Microlearning in solid state physics (16 risultati)

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

Taschenbuch. Condizione: Neu. Neuware - Vibrations, Dispersion, and Brillouin Zone in a Monoatomic LatticeThis book presents a clear and systematic exploration of vibrational motion in a one-dimensional monoatomic crystal, emphasizing how atomic arrangements and lattice periodicity determine the vibrational properties of solids. Beginning with the concept of lattice spacing and atomic displacements, it introduces the mathematical framework required to describe phonon behaviour and wave propagation in crystals.A major focus of the book is the First Brillouin Zone, the fundamental region in reciprocal space where all distinct wave vectors lie. The book explains why all physical phonon states are contained within-p/aand how any wave vector outside this range can be mapped back into it. This provides a deep understanding of the periodicity of the dispersion relation and the redundancy of k-values outside the Brillouin zone.The phonon dispersion relation for a monoatomic chain is carefully derived, showing how atomic forces lead to the frequency-wave-vector relation?=4Cm|sin(ka2)|.The book explains how this relation governs the allowed vibrational frequencies, why phonons have a maximum cutoff frequency, and how the dispersion curve repeats in successive Brillouin zones.A detailed discussion of the long-wavelength limit demonstrates that for small values of kkk, the dispersion becomes linear, ??k, omega propto k,??k, revealing that low-frequency lattice vibrations behave like ordinary sound waves.The concept of group velocity, vg=d?/dk=aCmcos(ka2), is introduced as the speed at which energy is carried through the lattice. The book explains why the group velocity becomes zero at the Brillouin zone boundary and reaches its maximum at the zone center.To strengthen understanding, the book includes: - Clear conceptual explanations- Short answer questions- Multiple-choice questions- Simple numerical problems with step-by-step solutionsOverall, this book provides a complete and accessible introduction to phonon dynamics, reciprocal space, and lattice wave propagation in monoatomic crystals. It serves as an excellent resource for students of solid-state physics, materials science, and condensed matter physics, offering both conceptual clarity and mathematical insight.…

Taschenbuch. Condizione: Neu. Neuware - Vibrations of Crystals with Monatomic BasisThis book provides a detailed, concept-oriented introduction to the vibrational behavior of crystals that contain one atom per primitive cell. It explains how atoms arranged in a regular lattice can oscillate collectively, forming waves that propagate through the crystal. These vibrations play a fundamental role in determining the mechanical, thermal, and electronic properties of solids.The analysis begins by defining the displacement usu_sus of the sss-th atom from its equilibrium position and describing how entire atomic planes move in phase when a vibrational wave travels through the lattice. For any wave vector kkk, the system supports three vibrational modes-one longitudinal (parallel to the wave direction) and two transverse (perpendicular to the wave direction).To determine how these vibrations behave, the book introduces the elastic restoring forces acting between neighboring atoms. Assuming a linear response and nearest-neighbour interactions, the force on any atom depends on the difference in displacement between that atom and its adjacent planes. Applying Newton's second law leads to the fundamental equation of motion for the lattice.Using a harmonic trial solution us=Ae-i?tu_s = A e^{-iomega t}us=Ae-i?t and expressing atomic displacements in terms of a wave vector, the book derives the dispersion relation: ?2=2Cm(1-coska), omega^2 = frac{2C}{m}(1 - cos ka),?2=m2C(1-coska), where CCC is the force constant, mmm is the atomic mass, aaa is the lattice spacing, and kkk is the wave vector.This relation describes how the vibrational frequency varies with kkk, showing that the frequency becomes zero at k=0k = 0k=0 (all atoms move together) and reaches a maximum at the boundary of the first Brillouin zone k=±p/ak = pm pi/ak=±p/a.Using trigonometric identities, this relation is rewritten as: ?=4Cm|sin(ka/2)|, omega = sqrt{frac{4C}{m}} sin(ka/2),?=m4C|sin(ka/2)|, revealing the periodic nature of lattice vibrations. The book explains how this dispersion curve governs the propagation of vibrational energy, the group velocity, and the behaviour of low- and high-frequency modes.Overall, this book gives a complete understanding of lattice dynamics in simple monatomic crystals. It builds the foundation for advanced topics such as phonons, thermal conductivity, heat capacity, scattering processes, and vibrations in more complex crystal structures.…

Taschenbuch. Condizione: Neu. Neuware - This book, 'Space Lattice and Basis', is the second volume in the Solid State Physics Series (SSP-01) and forms a conceptual backbone for understanding crystalline solids.The book introduces two fundamental ideas-space lattice and basis-which together explain how real crystal structures are formed in three-dimensional space. Special emphasis is placed on: - Clear definitions and explanations- Strong conceptual clarity- Step-by-step logical progression- Visualization-based learning- Exam-oriented 2-mark answers, MCQs, numericals, and reasoning questionsThe abstract nature of lattice geometry is carefully distinguished from the physical reality of atoms represented by the basis. Important relations such as: Crystal Structure = Space Lattice + Basisare repeatedly reinforced to ensure long-term retention.This book is designed to bridge the gap between definitions and understanding, making it especially suitable for learners who struggle with abstract crystallographic concepts.…

Paperback. Condizione: new. Paperback. Vibrations, Dispersion, and Brillouin Zone in a Monoatomic LatticeThis book presents a clear and systematic exploration of vibrational motion in a one-dimensional monoatomic crystal, emphasizing how atomic arrangements and lattice periodicity determine the vibrational properties of solids. Beginning with the concept of lattice spacing and atomic displacements, it introduces the mathematical framework required to describe phonon behaviour and wave propagation in crystals.A major focus of the book is the First Brillouin Zone, the fundamental region in reciprocal space where all distinct wave vectors lie. The book explains why all physical phonon states are contained within-p/aand how any wave vector outside this range can be mapped back into it. This provides a deep understanding of the periodicity of the dispersion relation and the redundancy of k-values outside the Brillouin zone.The phonon dispersion relation for a monoatomic chain is carefully derived, showing how atomic forces lead to the frequency-wave-vector relationw=4Cmsin(ka2).The book explains how this relation governs the allowed vibrational frequencies, why phonons have a maximum cutoff frequency, and how the dispersion curve repeats in successive Brillouin zones.A detailed discussion of the long-wavelength limit demonstrates that for small values of kkk, the dispersion becomes linear, wk, \omega \propto k,wk, revealing that low-frequency lattice vibrations behave like ordinary sound waves.The concept of group velocity, vg=dw/dk=aCmcos(ka2), is introduced as the speed at which energy is carried through the lattice. The book explains why the group velocity becomes zero at the Brillouin zone boundary and reaches its maximum at the zone center.To strengthen understanding, the book includes: Clear conceptual explanationsShort answer questionsMultiple-choice questionsSimple numerical problems with step-by-step solutionsOverall, this book provides a complete and accessible introduction to phonon dynamics, reciprocal space, and lattice wave propagation in monoatomic crystals. It serves as an excellent resource for students of solid-state physics, materials science, and condensed matter physics, offering both conceptual clarity and mathematical insight. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

Paperback. Condizione: new. Paperback. Vibrations of Crystals with Monatomic BasisThis book provides a detailed, concept-oriented introduction to the vibrational behavior of crystals that contain one atom per primitive cell. It explains how atoms arranged in a regular lattice can oscillate collectively, forming waves that propagate through the crystal. These vibrations play a fundamental role in determining the mechanical, thermal, and electronic properties of solids.The analysis begins by defining the displacement usu_sus of the sss-th atom from its equilibrium position and describing how entire atomic planes move in phase when a vibrational wave travels through the lattice. For any wave vector kkk, the system supports three vibrational modes-one longitudinal (parallel to the wave direction) and two transverse (perpendicular to the wave direction).To determine how these vibrations behave, the book introduces the elastic restoring forces acting between neighboring atoms. Assuming a linear response and nearest-neighbour interactions, the force on any atom depends on the difference in displacement between that atom and its adjacent planes. Applying Newton's second law leads to the fundamental equation of motion for the lattice.Using a harmonic trial solution us=Ae-iwtu_s = A e^{-i\omega t}us=Ae-iwt and expressing atomic displacements in terms of a wave vector, the book derives the dispersion relation: w2=2Cm(1-coska), \omega^2 = \frac{2C}{m}(1 - \cos ka),w2=m2C(1-coska), where CCC is the force constant, mmm is the atomic mass, aaa is the lattice spacing, and kkk is the wave vector.This relation describes how the vibrational frequency varies with kkk, showing that the frequency becomes zero at k=0k = 0k=0 (all atoms move together) and reaches a maximum at the boundary of the first Brillouin zone k=p/ak = \pm \pi/ak=p/a.Using trigonometric identities, this relation is rewritten as: w=4Cmsin(ka/2), \omega = \sqrt{\frac{4C}{m}} \sin(ka/2),w=m4Csin(ka/2), revealing the periodic nature of lattice vibrations. The book explains how this dispersion curve governs the propagation of vibrational energy, the group velocity, and the behaviour of low- and high-frequency modes.Overall, this book gives a complete understanding of lattice dynamics in simple monatomic crystals. It builds the foundation for advanced topics such as phonons, thermal conductivity, heat capacity, scattering processes, and vibrations in more complex crystal structures. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

Paperback. Condizione: new. Paperback. This book, "Space Lattice and Basis", is the second volume in the Solid State Physics Series (SSP-01) and forms a conceptual backbone for understanding crystalline solids.The book introduces two fundamental ideas-space lattice and basis-which together explain how real crystal structures are formed in three-dimensional space. Special emphasis is placed on: Clear definitions and explanationsStrong conceptual clarityStep-by-step logical progressionVisualization-based learningExam-oriented 2-mark answers, MCQs, numericals, and reasoning questionsThe abstract nature of lattice geometry is carefully distinguished from the physical reality of atoms represented by the basis. Important relations such as: Crystal Structure = Space Lattice + Basisare repeatedly reinforced to ensure long-term retention.This book is designed to bridge the gap between definitions and understanding, making it especially suitable for learners who struggle with abstract crystallographic concepts. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

Condizione: New. Print on Demand.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

Paperback. Condizione: new. Paperback. Vibrations of Crystals with Monatomic BasisThis book provides a detailed, concept-oriented introduction to the vibrational behavior of crystals that contain one atom per primitive cell. It explains how atoms arranged in a regular lattice can oscillate collectively, forming waves that propagate through the crystal. These vibrations play a fundamental role in determining the mechanical, thermal, and electronic properties of solids.The analysis begins by defining the displacement usu_sus of the sss-th atom from its equilibrium position and describing how entire atomic planes move in phase when a vibrational wave travels through the lattice. For any wave vector kkk, the system supports three vibrational modes-one longitudinal (parallel to the wave direction) and two transverse (perpendicular to the wave direction).To determine how these vibrations behave, the book introduces the elastic restoring forces acting between neighboring atoms. Assuming a linear response and nearest-neighbour interactions, the force on any atom depends on the difference in displacement between that atom and its adjacent planes. Applying Newton's second law leads to the fundamental equation of motion for the lattice.Using a harmonic trial solution us=Ae-iwtu_s = A e^{-i\omega t}us=Ae-iwt and expressing atomic displacements in terms of a wave vector, the book derives the dispersion relation: w2=2Cm(1-coska), \omega^2 = \frac{2C}{m}(1 - \cos ka),w2=m2C(1-coska), where CCC is the force constant, mmm is the atomic mass, aaa is the lattice spacing, and kkk is the wave vector.This relation describes how the vibrational frequency varies with kkk, showing that the frequency becomes zero at k=0k = 0k=0 (all atoms move together) and reaches a maximum at the boundary of the first Brillouin zone k=p/ak = \pm \pi/ak=p/a.Using trigonometric identities, this relation is rewritten as: w=4Cmsin(ka/2), \omega = \sqrt{\frac{4C}{m}} \sin(ka/2),w=m4Csin(ka/2), revealing the periodic nature of lattice vibrations. The book explains how this dispersion curve governs the propagation of vibrational energy, the group velocity, and the behaviour of low- and high-frequency modes.Overall, this book gives a complete understanding of lattice dynamics in simple monatomic crystals. It builds the foundation for advanced topics such as phonons, thermal conductivity, heat capacity, scattering processes, and vibrations in more complex crystal structures. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…

Paperback. Condizione: new. Paperback. Vibrations, Dispersion, and Brillouin Zone in a Monoatomic LatticeThis book presents a clear and systematic exploration of vibrational motion in a one-dimensional monoatomic crystal, emphasizing how atomic arrangements and lattice periodicity determine the vibrational properties of solids. Beginning with the concept of lattice spacing and atomic displacements, it introduces the mathematical framework required to describe phonon behaviour and wave propagation in crystals.A major focus of the book is the First Brillouin Zone, the fundamental region in reciprocal space where all distinct wave vectors lie. The book explains why all physical phonon states are contained within-p/aand how any wave vector outside this range can be mapped back into it. This provides a deep understanding of the periodicity of the dispersion relation and the redundancy of k-values outside the Brillouin zone.The phonon dispersion relation for a monoatomic chain is carefully derived, showing how atomic forces lead to the frequency-wave-vector relationw=4Cmsin(ka2).The book explains how this relation governs the allowed vibrational frequencies, why phonons have a maximum cutoff frequency, and how the dispersion curve repeats in successive Brillouin zones.A detailed discussion of the long-wavelength limit demonstrates that for small values of kkk, the dispersion becomes linear, wk, \omega \propto k,wk, revealing that low-frequency lattice vibrations behave like ordinary sound waves.The concept of group velocity, vg=dw/dk=aCmcos(ka2), is introduced as the speed at which energy is carried through the lattice. The book explains why the group velocity becomes zero at the Brillouin zone boundary and reaches its maximum at the zone center.To strengthen understanding, the book includes: Clear conceptual explanationsShort answer questionsMultiple-choice questionsSimple numerical problems with step-by-step solutionsOverall, this book provides a complete and accessible introduction to phonon dynamics, reciprocal space, and lattice wave propagation in monoatomic crystals. It serves as an excellent resource for students of solid-state physics, materials science, and condensed matter physics, offering both conceptual clarity and mathematical insight. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…

Paperback. Condizione: new. Paperback. This book, "Space Lattice and Basis", is the second volume in the Solid State Physics Series (SSP-01) and forms a conceptual backbone for understanding crystalline solids.The book introduces two fundamental ideas-space lattice and basis-which together explain how real crystal structures are formed in three-dimensional space. Special emphasis is placed on: Clear definitions and explanationsStrong conceptual clarityStep-by-step logical progressionVisualization-based learningExam-oriented 2-mark answers, MCQs, numericals, and reasoning questionsThe abstract nature of lattice geometry is carefully distinguished from the physical reality of atoms represented by the basis. Important relations such as: Crystal Structure = Space Lattice + Basisare repeatedly reinforced to ensure long-term retention.This book is designed to bridge the gap between definitions and understanding, making it especially suitable for learners who struggle with abstract crystallographic concepts. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…