A correlation among total vacancy concentration, grain boundary structure and grain growth behavior was found.
Further increase in the total vacancy concentration resulted in a change in grain boundary structure from faceted to rough and suppression of abnormal grain growth.
When the total vacancy concentration was low by any means, grain boundaries were well faceted and abnormal grain growth occurred in the presence of {1 1 1} double twins.
However, as the total vacancy concentration increased, the fraction of faceted grain boundary gradually decreased and the formation of {1 1 1} twins was suppressed.
We treat two limiting cases, one where the total vacancy number is conserved (that is, there are no available sources and sinks) and one where the vacancy concentration is kept in equilibrium (the case of dense sources and sinks).
These observed changes in grain growth behavior, including a grain growth anomaly with donor doping, can therefore be attributed to a change in boundary mobility with grain boundary structure, which was governed by the total vacancy concentration.
The total vacancy rate in the office market immediately around Penn Station, including the whole Gateway Complex, the Legal Center, One Newark Center, 744 Broad Street and Prudential's headquarters building, is slightly less than 8percentt, said Bryn Cinque, a broker at GVA Williams who specializes in Newark properties.
Accordingly, edge sites can lead to higher reactivity in a mineral like acid birnessite, even though it has a greater proportion of total vacancy sites.
It is a measure of the total vacancy concentration existing in the material and can be estimated using the following equation [34, 35]: beta =left(frac{a_{mathrm{th}}^3-{a}_{exp}^3}{a_{mathrm{th}}^3}right)times 100%.
The welfare measure consists of aggregate production minus total vacancy costs, i.e. note that (u_{l}Theta _{l}k=left ({v_{l}^{F}}+{v_{l}^{I}}right k,~l={m,h}), and minus the aggregate costs of education.
