1 / 40

Physical Metallurgy 9th Lecture

Physical Metallurgy 9th Lecture. MS&E 410 D.Ast dast@ccmr.cornell.edu 255 4140. ORDERING Ordered solids Influence of order on properties Mechanical (very complex) Electrical (less complex but you need QM)

donnan
Download Presentation

Physical Metallurgy 9th Lecture

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physical Metallurgy9th Lecture MS&E 410 D.Ast dast@ccmr.cornell.edu 255 4140

  2. ORDERING • Ordered solids • Influence of order on properties • Mechanical (very complex) • Electrical (less complex but you need QM) • Electronic (not covered by SiC is a classic..)

  3. If order appears enthalpy wins over entropy. Enthalpy is that of the electron gas and hence “electronic” and influenced be e-/a (electron to atom ratio, Fermi surface

  4. Ordering • In alloys • On the unit cell level • On the long range scale • In semiconductors (well Ga and As are both metals) • In magnetic alloys • Defect ordering • Grain boundary ordering

  5. Let there be order…. Think valence Think shell size Is Cu bigger or smaller than Zn ? Is Cu bigger or smaller than Au ? Is Fe bigger or smaller than Al ?

  6. A detour... What is “size” ? See http://www.crystalmaker.com/support/tutorials/crystalmaker/AtomicRadii.html • Size of neutral atom, isolated (VFI, CPK) • Size of covalent atom (in covalent bond) • Size of Ionic atom (in ionic bond) • Size in crystals (Shannon & Prewitt) When in doubt use this…..

  7. Memo : “Bigger” atom in “bigger” space

  8. Order on the unit cell level in Cu-Au

  9. Order on the “many unit cell” level in Cu-Au “Domains” Memo: The CuAu II system is fcc Au in which “ in the center plane” the Au atoms have be replaced by the much smaller Cu atoms. The result is an orthorombic lattice Memo: Since in the fcc lattice the “center plane” physically “ the same as the top and bottom, you may look at it as an Cu fcc lattice in which the center plane has been replaced by Au

  10. The above is a picture of 10 cells of CuAu. In this case, there is a shift between the “two fcc lattices” after the first 5. This is known as a (antiphase) domain boundary. The CuAu II superlattice is formed by a periodic array of these antiphase boundaries. The long range periodicity sets up “mini Brillioun zone” inside the first Brillioun” which are well known in semiconductor physics (Asaki diode) and constructed there by MBE. Thus, the long range order is an electronic effect

  11. Basics of dislocation theory (you had it in 261) • after passing of the dislocation the lattice must be as before • if the EA-A = EA-B = EB-B random solution • if not ordering (EA-B > EA-A ; EB-B) • Energy of dislocation ~ E b2 (b => Burgers vector) If the alloy insists on ordering, the energy of a dislocation is 4 times that of the solid solution. To move such a dislocation is difficult - even in steps. More later...

  12. It’s not the best reproduction but you can see domains that are vertically and horizontally arranged Domain boundaries occur in a wide variety of compounds. A particular important system is GaAs on a Ge substrate (space solar cells).

  13. Order - Disorder Phase transformation

  14. Antiphase boundaries: Most common reason in thin films is not entropy but nucleation and growth: Substrate has higher symmetry than film. Classical example Ge substrate with a deposited GaAs film

  15. Two antiphase domain boundaries originating from the Ge / GaAs interface meet and annihilate each other. Journal of Applied Physics, Vol. 89, No. 11, pp. 5972–5979, 1 June 2001 Self-annihilation of antiphase boundaries in GaAs epilayers on Ge substrates grown by metal-organic vapor-phase epitaxy J. Appl. Phys. 89, 5972 (2001); DOI:10.1063/1.1368870 Ge has the same lattice constant as GaAs but is mechanically stronger and weights less. Thus it is the preferred substrate for space solar cells

  16. Order - disorder transition

  17. Cu and Zn are similar in size an both have closed d shell and nearly behave like a free electron. Hence H-R and electronic phases apply v is the ordering energy. Tc 744oK

  18. The transition temperature depends weakly on temperature. It has been modeled by MD for this system as well as when Au is added (for Cu) Memo: higher T phase (bcc) more dense (NaCl)

  19. By far the best investigated order disorder systems are ternary semiconductors… unfortunately metallurgists do not read the semiconductor literature :-(

  20. In the mid eighties, it was known that size mismatch between the atomic constituents leads to positive mixing enthalpy D H(R) > 0 of random (R) alloys. The question we posed in the Fall of 1984 was: Does the fact that D H(R) > 0 for all random isovalent semiconductor alloys preclude the formation of long-range order? The time-honored prevailing paradigm in metal alloys was that D H(R) > 0 reflects the existence of fundamentally repulsive interactions between the alloy constituents, and since ordering requires attractive interactions, D H(R) > 0 excludes the possibility of ordering. What we found in what became the first published paper on spontaneous long-range order of size-mismatched semiconductor alloys [1] was that this paradigm was incorrect, and that long-range order is, in principle, consistent even with D H(R) > 0. The basic insight was that D H(R) > 0 merely reflects the fact that in a random alloy, there is a distribution of many different local environments ("clusters," such as PGa2In2, PGa3In1, PGa1In3), and that the statistical average of their energies is positive, because some of these clusters are strained. But if one were to isolate a single cluster type and repeat it periodically in a strain-minimizing three-dimensional geometric arrangement, long-range order will ensue. This basic observation published in early 1985 [1], started the pursuit by theorists, and experimentalists of long-range order in size-mismatched semiconductor alloys. The first experimental observations of ordering in size-mismatched semiconductor alloys were made by the NEC group of Gomyo and Suzuki, and by the Utah group of G. Stringfellow just a couple of years later.

  21. Translation • Ordering requires that free energy is lowered • Past idea : Ordering always requires attractive interactions • Past idea : Disorder always requires repulsive interactions • New idea : Free energy can be lowered even when repulsive ! • New idea : Reason “strain cancellation” of “clusters” • Memo: It is a bit like the Fe3C (cementite) where when one looks only at the unit cell the C atom should not sit on the center edge. Unfortunately, the semiconductor guys don’t read the metal literature either…….. The cluster calculations took on a life of their own, under Alex Zunger, and developed in beautiful theory tool, but for that you need to take Hennig’s course!

  22. Why this is so important to III-V guys • Can make alloys with bandgaps previously not accessible under the lattice match boundary condition (means epilayer lattice must match substrate lattice). • Can play with the bandgap by controlling degree of order • Can convert indirect s.c. into direct one • and

  23. The Heusler alloys are interesting beasts • They have the composition X2MnZ + L21 structure or XMnZ with C1b- structure . Mn must be there… it’s the d electron carrier. • They have a very high local magnetic moments of 4 µB at the Mn • Adjustable Curie temperatures ( Ni2MnSb TC 350 K, Ni2MnSn TC 340 K, NiMnSb TC730 K)

  24. A don’t want to put in too much Q chemistry but the trick for magnetism, I hope you remember, is a narrow d band (because then the penalty for “doing Hund’s rule for the whole crystal”) is small, and the electron gas can enjoy the energy benefit of the exchange hole. .

  25. Defect ordering

  26. Defect ordering • A compound such as Ga0.49999As0.50001 does not have As atoms sitting on Ga sites or vice versa. • Rather, it leaves part of the Ga sites empty* • Thus, we can introduce controlled vacancies of either type…. If we are really good crystal growers** • Some compounds can do this to an amazing degree. Key is that an atom can have different valence states at relatively low energy penalty. • Phase transitions can be treated as more and more vacancies appearing (as we change compo) and then ordering themselves into a the new phase. • Ordered vacancies are important for fast ion conductors as the charged ion “needs a chain of vacancies to hop along” * Happens involuntarily all the time when GaAs is in physical contact with say a Au contact. Au dissolves Ga, not As. The Ga vacancies pin the Fermi level ** Yes, and we do, because if Si goes on a Ga site, it acts like a donor, On the As site it acts like an acceptor. By controlling vacancies, we control the dopant

  27. SrFeO3 SrFeO2.5 An example of a phase transition by increasing “ordered vacancies” SrFeO2.5 is a fast ion conductor

  28. f) Electronic properties: Bandgap, effective mass….

  29. Mechanical Properties • below is for those who had dislocation theory (MS&E 261) • The movement of a “regular” a/2<110> type dislocation in Cu3Au (LI12 ‘disorders’ the lattice and generates an APB • To restore order to the lattice there must be a second a/2<110> (trailing dislocation) that restores order • Together they form a superdislocation. • The “regular” dislocations, in turn, are dissociated into partials that bound a stacking fault, of energy g/unit area • The stacking fault energy g in ordered CusAu is • smaller than the stacking fault energy in disordered • CuaAu (ordered= 13.0, disordered = 21.5 mJ/m2 ). • Both are smaller than the energy of the antiphase boundary • = 39 mJ/m2 . • When S(order parameter) is large => superdislocations, when S small + regular

  30. On a more primitive level • Dislocation motion is more difficult in an ordered alloy that strongly likes to be ordered (High order parameter) • An important parameter is the energy of the antiphase boundary. To have superdislocations you want an ordered compound with a high antiphase boundary energy. • The antiphase boundary energy goes with the square of S • The stress strain curve is controlled by glide obstacles • Let’s look at one example

  31. Unless you had a detailed course on dislocations the only point here is that it is very complex. Stress strain curve of SINGLE CRYSTALS. The plateau is stage III and controlled by cross slip. In Cu2NiZn the disordered lattice changes below 773 K into an LI,-structure and below 6.50 K from an LIZ- into an Lie- structure

  32. Electrical Properties • Disordered - higher resistivity • Ordered - lower resistivity • The disordered state can be studied at room temperature (where the phase diagram tells you that it should be ordered) by quenching the disordered phase from a higher temperature • By gently annealing, the disordered phase - if in the ordered field - will change to the ordered phase. • The kinetics of this transformation can be studied by resistivity. It is very interesting, because it is slower than expected from the diffusion of Cu in Au and vice versa. This is because the alloy not only needs to order, it also needs to set up a domain structure by nucleation and growth

  33. THE END

More Related