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Full-Text Articles in Physics

Grain Growth And Texture Development In Lithium Fluoride Thin Films, Hakkwan Kim, Alexander H. King Feb 2008

Grain Growth And Texture Development In Lithium Fluoride Thin Films, Hakkwan Kim, Alexander H. King

Alexander H. King

We have studied grain-growth and texture development in polycrystalline lithium fluoride thin films using dark-field transmission electron microscopy. We demonstrate that we can isolate the size distribution of 〈111〉 surface normal grains from the overall size distribution, based on simple and plausible assumptions about the texture. The {111} texture formation and surface morphology were also observed by x-ray diffraction and atomic force microscopy, respectively. The grain-size distributions become clearly bimodal as the annealing time increases, and we deduce that the short-time size distributions are also a sum of two overlapping peaks. The smaller grain-size peak in the distribution corresponds to …


Posterminaries: More Or Less Modern, Alexander H. King Nov 2007

Posterminaries: More Or Less Modern, Alexander H. King

Alexander H. King

It is yet another sign that I am aging. More and more often when young researchers hand me a written report of their research, I find myself criticizing their introductory section: “You need to start your literature survey with the original papers on this topic. Go and read…” followed by a citation to some classic of the learned literature.


Control Of Porosity In Fluoride Thin Films Prepared By Vapor Deposition, Alexander H. King Jul 2007

Control Of Porosity In Fluoride Thin Films Prepared By Vapor Deposition, Alexander H. King

Alexander H. King

We have measured the porosity in thin films of lithium fluoride (LiF), magnesium fluoride (MgF2), barium fluoride (BaF2), and calcium fluoride (CaF2) as a function of the substrate temperature for films deposited by thermal evaporation onto glass substrates. The amount of porosity in the thin films was measured using an atomic force microscope and a quartz crystal thickness monitor. The porosity was very sensitive to the substrate temperature and decreased as the substrate temperature increased. Consistent behavior was observed among all of the materials in this study.


Posterminaries: Full Circle, Alexander H. King Jul 2007

Posterminaries: Full Circle, Alexander H. King

Alexander H. King

A few years ago, I was walking near the old Union Station in Pittsburgh with a colleague only slightly younger than myself, when we happened upon some large-scale relics of the steel industry displayed for public viewing. “You don’t see too many of those in public parking lots,” I offered. “Um… what is it?” was the response. I suppose I was just a little surprised that a prominent materials scientist did not recognize a Bessemer converter—arguably the principal source of wealth during the U.S. industrial revolution—but this conversation took place back when steel was in decline, and many university Materials …


Thermal Effects On Mechanical Grinding-Induced Surface Texture In Tetragonal Piezoelectrics, Wonyoung Chang, Alexander H. King, Keith J. Bowman Jan 2007

Thermal Effects On Mechanical Grinding-Induced Surface Texture In Tetragonal Piezoelectrics, Wonyoung Chang, Alexander H. King, Keith J. Bowman

Alexander H. King

The effect of temperature on grinding-induced texture in tetragonal lead zirconate titanate (PZT) and lead titanate (PT) has been investigated using in situ x-ray diffraction (XRD) with an area detector. In contrast with previous results on electrical poling, mechanically-ground PT and soft PZT materials retain strong ferroelastic textures during thermal cycling, even after excursions to temperatures slightly above the Curie temperature. The relationship between the residual stresses in the surface region, caused by grinding, and those resulting from domain wall motion is elucidated by in situ texture measurements obtained during thermal cycling.


How Surface Stresses Lead To Size-Dependent Mechanics Of Tensile Deformation In Nanowires, M. Ravi Shankar, Alexander H. King Jan 2007

How Surface Stresses Lead To Size-Dependent Mechanics Of Tensile Deformation In Nanowires, M. Ravi Shankar, Alexander H. King

Alexander H. King

It has been proposed that surface and interface stresses can modify the elastic behavior in nanomaterials such as nanowires. The authors show that surface stresses modify the tensile response of nanowires only when nonlinear elastic effects become important leading to cross terms between the applied stress and the surface stress. These effects are only significant when the radius of the nanowire is of the order of a few nanometers. The resulting alteration of tensile stiffness, though effected in part by the nonlinear elastic modulus, is particularly wrought by a modification of the stress state in the deformed nanowire.


Posterminaries: After Nabarro, Alexander H. King Nov 2006

Posterminaries: After Nabarro, Alexander H. King

Alexander H. King

With the passing of Frank Nabarro in July of this year, we have lost one of the founding fathers of materials science. His name appears in many of the textbooks from which we train our students today, and also on the spines of several volumes on dislocation theory, including his classic monograph on the subject. He rightly stands among the gods of our field. Ninety years old at his death, he was a sprightly dancer at the frontiers of knowledge, right up to the end.


Posterminaries: The Scales Of Judgement, Alexander H. King Sep 2006

Posterminaries: The Scales Of Judgement, Alexander H. King

Alexander H. King

Materials scientists are generally well-versed in physics, and physics, above all, is a science of measurements. The first instinct of a physicist is to parse a problem in terms of its measurables in the dimensions of mass, length, and time, and it is the shifting of attention down the scale of length that particularly characterizes our present times as the Nano Age.


Posterminaries: Plain Text, Alexander H. King Jan 2006

Posterminaries: Plain Text, Alexander H. King

Alexander H. King

You just can’t win an argument with an English professor.


Thermal Effects On Domain Orientation Of Tetragonal Piezoelectrics Studied By In Situ X-Ray Diffraction, Wonyoung Chang, Alexander H. King, Keith J. Bowman Jan 2006

Thermal Effects On Domain Orientation Of Tetragonal Piezoelectrics Studied By In Situ X-Ray Diffraction, Wonyoung Chang, Alexander H. King, Keith J. Bowman

Alexander H. King

Thermal effects on domain orientation in tetragonal lead zirconate titanate (PZT) and lead titanate (PT) have been investigated by using in situ x-ray diffraction with an area detector. In the case of a soft PZT, it is found that the texture parameter called multiples of a random distribution (MRD) initially increases with temperature up to approximately 100 °C and then falls to unity at temperatures approaching the Curie temperature, whereas the MRD of hard PZT and PT initially undergoes a smaller increase or no change. The relationship between the mechanical strain energy and domain wall mobility with temperature is discussed.


Size-Driven Domain Reorientation In Hydrothermally Derived Lead Titanate Nanoparticles, Zhiyuan Ye, Elliot B. Slamovich, Alexander H. King Mar 2005

Size-Driven Domain Reorientation In Hydrothermally Derived Lead Titanate Nanoparticles, Zhiyuan Ye, Elliot B. Slamovich, Alexander H. King

Alexander H. King

High-resolution transmission electron microscopy studies of hydrothermally derived platelike lead titanate nanoparticles reveal that below a critical size of approximately 70 nm, the single ferroelectric domain polarization axis reorients from perpendicular to parallel to the plate. We suggest that during particle growth, ions in the hydrothermal processing medium compensate for the ferroelectric depolarization energy. When the processing medium is removed by washing and drying, single domain nanoparticles minimize their depolarization energy by c-axis flipping.


Mechanism Of Structural Transformation In Bismuth Titanate, Sudhanshu Mallick, Keith J. Bowman, Alexander H. King Jan 2005

Mechanism Of Structural Transformation In Bismuth Titanate, Sudhanshu Mallick, Keith J. Bowman, Alexander H. King

Alexander H. King

Sodium-doped bismuth titanate undergoes a transformation from Bi4Ti3O12 to Na0.5Bi4.5Ti4O15 on heating in air at temperatures exceeding 800 °C. This transformation proceeds through the intermediate Na0.5Bi8.5Ti7O27 structure which is an intergrowth phase of the two. High-resolution transmission electron microscopy was used to study this transformation. From the Moiré pattern that was obtained, the crystallographic orientation of the transformation front has been determined and a mechanism is proposed for this structural transformation.


Dislocation-Indenter Interaction In Nanoindentation, M. Ravi Shankar, Alexander H. King, Srinivasan Chandrasekar Jan 2005

Dislocation-Indenter Interaction In Nanoindentation, M. Ravi Shankar, Alexander H. King, Srinivasan Chandrasekar

Alexander H. King

A formulation of dislocation-indenter interaction in two-dimensional, isotropic elasticity is presented. A significant dislocation-indenter interaction is predicted when dislocations are nucleated very close to the indenter. This interaction is expected to have an important influence on dislocation motion and multiplication. Upon nucleation close to the indenter, the dislocations are shown to modify the load, load distribution, and moment acting on the indenter. This effect is seen to vary with the indentation contact length. Further away from the indenter, the indenter-dislocation interaction is shown to be negligible.


Low-Cost Manufacturing Process For Nanostructured Metals And Alloys, Travis L. Brown, Srinivasan Swaminathan, Srinivasan Chandrasekar, W. Dale Compton, Alexander H. King, Kevin P. Trumble Jan 2002

Low-Cost Manufacturing Process For Nanostructured Metals And Alloys, Travis L. Brown, Srinivasan Swaminathan, Srinivasan Chandrasekar, W. Dale Compton, Alexander H. King, Kevin P. Trumble

Alexander H. King

In spite of their interesting properties, nanostructured materials have found limited uses because of the cost of preparation and the limited range of materials that can be synthesized. It has been shown that most of these limitations can be overcome by subjecting a material to large-scale deformation, as occurs during common machining operations. The chips produced during lathe machining of a variety of pure metals, steels, and other alloys are shown to be nanostructured with grain (crystal) sizes between 100 and 800 nm. The hardness of the chips is found to be significantly greater than that of the bulk material.


Propagating Conformational Changes Over Long (And Short) Distances In Proteins, Edward Yu, Daniel E. Koshland Jr. Jan 2001

Propagating Conformational Changes Over Long (And Short) Distances In Proteins, Edward Yu, Daniel E. Koshland Jr.

Edward Yu

The problem of the propagation of conformational changes over long distances or through a closely packed protein is shown to fit a model of a ligand-induced conformational change between two protein states selected by evolution. Moreover, the kinetics of the pathway between these states is also selected so that the energy of ligand binding and the speed of the transition between conformational states are physiologically appropriate. The crystallographic data of a wild-type aspartate receptor that has negative cooperativity and a mutant that has no cooperativity but has native transmembrane signaling are shown to support this model.


Behavior Of Grain Boundary Resistivity In Metals Predicted By A Two-Dimensional Model, Rand Dannenberg, Alexander H. King Jan 2000

Behavior Of Grain Boundary Resistivity In Metals Predicted By A Two-Dimensional Model, Rand Dannenberg, Alexander H. King

Alexander H. King

The behavior of a model for the specific grain boundary resistivity in metallic bamboo conductor lines is developed and compared to other theoretical treatments, and to experiment. The grain boundary is modeled as an array of scatterers on a plane. The scatterers are called “vacancy-ion” complexes, in which the vacancy represents the boundary free volume, and the ion is an atom adjacent to the vacancy. Three cases are investigated, that of noninterfering scatterers, a continuum of interfering scatterers, and discrete interfering scatterers. The approximations used lead to a specific grain boundary resistivity ∼10−16 Ω m2 for aluminum, in agreement with …


Novel One-Phase Synthesis Of Thiol-Functionalized Gold, Palladium, And Iridium Nanoparticles Using Superhydride, Chanel K. Yee, Rainer Jordan, Abraham Ulman, Henry White, Alexander H. King, Miriam Rafailovich, Jonathan Sokolov May 1999

Novel One-Phase Synthesis Of Thiol-Functionalized Gold, Palladium, And Iridium Nanoparticles Using Superhydride, Chanel K. Yee, Rainer Jordan, Abraham Ulman, Henry White, Alexander H. King, Miriam Rafailovich, Jonathan Sokolov

Alexander H. King

A new, facile, general one-phase synthesis for thiol-functionalized gold, palladium, and iridium nanoparticles, using tetrahydrofuran (THF) as the solvent and lithium triethylborohydride (Superhydride) as the reducing agent, is presented. For octadecanethiol-functionalized gold (Au/ODT) nanoparticles, HRTEM of drop-cast particle-films revealed the formation of spherical particles of d = 4 ± 0.3 nm average size. Electron diffraction shows fcc packing arrangement, similar to that of bulk gold. The crystalline gold cores are surrounded with closely packed n-alkyl chains mainly in an all-trans conformation, adopting orthorhombic packing as confirmed by FTIR spectroscopy. Particles are arranged in a discrete solidlike assembly with a correlation …


Resistivity, Thermopower And The Correlation To Infrared Active Vibrations Of Mn1.56co0.96ni0.48o4 Spinel Films Sputtered In An Oxygen Partial Pressure Series, Rand Dannenberg, S. Baliga, R. J. Gambino, Alexander H. King, A. P. Doctor Jan 1999

Resistivity, Thermopower And The Correlation To Infrared Active Vibrations Of Mn1.56co0.96ni0.48o4 Spinel Films Sputtered In An Oxygen Partial Pressure Series, Rand Dannenberg, S. Baliga, R. J. Gambino, Alexander H. King, A. P. Doctor

Alexander H. King

Mn1.56Co0.96Ni0.48O4 spinel was sputter deposited using a series of oxygen partial pressures. Electrical resistivity versus temperature and thermopower versus temperature measurements at each oxygen partial pressure were made. The variations of the thermopower and resistivity with oxygen partial pressure are consistent with a change in the ratio of Mn3+ to Mn4+ cations, which occurs due to changes of oxygen content of the material. The weak temperature dependence of the thermopower indicates small polaron hopping is the charge transport mechanism. Combining the models of Mott and Schnakenberg to analyze the transport data, we find that the Debye temperature (or frequency) is …


Infrared Optical Properties Of Mn1.56co0.96ni0.48o4 Spinel Films Sputter Deposited In An Oxygen Partial Pressure Series, Rand Dannenberg, S. Baliga, R. J. Gambino, Alexander H. King, A. P. Doctor Jan 1999

Infrared Optical Properties Of Mn1.56co0.96ni0.48o4 Spinel Films Sputter Deposited In An Oxygen Partial Pressure Series, Rand Dannenberg, S. Baliga, R. J. Gambino, Alexander H. King, A. P. Doctor

Alexander H. King

Mn1.56Co0.96Ni0.48O4 spinel films were sputter deposited onto silicon substrates using a series of oxygen partial pressures. Fourier transform infrared transmission and reflectance, and Raman scattering measurements were made. The 1–25 μm wavelength range was examined using these optical techniques. The complex index of refraction was calculated for this entire wavelength range. Infrared active vibrations were analyzed using multiple oscillator analysis, Kramers–Kronig analysis, and derivative reflectance spectroscopy. The Raman and infrared active lattice vibrations were observed to shift with increasing oxygen partial pressure during film deposition, and were consistent with the earlier published shift in Debye frequency calculated from resistivity data. …


Segregation Of Bismuth To Triple Junctions In Copper, K.-M. Yin, Alexander H. King, T.E. Hsieh, F.-R. Chen, J.J. Kai, L. Chang Sep 1997

Segregation Of Bismuth To Triple Junctions In Copper, K.-M. Yin, Alexander H. King, T.E. Hsieh, F.-R. Chen, J.J. Kai, L. Chang

Alexander H. King

Bismuth segregation in copper has been studied using energy-dispersive X-ray spectrometry (EDX) in a JEOL 2010F transmission electron microscope. In addition to the expected solute enrichment at grain boundaries, we have observed extremely high concentrations of bismuth at certain triple junctions, with significantly greater enrichment factors than in the adjacent grain boundaries. It is shown here that the triple junction segregation is a function of the parameters of the grain boundaries at the triple line, and existence of this type of segregation implies that the affected triple junctions embody excess free energy. At least one of the observed triple junctions …


Synthesis And Characterization Of A New Class Of Μ3-Oh-Bridged Trimers That Contain Octahedrally Coordinated Divalent Metal Ions Bridged By Three Acetate Ligands And A Unique Catecholate Ligand. Solid State Molecular Structures Of The [(Py)5mii3(Oac)3(Μ3-Oh)((Cat)] Complexes (M = Mn(Ii), Fe(Ii), Co(Ii), Ni(Ii)), R.A. Reynolds, Edward Yu, W.R. Dunham, D. Coucouvanis Jan 1996

Synthesis And Characterization Of A New Class Of Μ3-Oh-Bridged Trimers That Contain Octahedrally Coordinated Divalent Metal Ions Bridged By Three Acetate Ligands And A Unique Catecholate Ligand. Solid State Molecular Structures Of The [(Py)5mii3(Oac)3(Μ3-Oh)((Cat)] Complexes (M = Mn(Ii), Fe(Ii), Co(Ii), Ni(Ii)), R.A. Reynolds, Edward Yu, W.R. Dunham, D. Coucouvanis

Edward Yu

The synthesis and structural characterization of a new class of “basic” trinuclear acetate clusters with solely divalent metal ions and a central μ3-OH ligand are reported. These molecules with the [(py)5MII3(OAc)3(μ3-OH)(cat)] stoichiometry (M = Mn, Fe, Co, Ni) are X-ray isomorphous and isostructural and contain octahedrally coordinated metal ions. The core consists of an antiferromagnetically coupled M3 unit with the metals arranged in the corners of an isosceles triangle. Two of the M−M distances vary between 2.98 and 3.16 Å, and the longer M−M distance is observed between 3.65 and 3.76 Å. As expected from the relative ionic radius lengths, …


Absolute Integrated Cross Sections For Some O2 Herzberg I Transitions Near 248–249 Nm, Zhen-Chuan Bao, Edward Yu, John R. Baker Jan 1995

Absolute Integrated Cross Sections For Some O2 Herzberg I Transitions Near 248–249 Nm, Zhen-Chuan Bao, Edward Yu, John R. Baker

Edward Yu

A frequency doubled tunable dye laser system with ∼0.4 cm−1 resolution was used to measure the integrated absorption cross sections of more than 20 rotational transitions in the O2 Herzberg I (A  3Σ+ u ←X  3Σ− g ) 8‐0 and 9‐0 vibrational bands near 248 nm and 249 nm. Oxygen pressures from 200 to 800 Torr and path lengths from 5 to 25 m were employed. The measured absorbances were fitted using a nonlinear least squares analysis and Beer’s Law to obtain absolute values for the individual transition integrated cross sections in good agreement with a recent spectral simulation and …


Surface-Induced Ordering In Asymmetric Block Copolymers, Y. Liu, W. Zhao, X. Zheng, Alexander H. King, A. Sing, M. H. Rafailovich, J. Sokolov, K. H. Dai, E. J. Kramer, S. A. Schwarz, O. Gebizlioglu, S. K. Sinha Jul 1994

Surface-Induced Ordering In Asymmetric Block Copolymers, Y. Liu, W. Zhao, X. Zheng, Alexander H. King, A. Sing, M. H. Rafailovich, J. Sokolov, K. H. Dai, E. J. Kramer, S. A. Schwarz, O. Gebizlioglu, S. K. Sinha

Alexander H. King

The surface-induced ordering in thin films of asymmetric deuterated polystyrene (dPS)- poly(viny1pyridine) (PVP) diblock and triblock copolymers of comparable polymerization index and PVP volume fraction - 0.25) was studied using transmission electron microscopy, atomic force microscopy, secondary ion massspectrometry, and neutron reflectivity. The morphology of both di- and triblock copolymer films was found to be cylindrical except for the layer adjacent to the silicon oxide surface, which due to the strong interaction of silica with PVP, was lamellar. The spacing between adjacent cylindrical layers was found to be consistent with mean field theory predictions. In the triblock copolymer films the …


Tables Of Coincidence Orientations For Ordered Tetragonal L Lo Alloys For A Range Of Axial Ratios, Abha Singh, Alexander H. King Jan 1993

Tables Of Coincidence Orientations For Ordered Tetragonal L Lo Alloys For A Range Of Axial Ratios, Abha Singh, Alexander H. King

Alexander H. King

In this paper we develop and apply techniques for computation of CSL, DSCL and step-vector data for grain boundaries in tetragonal materials for a range of axial ratios. This has application to L10 alloys including TiA1, which is a candidate for lightweight high-temperature structural applications. Our results are compared with others and found to be more accurate and complete. We provide data for a wider range of axial ratios than those considered by previous workers. We have also derived equivalent quaternions for tetragonal crystals in tetragonal-crystal coordinates and listed conditions for selecting a unique reduced rotation in tetragonal-crystal coordinates so …


A Geometrical Rationalization Of The Special Properties Of The 14° [001] Grain Boundary In Yba2cu3o7−Δ, Alexander H. King, Abha Singh Jan 1993

A Geometrical Rationalization Of The Special Properties Of The 14° [001] Grain Boundary In Yba2cu3o7−Δ, Alexander H. King, Abha Singh

Alexander H. King

14° [001] tilt grain boundaries in YBa2Cu3O7−δ have been found to exhibit anomalously good superconducting critical currents, associated with magnetic flux pinning, although no special interfacial structure has heretofore been associated with this misorientation. We present an analysis of the geometry of the grain boundary in question and show that it can correspond to a special interface, within the definition of constrained lattice coincidence, which may lead to new understanding of the superconducting behavior of grain boundaries. Our analysis shows that the tetragonal‐to‐orthorhombic phase transformation may have important effects upon grain boundary structure and properties, indicating new approaches to producing …


Tem Observations Of The Mechanism Of Delamination Of Chromium Films From Silicon Substrates, D. Goyal, Alexander H. King Feb 1992

Tem Observations Of The Mechanism Of Delamination Of Chromium Films From Silicon Substrates, D. Goyal, Alexander H. King

Alexander H. King

We have observed the complete delamination of polycrystalline chromium films from single crystal silicon substrates during deposition due to the formation of high internal stresses. These intrinsic stresses can give rise to interfacial defects which assist in the separation of the film from the substrate. Stresses in the film are balanced by stresses in the substrate, which cause mechanical failure in the substrate near the interface. Extensive arrays of dislocations and cracking of the substrate have been observed. We find that the delamination of the films from the substrate is initiated by the formation of damage in the substrate, rather …


The Interaction Between Dislocations And Intergranular Cracks, H. Zhang, Alexander H. King, R. Thomson Feb 1991

The Interaction Between Dislocations And Intergranular Cracks, H. Zhang, Alexander H. King, R. Thomson

Alexander H. King

The elastic interactions of dislocations and intergranular cracks in isotropic materials have been studied. In the first part of the paper, a model based on the Rice–Thomson theory is established under which the conditions for dislocation emission and crack propagation can be described in terms of an emission surface, cleavage surface, and loading line in the local k-space associated with a mixed mode intergranular crack. For a given crack, the local k-field changes with the emission of dislocations from the crack tip, which alters the balance of cleavage and emission. In the second part, we present experimental results of in …


Coincidence Orientations Of Crystals In Tetragonal Systems, With Applications To Yba2cu3o7, Abha Singh, N. Chandrasekhar, Alexander H. King Jan 1990

Coincidence Orientations Of Crystals In Tetragonal Systems, With Applications To Yba2cu3o7, Abha Singh, N. Chandrasekhar, Alexander H. King

Alexander H. King

We have developed a method for the characterization of coincidence-site lattices (CSL's) in tetragonal or near-tetragonal orthorhombic structures, by suitable modifications to the method of Grimmer & Warrington [Acta Cryst. (1987), A43, 232-243]. We have applied our method to determine coincidence rotations and the associated information appropriate for forming constrained CSL's in the high-To superconductor YBazCu307-n. The unit cell is orthorhombic with lattice parameters a = 3.82, b = 3"89 and c = 11.67 A for the nominal composition. We present tables of coincidence rotation angles, .Z, CSL, DSCL and associated step vectors up to ,~ = 50. We find …


Slip, Twinning, And Fracture At A Grain Boundary In The L12 Ordered Structure—Aς = 9 Tilt Boundary, Alexander H. King, M. H. Yoo Oct 1988

Slip, Twinning, And Fracture At A Grain Boundary In The L12 Ordered Structure—Aς = 9 Tilt Boundary, Alexander H. King, M. H. Yoo

Alexander H. King

The role of interaction between slip dislocations and a Σ = 9 tilt boundary in localized microplastic deformation, cleavage, or intergranular fracture in the Li2 ordered structure has been analyzed by using the anisotropic elasticity theory of dislocations and fracture. Screw superpartials cross slip easily at the boundary onto the (1$\overline 1$1) and the (001) planes at low and high temperatures, respectively. Transmission of primary slip dislocations onto the conjugate slip system occurs with a certain degree of difficulty, which is eased by localized disordering. When the transmission is impeded, cleavage fracture on the ($\overline 1$11) plane is predicted to …


The Further Geometry Of Grain Boundaries In Hexagonal Close-Packed Metals, Fu-Rong Chen, Alexander H. King Jan 1987

The Further Geometry Of Grain Boundaries In Hexagonal Close-Packed Metals, Fu-Rong Chen, Alexander H. King

Alexander H. King

A technique is given for finding partial DSC vectors appropriate to crystals with more than one atom per lattice site. The DSC lattice is made up of vectors that represent displacements of one crystal with respect to the other that leave the boundary structure shifted, but not complete. A new, rapid method for finding the step vectors associated with perfect DSC dislocations is described. Partial DSC vectors and step vectors for perfect DSC dislocations in hexagonal close-packed crystals are determined. The availability of reactions between lattice partial dislocations and grain boundaries in hexagonal close-packed crystals is also assessed.