On misorientation distribution evolution during anisotropic grain growth

TLDR: In this paper, the development of texture and boundary character during annealing, three-dimensional grain crystallography and crystallographically mediated grain boundary properties were incoporated into a finite temperature Monte Carlo model for grain growth.

About: This article is published in Acta Materialia.The article was published on 2001-09-03 and is currently open access. It has received 215 citations till now. The article focuses on the topics: Grain boundary strengthening & Grain boundary.

Figures

Fig. 7. Typical microstruclure during grain growth from a single-component initial texture. Grain boundaries are shaded according to misorienlation angle; high-angle boundaries are darker, low-angle boundaries are ligh1er. Grain boundary energy and mobilily are given by equation (2) with 8, = 15•, and the system was evolved from a 5002-sile random s1ruc1urc for 10,000 MCSS. Note the pre$ence of few-sided, highly curved grains and of slable four-grain junclions ( quadrijunctions).

Fig. 3. Time evolution of mean groin area during grain growth in textured polycrystals. Polycrystals with random texture exhibit power-law growth with the normal grain growth exponent 11 = 0.96 (dOlled line), independent of the value of 6m in equation (2). Polycrystnls with a single-component texture follow power-Jaw growth with a decreased exponent 11 = 0.62 (dashed line).

Fig. 2. Grain area distributions during grain growth. System~ with random crystallographic texture produce the s~me grain area distribution as nonnnl grain growth (isotropic boundosy propenies and no texture). Systems with a single texture component produce a grain area distribution that is weighted towards sm:11l grains. All distributions were measured at t = 1000 MCSS. The isotropic and r:~~tdom texture distributions are steady-state; however, there is some evidence that the single-component texture system may not reach a steady-state area distribution.

Fig. 9. Evolution of the mean misorientation angle (8) and the sltllldard deviation of the misorientation distribution G(6) during evolution of polycrystal~ with a single-component texture. Both (9) and G(8) decrease in time by a power Jaw with exponent Jl = -0.41 (solid line).

Frequently asked questions

Q1. What are the contributions in "On misorientation distribution evolution during anisotropic grain growth" ?

Holm et al. this paper studied the development of texture and boundary character during annealing and crystallographically mediated grain boundary properties were incoporated into a finite tempcrnture Monte Carlo model for grain growth. 

Q2. What are the future works in "On misorientation distribution evolution during anisotropic grain growth" ?

In order to study the development of texture and boundary character during annealing. 

Q3. How many equivalents of the rotation are there?

In this study the authors only consider cubic crystallography which, due to symmetry of the orientation space, has 24 geometrically equivalent representations of any rotation. 

Q4. What is the reason for the depressed exponents?

It is possible that such depressed exponents are a result of decreasing average boundary mobility arising from the tightening of crystallographic texture or from other effects such as solute accumulation. 

Q5. How can the orientation of the axes of a crystal be specified?

The orientation of the axes of a crystal with respect to an external frame of reference (the specimen axes)can be specified by a rotation in three-dimensional space (posessing three degrees of freedom). 

Q6. How can step flow processes be used to reduce lattice effects?

step flow processes can allow the boundary to find and track its energetically favored position, restoring correct grain junction angles and permitting free boundary motion. 

Q7. How many MCSSs are used to calculate the time clock?

After each flip attempt, the time clock is incremented by 1/(NQ) Monte Carlo steps per site per index (MCSS), where Q is the number of allowed orientations. 

Q8. What is the role of texture in polycrystalline materials?

It is well known that crystallographic texture plays an important role in determining the physical, electrical and magnetic properties of polycrystalline materials. 

Q9. How many orientations are assigned to each grain in the initial structure?

Each grain in the initial structure is assigned a crystallographic orientation from a list of 999 orientations, randomly distributed in Euler space. 

Q10. What is the common reason why CSLs are rarely observed in general materials?

CSL boundaries are seldom observed in general materials, as CSL formation requires three independent orientation relationships to be satisfied. 

Q11. Why do the boundary energy and mobility vary with small changes?

Because all boundaries in the system arc far below the high-angle cutoff 9., in equation (2}, the boundary energy and mobility vary greatly with small changes in misorientation. 

Q12. What is the effect of the numberweighted MDFs on the length of low-?

For tlle same structures, the numberweighted MDFs (plotting the number of each boundary type relative to the number of boundaries) show a minimal increase in low-angle boundaries. 

Q13. What is the purpose of this paper?

Thus the aim of this paper is twofold: (I) to discuss the incorporation of misorientation-dependent boundary properties in Potts model simulations, and (2) to investigate the development of texture and MDF during grain growth. 

Q14. Why is the y-jl effect poorly characterized?

Because J.l. is poorly characterized compared with y, in this study the authors generally ignore the effect of Jl (i.e., set Jl = l), so that M = r. 

Q15. How is the misorientation of the boundary in the system calculated?

(••sThe misorientation of each boundary in the system 1•"' is calculated, and the boundary energy and mobility "'" are assigned using equation (2) with 8,11 = 15°. 

Q16. What is the speed of grain growth in the single-component texture?

In the single-component texture, grain growth is considerably slower than for normal grain growth, with a time exponent n = 0.61, as shown in Fig. 

Q17. What is the way to improve the corrosion resistance of polycrystalline materials?

Tantalizing evidence of the effectiveness of this approach has been provided by Palumbo et al. [2, 3], who have developed processing routes that dramatically improve the corrosion resistance of certain alloys by increasing the fraction of coincident site lattice (CSL) boundaries present in the microstructure. 

Q18. What is the effect of the gcnernled MDFs?

The MDFs produced were identical to those gcnernled with the anisotropic mobilities, indicating that energy is more important than mobility in determining the steady-state MDF. 

Q19. What is the rate of change of the average grain size?

The rate of change of the average grain size, (R), is given byd(R) c 1(M} dt= (R}' (I I)where (M) is the average reduced mobility of the grain boundaries and c1 is a geometrical constant.