# US 2025/0085243 A1 · Method for Determining Phase Transition Temperature of Molten Salts

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- Number: US 2025/0085243 A1
- Document ID: US20250085243A1
- Status: Published application
- Kind: A1
- Application number: 18/826,351
- Filed: 2024-09-06
- Published: 2025-03-13
- Earliest claimed: 2023-09-08
- Assignees: Korea Atomic Energy Research Institute
- Applicants: Korea Atomic Energy Research Institute
- Inventors: Jong Yun KIM; Tae Hyeong KIM; Hwa Kyeung JEONG; Sang Ho LIM; Han Lim CHA; Chan Yong JEONG
- Web page: https://patentgrep.com/patent/US20250085243A1

## CPC

- G01N 25/04: of melting point; of freezing point; of softening point
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

According to the present disclosure, provided is a method for determining phase transition temperature using electrical conductivity. More specifically, according to the present disclosure, there is provided a method for determining phase transition temperature using electrical conductivity, including preparing a graph of the change in electrical conductivity of molten salts according to temperature, and performing at least one mathematical analysis of (i) performing a first-order differential on the graph, (ii) performing a second-order differential on the graph; and (iii) determining the number (n) of data and resolution (AT) based on the graph to derive Tn by Equation (1) below and performing linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, T n = T max - Δ ⁢ T × n Equation ⁢ ( 1 ) where n denotes the number of data, and ΔT denotes an interval of measurement temperature and means resolution.

## Claims

### Claim 1

A method for measuring phase transition temperature using electrical conductivity, comprising:
preparing a graph of change in electrical conductivity of molten salts according to temperature; and
performing at least one mathematical analysis of (i) performing a first-order differential on the graph,
(ii) performing a second-order differential on the graph, and
(iii) determining the number (n) of data and resolution (ΔT) based on the graph to derive Tn by Equation (1) below and performing linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation,
T
n
=
T
max
-
Δ
⁢
T
×
n
Equation
⁢
(
1
)
where n denotes the number of data, and ΔT denotes an interval of measurement temperature and means resolution.

### Claim 2 (depends on 1)

The method of claim 1, wherein in case of (i), a point where a value is highest when processing the first-order differential, in case of (ii), an inflection point where the value becomes 0 when processing the second-order differential, and in case of (iii), temperature corresponding to the outlier are determined as the phase transition temperature.

### Claim 3 (depends on 1)

The method of claim 1, wherein when a difference between liquidus temperature (TL) and solidus temperature (TS) is 25° C. or lower, the mathematical analysis of (iii) is performed.

### Claim 4 (depends on 1)

The method of claim 1, wherein the temperature change refers to cooling the temperature from melting temperature of the molten salts to be analyzed or 50 to 500° C. higher than the melting temperature to room temperature or increasing the temperature from solid molten salts to the melting temperature or higher.

### Claim 5 (depends on 1)

The method of claim 1, wherein the molten salts include at least one component selected from the group consisting of LiCl—KCl, NaCl—KCl, CsCl—KCl, LiCl—NaCl—CaCl2—BaCl2, NaCl—KCl—BaCl2, CaF2, NdCl3, CeCl3, and LaCl3.

### Claim 6 (depends on 1)

The method of claim 1, wherein the phase transition temperature is liquidus temperature (TL).

### Claim 7 (depends on 1)

The method of claim 1, wherein in Equation (1) of (iii) above, n is an integer from 10 to 100, and ΔT is 2 to 10° C.

### Claim 8 (depends on 1)

The method of claim 1, further comprising re-performing the linear regression analysis and adding n as n+1 if an absolute value of a distance constant is less than a discrimination reference value, and
determining as an outlier if the absolute value of the distance constant below is greater than or equal to a discrimination reference value, and determining temperature at that point as the liquidus temperature (TL),
when applying one or more of Equations A to E below.
Z
⁡
(
A
)
=
r
i
=
y
i
-
y
^
i
(
Equation
⁢
A
)
Z
⁡
(
B
)
=
h
i
=
1
n
+
(
x
i
-
x
_
)
2
SSX
(
Equation
⁢
B
)
Z
⁡
(
C
)
=
rs
i
=
r
i
MSE
i
×
(
1
-
h
i
)
(
Equation
⁢
C
)
Z
⁡
(
D
)
=
r
i
2
(
k
+
1
)
⁢
MSE
[
h
i
(
1
-
h
i
)
2
]
(
Equation
⁢
D
)
Z
⁡
(
E
)
=
rs
i
⁢
h
i
(
1
-
h
i
)
(
Equation
⁢
E
)
(In this case, definitions of items described in each equation are as follows:
n: Number of data
k: Number of independent terms in regression model
yi: i-th y value
ŷi: Predicted i-th y value
xi: i-th x value
x: Average of x value
SSX
=
∑
(
x
i
-
x
_
)
2
SSE
=
∑
(
y
i
-
y
^
i
)
2
df
=
n
-
k
-
1
MSE
=
SSE
df
MSE
i
=
MSE
-
r
i
2
(
1
-
h
i
)
×
df
×
df
df
-
1
)

### Claim 9 (depends on 8)

The method of claim 8, wherein in the detecting of the outlier based on the distance from the linear regression equation in (iii) above, when the absolute value of the distance constant representing the distance from the linear regression equation is greater than or equal to each of the following discrimination reference values in each distance constant derivation equations A to E, it is detected as the outlier.
Equation A: 2
Equation B: Smaller value of 6/n and 0.99
Equation C: 2
Equation D: 1
Equation E: When n is less than 30, it is 1, and when n is greater than or equal to 30, it is 2/n0.5

### Claim 10 (depends on 8)

The method of claim 8, wherein the detecting of the outlier based on the distance from the linear regression equation in (iii) above ends when the liquidus temperature (TL) becomes equal to the solidus temperature (TS).

### Claim 11 (depends on 1)

The method of claim 1, further comprising:
increasing the temperature of the solid molten salts and preparing a graph of the change in electrical conductivity of the molten salts according to the temperature increase;
determining solidus temperature (TS) by performing the first-order differential or the second-order differential on the graph of the change in electrical conductivity of the molten salts according to the temperature increase;
melting the molten salts by increasing the temperature to a temperature 50 to 500° C. higher than the melting temperature of the molten salts;
preparing the graph of the change in electrical conductivity of the molten salts as the temperature decreases while cooling the temperature to room temperature; and
determining the number (n) of data and resolution (ΔT) based on the graph of the change in electrical conductivity of the molten salts according to the temperature drop to derive Tn using Equation (1) above and performing linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation,
wherein the detecting of the outlier includes, re-performing the linear regression analysis and adding n as n+1, if an absolute value of a distance constant is less than a discrimination reference value, and
determining as an outlier if the absolute value of the distance constant below is greater than or equal to a discrimination reference value, and determining temperature at that point as the liquidus temperature (TL),
when applying one or more of Equations A to E below.
Z
⁡
(
A
)
=
r
i
=
y
i
-
y
^
i
(
Equation
⁢
A
)
Z
⁡
(
B
)
=
h
i
=
1
n
+
(
x
i
-
x
_
)
2
SSX
(
Equation
⁢
B
)
Z
⁡
(
C
)
=
rs
i
=
r
i
MSE
i
×
(
1
-
h
i
)
(
Equation
⁢
C
)
Z
⁡
(
D
)
=
r
i
2
(
k
+
1
)
⁢
MSE
[
h
i
(
1
-
h
i
)
2
]
(
Equation
⁢
D
)
Z
⁡
(
E
)
=
rs
i
⁢
h
i
(
1
-
h
i
)
(
Equation
⁢
E
)
(In this case, definitions of items described in each equation are as follows:
n: Number of data
k: Number of independent terms in regression model
yi: i-th y value
ŷi: Predicted i-th y value
xi: i-th x value
x: Average of x value
SSX
=
∑
(
x
i
-
x
_
)
2
SSE
=
∑
(
y
i
-
y
^
i
)
2
df
=
n
-
k
-
1
MSE
=
SSE
df
MSE
i
=
MSE
-
r
i
2
(
1
-
h
i
)
×
df
×
df
df
-
1
,
wherein each discrimination reference value in each distance constant derivation Equations A to E is as follows:
Equation A: 2
Equation B: Smaller value of 6/n and 0.99
Equation C: 2
Equation D: 1
Equation E: When n is less than 30, it is 1, and when n is greater than or equal to 30, it is 2/n0.5)