P–T phase diagram for NH4F

Solid State Sciences 4 (2002) 529–534 www.elsevier.com/locate/ssscie

P–T phase diagram for NH4F S. Saliho˘glu a,∗ , H. Yurtseven a , Y. Enginer a,b a Department of Physics, Istanbul Technical University, 80626 Maslak, Istanbul, Turkey b Department of Physics, I¸sık University, 80670 Maslak, Istanbul, Turkey

Received 4 February 2002; accepted 11 February 2002

Abstract In this study we obtain a P–T phase diagram of NH4 F using the mean-field theory. We fit our calculated phase line equations to the experimental P–T phase diagram. By choosing appropriately the coefficients in the free-energy expansions, our calculated phase diagram agrees well with the experimentally observed phase diagram of NH4 F.  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Phase diagram; Mean-field theory; Ammonium floride

1. Introduction Ammonium halides have the disordered β and the ordered phases, namely, antiferro-ordered γ and ferro-ordered δ phases. Regarding these phases in the ammonium halide structures, the P–T phase diagrams have been obtained experimentally in the literature [1–12]. Theoretically, the phase diagrams of ammonium halides have also been studied [13–19]. Ammonium floride exhibit various high-pressure phases. Among those phases I, II and III are well-known with their crystal structures. As a first time, Stevenson [1] obtained experimentally the phase transition between phases I and II at 3.6 kbar pressure at room temperature by means of the compressibility measurements in NH4 F. This initiated the second phase transition between phases II and III at 11.5 kbar at room temperature due to Svenson and Tedeschi [20]. There also occurs at moderately low pressures up to about 10 kbar at above 150 ◦ C phase IV. As the temperature increases further at these pressures, NH4 F melts into the liquid state. Among those phases, the crystal structure of phase II has been studied using X-ray diffraction by Morosin and Schirber [21]. By means of the X-ray and thermal analysis, the phases II and III have also been studied by Nabar et al. [22]. The crystal structure of phase I has been determined as a wurtzite-like structure by Wyckoff [23], whereas phase * Correspondence and reprints.

E-mail address: [email protected] (S. Saliho˘glu).

III has been determined to have a distorted CsCl-like structure, as reported in the work of Pistorius [7]. The crystal structure of phase II is unknown, as indicated in the P–T phase diagram due to Pistorius [4]. However, Morosin and Schirber [21] has given a tetragonal structure for phase II. The crystal structure of phase II has not been studied to calculate a P–T phase diagram of NH4 F by Raghurama and Narayan [11] who have predicted the ZnO structure (wurtzite-like) for phase I, CsCl structure for phase III and NaCl structure for phase IV using the distributed charge model. Their theory predicts a pressure transition at room temperature from the ZnO structure directly to the CsCl structure without an intermediate NaCl phase [11]. Phases I, II and III have been studied using Raman spectroscopic technique in the literature. Durig and Antion [24] have obtained the Raman spectrum of phase I in NH4 F at 1 bar and −170 ◦ C. The Raman spectra of phases I and II have been measured by Wong and Whalley [25]. Apart from the Raman spectra measured for phases I and II, Zou et al. [26] have measured the Raman spectrum of phase III at 25 ◦ C, where the pressure transition from phase II to phase III takes place at 11.5 kbar. Zou et al. [26] have also suggested two new phases, namely, phase V at 15 kbar and phase VI at 143 ± 0.5 kbar at 20 ◦ C, which have been obtained from the Raman spectra of phases V and VI. In this study we calculate the P–T phase diagram of NH4 F including the phases I, II, III and IV by means of the mean-field model which we have developed. We have calculated P–T phase diagrams in ammonium halides, in particular, NH4 Cl and NH4 Br using the mean-field

1293-2558/02/$ – see front matter  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 2 9 3 - 2 5 5 8 ( 0 2 ) 0 1 2 8 8 - 8

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theory [19]. The calculated phase line equations are fitted to the experimentally observed P–T phase diagram due to Zou et al. [26], which can also be compared with the phase diagram of NH4 F due to Pistorius [4]. In this study by choosing appropriately the coefficients in the free-energy expansions, our theoretical phase diagram calculated from the mean-field theory coincides with the experimentally observed phase diagram. We note that we have taken liquid– phase I, liquid–phase IV, liquid–phase III, phase I–phase II, phase I–phase IV, phase II–phase IV, phase II–phase III transitions as of first order. In Section 2 we present our mean-field model and give the phase line equations. In Section 3 we give our results and discussion. Finally, conclusions are given in Section 4.

2. Theory

where F0 is given by a22 (2.12) . 4a4 For the first order liquid–phase I transition we should have the condition that F0 = −

FL = FI .

(2.13)

Using this condition and Eq. (2.9) the phase line equation for the liquid–phase I transition becomes a6 a23 a22 + = 0. 4a4 8a43

(2.14)

The phase line equations for the other phases are tabulated in Table 1. In deriving these phase line equations we have used the ansatzs a2 a6 (2.15)  1, a42

The free energies of phases I, II, III, IV, V and VI can be written as

b2 b6  1, b42

(2.16)

FI = a2 Ψ 2 + a4 Ψ 4 + a6 Ψ 6 ,

(2.1)

6

FII = b2 µ + b4 µ + b6 µ ,

(2.2)

c2 c6  1, c42

(2.17)

FIII = c2 θ 2 + c4 θ 4 + c6 θ 6 ,

(2.3)

FIV = d2 η + d4 η + d6 η ,

(2.4)

d2 d6  1, d42

(2.18)

FV = e2 ρ 2 + e4 ρ 4 + e6 ρ 6 ,

(2.5)

FVI = g2 σ + g4 σ + g6 σ ,

(2.6)

e2 e6  1, e42

(2.19)

g2 g6  1. g42

(2.20)

2

2

2

4

4

4

6

6

where Ψ , µ, θ , η, ρ and σ are the order parameters of the phases I, II, III, IV, V and VI, respectively. And we take a2 > 0, a4 < 0 and a6 > 0; b2 > 0, b4 < 0 and b6 > 0; c2 > 0, c4 < 0 and c6 > 0; d2 > 0, d4 < 0 and d6 > 0; e2 > 0, e4 < 0 and e6 > 0; g2 > 0, g4 < 0 and g6 > 0. The free energy of the liquid phase is FL = 0. For the liquid–phase I transition minimizing Eq. (2.1) with respect to Ψ gives 
 1/2  1  Ψ2 = (2.7) −a4 − a42 − 3a2a6 . 3a6

we can simplify the Ψ value given by Eq. (2.7) as 
3 2∼ 2 Ψ = Ψ0 1 + x , 4

(2.8)

a2 . 2a4

Inserting Eq. (2.9) into Eq. (2.1) gives 
1 ∼ FI = F0 1 + x , 2

(3.1)

a4 = a40,

(3.2)

3/2 a6 = k0 a40 (2 + k0 )1/2



× 8 m0 m(P , T ) + (2 + y0 )

(2.9)

where Ψ0 is given Ψ02 = −

In order to satisfy phase line equations given in Table 1, it is convenient to write 1/2

2 d20 a2 = 8a40 m0 m(P , T ) + (2 + y0 ) 8f0 f (P , T ) × (2 + k0 )−1/2 ,

By making the ansatz a2 a6 x ≡ 2  1, a4

3. Results and discussion

−1/2



b2 = 8b40 n0 n(P , T ) + m0 m(P , T ) + u0 u(P , T )

(2.10)

(2.11)

2 d20 8f0 f (P , T )

+ (2 + y0 )

b4 = b40,

2 d20 8f0 f (P , T )

1/2

, (3.3)

(2 + l0 )−1/2 , (3.4) (3.5)

S. Saliho˘glu et al. / Solid State Sciences 4 (2002) 529–534

Table 1 Phase line equations which are obtained from the free energies given by Eqs. (2.1)–(2.6) for NH4 F Phase transition



e2 = 8e40 w0 w(P , T ) + n0 n(P , T ) + v0 v(P , T ) + (2 + y0 )

Phase line equation a22

Liquid–phase I

4a4 d22

Liquid–phase IV

4d4 c22

Liquid–phase III

4c4

+ + +

a6 a23 8a43 d6 d23 8d43 c6 c23 8c43

=0

Phase I–phase IV

2a22 a42 + a6 a23

Phase II–phase IV

2b22 b42 + b6 b23

=

8a43

=

8a43 8b43

=

Phase III–phase V

2c22 c42 + c6 c23

Phase V–phase VI

2e22 e42 + e6 e23

8c43 8e43

= =

2b22 b42 + b6 b23 8b43 2d22 d42 + d6 d23

2 d20 + (2 + y0 ) 8f0 f (P , T )

8d43

8e43 2g22 g42 + g6 g23

+ (2 + y0 )

2 d20 8f0 f (P , T )

1/2

d2 = d20 , d4 = f0 f (P , T ), d6 =

f02 f 2 (P , T )y0 , d20

−1/2 ,

−1  f (P , T ) = f1 (P , T ) + f2 (P , T ) + f3 (P , T ) . (3.6)

(3.18)

 f2 (P , T ) =

−1/2



(3.9) f3 (P , T ) = (3.10) (3.11) (3.12)

(3.19)

In Eqs. (3.1)–(3.19) a40 , b40 , c40 , e40 and g40 are negative constants in the units of J; d20 is a positive constant in the units of J; f0 , m0 , n0 , u0 , v0 , w0 and h0 are positive constants in the units of J ◦ C−1 , k0 , l0 , z0 , y0 , s0 and t0 are positive unitless constants. The functions f1 (P , T ), f2 (P , T ), f3 (P , T ), m(P , T ), n(P , T ), u(P , T ), v(P , T ), w(P , T ) and h(P , T ) in Eqs. (3.1)–(3.19) are given by  T − α11 + α12 P , for 0
P
4.65 kbar, f1 (P , T ) = 0, otherwise,

3/2

,

2 d20 8f0 f (P , T )

where

c6 = c40 (2 + z0 )1/2 z0

× 8 n0 n(P , T ) + v0 v(P , T ) 2 d20 8f0 f (P , T )

(2 + t0 )−1/2 ,

2 (2 + t0 )1/2 g6 = t0 g40

× 8g40 h0 h(P , T ) + w0 w(P , T ) + n0 n(P , T )

+ (2 + y0 )

(3.7) (3.8)

+ (2 + y0 )

1/2

+ v0 v(P , T )

(2 + z0 )−1/2 ,

c4 = c40 ,

(3.15)

(3.16) (3.17)

8g43

−1/2

+ (2 + y0 )

2 d20 8f0 f (P , T )

g4 = g40 ,

3/2

,

,

+ n0 n(P , T ) + v0 v(P , T )

2d22 d42 + d6 d23

2e22 e42 + e6 e23

−1/2



g2 = 8g40 h0 h(P , T ) + w0 w(P , T )

8d43

b6 = b40 (2 + l0 )1/2 l0

× 8 n0 n(P , T ) + m0 m(P , T ) + u0 u(P , T ) 2 d20 + (2 + y0 ) 8f0 f (P , T )

c2 = 8c40 n0 n(P , T ) + v0 v(P , T )

(2 + s0 )−1/2 ,

2 e6 = s0 e40 (2 + s0 )1/2

× 8e40 w0 w(P , T ) + n0 n(P , T ) + v0 v(P , T )

2b22 b42 + b6 b23 2c22 c42 + c6 c23 = 8b43 8c43

Phase II–phase III

1/2

(3.13) (3.14)

=0

2a22 a42 + a6 a23

2 d20 8f0 f (P , T )

e4 = e40 ,

=0

Phase I–phase II

531

 m(P , T ) =

(3.20) T − α21 − α22 P + α23 P 2 , 0, T − α31 − α32 P , 0,

for 4.65 < P
17.04 kbar, otherwise, (3.21) for P > 17.04 kbar, otherwise, (3.22)

T − α41 + α42 P , 0,

for 4.65
P
6.95 kbar, otherwise, (3.23)

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S. Saliho˘glu et al. / Solid State Sciences 4 (2002) 529–534



T − α51 − α52 P , 0,

for 6.95 < P < 17.04 kbar, otherwise, (3.24)  T + α61 − α62 P , for 2.5
P < 6.95 kbar, u(P , T ) = 0, otherwise, (3.25)  T + α71 v(P , T ) = − α72 P , for 10.5
P < 17.04 kbar, 0, otherwise, (3.26)  ◦ α81 (T − T1 ) for T1 = 20 C and w(P , T ) = + α82 (P − P1 ), P1 = 15 kbar, 0, otherwise, (3.27)  ◦ for T2 = 20 C and α91 (T − T2 ) h(P , T ) = + α92 (P − P2 ), P2 = 143 kbar, 0, otherwise, (3.28) n(P , T ) =

where α11 = 230.23 ◦ C,

α12 = 3 ◦ C kbar−1 ,

α21 = 141.05 ◦ C,

α22 = 18.820 ◦ C kbar−1 ,

(3.29)

α23 = 0.5714 ◦ C kbar−2 , α31

= 145.45 ◦ C,

α41 = 290.7

◦ C,

α51 = 100

◦ C,

α61 = 100

◦ C,

α71 = 486.36 ◦ C,

(3.30)

α32 = 8.8

◦ C kbar−1 ,

α42 = 15.99 α52

◦ C kbar−1 ,

= 11.45 ◦ C kbar−1 ,

α62 = 40

Fig. 1. Our calculated phase diagram of NH4 F. Calculated phase lines are obtained from a fitting to the experimental data given in Zou et al. [26] and Pistorius [4]. Both experimental and theoretical phase lines are represented by solid lines.

(3.31) (3.32) (3.33)

◦ C kbar−1 ,

(3.34)

α72 = 45.8 ◦ C kbar−1 ,

α82 = 1 ◦ C kbar−1 ,

(3.36)

α91 = 1,

α92 = 1 ◦ C kbar−1 .

(3.37)

Using Eqs. (3.1)–(3.19) we can write the free energies of phases I, II, III, IV, V and VI, given by Eqs. (2.1)–(2.6), respectively, as 2 d20 , 8f0 f (P , T ) FII = −n0 n(P , T ) − m0 m(P , T ) − u0 u(P , T ) 2 d20 , − (2 + y0 ) 8f0 f (P , T )

FIII = −n0 n(P , T ) − v0 v(P , T ) − (2 + y0 )

2 d20 = 0. 8f0 f (P , T )

(3.44)

Experimentally, the L–I transition occurs in the region 0
P
4.65 kbar. (See Fig. 1.) In this pressure region m(P , T ) = 0, f2 (P , T ) = 0 and f3 (P , T ) = 0. (See Eqs. (3.23), (3.21) and (3.22).) Hence in this region we get from Eq. (3.19) that f (P , T ) = (f1 (P , T ))−1 . Therefore from Eq. (3.44) we obtain the phase line equation for L–I transition as

(3.38)

f1 (P , T ) = 0.

(3.39)

This function f1 (P , T ) given by Eqs. (3.20) and (3.29) is found from fitting to the experimental data. (See Fig. 1.) For the liquid–phase IV transition the phase line equation is FIV = 0, so using Eq. (3.41) we get the phase line equation for L–IV transition as

2 d20 , 8f0 f (P , T ) (3.40)

2 d20 FIV = −(2 + y0 ) , 8f0 f (P , T ) FV = −w0 w(P , T ) − n0 n(P , T ) − v0 v(P , T ) 2 d20 , − (2 + y0 ) 8f0 f (P , T ) FVI = −h0 h(P , T ) − w0 w(P , T ) − n0 n(P , T ) 2 d20 − v0 v(P , T ) − (2 + y0 ) . 8f0 f (P , T )

−m0 m(P , T ) − (2 + y0 )

(3.35)

α81 = 1,

FI = −m0 m(P , T ) − (2 + y0 )

For the liquid–phase I transition the phase line equation is FI = 0, so using Eq. (3.38) we obtain the phase line equation for L–I transition as

(3.41)

(3.42)

(3.43)

−(2 + y0 )

2 d20 = 0. 8f0 f (P , T )

(3.45)

(3.46)

Experimentally, the L–IV transition occurs in the region 4.65 < P
17.04 kbar. (See Fig. 1.) In this pressure region f1 (P , T ) = 0, f3 (P , T ) = 0. (See Eqs. (3.20) and (3.22).) Hence in this region we get from Eq. (3.19) that f (P , T ) = (f2 (P , T ))−1 . Therefore from Eq. (3.46) we obtain the phase line equation for L–IV transition as f2 (P , T ) = 0.

(3.47)

S. Saliho˘glu et al. / Solid State Sciences 4 (2002) 529–534

This function f2 (P , T ) given by Eqs. (3.21) and (3.30) is found from fitting to the experimental data. (See Fig. 1.) For the liquid–phase III transition the phase line equation is FIII = 0, so using Eq. (3.40) we get the phase line equation for L–III transition as 2 d20 = 0. 8f0 f (P , T ) (3.48) Experimentally, the L–III transition occurs in the region P > 17.04 kbar. (See Fig. 1.) In this pressure region n(P , T ) = 0, v(P , T ) = 0, f1 (P , T ) = 0 and f2 (P , T ) = 0. (See Eqs. (3.24), (3.26), (3.20) and (3.21).) Hence, in this region we get from Eq. (3.19) that f (P , T ) = (f3 (P , T ))−1 . Therefore, from Eq. (3.48) we obtain the phase line equation for L–III transition as

−n0 n(P , T ) − v0 v(P , T ) − (2 + y0 )

f3 (P , T ) = 0.

(3.49)

This function f3 (P , T ) = 0 given by Eqs. (3.22) and (3.31) is found from fitting to the experimental data. (See Fig. 1.) For the phase I–phase II transition the phase line equation is FI = FII , so using Eqs. (3.38) and (3.39) we get the phase line equation for I–II transition as n0 n(P , T ) + u0 u(P , T ) = 0.

(3.50)

Experimentally, the I–II transition occurs in the region 2.5
P < 6.95 kbar. (See Fig. 1.) In this pressure region n(P , T ) = 0. (See Eq. (3.24).) Hence, from Eq. (3.50) we obtain the phase line equation for the I–II transition as u(P , T ) = 0.

(3.51)

This function u(P , T ) given by Eqs. (3.25) and (3.34) is found from fitting to the experimental data. (See Fig. 1.) For the phase I–phase IV transition the phase line equation is FI = FIV , so using Eqs. (3.38) and (3.41) we get the phase line equation for the I–IV transition as m0 m(P , T ) = 0.

(3.52)

Since m0 = 0 this equation becomes m(P , T ) = 0.

(3.53)

Hence, Eq. (3.53) is the phase line equation for I–IV transition. This function m(P , T ) given by Eqs. (3.23) and (3.32) is found from fitting to the experimental data. (See Fig. 1.) For the phase II–phase IV transition the phase line equation is FII = FIV , so using Eqs. (3.39) and (3.41) we get the phase line equation for II–IV transition as n0 n(P , T ) + m0 m(P , T ) + u0 u(P , T ) = 0.

(3.54)

Experimentally, the II–IV transition occurs in the region 6.95 < P < 17.04 kbar. (See Fig. 1.) In this pressure region m(P , T ) = 0 and u(P , T ) = 0. (See Eqs. (3.23) and (3.25).) Hence, from Eq. (3.54) we obtain the phase line equation for

533

II–IV transition as n(P , T ) = 0.

(3.55)

This function n(P , T ) given by Eqs. (3.24) and (3.33) is found from fitting to the experimental data. (See Fig. 1.) For the phase II–phase III transition the phase line equation is FII = FIII , so using Eqs. (3.39) and (3.40) we get the phase line equation for II–III transition as v0 v(P , T ) − m0 m(P , T ) − u0 u(P , T ) = 0.

(3.56)

Experimentally, the II–III transition occurs in the region 10.5
P < 17.04 kbar. (See Fig. 1.) In this pressure region m(P , T ) = 0 and u(P , T ) = 0. (See Eqs. (3.23) and (3.25).) Hence, from Eq. (3.56) we obtain the phase line equation for II–III transition as v(P , T ) = 0.

(3.57)

This function v(P , T ) given by Eqs. (3.26) and (3.35) is found from fitting to the experimental data. (See Fig. 1.) For the phase III–phase V transition the phase line equation is FIII = FV , so using Eqs. (3.40) and (3.42) we get the phase line equation for the III–V transition as w0 w(P , T ) = 0.

(3.58)

Hence, from Eq. (3.58) we obtain the phase line equation for the III–V transition as w(P , T ) = 0.

(3.59)

This function w(P , T ) given by Eqs. (3.27) and (3.36) is found from the experimental data. (See Fig. 1.) For the phase V–phase VI transition the phase line equation is FV = FVI , so using Eqs. (3.42) and (3.43) we get the phase line equation for the V–VI transition as h0 h(P , T ) = 0.

(3.60)

Hence, from Eq. (3.60) we obtain the phase line equation for the V–VI transition as h(P , T ) = 0.

(3.61)

This function h(P , T ) given by Eqs. (3.28) and (3.37) is found from the experimental data. (See Fig. 1.) By choosing the constants k0  1, l0  1, z0  1, y0  1, s0  1 and t0  1 we satisfy the ansatzs given by Eqs. (2.15)–(2.20). In our analysis by choosing the coefficients a2 , a4 , a6 ; b2 , b4 , b6 ; c2 , c4 , c6 ; d2 , d4 , d6 ; e2 , e4 , e6 ; g2 , g4 and g6 as in Eqs. (3.1)–(3.19), our phase line equations for the L–I, L–IV, L–III, I–II, I–IV, II–IV, II–III, III–V and V–VI transitions which are given in Table 1, become f1 (P , T ) = 0 (Eq. (3.45)) for L–I; f2 (P , T ) = 0 (Eq. (3.47)) for L–IV; f3 (P , T ) = 0 (Eq. (3.49)) for L–III; u(P , T ) = 0 (Eq. (3.51)) for I–II; m(P , T ) = 0 (Eq. (3.53)) for I–IV; n(P , T ) = 0 (Eq. (3.55)) for II–IV; v(P , T ) = 0 (Eq. (3.57)) for II–III; w(P , T ) = 0 (Eq. (3.59)) for III–V; h(P , T ) = 0 (Eq. (3.61)) for V–VI transitions. Hence, our phase line

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equations given in Table 1, which have a complicated form in terms of the coefficients a2 , a4 , a6 ; b2 , b4 , b6 ; c2 , c4 , c6 ; d2 , d4 , d6 ; e2 , e4 , e6 ; g2 , g4 and g6 , reduced to the simple functions which are given by Eqs. (3.45), (3.47), (3.49), (3.51), (3.53), (3.55), (3.57), (3.59) and (3.61). Now our theory does not predict the form of these functions, namely, f1 (P , T ), f2 (P , T ), f3 (P , T ), u(P , T ), m(P , T ), n(P , T ), v(P , T ), w(P , T ) and h(P , T ). Hence, we choose the form of the above functions from the experimental phase diagram, namely, they are given by Eqs. (3.20)–(3.28). Therefore, by this analysis our theoretical phase diagram was coincided with the experimental phase diagram. So, even though we cannot predict the form of the above functions (f1 (P , T ), f2 (P , T ), f3 (P , T ), u(P , T ), m(P , T ), n(P , T ), v(P , T ), w(P , T ) and h(P , T )), by obtaining their forms from the experimental phase diagram, we know the temperature and the pressure dependencies of the coefficients a2 , a4 , a6 ; b2 , b4 , b6 ; c2 , c4 , c6 ; d2 , d4 , d6 ; e2 , e4 , e6 ; g2 , g4 and g6 . Hence, using these coefficients, we can obtain the temperature and the pressure dependencies of the order parameters, namely, Ψ , µ, θ , η, ρ and σ and the free energies FI , FII , FIII , FIV , FV and FVI . Knowing the order parameters and the free energies, our theory can predict other thermodynamic functions such as the specific heat, susceptibility, thermal expansivity, compressibility etc., which can then be compared with the experimentally measured data. In Section 2 we obtained the phase line equations by making ansatzs given by Eqs. (2.15)–(2.20). Using Eqs. (3.1)–(3.19) we obtain a2 a6 = k0 , (3.62) a42 b2 b6 (3.63) = l0 , b42 c2 c6 (3.64) = z0 , c42 d2 d6 (3.65) = y0 , d42 e2 e6 (3.66) = s0 , e42 g2 g6 (3.67) = t0 . g42

4. Conclusions Using the mean-field theory, we obtained the phase line equations for L–I, L–IV, L–III, I–IV, I–II, II–IV, II–III, III–V and V–VI transitions in NH4 F. We fitted our phase line equations to the experimentally observed P–T phase diagram of NH4 F. The theoretical and experimental phase diagrams coincided by an appropriate choice of the coefficients in the free-energy expansions. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

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