Physical Properties

Lattice Structures of Transition Metals

What the Graph Shows

The figure plots melting point (in units of $10^3$ K) on the vertical axis against atomic number on the horizontal axis. Three separate curves are drawn, one for each transition series:

• 3d series: Sc Ti V Cr Mn Fe Co Ni Cu Zn
• 4d series: Y Zr Nb Mo Tc Ru Rh Pd Ag Cd
• 5d series: La Hf Ta W Re Os Ir Pt Au Hg

Each point on a curve is labelled with the element symbol. The curves are not continuous lines but connect the points for each series, showing how melting point changes as you move across the period.

What the Pattern Teaches

All three curves share a common shape: they rise to a maximum near the middle of the series (at Cr, Mo, and W respectively — the $d^5$ configuration region) and then fall towards the end. A notable dip occurs at Mn (3d series) and Tc (4d series); the 5d series shows a similar but less pronounced dip at Re.

The 5d series lies highest overall, the 4d series is intermediate, and the 3d series is lowest. This ordering reflects the increasing strength of metallic bonding as you go down a group: more diffuse $d$ orbitals in heavier elements allow greater overlap and stronger bonding.

The Physical Idea

Melting point in transition metals is determined by the strength of metallic bonding, which depends on the number of unpaired $d$ electrons available for bonding. In the middle of a series (around $d^5$), the maximum number of unpaired electrons gives the strongest bonding and highest melting point. At the ends (early $d^1$–$d^2$ or late $d^8$–$d^{10}$), fewer unpaired electrons weaken the bond, lowering the melting point. The dip at Mn/Tc arises because the half-filled $d^5$ subshell is stable and less willing to share electrons, temporarily reducing bond strength.

Key Formula Developed

The textbook uses this figure to introduce the concept of enthalpy of atomisation ($\Delta_a H^\ominus$), which is the energy required to convert one mole of a solid metal into isolated gaseous atoms. For transition metals, $\Delta_a H^\ominus$ is directly related to the melting point trend:

$\Delta_a H^\ominus \propto \text{(strength of metallic bonding)}$ …

The figure is a line graph plotting enthalpy of atomisation ($\Delta_a H^\circ$, in $\text{kJ mol}^{-1}$) on the vertical axis against atomic number (Z) on the horizontal axis. Three separate curves are drawn, one for each transition series:

• 3d series (Sc to Zn, atomic numbers 21–30)
• 4d series (Y to Cd, atomic numbers 39–48)
• 5d series (La to Hg, atomic numbers 57–80, excluding the lanthanides)

Each curve has nine data points (one per element) connected by a line. The y‑axis runs from 0 to 900 in steps of 100. All three curves show a common pattern: they rise from the left, reach a maximum near the middle of the series, and then fall toward the right end. The 5d series lies highest throughout, the 4d series is intermediate, and the 3d series is lowest.

What the figure teaches

The enthalpy of atomisation is the energy required to convert one mole of a solid metal into isolated gaseous atoms. For transition metals, this energy is directly related to the strength of metallic bonding in the solid. The key idea is:

More unpaired d‑electrons → stronger metallic bonding → higher enthalpy of atomisation.

In the middle of each series (e.g., Cr, Mo, W), the number of unpaired d‑electrons is largest, so the metallic bond is strongest and $\Delta_a H^\circ$ peaks. At the ends (e.g., Zn, Cd, Hg), the d‑subshell is fully filled (no unpaired electrons), metallic bonding is weak, and $\Delta_a H^\circ$ is low.

The higher values for 4d and 5d series compared to 3d arise because the 4d and 5d orbitals are more diffuse and extend further from the nucleus, allowing greater overlap between neighbouring atoms and thus stronger bonding.

Key formula developed from this figure

The textbook uses the figure to illustrate the relationship between enthalpy of atomisation and metallic bond strength, but no single formula is derived from the graph itself. Instead, the figure supports the general expression for the enthalpy change of atomisation:

$\Delta_a H^\circ = \sum (\text{bond dissociation energies}) - \text{lattice energy terms}$ …