieving multi-scale coupling of macrosegregation and microsegregation.

[0075] Step 5: Visualize the alloy segregation behavior and dendrite morphology in the segregation zone

[0076] In some embodiments of the present invention, based on the established macroscopic heat and mass flow model and phase field model, macroscopic heat and mass flow and microscopic phase field simulations are performed on the multi-element alloy Mg-9wt%Al-1wt%Zn alloy to obtain the macroscopic concentration distribution and microscopic morphology of the alloy, and analyze the segregation degree on different vertical lines, such as Figure 2 shown.

[0077] In some embodiments of the present invention, on a macroscopic scale, during the solidification process of the supercooled melt, solid nuclei grow into crystals. The liquid melt flows under the combined action of downward gravity, upward buoyancy, and resistance generated by settling particles, forming a local vortex. As the solidification process proceeds, the grains precipitated under the action of gravity gather at the bottom of the ingot, forming a negative segregation zone. Some grains are also carried to the center of the ingot by the vortex, forming positive segregation zones on both sides of the center of the ingot. At the top of the ingot corresponding to the final solidification zone, the solute is enriched to form a larger positive segregation zone. In the final solidified ingot, the uneven solute distribution presents a symmetrical W-shaped segregation pattern, such as Figure 2 The overall distribution of macrosegregation of the two elements Mg-9wt%Al-1wt%Zn in (a) and (d).

[0078] In some embodiments of the present invention, for multi-scale simulation, the present method extracts the undercooling and flow field characteristics of the macrosegregation zone and uses them as input variables of the phase field model to quantitatively characterize the multicomponent alloy microstructure in the macrosegregation zone, such as Figure 2 As shown in (c) and (f) in the figure, a numerical simulation of a multi-component alloy with macro- and micro-scale coupling is achieved. Based on the temperature and flow conditions at the macroscale and the crystallographic anisotropy at the microscale, a typical six-branch dendrite pattern is obtained. The growth rate of the dendrite tip is much greater than the rate at which the solute diffuses from the solute diffusion layer at the dendrite interface to the liquid phase, resulting in an increase in the enrichment of the solute at the solid-liquid interface. At the root of the dendrite, the high concentration area (red area) of the solute Zn is narrower than that of the solute Al, indicating that the solute Zn is more easily enriched at the front of the solid-liquid interface. This corresponds to the phenomenon of a large degree of solute segregation of the Zn element at the solid-liquid interface on a macro scale, reflecting the coupled solution of macro- and micro-scale segregation.

[0079] The present invention solves the macroscopic segregation distribution of the multi-component alloy by solving the macroscopic heat and mass flow equations. On this basis, with the macroscopic temperature field and flow field as boundary conditions, the phase field method is adopted to solve the microscopic dendrite growth of the multi-component alloy. The macroscopic segregation and microscopic dendrite growth are interconnected through physical field variables to solve the multi-scale simulation problem of metal casting defects.

[0080] The present invention adopts a method that combines mathematical derivation with macroscopic heat and mass flow simulation and phase field simulation at multiple scales, ensuring the rigor of mathematical and physical mechanisms, and realizing the numerical simulation of multi-scale macroscopic segregation, microscopic dendrite morphology and solute distribution of multi-component alloys. It provides guidance for the further improvement and application of multi-scale simulation of metal casting defects, and broadens the scope of application of multi-scale numerical simulation methods. It not only improves the comprehensiveness and accuracy of the research, but also provides a new perspective for in-depth understanding of the solidification process of multi-component alloys.

[0081] Parts of the present invention that are not described in detail may refer to the prior art or are well-known technologies to those skilled in the art, and this embodiment does not limit this and will not be described in detail here.

[0082] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A multi-scale simulation method for segregation defects in multicomponent alloys, characterized in that: The method comprises: S1. Constructing a macroscopic heat and mass flow model; the macroscopic heat and mass flow model includes: The momentum equation is used to describe the flow behavior of alloy melts and reveals the effect of convection on solute distribution; Temperature equation, which is used to describe the evolution of the temperature field during solidification, thereby regulating the solidification rate and phase change; Concentration equations, used to couple convection and diffusion mechanisms to describe the migration and partitioning of polyvalent solutes during solidification; Poisson's equation for pressure, used to correct the velocity field and ensure flow continuity; S2. Construct a microscopic phase field model by combining the phase field method and the lattice Boltzmann method; S3. Use the finite difference method to perform spatial and temporal discretization on the momentum equation, temperature equation, and concentration equation; S4. Couple multi-scale numerical simulations of macrosegregation and microsegregation; S5. Obtain the alloy segregation behavior and dendrite morphology in the segregation zone through visualization processing.

2. The multi-scale simulation method for multicomponent alloy segregation defects according to claim 1, characterized in that: In step S1, the momentum equation is based on the Navier-Strokes equation, taking into account the density, velocity, pressure, viscosity, gravity, temperature and concentration gradient of the fluid; The temperature equation includes heat conduction, specific heat capacity and latent heat effect caused by phase change; The concentration equation considers both convection and diffusion mechanisms based on Fick's law of diffusion. The convection term describes the transport of substances due to liquid flow, and the diffusion term describes the transport of substances due to concentration gradients.

3. The multi-scale simulation method of multi-component alloy segregation defects according to claim 1, characterized in that: When the momentum equation is discretized in time and space in step S3, the convection term is processed by central difference and the viscosity term is processed by second-order central difference to improve the accuracy and stability of the solution.

4. The multi-scale simulation method of multi-component alloy segregation defects according to claim 1, characterized in that: When the temperature equation is discretized in time and space in step S3, the convection term uses the first-order central difference format, and the diffusion term uses the second-order central difference format.

5. The multi-scale simulation method of multicomponent alloy segregation defects according to claim 1, characterized in that: When the concentration equation is discretized in time and space in step S3, the heat source term caused by phase change is directly added to the local temperature change, and the solute redistribution term is directly added to the concentration change.

6. The multi-scale simulation method of multicomponent alloy segregation defects according to claim 1, characterized in that: In step S2, the phase field method is used as a diffusion interface method, and the lattice Boltzmann model is used to calculate the microscopic flow around the dendrite, thereby simulating the growth of the microscopic dendrite; The phase field method is derived from the free energy density function; the lattice Boltzmann model describes fluid motion through a two-step evolution of repeated collision and flow; The temperature distribution and flow velocity distribution are calculated by the equations in S1 and used as boundary conditions for phase field simulation to characterize the microscopic dendrites under macroscopic conditions.

7. The multi-scale simulation method of multicomponent alloy segregation defects according to claim 1, characterized in that: The finite difference method is used to discretize the microscopic phase field model in S2; the time discretization is discretized by forward difference approximate derivative, and the space discretization is discretized by central difference approximate derivative.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the multi-scale simulation method of segregation defects in multicomponent alloys according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the multi-scale simulation method of segregation defects in multicomponent alloys according to any one of claims 1 to 7 are implemented.

10. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the multi-scale simulation method for segregation defects in multicomponent alloys as claimed in any one of claims 1 to 7.

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