Density of d-block elements

Question

Something that confuses me slightly is the trends in density when comparing periods 4, 5, and 6 in the d-block. Looking at periods 5 and 6, the density peaks at group 8, with ruthenium and osmium, respectively. The density slightly drops at group 9 and falls further through group 10-12 and the p-block.

But in period 4, just from assumption you would expect iron, the first group 8 member to be the densest of period 4, but it's not at all. Sure, iron is the densest yet, but the trend increases up to copper and only starts dropping at group 12 and beyond. Why is there this discrepancy?

Furthermore, why does density seem to peak at group 8 anyway? What is it about the d-shells that create this general pattern?

Answer 1

Density varies depending mainly upon i)atomic mass, ii) atomic radius and iii) packing type. i) Atomic masses increase across the period and this tend to increase densities across the period ii) Across the first transition series (3d series)-as in any other d-series- electrons are entering the same set of orbitals and so atomic sizes tend to decrease due to enhanced nuclear electron attractions. Beyond manganese electrons start pairing up in d- orbitals which has a counter effect of electron-electron repulsion that tend to expand the electron cloud as a whole. So we atomic sizes decrease up to the middle and then remain nearly same or register small increases as we see: Sc(162pm), Ti(147pm), V(134pm), Cr(128pm), Mn(127pm), Fe(126pm), Co(125pm), Ni(124pm), Cu(128pm), Zn(134pm)

iii) Packings: Sc(HCP), Ti(HCP), V(BCC), Cr(BCC), Mn(BCC),Fe(BCC),Co(HCP),Ni(FCC),Cu(FCC)),Zn(HCP); here BCC has 68% packing efficiency where as HCP as well as FCC(CCP) packings have 74%. So based on packing efficiencies an drop of densities are expected for V,Cr, Mn and Fe

Corresponding Densities:Sc(2.98), Ti(4.5), V(6.0), Cr(7.2), Mn(7.2), Fe(7.87),Co(8.9), Ni(8.9), Cu(8.96), Zn(7.14) P.S. For the first transition series there are no inner d-electrons or f-electrons to influence the atomic sizes and so densities.

Just qualitative evaluation alone cannot help to predict an order of densities because the factors are not all acting in the same directions.Probably Mother Nature has no intention that things always must be in regular order so that man can study them easily ;)

Answer 2

Electron are added when you go to the right of a $d$ line, they have the same principal quantic number and so they are not making the atom bigger, but at the same time there is more protons and neutron resulting in more attractive force : the density increase because the volume is slightly the same but the masses of nucleus increase.

This phenomena start to be inverted at some point of the line because the "shell" (repulsive force due to other electron) of previous electron start to be important enough, the new added electron is not able to penetrate this cloud of electron and make the volume of the atom bigger, resulting in a tendency of decreasing density.

This phenomena of "shell" is explain by Slater and even have rule.

https://en.wikipedia.org/wiki/Slater%27s_rules?wprov=sfla1

EDIT : The explanation for the peak of density of the last group is explained by the lanthanide contraction. The $f$ orbitals have really low shield power and will cause a contraction of all the new added electron : it will be easier for them to penetrate the cloud of electron. This result in higher density

https://en.wikipedia.org/wiki/Lanthanide_contraction?wprov=sfla1