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A collimator and beam-stop assembly that can be inserted inside a temperature-controlled pressure vessel, to reduce dramatically the parasitic Bragg scattering from the vessel, has been designed and evaluated. High-energy X-ray powder diffraction data, suitable for the Rietveld refinement of simple crystal structures, were collected using this background-reducing internal mask (BRIM). ZrW2O8 was examined at up to 540 K and 124 MPa, using quite large pressure and temperature steps. No pressure dependence of the order–disorder transition temperature of this material was apparent. An orthorhombic to monoclinic phase transition (onset ∼83 MPa) was observed for Al2W3O12. Upon going through the transition, the bulk modulus of the material decreased from 41.8 to 20.8 GPa. Bulk moduli estimated for CaF2 and α-Al2O3, from data collected at up to 280 MPa, were in good agreement with prior literature.
Supporting information
Program(s) used to refine structure: GSAS.
Crystal data top
CaF2 | a = 5.47082 (7) Å |
Mr = 78.08 | V = 163.74 (1) Å3 |
Cubic, Fm3m | Z = 4 |
Data collection top
2θmin = 0.004°, 2θmax = 15.996°, 2θstep = 0.008° | |
Refinement top
Least-squares matrix: full | Profile function: CW Profile function number 3 with 19 terms
Pseudovoigt profile coefficients as parameterized in
P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83.
Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994).
J. Appl. Cryst.,27,892-900.
#1(GU) = 703.466 #2(GV) = -119.364 #3(GW) = 6.454
#4(GP) = 0.000 #5(LX) = 0.000 #6(LY) = 8.631
#7(S/L) = 0.0005 #8(H/L) = 0.0005
#9(trns) = 0.00 #10(shft)= 0.0000
#11(stec)= 0.00 #12(ptec)= 0.00 #13(sfec)= 0.00
#14(L11) = 0.000 #15(L22) = 0.000 #16(L33) = 0.000
#17(L12) = 0.000 #18(L13) = 0.000 #19(L23) = 0.000
Peak tails are ignored where the intensity is below 0.0100 times the peak
Aniso. broadening axis 0.0 0.0 1.0 |
Rp = 0.037 | 14 parameters |
Rwp = 0.074 | 0 restraints |
Rexp = 0.098 | (Δ/σ)max = 0.04 |
R(F2) = 0.82567 | Background function: GSAS Background function number 1 with 6 terms.
Shifted Chebyshev function of 1st kind
1: 83.8739 2: -18.5157 3: -4.16936 4: 0.249283
5: -2.70281 6: 1.79589 |
2000 data points | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
CA1 | 0.0 | 0.0 | 0.0 | 0.0014 (8)* | |
F2 | 0.25 | 0.25 | 0.25 | 0.0059 (11)* | |
Crystal data top
O8W2Zr | a = 9.07371 (4) Å |
Mr = 586.91 | V = 747.06 (1) Å3 |
Cubic, P213 | Z = 4 |
Refinement top
Least-squares matrix: full | Profile function: CW Profile function number 3 with 19 terms
Pseudovoigt profile coefficients as parameterized in
P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83.
Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994).
J. Appl. Cryst.,27,892-900.
#1(GU) = 154.404 #2(GV) = -18.108 #3(GW) = 1.718
#4(GP) = 0.000 #5(LX) = 0.000 #6(LY) = 10.599
#7(S/L) = 0.0005 #8(H/L) = 0.0005
#9(trns) = 0.00 #10(shft)= 0.0000
#11(stec)= 0.00 #12(ptec)= 0.00 #13(sfec)= 0.00
#14(L11) = 0.000 #15(L22) = 0.000 #16(L33) = 0.000
#17(L12) = 0.000 #18(L13) = 0.000 #19(L23) = 0.000
Peak tails are ignored where the intensity is below 0.0100 times the peak
Aniso. broadening axis 0.0 0.0 1.0 |
Rp = 0.024 | 33 parameters |
Rwp = 0.031 | 0 restraints |
Rexp = 0.006 | (Δ/σ)max = 0.06 |
R(F2) = 0.45473 | Background function: GSAS Background function number 1 with 6 terms.
Shifted Chebyshev function of 1st kind
1: 3738.14 2: -1032.15 3: -121.824 4: 171.737
5: -4.78893 6: -53.6707 |
2048 data points | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Zr1 | 0.0018 (3) | 0.0018 (3) | 0.0018 (3) | 0.00521 | |
W1 | 0.34202 (17) | 0.34202 (17) | 0.34202 (17) | 0.01312 | |
W2 | 0.60117 (14) | 0.60117 (14) | 0.60117 (14) | 0.01188 | |
O1 | 0.050 (2) | −0.209 (2) | −0.058 (3) | 0.019 (4)* | |
O2 | 0.071 (3) | −0.056 (2) | 0.209 (3) | 0.023 (5)* | |
O3 | 0.514 (3) | 0.514 (3) | 0.514 (3) | 0.028 (9)* | |
O4 | 0.271 (2) | 0.271 (2) | 0.271 (2) | 0.023 (9)* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zr1 | 0.0052 (4) | 0.0052 (4) | 0.0052 (4) | 0.0042 (8) | 0.0042 (8) | 0.0042 (8) |
W1 | 0.0131 (6) | 0.0131 (6) | 0.0131 (6) | 0.0018 (5) | 0.0018 (5) | 0.0018 (5) |
W2 | 0.0119 (5) | 0.0119 (5) | 0.0119 (5) | 0.0023 (5) | 0.0023 (5) | 0.0023 (5) |
Geometric parameters (Å, º) top
Zr1—O1 | 2.04 (2) | W2—O2vi | 1.79 (3) |
Zr1—O1i | 2.04 (2) | W2—O2vii | 1.79 (3) |
Zr1—O1ii | 2.04 (2) | W2—O2viii | 1.79 (3) |
Zr1—O2 | 2.05 (3) | W2—O3 | 1.36 (5) |
Zr1—O2i | 2.05 (3) | O1—Zr1 | 2.04 (2) |
Zr1—O2ii | 2.05 (3) | O1—W1ix | 1.80 (2) |
W1—O1iii | 1.80 (2) | O2—Zr1 | 2.05 (3) |
W1—O1iv | 1.80 (2) | O2—W2x | 1.79 (3) |
W1—O1v | 1.80 (2) | O3—W2 | 1.36 (5) |
W1—O4 | 1.12 (4) | O4—W1 | 1.12 (4) |
| | | |
O1—Zr1—O1i | 90.7 (9) | O1iii—W1—O1iv | 115.4 (5) |
O1—Zr1—O1ii | 90.7 (9) | O1iii—W1—O1v | 115.4 (5) |
O1—Zr1—O2 | 86.3 (10) | O1iii—W1—O4 | 102.6 (7) |
O1—Zr1—O2i | 91.1 (8) | O1iv—W1—O1v | 115.4 (5) |
O1—Zr1—O2ii | 176.6 (8) | O1iv—W1—O4 | 102.6 (7) |
O1i—Zr1—O1ii | 90.7 (9) | O1v—W1—O4 | 102.6 (7) |
O1i—Zr1—O2 | 176.6 (8) | O2vi—W2—O2vii | 109.5 (7) |
O1i—Zr1—O2i | 86.3 (10) | O2vi—W2—O2viii | 109.5 (7) |
O1i—Zr1—O2ii | 91.1 (8) | O2vi—W2—O3 | 109.5 (7) |
O1ii—Zr1—O2 | 91.1 (8) | O2vii—W2—O2viii | 109.5 (7) |
O1ii—Zr1—O2i | 176.6 (8) | O2vii—W2—O3 | 109.5 (7) |
O1ii—Zr1—O2ii | 86.3 (10) | O2viii—W2—O3 | 109.5 (7) |
O2—Zr1—O2i | 91.9 (9) | Zr1—O1—W1ix | 151.8 (13) |
O2—Zr1—O2ii | 91.9 (9) | Zr1—O2—W2x | 171.0 (13) |
O2i—Zr1—O2ii | 91.9 (9) | | |
Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) −y, z+1/2, −x+1/2; (iv) −x+1/2, −y, z+1/2; (v) z+1/2, −x+1/2, −y; (vi) x+1/2, −y+1/2, −z+1; (vii) −z+1, x+1/2, −y+1/2; (viii) −y+1/2, −z+1, x+1/2; (ix) −y+1/2, −z, x−1/2; (x) x−1/2, −y+1/2, −z+1. |
Crystal data top
O8.00W2.00Zr | a = 9.05896 (6) Å |
Mr = 586.91 | V = 743.42 (2) Å3 |
Cubic, pa3 | Z = 4 |
Refinement top
Least-squares matrix: full | Profile function: CW Profile function number 3 with 19 terms
Pseudovoigt profile coefficients as parameterized in
P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83.
Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994).
J. Appl. Cryst.,27,892-900.
#1(GU) = 306.806 #2(GV) = -50.541 #3(GW) = 3.129
#4(GP) = 0.000 #5(LX) = 0.000 #6(LY) = 13.256
#7(S/L) = 0.0005 #8(H/L) = 0.0005
#9(trns) = 0.00 #10(shft)= 0.0000
#11(stec)= 0.00 #12(ptec)= 0.00 #13(sfec)= 0.00
#14(L11) = 0.000 #15(L22) = 0.000 #16(L33) = 0.000
#17(L12) = 0.000 #18(L13) = 0.000 #19(L23) = 0.000
Peak tails are ignored where the intensity is below 0.0100 times the peak
Aniso. broadening axis 0.0 0.0 1.0 |
Rp = 0.019 | 31 parameters |
Rwp = 0.027 | 0 restraints |
Rexp = 0.006 | (Δ/σ)max = 0.05 |
R(F2) = 0.64683 | Background function: GSAS Background function number 1 with 10 terms.
Shifted Chebyshev function of 1st kind
1: 5255.04 2: -1957.05 3: -294.410 4: 382.996
5: -146.265 6: -33.5563 7: 29.0338 8: -90.9287
9: 73.8570 10: 45.5314 |
2048 data points | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zr1 | 0.0 | 0.0 | 0.0 | 0.01048 | |
W1 | 0.33933 (18) | 0.33933 (18) | 0.33933 (18) | 0.01718 | 0.5 |
W2 | 0.60289 (18) | 0.60289 (18) | 0.60289 (18) | 0.01626 | 0.5 |
O1 | 0.058 (2) | −0.220 (2) | −0.063 (2) | 0.048 (4)* | |
O2 | 0.5055 | 0.5055 | 0.5055 | 0.042 (5)* | 0.5 |
O3 | 0.241 (3) | 0.241 (3) | 0.241 (3) | 0.028 (7)* | 0.5 |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zr1 | 0.0105 (4) | 0.0105 (4) | 0.0105 (4) | 0.0006 (7) | 0.0006 (7) | 0.0006 (7) |
W1 | 0.0172 (5) | 0.0172 (5) | 0.0172 (5) | 0.0021 (6) | 0.0021 (6) | 0.0021 (6) |
W2 | 0.0163 (4) | 0.0163 (4) | 0.0163 (4) | 0.0022 (7) | 0.0022 (7) | 0.0022 (7) |
Geometric parameters (Å, º) top
Zr1—O1 | 2.139 (17) | W2—O1xi | 1.694 (17) |
Zr1—O1i | 2.139 (17) | W2—O1xii | 1.694 (17) |
Zr1—O1ii | 2.139 (17) | W2—O2 | 1.528 (3) |
Zr1—O1iii | 2.139 (17) | W2—O2vi | 1.701 (3) |
Zr1—O1iv | 2.139 (17) | W2—O3vi | 2.45 (5) |
Zr1—O1v | 2.139 (17) | O1—Zr1 | 2.139 (17) |
W1—W2vi | 0.907 (3) | O1—W1xiii | 1.679 (16) |
W1—O1vii | 1.679 (16) | O1—W2xiv | 1.694 (17) |
W1—O1viii | 1.679 (16) | O2—W1 | 2.607 (3) |
W1—O1ix | 1.679 (16) | O2—W1vi | 2.435 (3) |
W1—O2 | 2.607 (3) | O2—W2 | 1.528 (3) |
W1—O2vi | 2.435 (3) | O2—W2vi | 1.701 (3) |
W1—O3 | 1.54 (5) | O2—O2vi | 0.1726 |
W2—W1vi | 0.907 (3) | O3—W1 | 1.54 (5) |
W2—O1x | 1.694 (17) | O3—W2vi | 2.45 (5) |
| | | |
O1—Zr1—O1i | 92.7 (8) | O1viii—W1—O3 | 104.7 (7) |
O1—Zr1—O1ii | 92.7 (8) | O1xviii—W1—O3 | 104.7 (7) |
O1—Zr1—O1iii | 180.0 | W1vi—W2—O1x | 73.5 (6) |
O1—Zr1—O1iv | 87.3 (8) | W1vi—W2—O1xi | 73.5 (6) |
O1—Zr1—O1v | 87.3 (8) | W1vi—W2—O1xii | 73.5 (6) |
O1i—Zr1—O1ii | 92.7 (8) | W1vi—W2—O2 | 180.0 |
O1i—Zr1—O1iii | 87.3 (8) | W1vi—W2—O2vi | 180.0 |
O1i—Zr1—O1iv | 180.0 | O1x—W2—O1xi | 112.3 (5) |
O1i—Zr1—O1v | 87.3 (8) | O1x—W2—O1xii | 112.3 (5) |
O1ii—Zr1—O1iii | 87.3 (8) | O1x—W2—O2 | 106.5 (6) |
O1ii—Zr1—O1iv | 87.3 (8) | O1x—W2—O2vi | 106.5 (6) |
O1ii—Zr1—O1v | 180.0 | O1xi—W2—O1xii | 112.3 (5) |
O1iii—Zr1—O1iv | 92.7 (8) | O1xi—W2—O2 | 106.5 (6) |
O1iii—Zr1—O1v | 92.7 (8) | O1xi—W2—O2vi | 106.5 (6) |
O1iv—Zr1—O1v | 92.7 (8) | O1xii—W2—O2 | 106.5 (6) |
W2vi—W1—O1xv | 75.3 (7) | O1xii—W2—O2vi | 106.5 (6) |
W2vi—W1—O1xvi | 75.3 (7) | O2—W2—O2vi | 0.0 |
W2vi—W1—O1ix | 75.3 (7) | Zr1—O1—W1xiii | 151.2 (12) |
W2vi—W1—O3 | 180.0 | Zr1—O1—W2xiv | 177.0 (12) |
O1xv—W1—O1xvi | 113.8 (6) | W1xiii—O1—W2xiv | 31.2 (3) |
O1xv—W1—O1ix | 113.8 (6) | W2—O2—W2vi | 180.0 |
O1xvii—W1—O3 | 104.7 (7) | W2—O2—O2vi | 180.0 |
O1xvi—W1—O1ix | 113.8 (6) | W2vi—O2—O2vi | 0.0 |
Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) −x, −y, −z; (iv) −z, −x, −y; (v) −y, −z, −x; (vi) −x+1, −y+1, −z+1; (vii) −x+1/2, −y, z+1/2; (viii) z+1/2, −x+1/2, −y; (ix) −y, z+1/2, −x+1/2; (x) x+1/2, y+1, −z+1/2; (xi) −z+1/2, x+1/2, y+1; (xii) y+1, −z+1/2, x+1/2; (xiii) −y+1/2, −z, x−1/2; (xiv) x−1/2, y−1, −z+1/2; (xv) −x+3/2, −y−1, z+1/2; (xvi) z+3/2, −x+1/2, −y−1; (xvii) −x+1/2, −y−1, z+3/2; (xviii) −y−1, z+1/2, −x+3/2. |
Crystal data top
Al2O3 | c = 13.0033 (4) Å |
Mr = 101.96 | V = 255.56 (1) Å3 |
Trigonal, R3c | Z = 6 |
a = 4.76380 (7) Å | |
Data collection top
2θmin = 0.004°, 2θmax = 15.996°, 2θstep = 0.008° | |
Refinement top
Least-squares matrix: full | Profile function: CW Profile function number 3 with 19 terms
Pseudovoigt profile coefficients as parameterized in
P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83.
Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994).
J. Appl. Cryst.,27,892-900.
#1(GU) = 1089.390 #2(GV) = -201.843 #3(GW) = 10.669
#4(GP) = 0.000 #5(LX) = 0.000 #6(LY) = 13.865
#7(S/L) = 0.0005 #8(H/L) = 0.0005
#9(trns) = 0.00 #10(shft)= 0.0000
#11(stec)= 0.00 #12(ptec)= 0.00 #13(sfec)= 0.00
#14(L11) = 0.000 #15(L22) = 0.000 #16(L33) = 0.000
#17(L12) = 0.000 #18(L13) = 0.000 #19(L23) = 0.000
Peak tails are ignored where the intensity is below 0.0050 times the peak
Aniso. broadening axis 0.0 0.0 1.0 |
Rp = 0.031 | 17 parameters |
Rwp = 0.052 | 0 restraints |
Rexp = 0.046 | (Δ/σ)max = 0.04 |
R(F2) = 0.40258 | Background function: GSAS Background function number 1 with 6 terms.
Shifted Chebyshev function of 1st kind
1: 371.203 2: -53.3158 3: 1.59218 4: 11.8174
5: -15.0398 6: 6.91125 |
2000 data points | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Al1 | 0.0 | 0.0 | 0.35184 (14) | −0.0032 (6)* | |
O1 | 0.3072 (7) | 0.0 | 0.25 | −0.0006 (9)* | |
Geometric parameters (Å, º) top
Al1—Al1i | 2.649 (4) | Al1—O1vii | 1.856 (2) |
Al1—Al1ii | 2.7922 (6) | Al1—O1viii | 1.856 (2) |
Al1—Al1iii | 2.7922 (6) | Al1—O1ix | 1.856 (2) |
Al1—Al1iv | 2.7922 (6) | O1—Al1 | 1.974 (3) |
Al1—O1 | 1.974 (3) | O1—Al1i | 1.974 (3) |
Al1—O1v | 1.974 (3) | O1—Al1iii | 1.856 (2) |
Al1—O1vi | 1.974 (3) | O1—Al1x | 1.856 (2) |
| | | |
Al1i—Al1—Al1iv | 80.07 (7) | Al1xii—Al1—O1vi | 121.12 (10) |
Al1i—Al1—Al1xi | 80.07 (7) | Al1xii—Al1—O1xiii | 143.91 (10) |
Al1i—Al1—Al1xii | 80.07 (7) | Al1xii—Al1—O1xiv | 44.87 (8) |
Al1i—Al1—O1 | 47.86 (7) | Al1xii—Al1—O1xv | 97.79 (8) |
Al1i—Al1—O1v | 47.86 (7) | O1—Al1—O1v | 79.90 (11) |
Al1i—Al1—O1vi | 47.86 (7) | O1—Al1—O1vi | 79.90 (11) |
Al1i—Al1—O1xiii | 117.01 (5) | O1—Al1—O1xiii | 86.43 (3) |
Al1i—Al1—O1xiv | 117.01 (5) | O1—Al1—O1xiv | 90.71 (8) |
Al1i—Al1—O1xv | 117.01 (5) | O1—Al1—O1xv | 164.56 (13) |
Al1iv—Al1—Al1xi | 117.09 (4) | O1v—Al1—O1vi | 79.90 (11) |
Al1iv—Al1—Al1xii | 117.09 (4) | O1v—Al1—O1xiii | 164.56 (13) |
Al1iv—Al1—O1 | 121.12 (10) | O1v—Al1—O1xiv | 86.43 (3) |
Al1iv—Al1—O1v | 83.36 (5) | O1v—Al1—O1xv | 90.71 (8) |
Al1iv—Al1—O1vi | 41.57 (6) | O1vi—Al1—O1xiii | 90.71 (8) |
Al1iv—Al1—O1xiii | 97.79 (8) | O1vi—Al1—O1xiv | 164.56 (13) |
Al1iv—Al1—O1xiv | 143.91 (10) | O1vi—Al1—O1xv | 86.43 (3) |
Al1iv—Al1—O1xv | 44.87 (8) | O1xiii—Al1—O1xiv | 100.99 (7) |
Al1xi—Al1—Al1xii | 117.09 (4) | O1xiii—Al1—O1xv | 100.99 (7) |
Al1xi—Al1—O1 | 41.57 (6) | O1xiv—Al1—O1xv | 100.99 (7) |
Al1xi—Al1—O1v | 121.12 (10) | Al1—O1—Al1i | 84.29 (14) |
Al1xi—Al1—O1vi | 83.36 (5) | Al1—O1—Al1xi | 93.57 (3) |
Al1xi—Al1—O1xiii | 44.87 (8) | Al1—O1—Al1x | 132.19 (7) |
Al1xi—Al1—O1xiv | 97.79 (8) | Al1i—O1—Al1xi | 132.19 (7) |
Al1xi—Al1—O1xv | 143.91 (10) | Al1i—O1—Al1x | 93.57 (3) |
Al1xii—Al1—O1 | 83.36 (5) | Al1xi—O1—Al1x | 120.68 (18) |
Al1xii—Al1—O1v | 41.57 (6) | | |
Symmetry codes: (i) x−y, −y, −z+1/2; (ii) −x−4/3, −y−5/3, −z−2/3; (iii) −x−1/3, −y−5/3, −z−2/3; (iv) −x−1/3, −y−2/3, −z−2/3; (v) −y, x−y, z; (vi) y−x, −x, z; (vii) y−x+1/3, y−1/3, z+1/6; (viii) −y+1/3, −x+2/3, z+1/6; (ix) x−2/3, x−y−1/3, z+1/6; (x) y−x+2/3, y+1/3, z−1/6; (xi) −x+2/3, −y−2/3, −z−2/3; (xii) −x+2/3, −y+1/3, −z−2/3; (xiii) y−x+1/3, y−1/3, z−11/6; (xiv) −y+1/3, −x+2/3, z−11/6; (xv) x−2/3, x−y−1/3, z−11/6. |
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