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RDS Instruments

WDXRF Engineering & Certification Suite

Authorized Field Engineering Access Only. All instrument data is processed 100% locally on this device — zero data is transmitted over the wire.

🔬 RDS Instruments WDXRF Suite

Unit: Not Loaded
Unassigned
🔒Local Sandbox

🔬 Instrument Ingestion: Parameter Bank (TDS) & Remote Diagnostics (RD)

Window 1 loads the machine Parameter Bank to build custom alignment tests and machine profile. Window 2 loads Remote Diagnostics for historical trend analysis.

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100% Local In-Browser Processing · Zero Data Transmitted Over The Wire: All loaded parameter banks, calibration matrices, and machine profiles are parsed strictly in your browser's local memory using the HTML5 FileReader API. Nothing is ever sent to or stored on any server. This tool functions completely offline once loaded.
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Window 1: TDS Folder / Parameter Bank

Machine Profile & Custom Tests: Builds 9-phase alignment procedure, 2θ Bragg angles, BOM & hardware profile.

Accepts: .ICF, .CAL, .IP, .CSF, .LOG, .TUB, TDS folder (e.g. DY######)
💡 Drag & drop TDS backup folder or parameter files here
Empty: Drop TDS folder/files or click Browse
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Window 2: RD Folder / Remote Diagnostics

Historical Data & Analysis: Tracks multi-run SPC performance trends, tube hours, stability & flags abnormalities.

Accepts: .RTF, .STB, .MUS, .ERR, .SES, .SPC (e.g. RD4400\DY######)
💡 Drag & drop RD remote diagnostics folder or run reports here
Empty: Drop RD folder/files or click Browse

📊 As-Found Parameter Bank Baseline (From Instrument Backup Files)

⚙️ Optical Hardware Configurator (8-Position Crystal Turret & Collimators)

Adjusting these components instantly recalculates all alignment phases, 2θ Bragg angles, and required standard samples.

🔧 Official PANalytical Preventive Maintenance (PM) Checklist

Authoritative 15-section maintenance protocol from svm_axios-max_en / Preventive Maintenance Checklist.htm (102 inspection items)

PM Checklist Progress:
0% (0/102 tasks)

🎯 3. Optical Goniometer Calibration & Alignment Protocol

Sequential 9-phase mechanical & optical calibration suite dynamically compiled for active goniometer optics and detectors.

Alignment Progress:
0% (0/0)

📊 Remote Diagnostics (RD) & TDS History, Multi-Run SPC Trends & Folder Comparison

Ingest two entire folders (Folder A: Baseline / TDS / Past Visit vs. Folder B: Current / RD / Evaluation). Automatic statistical process control (SPC) charting, performance drift tracking, and physical failure detection.

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Zero Server Transmission · Complete Device Privacy: Diagnostic logs (.RTF, .STB, .MUS) and SPC statistical trend runs remain strictly inside your device's memory. No customer data, tube hours, or proprietary telemetry is ever transmitted over the network.
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Window 1: TDS Folder / Parameter Bank (Baseline)

Machine Baseline: Factory zero angle corrections, goniometer offsets & tolerance registers.

.ICF, .CAL, .IP, .CSF, .LOG (e.g. DY###### or baseline visit)
💡 Drag & drop TDS backup folder or parameter files here
Empty: Drop TDS folder/files or click Browse
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Window 2: RD Folder / Remote Diagnostics (Runs)

Diagnostic Runs: Multi-run certificates, stability runs, scans & error logs.

.RTF, .STB, .MUS, .ERR, .SES, .SPC (e.g. RD4400\DY######)
💡 Drag & drop RD remote diagnostics folder or run reports here
Empty: Drop RD folder/files or click Browse

📈 Multi-Run Parameter Trend & Statistical Process Control (SPC) Chart

Interactive chronological timeline plotting Mean Centerline (x̄), ±2σ Warning Limits, and ±3σ Action Limits. Hover over data points for readings and outlier warnings.

🔍 Side-by-Side Dual Run Comparison & Drift Matrix

Direct parameter diff between any two historical or current runs with physical tolerance validation.

🚨 Automated Abnormality & Incident Detection Log

Rule-based diagnostic engine analyzing physical hardware failure signatures, interlock trips, and statistical outliers across all runs.

📚 Historical Diagnostic Runs Archive

Complete chronological registry of all parsed PANalytical .RTF, .STB, .MUS, and .CAL files.

🎯 Calibration & Alignment Reference Standards Matrix

Dynamically resolved from the installed crystals, collimators, and detectors in the active BOM.

Before beginning optical goniometer alignment, ensure the following certified reference sample disks are cleaned, inspected for surface flatness, and mounted in standard PANalytical sample cups (32 mm / 37 mm / 40 mm aperture).

📋 Official Channel Settings Reference (Service Manual Calibration Setups)

Standard goniometer parameters, kV/mA, crystal, detector, and PHD levels from 📄 Samples_and_Channel_Settings.htm ↗.

📡 PANalytical Remote Diagnostics (RD4400) Channel Master Bank 157 Channels

Official diagnostic channel definitions extracted from 📄 CH4401Rh.spc ↗ used by PANalytical Remote Diagnostics (RD4400 / RDS) for sequential optical alignment, detector linearity, reproducibility, and high-voltage calibration.

Channel Category Line / Elem Crystal(s) kV / mA Filt / Mask Coll Det Target kCPS Min..Max kCPS Sample PSC

💎 Official Crystal Scan Line Calibration Specifications (📄 deflines.spc ↗) 17 Crystal Calibrations

Standard coarse and fine angular 2θ scanning parameters, discriminator window levels, and calibration samples for all Axios crystal types.

Crystal Line Element Order Detectors LL (%) UL (%) Coarse Step (s) Coarse Range (°2θ) Fine Step (s) Fine Range (°2θ) Standard Sample

⚖️ Reference Sample Disk Selection & Verification Limits (📄 smpsel.spc ↗) 6 Verification Rules

Diagnostic countrate boundaries used by Remote Diagnostics software to verify that the operator placed the correct reference sample disk (Cu, C1, or C3) into the measuring cup prior to starting automated calibration.

Sample Disk Channel Min Allowed (kCPS) Max Allowed (kCPS) Verification Logic & Objective

🧮 Engineering Calculators & Service Formulas

Interactive service tools for detector dead times, optical alignments, vacuum/gas dynamics, and hardware verification.

Showing 21 tools
📖 Official Procedure: Adjust Dead Time: Flow Detector ↗

⏱️ Flow Detector Dead Time & Linearity

Dead Time update factor = 0.8 · Linearity tolerance ≤ 1.0%

Click Calculate. Formula: K = ((10*Ix - Iy)/Iy)*100; New DT = Old DT + K/0.8
📖 Official Procedure: Adjust Dead Time: Sealed Xe Detector ↗

⚡ Sealed Xenon Detector Dead Time

Dead Time update factor = 0.3 · Linearity tolerance ≤ 1.0%

Click Calculate. Formula: K = ((10*Ix - Iy)/Iy)*100; New DT = Old DT + K/0.3
📖 Official Procedure: Adjust Dead Time: Scintillation Detector ↗

🌟 Standard Scintillator Dead Time & Linearity

Dead Time update factor = 0.23 (Cu / Sn) · 50 mA reference

Click Calculate. Formula: K = ((5*Ix - Iy)/Iy)*100; New DT = Old DT + K/0.23
📖 Official Procedure: Adjust Dead Time: HiPer Scint Detector ↗

🚀 Hi-Per Scintillator Dead Time & Linearity

Cu factor = 1.3 · Sn factor = 1.5 · 80 mA reference

Click Calculate. Formula: K = ((8*Ix - Iy)/Iy)*100; New DT = Old DT + K/Factor
📖 Official Procedure: Linearity Test: Goniometer & Channels ↗

📈 Multi-Point Detector Linearity Regression (10 mA – 100 mA)

Zero-intercept linear regression y = Sx where S = Σ(x*y) / Σ(x²) · Tolerance ≤ 1.0% relative error per point

Tube mA Measured [kcps] Calculated [kcps] Deviation [kcps] Rel. Error % Verdict
Click Run Multi-Point Regression to evaluate best-fit slope and verify all points within ±1.0%.
📖 Official Procedure: Adjust Scintillation Detector Gain ↗

🎛️ Scanning Goniometer Scintillator Gain Correction

Calculates PMT high voltage / gain shift using Sb & Fe PHD centroids

Click Calculate. Formula: ROUND(155 * (Sb - Fe) / (4.19 * Fe - Sb), 0)
📖 Official Procedure: Do the PHD Test (Detector Resolution) ↗

📊 Detector Energy Resolution & Q-Factor

Resolution% = (FWHM / Peak) * 100 · Q-Factor = Resolution / √λ

Calculates peak energy dispersion and FPC counter performance quality.
📖 Official Procedure: Reference Samples & Channel Settings ↗

📐 Bragg's Law Dual-Unit Solver (nm & Å)

nλ = 2d sin θ · Solves 2θ angle or crystal 2d spacing in nm and Ångströms

Enter crystal 2d and wavelength to solve exact 2θ peak angle.
📖 Official Procedure: Calibrate the Goniometer (Linearity) ↗

🧭 Scanning Goniometer Linearity (Ti & Sb)

Ti Kα (86.10°) & Sb Kα (13.46°) · Specified limit |ΔTi - ΔSb| ≤ 0.030°

Click Check. Evaluates goniometer gear train and angle encoder linearity.
📖 Official Procedure: Calibrate the Goniometer (Motor Zero) ↗

🎯 Focusing Goniometer Motor Correction

Updates focusing goniometer motor zero position based on Ti Kα (86.10°)

Click Calculate. Formula: New Corr = Current Corr + (86.10 - Ti_meas) * 0.01
📖 Official Procedure: Calibrate Goniometer (Beam Split) ↗

🔦 XRD Direct Beam Half-Intensity Split

Target Half Intensity = Direct / 2 ± (Direct * Tol%)

Click Evaluate. Calculates lower/upper intensity acceptance boundary.
📖 Official Procedure: Calibrate Goniometer (OQ Standards) ↗

💎 NIST SRM 1976 & 640 OQ Reference Standard & Delta Calculator

Certified 2θ reflections and relative intensities for Corundum (SRM 1976/a/b) and Silicon (SRM 640c/d). Enter measured angles to calculate Δ2θ and verify OQ tolerance (≤ 0.030°).

h k l Certified 2θ [°] Certified Rel. Int. [%] Measured 2θ [°] Δ2θ [°] OQ Verdict
Select standard and enter measured peak 2θ angles to verify instrument OQ certification.
📖 Official Procedure: Do a Test of Vacuum Static Leakage ↗

💨 Vacuum Static Leak Rate Test

Statutory PANalytical limit ≤ 0.07 Pa/s over 60 seconds

Click Verify. Evaluates seal integrity of vacuum chamber, plunger, and MVV valve.
📖 Official Procedure: Do a Test of Gas Density Stabilizer ↗

🌡️ Gas Density Stabiliser (GDS) Stability

Verifies P10 gas density stability between 0.6 hPa & 1.1 hPa (Tolerance ≤ 4.0%)

Click Check. Formula: Diff% = ((I0.6 - I1.1) / I0.6) * 100 (Limit ≤ 4.0%)
📖 Official Procedure: About the Flow Detector (Escape Peaks) ↗

🧪 Gas Escape Peak Position Predictor

Predicts Ar Kα (2.957 keV) and Xe Lα (4.120 keV) escape peaks and PHD %

Click Predict. Calculates escape peak energy and PHD window position.
📖 Official Procedure: Adjust Measuring Circuit: Water Flow ↗

🌊 Water Flow Rate Sensor Pulse Check

Converts cooling sensor frequency (Hz) to L/min · Minimum threshold ≥ 3.5 L/min

Click Calculate. Formula: Flow (L/min) = (Hz * 60) / Impulse (Threshold ≥ 3.5 L/min)
📖 Official Procedure: PM of Optical Path (Al Foil) ↗

🛡️ Aluminium Foil Transmission Quality

He/Vac ratio ≥ 85% (nominal ≥ 90%) · He/Air ratio ≥ 1.8 (nominal ≥ 2.0)

Click Evaluate. Checks optical chamber flush quality, helium purity, and vacuum window transparency.
📖 Official Procedure: About Motor Drive Circuits & MDC ↗

🔌 MDC Board & Motor Hardware Decoder

Decodes Axios Error Instrument 9.5.X.1/2/3 to pin down exact card slot & motor axis

Click Decode. Resolves Board number B = ((X - 1) DIV 3) + 1 and Motor M = X - (3 * (B - 1)).
📖 Official Procedure: Do the X-ray Radiation Survey ↗

☢️ Radiation Survey Monitor Calibration & Dose

Converts monitor c/s to μSv/h and mSv/h · Statutory leakage limit < 1.0 μSv/h

Click Calculate. Checks statutory radiation safety on external chassis surfaces.
📖 Official Procedure: Goniometer Channels (CSE Counting Time) ↗

⌛ CSE & Required Counting Time Solver

CSE% = 100 / √(Intensity * Time) ↔ Time = (100 / CSE%)² / Intensity

Click Calculate to determine statistical precision or count duration.
📖 Official Procedure: Replace the X-ray Tube Procedure ↗

⚡ 21. X-Ray Tube Health, Aging & Intensity Degradation

Models operating hour consumption vs 40,000 hr rated life, radiative Cu emission retention %, cathode cooling flow margin, and HV arc stability.

Click Evaluate to analyze tube lifetime, radiative emission loss, and cathode flow safety margin.
A Reference for the Rest of Us!®

WDXRF Service Formulas For Dummies®

The Field Engineer's Pocket Guide to Spectrometer Math: Every detector dead time, Bragg angle, goniometer alignment, and vacuum formula laid out in plain English. No corporate OEM fluff—just step-by-step arithmetic you can punch into a $5 pocket calculator with a #2 pencil on a clipboard.

Worksheet #1 · Detector Subsystem

Flow Detector Dead Time & Linearity

What it actually means: Your P10 flow counter detects an X-ray pulse, but goes blind for a few hundred nanoseconds while the ionized gas clears. If the dead time setting in software is wrong, your counts at 100 mA won't equal 10× your counts at 10 mA.

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REMEMBER: The correction factor for the Flow Detector is 0.8. Counting time is 40 seconds at 10 mA and 4 seconds at 100 mA so counting statistics have equal weight.
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FIELD PRO-TIP: Before changing dead time in .CAL, confirm your detector gas flow rate is exactly 0.85 L/h and the density stabilizer temperature is rock solid. Bad gas will fake a dead time error every single time.
🧮 The Calculator Math (Step-by-Step Keystrokes):
Step 1 (Count Ratio K): K% = ((10 × Ix - Iy) ÷ Iy) × 100
Step 2 (Correction in ns): ΔDT = K% ÷ 0.8
Step 3 (New Setting): New DT = Old DT + ΔDT
Step 4 (Linearity Check): Error% = |(I50 - 5 × I10) ÷ (5 × I10)| × 100  (Spec: ≤ 1.0%)
Worked Field Example: Ix = 1.020 kcps (10 mA), Iy = 10.150 kcps (100 mA), Old DT = 150 ns.
10 × 1.020 = 10.200 → (10.200 - 10.150) ÷ 10.150 = 0.004926 → K = +0.493% → ΔDT = +0.493 ÷ 0.8 = +0.62 ns → New DT = 151 ns.
📋 Pen & Paper Field Worksheet Instrument Serial: __________________ · Date: ____________
Current Dead Time in .CAL: ns (Old DT)
Ix @ 10 mA (40s count): kcps × 10 = [ ]
Iy @ 100 mA (4s count): kcps
Calculated K%: [ (10×Ix - Iy) ÷ Iy ] × 100 = [ ] %
ΔDT Correction: K% ÷ 0.8 = [ ] ns
New Dead Time Value: Old DT + ΔDT = [ ] ns
Linearity Check @ 50 mA: I50 = [ ] vs 5×I10 = [ ] → Rel Error: [ ] %
VERDICT:   [   ] PASS (≤ 1.0% error)      [   ] FAIL (Re-tune Flow gas / replace wire)
Worksheet #2 · Detector Subsystem

Sealed Xenon Detector Dead Time

What it actually means: Exactly like the flow counter, but filled with pressurized Xenon gas. Xenon's ionization cascade is heavier and recovers at a different rate, so the magic divisor is 0.3 instead of 0.8.

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REMEMBER: The Xe divisor is 0.3. If K is positive, your detector is undercounting at high mA — you must INCREASE the dead time value.
🧮 Pocket Calculator Math:
Step 1: K% = ((10 × Ix - Iy) ÷ Iy) × 100
Step 2: ΔDT = K% ÷ 0.3
Step 3: New DT = Old DT + ΔDT
Worked Field Example: Ix = 0.980 kcps, Iy = 9.700 kcps, Old DT = 200 ns.
10 × 0.980 = 9.800 → (9.800 - 9.700) ÷ 9.700 = +0.01031 → K = +1.031% → ΔDT = +1.031 ÷ 0.3 = +3.4 ns → New DT = 203 ns.
📋 Pen & Paper Field Worksheet Unit: __________________ · Date: ____________
Old DT in .CAL: ns
Ix @ 10 mA (40s count): kcps × 10 = [ ]
Iy @ 100 mA (4s count): kcps
K%:( [ 10×Ix ] - Iy ) ÷ Iy × 100 = [ ] %
ΔDT:K% ÷ 0.3 = [ ] ns
New Xe Dead Time:Old DT + ΔDT = [ ] ns
VERDICT:   [   ] PASS (≤ 1.0% error)      [   ] FAIL
Worksheet #3 · Detector Subsystem

Standard Scintillator Dead Time

What it actually means: Scintillation crystals flash light when hit by hard X-rays, and a PMT tube amplifies it. Because scintillator signals are faster, we compare 10 mA against 50 mA (factor 5), and the tuning divisor is 0.23.

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REMEMBER: Reference is 50 mA (NOT 100 mA). Count times: 25s at 10 mA, 5s at 50 mA. Magic factor is 0.23.
🧮 Pocket Calculator Math:
Step 1: K% = ((5 × Ix - Iy) ÷ Iy) × 100
Step 2: ΔDT = K% ÷ 0.23
Step 3: New DT = Old DT + ΔDT
📋 Pen & Paper Field Worksheet Unit: __________________ · Date: ____________
Old DT in .CAL: ns
Ix @ 10 mA (25s count): kcps × 5 = [ ]
Iy @ 50 mA (5s count): kcps
K%:( [ 5×Ix ] - Iy ) ÷ Iy × 100 = [ ] %
ΔDT:K% ÷ 0.23 = [ ] ns
New Scintillator DT:Old DT + ΔDT = [ ] ns
VERDICT:   [   ] PASS (≤ 1.0% error)      [   ] FAIL
Worksheet #4 · Detector Subsystem

Hi-Per Scintillator Dead Time

What it actually means: The high-count-rate Scintillator pre-amplifier. Uses 80 mA reference (factor 8). Use divisor 1.3 when calibrating on Cu Kα, or 1.5 when calibrating on Sn Kα.

🧮 Pocket Calculator Math:
Step 1: K% = ((8 × Ix - Iy) ÷ Iy) × 100
Step 2: ΔDT = K% ÷ Factor  (Cu Factor = 1.3 · Sn Factor = 1.5)
Step 3: New DT = Old DT + ΔDT
📋 Pen & Paper Field Worksheet Unit: __________________ · Element: [   ] Cu   [   ] Sn
Old DT in .CAL: ns
Ix @ 10 mA: kcps × 8 = [ ]
Iy @ 80 mA: kcps
K%:( [ 8×Ix ] - Iy ) ÷ Iy × 100 = [ ] %
ΔDT:K% ÷ [ 1.3 or 1.5 ] = [ ] ns
New Hi-Per DT:Old DT + ΔDT = [ ] ns
Worksheet #5 · Counting Physics

True Count Rate vs. Measured Count Rate

What it actually means: If your detector has a 200 ns dead time and measures 1,000,000 counts per second, it was actually blind for 0.20 seconds out of that 1 second! The true count rate hitting the detector was actually 1,250,000 cps.

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WATCH OUT (UNITS TRAP): Dead time τ is stored in nanoseconds (e.g. 200 ns = 0.000000200 seconds). Count rates must be in counts per second (cps), NOT kcps, when doing this math!
🧮 Pocket Calculator Math:
R_true = R_meas ÷ (1 - R_meas × τ)
Where: R_meas = cps, τ = dead time in seconds (ns × 10^-9)
Pocket Example: R_meas = 1,000,000 cps, τ = 200 ns (0.0000002 s).
1 - (1,000,000 × 0.0000002) = 1 - 0.20 = 0.80 → 1,000,000 ÷ 0.80 = 1,250,000 true cps.
📋 Pen & Paper Field Worksheet Unit: __________________
Measured Rate (R_meas): cps
Detector Dead Time (τ): ns = [ 0.000000_____ ] sec
Loss Factor (R_meas × τ):[ ]
Denominator (1 - Loss):1 - [              ] = [ ]
True Count Rate (R_true):R_meas ÷ Denom = [ ] cps
Worksheet #6 · PMT Electronics

Scintillator PMT High Voltage & Gain Shift

What it actually means: As photomultiplier dynodes age, pulse heights sag. By measuring where the Antimony (Sb) and Iron (Fe) pulse height peaks land, this formula tells you how many DAC steps to crank the PMT high voltage supply to re-center everything at 50%.

🧮 Pocket Calculator Math:
ΔGain Steps = ROUND( 155 × (Sb - Fe) ÷ (4.19 × Fe - Sb) )
Nominal Target: Sb Top = 50.0% · Fe Top = 50.0%
Field Example: Sb measured at 52.0%, Fe measured at 48.0%.
Numerator: 155 × (52.0 - 48.0) = 155 × 4.0 = 620.
Denominator: (4.19 × 48.0) - 52.0 = 201.12 - 52.0 = 149.12.
Result: 620 ÷ 149.12 = +4.15 → Adjust PMT gain DAC by +4 steps.
📋 Pen & Paper Field Worksheet
Measured Fe Top Channel:[ ] %
Measured Sb Top Channel:[ ] %
Numerator: 155 × (Sb - Fe):155 × [ ] = [ ]
Denominator: (4.19 × Fe) - Sb:[ ] - Sb = [ ]
PMT DAC Step Adjustment:Num ÷ Denom = [ ] steps
Worksheet #7 · Detector Diagnostics

Detector Energy Resolution & Q-Factor

What it actually means: Pulse Height Distribution (PHD) resolution tells you how sharp your detector is. A contaminated anode wire or bad gas turns a sharp mountain peak into a blurry rolling hill.

⚠️
OFFICIAL PASS/FAIL SPECS: Flow Detector: < 18.5% on Fe Kα (or < 42% on Ti Kα).
Scintillator: < 55% on Cu Kα. If higher, your crystal has yellowed or the optical grease has dried out.
🧮 Pocket Calculator Math:
Resolution% = (FWHM ÷ Peak Centroid) × 100
Q-Factor = Resolution% ÷ √λ [nm]  (Cu Kα = 0.1542 nm → √λ = 0.3927)
📋 Pen & Paper Field Worksheet
Full Width at Half Max (FWHM):[ ] %
Peak Position (Centroid):[ ] %
Resolution Percentage:(FWHM ÷ Peak) × 100 = [ ] %
Wavelength λ [nm]:[ ] nm → √λ = [ ]
Quality Q-Factor:Resolution% ÷ √λ = [ ]
VERDICT:   [   ] PASS (< 18.5% Flow / < 55% Scint)      [   ] FAIL (Replace wire / service detector)
Worksheet #8 · Optical Physics

Bragg's Law & 2θ Peak Angles

What it actually means: The granddaddy equation of WDXRF. X-rays hit your analyzer crystal (like LiF200 or PE002) and reflect into the detector only when wave interference is constructive at exactly 2θ degrees.

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CALCULATOR MODE WARNING: Check your pocket calculator right now: does the screen say DEG or RAD? If it says RAD (radians), your answer will be total gibberish! Switch to DEGREES!
🧮 Pocket Calculator Math:
nλ = 2d × sin(θ) → θ = arcsin( (n × λ) ÷ 2d )
2θ Angle = 2 × θ
Common 2d spacings: LiF200 = 0.4028 nm · LiF220 = 0.2848 nm · Ge111 = 0.6532 nm · PE002 = 0.8742 nm · PX1 = 5.02 nm
Worked Field Example: Cu Kα (λ = 0.1542 nm, n=1) on LiF200 crystal (2d = 0.4028 nm).
sin(θ) = 0.1542 ÷ 0.4028 = 0.38282.
Punch sin⁻¹(0.38282) on calculator → θ = 22.509°.
Multiply by 2 → 2θ = 45.018° (Look for the peak right at 45.02° on your goniometer scan!).
📋 Pen & Paper Field Worksheet
Diffraction Order (n):[       ] (Usually 1)
Emission Line Wavelength λ:[ ] nm
Crystal 2d Spacing:[ ] nm
Ratio: (n × λ) ÷ 2d:[ ] = sin(θ)
Theta (θ = arcsin):sin⁻¹( [          ] ) = [ ] °
Theoretical 2θ Angle:2 × θ = [ ] °
Worksheet #9 · Optical Alignment

Goniometer Linearity & Angular Offset

What it actually means: If your goniometer is off by +0.010° at low angles and -0.020° at high angles, the mechanical arm is either eccentric or the optical backlash cords are stretched.

🧮 Pocket Calculator Math:
Offset = 2θ_measured - 2θ_theoretical
Slope Error = (Offset_high - Offset_low) ÷ (2θ_high - 2θ_low)
Tolerance: Peak position must be within ±0.005° across the full 15° to 145° scan range.
📋 Pen & Paper Field Worksheet
Low Angle (e.g. Al Kα ~ 144.8° or Scint):Meas: [ ] − Theo: [ ] = Offset: [
Mid Angle (e.g. Cu Kα ~ 45.02°):Meas: [ ] − Theo: [ ] = Offset: [
High Angle (e.g. Ba Lα ~ 20.4°):Meas: [ ] − Theo: [ ] = Offset: [
Max Linearity Spread:| Max Offset - Min Offset | = [ ] °
VERDICT:   [   ] PASS (≤ 0.005° spread)      [   ] FAIL (Re-zero DOPS / adjust backlash cord)
Worksheet #10 · Mechanics

Goniometer Stepper Motor Pulse Calibration

What it actually means: Exactly how many electrical stepper pulses does the drive board need to send to turn the goniometer optical disc exactly one full degree? Required when replacing motors or drive cards.

🧮 Pocket Calculator Math:
Pulses per Degree = Total Motor Pulses ÷ Δ2θ [degrees]
Nominal Factory Setting: Exactly 4,000 pulses / degree (or 8,000 in microstep mode).
📋 Pen & Paper Field Worksheet
Total Encoder Pulses:[ ] pulses
Angular Travel Δ2θ:[ ] degrees
Calibration Factor:Pulses ÷ Degrees = [ ] pulses/°
Worksheet #11 · Optical Alignment

Direct Beam Split & Absolute Optical Zero

What it actually means: Remove the crystal and shoot the unattenuated primary X-ray beam straight through to the detector. Scan past zero from both sides. Absolute optical zero is the exact mathematical midpoint between positive and negative half-intensity points.

2θ_zero = (2θ_pos + 2θ_neg) ÷ 2
Mechanical Zero Error = 2θ_zero - 0.000°  (Spec: ≤ ±0.002°)
Example: Positive half-intensity = +0.124°, Negative half-intensity = -0.120°.
(+0.124 + -0.120) ÷ 2 = +0.004 ÷ 2 = +0.002° (Pass! In spec).
📋 Pen & Paper Field Worksheet
Positive Scan Half-Max (2θ+):[ ] °
Negative Scan Half-Max (2θ-):[ ] °
True Optical Zero (2θ0):(2θ+ + 2θ-) ÷ 2 = [ ] °
VERDICT:   [   ] PASS (≤ ±0.002°)      [   ] FAIL (Update DOPS zero in .CAL)
Worksheet #12 · Quality Assurance

NIST SRM Standard Count Rate Drift

What it actually means: Did the spectrometer lose sensitivity since last year's certification? Measure your reference monitor disk (e.g. SRM 1155a Stainless Steel) and check percentage change against baseline.

Drift% = ((I_current - I_baseline) ÷ I_baseline) × 100
Tolerance: ≤ ±2.0% for major elements (Fe, Cr, Ni, Cu).
📋 Pen & Paper Field Worksheet
Baseline Intensity (Commissioning):[ ] kcps
Today's Measured Intensity:[ ] kcps
Difference (Today - Baseline):[ ] kcps
Percentage Drift:(Diff ÷ Baseline) × 100 = [ ] %
VERDICT:   [   ] PASS (≤ ±2.0%)      [   ] WARN (> 2% Tube aging or crystal clouding)
Worksheet #13 · Vacuum Subsystem

Chamber Vacuum Static Leakage Rate

What it actually means: Pump down to 3 Pa, close the main valve, start a stopwatch for 10 minutes, and write down how many Pascals the pressure climbed. If it rises faster than 0.5 Pa per minute, you have a leaking seal.

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OFFICIAL FACTORY SPEC: Rate must be ≤ 0.50 Pa / min. Axios optical chamber internal volume is 28 Liters.
Leak Rate = (P_final - P_initial) ÷ Elapsed Minutes  [Pa/min]
Q_leak = (28 L × (P_final - P_initial) × 0.01 mbar/Pa) ÷ (Seconds)  [mbar·L/s]
📋 Pen & Paper Field Worksheet
Initial Pressure at Valve Closure:[ ] Pa (Target ≤ 5 Pa)
Final Pressure after Hold:[ ] Pa
Elapsed Hold Time:[ ] minutes
Static Rise Rate:(P_fin - P_init) ÷ Minutes = [ ] Pa/min
VERDICT:   [   ] PASS (≤ 0.50 Pa/min)      [   ] FAIL (Check turret Quad ring / plunger O-rings)
Worksheet #14 · Fluidics & Gas

Gas Density Stabilizer (GDS) Law: P/T

What it actually means: The number of P10 gas molecules inside your flow detector must remain strictly constant so pulse heights don't wander. When ambient temperature rises, the GDS bellows must increase pressure proportionally.

💣
KELVIN CONVERSION: Always add 273.15 to convert Celsius into absolute Kelvin! Never do gas calculations in °C directly!
P2 = P1 × ( (T2 + 273.15) ÷ (T1 + 273.15) )  [hPa]
Nominal Baseline: ~680 hPa @ 20.0°C (293.15 K)
📋 Pen & Paper Field Worksheet
Baseline Pressure (P1):[ ] hPa
Baseline Temp (T1):[ ] °C + 273.15 = [ ] K
Current Temp (T2):[ ] °C + 273.15 = [ ] K
Required GDS Pressure (P2):P1 × (T2_K ÷ T1_K) = [ ] hPa
Worksheet #15 · Spectral Physics

Detector Gas Escape Peak Energies

What it actually means: When an incoming X-ray strikes an Argon or Xenon atom inside your counter, it kicks out an inner electron. The gas atom radiates its own fluorescent X-ray which escapes the detector without getting measured. You see a ghost peak at exactly (Incident Energy - Gas Energy).

E_escape = E_incident - E_gas
Argon Kα = 2.96 keV (Flow Counter) · Xenon Lα = 4.10 keV (Xe Detector)
Field Example: Measuring Iron (Fe Kα = 6.40 keV) on flow counter.
E_escape = 6.40 - 2.96 = 3.44 keV. Don't mistake this ghost peak for Potassium or Calcium!
📋 Pen & Paper Field Worksheet
Element Line & Energy (E_inc):[ ] keV
Detector Gas Energy (E_gas):[ 2.96 keV for Ar / 4.10 keV for Xe ]
Escape Peak Energy:E_inc - E_gas = [ ] keV
Worksheet #16 · Tube Protection

Cooling Water Heat Dissipation & Flow

What it actually means: Your 4 kW X-ray tube converts 99% of its power into heat. If the cooling water doesn't remove it, the anode melts in seconds. This checks if your chiller is removing the kilowatts you're putting into it.

💣
MINIMUM FLOW LIMIT: Cathode cooling flow must NEVER drop below 3.5 L/min at full power. If ΔT exceeds 15°C across the tube, your heat exchanger is clogged with algae or mineral scale!
Q_dissipated [kW] = Flow [L/min] × 0.0697 × (T_out - T_in) [°C]
Constant 0.0697 = (1000 g/L × 4.184 J/g·K ÷ 60 s) ÷ 1000 W/kW
📋 Pen & Paper Field Worksheet
Water Flow Rate:[ ] L/min (Spec ≥ 3.5 L/min)
Water Return Temp (T_out):[ ] °C
Water Supply Temp (T_in):[ ] °C
Temp Rise (ΔT):T_out - T_in = [ ] °C
Heat Removed:Flow × 0.0697 × ΔT = [ ] kW
VERDICT:   [   ] PASS (ΔT normal < 15°C)      [   ] WARN (Flush heat exchanger / service chiller)
Worksheet #17 · Optical Filters

Primary Beam Filter Transmission %

What it actually means: How much X-ray flux actually gets through a 300 µm Aluminum or 100 µm Brass tube filter according to Beer-Lambert's absorption law.

Transmission% = 100 × e^(-(μ/ρ) × ρ × x)
μ/ρ = mass attenuation coefficient (cm²/g) · ρ = density (g/cm³) · x = thickness (cm)
📋 Pen & Paper Field Worksheet
Mass Attenuation (μ/ρ):[ ] cm²/g
Filter Density (ρ):[ ] g/cm³
Thickness (x):[ ] cm (e.g. 100 µm = 0.010 cm)
Exponent (μ/ρ × ρ × x):[ ]
Transmission Result:100 × e^(-Exp) = [ ] %
Worksheet #18 · Analytical Chemistry

Minimum Detectable Concentration (MDC / LOD)

What it actually means: What is the absolute lowest concentration in parts per million (ppm) your spectrometer can legally prove is present above background noise? Standard 3-sigma Currie detection limit.

MDC = ( 3 × √( R_bkg ÷ T_bkg ) ) ÷ Sensitivity [cps/ppm]
Field Example: Background count rate = 500 cps, measured for 20 seconds. Sensitivity = 25 cps/ppm.
√(500 ÷ 20) = √25 = 5.
3 × 5 = 15 → 15 ÷ 25 = 0.60 ppm (Your Limit of Detection is 0.6 ppm!).
📋 Pen & Paper Field Worksheet
Background Rate (R_bkg):[ ] cps
Background Count Time (T_bkg):[ ] seconds
Noise: 3 × √(R_bkg ÷ T_bkg):3 × √[ ] = [ ] cps
Analytical Sensitivity:[ ] cps / ppm
Lower Limit of Detection:Noise ÷ Sensitivity = [ ] ppm
Worksheet #19 · Radiation Safety

Radiation Survey & Inverse Square Distance Law

What it actually means: If you measure a tiny leak of 2.5 µSv/h right touching the shutter shield (10 cm away), how much dose is hitting an operator standing 1 meter away? Double the distance, cut the dose to one-fourth!

💣
LEGAL RADIATION LIMIT: Dose rate must be strictly < 1.0 µSv/h (0.1 mrem/h) at 10 cm from ANY accessible surface of the cabinet with X-ray tube at maximum 4.0 kW output!
I2 = I1 × ( d1 ÷ d2 )²
Pocket Example: I1 = 2.5 µSv/h at d1 = 10 cm (0.1 m). Operator standing at d2 = 100 cm (1.0 m).
(10 ÷ 100)² = (0.1)² = 0.01 → 2.5 × 0.01 = 0.025 µSv/h (Totally safe background level).
📋 Pen & Paper Field Worksheet
Measured Dose Rate (I1):[ ] µSv/h
Measurement Distance (d1):[ ] cm
Target Distance (d2):[ ] cm
Distance Ratio Squared:(d1 ÷ d2)² = [ ]
Calculated Dose at d2:I1 × (d1÷d2)² = [ ] µSv/h
SURFACE LIMIT:   [   ] PASS (< 1.0 µSv/h @ 10cm)      [   ] DANGER (Immediate shutdown!)
Worksheet #20 · Counting Statistics

Counting Statistics, Standard Deviation & RSD%

What it actually means: Because radioactive X-ray emission is purely random Poisson decay, you can never get a 'perfect' count. The more counts N you collect, the smaller your percentage uncertainty.

💡
THE SQUARE ROOT RULE: For N total counts, uncertainty is √N. Relative Standard Deviation is 100% ÷ √N.
• 10,000 counts → 1.0% RSD    • 100,000 counts → 0.32% RSD    • 1,000,000 counts → 0.10% RSD.
Standard Deviation (σ) = √N
Relative Error (RSD%) = ( √N ÷ N ) × 100 = 100 ÷ √N
📋 Pen & Paper Field Worksheet
Total Counts Collected (N):[ ] counts
Standard Deviation (√N):√[                ] = [ ] counts
Relative Error (RSD%):100 ÷ √N = [ ] %
Worksheet #21 · Hardware Protection

X-Ray Tube Power & Filament Burn Factor

What it actually means: Are you exceeding the tube's maximum continuous wattage? And how fast are you boiling away the tungsten filament? Running at maximum 160 mA burns tungsten 8 times faster than running at 80 mA due to cubic thermal evaporation!

Power [kW] = ( kV × mA ) ÷ 1000  (Limit: ≤ 4.0 kW or 3.0 kW per unit spec)
Filament Burn Stress Factor = ( mA ÷ 80 mA )³
Pocket Example: Running 60 kV at 66 mA → (60 × 66) ÷ 1000 = 3.96 kW (Safe, < 4.0 kW).
Running at 160 mA → (160 ÷ 80)³ = 2³ = 8× filament wear rate compared to standard 80 mA!
📋 Pen & Paper Field Worksheet
Operating Voltage (kV):[ ] kV
Operating Current (mA):[ ] mA
Total Power Output:(kV × mA) ÷ 1000 = [ ] kW
Filament Stress Ratio:(mA ÷ 80)³ = [ ] × wear rate
POWER VERDICT:   [   ] PASS (≤ 4.0 kW rated max)      [   ] OVERPOWER (Generator Trip!)

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