Mass Metrology (eBook)

Dr. S.V. Gupta holds Master’s degrees in Physics from Allahabad University and in Mathematics from Agra University. He obtained his Ph.D. in the area of diffrimoscopic imaging at Delhi University. Dr. Gupta subsequently completed advanced training at the International Bureau of Weights and Measures, BIPM, France; International Organisation of Legal Metrology, OIML, Paris France; National Physical Laboratory, UK; and PTB (Physikalisch-Technische Bundesanstalt), Germany. He has been involved in various projects with the National Institute for Standards and Technology, NIST, USA and with the PTB, Germany. Dr. Gupta was recently awarded the title of “Mapiki Ratan” (a Jewel in Metrology). Further international awards include Membership in The Institute of Physics, UK, and the Honours and Awards List of the OIML since 2004.

Preface to the Second Edition 7
Preface to the First Edition 9
Contents 11
1 Unit of Mass and Standards of Mass 25
1.1 Concepts of Mass 25
1.1.1 Gravitational Mass 26
1.1.2 Inertial Mass 26
1.1.3 Equality of Inertial and Gravitational Mass 27
1.2 Mass and Weight of a Body 27
1.2.1 Conventional Mass 28
1.2.2 Variation of the Weight of a Body on Surface of Earth 28
1.3 Unit of Mass 31
1.3.1 History of the Units of Metre and Kilogram 31
1.3.2 Unit of Length 32
1.3.3 Kilogram de Archives 32
1.4 Metric Convention 33
1.4.1 International Kilogram 33
1.4.2 National Standard of Kilogram 34
1.4.3 National Kilogram and Other Standards in India 35
1.4.4 Calibration of Transfer Standards of Mass 36
1.5 Hierarchy of Mass Standards 37
1.5.1 Nomenclature 37
1.5.2 Measurement Chain 39
1.5.3 Tracking the Mass Values of Standards 39
1.5.4 Period of Verification or Calibration 40
1.5.5 Maximum Permissible Errors 40
1.6 Traceability of Measurements 41
1.6.1 Traceability 41
1.6.2 CIPM MRA 42
References 43
2 Two-Pan Equal-Arm Balances 44
2.1 Introduction 44
2.2 Brief History 44
2.3 Other 1-kg Balances 45
2.3.1 Equal-Arm Interchangeable Pan Balance UK 45
2.3.2 Equal Arm with Double Interchangeable Pan Balance 46
2.3.3 Substitution Balance NPL-India 47
2.3.4 Electronic Balance with Automation at NPL-India 49
2.3.5 Hydrostatic Balance 50
2.4 Installation of a Balance 52
2.4.1 Proper Environmental Conditions for Balance Room 52
2.4.2 Requirements for Location of the Balance 52
2.5 Evaluation of Metrological Data for a Balance 55
2.5.1 Need for Evaluation 55
2.5.2 Visual Examination 55
2.5.3 Sensitivity 56
2.5.4 Period of Swing or Time Period 58
2.5.5 Accuracy of Rider Bar 59
2.5.6 Stability/Repeatability 61
2.5.7 Repeatability of Weighing 61
2.5.8 Equality of Arm Lengths 62
2.5.9 Calculation of Arm Ratio, Repeatability of Single and Double Weighing 63
2.5.10 Requirement for Arm Ratio and Repeatability of Weighing 65
2.5.11 Test for Parallelism of Knife Edges 65
2.6 Methods of Weighing 67
2.6.1 Direct Weighing 67
2.6.2 Transposition Weighing 68
2.6.3 Substitution Weighing 68
2.7 Double Transposition and Substitution Weighing 69
2.7.1 Double Transposition Method 69
2.7.2 Double Transposition with Simultaneous Determination of S.R. 70
2.7.3 Double Substitution 71
2.7.4 Double Substitution Weighing with Simultaneous Determination of S.R. 72
2.8 Maintenance of Standard Balances 72
2.8.1 Category of Balances 73
2.8.2 Reference Balances 73
2.8.3 Secondary Standard Balances 73
2.8.4 Working Standard Balances 74
References 74
3 Single-Pan Mechanical Balances 76
3.1 Introduction 76
3.2 Description of a Single-Pan Balance 76
3.3 Evaluation of Single-Pan Balance 80
3.3.1 Verification Interval 80
3.3.2 General Examination 80
3.3.3 Sensitivity of the Sprit Level of the Balance 81
3.3.4 Hardness of Knife Edges and Bearing Planes 81
3.3.5 Sensitivity Setting 82
3.3.6 Tests 82
3.3.7 Test for Smallest Built-in Weight and Calibration of Illuminated Scale 82
3.3.8 Calibration of Lower Half and Upper Half of the Optical Scale 83
3.3.9 Short Duration Test for Precision of the Balance 85
3.3.10 Calibration of Built-in Weights for All Dial Settings 86
3.3.11 Performance Test 88
3.4 Uncertainty in Calibration of the Balance 90
3.4.1 Uncertainty of Mass Determination by the Balance 91
References 91
4 Electronic Balances and Effect of Gravity 92
4.1 Introduction 92
4.2 Electromagnetic Force Compensation 93
4.2.1 Principle of EMFC 93
4.2.2 Principle of EMFC Balance 94
4.3 Partially Electromagnetic Force Compensated Balance 95
4.3.1 Partially EMFC Two-Pan Balance 95
4.3.2 Partially EMFC Single-Pan Balance 97
4.4 Fully EMFC Balance 98
4.4.1 Without Lever 98
4.4.2 Balance with Mechanical Levers 98
4.4.3 Working of EMFC Balances 99
4.4.4 Electronic Circuitry 100
4.5 Range of Capacity of EMFC Balance 102
4.6 Availability of EMFC Cells 103
4.7 Effect of Variation in Gravity on Electronic Balances 103
4.7.1 Instruments Affected by Gravity 103
4.7.2 Error Due to Variation in g 105
4.7.3 Variation of g with Respect to Latitude 106
4.7.4 Error Per Degree Change in Latitude at Different Places 106
4.7.5 Significant Error 109
4.7.6 Choice of Values of ``n'' to Calculate Error at Various Latitudes 109
4.7.7 Latitude Differences to Cause Significant Error 109
4.7.8 Intra-state Movement of Electronic Weighing Instruments 115
4.7.9 Error Due to Altitude 115
4.8 Conclusion About the Movement of Electronic Weighing Instruments 117
References 118
5 Strain Gauge Load Cells 119
5.1 Load Cell 119
5.2 Construction 119
5.2.1 Elastic Spring Element 119
5.2.2 Detector 119
5.2.3 Pasting 120
5.3 Resistance Strain Gauge 120
5.3.1 Change in Resistance 120
5.3.2 Measurement of Resistance 121
5.3.3 Configuration of Strain Gauges on Spring Element 124
5.3.4 Dimensions of the Spring Element 126
5.3.5 Methods of Connecting Several Load Cells 127
5.3.6 Trimming Devices in the Load Cell 128
5.4 Some Important Terms 131
5.4.1 Definitions 131
5.4.2 Notations Used on Load Cells 133
5.5 Classification of Load Cells 134
5.5.1 Accuracy Class 134
5.5.2 Number of Intervals 134
5.5.3 Load Application 135
5.6 Maximum Permissible Errors for Load Cells 135
5.6.1 Maximum Permissible Error at Verification/Model Approval 135
5.6.2 Maximum Permissible Error at Inspection 136
5.6.3 Determination of Error for Digital Instruments 136
5.7 Tests to Be Conducted 136
5.7.1 Performance Tests 137
5.7.2 Influence Factors Tests 137
5.7.3 Test Conditions 137
5.8 Performance Tests 139
5.8.1 Permissible Error, Repeatability, Nonlinearity and Hysteresis Tests 139
5.8.2 Creep and Minimum Dead Load Return Tests 139
5.8.3 Performance Tests at Different Temperatures 141
5.8.4 Temperature Effect on Minimum Dead Load Output 142
5.8.5 Effect of Barometric Pressure Test 142
5.8.6 Humidity Test 142
5.9 Additional Tests 143
5.9.1 Voltage Variations 144
5.9.2 Short-Time Power Reductions 144
5.9.3 Bursts (Electrical Fast Transients) 145
5.9.4 Electrostatic Discharge 146
5.9.5 Electromagnetic Susceptibility 146
5.9.6 Span Stability 147
5.10 Requirements for Load Cells 149
References 149
6 Various Types of Transducers for Weighing 150
6.1 Introduction 150
6.1.1 Classification 151
6.1.2 Force Applied by a Body 151
6.2 Vibrating String/Vibrating Strip Devices 151
6.2.1 Single-String Transducer Cell 152
6.2.2 Double-String Transducer Cell 153
6.2.3 S-Shaped Vibrating Strip Transducer 154
6.2.4 Transducer with String Vibrating in Heterodyne Mode 154
6.2.5 Use of Vibrating String Transducers 155
6.3 Tuning Fork Transducer 156
6.4 Gyroscopic Devices 158
6.5 Optical Interference Transducer 160
6.6 Magneto-elastic Transducer (Pressductor) 161
6.6.1 Construction 161
6.6.2 Principle of Magneto-elastic Transducer 162
6.7 Change in Capacitance Transducer 163
6.8 Photoelectric Device 164
6.9 Hydraulic Load Transducer 165
6.10 Piezoelectric Transducer 165
6.10.1 Longitudinal and Transverse Effect 166
6.10.2 Piezoelectric Device and Cascading to Increase the Output 167
6.10.3 Sensitivity in Different Modes 168
6.10.4 Electronic Measurement Circuits 168
6.10.5 Particulars of Piezoelectric Transducers 170
6.11 Strain Gauge of Semiconductor Material 170
6.12 Piezo-resistant Force Transducer 170
6.13 Linear Variable Differential Transformer 171
6.14 Inductive Worm-Spring Transducer 174
6.15 Surface Wave Resonator 174
6.16 Nucleonic Weighing 176
6.16.1 Principle 176
References 178
7 Testing of Electronic Balances 179
7.1 Introduction 179
7.2 Principle of Digital Indications 179
7.2.1 Digital and Analogue Instruments 179
7.2.2 Principle of Digital Indication Device 180
7.2.3 Equality in Error of Digital and Analogue Instruments 184
7.2.4 Maximum Permissible Errors 184
7.2.5 Definitions of Some Important Terms 184
7.2.6 Practical Determination of the Error of a Digital Machine 186
7.2.7 Verification of Digital Instruments for Compliance 186
7.2.8 Rule for Errors of the Combined System 187
7.3 Testing of Electronic Balances/Weighing Machines 188
7.3.1 Introduction 188
7.3.2 General Requirements 189
7.3.3 Descriptive Requirements 189
7.3.4 Classes of Weighing Instruments 190
7.3.5 Performance Tests 190
7.4 Type Approval Tests 194
7.4.1 Tests to Meet the Requirements for the Effect of Influence Quantities 194
7.4.2 Extreme Temperature Test 195
7.4.3 Variation in Supply Voltage and Frequency Test 196
7.4.4 Short Time Power Reduction Test 196
7.4.5 Electrical Bursts Test 196
7.4.6 Electrostatic Discharge Test 197
7.4.7 Electromagnetic Susceptibility Test 197
7.5 Nonlinearity 198
7.5.1 Methods of Estimating Nonlinearity 198
7.6 Hysteresis Error 199
7.7 Guidelines for Choosing Balances 199
7.8 Class of Electronic Balances Not Covered by OIML 200
References 200
8 Air Density and Buoyancy Correction 201
8.1 Introduction 201
8.2 Equation for Density of Air 203
8.2.1 Parameters of the Gas Equation 204
8.2.2 Molar Mass of Water Vapour 205
8.2.3 Constants Involved in psv, f and Z 207
8.2.4 Variable Parameters 208
8.2.5 Uncertainty Budget of Air Density Evaluation from CIPM Formula 208
8.2.6 Air Density Tables 208
8.3 Air Buoyancy Artefact Method 210
8.3.1 Principle 210
8.3.2 Artefacts 213
8.3.3 Uncertainty Budget 219
8.4 Optical Method for Determination of Air Density 222
8.4.1 Relation of Refractive Index and Density of Air 222
8.4.2 Experimental Work 223
8.4.3 BIPM Refractometer 224
References 230
9 Weights—Standards of Mass 234
9.1 Introduction 234
9.2 OIML Classification of Weights 235
9.3 Maximum Permissible Errors 236
9.3.1 OIML Maximum Permissible Errors 236
9.3.2 Maximum Permissible Errors in Weights in USA 236
9.3.3 Maximum Permissible Errors in Commercial Weights in India 238
9.4 Maximum Permissible Errors for Other Weights 239
9.4.1 Maximum Permissible Errors for Weights Used in Scientific and Industrial Fields 239
9.4.2 Maximum Permissible Errors in Standard Weights for Legal Metrology 240
9.4.3 Special Purpose Reference Standards (Germany) 240
9.5 Material of Weights 241
9.5.1 Property Requirements for Material of Weights 241
9.5.2 Material for Weights of 1g and Above 243
9.5.3 Material for Fractional Weights 245
9.5.4 Material for Adjustment of Weights 246
9.6 Design and Finish of the Weights 247
9.6.1 Basics of Design of Weights 247
9.6.2 Surface Finish of Gram Weights 250
9.6.3 Fractional Weights 251
9.6.4 Weight Box 252
9.7 Effect of Finite Magnetic Susceptibility 252
9.7.1 Expression for Magnetic Force 253
9.7.2 Measurement of Magnetic Susceptibility of Weights 254
9.8 Electrostatic Charges 257
9.9 Effect of Inequality of Temperature of Weight and Its Surroundings 257
9.9.1 Buoyant Force 258
9.9.2 Change in Mass Due to Convection of Air 258
9.9.3 Change in Indication with Time 259
9.9.4 Change in Mass Due to Adsorption 260
9.10 Effect of Density of Material of Weights 263
9.10.1 Criterion for Density Range of the Weight 264
9.10.2 Determination of Density of a Weight 265
9.11 Physical Properties 268
9.12 Surface Resistance of Platinum–Iridium Mass Standards 268
9.12.1 Effect of Change in Relative Humidity 269
9.12.2 Effect of Change in Temperature 269
9.12.3 Effect of Change in Pressure 269
9.13 Effect of Weighing in Air and Vacuum 270
9.14 Stability of Mass Standards 270
9.14.1 Instability in Mass Standards Due to Mercury Contamination 270
9.14.2 Instability in Mass Standards Due to Atmospheric Carbon and Oxygen 271
References 272
10 Group Weighing Method 274
10.1 Introduction 274
10.2 Different Sets of Weights 275
10.2.1 Sets of Weights 275
10.2.2 Head Weights 276
10.3 Principal of Group Weighing 276
10.3.1 Linear Equations and Method of Least Squares 277
10.3.2 Design Matrix 278
10.3.3 Variance Covariance Matrix 279
10.3.4 Weighting Factor 280
10.3.5 Improving a Weighing Design 281
10.3.6 Efficiency of a Weighing Design 283
10.3.7 Average of Squares of Residual Errors 283
10.4 Calibration of Set of Weights 283
10.4.1 Series 5, 2, 2, 1 283
10.4.2 Series 5, 2, 1, 294
10.4.3 Series 5, 2, 1, (BIPM) 297
10.4.4 Series 4, 3, 2, 1 (BIPM) 300
10.4.5 Series 5, 3, 2, 1 305
10.5 Calculations with Weighing Factors 308
10.6 Multiples of Unit of Mass 313
10.7 Weights of Same Denominations 315
10.7.1 Optimum Value of N 316
10.7.2 Experimental Work 317
10.7.3 Numerical Example 318
References 319
11 Nanotechnology for Detection of Small Mass Difference 321
11.1 Introduction 321
11.2 Cantilever Vibration 321
11.2.1 Characterisation of Cantilever 322
11.2.2 Dimensions and Mass of an Attogram Cantilever 324
11.3 Nanotechnology 325
11.4 Examples of Fabrication of Micro-cantilevers 326
11.4.1 Etching Process 326
11.4.2 Electron Beam Lithography 328
11.4.3 Various Micro-cantilevers in Use 330
11.5 Principles of Detection of Micro-cantilever Motion 330
11.6 Examples of Detection Micro-cantilever Response 330
11.6.1 Detection by Using an Interferometer 330
11.6.2 Detection by Capacity Measurement 331
11.6.3 Improved Fibre-Optic Interferometer 333
11.7 Mass Sensitivity of Cantilevers 334
11.7.1 No Change in Spring Constant (End-Point Loading) 334
11.7.2 Changing Spring Constant (Uniform Loading) 335
11.8 Mass Detector Cantilevers 335
11.8.1 At Femtogram Level 335
11.8.2 At Attogram Level 336
11.8.3 Sub-attogram Level 337
11.8.4 Zeptogram Level 337
11.8.5 Sub-zeptogram Level (One Gold Atom) 338
11.8.6 At Attonewton Level 338
11.8.7 A Final Goal 339
11.8.8 Viscosity: A Problem 340
11.9 Minimum Detectable Force/Mass 340
11.10 Micro-cantilever Applications 341
11.10.1 Large Surface to Volume Ratio 341
11.10.2 Examination of Surface 341
11.10.3 Thermal/Photo-thermal 342
11.10.4 Low Power Consumption Micro-cantilevers 343
11.10.5 Chemistry 343
11.10.6 Biology 343
11.10.7 Health Care 344
11.10.8 Physics (Viscosity and Density) 345
11.10.9 Magnetometry 346
11.10.10 Data Storage 346
11.10.11 Terrorist Threat Detection 347
References 347
12 Redefining the Unit of Mass 353
12.1 Introduction 353
12.1.1 Requirements for Defining a Base Unit 354
12.2 History of Kilogram and It Stability in Mass 354
12.2.1 Brief History of Kilogram de Archive (KA) 354
12.2.2 Preparation of the Artefact Defining kg 355
12.2.3 Fabrication 356
12.2.4 Continuity with the Mass of KA 357
12.2.5 Stability of m(KA) with Respect of m(IPK) 357
12.2.6 Stability of m(IPK) 358
12.2.7 Outcome of Redefining a Unit of Measurement 359
12.2.8 Meaning of Taking a Measured Value as Exact 360
12.3 Possibilities to Redefine Kilogram 360
12.3.1 NA by Measurements 361
12.3.2 kg and NA Relation 361
12.3.3 Relation Between of H and NA 362
12.4 Values of Avogadro Constant 363
12.5 Other Methods of Defining kg 365
12.5.1 The Kilogram Through Ion Collection Method 365
12.5.2 The Kilogram Through Levitation Method 368
12.5.3 The Kilogram Through Voltage Balance 370
12.5.4 The Kilogram Through Watt Balance 373
12.5.5 The Kilogram, Einstein Energy Equation and Planck Constant 375
12.5.6 Another Way of Redefining the Kilogram 376
12.6 Planck Constant h in Terms of Other Constants 376
12.7 Status of Watt Balance 377
12.8 Practical Standards to Realize Kilogram 378
12.9 Author’s Observations 379
References 379
13 Redefining the Base Units 383
13.1 Preparations for Redefining Base Units 383
13.1.1 A Brief History of the CGPM Decisions 383
13.1.2 Resolution About Redefinitions 384
13.2 Revised Definitions of SI Base Units 389
13.2.1 CODATA Efforts for New Definitions 391
13.3 Fundamental Constants for Kilogram 392
13.4 New Definition of Base Units 392
13.4.1 Base Units in Terms of Fundamental Constants 393
13.5 Inter Dependence of Base Units 394
13.5.1 New SI Units 395
13.5.2 Old SI Units 395
13.6 Relationship Matrix 396
13.6.1 Defining Constants in Terms of Base Units 397
13.6.2 Base Units in Terms of Defining Constants 397
13.6.3 Use of the Tables 397
13.7 Vacuum and Air Dissemination of Kilogram 398
13.7.1 Conclusions and Recommendations 399
13.8 Traceability 400
13.8.1 Traceability and Uncertainty Before Redefinition 400
13.8.2 Traceability and Uncertainty After Redefinition 401
13.9 Hierarchy of Mass 401
References 402
14 Realisation of Mass Unit 403
14.1 Introduction 403
14.2 Kibble Balance 403
14.2.1 Title of the Balance 403
14.2.2 Importance of Kibble Balance 404
14.2.3 Basic Principle 404
14.3 Kibble Balances at Metrology Institutes 407
14.3.1 Conventional Two-Mode Two Measurement Phase Kibble Balances 408
14.3.2 Korea Research Institute of Standards and Science KRISS, Korea 408
14.3.3 Laboratoire National de Métrologie et d’Essais (LNE), France 408
14.3.4 Federal Institute of Metrology (METAS), Switzerland 408
14.3.5 Measurement Standard Laboratory of New Zealand MSL 409
14.3.6 National Institute of Metrology (NIM), China 409
14.3.7 National Institute of Standards and Technology (NIST), USA 409
14.3.8 National Physical Laboratory (NPL), UK 410
14.3.9 National Research Council (NRC), Canada 410
14.4 The Original Joule Balance 410
14.4.1 National Institute of Metrology (NIM), China 410
14.4.2 Single-Mode One Measurement Phase Kibble Balances 410
14.4.3 Single-Mode Two Measurement Phase Watt Balances 411
14.4.4 Moving Magnet Balance at Ulusal Metroloji Enstitüsü (UME), Turke 411
14.5 Measurement of Velocity of the Pan 412
14.5.1 Interferometers 412
14.5.2 Refractive Index of Air 412
14.5.3 Light Source 413
14.6 Mass of Weight Used (M) 413
14.6.1 Measurement of the Working Masses 413
14.6.2 Substitution Weighing 414
14.6.3 Balances Used in Kibble Balance 414
14.6.4 Alignment of the Mass on the Mass Pan 415
14.6.5 Alignment of the Mass Comparator 415
14.7 Gravity Measurement 416
14.7.1 Instruments for Measurement 416
14.7.2 Corrections 417
14.8 Constant Magnetic Field 420
14.8.1 Magnets 421
14.9 Demagnetization of the Rare Earth Magnets 425
14.10 Change of the Reluctance of the Yoke 426
14.10.1 The Reluctance Force 426
14.10.2 Temperature Change of the Rare Earth Magnet 426
14.10.3 Temperature Change of the Yoke Material 426
14.10.4 Engineering of Magnets with Smaller Temperature Coefficients 427
14.10.5 Actively Controlling the Temperature 428
14.11 Voltage Measurements 428
14.11.1 Measurement Techniques 429
14.11.2 Josephson Reference 429
14.11.3 Hysteretic Arrays 429
14.11.4 Programmable Arrays 430
14.11.5 Voltmeter 430
14.11.6 Amplifiers 431
14.11.7 Synchronisation of the Voltmeter and Counter 431
14.12 Current Generation and Measurement 432
14.12.1 Current Sources 433
14.12.2 The Measurement Resistor 435
14.13 Resistance Determination with the Quantum Hall Effect 436
14.14 Joule Balance Measurements 437
14.15 Environmental Effects 437
14.15.1 Ground Vibration 437
14.15.2 Anti-vibration Systems 438
14.15.3 External Magnetic Fields 438
14.15.4 Temperature Effects 438
14.15.5 Shielding and Electrical Isolation 438
14.16 Reduction in Mass Values of BIPM Working Standards Against IPK 439
14.17 Relation Between RK?90, KJ?90 and h 439
14.18 Results 441
14.19 XRCD Method 443
14.19.1 Sphere 444
14.19.2 Volume of Sphere 444
14.19.3 Principle 444
14.19.4 Realization of the Kilogram Using Already Characterized Crystals 445
14.19.5 Relation Between IPK and kg (Revised Definition) 445
14.20 Characterization of Silicon Crystal 446
14.20.1 Enrichment of Crystal 446
14.20.2 Single Crystal Growth 447
14.20.3 Isotopic Composition of Silicon 447
14.20.4 Crystal Perfection: Evaluation of Point Defects 447
14.20.5 mSL Layers 449
14.20.6 Molar Mass 451
14.20.7 Lattice Parameter 452
14.20.8 Uncertainty in XRCD Method 455
14.21 Pilot Study for Equivalence of Two Methods 456
14.21.1 New Definition of kg 456
14.21.2 Sponsor 456
14.21.3 Aim 457
14.21.4 Organisation and Participants 457
14.21.5 Comparison Protocol 457
14.21.6 Particulars of Travelling Standard 458
14.21.7 Calculations 459
14.21.8 Conclusions 460
References for Kibble Balance 460
Index 467