The Provisional Low Temperature Scale from 0.9⁢mK to 1⁢K , PLTS-2000

1. The scale

The scale is defined by the following equation relating the melting pressure $p$ of ³He to temperature $T_{2 000}$ :

$p / MPa = \sum_{i = - 3}^{+ 9} a_{i} {(T_{2 000} / K)}^{i}$

$a_{- 3} = - 1.385 544 2 \cdot 10^{- 12}$

$a_{- 2} = 4.555 702 6 \cdot 10^{- 9}$

$a_{- 1} = - 6.443 086 9 \cdot 10^{- 6}$

$a_{0} = 3.446 743 4 \cdot 10^{0}$

$a_{1} = - 4.417 643 8 \cdot 10^{0}$

$a_{2} = 1.541 743 7 \cdot 10^{1}$

$a_{3} = - 3.578 985 3 \cdot 10^{1}$

$a_{4} = 7.149 912 5 \cdot 10^{1}$

$a_{5} = - 1.041 437 9 \cdot 10^{2}$

$a_{6} = 1.051 853 8 \cdot 10^{2}$

$a_{7} = - 6.944 376 7 \cdot 10^{1}$

$a_{8} = 2.683 308 7 \cdot 10^{1}$

$a_{9} = - 4.587 570 9 \cdot 10^{0}$

2. Background to the PLTS-2000

The melting pressure of ³He was chosen as the property on which the extension of the ITS-90 should be based because of the sensitivity and reliability with which it may be measured over a wide range (covering more than three decades of temperature) apart from a narrow region around the pressure minimum at $315.24 mK$ (see Figure 1). The pressure minimum itself has the compensating advantage of providing a convenient pressure fixed point for calibrating the pressure transducer (the pressure must be measured using a transducer in situ because for temperatures below the minimum a sensing line will be blocked with solid ³He and the cell is therefore isolated).

The pressure minimum is one of four natural features which may be located and used as fixed points of pressure and temperature, the others being the transition to the superfluid ‘A’ phase, the ‘A to B’ transition in the superfluid and the Néel transition in the solid. The pressure and temperature values of these four points on the PLTS-2000 are:

Point	$p / MPa$	$T_{2 000} / mK$
minimum	$2.931 13$	$315.24$
A	$3.434 07$	$2.444$
A-B	$3.436 09$	$1.896$
Néel	$3.439 34$	$0.902$

The standard uncertainty of the scale in thermodynamic terms is estimated to be $0.5 mK$ down to $500 mK$ , decreasing linearly to $0.2 mK$ at $100 mK$ . It decreases further with falling temperature, but in percentage terms it increases to about $0.3 %$ of $T$ at $25 mK$ and $2 %$ of $T$ at $0.9 mK$ . The standard uncertainties in the absolute pressures are estimated to be about $60 Pa$ (in about $3 MPa$ ).

Figure 1 — The ³He melting pressure $p$ (full line) and the absolute value of the derivative $d p / d T$ (dashed line) vs. temperature. $T_{N}$ , $T_{B}$ and $T_{A}$ indicate the temperatures of three phase transitions in solid or liquid ³He.