Gupta Mass Metrology

The Newly Defined Kilogram
2. Auflage 2019
ISBN: 978-3-030-12465-6
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 155, 471 Seiten

Reihe: Springer Series in Materials Science

This second edition of Mass Metrology: The Newly Defined Kilogram has been thoroughly revised to reflect the recent redefinition of the kilogram in terms of Planck's constant. The necessity of defining the kilogram in terms of physical constants was already underscored in the first edition. However, the kilogram can also be defined in terms of Avogadro's number, using a collection of ions of heavy elements, by the levitation method, or using voltage and watt balances. The book also addresses the concepts of gravitational, inertial and conventional mass, and describes in detail the variation of acceleration due to gravity. Further topics covered in this second edition include: the effect of gravity variations on the reading of electronic balances derived with respect to latitude, altitude and earth topography; the classification of weights by the OIML; and maximum permissible error in different categories of weights prescribed by national and international organizations. The book also discusses group weighing techniques and the use of nanotechnology for the detection of mass differences as small as 10-24 g. Last but not least, readers will find details on the XRCD method for defining the kilogram in terms of Planck's constant.

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.

Autoren/Hrsg.

Gupta, S. V.

Inhaltsverzeichnis

1;Preface to the Second Edition;7
2;Preface to the First Edition;9
3;Contents;11
4;1 Unit of Mass and Standards of Mass;25
4.1;1.1 Concepts of Mass;25
4.1.1;1.1.1 Gravitational Mass;26
4.1.2;1.1.2 Inertial Mass;26
4.1.3;1.1.3 Equality of Inertial and Gravitational Mass;27
4.2;1.2 Mass and Weight of a Body;27
4.2.1;1.2.1 Conventional Mass;28
4.2.2;1.2.2 Variation of the Weight of a Body on Surface of Earth;28
4.3;1.3 Unit of Mass;31
4.3.1;1.3.1 History of the Units of Metre and Kilogram;31
4.3.2;1.3.2 Unit of Length;32
4.3.3;1.3.3 Kilogram de Archives;32
4.4;1.4 Metric Convention;33
4.4.1;1.4.1 International Kilogram;33
4.4.2;1.4.2 National Standard of Kilogram;34
4.4.3;1.4.3 National Kilogram and Other Standards in India;35
4.4.4;1.4.4 Calibration of Transfer Standards of Mass;36
4.5;1.5 Hierarchy of Mass Standards;37
4.5.1;1.5.1 Nomenclature;37
4.5.2;1.5.2 Measurement Chain;39
4.5.3;1.5.3 Tracking the Mass Values of Standards;39
4.5.4;1.5.4 Period of Verification or Calibration;40
4.5.5;1.5.5 Maximum Permissible Errors;40
4.6;1.6 Traceability of Measurements;41
4.6.1;1.6.1 Traceability;41
4.6.2;1.6.2 CIPM MRA;42
4.7;References;43
5;2 Two-Pan Equal-Arm Balances;44
5.1;2.1 Introduction;44
5.2;2.2 Brief History;44
5.3;2.3 Other 1-kg Balances;45
5.3.1;2.3.1 Equal-Arm Interchangeable Pan Balance UK;45
5.3.2;2.3.2 Equal Arm with Double Interchangeable Pan Balance;46
5.3.3;2.3.3 Substitution Balance NPL-India;47
5.3.4;2.3.4 Electronic Balance with Automation at NPL-India;49
5.3.5;2.3.5 Hydrostatic Balance;50
5.4;2.4 Installation of a Balance;52
5.4.1;2.4.1 Proper Environmental Conditions for Balance Room;52
5.4.2;2.4.2 Requirements for Location of the Balance;52
5.5;2.5 Evaluation of Metrological Data for a Balance;55
5.5.1;2.5.1 Need for Evaluation;55
5.5.2;2.5.2 Visual Examination;55
5.5.3;2.5.3 Sensitivity;56
5.5.4;2.5.4 Period of Swing or Time Period;58
5.5.5;2.5.5 Accuracy of Rider Bar;59
5.5.6;2.5.6 Stability/Repeatability;61
5.5.7;2.5.7 Repeatability of Weighing;61
5.5.8;2.5.8 Equality of Arm Lengths;62
5.5.9;2.5.9 Calculation of Arm Ratio, Repeatability of Single and Double Weighing;63
5.5.10;2.5.10 Requirement for Arm Ratio and Repeatability of Weighing;65
5.5.11;2.5.11 Test for Parallelism of Knife Edges;65
5.6;2.6 Methods of Weighing;67
5.6.1;2.6.1 Direct Weighing;67
5.6.2;2.6.2 Transposition Weighing;68
5.6.3;2.6.3 Substitution Weighing;68
5.7;2.7 Double Transposition and Substitution Weighing;69
5.7.1;2.7.1 Double Transposition Method;69
5.7.2;2.7.2 Double Transposition with Simultaneous Determination of S.R.;70
5.7.3;2.7.3 Double Substitution;71
5.7.4;2.7.4 Double Substitution Weighing with Simultaneous Determination of S.R.;72
5.8;2.8 Maintenance of Standard Balances;72
5.8.1;2.8.1 Category of Balances;73
5.8.2;2.8.2 Reference Balances;73
5.8.3;2.8.3 Secondary Standard Balances;73
5.8.4;2.8.4 Working Standard Balances;74
5.9;References;74
6;3 Single-Pan Mechanical Balances;76
6.1;3.1 Introduction;76
6.2;3.2 Description of a Single-Pan Balance;76
6.3;3.3 Evaluation of Single-Pan Balance;80
6.3.1;3.3.1 Verification Interval;80
6.3.2;3.3.2 General Examination;80
6.3.3;3.3.3 Sensitivity of the Sprit Level of the Balance;81
6.3.4;3.3.4 Hardness of Knife Edges and Bearing Planes;81
6.3.5;3.3.5 Sensitivity Setting;82
6.3.6;3.3.6 Tests;82
6.3.7;3.3.7 Test for Smallest Built-in Weight and Calibration of Illuminated Scale;82
6.3.8;3.3.8 Calibration of Lower Half and Upper Half of the Optical Scale;83
6.3.9;3.3.9 Short Duration Test for Precision of the Balance;85
6.3.10;3.3.10 Calibration of Built-in Weights for All Dial Settings;86
6.3.11;3.3.11 Performance Test;88
6.4;3.4 Uncertainty in Calibration of the Balance;90
6.4.1;3.4.1 Uncertainty of Mass Determination by the Balance;91
6.5;References;91
7;4 Electronic Balances and Effect of Gravity;92
7.1;4.1 Introduction;92
7.2;4.2 Electromagnetic Force Compensation;93
7.2.1;4.2.1 Principle of EMFC;93
7.2.2;4.2.2 Principle of EMFC Balance;94
7.3;4.3 Partially Electromagnetic Force Compensated Balance;95
7.3.1;4.3.1 Partially EMFC Two-Pan Balance;95
7.3.2;4.3.2 Partially EMFC Single-Pan Balance;97
7.4;4.4 Fully EMFC Balance;98
7.4.1;4.4.1 Without Lever;98
7.4.2;4.4.2 Balance with Mechanical Levers;98
7.4.3;4.4.3 Working of EMFC Balances;99
7.4.4;4.4.4 Electronic Circuitry;100
7.5;4.5 Range of Capacity of EMFC Balance;102
7.6;4.6 Availability of EMFC Cells;103
7.7;4.7 Effect of Variation in Gravity on Electronic Balances;103
7.7.1;4.7.1 Instruments Affected by Gravity;103
7.7.2;4.7.2 Error Due to Variation in g;105
7.7.3;4.7.3 Variation of g with Respect to Latitude;106
7.7.4;4.7.4 Error Per Degree Change in Latitude at Different Places;106
7.7.5;4.7.5 Significant Error;109
7.7.6;4.7.6 Choice of Values of ``n'' to Calculate Error at Various Latitudes;109
7.7.7;4.7.7 Latitude Differences to Cause Significant Error;109
7.7.8;4.7.8 Intra-state Movement of Electronic Weighing Instruments;115
7.7.9;4.7.9 Error Due to Altitude;115
7.8;4.8 Conclusion About the Movement of Electronic Weighing Instruments;117
7.9;References;118
8;5 Strain Gauge Load Cells;119
8.1;5.1 Load Cell;119
8.2;5.2 Construction;119
8.2.1;5.2.1 Elastic Spring Element;119
8.2.2;5.2.2 Detector;119
8.2.3;5.2.3 Pasting;120
8.3;5.3 Resistance Strain Gauge;120
8.3.1;5.3.1 Change in Resistance;120
8.3.2;5.3.2 Measurement of Resistance;121
8.3.3;5.3.3 Configuration of Strain Gauges on Spring Element;124
8.3.4;5.3.4 Dimensions of the Spring Element;126
8.3.5;5.3.5 Methods of Connecting Several Load Cells;127
8.3.6;5.3.6 Trimming Devices in the Load Cell;128
8.4;5.4 Some Important Terms;131
8.4.1;5.4.1 Definitions;131
8.4.2;5.4.2 Notations Used on Load Cells;133
8.5;5.5 Classification of Load Cells;134
8.5.1;5.5.1 Accuracy Class;134
8.5.2;5.5.2 Number of Intervals;134
8.5.3;5.5.3 Load Application;135
8.6;5.6 Maximum Permissible Errors for Load Cells;135
8.6.1;5.6.1 Maximum Permissible Error at Verification/Model Approval;135
8.6.2;5.6.2 Maximum Permissible Error at Inspection;136
8.6.3;5.6.3 Determination of Error for Digital Instruments;136
8.7;5.7 Tests to Be Conducted;136
8.7.1;5.7.1 Performance Tests;137
8.7.2;5.7.2 Influence Factors Tests;137
8.7.3;5.7.3 Test Conditions;137
8.8;5.8 Performance Tests;139
8.8.1;5.8.1 Permissible Error, Repeatability, Nonlinearity and Hysteresis Tests;139
8.8.2;5.8.2 Creep and Minimum Dead Load Return Tests;139
8.8.3;5.8.3 Performance Tests at Different Temperatures;141
8.8.4;5.8.4 Temperature Effect on Minimum Dead Load Output;142
8.8.5;5.8.5 Effect of Barometric Pressure Test;142
8.8.6;5.8.6 Humidity Test;142
8.9;5.9 Additional Tests;143
8.9.1;5.9.1 Voltage Variations;144
8.9.2;5.9.2 Short-Time Power Reductions;144
8.9.3;5.9.3 Bursts (Electrical Fast Transients);145
8.9.4;5.9.4 Electrostatic Discharge;146
8.9.5;5.9.5 Electromagnetic Susceptibility;146
8.9.6;5.9.6 Span Stability;147
8.10;5.10 Requirements for Load Cells;149
8.11;References;149
9;6 Various Types of Transducers for Weighing;150
9.1;6.1 Introduction;150
9.1.1;6.1.1 Classification;151
9.1.2;6.1.2 Force Applied by a Body;151
9.2;6.2 Vibrating String/Vibrating Strip Devices;151
9.2.1;6.2.1 Single-String Transducer Cell;152
9.2.2;6.2.2 Double-String Transducer Cell;153
9.2.3;6.2.3 S-Shaped Vibrating Strip Transducer;154
9.2.4;6.2.4 Transducer with String Vibrating in Heterodyne Mode;154
9.2.5;6.2.5 Use of Vibrating String Transducers;155
9.3;6.3 Tuning Fork Transducer;156
9.4;6.4 Gyroscopic Devices;158
9.5;6.5 Optical Interference Transducer;160
9.6;6.6 Magneto-elastic Transducer (Pressductor);161
9.6.1;6.6.1 Construction;161
9.6.2;6.6.2 Principle of Magneto-elastic Transducer;162
9.7;6.7 Change in Capacitance Transducer;163
9.8;6.8 Photoelectric Device;164
9.9;6.9 Hydraulic Load Transducer;165
9.10;6.10 Piezoelectric Transducer;165
9.10.1;6.10.1 Longitudinal and Transverse Effect;166
9.10.2;6.10.2 Piezoelectric Device and Cascading to Increase the Output;167
9.10.3;6.10.3 Sensitivity in Different Modes;168
9.10.4;6.10.4 Electronic Measurement Circuits;168
9.10.5;6.10.5 Particulars of Piezoelectric Transducers;170
9.11;6.11 Strain Gauge of Semiconductor Material;170
9.12;6.12 Piezo-resistant Force Transducer;170
9.13;6.13 Linear Variable Differential Transformer;171
9.14;6.14 Inductive Worm-Spring Transducer;174
9.15;6.15 Surface Wave Resonator;174
9.16;6.16 Nucleonic Weighing;176
9.16.1;6.16.1 Principle;176
9.17;References;178
10;7 Testing of Electronic Balances;179
10.1;7.1 Introduction;179
10.2;7.2 Principle of Digital Indications;179
10.2.1;7.2.1 Digital and Analogue Instruments;179
10.2.2;7.2.2 Principle of Digital Indication Device;180
10.2.3;7.2.3 Equality in Error of Digital and Analogue Instruments;184
10.2.4;7.2.4 Maximum Permissible Errors;184
10.2.5;7.2.5 Definitions of Some Important Terms;184
10.2.6;7.2.6 Practical Determination of the Error of a Digital Machine;186
10.2.7;7.2.7 Verification of Digital Instruments for Compliance;186
10.2.8;7.2.8 Rule for Errors of the Combined System;187
10.3;7.3 Testing of Electronic Balances/Weighing Machines;188
10.3.1;7.3.1 Introduction;188
10.3.2;7.3.2 General Requirements;189
10.3.3;7.3.3 Descriptive Requirements;189
10.3.4;7.3.4 Classes of Weighing Instruments;190
10.3.5;7.3.5 Performance Tests;190
10.4;7.4 Type Approval Tests;194
10.4.1;7.4.1 Tests to Meet the Requirements for the Effect of Influence Quantities;194
10.4.2;7.4.2 Extreme Temperature Test;195
10.4.3;7.4.3 Variation in Supply Voltage and Frequency Test;196
10.4.4;7.4.4 Short Time Power Reduction Test;196
10.4.5;7.4.5 Electrical Bursts Test;196
10.4.6;7.4.6 Electrostatic Discharge Test;197
10.4.7;7.4.7 Electromagnetic Susceptibility Test;197
10.5;7.5 Nonlinearity;198
10.5.1;7.5.1 Methods of Estimating Nonlinearity;198
10.6;7.6 Hysteresis Error;199
10.7;7.7 Guidelines for Choosing Balances;199
10.8;7.8 Class of Electronic Balances Not Covered by OIML;200
10.9;References;200
11;8 Air Density and Buoyancy Correction;201
11.1;8.1 Introduction;201
11.2;8.2 Equation for Density of Air;203
11.2.1;8.2.1 Parameters of the Gas Equation;204
11.2.2;8.2.2 Molar Mass of Water Vapour;205
11.2.3;8.2.3 Constants Involved in psv, f and Z;207
11.2.4;8.2.4 Variable Parameters;208
11.2.5;8.2.5 Uncertainty Budget of Air Density Evaluation from CIPM Formula;208
11.2.6;8.2.6 Air Density Tables;208
11.3;8.3 Air Buoyancy Artefact Method;210
11.3.1;8.3.1 Principle;210
11.3.2;8.3.2 Artefacts;213
11.3.3;8.3.3 Uncertainty Budget;219
11.4;8.4 Optical Method for Determination of Air Density;222
11.4.1;8.4.1 Relation of Refractive Index and Density of Air;222
11.4.2;8.4.2 Experimental Work;223
11.4.3;8.4.3 BIPM Refractometer;224
11.5;References;230
12;9 Weights—Standards of Mass;234
12.1;9.1 Introduction;234
12.2;9.2 OIML Classification of Weights;235
12.3;9.3 Maximum Permissible Errors;236
12.3.1;9.3.1 OIML Maximum Permissible Errors;236
12.3.2;9.3.2 Maximum Permissible Errors in Weights in USA;236
12.3.3;9.3.3 Maximum Permissible Errors in Commercial Weights in India;238
12.4;9.4 Maximum Permissible Errors for Other Weights;239
12.4.1;9.4.1 Maximum Permissible Errors for Weights Used in Scientific and Industrial Fields;239
12.4.2;9.4.2 Maximum Permissible Errors in Standard Weights for Legal Metrology;240
12.4.3;9.4.3 Special Purpose Reference Standards (Germany);240
12.5;9.5 Material of Weights;241
12.5.1;9.5.1 Property Requirements for Material of Weights;241
12.5.2;9.5.2 Material for Weights of 1g and Above;243
12.5.3;9.5.3 Material for Fractional Weights;245
12.5.4;9.5.4 Material for Adjustment of Weights;246
12.6;9.6 Design and Finish of the Weights;247
12.6.1;9.6.1 Basics of Design of Weights;247
12.6.2;9.6.2 Surface Finish of Gram Weights;250
12.6.3;9.6.3 Fractional Weights;251
12.6.4;9.6.4 Weight Box;252
12.7;9.7 Effect of Finite Magnetic Susceptibility;252
12.7.1;9.7.1 Expression for Magnetic Force;253
12.7.2;9.7.2 Measurement of Magnetic Susceptibility of Weights;254
12.8;9.8 Electrostatic Charges;257
12.9;9.9 Effect of Inequality of Temperature of Weight and Its Surroundings;257
12.9.1;9.9.1 Buoyant Force;258
12.9.2;9.9.2 Change in Mass Due to Convection of Air;258
12.9.3;9.9.3 Change in Indication with Time;259
12.9.4;9.9.4 Change in Mass Due to Adsorption;260
12.10;9.10 Effect of Density of Material of Weights;263
12.10.1;9.10.1 Criterion for Density Range of the Weight;264
12.10.2;9.10.2 Determination of Density of a Weight;265
12.11;9.11 Physical Properties;268
12.12;9.12 Surface Resistance of Platinum–Iridium Mass Standards;268
12.12.1;9.12.1 Effect of Change in Relative Humidity;269
12.12.2;9.12.2 Effect of Change in Temperature;269
12.12.3;9.12.3 Effect of Change in Pressure;269
12.13;9.13 Effect of Weighing in Air and Vacuum;270
12.14;9.14 Stability of Mass Standards;270
12.14.1;9.14.1 Instability in Mass Standards Due to Mercury Contamination;270
12.14.2;9.14.2 Instability in Mass Standards Due to Atmospheric Carbon and Oxygen;271
12.15;References;272
13;10 Group Weighing Method;274
13.1;10.1 Introduction;274
13.2;10.2 Different Sets of Weights;275
13.2.1;10.2.1 Sets of Weights;275
13.2.2;10.2.2 Head Weights;276
13.3;10.3 Principal of Group Weighing;276
13.3.1;10.3.1 Linear Equations and Method of Least Squares;277
13.3.2;10.3.2 Design Matrix;278
13.3.3;10.3.3 Variance Covariance Matrix;279
13.3.4;10.3.4 Weighting Factor;280
13.3.5;10.3.5 Improving a Weighing Design;281
13.3.6;10.3.6 Efficiency of a Weighing Design;283
13.3.7;10.3.7 Average of Squares of Residual Errors;283
13.4;10.4 Calibration of Set of Weights;283
13.4.1;10.4.1 Series 5, 2, 2, 1;283
13.4.2;10.4.2 Series 5, 2, 1,;294
13.4.3;10.4.3 Series 5, 2, 1, (BIPM);297
13.4.4;10.4.4 Series 4, 3, 2, 1 (BIPM);300
13.4.5;10.4.5 Series 5, 3, 2, 1;305
13.5;10.5 Calculations with Weighing Factors;308
13.6;10.6 Multiples of Unit of Mass;313
13.7;10.7 Weights of Same Denominations;315
13.7.1;10.7.1 Optimum Value of N;316
13.7.2;10.7.2 Experimental Work;317
13.7.3;10.7.3 Numerical Example;318
13.8;References;319
14;11 Nanotechnology for Detection of Small Mass Difference;321
14.1;11.1 Introduction;321
14.2;11.2 Cantilever Vibration;321
14.2.1;11.2.1 Characterisation of Cantilever;322
14.2.2;11.2.2 Dimensions and Mass of an Attogram Cantilever;324
14.3;11.3 Nanotechnology;325
14.4;11.4 Examples of Fabrication of Micro-cantilevers;326
14.4.1;11.4.1 Etching Process;326
14.4.2;11.4.2 Electron Beam Lithography;328
14.4.3;11.4.3 Various Micro-cantilevers in Use;330
14.5;11.5 Principles of Detection of Micro-cantilever Motion;330
14.6;11.6 Examples of Detection Micro-cantilever Response;330
14.6.1;11.6.1 Detection by Using an Interferometer;330
14.6.2;11.6.2 Detection by Capacity Measurement;331
14.6.3;11.6.3 Improved Fibre-Optic Interferometer;333
14.7;11.7 Mass Sensitivity of Cantilevers;334
14.7.1;11.7.1 No Change in Spring Constant (End-Point Loading);334
14.7.2;11.7.2 Changing Spring Constant (Uniform Loading);335
14.8;11.8 Mass Detector Cantilevers;335
14.8.1;11.8.1 At Femtogram Level;335
14.8.2;11.8.2 At Attogram Level;336
14.8.3;11.8.3 Sub-attogram Level;337
14.8.4;11.8.4 Zeptogram Level;337
14.8.5;11.8.5 Sub-zeptogram Level (One Gold Atom);338
14.8.6;11.8.6 At Attonewton Level;338
14.8.7;11.8.7 A Final Goal;339
14.8.8;11.8.8 Viscosity: A Problem;340
14.9;11.9 Minimum Detectable Force/Mass;340
14.10;11.10 Micro-cantilever Applications;341
14.10.1;11.10.1 Large Surface to Volume Ratio;341
14.10.2;11.10.2 Examination of Surface;341
14.10.3;11.10.3 Thermal/Photo-thermal;342
14.10.4;11.10.4 Low Power Consumption Micro-cantilevers;343
14.10.5;11.10.5 Chemistry;343
14.10.6;11.10.6 Biology;343
14.10.7;11.10.7 Health Care;344
14.10.8;11.10.8 Physics (Viscosity and Density);345
14.10.9;11.10.9 Magnetometry;346
14.10.10;11.10.10 Data Storage;346
14.10.11;11.10.11 Terrorist Threat Detection;347
14.11;References;347
15;12 Redefining the Unit of Mass;353
15.1;12.1 Introduction;353
15.1.1;12.1.1 Requirements for Defining a Base Unit;354
15.2;12.2 History of Kilogram and It Stability in Mass;354
15.2.1;12.2.1 Brief History of Kilogram de Archive (KA);354
15.2.2;12.2.2 Preparation of the Artefact Defining kg;355
15.2.3;12.2.3 Fabrication;356
15.2.4;12.2.4 Continuity with the Mass of KA;357
15.2.5;12.2.5 Stability of m(KA) with Respect of m(IPK);357
15.2.6;12.2.6 Stability of m(IPK);358
15.2.7;12.2.7 Outcome of Redefining a Unit of Measurement;359
15.2.8;12.2.8 Meaning of Taking a Measured Value as Exact;360
15.3;12.3 Possibilities to Redefine Kilogram;360
15.3.1;12.3.1 NA by Measurements;361
15.3.2;12.3.2 kg and NA Relation;361
15.3.3;12.3.3 Relation Between of H and NA;362
15.4;12.4 Values of Avogadro Constant;363
15.5;12.5 Other Methods of Defining kg;365
15.5.1;12.5.1 The Kilogram Through Ion Collection Method;365
15.5.2;12.5.2 The Kilogram Through Levitation Method;368
15.5.3;12.5.3 The Kilogram Through Voltage Balance;370
15.5.4;12.5.4 The Kilogram Through Watt Balance;373
15.5.5;12.5.5 The Kilogram, Einstein Energy Equation and Planck Constant;375
15.5.6;12.5.6 Another Way of Redefining the Kilogram;376
15.6;12.6 Planck Constant h in Terms of Other Constants;376
15.7;12.7 Status of Watt Balance;377
15.8;12.8 Practical Standards to Realize Kilogram;378
15.9;12.9 Author’s Observations;379
15.10;References;379
16;13 Redefining the Base Units;383
16.1;13.1 Preparations for Redefining Base Units;383
16.1.1;13.1.1 A Brief History of the CGPM Decisions;383
16.1.2;13.1.2 Resolution About Redefinitions;384
16.2;13.2 Revised Definitions of SI Base Units;389
16.2.1;13.2.1 CODATA Efforts for New Definitions;391
16.3;13.3 Fundamental Constants for Kilogram;392
16.4;13.4 New Definition of Base Units;392
16.4.1;13.4.1 Base Units in Terms of Fundamental Constants;393
16.5;13.5 Inter Dependence of Base Units;394
16.5.1;13.5.1 New SI Units;395
16.5.2;13.5.2 Old SI Units;395
16.6;13.6 Relationship Matrix;396
16.6.1;13.6.1 Defining Constants in Terms of Base Units;397
16.6.2;13.6.2 Base Units in Terms of Defining Constants;397
16.6.3;13.6.3 Use of the Tables;397
16.7;13.7 Vacuum and Air Dissemination of Kilogram;398
16.7.1;13.7.1 Conclusions and Recommendations;399
16.8;13.8 Traceability;400
16.8.1;13.8.1 Traceability and Uncertainty Before Redefinition;400
16.8.2;13.8.2 Traceability and Uncertainty After Redefinition;401
16.9;13.9 Hierarchy of Mass;401
16.10;References;402
17;14 Realisation of Mass Unit;403
17.1;14.1 Introduction;403
17.2;14.2 Kibble Balance;403
17.2.1;14.2.1 Title of the Balance;403
17.2.2;14.2.2 Importance of Kibble Balance;404
17.2.3;14.2.3 Basic Principle;404
17.3;14.3 Kibble Balances at Metrology Institutes;407
17.3.1;14.3.1 Conventional Two-Mode Two Measurement Phase Kibble Balances;408
17.3.2;14.3.2 Korea Research Institute of Standards and Science KRISS, Korea;408
17.3.3;14.3.3 Laboratoire National de Métrologie et d’Essais (LNE), France;408
17.3.4;14.3.4 Federal Institute of Metrology (METAS), Switzerland;408
17.3.5;14.3.5 Measurement Standard Laboratory of New Zealand MSL;409
17.3.6;14.3.6 National Institute of Metrology (NIM), China;409
17.3.7;14.3.7 National Institute of Standards and Technology (NIST), USA;409
17.3.8;14.3.8 National Physical Laboratory (NPL), UK;410
17.3.9;14.3.9 National Research Council (NRC), Canada;410
17.4;14.4 The Original Joule Balance;410
17.4.1;14.4.1 National Institute of Metrology (NIM), China;410
17.4.2;14.4.2 Single-Mode One Measurement Phase Kibble Balances;410
17.4.3;14.4.3 Single-Mode Two Measurement Phase Watt Balances;411
17.4.4;14.4.4 Moving Magnet Balance at Ulusal Metroloji Enstitüsü (UME), Turke;411
17.5;14.5 Measurement of Velocity of the Pan;412
17.5.1;14.5.1 Interferometers;412
17.5.2;14.5.2 Refractive Index of Air;412
17.5.3;14.5.3 Light Source;413
17.6;14.6 Mass of Weight Used (M);413
17.6.1;14.6.1 Measurement of the Working Masses;413
17.6.2;14.6.2 Substitution Weighing;414
17.6.3;14.6.3 Balances Used in Kibble Balance;414
17.6.4;14.6.4 Alignment of the Mass on the Mass Pan;415
17.6.5;14.6.5 Alignment of the Mass Comparator;415
17.7;14.7 Gravity Measurement;416
17.7.1;14.7.1 Instruments for Measurement;416
17.7.2;14.7.2 Corrections;417
17.8;14.8 Constant Magnetic Field;420
17.8.1;14.8.1 Magnets;421
17.9;14.9 Demagnetization of the Rare Earth Magnets;425
17.10;14.10 Change of the Reluctance of the Yoke;426
17.10.1;14.10.1 The Reluctance Force;426
17.10.2;14.10.2 Temperature Change of the Rare Earth Magnet;426
17.10.3;14.10.3 Temperature Change of the Yoke Material;426
17.10.4;14.10.4 Engineering of Magnets with Smaller Temperature Coefficients;427
17.10.5;14.10.5 Actively Controlling the Temperature;428
17.11;14.11 Voltage Measurements;428
17.11.1;14.11.1 Measurement Techniques;429
17.11.2;14.11.2 Josephson Reference;429
17.11.3;14.11.3 Hysteretic Arrays;429
17.11.4;14.11.4 Programmable Arrays;430
17.11.5;14.11.5 Voltmeter;430
17.11.6;14.11.6 Amplifiers;431
17.11.7;14.11.7 Synchronisation of the Voltmeter and Counter;431
17.12;14.12 Current Generation and Measurement;432
17.12.1;14.12.1 Current Sources;433
17.12.2;14.12.2 The Measurement Resistor;435
17.13;14.13 Resistance Determination with the Quantum Hall Effect;436
17.14;14.14 Joule Balance Measurements;437
17.15;14.15 Environmental Effects;437
17.15.1;14.15.1 Ground Vibration;437
17.15.2;14.15.2 Anti-vibration Systems;438
17.15.3;14.15.3 External Magnetic Fields;438
17.15.4;14.15.4 Temperature Effects;438
17.15.5;14.15.5 Shielding and Electrical Isolation;438
17.16;14.16 Reduction in Mass Values of BIPM Working Standards Against IPK;439
17.17;14.17 Relation Between RK?90, KJ?90 and h;439
17.18;14.18 Results;441
17.19;14.19 XRCD Method;443
17.19.1;14.19.1 Sphere;444
17.19.2;14.19.2 Volume of Sphere;444
17.19.3;14.19.3 Principle;444
17.19.4;14.19.4 Realization of the Kilogram Using Already Characterized Crystals;445
17.19.5;14.19.5 Relation Between IPK and kg (Revised Definition);445
17.20;14.20 Characterization of Silicon Crystal;446
17.20.1;14.20.1 Enrichment of Crystal;446
17.20.2;14.20.2 Single Crystal Growth;447
17.20.3;14.20.3 Isotopic Composition of Silicon;447
17.20.4;14.20.4 Crystal Perfection: Evaluation of Point Defects;447
17.20.5;14.20.5 mSL Layers;449
17.20.6;14.20.6 Molar Mass;451
17.20.7;14.20.7 Lattice Parameter;452
17.20.8;14.20.8 Uncertainty in XRCD Method;455
17.21;14.21 Pilot Study for Equivalence of Two Methods;456
17.21.1;14.21.1 New Definition of kg;456
17.21.2;14.21.2 Sponsor;456
17.21.3;14.21.3 Aim;457
17.21.4;14.21.4 Organisation and Participants;457
17.21.5;14.21.5 Comparison Protocol;457
17.21.6;14.21.6 Particulars of Travelling Standard;458
17.21.7;14.21.7 Calculations;459
17.21.8;14.21.8 Conclusions;460
17.22;References for Kibble Balance;460
18;Index;467