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CH403 Syllabus: Properties of MaterialsNCSU

Instructor: Paul Maggard – Rm. 422 Dabney Hall, Phone: 515-3616 (Paul_Maggard@ncsu.edu)

Class meets: Mon., Wed. & Fri. @ 9:10 – 10:00 AM – Rm. 330 Dabney Hall

Office hours: Mon., Wed. & Fri. @ 10:00 – 11:00 AM

Course description: Selected topics in inorganic materials chemistry will be covered. Chemical bonding and structure of solids, physical properties of solids: optical thermal, surfaces, electrical, magnetic and mechanical.

Text: Properties of Materials, 1999, by Mary Anne White; Scientific articles and supplementary information will be assigned or provided in class.

Attendance: Attendance will not be taken during lectures. A significant number of absences will decrease your chances of scoring well in this course.

CH403 Syllabus: Properties of MaterialsNCSU

Grading: Your final grade will be based on the following items: Two mid-term exams (200pts), one final exam (100pts), and the in-class problem sets (100pts). Total possible = 400 pts.

In-Class Problem Sets: During the semester, there will be unannounced in-class problem sets which will be given at the end of the class periods, counting a total of 100 pts toward your final grade. This point total will represent your average out of 100%, e.g. 78 / 105 pts = 74.3% or 74 pts.

Exam schedule: The two mid-term exams will be given in class and will be announced about one week in advance. There will be no makeup exams.

Academic Integrity: It is the understanding and expectation that the student's signature on any test or assignment means that the student neither gave nor received unauthorized aid. The University policy on academic integrity can be found in the Code of Student Conduct: www.ncsu.edu/policies/student_services/student_discipline/POL11.35.1.php

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CH403 Syllabus: Properties of MaterialsNCSU

Statement for students with disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653

Regular Class Schedule*

Jan. 9, 11, 13, 18, 20, 23, 25, 27, 30

Feb. 1, 3, 6, 8, 10, 13, 15, 17, 20, 22, 24, 27

Mar. 1, 3, 13, 15, 17, 20, 22, 24, 27, 29, 31

Apr. 3, 5, 7, 10, 12, 17, 19, 21, 24, 26, 28

Date of Final: TBA

* It is your responsibility to come to each class prepared (43).

Materials Chemistry: Extended Structure and Bonding

How common are Inorganic Materials?

What are some natural materials?

1st section of course: Groundwork for describing the structure of materials – unit cell, structure types, symmetry and bonding and electronic structure of extended systems.

2nd section of course: Understanding the chemical origin of materials’ properties – Optical, thermal, electronic, magnetic mechanical.

Technological importance: Different eras in civilization are named for material’s advances – Bronze, Iron, Semiconductors, etc.

White (pp. 1-7)

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‘Extended’ Structure and BondingNCSU

Application of the chemical concepts of symmetry, structure, and bonding in extended systems.

Materials Chemistry: Extended Structure and Bonding

Some ways to classify the structure of a material:

(1) Size domain (nm, µm, mm)

(2) Dimensionality (0D, 1D, 2D, 3D)

(3) Bond types

(4) Symmetry (order or disorder)

(5) Surface structure and area

(6) Connectivity (near neighbors)

(7) Homogeneous or heterogeneous

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Structures of MaterialsStructures of Materials

Material Material –– A group of chemical species that functions collectively.A group of chemical species that functions collectively.

How do we begin to describe the structure of groups of chemical How do we begin to describe the structure of groups of chemical species?species?

CuCu44((pyrazinepyrazine))12128+8+

CuCu88((pyrazinepyrazine))232316+16+

Cu(Cu(pyrazinepyrazine))442+2+

The chemical formula does not imply the structure or bonding.The chemical formula does not imply the structure or bonding.

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CrystalCrystal –– A solid which has perfect long range order.A solid which has perfect long range order.DomainDomain –– An area bounding a perfect crystal.An area bounding a perfect crystal.

1 1 –– 100 mm = polycrystalline100 mm = polycrystalline

1 1 –– 1000 1000 ::m = microcrystallinem = microcrystalline1 1 –– 1000 nm = 1000 nm = nanocrystallinenanocrystalline0.1 0.1 –– 1.0 nm = amorphous1.0 nm = amorphous

The contents of crystalline materials are defined by The contents of crystalline materials are defined by Unit Cells.Unit Cells.* Smallest repeating unit which shows the full symmetry of * Smallest repeating unit which shows the full symmetry of the crystal structure.the crystal structure.

Crystal symmetry includes Crystal symmetry includes both both rotationrotation and and translationtranslation..

Synthetic SiOSynthetic SiO22 crystalcrystal

NCSUSymmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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How is the study of symmetry useful?

To precisely describe the structure in a compact form (especially if complex)

Relevant to spectroscopy (selection rules), or the numbers of different types of atoms/bonds.

Electronic structure (e.g. Orbital splitting, energy diagram), which can be used to predict chemical reactivity or many types of physical properties.

Utilization of the mathematical properties of symmetry groups greatly aids the chemical interpretation of their physical properties.

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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In solids, translation is a symmetry operator that is also part of the symmetry group in what is called a space group.

x

y

z

T = n1x + n2y + n3z n1,2,3 runs from 0 to ∞

Three vectors (a, b, c) and three angles (",$,() define the unit cell.

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

Periodicity Periodicity –– The chemical The chemical contents of every unit cell contents of every unit cell within the crystal are within the crystal are identical. identical.

Lattice ConstantsLattice Constants –– The three The three vectors (a, b, c) and three vectors (a, b, c) and three angles (angles ("",,$$,,(() that define ) that define the unit cell.the unit cell.

White White –– Appendix 3Appendix 3

Seven crystal systemsSeven crystal systemsNCSU

NCSUThe Fourteen Bravais Lattices

triclinica ≠ b ≠ cα ≠ β ≠ γ

monoclinica ≠ b ≠ cα = γ = 90° ≠ β

orthorhombica ≠ b ≠ cα = β = γ = 90°

tetragonala = b ≠ cα = β = γ = 90°

hexagonal/trigonala = b ≠ cα = β = 90° γ = 120°

rhombohedrala = b = cα = β = γ ≠ 90°

cubica = b = cα = β = γ = 90°

White White –– Appendix 3Appendix 3

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Can you draw the unit cell?Can you draw the unit cell?

Can you label the rotational, mirror, inversion symmetries?Can you label the rotational, mirror, inversion symmetries?

NCSUSymmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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Operations of symmetry groups is used to determine if the distribution of matter is the same before and after.

Rotation axes

-1 0 0 0 -1 0 0 0 1

C2z takes x -x y -y z z

x y z

-x -y z

=

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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Symmetry equivalent atoms are the sets of atoms which are interchanged by the symmetry operations of the group.

0 -1 0 1 0 0 0 0 1

C4z takes x -y y x z z

x y z

-y x z

=

A proper rotational symmetry operation in a cartesian space about the z-axis corresponds to the 3x3 matrix:

cos φ -sinφ 0 sin φ cosφ 0 0 0 1

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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Cnx, Cny, Cnz are n-fold rotational axes down the x-, y-, z-axes. σx,σy, σz are mirror planes perpendicular to the x-, y-, z-axes.

Mirror plane and

Inversion

1 0 0 0 1 0 0 0 -1

σz takes:x y z

x y -z

=

-1 0 0 0 -1 0 0 0 -1

i takes:x y z

-x -y -z

=

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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Carrying out two symmetry operations consecutively is identical to their dot product.

-1 0 0 0 -1 0 0 0 1

Rotoreflection

Sn

Rotoinversion

N-1 0 0 0 -1 0 0 0 1

Improper rotations

1 0 0 0 1 0 0 0 -1

-1 0 0 0 -1 0 0 0 -1

C2z

C2z

σz

i

=

=

-1 0 0 0 -1 0 0 0 -1

1 0 0 0 1 0 0 0 -1

S2z = i

2 = σz

Schoenflies

(point groups)

Hermann –Maguin

(space groups)

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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In solids with periodic translational symmetry, only 1-, 2-, 3-, 4-, and 6-fold rotation axes are allowed.

Herman-Maguinn vs. Schoenflies notation and symbols for some symmetric objects.

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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The operations { β | t } combined with the operations { ε | T } form the space group of a crystalline solid.

The set of rotational parts (β) are isomorphic to point groups, and are called crystal classes.

1414 BravaisBravais lattices + point grouplattices + point groupsymmetries = 230 Space Groupssymmetries = 230 Space Groups

The space groups represent all The space groups represent all (group) allowed combinations of (group) allowed combinations of rotations and translations.rotations and translations.

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials

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Crystal System Unit Cell Metrics

Herman-MauguinPoint Group

Schoenflies Point Group

Triclinic a≠b≠cα≠β≠γ

1,⎯1 C1, Ci­

Monoclinic a≠b≠cα=γ=90o≠β

2, m, 2/m C2, Cs, C2h

Orthorhombic a≠b≠cα= β=γ=90o

222, mm2, mmm D2, C2v, D2h

Trigonal a=b=cα=β=γ≠90o

a=b≠cα=β=90o; γ=120o

3,⎯3, 32, 3m,⎯3m

C3, S6, D3, C3v, D3d

Hexagonal 6,⎯6, 6/m, 622, 6mm,⎯62m, 6mm

C6, C3h, C4h, D6, C6v, D3h, D6h

Tetragonal a=b≠cα= β=γ=90o

4,⎯4, 4/m, 422, 4mm,⎯42m, 4/mmm

C4, S4, C4h, D4, C4v, D2d, D4h

Cubic a=b=cα= β=γ=90o

23, m3, 432,⎯432, m⎯3m

T, Th, O,Td, Oh

32 Point Groups + 14 Bravais Lattice = 230 Space Groups

Symmetry In Crystalline MaterialsSymmetry In Crystalline Materials