ZrC First Principle Calculations

Band Structure and Electronic DOS

• Comparison between Zr metal, diamond, and ZrC

Cohesive Energies

• Comparisons (scanned image, re-fitted: Matlab, eps) (converted by Graph Reader)

  Structure	y: energy/unit cell [eV]; x: density [g/cm^3]	y_min [eV]	x_min [g/cm^3]	volume/cell [A^3]	lattice constant [A]	Bulk Modulus [GPa]
  NaCl	y = 0.419379x^2 - 5.498075x - 1534.978880	-1552.998852	6.555012	26.151802	4.711804	220.7969
  ZnS	y = 0.512786x^2 - 5.369512x - 1537.816979	-1551.873355	5.235625	32.742102	5.078345	137.5648
  CsCl	y = 0.334708x^2 - 4.585749x - 1534.799776	-1550.506803	6.850364	25.024271	2.924964	201.1283

• WebElements Zr-C bond enthalpy:   561   ±   25 kJ/mol = 5.81435667127209 eV per bond (1 eV = 96.485308989 kJ/mol).

• WebElements Zr enthalpy of atomization: 605 kJ/mol = 6.27038464548951 eV;
  WebElements C enthalpy of atomization: 717 kJ/mol = 7.43118312531567 eV;
  Thus, assuming insignificant heat of formation, the ground state ZrC should have 1322 kJ/mol atomization energy per pair of Zr/C atoms, or 13.70156777080518 eV/pair.

Elastic Constants

[GPa]	Calculated Value	Chang & Graham	Brown & Kempter
Bulk Modulus	259.	223.12	168.2
C11	538.	471.95	423.0
C12	120.	98.71	40.8
(C11-C12)/2	209.	186.62	191.1
C44	190.	159.30	146.4

Schottky Defect Energy

Configuration	Energy [eV]
Perfect Lattice (8 ions)	-6212.1834293
Perfect Lattice (unit cell)	-1553.04586
Zr Vacancy (unrelaxed)	-4814.9679547
Zr Vacancy (relaxed)	-4814.9679888
Zr Extraction Energy	1397.21544
C Vacancy (unrelaxed)	-6047.4106738
C Vacancy (relaxed)	-6047.4106977
C Extraction Energy	164.77276
Schottky Energy	8.94234