CHEM&152

WINTER 2009

SOLID-STATE STRUCTURES AND P ROPERTIES Fill-in

Name _______________________ Stamp here

Prelab Attached (p 10)

Partner(s)____________________

Lecturer

Date

Please bring your textbook to laboratory for this experiment. textbooks in the lab with useful figures – use them!

There are also additional

Students should be sure to pair up as it will save time. This is a relatively long lab, but it can be done in parts! Adapted from Ellis et al., Teaching General Chemistry: A Materials Science Companion, ACS, 1993. This experiment was originally written by George C. Lisensky, Department of Chemistry, Beloit College; Ludwig A. Mayer, Department of Chemistry, San Jose State University. Review covalent, ionic and metallic bonding types and their relative bonding strengths and bond properties. Also review intermolecular forces including Van der Waal’s forces and polar attractions. Purpose

To construct portions of extended three-dimensional solids; on the basis of the structure, to determine a variety of information: the coordination number and geometry for each atom, the empirical formula of the material and the relationship of structure to physical properties.

Introduction Crystalline materials in the solid state, including metals, semiconductors, and ionic compounds, have a patterned arrangement of atoms that in principle can extend infinitely in all three dimensions. This patterned arrangement of objects forms an extended structure that can be described by layers of stacked spheres. More than two-thirds of the naturally occurring elements are metals. Most of the metallic elements have three-dimensional structures that can be described in terms of close-packing of spherical atoms. Many of the other metallic elements can be described in terms of a different type of extended structure that is not as efficient at space-filling, called body centered cubic. The packing arrangements exhibited by metals will be explored in this activity. In any scheme involving the packing of spheres there will be unoccupied spaces between the spheres. This void space gives rise to the so-called interstitial sites. A very useful way to describe the extended structure of many substances, particularly ionic compounds, is to assume that ions, which may be of different sizes, are spherical. The overall structure then is based on some type of sphere-packing scheme exhibited by the larger ion, with the smaller ion occupying the unused space (interstitial sites). Salts exhibiting these packing arrangements will be explored in this lab activity. The coordination number and geometry for sphere packing schemes are shown in Figure 1. Another useful and efficient way to describe the basic pattern of an extended structure is to conceive a three-dimensional, six-sided figure having parallel faces that encloses only a portion of the interior of an extended structure. A cube is one example, but the more general case does not have 90° angles and is called a parallelepiped. If the parallelepiped is chosen so that when replicated and moved along its edges, by a distance equal to the length of that edge, it generates the entire structure of the crystal, it is a unit cell. The unit cell is a pattern for the atoms as well as for the void spaces among Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 1 of 10

the atoms. The contents of the unit cell give the chemical formula or stoichiometry for the solid. Figure 2 corresponds to one large ion for each small ion with a formula of (large ions)4(small ions)4 or a 1:1 ratio in the formula.

CN 12 CN 6

CN 8

CN 4

Figure 1. Close-packing of spheres gives a coordination number (CN) of 12 and leaves interstitial sites capable of coordination numbers 6 or 4. Square-packing of spheres leaves an interstitial site capable of coordination number 8. Large Ions

Small Ions

1 8 corners x 8

1 12 edges x 4

1 6 faces x 2

1 center x 1 ________ 4 small ions

___________ 4 large ions

Figure 2. Counting ions in a unit cell. Some useful information: A. Selected radii of atoms and ions in this exercise. atom

radii

ion

radii

Na Ca Zn Mo Ga F Cl S

1.6 Å 1.74 1.25 1.30 1.26 0.64 0.99 1.04

Na+ Ca+2

0.98 Å 0.94

FClS-2

1.33 1.81 1.90

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 2 of 10

The model kit comes with an instruction book for the structures. When using it, be sure to match the correct template A through Z with the correct plastic base: they are either color-coded or have half or whole dots in corners. B. Calculating atomic/ionic radii. The atomic or ionic radii of the particles within a unit cell can be derived from the edge length of the unit cell, and how the atoms are arranged within the unit cell (sc, bcc, fcc). If the edge length, a, is known, we can use the Pythagorean theorem (a2 + b2 = c2) to find a face diagonal, f, and the internal diagonal, i.

a i

f

f = a 2 (for an fcc structure)

a

i = a 3 (for a bcc structure)

a (edge length)

C. Calculating the packing efficiency of a unit cell. Packing efficiency is the ratio of the volume of space occupied by atoms divided by the total volume of the designated unit cell, times 100. It is related to the density of the solid. Using vernier calipers measure (to the appropriate accuracy) the radius of the atom (diameter divided by 2) and the dimensions of the unit cell. Remember that you measure to the center of the atom on corners because the atom is shared by other unit cells. The volume of a cubic unit cell is simply the distance on a side cubed (Vuc = a3). If we assume a sphere, the volume of an atom is Va = 4/3 π r3. % Eff =

(Volume of one atom ) x (# of atoms in the unit cell) x 100 Volume of the unit cell

D. Structures and Geometry Simple Cubic structures (sc) have a packing efficiency of 52% and a coordination number of 6 with a geometry that is octahedral about each atom or ion. This is not a close-packed structure. Body-centered Cubic structures (bcc) have a packing efficiency of 68% and a coordination number of 8 with a geometry that is cubic about each atom or ion. This is not a close-packed structure. Close-packed structures have a packing efficiency of 74% and a coordination number of 12 with a geometry that is either hexagonal (hcp) or cubic close-packed (ccp) about each atom. If the stucture is ionic the packing efficiency may not be appropriate. Hexagonal has ABA layering and ccp has ABCA layering. Cubic cp is also called a face-centered cubic structure (fcc).

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 3 of 10

Pr ocedur e This experiment will consist of a number of exercises and demonstrations. The crystal structures will be built in teams using the model kits available. Both teams will then compare and contrast their structures and as a group answer the questions. Look in the Table of Contents for the page # with directions. Use the face-centered cubic or cubic close-packed option if there is more than one choice for the structure. Each group should do their own calculations and observations for each cell built. Make sure you are using the correct template and the correct base when building models! 1.

Simple Cubic and Body-centered Cubic Systems (main headings) Team A Simple Cubic Team B Body-Centered Cubic

Q. Analyze the structure and visually identify the unit cell. How many total atoms are counted as being inside the unit cell? Sketch each structure

A

B

Q. What is the coordination number for each atom? A

B

Q. Using the Vernier calipers, measure the diameter of one of the spheres and calculate the volume of one atom. See page 3 for hints and show your work. Diameter

Volume Instructor’s initials:

Q. Using Vernier calipers, measure the diameter of one of the spheres and the dimension of the unit cell. Remember the dimension is center to center of the corner atoms. Calculate the packing efficiency for each cell. See page 3 for tips and show your work. A

B Instructor’s initials: _________________

Find the % difference between your calculated value and the actual efficiency listed on page 3 for each structure. Show your work.

A Exp #3 Solid State Structures

B Rev W09AA Winter 2009

Page 4 of 10

2.

Close-packing systems Team A Hexagonal close-packing Team B Cubic close-packing

Q. Examine the pre-made structures, and visually identify the unit cell. In the space below sketch a diagram of the structures. The sketch may be done in various ways, but must show the difference in the structures. A good way to note the differences is to sketch the different layers! hcp

ccp

List the packing efficiency for hcp and ccp (as stated in the lab packet). hcp ________

ccp ___________

Q. Which has the greatest packing efficiency ccp, bcc, or simple cubic? ___________ Q. Copper is a cubic-close packed structure. Bend a piece of copper wire. Does it break? Why or why not? Look at the model of the structure of the Cu (ccp) to help you determine why.

Q. Lift one of the bottom corner spheres of the cubic close-packed model. What happens? Does it matter which corner sphere is lifted?

Follow-up questions: Q: Would the densities of the same element in a cubic close-packed, simple cubic and body-centered cubic structures be the same or different (relates to packing efficiency)? Give a brief explanation.

Q: List ccp, sc and bcc structures in order of increasing density.

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 5 of 10

3.

Diamond and Graphite

These structures are models available in the lab, observe them and answer the questions. Both substances are composed entirely of carbon atoms. Q. Use a graphite pencil and a diamond tipped scribe to write on a glass slide. What observations can you make?

Q. Note the bond lengths within the structures. Using the models and your knowledge of bonding explain why: a) diamond is very hard

b) graphite is used as a lubricant.

Follow-up question: Which of these two forms of carbon would be more dense? Why?

4. Ionic Crystal Structures Atoms that lose an electron forms as ion with a positive charge which has a smaller radius than the neutral species. Correspondingly, an atom that gains electrons creates a negative ion and increases in size compared to the neutral atom. Build the following structures. A.

Team A Rock Salt (NaCl use the fcc directions to build it) Team B Rock Salt (NaCl Body diagonal) Instructor’s initials: (obtained after building both structures)

Q. Sketch the two structures. Do these two structures look the same? Remember you can rotate them or look at them from different angles.

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 6 of 10

Q. What is the structure of just the large spheres (ie, sc, bcc, fcc)? Of just the small spheres? Report your answers in the table. Substance Structure of Large Spheres Structure of Small Spheres NaCl, rock salt Body-diagonal NaCl, rock salt Note: See pg. 2 for a table of ionic and atomic radii. Q. Which species generally are larger:

cations

or

anions

Q. Therefore, which color sphere represents the Na+ ion? _________ The Cl- ion? ____________ How many of the Na+ spheres are counted as being inside the unit cell? __________ How many of the Cl- spheres are counted as being inside the unit cell? __________ What is the ratio of Na+ to Cl- ions in the unit cell? ____________ What then is the formula for the compound? ____________ Q. Take a piece of rock salt and align a metal spatula on edge parallel to a face. Tap the spatula sharply with something heavier than a pencil and lighter than a hammer. How does the crystal break?

The planes of cleavage are the planes that have the weakest intermolecular forces between them. Which plane in the model corresponds to the cleavage plane? Draw a sketch of the structure indicating a plane of cleavage. You may want to lift a corner of the model to help answer the question.

B.

Team A Fluorite (CaF2) Team B Zinc Blende (ZnS, use fcc directions)

Instructor’s initials:

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 7 of 10

Q. Which color sphere represents Ca+2 (Zn+2) and which represents F- (S-2)? A Ca+2

F-

B Zn+2

S-2

Q. What is the structure of just the large spheres? Of just the small spheres? Substance

Structure of Large Spheres

Structure of Small Spheres

Fluorite Zinc Blende Q. Count the number of each ion in the unit cell and give the cation-to-anion ratio. Does the stoichiometry, or ion ratio in each structure agree with the formulas of the compound?

Fluorite

C.

zinc blende

Molybdenum Sulfide and Gallium Selenide

Note: Observe the pre-made structures and analyze them to answer the questions. Q. Which color sphere should be assigned to each ion? A Mo+x

S-2

B Ga+x

Se-2

Press a piece of cellophane tape onto a sample of molybdenum sulfide already stuck onto a piece of tape. Peel apart the two pieces of tape Q. What happens to the molybdenum sulfide? Looking at the structure, why do you think this happens?

Q. Make a prediction about the properties (cleavage, density, etc…) of gallium selenide. Explain your reasoning.

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 8 of 10

Homework (you may have to use right angle trig. properties!) 1. Calculate the radius of a Cu atom in a face centered cubic structure if the unit cell dimension is 0.3615 nm.

2. Calculate Avogadro's number for the above Cu structure. The density of Cu is 8.92 g/cm3.

3. Assuming iron has a body-centered cubic structure with an atomic radius of 0.124 nm, calculate the unit cell dimension of the structure

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 9 of 10

Prelab Exercises

Solid State Structures and Properties Stamp here

1. A cube has

corners,

edges, and

faces.

Using the figures below – answer questions 2 and 3

2. How many atoms are there in one unit cell of: a. a body-centered cubic arrangement of spheres of the same size? _______ b. a face-centered cubic arrangement of spheres of the same size? _______ c. a simple cubic arrangement? _______ 3. Label unit cells by placing the letter next to the diagram. 4. Ionic structures are usually defined by the larger ions with the smaller ions occupying interstitial sites or holes. How many larger ions surround a smaller ion if it occupies: Hint, drawing the “base” shape like the tetrahedral shape and putting an ion in the center of the shape may help you visualize how many ions surround the species in the “hole”. a. a tetrahedral hole ______

c. the center of a simple cubic arrangement _____

b. an octahedral hole ______

5. Face-centered cubic arrays are the same as what close-packed structure? _____________ 6. Describe in your own words what the term packing efficiency means.

Exp #3 Solid State Structures

Rev W09AA Winter 2009

Page 10 of 10