[1] A simple formalism is presented to model chemical interactions between aerosols and reactive trace gases over a wide range of conditions. The model takes into account gas phase diffusion, mass accommodation, bulk phase chemical reactions, surface reactions and particle phase reactant diffusion from the aerosol interior toward the surface. While previous models have focused on the heterogeneous uptake of trace gases by atmospheric droplets and particles, this model focuses on the reactive transformation of condensed phase species. In limiting cases, the model leads to simple analytical expressions for the condensed phase species depletion as a function of aerosol/gas interaction time.

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Advanced research on structural steels has recently focused on the improvement of properties through the control of grain size. Grain refinement increases strength via the Hall-Petch relation, lowers the ductilebrittle transition by increasing resistance to transgranular cleavage, and reduces hydrogen embrittlement by minimizing interfacial fracture along grain or lath boundaries. However, given their different mechanisms, these properties require slightly different measures of the effective grain size. When the grains are smooth and random, all measures of the effective grain size are roughly equivalent. However, transformations in steel are often crystallographically coherent, producing a martensitic, bainitic or ferritic product that has either a Kurdumov-Sachs (KS) or a Nishiyama-Wasserman (NW) relation to the parent austenite. The 24 KS variants and 12 NW variants divide into three sets of eight, corresponding to the three Bain variants of the fcc→bcc transformation. Grain, packet or block boundaries that separate different Bain variants have significant misorientations of the {100} cleavage planes, but may have only slight misorientations of the {110} slip planes. It follows that grain refinement through coherent transformation is very effective in improving resistance to cleavage fracture and, if the boundary facets are small, to hydrogen embrittlement, but is often relatively ineffective in increasing strength. For this reason, grain refinement for increased strength is best done with incoherent transformations (such as the strain-induced ferrite transformation) while grain refinement for low-temperature toughness or hydrogen resistance is best done with coherent transformations that refine the effective grain size without overstrengthening to unacceptably low ductility.KEY WORDS: grain refinement; coherent transformations; strength; ductile-brittle transition; hydrogen embrittlement.and ductile-brittle transition temperature of structural steels obey relations of the Hall-Petch form. The yield strength is given by the classic Hall-Petch relation: (3) where K B is the appropriate Hall-Petch coefficient. While the same parameter, the grain size, d, appears in each of these equations, it is important to recognize that "grain size" has a different meaning for each of the properties of interest. The Effective Grain Size for StrengthAs we have discussed elsewhere, 5) several different theories have been advanced to explain the Hall-Petch relation for strength. Without taking a firm position with respect to these, they have the common feature that grain size limits the distance over which free slip can occur. In Fe, the primary slip planes are the {110} planes, so slip is limited by the dimension of the {110} planes within a grain. Hence the appropriate measure of grain size would appear to be the coherence length along {110}.The dependence of the Hall-Petch coefficient, K y , on the properties of the steel are also at least qualitatively common to the various theories. (4) where we have approximated the yie...

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The inherent brittle mode in dislocated lath martensitic steel is cleavage on {100} planes in the microstructure. The transition to {100} cleavage fracture on cooling determines the minimum value of the ductiule-brittle transition temperature. A half-century of research on the microstructure and toughness of lath martensitic steels has produced a semi-quantitative understanding of the brittle transition to cleavage. The results identify the crystallographic "block" of lath martensite as the effective grain size that controls cleavage, and clarify why the internal structure of a block has the microstructure it adopts. The ductilebrittle transition temperature is strongly affected by the block size. Several effective metallurgical processes are now available to refine the block size without excessive strengthening, leading to martensitic structural steels that combine high strength with good low-temperature toughness.

The geometric properties of polygranular microstructures of the Johnson-Mehl and cellular types have been studied through computer simulation. These prototypic microstructures arise naturally from the classical model of a phase transformation in a one-component solid through growth from a random distribution of nucleation sites. The

Many of the important mechanical properties of steel, including yield strength and hardness, the ductile-brittle transition temperature and susceptibility to environmental embrittlement can be improved by refining the grain size. The improvement can often be quantified in a constitutive relation that is an appropriate variant on the familiar Hall-Petch relation: the quantitative improvement in properties varies with d-1/2 , where d is the grain size. Nonetheless, there is considerable uncertainty regarding the detailed mechanism of the grain size effect, and appropriate definition of "grain size". Each particular mechanism of strengthening and fracture suggests its own appropriate definition of the "effective grain size", and how it may be best controlled.

The present paper addresses several connected issues that concern the mechanical properties of ultrafine grained martensitic steels. Recent research, particularly including EBSD studies, has clarified the complex microstructure of dislocated martensitic steels and shown the central importance of martensite blocks, which are subvolumes of laths that share a Bain variant of the parent austenite. The block-and-packet structure of the martensite appears well-designed to minimize the elastic energy introduced during the martensitic transformation. The martensite block is, ordinarily, the effective grain size for both strength and cleavage fracture. However, the role of the block in imparting strength is sensitive to carbon contamination of the block boundaries. To optimize strength carbon should be present; to minimize the ductile-brittle transition temperature it should be eliminated. When fine grain size produces high strength, it also causes low elongation. The elongation can be improved by including mechanisms, such as TRIP, that lower the initial work hardening rate.KEY WORDS: ultrafine-grained steel; martensitic steel; dislocated martensite microstructure; strength; toughness; ductility 1063© 2008 ISIJ Large prior austenite grains are divided into "packets" that are subdivided into "blocks" of martensite laths. When the blocks are small the laths are almost identical in their crystallography; they have the same KS variant. When the blocks are larger they are sometimes found to contain two interleaved KS variants in the specific pairs: V1-V4. V2-V5, V3-V6. When the blocks are interleaved pairs then the packets ordinarily contain three crystallographically distinct blocks, one made from each pair. When the blocks are single-variant the packets contain up to six distinct blocks so that each KS variant is represented. The Structural Composition of Blocks andPackets The microstructure that is described by Maki et al. [3][4][5][6][7][8] can be understood from the elastic theory of phase transformations.The energetic considerations that influence the choice of martensite variant can be developed as follows.9,10) The bcc structure is derived from the fcc by applying the "Bain strain" illustrated in Fig. 2. The fcc structure is compressed by about 23 % along one cube axis and expanded by about 12 % along the perpendicular axes (depending on the volume change) to create bcc. Since there are three choices for the compression axis, the transformation produces three distinct "Bain variants".Of course, a Bain strain that is imposed within the bulk of a fcc crystal would require a prohibitively high elastic energy. As has long been recognized, [11][12][13] that energy is lowered dramatically if the Bain strain is supplemented by a rotation and a small shear to bring the close-packed (011) plane of the bcc product into registry with one of the closepacked {111} planes of the fcc parent, and orient the plane so that low-index crystallographic directions in the plane are also aligned. If we choose the [110] g direction in the (1...