diff --git a/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpAlpha.rst b/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpAlpha.rst new file mode 100644 index 0000000000000000000000000000000000000000..e49b53f3f59313f97cd5d3025290a8160091a3f7 --- /dev/null +++ b/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpAlpha.rst @@ -0,0 +1,31 @@ +.. _func-ThermalNeutronBk2BkExpAlpha: + +=========================== +ThermalNeutronBk2BkExpAlpha +=========================== + +.. index:: ThermalNeutronBk2BkExpAlpha + +Description +----------- + +ThermalNeutronBk2BkExpAlpha is a function to calculate :math:`\alpha` of :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`. +It is defined as + +.. math:: \alpha(d_h) = \left(n\alpha_0 + \alpha_1 d_h + (1-n)\alpha_0^t - \frac{\alpha_1^t}{d_h}\right)^{-1} + +where + +.. math:: n = \frac{1}{2} \mathit{erfc}(\text{Width}(t_\text{cross} - d^{-1})) + +and + +.. math:: erfc(x) = 1-erf(x) = 1-\frac{2}{\sqrt{\pi}}\int_0^xe^{-u^2}du. + +.. attributes:: + +.. properties:: + +.. categories:: + +.. sourcelink:: diff --git a/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpBeta.rst b/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpBeta.rst new file mode 100644 index 0000000000000000000000000000000000000000..bf83cea3d61e1b8d684a11e4d2cd75ff33c2ebd1 --- /dev/null +++ b/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpBeta.rst @@ -0,0 +1,31 @@ +.. _func-ThermalNeutronBk2BkExpBeta: + +========================== +ThermalNeutronBk2BkExpBeta +========================== + +.. index:: ThermalNeutronBk2BkExpBeta + +Description +----------- + +ThermalNeutronBk2BkExpBeta is a function to calculate :math:`\beta` of :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`. +It is defined as + +.. math:: \beta(d_h) = \left(n\beta_0 + \beta_1 d_h + (1-n)\beta_0^t - \frac{\beta_1^t}{d_h}\right)^{-1} + +where + +.. math:: n = \frac{1}{2} \mathit{erfc}(\text{Width}(t_\text{cross} - d^{-1})) + +and + +.. math:: erfc(x) = 1-erf(x) = 1-\frac{2}{\sqrt{\pi}}\int_0^xe^{-u^2}du. + +.. attributes:: + +.. properties:: + +.. categories:: + +.. sourcelink:: diff --git a/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpSigma.rst b/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpSigma.rst new file mode 100644 index 0000000000000000000000000000000000000000..6b8e1a5b33614328f330c140e712382b5d0de7b4 --- /dev/null +++ b/docs/source/fitting/fitfunctions/ThermalNeutronBk2BkExpSigma.rst @@ -0,0 +1,23 @@ +.. _func-ThermalNeutronBk2BkExpSigma: + +=========================== +ThermalNeutronBk2BkExpSigma +=========================== + +.. index:: ThermalNeutronBk2BkExpSigma + +Description +----------- + +ThermalNeutronBk2BkExpSigma is a function to calculate :math:`\sigma` of :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`. +It is defined as + +.. math:: \sigma(d_h) = \left(\sigma_0^2 + \sigma_1^2 + d_h^2 + \sigma_2^2 + d_h^4\right)^{0.5} + +.. attributes:: + +.. properties:: + +.. categories:: + +.. sourcelink:: diff --git a/docs/source/fitting/fitfunctions/ThermalNeutronDtoTOFFunction.rst b/docs/source/fitting/fitfunctions/ThermalNeutronDtoTOFFunction.rst new file mode 100644 index 0000000000000000000000000000000000000000..bce2c358cd8a57b39bd220801ff7c001e028fdd7 --- /dev/null +++ b/docs/source/fitting/fitfunctions/ThermalNeutronDtoTOFFunction.rst @@ -0,0 +1,27 @@ +.. _func-ThermalNeutronDtoTOFFunction: + +============================ +ThermalNeutronDtoTOFFunction +============================ + +.. index:: ThermalNeutronDtoTOFFunction + +Description +----------- + +ThermalNeutronDtoTOFFunction is a function to calculate TOF from d-spacing values for :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`. +It is defined as + +.. math:: TOF = n(zero + dtt1 \cdot dh)+(1-n)(zero_t + dtt1t\cdot dh - \frac{dtt2t}{dh}) + +where + +.. math:: n = \frac{1}{2} \mathit{erfc}(\text{Width}(t_\text{cross} - d^{-1})). + +.. attributes:: + +.. properties:: + +.. categories:: + +.. sourcelink::