Thermal Diffusion – is a process where atoms or molecules migrate within or between solid materials due to a concentration gradient, temperature gradient, or both, without the material undergoing a phase change (e.g., melting). It involves the movement of atoms through the crystal lattice of a solid, typically driven by thermal energy that increases atomic mobility.
This process is governed by Fick’s laws of diffusion, where the rate of diffusion depends on the concentration gradient, temperature, and the material’s properties.
Key Mechanisms of Solid-State Thermal Diffusion
The diffusion rate is described by the Arrhenius equation: where:
D is the diffusion coefficient,D0 is a material-specific constant,Q is the activation energy for diffusion,R is the gas constant,T is the absolute temperature.Higher temperatures increase , accelerating diffusion.
By leveraging Fick’s and Kirkendall’s principles, we create a predictable, graded coating structure that eliminates sharp boundaries and ensures maximum resistance to mechanical stress and corrosion.
Fick’s Second Law describes how the concentration of diffusing species (here, zinc) changes over time and position in a non-steady-state system, where the concentration profile evolves as zinc spreads into the iron lattice. This law ensures the coating forms a predictable, graded structure—from a zinc-rich surface to an iron-rich base—rather than a sharp, abrupt boundary.
Mathematical Foundation:
The one-dimensional form of Fick’s Second Law for constant diffusivity is:
• C(x,t) Zinc concentration at depth (from the surface) and time t.
• D: Diffusion coefficient of zinc in iron, thermally activated where , Q ≈ 100-120 kJ/mol for Zn in Fe (activation energy for vacancy-assisted diffusion)6, R is the gas constant (8.314 J/mol·K), and is absolute temperature.
• At zinc diffusing temperatures (e.g., allowing measurable diffusion over hours.
ziPLY96+ optimizes well integrity and production efficiency by superior corrosion mitigation.
Step-by-Step Role in Forming the Coating:
• Initial Setup: At t = o, zinc concentration is high at the surface (c(0,0) =cs , saturated from zinc powder contact) and zero deep in the substrate . This creates a steep gradie.
• Time Evolution: As heat is applied, zinc atoms jump via vacancies or along grain boundaries. The second derivative (curvature of the profile) drives flux changes. Positive curvature (concave up) near the surface causes zinc to spread inward, flattening the profile over time.
– Solution for semi-infinite diffusion (common approximation for thin coatings): where /erf is the error function.
– How to Arrive at This: Integrate Fick’s First Law , with the continuity equation . For constant D separation of variables yields the error function solution, verified experimentally.
• Coating Formation: After 2–6 hours, the profile stabilizes, forming a 20–120 μm diffusion zone. Zinc concentration drops from ~90 wt% at the surface (forming zeta phase, FeZn₁₃) to <10 wt% at the base (gamma phase, Fe₃Zn₁₀). This gradient creates intermetallic layers, providing a metallurgical bond and sacrificial corrosion protection. Which has a gradient circuit potential from the zeta to the gamma phase. Which allows the coating to be buried, come in contact with dissimilar metals and not be affected by circuit indifferences caused by contact or moisture in the environment.
– Predictive Value: Engineers solve for case depth xc, where . For t = 4 hours at 350°C, , matching typical sherardized coating.
(Without Fick’s Second Law, diffusion would be modeled statically (ignoring profile changes), leading to uneven coatings or over-/under-diffusion.)
The Kirkendall Effect occurs during interdiffusion (zinc into iron and iron into zinc), where unequal diffusion rates () cause a net vacancy flux, shifting the diffusion interface and potentially forming voids. In thermal diffused zinc, this asymmetry refines the coating’s layered structure but requires control to avoid defects.
The effect arises from differing diffusivities in the interdiffusion flux. The Kirkendall velocity (interface shift rate) is:
• (faster, due to zinc’s smaller size and lower activation energy in Fe lattice).
• (slower, substitutional diffusion).
• From Fick’s law, this gradient drives the imbalance.
Excess vacancies () migrate to the faster-diffusing side (zinc-rich), collapsing into voids or dislocations.
• Interdiffusion Onset: Zinc diffuses inward faster than iron outward, creating more vacancies on the substrate side (iron lattice loses atoms quicker).
• Interface Shift: The original Zn-Fe interface moves toward the iron (slower) side by ~5–10% of coating thickness, as predicted by VK Markers (e.g., oxide lines) would displace, confirming vacancy mediation.
– How to Arrive at This: From Fick’s Second Law, solve for each species separately ( , similarly for Fe). The net flux imbalance yields VK, experimentally observed in diffusion couples annealed at 350°C.
• Structural Impact:
– Layering: The shift promotes distinct intermetallic phases (e.g., delta phase FeZn₇ forms where vacancy flux is high), enhancing coating hardness (200–400 HV) and adhesion.
– Defect Control: Minor voids (~1–5 μm) on the zinc side can form but are mitigated by fillers (e.g., sand in sherardizing), ensuring uniformity. Excessive voids would embrittle the coating, but controlled conditions (short times) minimize this.
• Coating Enhancement: The effect ensures a compact, gradient structure, improving corrosion resistance (zinc sacrificially protects iron).
(Figure. 1. We see in the SEM, where (Fe) and (Zn) have diffused together)
Maintains the steel’s original properties and dimensions.
Compatible with standard handling and operations.
Extends the lifespan of production tubing under extreme conditions.
Purpose: Corrosion Protection:
o Sacrificial Protection: Zinc is more electronegative than iron (standard electrode potentials: Zn = -0.76 V, Fe = -0.44 V). In corrosive environments (e.g., moisture, salt), zinc corrodes preferentially, protecting the steel substrate via gradient galvanic action.
o Barrier Protection: The zinc-iron alloy layer acts as a physical barrier, preventing corrosive agents (e.g., chlorides, water, oxygen) from reaching the substrate.
o Durability: The metallurgical bond ensures the coating resists peeling or flaking, unlike loosely adhered coatings.
Why Diffusion is Effective:
o Uniform Coating: Solid-state diffusion allows zinc to penetrate complex geometries (e.g., threads, recesses, voids), unlike line-of-sight methods like electroplating, or electroless applications.
o Controlled Alloying: The formation of Fe-Zn intermetallic creates a robust, hard coating that combines zinc’s corrosion resistance with iron’s strength.
o No Internal Hydrogen Embrittlement: Unlike electroplating, thermal diffusion avoids introducing hydrogen, which can embrittle high-strength steels.
o No External Hydrogen Embrittlement: Zinc thermal diffusion occurs where shallow hydrogen cell formation forms, in the first ten microns of the substrate surface. This area is also thermally diffused with polycrystalline developed by (Fe-Zn), which fills voids and vacancies in the substrate. Preventing hydrogen-cell formation and strengthening the substrate cell structure.
Thermal Energy’s Role:
o Heating to 300–400°C provides sufficient energy for zinc atoms to diffuse into the steel lattice without melting either material.
o The temperature range optimizes diffusion kinetics while preserving the substrate’s mechanical properties (e.g., avoiding softening or phase changes in steel).
Material Compatibility:
o Zinc diffuses well into iron and low-alloy steels due to their compatible crystal structures (zinc: hexagonal close-packed, iron: body-centered cubic at process temperatures).
o The formation of stable Fe-Zn intermetallic ensures a durable, corrosion-resistant coating.
Environmental and Practical Benefits:
o The process is environmentally friendly compared to hot-dip galvanizing, as it avoids molten zinc baths and produces minimal waste.
o It’s cost-effective, it services intricate parts (e.g., threads, fittings) used in under carriage automotive, in ground construction, marine applications and/or oil and gas downhole.
Key Features of the Coating
· Corrosion Resistance: Outperforms coated steel in salt spray tests. At 50µms thermal diffused zinc (e.g., 1500–2500 hours per ASTM B117). At 50µms with make-up and break-out of threads, with (Al/Zn) spin dip, we see nearly 8,000+ salt spray hours. With corrosion only appearing on thermal growth alloy not the substrate.)· Adhesion: Metallurgical bonding ensures the coating withstands mechanical stress. (such as (MUBO) make up and break out).· Uniformity: Diffusion ensures even coating on complex shapes, such as thread dimensions, unlike electroplating or spraying.· Hardness: Intermetallic phases provide wear resistance, suitable for abrasive environments. Usually 1.7–2x harder than the substrate material.
By optimizing time and temperature parameters, we eliminate structural defects and ensure a uniform alloy gradient, providing superior resistance to operational stress and environmental challenges.
Challenges
· Temperature Sensitivity: Excessive temperatures (>400°C/ 752ºF) may cause liquid-phase formation or substrate damage. (While in service.)· Substrate Limitation: Best suited for carbon or low-alloy steels; less common for stainless steel due to its inherent chromium-oxide passivation.· Process Control: Time, temperature, and zinc concentration must be precisely controlled to achieve desired coating thickness and phase composition.
Hardness is a key mechanical property indicating resistance to indentation and wear. The thermal diffused zinc coating is generally significantly harder than the L80 substrate, offering better wear resistance on the surface while the softer substrate provides ductility. Below is a summary comparison based on standard hardness scales (Rockwell C [HRC] and Vickers [HV]). Values can vary slightly by process parameters, but typical ranges are provided.
The elevated hardness stems from the solid-state diffusion process, which transforms the coating into a composite of hard, brittle intermetallic phases rather than a soft, pure zinc layer. Here’s the step-by-step explanation:
Why the Diffused Zinc Coating is Harder
1. Formation of Intermetallic Compounds:
During sherardizing (300–400°C), zinc atoms interdiffusion into the iron lattice of the L80 steel, reacting to form layered Zn-Fe intermetallic:
These phases have higher lattice strain and stronger atomic bonding than the substrate’s ferrite or pearlite grains, resisting deformation under indentation (e.g., Vickers testing). Pure zinc (as in non-diffused plating) is only ~50–100 HV and ductile but alloying with iron increases hardness by 4–8x.
2. Microstructural Refinement via Diffusion:
3. Absence of Ductile Softening:
4. Process-Specific Enhancements:
Practical Implications
Notes:
Wear Resistance Comparison: L80 vs. Thermal Diffused Zinc Coating vs. 13Cr/L80 Steel
Problems in MR0175/ISO 15156/ CAPPs related to chemical stresses and mechanisms downhole
Wear Resistance Comparison: L80 vs. ThermaMitigation of Stress Cracking Effectsl Diffused Zinc Coating vs. 13Cr/L80 Steel
The Thermal Growth Alloy of the solid-state thermal diffusion does not have the same crystalline cell structure as the substrate, because it is an Intermetallic Layer made up of three different cell structure layers all protecting in different ways.
(ζ) Zeta layer has submicron and nano size polycrystalline structure packed tightly to inhibit and resist stress cracking. This layer is the first layer that meets the environment, so shallow hydrogen cells (10µms and less) have trouble forming as well. The lack and removal of internal hydrogen (IHE) in the process also helps reduce hydrogen cell formation and stress cracking in the substrate.
Thermal Growth Alloy is made up of three layers. Crystalline Structure:
This layer excels in atmospheric corrosion protection for small, intricate steel parts (e.g., fasteners, chains, or fittings) due to its uniformity on complex geometries and lack of hydrogen embrittlement risk, though it’s less common for large structures compared to hot-dip methods.
Overview
CSCC is a form of stress corrosion cracking that occurs in austenitic stainless steels, duplex stainless steels, and other alloys (e.g., nickel-based alloys) when exposed to chloride-containing environments under tensile stress and elevated temperatures (typically >50°C). It is driven by the interaction of chlorides, stress, and a susceptible microstructure, leading to trans granular or intergranular cracking.
Chloride Stress Corrosion Cracking (CSCC)
Mechanism
Affected Materials and Applications
How TDZ Helps
This offsets:
SOHIC is a specific form of hydrogen-induced damage that combines elements of HIC and stress corrosion cracking. It occurs in carbon and low-alloy steels in sour environments under tensile stress, where hydrogen-induced microcracks align perpendicular to the stress direction, often in the HAZ or near welds. SZC (discussed previously) is a subtype of SOHIC, localized to softened HAZ regions.
Stress-Oriented Hydrogen-Induced Cracking (SOHIC)
Summary of TDZ Effectiveness
General TDZ Benefits Across Mechanisms
Practical Considerations
Notes for CSCC
Since CSCC primarily affects stainless steels, TDZ is less relevant unless carbon steel components are part of a galvanic couple in a chloride environment. For CSCC, focus on low alloy selection (e.g., MR0175 selected materials) and for flow coatings (e.g., epoxy).
SZC occurs in the heat-affected zone (HAZ) of welds in sour (H₂S-containing) environments, where hydrogen from corrosion diffuses into softened microstructural zones, leading to cracking under stress.
How TDZ Helps:
Corrosion Barrier:
Reduced Hydrogen Ingress:
Sacrificial Protection:
Compatibility with Welds:
Limitations for SZC:
GHSC occurs when a metal (e.g., steel) is galvanically coupled to a more cathodic material in a corrosive environment, leading to enhanced hydrogen production and embrittlement under stress.
Galvanic Protection:
Uniform Coating:
Hydrogen Barrier:
Stress Corrosion Resistance:
Gradient Open Ciurcuit Potential:
Limitations for GHSC:
Summary
Scientific tests confirm that ziPLY technology reduces active microbial biomass (ATP) by 68–99%. The zinc-infused surface acts as a continuous biocide, preventing bacteria from reaching the steel lattice and colonizing the metal.”
ziPLY Pipe, is a type of thermal diffused zinc-infused steel pipe with an interior plastic coating. It’s designed for use in oil and gas applications where corrosion resistance is critical. A 2017 progress report evaluates its potential for microbiologically influenced corrosion (MIC), focusing on whether MIC-associated organisms (e.g., sulfate-reducing bacteria or SRB, and general heterotrophs tracked via aerobic plate count or APB) can form biofilms on the surface or corrode the metal.
(Figure 2) We see a diagram of how biofilm works to cause sulfide stress cracking (SSC).
The way in which TDZ negates this is by disallowing the biofilm to reach the substrate crystalline. The TDZ acts as both a barrier to the lattice of the substrate and also as a known biocide. The biofilm (CRUST) needs to attach itself and grow within the surface of the metal in order to colonize. This never takes place due to the % of Zinc in the TDZ , but also in the substrate as well. The biofilm would need to first eat through the entire TDZ layer, then >10µms deep into the substrate prior to establishing a colony that would produce (SSC).
After 10 weeks, the results indicate strong performance by TDZ in resisting biofilm formation and microbial growth compared to coated and uncoated carbon steel.
Bacterial Counts (APB/SRB)
Visual and Physical Observations