Vacuum Measurement: Pressure Gauges PDF Study Guide

Vacuum Measurement: Pressure Gauges A Comprehensive Study Guide Compiled and LaTeXified January 21, 2025 Contents 1 Introduction to Pressure...

Vacuum Measurement: Pressure Gauges A Comprehensive Study Guide Compiled and LaTeXified January 21, 2025 Contents 1 Introduction to Pressure 3 1.1 Units of Pressure............................... 3 1.2 Types of Pressure............................... 3 2 Types of Pressure Scales 3 2.1 Absolute Pressure (Pabs )........................... 3 2.2 Gauge Pressure (Pgauge )........................... 3 2.3 Vacuum Pressure............................... 4 3 Understanding Pressure Ranges 4 3.1 General Ranges................................ 4 4 Vacuum Pressure Measurement Techniques 4 4.1 Main Gauge Types for Vacuum....................... 4 5 Exam Preparation Checklist (Overview) 5 6 Additional Topics and Extended Study Guides 5 6.1 Types of Pressure and Their Measurement................. 5 6.2 Daltons Law of Partial Pressures...................... 5 6.3 Methods of Pressure Measurement...................... 5 6.4 Vacuum Measurement Instruments (Recap)................ 5 6.5 Three Main Principles in Vacuum Gauge Operation............ 5 6.6 Range of Pressure Measurements...................... 6 6.7 Key Exam Topics (Recap).......................... 6 7 Detailed Gauge Explanations 6 7.1 McLeod Gauge................................ 6 7.2 Thermal Conductivity Gauges........................ 6 7.2.1 Pirani Gauge............................. 6 7.2.2 Thermocouple Gauge......................... 7 7.3 Mechanical (Piezo) Gauges.......................... 7 1 8 Thermocouple vs. Penning (Cold Cathode) Gauges 7 8.1 Thermocouple Vacuum Gauge (Review).................. 7 8.2 Penning Gauge (Cold Cathode)....................... 7 9 Bayard-Alpert Ionization Gauge and Hot Cathode Gauges 8 9.1 Bayard-Alpert (B-A) Gauge......................... 8 9.2 Hot Cathode Ionization Gauges (General)................. 8 10 Electron Speed, Vacuum Components, and UHV Design 8 10.1 Electron Speed in Ionization Gauges.................... 8 10.2 Vacuum Components............................. 9 10.3 Designing for UHV.............................. 9 11 Final Exam Preparation Checklist 9 2 1 Introduction to Pressure Pressure is defined as the force exerted per unit area: F P = , A where: F is the force (Newtons, N), A is the area (square meters, m2 ). 1.1 Units of Pressure 1 psi = 6895 Pa 1 Bar = 105 Pa 1 atm = 101325 Pa 1 Torr = 133.3 Pa 1.2 Types of Pressure Static Pressure Exerted by a fluid or gas at rest. Analogous to water pushing against tank walls. Dynamic Pressure Exerted by a fluid or gas in motion. Example: Wind pressing against your face. 2 Types of Pressure Scales 2.1 Absolute Pressure (Pabs ) Measured relative to a perfect vacuum. For instance, outer space is near-zero absolute pressure. 2.2 Gauge Pressure (Pgauge ) Measured relative to atmospheric pressure: Pabs = Pgauge + Patm. Example: A car tires gauge reading excludes the weight of atmospheric air. 3 2.3 Vacuum Pressure Pressure below atmospheric (negative gauge). Common in vacuum chambers. 3 Understanding Pressure Ranges Atmospheric Pressure: at sea level is about 101325 Pa (≈ 14.7 psi). 3.1 General Ranges Very High Pressure: above 1000 atm Moderate Pressure: between 1–1000 atm Very Low Pressure (Vacuum): below 133 Pa (i.e., 1 Torr) 4 Vacuum Pressure Measurement Techniques Pressure gauges measure pressure in different reference modes: Absolute Gauges: measure total pressure (including atmospheric). Gauge Gauges: measure relative to atmosphere. Compound Gauges: measure both vacuum and positive pressures. 4.1 Main Gauge Types for Vacuum Manometers Use liquid columns (often mercury). Sensitive and accurate at low pressures. Mechanical Gauges Use deformation of diaphragms, Bourdon tubes, or bellows. Suitable for vacuum or higher-pressure applications. Thermal Conductivity Gauges Rely on gas heat transfer (e.g., Pirani gauge). Detect changes in thermal conductivity at lower pressures. Ionization Gauges Ionize gas molecules and measure the ion current. Useful for ultra-high vacuum (UHV). Capacitance Manometers Measure diaphragm deflection via capacitance changes. Very precise for low pressures. 4 5 Exam Preparation Checklist (Overview) Absolute vs. Gauge Pressure: Know the difference thoroughly. Unit Conversions: atm, Pa, Torr, psi, etc. Operational Principles: Manometers, mechanical, thermal conductivity, ioniza- tion gauges. Thermal & Ionization Gauges: Understand how these work at low pressure. Pressure Scales: Understand absolute vs. gauge references. 6 Additional Topics and Extended Study Guides 6.1 Types of Pressure and Their Measurement 1. Absolute Pressure (psia): Relative to perfect vacuum. 2. Gauge Pressure (psig): Relative to atmospheric pressure. 3. Atmospheric Pressure: ≈ 14.7 psi or 101.3 kPa at sea level. 4. Hydrostatic Pressure: P = ρgh (liquid column). 6.2 Daltons Law of Partial Pressures Ptotal = PA + PB + PC + · · · Essential in vacuum systems with multiple gas species. 6.3 Methods of Pressure Measurement Direct Measurement: Force on a surface (e.g., Bourdon gauge). Indirect Measurement: Relies on properties like thermal conductivity or ionization (e.g., Pirani, Ionization gauges). 6.4 Vacuum Measurement Instruments (Recap) High Pressure Measurement: Electrical resistance gauges. Moderate Pressure: Manometers, elastic elements (Bourdon tubes). Low Pressure/Vacuum: McLeod, Pirani, Ionization gauges, etc. 6.5 Three Main Principles in Vacuum Gauge Operation 1. Mechanical (Piezo-like): Deformation-based (e.g., Bourdon tubes). 2. Thermal Conductivity: Gas heat transfer changes with pressure. 3. Ionization: Ion current proportional to pressure in UHV. 5 6.6 Range of Pressure Measurements 1 psi = 6895 Pa 1 Bar = 105 Pa 1 atm = 101325 Pa 1 Torr = 133.3 Pa 6.7 Key Exam Topics (Recap) Derive/apply P = ρgh. Use Daltons Law in multi-gas vacuum systems. Differentiate direct vs. indirect gauges. Principles of Pirani, McLeod, Ionization gauges. Convert among main pressure units. 7 Detailed Gauge Explanations 7.1 McLeod Gauge Principle: Compresses low-pressure gas into a smaller volume for measurement (as- suming ideal gas behavior). Details: Measures down to 10−6 Torr. Uses mercury (ρ ≈ 13.6 g/cm3 ). P = ρgh. 7.2 Thermal Conductivity Gauges Basic Principle: Heat loss from a hot wire depends on gas density (pressure). Fewer molecules at lower pressure ⇒ lower heat conduction. 7.2.1 Pirani Gauge Measures filament resistance change due to temperature. Range: roughly 0.5 Torr down to 10−4 Torr. Requires calibration; sensitive to contamination. 6 7.2.2 Thermocouple Gauge A thermocouple detects the filament temperature. Range: ∼ 10−3 Torr to 10−1 Torr. Voltage from thermocouple ∝ filament temperature ∝ pressure. Thermal Conductivity of Gases Cv v λ 1 k= , λ=. 3 π d2 n 7.3 Mechanical (Piezo) Gauges Rely on diaphragm deformation. Examples: Bourdon tube, bellows, capacitance manometers. 8 Thermocouple vs. Penning (Cold Cathode) Gauges 8.1 Thermocouple Vacuum Gauge (Review) Heater element + thermocouple measuring temperature. Pressure range: 1 Torr to 1 mTorr. Advantages: Simple, reliable; Disadvantages: sensitive to gas type. 8.2 Penning Gauge (Cold Cathode) Principle: Ionizes gas molecules with a high voltage in a magnetic field; measures ion current. Effective down to 10−7 Torr (UHV). No filament (cold cathode) ⇒ more durable. Limitations: Gas-type dependent calibration. Aspect Thermocouple Penning (Cold Cathode) Pressure Range 1 Torr to 10−3 Torr down to 10−7 Torr Working Principle Heat dissipation Ion current in magnetic field Key Components Heater + thermocouple Cathodes, anode, magnet Table 1: Comparison of Thermocouple and Penning Gauges 7 9 Bayard-Alpert Ionization Gauge and Hot Cathode Gauges 9.1 Bayard-Alpert (B-A) Gauge Principle: A specialized hot cathode ionization gauge that reduces X-ray-induced er- rors by using a fine collector wire inside the grid. Pressure range: 10−8 Torr or lower. Relationship: ic = K · ie · P, where ic is the ion (collector) current, ie is the electron emission current, and K is a constant. How It Works: 1. Electrons emitted by a hot filament (cathode). 2. Accelerated to an anode grid. 3. Collide with gas molecules → create ions (G + e− → G+ + 2e− ). 4. Ions collected; current ∝ pressure. 9.2 Hot Cathode Ionization Gauges (General) Filament is heated for thermionic emission. High sensitivity in UHV regime. Disadvantages: Filament burnout, sensitive to contamination. 10 Electron Speed, Vacuum Components, and UHV Design 10.1 Electron Speed in Ionization Gauges Kinetic Energy: Ek = 12 me v 2 √ 2W Overcoming Work Function W : Ek = W =⇒ v = me Ionization gauge operation often involves accelerating electrons to specific energies for effective ionization. 8 10.2 Vacuum Components Essential for Ultra-High Vacuum (UHV) systems: 1. Chamber: Stainless steel with minimal outgassing. 2. Flanges + Seals: CF (ConFlat) flanges with copper gaskets. 3. View Ports: Often fused silica or borosilicate windows. 4. Valves: Gate valves, angle valves to control sections. 5. Feedthroughs: Electrical/mechanical feedthroughs while maintaining vacuum. 6. Manipulators: Move samples precisely inside the vacuum. 10.3 Designing for UHV Material choice (low outgassing, e.g. stainless steel, some alloys). Bake-out procedures to reduce residual gases. Multiple ports for gauges, sample transfer, electron/ion guns, etc. 11 Final Exam Preparation Checklist Pressure Definitions: Absolute, gauge, atmospheric; use ρgh for hydrostatic. Daltons Law: Summation of partial pressures in a gas mixture. Direct vs. Indirect Gauges: Force-based vs. property-based (thermal/ionization). Gauge Principles: – McLeod: Mercury compression for very low pressures. – Thermal Conductivity (Pirani/TC): Filament heat loss depends on gas density. – Ionization (Penning, Bayard-Alpert): Ion current ∝ pressure in UHV. Electron Kinetics: Work function, kinetic energy, and how electrons ionize gas molecules. UHV Design Basics: Materials, flanges, feedthroughs, outgassing/bake-out. Unit Conversions: Pa, atm, Torr, psi, bar. 9 Index Absolute Pressure, 3 Atmospheric Pressure, 4 Bayard-Alpert Gauge, 8 Capacitance Manometer, 4 Daltons Law, 5 Electron Speed, 8 Gauge absolute, 4 compound, 4 relative, 4 Gauge Pressure, 3 Ionization, 5 Ionization Gauge, 4 Manometer, 4 McLeod Gauge, 6 Mechanical Gauge, 4 Penning Gauge, 7 Piezo Gauge, 5 Pirani Gauge, 6 Pressure, 3 definition, 3 dynamic, 3 static, 3 Pressure Gauge, 4 Thermal Conductivity, 5 Gas, 7 Thermal Conductivity Gauge, 4 Thermocouple Gauge, 7 UHV design, 9 Vacuum Components, 9 Vacuum Pressure, 4 10