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Previously in Chem 104: types of solids Unit Cell 3 types of cubic cells

Previously in Chem 104: types of solids Unit Cell 3 types of cubic cells

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## Previously in Chem 104: types of solids Unit Cell 3 types of cubic cells

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**Previously in**• Chem 104: • types of solids • Unit Cell • 3 types of cubic cells • contents of unit cell • Lecture 1 posted! • TODAY • Z • quantify relationship between cell and density • ionic solid unit cells • solid stability • thermodynamics and lattice energy • “why doesn’t that solid exist” • QUIZ later today**Three Types of Cubic Unit Cells**c b a Body Centered Cubic Face Centered Cubic Simple Cubic**What is one result of a metal’s “choice”**to adopt a cubic, bcc or fcc lattice? Simple Cubic Body Centered Cubic Face Centered Cubic**What is one result of a metal’s “choice”**to adopt a cubic, bcc or fcc lattice? Simple Cubic Body Centered Cubic Face Centered Cubic Z = 1 atom/cell Least Dense Z = 2 atom/cell Z = 4 atom/cell Most Dense**Simple Cubic**Body Centered Cubic Face Centered Cubic Z = 1 Z = 2 Z = 4 Knowing the unit cell structures can be used with other physical data and relationships: Cell volume, V = a3 = l3, l is cell length Cell mass, m = Z x at.wt. A Cell Density = solid density = mass = Z x at.wt. volume A x a3**Cell edge, a or cell length, l**is related to the atomic radius but depends on which structure: Simple Cubic Body Centered Cubic Face Centered Cubic Z = 1 Z = 2 Z = 4 a = l = 2r**Cell edge, a or cell length, l**is related to the atomic radius but depends on which structure: Simple Cubic Body Centered Cubic Face Centered Cubic Z = 1 Z = 2 Z = 4 Diagonal 4r = √2a = √2l Solve for edge: 4r /√2 = a = l a = l = 2r a = l = 2√2r**Cell edge, a or cell length, l**is related to the atomic radius but depends on which structure: Simple Cubic Body Centered Cubic Face Centered Cubic Z = 1 Z = 2 Z = 4 Diagonal 4r a = l = 2r 4r = √3a = √3l a = l = 4r /√3 a = 2.3 r a = l = 2√2r a = 2.8 r**Rh metal crystallizes in a cubic lattice where a = 380.34**pm. What is the crystal structure of Rh? Find Z: defines if simple, bcc or fcc Density = Z x at.wt. A x a3 This is a summary of the relationships What do we need? Z What do we have? Nothing here, but can’t we look up Density of Rh metal ? Web Elements: at. weight = 102.91 g/mol Density = 12450 kg m-3 Atomic radius = 173 pm**Packing a Square Lattice:**Makes a simple cubic cell**Can you pack spheres more densely?**The Rhomb is the Unit Cell Shape of Hexagonal Lattices**Closest Packing:**hexagonal layers build up 3D solid**Note how layers “sit” on top of each other:**The Cyan layer covers the “up” triangles of the Pink layer The Yellow layer covers the “down” triangles of the Pink layer**This packing sequence is ABCA BC,**Where B and C cover different “holes” in A A B C A B C**Packing direction**A B C A B C A C B A C B A ccp Cubic Closest Packing: A B C A B C … Packing direction**Packing direction**A C B A C B A ccp Cubic Closest Packing: A B C A B C … Packing direction**CCP viewed as packing layers**CCP viewed unit cell; LOOK! It’s face centered cubic!!! CCP = FCC!! ….mmmMMM C B A C B A**Packing direction**ABABA . . . . Packed towards you**Packing direction**A B A B A B A hcp Hexagonal Closest Packing: A B A B … ….mmmMMM Packing direction**From Metals to Ionic Solids**Will ionic solids pack exactly like metallic solids? Na bcc unit cell as metal NaCl unit cell?**From Metals to Ionic Solids**• Build up Ionic Solids conceptually like this: • assume Anions are larger than Cations, r- > r+ • pack the Anions into a cubic lattice: ccp, simple or bcc • add Cations to the interstitial spaces (“Mind the gap!”) r- + r+ 2 x r- 2 x r-**The Simplest Ionic Solid is CsCl, simple cubic**Start with simple cubic Unit cell of Cl- ions Then add one Cs+ in center Z = C. N. (Cs) =**Z =**C. N. (Na) =