The Periodic Table

In 1869, Dmitri Mendeleev (1834-1907) noticed that certain elements exhibited similar behaviour – most notably, the ratios with which they formed molecules with hydrogen and with oxygen. By arranging the elements in order of increasing mass and such that similar elements formed columns, he developed the first periodic table:

Mendeleev’s periodic table was incomplete – all of the _______ ______ were missing, but it was remarkably accurate in other respects. If there appeared to be a ‘missing’ element, he left a blank space, assuming that it would be discovered at a later date. He was proven correct with the discoveries of ________ (69.7 u) in 1875 and __________________ (72.6 u) in 1886.

In 1913, H.G.J. Moseley (1887-1915) noted that the periodic table would be more descriptive if the elements were listed in order of increasing ____________ rather than increasing mass. This led to the modern periodic table and law of periodicity:

The Periodic Table

The Periodic Table

Terminology used to describe regions of the periodic table:PeriodsGroupss-block (“alkali metals” and “alkaline earth metals”)p-block (group 13, group 14, “pnictogens”, “chalcogens”, “halogens” and “noble gases”)d-block (“transition metals”)f-block (“lanthanides” and “actinides”)Metals (conductors)Nonmetals (insulators)Metalloids (intrinsic semiconductors)

You are expected to memorize know the names, symbols and atomic numbers for the first 36 elements on the periodic table. (i.e. hydrogen to krypton)

The Periodic Table

•Most of the elements in the periodic table are metals. How can we recognize if an element is a metal?

•It’s opaque and its smooth surfaces reflect light (“metallic luster”). •It’s malleable (can be hammered into sheets without breaking).•It’s ductile (can be stretched into wires without breaking).•It has a high boiling point. (The melting points of metals vary widely – though most have high melting points too.)•It conducts heat and electricity.

Metals

•These properties arise because of the structure of metals. The simplest metals can be considered to behave as an organized arrangement of ‘cations’ surrounded by a ‘sea of electrons’:

Structure of Metals

Metals usually form crystal lattices in which the atoms are closely packed. These lattices are held together by electrostatic attractions between the cations and the electrons.

These crystal lattices are made up of repeating units called unit cells. All of the unit cells in a crystal lattice are identical and have the same symmetry as the overall lattice. There can be no “gaps” between unit cells and all cells must have the same orientation.

lattice

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Symmetry

Forms of symmetry that must be present in the unit cell if they are present in the overall lattice:

Find the smallest “unit cell” in each of the following pictures:

•The smallest unit cell in a lattice is called the primitive unit cell.•Note that these are two-dimensional pictures while metals are three-dimensional!

Lattices and Units Cells

There are seven three-dimensional crystal systems:

In CHEM 1000, we will focus only on the cubic and the hexagonal crystal systems as they describe the vast majority of metallic elements.

Lattices and Units Cells

•How do these structures arise? Consider what would happen if you poured marbles into the bottom of a box. How would they naturally arrange themselves? Why?

•If you were to add a second layer of marbles, where would they go?

Lattices and Closest Packing

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The marbles on the previous page adopted a “closest packing” arrangement that is observed in the structures of many metals. There are two kinds of “closest packing” lattices: cubic closest packed and hexagonal closest packed. The difference between these two lattices arises when the third row of atoms is added:

Lattices and Closest Packing

•Where’s the hexagon in hexagonal closest packing (hcp)? •Rotate the image from the previous page so that we can see the lattice in three-dimensions:

•Note that the layer sequence is red-blue-red-blue (more generally referred to as ABAB)

•Can you find a unit cell smaller than the hexagon shown on the right? Outline a primitive (i.e. smallest) unit cell on each picture.

Lattices and Closest Packing

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•Where’s the cube in cubic closest packing (ccp)? •Rotate the image from the previous page so that we can see the lattice in three-dimensions:

•Note that the layer sequence is red-blue-yellow-red-blue-yellow (more generally referred to as ABCABC)•A unit cell contains atoms from four of the layers from the picture on the left. On the unit cell at the left, label which layer each atom comes from (A, B or C).•Note that, in addition to the atom at each corner of the cube, there is also an atom in the center of each face of the cube. For this reason, cubic closest packing (ccp) is also called face centered cubic (fcc).

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Lattices and Closest Packing

•Face-centered cubic (fcc or ccp) is one of three types of cubic unit cells. The other two are body-centered cubic (bcc) and simple cubic:

•Note that these pictures include parts of the atoms that are not contained by the unit cell. The unit cell only contains the fraction of each atom that is *inside* the cube!

Cubic Lattices

•To see what fraction of each atom is actually inside the unit cell, we look at “sliced” views:

•Every atom completely inside a cell is only in 1 cell.•Every atom along a cell face is in 2 cells. (½ in each)•Every atom along an edge is in 4 cells. (¼ in each)•Every atom in the corner is in 8 cells. (1/8 in each)

•How many atoms are inside each of the three cubic cells?

Cubic Lattices

•Every atom in a lattice is touching the same number of other atoms. This is referred to as its co-ordination number.

•What is the co-ordination number of an atom in each kind of lattice we’ve seen? Be sure to consider all unit cells in which the atom resides.

Simple cubic (e.g. Po) Face-centered cubic (e.g. Cu)

Body-centered cubic (e.g. Na) Hexagonal closest packed (e.g. Mg)

Lattices and Co-ordination Number

Crystalline solids (including metals) can be analyzed by x-ray crystallography, in which an x-ray is passed through a crystal. The crystal acts as a diffraction grating (the x-rays can pass through gaps in the crystal structure but not through the atoms themselves), and analysis of the resulting diffraction pattern allows a chemist to determine the structure of the crystal (elements as well as arrangement of atoms).

How Can We Determine a Lattice’s Structure?

As you might expect from looking at the unit cells, lattice type is often related to density. As a general rule, _____________ lattices are the least dense, ________ have middling densities and _________ and _________ lattices are the most dense.

One way to experimentally determine a metallic radius is via x-ray crystallography. Another is to measure the density of a metal for which you know the lattice type. How would you go about measuring the density of a sample of metal (assuming that it is safe to handle and relatively unreactive)?

Lattices, Density, and Metallic Radii

Lattices, Density, and Metallic Radii

•Aluminum has a density of 2.699 g/cm3, and the atoms are packed into a face-centered cubic unit cell. Calculate the metallic radius of an aluminum atom.

Lattices, Density, and Metallic Radii

•Lithium has a metallic radius of 152 pm and the atoms are packed into a body-centered cubic unit cell. Calculate the density of lithium.