Experimental Techniques. Andy Watson. The University of Leeds
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1 Experimental Techniques Andy Watson The University of Leeds
2 Outline Phase Diagram Phase Diagram - Dynamic Liquidus & Solidus Thermal Analysis DTA DSC Phase Equilibria - static XRD EPMA» Diffusion couple studies Thermodynamic Properties Enthalpies of formation, enthalpies of mixing, Cp Calorimetry Activities / partial Gibbs energies Effusion Knudsen cell Torsion EMF studies Friday 20 January 2017 Hume-Rothery Seminar Derby 2
3 Determination of Phase Diagrams Friday 20 January 2017 Hume-Rothery Seminar Derby 3
4 Thermal Analysis 2500 Ni-V 2000 LIQUID Temperature / K 1500 FCC_A1 BCC_A2 SIGMA 1000 FCC_A1 + NI3V Ni2V + SIGMA BCC_A2 + NiV Ni x V V Friday 20 January 2017 Hume-Rothery Seminar Derby 4
5 DTA Signal Friday 20 January 2017 Hume-Rothery Seminar Derby 5
6
7 Non-dynamic methods (X-ray analysis) Incident X-rays Crystal planes nλ = 2dsinθ Powder photo Quartz Diffractometer trace Friday 20 January 2017 Hume-Rothery Seminar Derby 7
8 Friday 20 January 2017 Hume-Rothery Seminar Derby 8
9 Scanning Electron Microscopy Friday 20 January 2017 Hume-Rothery Seminar Derby 9
10 a) 10 kev b) 20 kev c) 30 kev Activation volume Friday 20 January 2017 Hume-Rothery Seminar Derby 10
11 Determination of thermodynamic properties Friday 20 January 2017 Hume-Rothery Seminar Derby 11
12 Background Calculating phase equilibria Using thermodynamics Friday 20 January 2017 Hume-Rothery Seminar Derby 12
13 Background Calculating phase equilibria Using thermodynamics Need to have a correct description of thermodynamic properties Temperature dependence of Gibbs energy» Calculations related to Heat changes» Solidification modelling»thermophysical properties modelling of surface tension Not enough to have the phase diagram Friday 20 January 2017 Hume-Rothery Seminar Derby 13
14 What do we want to measure? Enthalpies of formation (reaction) f H, r H Heat capacities Cp Enthalpies of mixing (solution phases) Hmix Enthalpies of transformation Htr Component activities in solutions a(m) Vapour pressures Partial pressures, total pressure.. Friday 20 January 2017 Hume-Rothery Seminar Derby 14
15 Isoperibol Calorimeter Ts = constant Surroundings Held at constant temperature Outer Jacket (T = const.) Thermometer D CD = corrected temperature rise T Baffle Temperature A B C T 0 Calorimeter Time Q T = W T Friday 20 January 2017 Hume-Rothery Seminar Derby 15
16 Isothermal Calorimetry Ts = Tc = constant No temperature rise, temperature not measured Heat evolved melts solid Measure amount of liquid produced Calculate heat evolved from Heat of fusion Liquid collection Ice calorimeter (Bunsen) Insulating Gap Solid (ice) Reaction zone Friday 20 January 2017 Hume-Rothery Seminar Derby 16
17 Adiabatic Calorimetry Ts = Tc constant Thermometer No heat losses to the surrounding Measure the heat input to raise sample over a prescribed temperature range. Reaction zone Insulating gap Jacket good thermal conductor Friday 20 January 2017 Hume-Rothery Seminar Derby 17
18 Adiabatic Calorimetry (Direct reaction) Thermocouple Calorimeter Adiabatic furnace Sample heater Sample Differential thermocouple Determination of enthalpies of formation. Sample heated from safe temperature to final temperature Safe = max. temperature where no alloying takes place Final = min. temperature where complete alloying takes place within 30 mins m 1 + m 2 m 1 m 2 H 1 Water-cooled vacuum chamber T s T f m 1 + m 2 m 1 + m 2 H 2 T s T f f H (T f ) = H 1 - H 2 Friday 20 January 2017 Hume-Rothery Seminar Derby 18
19 Enthalpies of Formation of Cr-Ni alloys at 1265 C Friday 20 January 2017 Hume-Rothery Seminar Derby 19
20 Heat-flow calorimeters Tian-Calvet Reaction vessel connected to surroundings by a series of thermocouple junctions Thermopile Heat flow between reaction vessel and surroundings realised as an emf Seebeck effect A : Reaction vessel C : External jacket Proportion of the heat flux conducted by a single thermocouple wire: λφ 1 = C(θ A - θ C ) Total emf in relation to heat flux: ε = de/dθ For n thermocouples E = nε (θ A - θ C ) ε = thermoelectric power E = emf θ = temperature E = ελ Φ C Friday 20 January 2017 Hume-Rothery Seminar Derby 20
21 Twin microcalorimeter A: Main Heater B: Top Heater C: Heat Shield D: Aluminium/nickel jacket E: Calorimeter F: Protection Tube G: Radiation Shields H: Dropping Tube Kleppa (500/800 C) Friday 20 January 2017 Hume-Rothery Seminar Derby 21
22 SETARAM HT1500 Water-cooled vertical furnace Thermopile Calorimeter Friday 20 January 2017 Hume-Rothery Seminar Derby 22
23 Drop Calorimetry Sample T 1 Sample is dropped into the calorimeter From T 1, Typically room temperature To T 2 The calorimeter temperature Reaction zone Electrical output from thermopile H(T 2 ) H(T 1 ) H(T 2 ) H(T 1 ) + r H T 2 Friday 20 January 2017 Hume-Rothery Seminar Derby 23
24 Direct Reaction Calorimeter Samples are synthesized directly in the calorimeter starting from a mixture of the finely powdered components. High T drop calorimeter Mass 1g Ta crucible Arc-welding under argon G.Cacciamani, G.Borzone, R.Ferro, JALCOM 220 (1995) 106 Friday 20 January 2017 Hume-Rothery Seminar Derby 24
25 Enthalpy of Formation by Direct Reaction Drop Calorimetry First drop (reaction drop) Q1 = H(cru,Tc-Tr) Second drop (reference drop) Q2 = + x H(A,Tc-Tr) H (cru, Tc-Tr) + H(AxByCz, Tc-Tr) + y H(B,Tc-Tr) + z H(C,Tc-Tr) + ΔfH(AxByCz,Tc) fh ( AxByCz, Tr) = Q1 - Q2 4Au + 3In + 3Sn = Au4In3Sn3 300K Q1 653K Au4In3Sn3 = Au4In3Sn3 300K Q2 653K Au 4In3Sn3 : Δf H 0 = 21.0 ± 1.0 kj/mol.at. Friday 20 January 2017 Hume-Rothery Seminar Derby 25
26 Enthalpy of Formation by Metal Dissolution Drop Calorimetry Sample Samples are dissolved in an appropriate solvent moles solvent» moles solute T 1 Samples of the component elements Samples of the compound of interest Au (T 1 ) + Sn (T 2 ) = [Au] Sn (T 2 ) Q 1 In (T 1 ) + Sn (T 2 ) = [In] Sn (T 2 ) Q 2 Sn (T 1 ) = Sn (T 2 ) Q 3 Liquid metal solvent Au 4 In 3 Sn 3 (T 1 ) + Sn (T 2 ) = [4Au + 3In] Sn (T 2 ) Q 4 4Au (T 1 ) + 3In (T 1 ) + 3Sn (T 1 ) = Au 4 In 3 Sn 3 (T 1 ) f H (Au 4 In 3 Sn 3 ) = 4Q 1 + 3Q 2 + 3Q 3 Q 4 T 2 = kj/mol Friday 20 January 2017 Hume-Rothery Seminar Derby 26
27 Enthalpy of Mixing by Metal Dissolution Drop Calorimetry Sample Small solute samples added incrementally to liquid solvent T 1 x 1 Au (cr, T 1 ) + In y Sn z (sol n, T 2 ) Au x1 In y Sn z (sol n, T 2 ) Q 1 x 2 Au (cr, T 1 ) + Au x1 In y Sn z (sol n, T 2 ) Au x1+x2 In y Sn z (sol n, T 2 ) Q 2 Q i = x i (H(Au, cr, T 2 )-H(Au, cr, T 1 )) + x i H(fus, Au, T 2 ) + H r,i h i H r,i / x i Liquid metal solvent H mix ( y + z) Hm, = y + z + B i x i H i r, i T 2 Friday 20 January 2017 Hume-Rothery Seminar Derby 27
28 Integral Enthalpies of Mixing of Au-In-Sn alloys Thermogram Friday 20 January 2017 Hume-Rothery Seminar Derby 28
29 Determination of component activities in solutions Friday 20 January 2017 Hume-Rothery Seminar Derby 29
30 Determination of Component Activities Change of pressure of 1 mole of A from p to p Vaporise 1 mole of A under equilibrium conditions p G 2 =RTln p A o A Condense 1 mole of A under equilibrium conditions G 1 = 0 Transfer of 1 mole of A G 3 = 0 G A Pure A G A = G + G + G 1 pa = RTln p o = RTlna A A 2 3 Alloy of A Friday 20 January 2017 Hume-Rothery Seminar Derby 30
31 Knudsen Effusion Tracer Method Samples made using radioactive Cr Effusing species condenses in Mo tube and on target Collected by dissolution in acid Mass effused determined by radiochemical assay p = pressure of effusing species m = mass of material effused t = effusion time A = cross-sectional area of effusion orifice T = temperature M = molecular mass of effusing species m 2πRT p = = ta M m ta T M Kubaschewski & Heymer, Acta. Met., 1960, 8, 416 Friday 20 January 2017 Hume-Rothery Seminar Derby 31
32 Knudsen Effusion + Mass Spectrometry Molecular beam from K cell ionised by beam of monoenergetic electrons Ions produced per unit time is proportional to molecular beam flux Related to pressure Related to nature of effusing species Charge/mass ratio Time of Flight Pulsed accelerating potential Allows ions to be separated in group of constant Time of Flight Fast analysis of a number of ionic species Magnetic Separation Constant accelerating potential Fixed magnetic field separates ions into groups of constant charge/mass ratio Continuous analysis higher sensitivity Friday 20 January 2017 Hume-Rothery Seminar Derby 32
33 Knudsen Effusion + Mass Spectrometry Friday 20 January 2017 Hume-Rothery Seminar Derby 33
34 Knudsen Effusion + Mass Spectrometry p i = pressure of effusing species S i = sensitivity of the mass spec. I i = ionic intensity for species I T = Cell temperature p i S i = I i T S i = Aσ i γ i f i A = geometrical factor of the coupling of the K cell and the mass spec. σ I = ionisation cross-section γ I = detector yield f i = isotopic abundance a = p p o = IT S S o IT o o = I I o A A o I I o Friday 20 January 2017 Hume-Rothery Seminar Derby 34
35 Dual Cell Friday 20 January 2017 Hume-Rothery Seminar Derby 35
36 EMF methods Friday 20 January 2017 Hume-Rothery Seminar Derby 36
37 EMF Methods Pt <M, MO> electrolyte (O 2, I atm) Pt 1/2O 2 + 2e - O 2- M + O 2- MO + 2e - 1/2O 2 + <M> <MO> - G = zfe Friday 20 January 2017 Hume-Rothery Seminar Derby 37
38 Electrolytes Liquid Mixtures of molten salts LiCl-KCl eutectic mixture Lead-free solders In-Sn, Sb-Sn. LiCl-RbCl Lu-Pb KCl-LiCl-BaCl 2 Pb-Pd Solid Current carried by ions Halides, sulphides, chlorides Caused by lattice defects Doping with aliovalent ions -> vacancies ZrO 2 based CaO, MgO Y 2 O 3 Friday 20 January 2017 Hume-Rothery Seminar Derby 38
39 EMF studies of a In in Ag-Cu-In liquid alloys ZrO 2 -Y 2 O 3 Kanthal Re tip Ni(s),NiO(s) Pt wire In 2 O 3 Ag-Cu-In Argon inlet Argon outlet Brass head Quartz tube Alumina capillary with current lead Resistance furnace Cell Thermocouple Leszek Zabdyr, IMM/PAS, Krakow, Poland Friday 20 January 2017 Hume-Rothery Seminar Derby 39
40 (-)Kanthal,Re Ag-Cu-In,In 2 O 3 (s) ZrO 2 - Y 2 O 3 Ni(s),NiO(s) Pt(+) (+) 3NiO 3Ni + 3/2 O 2 6e (-) 2In + 3/2 O 2 In 2 O 3 + 6e 3NiO + 2In +3/2O 2 3Ni + 3/2O 2 + In 2 O 3 ΔG = 6FE = 3μo Ni + 3/2μo O 2 + μo In O 2 3 3μo NiO (2μo + 2RTlna ) 3/2μO In In O 2 o o 3ΔG f,nio + ΔG f,in 2 O 3 lna In = + 2RT 3EF RT G, where: o and o - Gibbs energies of formation of nickel and indium oxides, f NiO f, In O respectively; G 2 3 F - Faraday constant; R gas constant; E electromotive force; Friday 20 January 2017 Hume-Rothery Seminar Derby 40
41 EMF [mv] %Ag22.5%Cu67.5%In 20%Ag20%Cu60%In 30%Ag17.5%Cu52.5%In 40%Ag15%Cu45%In 50%Ag12.5%Cu37.5%In 60%Ag10%Cu30%In 70%Ag7.5%Cu22.5%In 80%Ag5%Cu15%In 90%Ag2.5%Cu7.5%In T [K] EMF [mv] %Ag45%Cu45%In 20%Ag40%Cu40%In 30%Ag35%Cu35%In 40%Ag30%Cu30%In 50%Ag25%Cu25%In 60%Ag20%Cu20%In 70%Ag15%Cu15%In 80%Ag10%Cu10%In 90%Ag5%Cu5%In T [K] Friday 20 January 2017 Hume-Rothery Seminar Derby 41
42 In Activity in liquid Ag-Cu-In at 1273K indium activity indium avtivity 1 0,8 0,6 0,4 0,2 1 0,8 0,6 0,4 0, ,005 0,012 0,021 0,039 0,050 0,061 0, ,1 0,2 0,3 0,4 0,5 0,007 0,020 X Cu /X In =1 0,045 X In X Cu /X In 0,093 In =1/3 0,154 0,280 0,245 0,360 0,432 0,594 0, ,2 0,4 0,6 0,8 X In 0,062 0,043 0,015 0,026 Friday 20 January 2017 Hume-Rothery Seminar Derby 42 indium activity 0,12 0,1 0,08 0,06 0,04 0,02 0 0,004 X Cu /X In =3 0,007 0,010 0, ,05 0,1 0,15 0,2 0,25 X In
43 Conclusions Experiments are still important Range of techniques available Complementary to ab initio techniques for improved modelling We need more experiments Friday 20 January 2017 Hume-Rothery Seminar Derby 43
44 Thank you Friday 20 January 2017 Hume-Rothery Seminar Derby 44
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