Patent ID: 8008621

Claim:
An apparatus for measuring the orientation relationship between neighboring grains and characteristics of grain boundaries by using a goniometer of a transmission electron microscope, the apparatus comprising: a goniometer mounted at the transmission electron microscope; and a measurement unit for revealing the characteristics of grain boundaries of a specimen by linear-algebraically interpreting a relationship between crystal axes and tilt axes of the specimen using the goniometer; wherein, the relationship between the crystal axes and the tilt axes of the specimen is related to a first interplanar angle θ 1 , a second interplanar angle θ 2 , and a third interplanar angle θ 3 between a first crystal axis H 4 desired to be estimated and respectively measured crystal axes H 1 , H 2 , H 3 after disposing the measured crystal axes of H 1 , H 2 , H 3 with respect to coordinates formed by a Tx axis and a Ty axis that is perpendicular to an X tilting axis and a Y tilting axis of the goniometer mounted on a transmission electron microscope; wherein, the first crystal axis H 4 is calculated by ( h 1 ′ k 1 ′ l 1 ′ h 2 ′ k 2 ′ l 2 ′ h 3 ′ k 3 ′ l 3 ′ ) ⁢ ( h k 1 ) = ( cos ⁢ ⁢ θ 1 cos ⁢ ⁢ θ 2 cos ⁢ ⁢ θ 3 ) wherein h′i=hi/√{square root over (hi 2 +ki 2 +li 2 )}, k′i=ki/√{square root over (hi 2 +ki 2 +li 2 )}, l′i=li/√{square root over (hi 2 +ki 2 +li 2 )}, i=1 2, 3; wherein the first, second, and third interplanar angles of θ 1 , θ 2 , and θ 3 have a relationship with tilt angles described by: ( cos ⁢ ⁢ θ 1 cos ⁢ ⁢ θ 2 cos ⁢ ⁢ θ 3 ) = ( cos ⁢ ⁢ Δ ⁢ ⁢ Tx 1 + cos ⁢ ⁢ Δ ⁢ ⁢ Ty 1 - 1 cos ⁢ ⁢ Δ ⁢ ⁢ Tx 2 + cos ⁢ ⁢ Δ ⁢ ⁢ Ty 2 - 1 cos ⁢ ⁢ Δ ⁢ ⁢ Tx 3 + cos ⁢ ⁢ Δ ⁢ ⁢ Ty 3 - 1 ) ; and wherein differences between (Tx 1 ,Ty 1 ) correspond to crystal axis H(A) 1 (h 1 k 1 l 1 ), differences between (Tx 2 ,Ty 2 ) correspond to crystal axis H(A) 2 (h 2 k 2 l 2 ), and differences between (Tx 3 ,Ty 3 ) correspond to crystal axis H(A) 3 (h 3 k 3 l 3 ).