PHYSICAL METALLURGY AND ADVANCED MATERIALS
CONTENTS CHAPTER ATOMS AND ATOMIC ARRANGEMENTS THE REALM OF MATERIALS SCIENCE THE FREE ATOM THE FOUR ELECTRON QUANTUM NUMBERS NOMENCLATURE FOR THE ELECTRONIC STATES THE PERIODIC TABLE INTERATOMIC BONDING IN MATERIALS BONDING AND ENERGY LEVELS CRYSTAL LATTICES AND STRUCTURES CRYSTAL DIRECTIONS AND PLANES STEREOGRAPHIC PROJECTION SELECTED CRYSTAL STRUCTURES PURE METALS DIAMOND AND GRAPHITE COORDINATION IN IONIC CRYSTALS AB-TYPE COMPOUNDS CHAPTER PHASE EQUILIBRIA AND STRUCTURE CRYSTALLIZATION FROM THE MELT FREEZING OF A PURE METAL PLANE-FRONT AND DENDRITIC SOLIDI?CATION AT A COOLED SURFACE FORMS OF CAST STRUCTURE GAS POROSITY AND SEGREGATION DIRECTIONAL SOLIDI?CATION PRODUCTION OF METALLIC SINGLE CRYSTALS FOR RESEARCH PRINCIPLES AND APPLICATIONS OF PHASE DIAGRAMS THE CONCEPT OF A PHASE THE PHASE RULE STABILITY OF PHASES TWO-PHASE EQUILIBRIA THREE-PHASE EQUILIBRIA AND REACTIONS INTERMEDIATE PHASES LIMITATIONS OF PHASE DIAGRAMS SOME KEY PHASE DIAGRAMS TERNARY PHASE DIAGRAMS PRINCIPLES OF ALLOY THEORY PRIMARY SUBSTITUTIONAL SOLID SOLUTIONS INTERSTITIAL SOLID SOLUTIONS TYPES OF INTERMEDIATE PHASES ORDER–DISORDER PHENOMENA THE MECHANISM OF PHASE CHANGES KINETIC CONSIDERATIONS HOMOGENEOUS NUCLEATION HETEROGENEOUS NUCLEATION NUCLEATION IN SOLIDS CRYSTAL DEFECTS TYPES OF IMPERFECTION POINT DEFECTS POINT DEFECTS IN METALS POINT DEFECTS IN NON-METALLIC CRYSTALS IRRADIATION OF SOLIDS POINT DEFECT CONCENTRATION AND ANNEALING LINE DEFECTS CONCEPT OF A DISLOCATION EDGE AND SCREW DISLOCATIONS THE BURGERS VECTOR MECHANISMS OF SLIP AND CLIMB STRAIN ENERGY ASSOCIATED WITH DISLOCATIONS DISLOCATIONS IN IONIC STRUCTURES PLANAR DEFECTS GRAIN BOUNDARIES TWIN BOUNDARIES EXTENDED DISLOCATIONS AND STACKING FAULTS IN CLOSE-PACKED CRYSTALS VOLUME DEFECTS VOID FORMATION AND ANNEALING IRRADIATION AND VOIDING VOIDING AND FRACTURE DEFECT BEHAVIOR IN COMMON CRYSTAL STRUCTURES DISLOCATION VECTOR DIAGRAMS AND THE THOMPSON TETRAHEDRON DISLOCATIONS AND STACKING FAULTS IN FCC STRUCTURES DISLOCATIONS AND STACKING FAULTS IN CPH STRUCTURES DISLOCATIONS AND STACKING FAULTS IN BCC STRUCTURES DISLOCATIONS AND STACKING FAULTS IN ORDERED STRUCTURES STABILITY OF DEFECTS DISLOCATION LOOPS VOIDS NUCLEAR IRRADIATION EFFECTS CHARACTERIZATION AND ANALYSIS TOOLS OF CHARACTERIZATION LIGHT MICROSCOPY BASIC PRINCIPLES SELECTED MICROSCOPICAL TECHNIQUES X-RAY DIFFRACTION ANALYSIS PRODUCTION AND ABSORPTION OF X-RAYS DIFFRACTION OF X-RAYS BY CRYSTALS X-RAY DIFFRACTION METHODS TYPICAL INTERPRETATIVE PROCEDURES FOR DIFFRACTION PATTERNS ANALYTICAL ELECTRON MICROSCOPY INTERACTION OF AN ELECTRON BEAM WITH A SOLID THE TRANSMISSION ELECTRON MICROSCOPE (TEM) THE SCANNING ELECTRON MICROSCOPE THEORETICAL ASPECTS OF TEM CHEMICAL MICROANALYSIS ELECTRON ENERGY-LOSS SPECTROSCOPY (EELS) AUGER ELECTRON SPECTROSCOPY (AES) OBSERVATION OF DEFECTS ETCH PITTING DISLOCATION DECORATION DISLOCATION STRAIN CONTRAST IN TEM CONTRAST FROM CRYSTALS IMAGING OF DISLOCATIONS IMAGING OF STACKING FAULTS APPLICATION OF DYNAMICAL THEORY WEAK-BEAM MICROSCOPY SCANNING PROBE MICROSCOPY SCANNING TUNNELING MICROSCOPY (STM) ATOMIC FORCE MICROSCOPY (AFM) APPLICATIONS OF SPM NANOINDENTATION SPECIALIZED BOMBARDMENT TECHNIQUES NEUTRON DIFFRACTION SYNCHROTRON RADIATION STUDIES SECONDARY ION MASS SPECTROMETRY (SIMS) THERMAL ANALYSIS GENERAL CAPABILITIES OF THERMAL ANALYSIS THERMOGRAVIMETRIC ANALYSIS DIFFERENTIAL THERMAL ANALYSIS DIFFERENTIAL SCANNING CALORIMETRY PHYSICAL PROPERTIES INTRODUCTION DENSITY THERMAL PROPERTIES THERMAL EXPANSION SPECI?C HEAT CAPACITY THE SPECI?C HEAT CURVE AND TRANSFORMATIONS FREE ENERGY OF TRANSFORMATION DIFFUSION DIFFUSION LAWS MECHANISMS OF DIFFUSION FACTORS AFFECTING DIFFUSION ANELASTICITY AND INTERNAL FRICTION ORDERING IN ALLOYS LONG-RANGE AND SHORT-RANGE ORDER DETECTION OF ORDERING IN?UENCE OF ORDERING ON PROPERTIES ELECTRICAL PROPERTIES ELECTRICAL CONDUCTIVITY SEMICONDUCTORS HALL EFFECT SUPERCONDUCTIVITY OXIDE SUPERCONDUCTORS MAGNETIC PROPERTIES MAGNETIC SUSCEPTIBILITY DIAMAGNETISM AND PARAMAGNETISM FERROMAGNETISM MAGNETIC ALLOYS ANTI-FERROMAGNETISM AND FERRIMAGNETISM DIELECTRIC MATERIALS POLARIZATION CAPACITORS AND INSULATORS PIEZOELECTRIC MATERIALS PYROELECTRIC AND FERROELECTRIC MATERIALS 5 10 OPTICAL PROPERTIES RE?ECTION, ABSORPTION AND TRANSMISSION EFFECTS OPTICAL ?BERS LASERS CERAMIC ‘WINDOWS’ ELECTRO-OPTIC CERAMICS MECHANICAL PROPERTIES I MECHANICAL TESTING PROCEDURES THE TENSILE TEST INDENTATION HARDNESS TESTING IMPACT TESTING CREEP TESTING FATIGUE TESTING ELASTIC DEFORMATION PLASTIC DEFORMATION SLIP AND TWINNING RESOLVED SHEAR STRESS RELATION OF SLIP TO CRYSTAL STRUCTURE LAW OF CRITICAL RESOLVED SHEAR STRESS MULTIPLE SLIP RELATION BETWEEN WORK HARDENING AND SLIP DISLOCATION BEHAVIOR DURING PLASTIC DEFORMATION DISLOCATION MOBILITY VARIATION OF YIELD STRESS WITH TEMPERATURE AND STRAIN RATE DISLOCATION SOURCE OPERATION DISCONTINUOUS YIELDING YIELD POINTS AND CRYSTAL STRUCTURE DISCONTINUOUS YIELDING IN ORDERED ALLOYS SOLUTE–DISLOCATION INTERACTION DISLOCATION LOCKING AND TEMPERATURE INHOMOGENEITY INTERACTION KINETICS OF STRAIN AGEING IN?UENCE OF GRAIN BOUNDARIES ON PLASTICITY SUPERPLASTICITY MECHANICAL TWINNING CRYSTALLOGRAPHY OF TWINNING NUCLEATION AND GROWTH OF TWINS EFFECT OF IMPURITIES ON TWINNING EFFECT OF PRESTRAIN ON TWINNING DISLOCATION MECHANISM OF TWINNING TWINNING AND FRACTURE STRENGTHENING AND HARDENING MECHANISMS POINT DEFECT HARDENING WORK HARDENING DEVELOPMENT OF PREFERRED ORIENTATION MACROSCOPIC PLASTICITY TRESCA AND VON MISES CRITERIA EFFECTIVE STRESS AND STRAIN ANNEALING GENERAL EFFECTS OF ANNEALING RECOVERY RECRYSTALLIZATION GRAIN GROWTH ANNEALING TWINS RECRYSTALLIZATION TEXTURES METALLIC CREEP TRANSIENT AND STEADY-STATE CREEP GRAIN BOUNDARY CONTRIBUTION TO CREEP TERTIARY CREEP AND FRACTURE CREEP-RESISTANT ALLOY DESIGN 6 10 DEFORMATION MECHANISM MAPS 6 11 METALLIC FATIGUE NATURE OF FATIGUE FAILURE ENGINEERING ASPECTS OF FATIGUE STRUCTURAL CHANGES ACCOMPANYING FATIGUE CRACK FORMATION AND FATIGUE FAILURE FATIGUE AT ELEVATED TEMPERATURES MECHANICAL PROPERTIES II – STRENGTHENING AND TOUGHENING STRENGTHENING OF NON-FERROUS ALLOYS BY HEAT TREATMENT PRECIPITATION HARDENING OF AL–CU ALLOYS PRECIPITATION HARDENING OF AL–AG ALLOYS MECHANISMS OF PRECIPITATION HARDENING VACANCIES AND PRECIPITATION DUPLEX AGEING PARTICLE COARSENING SPINODAL DECOMPOSITION STRENGTHENING OF STEELS BY HEAT TREATMENT TIME–TEMPERATURE–TRANSFORMATION DIAGRAMS AUSTENITE–PEARLITE TRANSFORMATION AUSTENITE–MARTENSITE TRANSFORMATION AUSTENITE–BAINITE TRANSFORMATION TEMPERING OF MARTENSITE THERMOMECHANICAL TREATMENTS FRACTURE AND TOUGHNESS GRIF?TH MICROCRACK CRITERION FRACTURE TOUGHNESS CLEAVAGE AND THE DUCTILE–BRITTLE TRANSITION FACTORS AFFECTING BRITTLENESS OF STEELS HYDROGEN EMBRITTLEMENT OF STEELS INTERGRANULAR FRACTURE DUCTILE FAILURE RUPTURE VOIDING AND FRACTURE AT ELEVATED TEMPERATURES FRACTURE MECHANISM MAPS CRACK GROWTH UNDER FATIGUE CONDITIONS ATOMISTIC MODELING OF MECHANICAL BEHAVIOR MULTISCALE MODELING ATOMISTIC SIMULATIONS OF DEFECTS ADVANCED ALLOYS COMMERCIAL STEELS PLAIN CARBON STEELS ALLOY STEELS MARAGING STEELS HIGH-STRENGTH LOW-ALLOY (HSLA) STEELS DUAL-PHASE (DP) STEELS MECHANICALLY ALLOYED (MA) STEELS DESIGNATION OF STEELS CAST IRONS SUPERALLOYS BASIC ALLOYING FEATURES NICKEL-BASED SUPERALLOY DEVELOPMENT DISPERSION-HARDENED SUPERALLOYS TITANIUM ALLOYS BASIC ALLOYING AND HEAT-TREATMENT FEATURES COMMERCIAL TITANIUM ALLOYS PROCESSING OF TITANIUM ALLOYS STRUCTURAL INTERMETALLIC COMPOUNDS GENERAL PROPERTIES OF INTERMETALLIC COMPOUNDS NICKEL ALUMINIDES TITANIUM ALUMINIDES OTHER INTERMETALLIC COMPOUNDS ALUMINUM ALLOYS DESIGNATION OF ALUMINUM ALLOYS APPLICATIONS OF ALUMINUM ALLOYS ALUMINUM–LITHIUM ALLOYS PROCESSING DEVELOPMENTS OXIDATION, CORROSION AND SURFACE TREATMENT THE ENGINEERING IMPORTANCE OF SURFACES METALLIC CORROSION OXIDATION AT HIGH TEMPERATURES AQUEOUS CORROSION SURFACE ENGINEERING THE COATING AND MODI?CATION OF SURFACES SURFACE COATING BY VAPOR DEPOSITION SURFACE COATING BY PARTICLE BOMBARDMENT SURFACE MODI?CATION WITH HIGH-ENERGY BEAMS THERMAL BARRIER COATINGS DIAMOND-LIKE CARBON DUPLEX SURFACE ENGINEERING NON-METALLICS I – CERAMICS, GLASS, GLASS-CERAMICS 10 1 INTRODUCTION 10 2 SINTERING OF CERAMIC POWDERS POWDERING AND SHAPING SINTERING 10 3 SOME ENGINEERING AND COMMERCIAL CERAMICS 10 3 1 ALUMINA SILICA SILICATES PEROVSKITES, TITANATES AND SPINELS SILICON CARBIDE SILICON NITRIDE SIALONS ZIRCONIA 10 4 GLASSES STRUCTURE AND CHARACTERISTICS PROCESSING AND PROPERTIES GLASS-CERAMICS 10 5 CARBON DIAMOND GRAPHITE FULLERENES AND RELATED NANOSTRUCTURES 10 6 STRENGTH OF CERAMICS AND GLASSES STRENGTH MEASUREMENT FOR BRITTLE MATERIALS STATISTICAL NATURE AND SIZE DEPENDENCE OF STRENGTH STRESS CORROSION CRACKING OF CERAMICS AND GLASSES 10 7 A CASE STUDY: THERMAL PROTECTION SYSTEM IN SPACE SHUTTLE ORBITER NON-METALLICS II – POLYMERS, PLASTICS, COMPOSITES 11 1 POLYMER MOLECULES 11 2 MOLECULAR WEIGHT 11 3 POLYMER SHAPE AND STRUCTURE 11 4 POLYMER CRYSTALLINITY 11 5 POLYMER CRYSTALS 11 6 MECHANICAL BEHAVIOR DEFORMATION 11 6 2 VISCOELASTICITY FRACTURE 11 7 PLASTICS AND ADDITIVES 11 8 POLYMER PROCESSING 11 9 ELECTRICAL PROPERTIES 11 10 COMPOSITES 11 10 1 PARTICULATE COMPOSITES CONTENTS 11 10 2 FIBER-REINFORCED COMPOSITES 11 10 3 FIBER ORIENTATIONS 11 10 4 IN?UENCE OF ?BER LENGTH 11 10 5 COMPOSITE ?BERS 11 10 6 POLYMER–MATRIX COMPOSITES (PMCS) 11 10 7 METAL–MATRIX COMPOSITES (MMCS) 11 10 8 CERAMIC–MATRIX COMPOSITES (CMCS) CASE EXAMINATION OF BIOMATERIALS, SPORTS MATERIALS AND NANOMATERIALS 12 1 INTRODUCTION 12 2 BIOMATERIALS INTRODUCTION AND BIO-REQUIREMENTS INTRODUCTION TO BONE AND TISSUE CASE CONSIDERATION OF REPLACEMENT JOINTS BIOMATERIALS FOR HEART REPAIR RECONSTRUCTIVE SURGERY OPHTHALMICS DENTAL MATERIALS DRUG DELIVERY SYSTEMS 12 3 SPORTS MATERIALS GOLF EQUIPMENT 12 3 3 TENNIS EQUIPMENT BICYCLES SKIING MATERIALS 12 3 6 ARCHERY FENCING FOILS SPORTS PROTECTION 12 4 MATERIALS FOR NANOTECHNOLOGY NANOPARTICLES FULLERENES AND NANOTUBES QUANTUM WELLS, WIRES AND DOTS BULK NANOSTRUCTURED SOLIDS MECHANICAL PROPERTIES OF SMALL MATERIAL VOLUMES BIO-NANOTECHNOLOGY NUMERICAL ANSWERS TO PROBLEMS THE FOUR ELECTRON QUANTUM NUMBERS RUTHERFORD CONCEIVED THE ATOM TO BE A POSITIVELY CHARGED NUCLEUS, WHICH CARRIED THE GREATER PART OF THE MASS OF THE ATOM, WITH ELECTRONS CLUSTERING AROUND IT HE SUGGESTED THAT THE ELECTRONS WERE REVOLVING ROUND THE NUCLEUS IN CIRCULAR ORBITS SO THAT THE CENTRIFUGAL FORCE OF THE REVOLVING ELECTRONS WAS JUST EQUAL TO THE ELECTROSTATIC ATTRACTION BETWEEN THE POSITIVELY CHARGED NUCLEUS AND THE NEGATIVELY CHARGED ELECTRONS IN ORDER TO AVOID THE DIF?CULTY THAT REVOLVING ELECTRONS SHOULD, ACCORDING TO THE CLASSICAL LAWS OF ELECTRODYNAMICS, EMIT ENERGY CONTINUOUSLY IN THE FORM OF ELECTROMAGNETIC RADIATION, BOHR, IN 1913, WAS FORCED TO CONCLUDE THAT, OF ALL THE POSSIBLE ORBITS, ONLY CERTAIN ORBITS WERE IN FACT PERMISSIBLE THESE DISCRETE ORBITS WERE ASSUMED TO HAVE THE REMARKABLE PROPERTY THAT WHEN AN ELECTRON WAS IN ONE OF THESE ORBITS, NO RADIATION COULD TAKE PLACE THE SET OF STABLE ORBITS WAS CHARACTERIZED BY THE CRITERION THAT THE ANGULAR MOMENTA OF THE ELECTRONS IN THE ORBITS WERE GIVEN BY THE EXPRESSION NH/2?, WHERE H IS PLANCK’S CONSTANT AND N COULD ONLY HAVE INTEGRAL VALUES (N = 1, 2, 3, ETC ) IN THIS WAY, BOHR WAS ABLE TO GIVE A SATISFACTORY EXPLANATION OF THE LINE SPECTRUM OF THE HYDROGEN ATOM AND TO LAY THE FOUNDATION OF MODERN ATOMIC THEORY IN LATER DEVELOPMENTS OF THE ATOMIC THEORY, BY DE BROGLIE, SCHRÖDINGER AND HEISENBERG, IT WAS REALIZED THAT THE CLASSICAL LAWS OF PARTICLE DYNAMICS COULD NOT BE APPLIED TO FUNDAMENTAL PARTICLES IN CLASSICAL DYNAMICS IT IS A PREREQUISITE THAT THE POSITION AND MOMENTUM OF A PARTICLE ARE KNOWN EXACTLY: IN ATOMIC DYNAMICS, IF EITHER THE POSITION OR THE MOMENTUM OF A FUNDAMENTAL PARTICLE IS KNOWN EXACTLY, THEN THE OTHER QUANTITY CANNOT BE DETERMINED IN FACT, AN UNCERTAINTY MUST EXIST IN OUR KNOWLEDGE OF THE POSITION AND MOMENTUM OF A SMALL PARTICLE, AND THE PRODUCT OF THE DEGREE OF UNCERTAINTY FOR EACH QUANTITY IS RELATED TO THE VALUE OF PLANCK’S CONSTANT (H = 6 6256 × 10?34 J S) IN THE MACROSCOPIC WORLD, THIS FUNDAMENTAL UNCERTAINTY IS TOO SMALL TO BE MEASURABLE, BUT WHEN TREATING THE MOTION OF ELECTRONS REVOLVING ROUND AN ATOMIC NUCLEUS, APPLICATION OF HEISENBERG’S UNCERTAINTY PRINCIPLE IS ESSENTIAL THE CONSEQUENCE OF THE UNCERTAINTY PRINCIPLE IS THAT WE CAN NO LONGER THINK OF AN ELECTRON AS MOVING IN A ?XED ORBIT AROUND THE NUCLEUS, BUT MUST CONSIDER THE MOTION OF THE ELECTRON IN TERMS OF A PHYSICAL METALLURGY AND ADVANCED MATERIALS WAVE FUNCTION THIS FUNCTION SPECI?ES ONLY THE PROBABILITY OF ?NDING ONE ELECTRON HAVING A PARTICULAR ENERGY IN THE SPACE SURROUNDING THE NUCLEUS THE SITUATION IS FURTHER COMPLICATED BY THE FACT THAT THE ELECTRON BEHAVES NOT ONLY AS IF IT WERE REVOLVING ROUND THE NUCLEUS, BUT ALSO AS IF IT WERE SPINNING ABOUT ITS OWN AXIS CONSEQUENTLY, INSTEAD OF SPECIFYING THE MOTION OF AN ELECTRON IN AN ATOM BY A SINGLE INTEGER N, AS REQUIRED BY THE BOHR THEORY, IT IS NOW NECESSARY TO SPECIFY THE ELECTRON STATE USING FOUR NUMBERS THESE NUMBERS, KNOWN AS ELECTRON QUANTUM NUMBERS, ARE N, L, M AND S, WHERE N IS THE PRINCIPAL QUANTUM NUMBER, L IS THE ORBITAL (AZIMUTHAL) QUANTUM NUMBER, M IS THE MAGNETIC QUANTUM NUMBER AND S IS THE SPIN QUANTUM NUMBER ANOTHER BASIC PREMISE OF THE MODERN QUANTUM THEORY OF THE ATOM IS THE PAULI EXCLUSION PRINCIPLE THIS STATES THAT NO TWO ELECTRONS IN THE SAME ATOM CAN HAVE THE SAME NUMERICAL VALUES FOR THEIR SET OF FOUR QUANTUM NUMBERS IF WE ARE TO UNDERSTAND THE WAY IN WHICH THE PERIODIC TABLE OF THE CHEMICAL ELEMENTS IS BUILT UP IN TERMS OF THE ELECTRONIC STRUCTURE OF THE ATOMS, WE MUST NOW CONSIDER THE SIGNI?CANCE OF THE FOUR QUAN- TUM NUMBERS AND THE LIMITATIONS PLACED UPON THE NUMERICAL VALUES THAT THEY CAN ASSUME THE MOST IMPORTANT QUANTUM NUMBER IS THE PRINCIPAL QUANTUM NUMBER, SINCE IT IS MAINLY RESPONSIBLE FOR DETER- MINING THE ENERGY OF THE ELECTRON THE PRINCIPAL QUANTUM NUMBER CAN HAVE INTEGRAL VALUES BEGINNING WITH N = 1, WHICH IS THE STATE OF LOWEST ENERGY, AND ELECTRONS HAVING THIS VALUE ARE THE MOST STABLE, THE STABILITY DECREASING AS N INCREASES ELECTRONS HAVING A PRINCIPAL QUANTUM NUMBER N CAN TAKE UP INTEGRAL VALUES OF THE ORBITAL QUANTUM NUMBER L BETWEEN 0 AND (N ?1) THUS, IF N = 1, L CAN ONLY HAVE THE VALUE 0, WHILE FOR N = 2, L = 0 OR 1, AND FOR N = 3, L = 0, 1 OR 2 THE ORBITAL QUANTUM NUMBER IS ASSOCIATED WITH THE ANGULAR MOMENTUM OF THE REVOLVING ELECTRON, AND DETERMINES WHAT WOULD BE REGARDED IN NON-QUANTUM MECHANICAL TERMS AS THE SHAPE OF THE ORBIT FOR A GIVEN VALUE OF N, THE ELECTRON HAVING THE LOWEST VALUE OF L WILL HAVE THE LOWEST ENERGY, AND THE HIGHER THE VALUE OF L, THE GREATER WILL BE THE ENERGY THE REMAINING TWO QUANTUM NUMBERS M AND S ARE CONCERNED, RESPECTIVELY, WITH THE ORIENTATION OF THE ELECTRON’S ORBIT ROUND THE NUCLEUS, AND WITH THE ORIENTATION OF THE DIRECTION OF SPIN OF THE ELECTRON FOR A GIVEN VALUE OF L, AN ELECTRON MAY HAVE INTEGRAL VALUES OF THE INNER QUANTUM NUMBER M FROM +L THROUGH 0 TO ?L THUS, FOR L = 2, M CAN TAKE ON THE VALUES +2, +1, 0, ?1 AND ?2 THE ENERGIES OF ELECTRONS HAVING THE SAME VALUES OF N AND L BUT DIFFERENT VALUES OF M ARE THE SAME, PROVIDED THERE IS NO MAGNETIC ?ELD PRESENT WHEN A MAGNETIC ?ELD IS APPLIED, THE ENERGIES OF ELECTRONS HAVING DIFFERENT M VALUES WILL BE ALTERED SLIGHTLY, AS IS SHOWN BY THE SPLITTING OF SPECTRAL LINES IN THE ZEEMAN EFFECT THE SPIN QUANTUM NUMBER S MAY, FOR AN ELECTRON HAVING THE SAME VALUES OF N, L AND M, TAKE ONE OF TWO VALUES, THAT IS, + 1 THE LETTERS, S, P, D AND F AROSE FROM A CLASSI?CATION OF SPECTRAL LINES INTO FOUR GROUPS, TERMED SHARP, PRINCIPAL, DIFFUSE AND FUNDAMENTAL, IN THE DAYS BEFORE THE PRESENT QUANTUM THEORY WAS DEVELOPED ATOMS AND ATOMIC ARRANGEMENTS ALLOCATION OF STATES IN THE ?RST THREE QUANTUM SHELLS SHELL N L M S NUMBER OF STATES MAXIMUM NUMBER OF ELECTRONS IN SHELL 1ST K TWO 1S-STATES WHEN THE PRINCIPAL QUANTUM NUMBER N = 1, L MUST BE EQUAL TO ZERO, AND AN ELECTRON IN THIS STATE WOULD BE DESIGNATED BY THE SYMBOL 1S SUCH A STATE CAN ONLY HAVE A SINGLE VALUE OF THE INNER QUANTUM NUMBER M = 0, BUT CAN HAVE VALUES OF + 2 FOR THE SPIN QUANTUM NUMBER S IT FOLLOWS, THEREFORE, THAT THERE ARE ONLY TWO ELECTRONS IN ANY ONE ATOM WHICH CAN BE IN A 1S-STATE, AND THAT THESE ELECTRONS WILL SPIN IN OPPOSITE DIRECTIONS THUS, WHEN N = 1, ONLY S-STATES CAN EXIST AND THESE CAN BE OCCUPIED BY ONLY TWO ELECTRONS ONCE THE TWO 1S-STATES HAVE BEEN ?LLED, THE NEXT LOWEST ENERGY STATE MUST HAVE N = 2 HERE L MAY TAKE THE VALUE 0 OR 1, AND THEREFORE ELECTRONS CAN BE IN EITHER A 2S- OR A 2P-STATE THE ENERGY OF AN ELECTRON IN THE 2S-STATE IS LOWER THAN IN A 2P-STATE, AND HENCE THE 2S-STATES WILL BE ?LLED ?RST ONCE MORE THERE ARE ONLY TWO ELECTRONS IN THE 2S-STATE, AND INDEED THIS IS ALWAYS TRUE OF S-STATES, IRRESPECTIVE OF THE VALUE OF THE PRINCIPAL QUANTUM NUMBER THE ELECTRONS IN THE P-STATE CAN HAVE VALUES OF M = +1, 0, ?1, AND ELECTRONS HAVING EACH OF THESE VALUES FOR M CAN HAVE TWO VALUES OF THE SPIN QUANTUM NUMBER, LEADING THEREFORE TO THE POSSIBILITY OF SIX ELECTRONS BEING IN ANY ONE P-STATE THESE RELATIONSHIPS ARE SHOWN MORE CLEARLY IN TABLE 1 1 NO FURTHER ELECTRONS CAN BE ADDED TO THE STATE FOR N = 2 AFTER TWO 2S- AND SIX 2P-STATES ARE ?LLED, AND THE NEXT ELECTRON MUST GO INTO THE STATE FOR WHICH N = 3, WHICH IS AT A HIGHER ENERGY HERE THE POSSIBILITY ARISES FOR L TO HAVE THE VALUES 0, 1 AND 2 AND HENCE, BESIDES S- AND P-STATES, D-STATES FOR WHICH L = 2 CAN NOW OCCUR WHEN L = 2, M MAY HAVE THE VALUES +2, +1, 0, ?1, ?2 AND EACH MAY BE OCCUPIED BY TWO ELECTRONS OF OPPOSITE SPIN, LEADING TO A TOTAL OF TEN D-STATES FINALLY, WHEN N = 4, L WILL HAVE THE POSSIBLE VALUES FROM 0 TO 3, AND WHEN L = 3 THE READER MAY VERIFY THAT THERE ARE THE PERIODIC TABLE OF THE ELEMENTS (FROM PUDDEPHATT AND MONAGHAN, 1986; BY PERMISSION OF OXFORD UNIVERSITY PRESS)