cd212 aug 2013 inorganic chemistry e. d. jemmis

E. D. Jemmis IISc Bangalore

CD212 Aug 2013 Inorganic Chemistry E. D. Jemmis, Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560012 BORON SLIDES – set 2

B12H12-2

N+1 electron pairs - Wade

B20H16

B30H24



Beta-Rhombohedral Boron, Thermodynamically most stable allotrope B105 idealized unit cell

B12H12(-2)


Beta-Rhombohedral Boron, Thermodynamically most stable allotrope

B84 B12@B72 B12@B12@B60

TWO OF THE B84 UNITS COMING TOGETHER MAKES ANOTHER ICOSAHEDRON. BUT ONLY 6 B84 UNITS CAN BE BROUGHT AROUND ONE B84 UNIT. WHAT HAPPENS TO THE REMAINING 6 PENTAGONAL PYRAMIDS? ADDITIONAL 21 ATOMS AROUND


B84 + B10 TWO ADDITIONAL B84 UNITS CAN BENEFIT FROM THE REMAING TWO PENTAGONAL FACES


B57 = B28-B-B28 B48 = B12 + B36

β-Boron Unit Cell: B105 = B84 +B10-B-B10 Or More logically B48+B57


Idealised Unit Cell B105 and Electron Count

B105 = B84 + B10-B-B10 OR

B48 + B28-B-B28 OR

4(B12) + B57 (-8) + ?

B57H36



The mno Rule for Polycondensed Boranes, Metallaboranes, and Metallocenes

§  m+n+o skeletal electron pairs §  m number of polyhedra §  n number of vertices §  o number of single atom bridging

E. D. Jemmis, et al. J. Am. Chem. Soc., 122, 4516-4517 (2000); 123, 4313-4323 (2001); 123, 4324-4330 (2001), Chem. Rev., 102(1) 93-144 (2002). Acc. Chem. Res. 36, 816-824, (2003). Phys. Rev. B. 72, 195102 (2005). Angewandte Chemie, 47, 5561-5564 (2008).


m + n + o =2 + 20 +0 = 22ep 16BH + 4B 16 + 6 = 22ep, Neutral

Synthesised 40 years ago by Lipscomb and Muettertties. Neutral Molecule.

B12H122- m=1, n=12, o=0 à Wades n+1 Rules

B20H16


m+n+o = 2+21+0 = 23 ep 18BH + 3B = 18+4.5 = 22.5 ep -1 charge

E.Bernhardt, D. J. Brauer, M. Finze, H. Willner, Angew.Chem., 2007, 119, 2985.

B21H18-

m = # polyhedra n = # vertices o = # single atom bridges

B30H24 m+n+o = 3+30+0 = 33 ep 24BH + 6B à 24 + 9 =33 ep.

neutral


MNO RULE REDUCES TO HUCKEL RULE IN 2-DIMENSIONS

B57H36 = B28H18-B-B28H18 m+n+o = 8+57+1 = 66 (BH)36B21 = 36+ 31.5 = 67.5 1.5 e pair, 3 electrons extra: must be +3 B57H36

+3 is aromatic.


Idealised Unit Cell B105 and Electron Count

B105 ≡ B84 + B10-B-B10 OR

B48 + B28-B-B28 OR

4(B12) + B57

B57H36


Careful analysis shows That B57 part is better Refined with only 56 atoms


Partially vacant and interstitially occupied sites of different crystal structures of beta-rhombohedral boron

B57 actually has only 56 atoms. 3 VE less. The +3 charge is Removed. B48 is better refined with 50.66 atoms 2.66x3 = 8 VE more Unit cell is 105 - 1 + 2.66 = 106.66 atoms. Thus the extra 5 electrons are available from extra occupancies

B106.66 , not B105

4 B12 + B2.66 B56, not B57

B50.66 8e from 2.66 B (2.66 x 3)

B28-B-B27 Neutral


Extra atoms within the B84 region,

at four different 6-fold Positions adding up to 38.8, 44.0 and 47.8% in the three samples

Adding 2.66 boron. 2.66x3 = 8 electrons


B106.66 ≡ B56 + B48 + B 2.66

105  ⇒ 104 Needs 8e 2.66B

Unit Cell 104 + 2.6 = 106.6

What do we do with this?

We could provide the extra 8 electrons and retain the β-rhombohedral structure


B48B2.66B56 B48Li8B56 B104Li8 LiB13 *

B104Fe2.66 B104Fe4 Mössbauer B102.66C3 B98.66C6 B96C8 Nature finds the right structure for any combination Vast amount of experimental data available And yet infinite combinations to be explored *M. Kobayashi, I. Higashi, H. Matsuda, K. Kimura, J. Alloys Compd., 221, 120(1995).



Hardness of Boron close to diamond yet lighter than Aluminium. How to make it even harder? Applications of Boron plentiful; a lot more anticipated if it can be made even harder.

83.33%

TCS10-December 2010. Jemmis IISER Thiruvananthapuram

Percentage of partially substituted and interstitially occupied sites of different crystal structures of beta-rhombohedral boron

Table 1. Percentage of partially substituted and interstitially occupied sites of different crystal structures of -rhombohedral boron:

Site No [symmetry multiplicity] % of occupancy N o Crystal

structure 13[6] 16[6] 17[6] 18[6] 19[6] 20[12] # of B / unit cell

1 Hoard 1970 100.0 0.000 0.000 0.000 0.000 0.000 105.00 2 Geist 1970 66.67 33.33 0.000 0.000 0.000 0.000 105.00 3 Callmer 1977 73.40 24.80 0.000 0.000 0.000 0.000 104.89 4 Slack(i) 1988 73.00 28.40 9.700 7.400 7.000 2.50 106.83 5 Slack(ii) 1988 74.50 27.20 8.500 6.600 6.800 3.70 106.86 6 Slack(iii) 1988 77.70 25.80 3.200* 5.800 7.200 0.000 106.37

83.33 0.00



Hardness of Boron close to diamond yet lighter than Aluminium. How to make it even harder? Applications of Boron plentiful; a lot more anticipated if it can be made even harder.

D.L.V.K. Prasad, M.M. Balakrishnarajan, E D Jemmis, Phys Rev B, 72, 195102 (2005).

83.33%


Percentage of partially substituted and interstitially occupied sites of different crystal structures of beta-rhombohedral boron

Table 1. Percentage of partially substituted and interstitially occupied sites of different crystal structures of -rhombohedral boron:

Site No [symmetry multiplicity] % of occupancy N o Crystal

structure 13[6] 16[6] 17[6] 18[6] 19[6] 20[12] # of B / unit cell

1 Hoard 1970 100.0 0.000 0.000 0.000 0.000 0.000 105.00 2 Geist 1970 66.67 33.33 0.000 0.000 0.000 0.000 105.00 3 Callmer 1977 73.40 24.80 0.000 0.000 0.000 0.000 104.89 4 Slack(i) 1988 73.00 28.40 9.700 7.400 7.000 2.50 106.83 5 Slack(ii) 1988 74.50 27.20 8.500 6.600 6.800 3.70 106.86 6 Slack(iii) 1988 77.70 25.80 3.200* 5.800 7.200 0.000 106.37

83.33 0.00


*Here percentage of occupancy has [12] fold symmetry.

Site No [symmetry multiplicity] % of occupancy

# of e- Vol (Ao)

No Crystal structure

13[6] 16[6] A[2] E[2] D[6]

1 Li8 B103.44a 64.00 10.00 0.000 100.0 100.0 318.32 834.765 2 Cu3.72 B103.92b 61.10 20.90 6.100 50.50 22.1,10* 319.12 829.963 3 Cu4.14 B103.92c 69.00 13.00 8.000 61.00 22.0,12* 320.04 833.415 4 Fe2.12 B103.36d 72.60 0.000 50.70 0.000 18.50 316.44 826.105 5 Hf2.07 B103.42e 65.50 8.100 0.500 9.800 31.10 314.40 835.689 6 Zr2.04 B103.04f 52.80 14.50 0.000 18.10 27.90 313.20 832.377 7 Cr2.52 B103.30g 71.17 0.000 71.90 0.000 18.00 314.94 831.321 8 Li8Be3 B102h 100.0 0.000 100.0 100.0 0.000 320.00 815.339 9 Li10CB102

h 100.0 0.000 100.0 100.0 0.000 320.00 807.985

E. D. Jemmis, D. L. V. K. Prasad, J. Solid State Chemistry, 179, 2768, (2006). Applied Physics Letters, 96,23108 (2010).

An electron counting rule for qualitative understanding.

cd212 aug 2013 inorganic chemistry e. d. jemmis

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