This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks.
How to read it
Use the main plot to read the controlling trend, including break points that a single result card can hide.
Use the sensitivity view to find input combinations where margin collapses quickly.
For early design, focus on which input controls margin before trusting the absolute value.
Learn Diffusion FICK Second Law by dialogue
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When reading Diffusion FICK Second Law, where should I look first? Moving Diffusion coefficient D changes both the plots and the result cards.
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Start with Diffusion length, but do not treat the number as the whole answer. Use Concentration profile to confirm the assumed state, then read Diffusion length and time scale for the distribution or trend. Use the main plot to read the controlling trend, including break points that a single result card can hide.
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I can see why Diffusion coefficient D changes Diffusion length. How should I judge the influence of Elapsed time?
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Move Elapsed time in small steps and watch Concentration ratio. That reveals which term is controlling the result. This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks. A single operating point is not enough; sweep the realistic scatter range.
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What is D-time concentration map for? It feels like the ordinary curve already tells the story.
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D-time concentration map is for finding boundaries where the condition becomes risky or margin collapses quickly. Use the sensitivity view to find input combinations where margin collapses quickly. In First-pass comparison of design options before review, the important question is often what happens after a small change, not only the nominal value.
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So if Diffusion length is within the target, can I accept the condition?
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Treat this as a first-pass review. It helps with Narrowing controlling factors and worst-side conditions before detailed analysis and Teaching or explaining the equation, numbers, and visualization under the same inputs, but final decisions still need standards, measured data, detailed analysis, and vendor limits. For early design, focus on which input controls margin before trusting the absolute value.
Practical use
First-pass comparison of design options before review.
Narrowing controlling factors and worst-side conditions before detailed analysis.
Teaching or explaining the equation, numbers, and visualization under the same inputs.
FAQ
Start with Diffusion length and Concentration ratio. Then use Concentration profile to confirm the assumed state and Diffusion length and time scale to read distribution or bias. Use the main plot to read the controlling trend, including break points that a single result card can hide
Move Diffusion coefficient D alone, then move Elapsed time by a comparable amount and compare the change in Diffusion length. D-time concentration map shows combinations where margin or performance changes quickly.
Use it for First-pass comparison of design options before review. Instead of trusting a single point, widen the input range and check whether Diffusion length keeps enough margin before moving to detailed analysis.
This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks. Final decisions still require standards, measured data, detailed analysis, and vendor limits.
How to Use
Enter diffusion coefficient D (m²/s) for your material—typical values: steel 1e-11, silicon 1e-13, polymer 1e-9
Set initial concentration C₀ (mol/m³) at the surface and observation distance x (mm) into the bulk
Input elapsed time t (seconds); simulator solves ∂C/∂t = D∂²C/∂x² using complementary error function
Read concentration ratio C(x,t)/C₀, diffusion length √(4Dt), flux index −D∂C/∂x at x, and characteristic time scale x²/D
Worked Example
Carburizing a steel component: D=8e-12 m²/s, C₀=1.2e6 mol/m³ at surface, observe x=0.5 mm depth after t=3600 s (1 hour). Diffusion length = √(4×8e-12×3600) = 0.34 mm. Concentration ratio at 0.5 mm ≈ 0.16, meaning only 16% of surface carbon has penetrated. Flux index ≈ 67 mol/(m²·s) drives further carburization. Time scale estimate: (0.5e-3)²/(8e-12) = 31 hours—validate case-hardening feasibility.
Practical Notes
Diffusion length √(4Dt) defines the "active zone"—beyond 3× this distance, concentration remains near zero; use for coating thickness and doping depth design
For transient metal diffusion (e.g., copper into aluminum at 500°C), account for temperature-dependent D via Arrhenius; simulator assumes constant D
Flux index reversal indicates concentration gradient inversion; in semiconductor doping, negative flux means dopant withdrawal at later stages
Check Fourier number Fo = Dt/x² < 0.2 for semi-infinite solid assumption validity; larger Fo requires finite-domain boundary conditions