Solid solution and non stoichiometry

This slide talks about the solid solution and non-stoichiometry in solid state chemistry.

1. Non-Stoichiometry & Solid Solution Debabrata Bagchi Ph. D. Student, NCU JNCASR, Bangalore

2. Schottky defects Cation and anion vacancies Anti- Schottky defects Cation and anion interstitials (not common) Frenkel defects Cation vacancies and interstitials Anti- or anion- Frenkel defects Anion vacancies and interstitials Anti-site defects Cation and anion swap (not common) Stoichiometric compounds: intrinsic point defect

3. Examples for oxides: Metal deficient oxides, e.g. M 1-x O Metal vacancies are majority point defects, compensated by electron holes Examples: Co 1-x O, Ni 1-x O, and Fe 1‑x O Metal excess oxides, e.g. M 1+x O Metal interstitials are majority point defects, compensated by defect electrons Example: Cd 1+x O Oxygen deficient oxides, e.g. MO 2-y Oxygen vacancies are majority point defects, compensated by defect electrons Examples: ZrO 2-y , CeO 2-y Oxygen excess oxides, e.g. MO 2+y Oxygen interstitials are majority point defects, compensated by electron holes Example: UO 2+y N on-stoichiometric compounds have formulae that do not have simple integer ratios of atoms they exhibit a range of composition and can be made by introducing impurities into a system, Non-stoichiometric compounds

4. Non-Stoichiometric Defects Anion vacancies Interstitial anion/ cation Cation vacancies F-centre NaCl in Na vapor

5. Defect Concentration

6. Effect of Non-Stoichiometry Electrical Kinetic (e.g. diffusion) Mechanical (e.g. Strength, toughness, hardness) Magnetic Optical

7. Effect of Non-Stoichiometry

8. Non stoichiometry in 1 st row TM Oxides

9. Non-Stoichiometry in Wustite ( FeO ) Ferrous oxide is known as wustite it has the NaCl (rock salt) crystal structure . C hemical analysis proved that it is non-stoichiometric and deficient in iron Below 570°C, wustite disproportionate to α-iron and Fe 3 O 4 . Fe deficiency can be happened in two ways : 1 . Fe vacancy (leads to Fe 1-x O), or 2. E xcess of oxygen in interstitial positions (giving FeO 1+x ).

10. Cation Vacancy or Interstitial Anion Experimental Observations a = 430.1 pm d =5.728 kg m -3 Fe/O = 0.945 V = (430.1 pm) 3 = 7.956 x 10 -29 m 3 4 formula units of FeO in a perfect unit cell (rock salt structure) 1 mole of FeO weighs (55.85 + 16.00) g = 0.07185 kg 4 mole weigh = 4 x 0.07185 kg 4 formula units weigh = 4 x 0.07185 kg / N A = 4.733 x 10 -25 kg

11. Cation Vacancy Experimental Observations a = 430.1 pm Fe/O = 0.945 V = (430.1 pm) 3 = 7.956 x 10 -29 m 3 If Fe 0.945 O 1 1 mole of Fe 0.945 O 1 weighs ((55.85x0.945) + 16.00) g = 0.06877 kg 4 mole is 3.78Fe + 4 O weigh = 4 x 0.06877 kg 4 formula units weigh = 4 x 0. 06877 kg / N A = 4.567 x 10 -25 kg d cv = 4.567x10 -25 /7.956x10 -29 kg m -3 = 5.742 x 10 3 kg m -3

12. Interstitial Anion Experimental Observations a = 430.1 pm Fe/O = 0.945 O/Fe = 1/0.945 = 1.058 V = (430.1 pm) 3 = 7.956 x 10 -29 m 3 If Fe 1 O 1.058 1 mole of Fe 1 O 1.058 weighs (55.85 + (16.00x1.058)) g = 0.07277 kg 4 mole is 4Fe + 4.232O weigh = 4 x 0.07277 kg 4 formula units weigh = 4 x 0.07277 kg / N A = 4.832x 10 -25 kg d ia = 4.832x10 -25 /7.956x10 -29 kg m -3 = 6.076 x 10 3 kg m -3

13. Cation Vacancy or Interstitial Anion Experimental density d =5.728 kg m -3 If Fe 0.945 O 1 d cv = 5.742 x 10 3 kg m -3 If Fe 1 O 1.058 d ia = 6.076 x 10 3 kg m -3 Thus, FeO has cation vacancy N on-stoichiometric compounds are found to exist over a range of composition. It is possible to determine whether the non-stoichiometry is accommodated by vacancy or interstitial defects using density measurements.

14. Electronic Defects in FeO

15. Koch-Cohen Cluster NaCl type structure with 4 interstitial Fe 3+ ions in tetrahedral voids, 13 immediately surrounding octahedral Fe 2+ sites must be vacant. This is referred to as sueperstructure or superlattice Fe 2+ Oh site vacant Fe 3 + Td interstitial

16. Uranium Dioxide

17. Vegard's law For most of the non-stoichiometric compounds, their unit cell size varies smoothly with composition but the symmetry is unchanged . This is known as Vegard’s Law . Experimental and theoretical densities (10 3 kg m -3 ) for FeO

18. This law simply states that when you combine elements to form an alloy, the lattice constant will follow a linear trend with the element concentrations, provided that there is no  phase change and lattice parameters do not differ by more than 5%. Vegard's law continued… Mathematical expression for Vegard’s law for a binary system A-B is: where X is the mole fraction of component B and a = lattice parameters of pure components

19. Application of Vegard's law L attice constant increases with increase in Cr   substitution for Al in CuAlO 2 .

20. Application of Non-stoichiometric compound Oxidation catalysis: R eactions of  hydrocarbon with   oxygen, a conversion that is  catalysed  by metal oxides.   Here transfer of "lattice" oxygen to the hydrocarbon substrate, a step that temporarily generates a vacancy (or defect ). Such catalysts rely on the ability of the metal oxide to form phases that are not stoichiometric Ion conduction:   The defect sites provide pathways for atoms and ions to migrate through the otherwise dense ensemble of atoms that form the crystals .   Oxygen sensors and solid state batteries are two applications that rely on oxide vacancies.  Superconductivity: Many superconductors are non-stoichiometric . Y x Ba 2 Cu 3 O 7− x . arguably the most notable  high temperature superconductor, is a non-stoichiometric solid with the formula Y x Ba 2 Cu 3 O 7− x . The critical temperature of the superconductor depends on the exact value of  x .

21. Solid Solution Solid Solution is a solid mixture containing one or more minor components (solute) uniformly distributed within the crystal lattice (matrix) of the major component (solvent). Such a mixture is considered a solution rather than a compound when the crystal structure of the solvent remains unchanged by addition of the solutes, and when the mixture remains in a single homogeneous phase.  Figure : This binary phase diagram shows two solid solutions . Solid solution formation usually causes increase of electrical resistance and mechanical strength and decrease of plasticity of the alloy. 

22. Types of Solid Solution Interstitial solid solution Substitutional solid solution Ordered solid solution Disordered solid solution

23. Solute atoms are much smaller than solvent atoms ( size of the solute is less than 40% that of solvent), so they occupy interstitial position in solvent lattice. Carbon ,nitrogen ,hydrogen , oxygen, lithium, sodium and boron are the element which commonly form interstitial solid solution. Steel : C atoms solute in Fe. Solvent Atoms Solute Atoms Interstitial Solid Solution

24. Substitutional Solid Solution Solute atoms sizes are roughly similar to solvent atoms. Due to similar size solute atoms occupy vacant site in solvent atoms. Cu and Zn, Cu and Ni, are the example of substitutional solid solution. Solvent Atoms Solute Atoms

25. Hume R othery studied a number of alloy systems and formulated condition that favour extensive substitutional solid solubility. C onditions of Hume Rothery’s rule The size difference between solute and solvent atoms must be less than 15 %. The solubility of a metal with higher valence in a solvent of lower valence is more compared to the reverse situation e.g. Zn is much more soluble in Cu than Cu in Zn. The crystal structures of metals must be same. The electronegativity difference between the metals must be small. Hume Rothery’s Rule

26. Ordered Substitutional Solid Solution If the atoms of the solute occupy certain preferred sites in the lattice of the solvent, an ordered solid solution is formed. It may occur only at certain fixed ratios of the solute and solvent atoms . In Cu – Au system, Cu atoms occupying the face-centred sites and Au atoms occupying the corner sites of the FCC unit cell . Solvent Atoms Solute Atoms

27. If the atoms of the solute are present randomly in the lattice of the solute, it is known as disordered solid solution . Most of the solid solutions are disordered solid solutions Disordered Substitutional Solid Solution Solute Atoms Solvent Atoms

28. X-ray powder diffraction, XRD : F ingerprint method : Determination of the crystalline phases that are present (the detection limit of phases in a mixture is usually of the order of 2–3 wt %) 2. M easure the XRD pattern of solid solutions accurately and obtain their unit cell dimensions , which may undergo a small contraction or expansion as composition varies. The calibration graph of unit cell dimensions against composition can be used to determine the composition of solid solutions in a particular sample. Usually, a unit cell expands if a small ion is replaced by a larger ion and vice versa, contracts if a smaller ion is substituted into the structure. From Bragg’s law and the d -spacing formulae, the whole pattern shifts to lower values of 2 q with increasing unit cell parameters.. According to Vegard’s law, unit cell parameters should change linearly with solid solution composition. 3 . Third , using Rietveld refinement of the powder XRD patterns of solid solutions, and in particular the intensities of the XRD reflections, it is possible to gain detailed crystallographic information such as the sites occupied by atoms and the location of vacancies and interstitials . Experimental methods for studying solid solutions

29. The mechanism of solid solution formation may be inferred by a combination of density and unit cell volume measurements for a range of compositions. The key parameter is the mass of the average unit cell contents and whether it increases or decreases on solid solution formation. Density data for cubic CaO -stabilised zirconia solid solutions for samples quenched from 1600 ◦C Density measurements

30. Many materials undergo abrupt changes in structure or property on heating and, if the material forms a solid solution, the temperature of the change usually varies with composition. The changes can often be studied by differential thermal analysis/differential scanning calorimetry (DTA/DSC) since most phase transitions have an appreciable enthalpy of transition. Effect of dopants on the ferroelectric Curie temperature of BaTiO 3 showing the effect of isovalent substitution of Sr , Ca and Pb for Ba, isovalent substitution of Zr for Ti and aliovalent substitution of Ca for Ti . Changes in other properties – thermal activity and DTA/DSC

31. Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. Why strengthening of metal is required ? As pure metal are inherently weak due to presence of dislocation. So , We can enhance the mechanical properties by eliminating dislocation. So , by introducing some mechanism that prohibits the mobility of dislocations , that are called Strengthening mechanism. Methods For Strengthening Of Metal Strain hardening Grain boundary strengthening Precipitation hardening Solid solution strengthening Solid solution strengthening

32. Factors affecting Solid Solution Strengthening Difference in size between solute and solvent atoms Amount of solute added Nature of distortion produced by solute atoms size difference increases the intensity of stress field around solute atom resistance to dislocation is increases strength of metal increases. A large concentration means more frequent obstacles to dislocation. The strength increases in proportion of C ½ Spherical distortion produced by Substitutional solute atoms Non spherical distortion produced by interstitial solute atoms .

33. Why is S teel s o s trong ? Smaller carbon atoms fill some of the small spaces available between the iron atoms and form Interstitial Solid Solution. Usually materials deform by the movement of dislocations. T he carbon interstitials make steel stronger by fully or partially blocking the movement of dislocations. Fe C Application of Solid Solution