Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf ·...

17
Second Lecture

Transcript of Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf ·...

Page 1: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

SecondLecture

Page 2: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

Separateatoms Bands

Page 3: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 4: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

Somesimpleexamplesofbandstructure

Page 5: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

(4/3)πrs3=1/ρ

BM=‐V(ΔP/ΔV)

Page 6: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 7: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 8: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 9: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 10: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 11: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 12: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 13: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

ICOMAT

BruceHarmon

IowaStateUniversity

And

AmesLaboratory

Phonons, Energy Landscapes,and Electronic Structure

Page 14: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

Outline

Soft phonon modes associationwith some

Martensitic Transformations

Energy Landscapes

Dynamics

Magnetic Influences

Page 15: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

Theory - G.L. Zhao and B.N.Harmon, Phys. Rev. B48, 2031 (1993)

Experiment - H. Tietz, M. Müllner, and B Renker, J. Phys. F 14, 2517 (1984)

NiTi

T = 0 K

320 K

500 K

1000 K

Page 16: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.
Page 17: Second Lecture - Iowa State Universitycmp.physics.iastate.edu/canfield/course/EM2_19.pdf · Dynamical Matrix - Conduction electrons Importance of el-ph Matrix elements. Fig. 4.1.

Dynamical Matrix -Conduction electrons

Importance of el-ph

Matrix elements


Efficient matrix multiplication

Efficient matrix multiplication

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