US 8,008,621 B2Granted

Apparatus of measuring the orientation relationship between neighboring grains using a goniometer in a transmission electron microscope and method for revealing the characteristics of grain boundaries

AssigneeKorea Institute of Machinery & Materials

InventorsHi Won Jeong, Seong Moon Seo, Hyun Uk Hong, Young Soo Yoo, In Soo Kim, Baig Gyu Choi, Chang Yong Jo

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Abstract

An apparatus and method for measuring the crystallographic orientation relationship of neighboring grains and the characteristics of grain boundaries using a goniometer of a transmission electron microscope are disclosed to check the orientation relationship between two crystals and the characteristics of grain boundaries with a small error in real time. An apparatus for measuring the orientation relationship between neighboring grains and the characteristics of grain boundaries by using a goniometer of a transmission electron stereoscope, the apparatus comprising a goniometer mounted at a transmission electron microscope and a measurement unit for revealing the characteristics of grain boundaries of a specimen by linear-algebraically interpreting the relationship between crystal axes and tilt axes of the specimen using the goniometer.

Claims8

Dependent claims

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 θ1, a second interplanar angle θ2, and a third interplanar angle θ3 between a first crystal axis H4 desired to be estimated and respectively measured crystal axes H1, H2, H3 after disposing the measured crystal axes of H1, H2, H3 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 H4 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 (hi2+ki2+li2)}, k′i=ki/√{square root over (hi2+ki2+li2)}, l′i=li/√{square root over (hi2+ki2+li2)}, i=1 2, 3;
wherein the first, second, and third interplanar angles of θ1, θ2, and θ3 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 (Tx1,Ty1) correspond to crystal axis H(A)1(h1k1l1), differences between (Tx2,Ty2) correspond to crystal axis H(A)2(h2k2l2), and differences between (Tx3,Ty3) correspond to crystal axis H(A)3(h3k3l3).

137 more elements

A method for measuring the orientation relationship between neighboring grains and characteristics of grain boundaries by using a goniometer of a transmission electron microscope, the method comprising:

measuring crystal axes H1, H2, and H3 by using the goniometer;
comparing measured interplanar angles among the crystal axes of H1, H2, and H3 measured with (Tx, Ty) angle pairs of the goniometer mounted at the transmission electron microscope and crystallographically calculated interplanar angles among the crystal axes of H1, H2, and H3;
selecting a (Tx, Ty) angle pair at which a difference between the measured interplanar angles and the crystallographically calculated interplanar angles is minimized;
establishing relationship between tilt axes and the crystal axes;
obtaining a misorientation matrix between two crystals;
and
revealing the characteristics of a grain boundary by using the misorientation matrix;
wherein, the relationship between the crystal axes and the tilt axes of the specimen is related to a first interplanar angle θ1, a second interplanar angle θ2 and a third interplanar angle θ3 between a first crystal axis H4 desired to be estimated and respectively measured crystal axes H1, H2, and H3 after disposing the measured crystal axes of H1, H2, and H3 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 goniometer mounted on a transmission electron microscope;
wherein, the first crystal axis H4 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 (hi2+ki2+li2)}, k′i=ki/√{square root over (hi2+ki2+li2)}, l′i=li/√{square root over (hi2+ki2+li2)}, i=1 2, 3;
wherein the first, second and third interplanar angles of θ1, θ2 and θ3 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 (Tx1,Ty1) correspond to crystal axis H(A)1(h1k1l1), differences between (Tx2,Ty2) correspond to crystal axis H(A)2(h2k2l2), and differences between (Tx3,Ty3) correspond to crystal axis H(A)3(h3k3l3).

141 more elements

Dependencies are inferred from the claim text.