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Technical depth

Technical models

Decision point → system boundary → dominant balance → measurement data → conclusion.

Evidence

Engineering assessmentModel boundaryMeasurement dataProject-specific checks

Engineering review sequence

StepEngineering itemRequired definitionOutput
1Decision pointequipment acceptance, supplier comparison, process transfer, failure analysis, or test readinessreview target
2System boundarychamber, pump train, hot zone, plasma source, treated surface, cathode, or full test benchmodel domain
3Dominant balancegas load, effective pumping speed, diffusion, heat transfer, ion flux, or emission stabilityreduced calculation
4Measurementspressure-time curve, leak test, temperature log, profile, cross-section, I-V data, or test coupondata request
5Conclusionaccepted, conditionally accepted, rejected, or returned for additional measurementtechnical memo / FAT question / test plan

System boundary and dominant balance

SystemBoundaryDominant balancePrimary dataReject condition
Vacuum chambervessel + ports + seals + pump connectiongas load vs effective pumping speedpump-down, pressure-rise, helium leak testultimate pressure stated without pressure-time data
Process gas systemMFCs + valves + chamber conductance + exhaustprocess gas load vs Seffflow-pressure lognominal pump speed stated without conductance/gas-load check
LPC / carburizing loadsteel grade + load geometry + boost/diffusion schedulecarbon diffusion and boundary carbon fluxcarbon profile, hardness profile, recipe logrecipe name without measured profile
Plasma nitridingpart surface + plasma sheath + fixture + thermal pathion flux, bias, chemistry and temperaturebias/current log, cross-section, hardness profilesurface-treatment claim without layer/profile data
Coating processsubstrate + interface + coating + contact environmentadhesion, stress, load support and tribological responsecross-section, thickness, adhesion, tribologycoating photo without functional data
Cathode-neutralizeremitter + insert + thermal path + gas/plasma couplingemission stability and thermal stateI-V curves, restart cycles, drift datasingle ignition event presented as validation
TVAC / EP chamberchamber + pumping + thruster gas flow + diagnosticsgas load vs effective pumping during operationgas-load pressure, Seff, diagnostic layoutempty-chamber base pressure used as test-condition proof
Core engineering checks

After the system boundary is fixed, the review moves to the physical balance that controls the decision.

A vacuum problem starts with gas load, chamber volume and effective pumping speed. A diffusion-treatment problem starts with temperature, material response and boundary carbon or nitrogen flux.

A plasma-treatment problem starts with ion flux, bias, chemistry and surface temperature. A cathode problem starts with thermal state, gas/plasma coupling and emission drift.

The blocks below keep the same structure: variables to define, records to request, and the decision that can be made from those records.

Vacuum / gas balance

Used when chamber pressure must be checked under pump-down or process gas flow.

dP/dt = Q/V - (Seff/V)·P
P ≈ Q/Seff at steady gas load
InputsV, Q, Seff, conductance, gas species
Recordspump-down curve, process-pressure curve, pump data
Decisionbase-pressure and process-pressure plausibility

Pressure rise / leak separation

Used when the chamber reaches pressure slowly or cannot hold pressure after isolation.

Qrise = V·dP/dt
Qrise = Qleak + Qoutgassing + Qvirtual
Inputsisolated volume, pressure-rise slope, material state
Recordspressure-rise curve, helium leak test, bakeout/cleaning history
Decisionleak repair, bakeout, cleaning, or geometry correction

Diffusion treatment

Used for LPC, carburizing and nitriding when the required result is a measured depth/profile, not only a recipe name.

∂C/∂t = ∂/∂x[D(C,T,steel)·∂C/∂x]
-D·∂C/∂x = JC(t)
Inputssteel grade, temperature, time, boost/diffusion schedule
Recordscarbon/nitrogen profile, hardness profile, microstructure
Decisioncase depth, surface state, recipe transferability

Thermal balance

Used when controller temperature, load temperature and thermal gradients may differ.

Cth·dT/dt = Pin - Prad - Pcond - Pgas
Prad = εσA(T⁴ - Tw⁴)
Inputsheater power, load mass, emissivity, fixture contact, gas state
Recordsthermal map, ramp/soak logs, TUS/SAT where applicable
Decisionthermal uniformity and load-temperature validity

Plasma surface interaction

Used when activation, nitriding, etching or coating adhesion depends on ion energy, flux and chemistry.

Γi ≈ ni·cs
Eion ≈ e·Vbias
R = f(Γi, Eion, chemistry, T)
Inputspressure, gas composition, bias, current, source geometry
Recordsbias/current log, witness coupon, profile, roughness
Decisionactivation, nitriding, etching, adhesion risk

Cathode emission stability

Used when ignition must be separated from stable operation, restart behaviour and drift.

Ie = f(T, φ, A, surface state)
drift = ΔI/Δt at fixed operating point
Inputstemperature, emitter state, gas flow, operating current
RecordsI-V curve, restart cycles, drift, vacuum/gas log
Decisionactivation quality and operational stability

Example review paths

CaseGivenCheckOutput
Vacuum chamber acceptanceV, pump train, pressure-time curve, leak-test target, process gas flowSeff, Q = V·dP/dt, P ≈ Q/Seff, conductance constraintsacceptance questions for leak, outgassing, conductance and gas-load pressure
LPC recipe transfersteel grade, boost/diffusion schedule, target case depth, HPGQ routecarbon profile, hardness profile, surface carbon, quench resultrecipe accepted, corrected, or returned for profile measurement
Cathode-neutralizer validationignition trace, current setpoint, gas flow, pressure, thermal routeI-V curve, drift, restart cycles, post-test stateactivation accepted or additional stability test requested
PVD/CVD coating routesubstrate, contact medium, load, temperature, coating routeinterface, thickness, stress/load support, tribology dataroute accepted for component test or rejected as insufficiently documented

Minimum records

AreaRequired recordsEngineering conclusion
Vacuum equipmentpump-down curve, ultimate pressure, pressure-rise curve, helium leak-test reportvacuum integrity and gas-load plausibility
Vacuum thermal processtemperature map, ramp/soak log, vacuum/gas log, load descriptionthermal regime and process repeatability
Diffusion treatmentrecipe log, carbon/nitrogen profile, hardness profile, microstructurecase depth, surface condition and process transferability
Coatingcross-section, thickness, adhesion, roughness, tribology or component testcoating architecture and functional suitability
CathodeI-V data, current drift, restart cycles, vacuum/gas log, post-test inspectionactivation quality and operational stability
TVAC / EP testgas-load pressure, effective pumping estimate, diagnostic layout, contamination-control datatest-environment readiness

Application link

Application Map

Scientific model boundaries

Vacuum balance

Model boundary: chamber volume, conductance, effective pumping speed, gas source and pressure measurement location.

Q_total = Q_leak + Q_outgas + Q_process
P(t) depends on V, S_eff and Q_total

Diffusion treatment

Model boundary: steel composition, temperature history, carbon / nitrogen boundary flux, phase constraints and quench route.

C(x,t) → measured profile
hardness depth → material response

Coating route

Model boundary: substrate support, interface, layer sequence, residual stress, roughness and contact environment.

functional response ≠ coating name
response = layer + substrate + contact

Cathode test

Model boundary: emitter condition, temperature, vacuum/gas environment, geometry, current regime and restart sequence.

ignition event ≠ stable emission
validation requires drift and restart data

Basis

Data
Inputs, boundary conditions, dominant balance, measured data and rejection conditions.
Interpretation
Models are applied to structure decisions and identify missing records, not to replace measurement.
Project use
Each project requires its own boundary conditions, calibration data and acceptance criteria.

Diffusion modelling and high-temperature degradation

Diffusion modelling

Diffusion-controlled decomposition and thermal stability

Numerical diffusion models are part of the technical data for diffusion-controlled phase redistribution, precipitate evolution and thermal-stability assessment in multiphase materials.

Checks: model boundary, diffusion data, time/temperature condition, numerical result, publication list.

Aggressive media

Coating behaviour in optical-glass melting environments

Multicomponent coatings exposed to aggressive optical-glass-melting media require chemical-compatibility, dissolution/degradation and interface-stability records.

Checks: coating composition, exposure medium, temperature / process condition, post-exposure microstructure and degradation pattern.