Programmatically add controls in Grid Cell

I have a 2x2 grid and I want to add a control in the 2nd row 2nd column.  The below adds it to the 1st row and 1st column.  How can I do this?

<Grid ShowGridLines="True" Name="Grid1"><Grid.RowDefinitions><RowDefinition Height="*"></RowDefinition><RowDefinition Height="*"></RowDefinition></Grid.RowDefinitions><Grid.ColumnDefinitions><ColumnDefinition Width="*"></ColumnDefinition><ColumnDefinition Width="2*"></ColumnDefinition></Grid.ColumnDefinitions><StackPanel Grid.Column="1" Grid.RowSpan="2" Name="stackPanel1" ><TextBlock Text="Title" /><TextBlock Text="This is a line of text" /></StackPanel><Button Content="Press me" Name="button1" Margin="30" Click="button1_Click" /></Grid>

        private TextBox textBox2;

        private void button1_Click(object sender, RoutedEventArgs e)
        {
            this.textBox2 = new TextBox();
            this.textBox2.Text = "Here is a new textbox";           
            Grid1.Children.Add(this.textBox2);
        }