Theoretical Studies of Epitaxial Bain Paths of Metals

Epitaxial growth is an important technique for the fabrication of film structures with good crystalline quality, e.g., monoatomic overlayers, multilayers, compound materials, and ordered alloys. Such epitaxially grown films are technologically important materials with, e.g., adjustable electronic, magnetic, and optical properties. In case of coherent or pseudomorphic epitaxy, the overlayer adapts the in-plane lattice parameters of the substrate, i.e., the overlayer is strained to match the lattice parameters parallel to the substrate surface (in-plane directions). Simultaneously, a relaxation of the film dimension perpendicular to the substrate-film interface occurs (out-of-plane direction). Thus, coherent epitaxy provides a method to put phases under strain, and it can stabilise a metastable state of the film material, if the substrate lattice matches this metastable structure. Bulk-like properties in thick overlayers, which adopt the body-centred tetragonal (BCT) crystal structure and which grow coherently on a suitable substrate with quadratic surface symmetry, are modelled by the epitaxial Bain path (EBP) in this thesis. The knowledge of the EBP allows to study properties of the overlayer as function of the substrate lattice parameter. In particular, strain effects on the film material, magnetic order in the overlayer, and the existence of possible metastable states are investigated by means of density functional theory (DFT) in the local spin density approximation (LSDA), and in the singular case of uranium, employing the generalised gradient approximation (GGA). Note that a symmetry property of the BCT structure states, that it is identical to the body-centred cubic (BCC) structure or the face-centred cubic (FCC) structure for definite ratios of the tetragonal lattice parameters. Our definition of the EBP has two, previously not considered consequences for EBPs in general: an EBP can be discontinuous, and the high symmetry cubic structures (FCC and BCC) need not be points on the EBP. Both cases occurred for several elements considered in this thesis. If, however, a cubic structure is a point on the EBP, then a symmetry property guarantees that the total energy along the EBP, E(a), is stationary at this cubic structure. We computed the EBPs of all transition metals (TMs), the post TMs Zn, Cd, and Hg, the alkaline earth metals Ca, Sr, and Ba, the lanthanides La and Lu, and the actinide U (35 elements were treated in total). For each element but Zr, Hg, and U, there are exactly two structures whose energies are minima on the EBP, and which exhibit neither in-plane nor out-of-plane stresses; for Zr, Hg, and U there are three minima each. All other states on the EBP exhibit in-plane stresses because they are a strained form of the stress-free structures. The possibility of metastability of these particular, stress-free structures, i.e., stabilisation of these structures without bonding to the substrate, was investigated by stability conditions based on linear elasticity theory (except for U). We predict that ten FCC structures and three BCT structures not known from the respective phase diagrams may be metastable. We studied the properties of ferromagnetic (FM) states on the EBP for the elements Fe, Co, and Ni, and moreover predict, that Mn, Ru, Os, and U order ferromagnetically for certain states of the EBP. The latter three elements are paramagnetic in their ground states. The onset of ferromagnetism in Os and U is not accompanied by a simultaneously fulfilled Stoner criterion. According to our results, antiferromagnetic order (with moment sequences up-down or up-up-down-down on successive (001) planes) is never more stable than FM order on any EBP for any element investigated. On the basis of our comprehensive results for all TMs, we analysed trends across each of the three TM series and similarities among the three series. We demonstrate, that the type of the EBP (a classification of extrema of E(a) by symmetry into types) follows a characteristic trend across each of the three TM series. We discuss exceptions (Mn, Fe, and Zr) to this trend. Another trend, identical for the three series, is found for the BCT­-FCC structural energy difference as function of the d-band filling (evaluated for BCT structures that define extrema of E(a)), which follows a similar trend as the well studied BCC­-FCC structural energy difference. Clear similarities among the three periods of elements are also reflected in the bulk moduli and in the elastic constants of the cubic or tetragonal structures, that define the global and local minima of E(a). The mentioned similarities suggest, that many properties which are associated with the EBPs of TMs, can be attributed to the occupation of the d-band, which is the most dominant feature of the electronic structure of TMs

First-principles approach to thin superconducting slabs and heterostructures

We present a fully first-principles method for superconducting thin films. The layer dependent phonon spectrum is calculated to determine the layer dependence of the electron-phonon coupling for such systems, which is coupled to the Kohn-Sham-Bogoliubov-de Gennes equations, and it is solved in a parameter free way. The theory is then applied to different surface facets of niobium slabs and to niobium-gold heterostructures. We investigate the dependence of the transition temperature on the thickness of the slabs and the inverse proximity effect observed in thin superconducting heterostructures

Alloying effect on the ideal tensile strength of ferromagnetic and paramagnetic bcc iron

Using \emph{ab initio} alloy theory formulated within the exact muffin-tin orbitals theory in combination with the coherent potential approximation, we investigate the ideal tensile strength (ITS) in the $[001]$ direction of bcc ferro-/ferrimagnetic (FFM) and paramagnetic (PM) Fe$_{1-x}M_{x}$ ($M=$ Al, V, Cr, Mn, Co, or Ni) random alloys. The ITS of ferromagnetic (FM) Fe is calculated to be $12.6$\,GPa, in agreement with available data, while the PM phase turns out to posses a significantly lower value of $0.7\,$GPa. Alloyed to the FM matrix, we predict that V, Cr, and Co increase the ITS of Fe, while Al and Ni decrease it. Manganese yields a weak non-monotonic alloying behavior. In comparison to FM Fe, the alloying effect of Al and Co to PM Fe is reversed and the relative magnitude of the ITS can be altered more strongly for any of the solutes. All considered binaries are intrinsically brittle and fail by cleavage of the $(001)$ planes under uniaxial tensile loading in both magnetic phases. We show that the previously established ITS model based on structural energy differences proves successful in the PM Fe-alloys but is of limited use in the case of the FFM Fe-based alloys. The different performance is attributed to the specific interplay between magnetism and volume change in response to uniaxial tension. We establish a strong correlation between the compositional effect on the ITS and the one on the shear elastic constant $C'$ for the PM alloys and briefly discuss the relation between hardenability and the ITS.Comment: 6 figure

Prediction of first-order martensitic transitions in strained epitaxial films

Coherent epitaxial growth allows to produce crystalline films with strained structures which are unstable in the bulk. Thereby, the relationship between the lattice parameters of the overlayer in the interface plane, $(a,b)$, and its minimum-energy out-of-plane lattice parameter, $c_{\text{min}}(a,b)$, need not be continuous. This general statement is proven by examples of total energy calculations. As a consequence, $c_{\text{min}}$, which is determined by the choice of the substrate, and $c_{\text{min}}$-dependent intrinsic properties of the overlayer cannot always be tuned in a continuous way as one may aim to do by means of strained epitaxy. Employing the model of the epitaxial Bain path we predict that such discontinuities occur in films of the elements V, Nb, Ru, La, Os, and Ir. The abrupt change of $c_{\text{min}}$ can be exploited to switch properties specific to the overlayer material. This is demonstrated for the example of the superconducting critical temperature of a V film which we predict to jump by 20% at a discontinuity of $c_{\text{min}}

Ab initio prediction of the mechanical properties of alloys: The case of Ni/Mn-doped ferromagnetic Fe

First-principles alloy theory, formulated within the exact muffin-tin orbitals method in combination with the coherent-potential approximation, is used to study the mechanical properties of ferromagnetic body-centered cubic (bcc) Fe$_{1-x}$M$_x$ alloys (M=Mn or Ni, $0\le x \le 0.1$). We consider several physical parameters accessible from \emph{ab initio} calculations and their combinations in various phenomenological models to compare the effect of Mn and Ni on the properties of Fe. Alloying is found to slightly alter the lattice parameters and produce noticeable influence on elastic moduli. Both Mn and Ni decrease the surface energy and the unstable stacking fault energy associated with the $\{110\}$ surface facet and the $\{110\}\langle111\rangle$ slip system, respectively. Nickel is found to produce larger effect on the planar fault energies than Mn. The semi-empirical ductility criteria by Rice and Pugh consistently predict that Ni enhances the ductility of Fe but give contradictory results in the case of Mn doping. The origin of the discrepancy between the two criteria is discussed and an alternative measure of the ductile-brittle behavior based on the theoretical cleavage strength and single-crystal shear modulus $G\{110\}\langle111\rangle$ is proposed.Comment: 14 pages, 11 figure